FI9800048

P O S I V A 9 7 - 1 2

Principles ofMechanical Excavation

Arne LislerudTarn rock Corp.

December 1997

POSIVA OY

M i k o n k a t u 1 5 A . F I N - O O 1 O O H E L S I N K I . F I N L A N D

P h o n e ( 0 9 ) 2 2 8 0 3 0 ( n a t . ) . ( + 3 5 8 - 9 - ) 2 2 8 0 3 0 ( i n t . )

F a x ( 0 9 ) 2 2 8 O 3 7 1 9 ( n a t . ) , ( + 3 5 8 - 9 - ) 2 2 8 0 3 7 1 9 ( i n t . )

ISBN 951-652-037-5ISSN 1239-3096

The c o n c l u s i o n s and v i e w p o i n t s p r esen ted in the report are

those of a u t h o r ( s ) and do not necessar i ly co inc ide

w i t h t h o s e of Posiva

Posiva-raportti - Posiva report

Posiva OyMikonkatu 15 A, FIN-00100 HELSINKI, FINLANDPuh. (09) 2280 30 - Int. Tel. +358 9 2280 30

Raportin tunnus - Report code

POSIVA97-12

Julkaisuaika - Date

December 1997

Tekija(t) - Author(s)

Arne LislerudTamrock Corp.

Toimeksiantaja(t) - Commissioned by

Posiva Oy

Nimeke - Title

PRINCIPLES OF MECHANICAL EXCAVATION

Tiivistelma - Abstract

Mechanical excavation of rock today includes several methods such as tunnel boring, raiseboring,roadheading and various continuous mining systems. Of these raiseboring is one potential techniquefor excavating shafts in the repository for spent nuclear fuel and dry blind boring is promisingtechnique for excavation of deposition holes, as demonstrated in the Research Tunnel at Olkiluoto.In addition, there is potential for use of other mechanical excavation techniques in different parts ofthe repository. One of the main objectives of this study was to analyze the factors which affect thefeasibility of mechanical rock excavation in hard rock conditions and to enhance the understandingof factors which affect rock cutting so as to provide an improved basis for excavator performanceprediction modeling. The study included the following four main topics: a) phenomenological modelbased on similarity analysis for roller disk cutting, b) rock mass properties which affect rockcuttability and tool life, c) principles for linear and field cutting tests and performance predictionmodeling and d) cutter head lacing design procedures and principles. As a conclusion of this study,a test rig was constructed, field tests were planned and started up. The results of the study can beused to improve the performance prediction models used to assess the feasibility of differentmechanical excavation techniques at various repository investigation sites.

Avainsanat - Keywords

mechanical excavation, cuttability, drillabilityISBN

ISBN 951-652-037-5ISSN

ISSN 1239-3096Sivumaara - Number of pages

186 + AppendicesKieli - Language

English

Posiva-raportti - Posiva report

Posiva OyMikonkatu 15 A, FIN-00100 HELSINKI, FINLANDPuh. (09) 2280 30 - Int. Tel. +358 9 2280 30

Raportin tunnus - Report code

POSIVA 97-12

Julkaisuaika - Date

Joulukuu 1997

Tekijä(t) - Author(s)

Arne LislerudTamrock Corp.

Toimeksiantaja(t) - Commissioned by

Posiva Oy

Nimeke - Title

MEKAANISEN LOUHINNAN PERUSTEET

Tiivistelmä - Abstract

Nykyään on yleisesti käytössä useita erityyppisiä mekaanisia louhintamenetelmiä kuten tunnelinporaus, nousuporaus ja muita esimerkiksi rouhintaan (roadheading) perustuvia menetelmiä. Näistänousuporausta voidaan hyödyntää käytetyn ydinpolttoaineen loppusijoitustilojen kuilujen lou-hinnassa, ja Olkiluodon tutkimustunnelissa demonstroitu kuiva sokkoporaus on lupaava tekniikkaloppusijoitusreikien poraukseen. Myös muiden mekaanisten louhintamenetelmien käytölle onmahdollisuuksia loppusijoitustilojen eri osissa. Tämän selvityksen tavoitteena oli analysoidakovassa kivessä tapahtuvan mekaanisen louhinnan toteutettavuuteen vaikuttavia tekijöitä ja parantaakiven rikkomiseen vaikuttavien tekijöiden ymmärrystä louhintalaitteiden tehokkuuden arvioinninlähtökohtien tarkentamiseksi. Työssä keskityttiin seuraavaan neljään pääkohtaan: a) pyörivänkiekkoterän similariteettianalyysiin perustuva fenomenologinen malli, b) kiven rikkomiseen ja terienkulumiseen vaikuttavat kivilajiominaisuudet, c) lineaarisen kiekkoterällä tapahtuvan kiven rikko-misen, sen kenttäkokeen ja tehokkuuden ennustamisen perusteet ja d) mekaanisen louhintalaitteenteräpään yksittäisten terien sijoitus ja sen perusteet. Selvityksen tuloksena rakennettiin koelaite kivenrikkomiseksi kiekkoterällä ja suunniteltiin sekä aloitettiin kenttäkokeet. Selvityksen tulostenperusteella voidaan parantaa eri mekaanisten louhintamenetelmien soveltuvuuden ja tehokkuudenarviointia loppusijoitustilojen erilaisissa mahdollisissa kallioperäolosuhteissa.

Avainsanat - Keywords

mekaaninen louhinta, louhittavuus, porattavuusISBN

ISBN 951-652-037-5ISSN

ISSN 1239-3096

Sivumäärä - Number of pages

186 +liitteetKieli - Language

Englanti

TABLE OF CONTENTS

PREFACE

ABSTRACT

TIIVISTELMA

TABLE OF CONTENTS

0 INTRODUCTION 1

1 MECHANICS OF CUTTING AND BORING 3

1.1 TOOL TRAJECTORIES AND VELOCITIES ON AXIAL ROTATIONMACHINES 3

1.2 ROLLER DISK CUTTER INDENTATION MECHANISMS 12

1.3 TOOL CONFIGURATION AND TOOL RIM DIMENSIONS 26

2 A PHENOMENOLOGICAL MODEL FOR THE CUTTINGACTION OF ROLLER DISK CUTTERS 29

2.1 INTRODUCTION 29

2.2 CONDITIONS OF SIMILITUDE 30

2.2.1 Forming the Non-Dimensional Products 31

2.3 APPLICATION OF SIMILARITY ANALYSIS 34

2.3.1 Roller Disk Kerf Cutting of Rock 35

2.3.2 Forming the Dimensional Matrix 37

2.3.3 Forming the Unity Matrix and Remaining n-Terms 38

2.2.4 Similarity and Scale Factors 39

2.4 PRACTICAL USE OF THE NON-DIMENSIONALTI-TERMS 40

2.4.1 Functional Relationship between Normal Force, Depth of Cut andIntact Rock Strength 40

2.4.2 Functional Relationship between Normal Force, Depth of Cut,Intact Rock Strength and Kerf Spacing 41

2.4.3 Functional Relationship between Normal Force, Depth of Cut,Intact Rock Strength and Degree of Rock Mass Fracturing 41

2.4.4 Functional Relationship between Normal Force, Depth of Cut andIntact Rock Toughness 42

2.5 ADDITIONAL FUNCTIONAL RELATIONSHIPS FOR ROLLERDISK CUTTING 44

2.6 SUMMARY OF FUNCTIONAL RELATIONSHIPS FOR ROLLERDISK KERF CUTTING ESTABLISHED IN CHAPTERS 1 & 2 46

3 ROCK MASS CHARACTERISATION 48

3.1 INTRODUCTION 48

3.2 ROCK MASS CHARACTERISATION 51

3.3 CLASSIFICATION OF ROCK MASS CUTTABILITY ANDDRILLABILITY 63

3.4 CHARACTERISATION OF TOOL CONSUMPTION 80

3.4.1 Classification of Wear Mechanisms 803.4.2 Macroscopic Fracture and Structural Failure 823.4.3 Microscopic Fracture and Wear Mechanisms 873.4.4 Classification of Tool Wear Modes for Sliding Wear 943.4.5 Methods for Rating the Wear Capacity of a Rock Mass 99

3.5 SOME ADDITIONAL ASPECTS OF TOOL CONSUMPTION 106

3.5.1 Laboratory Studies of Disk Cutter Life for Off-Line Kerf Cutting 1083.5.2 Field Studies of Disk Service Life for In-Line Kerf Cutting 110

3.6 ROCK CUTTABILITY WINDOWS 113

4 LINEAR CUTTING TESTS 115

4.1 LINEAR CUTTING TEST APPARATUS 115

4.2 PERFORMANCE PREDICTION MODELLING OF ROLLERDISK CUTTING 119

4.3 PERFORMANCE PREDICTION MODEL FOR ROLLER DISKCUTTING 120

4.4 RELEVANCE OF LCM TEST CUTTING RESULTS TO FACECUTTING PERFORMANCE 125

5 TOOL AND CUTTERHEAD FORCES ON DOMED AXIALROTATION MACHINES 134

5.1 TOOL PATHS, DEPTH OF CUT AND CUTTERHEADADVANCE RATES 134

5.2 CUTTING WITH DOMED AXIAL ROTATION CUTTERHEADS 136

5.3 CUTTING FORCES ON DOMED AXIAL ROTATIONCUTTERHEADS 138

5.4 THE PRINCIPLE CUTTERHEAD FORCES 141

5.5 BALANCING OF INDIVIDUAL TOOL NORMAL FORCES ANDLINE SPACINGS 143

5.6 SUMMARY OF PREDICTION EQUATIONS FOR AXIALROTATION MACHINES TOOLED WITH ROLLER DISKCUTTERS 143

5.7 SEQUENTIAL CUTTING WITH DOMED CUTTERHEADS 144

6 CUTTERHEAD TOOL LACING DESIGN 153

6.1 TOOL LACING DESIGN PARAMETERS 153

6.2 THE STEPWISE TOOL LACING DESIGN PROCEDURE 158

6.3 CUTTERHEAD FORCES AND TORQUE EQUALIZATIONON DOMED AXIAL ROTATION CUTTERHEADS 163

7 FIELD PERFORMANCE PREDICTION 168

8 TERMINOLOGY 172

8.0 GENERAL EXPRESSIONS 172

8.1 CUTTING TOOLS 173

8.2 CUTTERHEADS FOR AXIAL ROTATION MACHINES 175

8.3 ROCK CUTTING MODES 177

8.4 CUTTING FORCES AND SPECIFIC ENERGY 179

8.5 ROCK MASS CUTTABILITY AND WEAR CAPACITY 180

8.6 LIST OF ABBREVIATIONS 181

SUMMARY AND CONCLUSIONS 183

LITERATURE 184

APPENDICES 186

PREFACE

The study of mechanical rock cutting by roller cutters presented in thisreport is a co-operation project between Posiva Oy and Tamrock Corp. aspart of the research and development project "Development of Disposal ofSpent Nuclear Fuel and Advanced Rock Engineering" for Posiva Oysupported by the Technology Development Center of Finland, TEKES.

The author wishes to thank Jukka-Pekka Salo of Posiva Oy and Jorma Autioof Saanio & Riekkola Oy who acted as contact persons, and to acknowledgewith appreciation and thanks the valuable contribution made by TimoKirkkomaki of Saanio & Riekkola Oy for the final editing of this report.

0 INTRODUCTION

Mechanical excavation of rock today includes several methods such astunnel boring, raiseboring, roadheading and various continuous miningsystems. Raiseboring is one potential technique for excavating canister andpersonnel shafts in high level spent nuclear fuel repositories as illustrated inFigure 0-1. Excavation of deposition holes using a novel dry blind boringtechnique demonstrated in the Olkiluoto Research Tunnel (Autio &Kirkkomaki 1996) is currently being planned by Posiva Oy.

The selected method to date for the excavation of deposition tunnels is Drill& Blast, but Horizontal Raiseboring has been identified as one possibleexcavation method applicable in certain conditions. In addition, there ispotential for use of mechanical excavation techniques such as the TM60developed by Tamrock/EIMCO or the Robbins Mobile Miner in differentparts of the repository where wall surface smoothness and negligibleexcavation disturbance is required.

Encapsulation plant\

Canistertransfer shaft

Personei shaft

Work shaft.Centrat tunnel

Deposition tunnel

Figure 0-1. The basic concept of a final repository for spent nuclear fuelwhere spent fuel canisters will be placed in deposition holes in the tunnelfloor (TVO 1992).

At present no mobile mechanical excavator with acceptable excavatingperformance in hard rock is presently available; although the experiences ofexisting prototypes such as the TM60 and the Robbins Mobile Miner implythat these concepts can be used - and has motivated research anddevelopment efforts by different equipment manufacturers.

In situ rock mass quality and stress conditions give rise to site specificdifferences in the cuttability of rock and tool consumption. The influence ofstresses around openings on excavation performance and costs formechanical rock excavation are not fully understood or quantified. Some ofthe factors affecting machine performance are shown in Figure 0-2.

One of the objectives of this study was to analyse the factors which affectthe feasibility of mechanical rock excavation in hardrock conditions - and toestablish a baseline with regard to cost effectiveness versus Drill & Blast.Another objective has been to enhance the understanding of factors whichaffect rock cutting so as to provide an improved basis for excavatorperformance prediction modelling; including a basis for a cutterhead designprocedures based on linear cutting test and field trial results.

FIELD FOLLOWUP CHART

Excavation SiteCharacterization

TunnellingMachinePerformance

Tunnel SizeTunnel AlignmentFace/Wall MappingIntact Rock Material TestingIn Situ Rock StressGround Support Measures

Net Advance RatesTool LifeTool Replacement ProfilesCutterhead BouncingMachine Utilisation

Station No.or

Tunnel Zone

Figure 0-2. Field follow-up chart for matching site characterisation andmachine performance.

1 MECHANICS OF CUTTING AND BORING

1.1 TOOL TRAJECTORIES AND VELOCITIES ON AXIALROTATION MACHINES

Trajectories of Fixed Tools

As a cutterhead rotates at a constant angular frequency / and simultaneouslyadvances at a constant axial rate AR, any tool on the cutterhead at a givenradius Rj will follow a helical path around a circular surface of radius Rj asillustrated in Figure 1-1. The Cartesian description of the helix is usuallygiven in parametric form for tool / as:

Xj = R, cos ip

Yj = Rs - Jin q> 1

Z, = A R ( t / 6 0 2 ) - 1000 J [

Xj, Yj, Zj = coordinates for tool i at time t

where co is the angular velocity (co = 2K • f ), 9 the total cutterhead rotationangle (tp = cot), and / = ( RPM / 60 ) the angular frequency.

Pitch A

Advance Rate AR

Figure 1-1. The helical tool path for axial rotation machines.

The helix pitch A or advance per cutterhead revolution is:

A = AR/(/-60 2 /1000)= AR/(RPM-60/ 1000)

and the helical path length Sj is:

S, = ( ( p / 2 j r ) - [ ( 2 7 t - R i ) 2 + ( A ) 2 ] 1 / 2

= (pR, • [ 1 + ( A / 2 T C - R , ) 2 ] " 2 [ 1 - 3 ]

and the helix angle p; , defined at a given point as the angle between thetangent to the helix of radius Rj and the tangent to the concentric circle ofradius Rj passing through the same point, is:

tan Pi = vadvance / vrotauon = A / ( 2JI • Rj) [1-4]

These relations describe the motion of fixed cutting tools, or the motion ofthe bearing centers for roller disk cutters. They illustrate one of the majorproblems typical for axial rotation cutterhead design; i.e.

pi -=> 90° as Rj -» 0

In other words, a tool at the center of a cutterhead has to progress directlyinto the rock in the axial direction with cutter rotation approaching nil.

Trajectories of Continuous Disk Rings and Studded Disk Roller Cutters

The helical path of a roller cutter traced out in the rock is described byequations [1-1] to [1-4]. If the cutter is a symmetrical roller disk set with itsbearing axis along a radial of the cutterhead, the center of the cutter bearingalso traces out a similar helical path. A point on the periphery or rim of anon-skidding disk describes a cycloidal trajectory relative to the helical trackin the rock surface.

Continuous Disk Ring Cutters

Consider a single continuous disk ring cutter mounted so that its axis ofrotation is along a radial of the cutterhead and perpendicular to the main axisof cutterhead advance (i.e. with zero skew). Assume that the cuttermounting is "stiff, so that the disk cuts a kerf of fixed depth without ridingup between chipping stages. If the helical tool path in the rock is developedinto a plane, and x and v axes are taken from an arbitrary origin on the path,with x and y directions tangential and normal to the path respectively, then aparticular point on the disk rim describes a regular cycloid whose equationis:

x = r •(<))- sin (j)) -»y = r - ( 1 -cos$) J [1-5]

where r is the disk radius, and <J) is the angle of cutter rotation measuredfrom an initial condition of x = 0, y - 0, <)) = 0 as illustrated in Figure 1-2. Analternative expression is:

x = r • ( acos { I - y / r } ± [ ( 2>> / r ) - ( y I r ) 2 ] m )

For one complete disk revolution, i.e. JC = 2rc • r, the cycloidal arc length is

8r.

It is often assumed for simplicity that a rolling indenter penetrates the rocknormally, but this is not strictly true. Any point on the rim of a non-skiddingindenting disk cutter will penetrate the rock along a part of the cycloidalpath; travelling forward as well as downward as shown in Figure 1-3. If thedepth of cut measured normal to the helical path is DOC, then the forwardtravel of a rim-point during indentation is:

Ax = r • 6 • 2n / 360 - [ r2 - ( r - DOC )2 ] m

= r • ( 27t / 360 • acos { 1 - DOC / r } - [ ( 2 • DOC / r ) - ( DOC / r )2 ] m )

Example 1-1. For a 305 mm (12") diameter disk, with depths of cut 1.0 mmand 10.0 mm, Ax would be 0.04 mm and 1.22 mm respectively. Thuspenetration is very close to being perpendicular to the surface of the rock inmost practical circumstances.

Combining the cycloidal and helical motions, the trajectory of a point on therim of a radial-axis non-skidding roller disk cutter can be expressed incylindrical coordinates as:

Rj' = Rj -.

(p' = (r / R-,) •($-sin $)• cos $ j [i_6]Z' = r • [ (([) - sin (j)) • sin (3 - ( 1 - cos <])) • cos P ]

in which R, is the radius at which the disk is set on the cutterhead, and (3 isthe helix angle of the tool path as given by equation [1-4]. In Cartesiancoordinates the combined motion is described by taking r and cp fromequation [1-6] and setting X,' = Rj' • cos (p\ Yj' = RY • sin (p\

When a disk cutter rotates without skidding, there is a simple relationbetween cutter rotation <j) and cutterhead rotation :

0r = Si = <pRj-[ 1 + ( A / 2 T C R , ) 2 ] I / 2 [1-7]

Figure 1-2. The regular cycloidal motion of a disk rim-point.

AX

Figure 1-3. The cycloidal indentation path of a disk rim-point.

Except for locations very close to the center of the cutterhead, ( A / 2TCRJ ) istypically much less than unity, so that:

<|) • r = cpRj [1-8]

By substituting into equation [1-6] from equation [1-7] or [1-8], cp' can beexpressed in terms of the cutterhead rotation angle cp.

Studded Disk Cutters

If, instead of a continuous disk ring, the disk rim is studded with indenters,the trajectory of an indenter will be the same as the trajectory of a rim-pointon a continuous disk ring cutter as long as the machine is "stiff, depth ofcut is less than indenter protrusion, and the cutter does not skid. However, inthe case of a cutter with hemispherical indenters, the first contact betweenthe indenter and the rock is made at a point a shown in Figure 1-4, where ais off-center from the extreme tip of the indenter by an angle 5 that is givenapproximately by:

= acos { 1 - DOC / r } [1-9]

[r 5 - ( r - p ) s i n5 ]

DOC

Figure 1-4. The rolling action of hemispherical indenter studs.

In this case the effective point of thrust moves forward during the workingstroke by a distance of approximately [ r • 8 • 2K I 360 - ( r - p ) • sin 8 ],where r is the radius of the stud tip, p is the protrusion of the hemisphericalindenter stud, and 8 is given by equation [1-9].

Example 1-2. For a studded 305 mm (12") diameter disk, the angle 8 is 6.6°with depth of cut DOC = 1.0 mm, or 20.9° with DOC = 10.0mm. If theprotrusion of the stud p is 10.0 mm, then [ r • 8 • 2K I 360 - ( r - p ) • sin 5 ] is1.18 mm with DOC = 1.0 mm, and 4.78 mm with DOC = 10.0 mm. Therespective values of Ax for a continuous disk ring, or a disk with sharp-tipped indenters, are 0.04 mm and 1.22 mm as shown previously. Thus,under these circumstances, the rolling action of the stud relative to the rockcontributes more forward component than does the cycloidal motion; i.e. itdoes more to move the effective path of indentation away from the normaldirection.

Speed of Fixed Cutting Tools

The velocity components relative to the rock for fixed cutting tools can beobtained directly by differentiating equation set [1-1] with respect to time:

X,

Y,

z,

= -R,n

= A

cp-sincp

cp-sin(p

= -2nf

= -27rf

•R,

R,

- sincp

• c o s 9

; CO = q? = 2?rf

Alternatively, the absolute tool speed relative to the rock, vtoo], is given bythe time derivative of equation [1-3]:

Vtool = Si = 2 T C / • Rj • [ 1 + ( A / 27C. 2 , 1 / 2 [1-10]

Speed of Rolling Disk Cutters

The speed of the roller cutter bearing center is given by equation [1-10]where Rj is the radius to the cutter center measured from the center of thecutterhead. If the cutter is rolling without skidding, then a given point on thedisk rim has tangential and normal velocity components relative to the rockthat are given by the time derivative of equation [1-5].

x = r (j> • ( 1 - coscj))

y = r 0 • sin<J>

where $, the angular roller cutter velocity relative to its own center, is

related to the angular velocity of the cutterhead *P by the time derivative ofequation [1-7].

(j)-r = <p R • I" 1 + ( A / 2 j t R ) 2 j " *

1 1 / 2

R / r ) - I 1 + ( A / 2TTR )-

II / 2= (27rf • R ( / r ) - [ l + ( A / 2TCR | )

2 ] '

Speed and Geometry of Studded Multi-Row Roller Cutters

Multi-row roller cutters have a finite thickness in the radial direction; thecutter is more of a drum than a disk in that it consists of several disk rings orcarbide insert rows joined together on the same shaft as illustrated inFigure 1-5. Since the whole cutter unit rotates with a single rotational speed,the cutter diameter has to vary systematically if skidding is to be avoided.Thus, on a flat-faced cutterhead, the multi-row cutter has to take the form ofa frustum of a cone.

If a multi-row roller cutter, as in Figure 1 -6, is set with its axis radial to themain cutterhead (but not necessarily exactly normal to the axis of advance),the required cutter cone diameters at the inner and outer ends, dinner anddouter, can be related to the radial distances of the cone ends on thecutterhead, Rjnner and Router» by equalizing the angular velocities as describedby equation [1-11], i.e.

( 2nf • R / r ) • [ 1 + ( A / 2TIR ): T ' "L "u'« Jouter uuier

(27tf • R / r )• I" 1 + ( A / 2rcR )2 1 " 'inner inner [_ inner J

DOC

Figure 1-5. Geometry of a studded multi-row roller cutter.

In most practical cases, the square root term is very close to unity, so that:

(. Qouler ' Ujnner ) ~ \ *V>uter '

or as:

douter / dinner - ( Ri CW / Rln CW [1-12]

where CW is the slant width of the cutter measured radially on thecutterhead, Figure 1-6. The half-angle of the coney is:

= atari ( dinner / 2Rmner) = atan ( douter

Equation [1-12] can be used to calculate the best position on the cutterheadfor a multi-row cutter of given dimensions. For this purpose it is rewrittenas:

Ri nner-optimum — v_W / ( douter ' dinner " * [1-13]

where Rinner-optimum is the inner multi-row cone cutter radius on thecutterhead where skidding does not occur.

10

Figure 1-6. Multi-row roller cutters on a large cutterhead.

From the above relations it can be seen that cutter skidding is unavoidablewhen non-tilted multi-row roller cutters of standard design are fitted to flat-faced cutterheads at different radii.

However, if the working face of the cutter cone is tilted relative to the maincutterhead advance axis by an angle a as shown in Figure 1-7, then inprinciple it may be possible to avoid skidding while using multi-row cuttersof standard design. Equation [1-12] can be rewritten as:

( dOUIer / dinner ) = 1 + C W • Sin 0C I R,nner

and the conditions for non-skid operation of a standard cutter is obtained as:

Sin a I R,nner = ( douter / dinner - 1 ) / CW [1-14]

hi other words, sin a has to be proportional to the setting radius (measurednormal to the advance axis). Substituting into equation [1-14] from equation[1-13]; the non-skid condition can also be written as:

sin a — Rinner ' ^inner-optimum [1-15]

from which it can be seen that, while a multi-row coned roller cutteroptimized for use at a large radius can be adjusted for use at a smallerradius, the converse is not true.

11

Directionof

Advance

CW

1 inner

1 outer

inner

f

"inner-optimum

Rotation Axis of Cutterhead

Figure 1-7. Multi-row roller cutters on a domed cutterhead.

Example 1-3. A 2.75 m (9') diameter cutterhead of typical full-face designis to be fitted with multi-row cutters of a standard design. Diameters of thelarge and small ends are 279 mm and 229 mm respectively, and the lengthof the cone is 254 mm. Calculate the optimum setting position for non-skidoperation of this cutter, and consider the feasibility of shaping the face of thecutterhead so as to permit non-skid operation of the other face positions.

Slant length of the cone is CW = 255 mm, and the optimum radius to theinner end of the cone is:

Rinner-optimum = 255 / ( 279 / 229 - 1 ) = 1 168 Him

For cutter radii less than the gauge radius, the standard roller cone can bemade to run without skidding by tilting its axis so that the small end leadsthe large end. At any radius Rjnner. the angle a required to prevent skiddingis:

a = asin (Rinner/ 1 168 )

where Rinner is in millimeters. The required value of a would be 45° atRinner = 827 mm, and 30° at Rinner = 584 mm. It therefore seems likely that adifferent cutter cone design would be required for the central part of thecutterhead, since the cutterhead profile would have to be shaped into a ratherextreme point or prow in order to utilize the standard cutters at small radii.

12

1.2 ROLLER DISK CUTTER INDENTATION MECHANISMS

The most common mechanism that employs normal indentation and quasi-static thrust is the roller disk cutter. The simplest roller cutter is a sharp-edged wheel, exemplified on a small scale by the roller glass cutter.

For indentation cutting in very strong rocks, the simple or continuous diskring cutter is modified by inserting carbide studs into the rim, thussimultaneously reducing the indentation contact area of the rim andenhancing the rim resistance to abrasive wear. In order to limit the numberof individual cutters on a cutterhead, several disks may be set onto acommon cutter bearing. Alternatively, the roller cutter may be a frustum of acone with hemispherical or conical studs set into the periphery as describedearlier for multi-rowed cutters.

For cutting in rocks that are weak, ductile or compressible; roller cuttersmay be studded with teeth similar to those of a gear wheel. Gear-toothedcutters are capable of digging out cohesive fragments when the teethpenetrate deeply into the rock.

Dynamics of Simple Roller Disk Cutters

Consider the simple disk shown in Figure 1-8, with uniform thickness W, sothat the perimeter has sharply squared edges. When rolled along the surfaceof a rock, and thrust into the material at a constant depth of cut DOC byapplication of an axle force; this force can be resolved into components Frand Fn that are respectively parallel and normal to the surface of the rock.These forces are assumed to be invariant with time (i.e. the cutting processis a continuous one, as distinct from the process of intermittent chipformation in brittle rock).

Since the depth of cut is constant, the path traced out by any point on thedisk rim is a regular cycloid, Figure 1-2. Thus, if an elementary segment ofthe disk rim is regarded as an indenter, it penetrates into the rock along acycloidal path, Figure 1-3. At any stage of the penetration, as defined by thecontact arc angle co in Figure 1-9, the slope of the disk rim elementarysegment penetration path is given by the standard cycloid equation [1-5] asdy/dx:

dy/dx = dy/d§ • d§ /dx = r • sin <)) / r • ( 1 - cos ())) = cot (|) II

where 0 is the conventional angular position used in the standard cycloidequation such that <(> = ( 271 - co ). Thus:

dy/dx = cot ( n - co/2 ) - - cot ca/2

and the inclination from the normal direction is:

13

dx/dy = - tan co/2

In other words, for any position defined by the contact arc angle 0), thepenetration path is inclined at an angle co/2 to the normal direction.

W

resultant

Fn

^indent

L chord

Fr

DOC

d/2 - DOC

DOC

W

tool path

Figure 1-8. Tool cutting forces and contact geometry at the disk rim/rockinterface for a simple roller disk cutter.

14

Fn

Fr

dFradial

Figure 1-9. Force components on the rim of a simple roller disk cutter.

If S is the distance measured along the cycloidal penetration path, then:

dS/d§ = [ ( dx/d§ )2 + ( dy/d§ ) 2 ] "2 = 2r • cos 0/2

If the elementary indenter enters the rock at a position defined by the contactarc angle 0), as in Figure 1-9, the penetration length for the disk rimelementary segment along the cycloidal penetration path S' is:

S' = / 2r • cos <|>/2 dty = 4r • sin = 2 • ( d • DOC ) 1/2

As each elementary segment of the rim penetrates the rock, an elementaryforce dF whose direction ought to be tangential to the cycloidal penetrationpath can be resolved into components JFradiai and £/Ftangentiai that arerespectively normal and tangential to the disk rim, Figure 1-9. If the cutterbearing is frictionless, the tangential force components dFtangentiai must sumto zero since there can be no net moment about the center of the disk. Underthese circumstances, the net elementary forces are purely radial.

For resolution of forces parallel and normal to the rock surface for rollerdisk cutters of uniform thickness:

^ r a d i a l = <* ' ^M radial

= O • dWrddliil • dS

dFy

- dFridl.d\ • sin CO

= t /F r a d i a i • cos co

15

Fx = -\dFx = - W • / a • 27tr • sin co da

Fy = -jdFy = - W • j a • 27cr • cos co d(a

Hence, the axle force components are:

Fr = Fx

= constant • o" • W • 2nr ( I - cos co ) [1-16]

= constant • a • W • 271 • DOC [1-17]

Fn = Fy

= constant • a • W • 27tr sin CO [1-18]= constant • <r • W • 2rc • [ d • DOC • ( 1 - DOC / d ) ] "2

= constant • a • W • 2TI • ( d • DOC ) m [1-19]

where the constant is defined by the failure criterion of the rock and the kerfcutting geometry; ando is the uniaxial compressive strength of the rock.

The resultant force on the cutter axle is:

Fresuuam = [ F r 2 + Fn 2 ] m

= constant • a • W • 27tr • [ 2 - 2 • cos CO ] m

= constant • a • W • 2rc • ( d • D O C ) m

and the inclination of the resultant axle force from the normal direction isgiven by equations [1-16] and [1-18]:

tan cOresuitant = Fr / Fn = ( 1 - cos co ) / sin CO = tan co/2

and therefore:

resultant = acos co/2 = acos ( 1 - D O C / r ) / 2

The ratio of the axle force components is termed the cutting coefficient k,and can be expressed as:

k = Fr/Fn = ( 1 - cos co ) / sin CO = [ DOC / ( d - DOC ) ] m

k = ( D O C / d ) l / 2 [1-20]

To summarize; the theoretical one-dimensional considerations forindentation cutting by a simple disk ring of uniform thickness leads to theexpectation that:

• Fr will be proportional to W • DOC

8 Fn will be approximately proportional to W • ( d • DOC ) l / 2

* Fresuitant will be proportional to W • ( d • DOC ) 1 / 2

* Fresuitant will be inclined at an angle co/2 = acos ( 1 - DOC / r ) / 2from the normal direction

16

Some Practical Aspects of the Simple Disk Indentation Contact Area, Acon

The trigonometric disk contact angle formulae found for indentating rollerdisk cutters are impractical as a basis for prediction model upbuilding.However, the formulae are readily approximated by power functions. Theerror introduced by approximation is illustrated on the Appendix 1contangl.xls file printout. The actual and approximated relations are:

Actual disk contact arc Larc' = raJ • co / 360

Approx. disk contact arc Larc = Vi • Lchord = ( d • DOC ) l / 2

Actual chord length Lthord' = 2 • [ r2 - ( r - DOC )2 ] "2

= 2 [d DOC-DOC 2 ]" 2

Approx. chord length Lchord = 2 ( d • DOC ) m ; D O C 2 « d • DOC

Actual disk contact angle co' = acos ( 1 - DOC / r )

Approx. disk contact angle co = Larc • 360 / rcd = ( DOC / d ) m • 360 In

Actual disk contact area Acon ' = W • Larc ' = W • 7id • t o / 360

Approx. disk contact area Acon = W Larc = W • ( d • DOC )1 / 2

T h e resul tant axle force F resui t an t at tack angle (Oresuitant can be found by

iteration using the depth of cut ratio p and the disk cross-sectionalindentation area A;ndent- The resultant force attack point is determined whenAjndem'/2 equals Ajnt]em- The calculation procedure is as follows:

Actual depth of cut at resultant force attack point:

DOCresul(anl = p • DOC

Actual resultant force attack angle:

COresultani = OCOS ( ( T - D O C + DOC r e sultam ) / T )

= acos ( r - DOC • ( 1 - p ) / r)

Actual cross-sectional indentation area of the disk for DOC:

A.ndem* = Ttr2 • ( co / 360 ) - Vi • ( r - DOC ) • [ d • DOC - D O C 2 ] m

Approximate cross-sectional area of the disk for DOCresuitant:

A = nr2 • ( ajtauna,,/ 360 ) - Vi • ( r - p • DOC ) • ( d • p • DOC - D O C 2 ) m

= r2 ( p • DOC / d ) m - Vi • ( r - p • DOC ) • ( d • p • DOC ) "2

17

In practice, the above equations are used for normalizing field test cuttingdata; i.e. the cutter coefficient k can be expressed as:

= ( D O C / d ) mk = Fr/Fn

= (DOC= C, • DOC

where the cutter constant C| is dependent on:

} [1-21]

S disk diameter as d" m

M the interaction between rock mass jointing and large diameterroller disk cutters is denoted as the "buggy wheel effect"

whereas the mean normal force Fn can be expressed as:

Fn = constant • o • W • 2w • ( d • DOC ) m 1= Fn,DOC1/2 / [1-22]

where the critical normal force Fni (normal force for a unit depth of cut) isdependent on:

8 disk rim geometry as W • d w2

* intact rock strength, degree and type of rock mass jointing.

For normalization of laboratory and field cutting tests; the effects of kerfspacing, degree and type of rock mass jointing, joint orientation etc. must beincluded. The functional relationships between all relevant parameters as tokerf cutting with roller disks has been established in Chapter 2.

Dynamics of Wedge-Shaped Disk Cutters

The preceding analysis deals with continuous rock cutting by a disk cutter ofuniform rim width; the next step is to consider a disk which has a wedge-shaped rim as in Figure 1-10.

As each element of the rim penetrates the rock, an elementary force dFwhose direction ought to be tangential to the cycloidal penetration path canbe resolved into components JFradiai and dFtangentiai that are respectivelynormal and tangential to the disk rim, Figure 1-10. If the cutter bearing isfrictionless, the tangential force components JFiangentia[ must sum to zerosince there can be no net moment about the center of the disk. Under thesecircumstances, the net elementary forces are purely radial.

For resolution of forces parallel and normal to the rock surface for pristinewedge-shaped roller disk cutters:

18

= a • 2 tan p/2 2m • dco

dFy

sin co

CO

Fx = -1 dFx = -\\o-2tan p/2 • 2OT • sin co Jco

Fy = -ldFy = -\\c-2tan (3/2 • 27ir • cos co Jco dDOC

Hence, the axle force components are:

Fr

Fn

= Fx

= constant • a • 2 tan 0/2 • DOC • 2nr • ( 1 - cos CO )= constant • c • 2 tan 0/2 • 2n • DOC 2

= constant • a • 2 tan [3/2 • DOC • 27ir • sin co

= constant • a • 2 tan p/2 • 2rc • d m • DOC3 / 2

where the constant is defined by the failure criterion of the rock and the kerfcutting geometry; and a is the uniaxial compressive strength of the rock.

Fn

P/2

dF,adial'2

DOC

radial

Figure 1-10. Indentation geometry of wedge-shaped roller disk cutters.

19

The resultant force on the cutter axle is:

Fre,.ullant = [ F r 2 + F n 2 ] " 2

= constant • o • 2 tan (3/2 • DOC • 2rcr • [ 2 - 2 • cos co ] m

= constant • c • 2 tan [3/2 • 2n • d "2 • DOC m

and the inclination of the resultant axle force from the normal direction isgiven as:

tan consultant = Fr / Fn = ( 1 - cos co ) / sin co = tan co/2

and therefore:

consultant = acos co/2 = acos ( 1 - DOC / r ) / 2

The ratio of the axle force components is termed the cutting coefficient k,and can be expressed as:

k = Fr/Fn= ( 1 - cos co ) / sin co= [DOC/(d-DOC)]1 / 2

= ( D O C / d ) 1/2

To summarize; the theoretical two-dimensional considerations forindentation cutting by a wedged-shaped disk cutter leads to the expectationthat:

• Fr will be proportional to tan (3/2 • DOC2

• Fn will be approximately proportional to tan (3/2 d "2 • DOC m

* Fresuitant will be proportional to tan p/2 • d "2 • DOC m

* Fresuitan, will be inclined at an angle co/2 = acos ( 1 - DOC / r ) / 2

from the normal direction.

The use of wedge-shaped roller disk cutters has decreased in the last 10

years since:

(i) in soft rocks; wedge-shaped disk cutters require more torque forlarge depths of cut than constant section disk cutters.

(ii ) in hard and abrasive rocks; the pristine wedge-shaped rim is quicklyworn down resulting in a very blunt cutting edge when compared to aconstant section disk. As the blunting of the tool progresses; thefunctional relationships found for pristine wedge-shaped disk cutterschange dramatically, and tend to follow the relationships developedfor constant section disk cutters.

( Hi) increased use of studded disk cutters to enhance tool life; especiallyin the gauge area of TBM cutterheads.

20

Dynamics of Studded Roller Disk Cutters

An alternative to the wedge-shaped disk is a disk whose rim is studded withcemented carbide inserts or wedge-shaped steel teeth. The studs are typicallyhemispherical, conical or tapered projections with rounded tips. As the diskis rolled along the rock, the studs or teeth descend successively with theaction of three-dimensional indenters.

There are obviously some practical limits set by the size and spacing ofstuds. As illustrated in Figure 1-11, the maximum depth of cut DOCmaxcannot exceed the length by which studs protrude from the disk rim; or elsethe whole disk rim would be thrust into the rock, i.e.

DOCmax < p [1-23]

Another limit set for cutting with a single studded disk is the necessity ofalways having at least one stud in the rock.

There could obviously be operating difficulties if two adjacent studs are ableto lie above line AA' at the same time as in Figure 1-12. With n studs set atequal intervals around the rim of the disk, the angular spacing 8 betweenstuds in a row is 2n/n. If the disk is rigidly mounted for cutting to a constantdepth of cut DOCmax, the condition which guarantees that at least one studwill always be below the surface level is:

DOCmM > r ( 1 -cosb/2) [1-24]

> r • ( 1 - cos nln )

where r is the radius to the tip of the stud.

iDOC

Figure 1-11. Maximum depth of cut for a studded roller disk cutter beforedisk rim contact with rock occurs.

21

A1

r - r • cos 5/2

Figure 1-12. Minimum depth of cut required for positive operation of astudded roller disk cutter.

To provide a positive guarantee that there will always be at least one stud inthe rock and under load, the relative stud spacing has to be half that given byequation [1-24] since a new stud has to enter the rock before the precedingone departs from the point of maximum depth of cut, i.e.

DOCn > r • ( I - cos 8 ) [1-25]

In practice, there are factors which allow a studded disk to operate when theabove conditions are not met. A rough rock surface will catch the studs androtate the cutter, or the cutter itself may have low enough bearing frictionand high enough inertia to give a fly-wheel effect, or the mounting of thecutter may be compliant (i.e. "springy"). Nevertheless, it is prudent to designand operate so that:

• depth of cut is less than the protruding length of the stud• the disk should always have at least one stud in the rock and

under load.

This means that under normal operational conditions:

p > DOC™* > r • ( 1 - cos 5 ) [1-26]

The spacing of studs around the disk perimeter ought to be determined, atleast in part, by the requirements for efficient indexing, i.e. "optimum"spacing between adjacent indentation craters. However, this distance varieswith the depth of cut, and the upper limit of disk rim studs n may be set bythe practical matter of maintaining adequate structural insert support. Forhemispherical buttons and 90° cones, the base diameter is 2t, while for sharp

22

60° cones it is t. In general, the base diameter of a stud can be expressed ask| • t and the stud rim spacing as RS; so that the number of rim studs n is theinteger given by:

n = lit- ( r - p ) / ( k , • t + RS)

Typical values for stud diameter, kerf spacing and mean roller cutterdiameter are listed in Table 1-1 and illustrated in Figure 1-15 as a functionof cutter diameter.

If the thrust capability is limited to the extent that the sharing of loadsbetween two or more operative studs is undesirable, then an additionalcondition that tends to conflict with the foregoing ones is:

D O C m a x > T ( \ - c o s 2n/n )

Thus the optimum operating condition for a single studded disk is:

DOCmaJl / r = ( 1 - cos Inln )

Because of the variability of rock properties, this may not be a realisticcondition to impose. However, the problem tends to disappear when two ormore disks are set on an axle with their stud positions staggered. Figure 1-5.The main practical concern is to recognize what is going on, so that amachine is not operated inappropriately, either when there is a generousreserve of thrust available in soft rock, or when the machine is at the limit ofits thrust capability in very hard rock.

Forces on Studded Disks

In theory, a smooth-rim disk is capable of constant-force operation (ignoringintermittent formation of chips in brittle material). By contrast, a disk withstuds on its rim necessarily experiences force fluctuations as the separatestuds penetrate and disengage. For a typical stud, penetration resistanceought to increase as depth of cut increases, reaching a maximum as it passesunder the lowest point of the disk. If a second stud enters the rock while thepreceding one is still operating, there should be an immediate jump in theaxle force of the cutter.

Since a studded disk is quite likely to have only one stud at a time underhigh load, the forces developed by a single cycle of stud indentation are ofdirect significance. If more than one stud is working at a given time, theforces on the cutter can be obtained by appropriate summation if the studsare widely spaced (significantly greater than

23

Fn

DOC max

dF.radial

Figure 1-13. Forces on a studded disk.

Consider the cutter shown in Figure 1-13. Each stud enters the rock at aposition defined by the contact arc angle co. As the disk rotates, the tip of thestud descends to depth DOCmax along a cycloidal path as previouslydescribed. As the stud descends, it also rotates, turning through angle co indescending to its maximum depth DOCmax.

The effective stud tip depth of cut is a function of the contact arc angle co,i.e.

DOC { co } = DOCmilx sin co

The stud contact area is dependent on the stud tip geometry, i.e.

Tapered studs Abuuon-radiai

[1-27]

Hemispherical studs Abu iton-radial

= individual stud contact area= WL

= 2nt • D O C { CO }

24

For resolution of forces parallel and normal to the rock surface for taperinsert studded roller disk cutters.

" ' r a d i a l = ^ " "'"bullon-radial ' " ^

= a • f/Wradia| • dL r a d i a | • n • d(O

dFx = dF r a d i ai • sin co

dFy = J F r a d i a l • cos CO

Fx = -jdFx = - WL • n | o sin co dw

Fy = - J dFy = - WL • n • I a • cos co dw

Hence, the axle force components are:

Fr = Fx

= constant • G • W L • n • ( 1 - cos CO )

= constant • G • WL • n • 2 ( DOC / d ) [1-28]

Fn = Fy

= constant • G • W L • n • sin CO

= constant • a • WL • n • 2 ( DOC / d ) "2 [1-29]

where the constant is defined by the failure criterion of the rock and the kerfcutting geometry; and a is the uniaxial compressive strength of the rock.

The resultant force on the cutter axle is:

Folium = [F r 2 + F n 2 ] " 2

= constant • o • WL • n • [ 2 - 2 • cos CO ] "2

= constant • G • WL • n • 2 ( DOC / d ) m

and the inclination of the resultant axle force from the normal direction isgiven by equations [1-28] and [1-29]:

tan cOresuium = Fr / Fn = ( 1 - cos (a) I sin (a = tan co/2

and therefore:

G>reSuium = acos co/2 = acos ( 1 - D O C / r ) / 2

25

For resolution of forces parallel and normal to the rock surface forhemispherical insert studded roller disk cutters:

^^radia] = O ' ^button-radial ' dtl

= a • 2nt sin co • n • dm

dFx = JFradja! • Sin CO

J F y = dF r a d l a l • COS CO

Fx = - j dFx = - 2nt • n • I a • sin2 on dm

Fy = -1 dFy = - 2;ct • n • | a -sin co • cos co rfco

Hence, the axle force components are:

Fr = Fx

= constant • o • 27it • n • ( co/2 - ( sin 2(0 ) / 4 ) )

= constant • o • 27tt • n • 2 ( D O C / d ) 3 / 2 [1-30]

Fn = Fv

= constant • a • 7tt • n • ( 1 - cos 2to) / 2

= constant • a • 27it n • 2 ( DOC / d ) [1-31]

where the constant is defined by the failure criterion of the rock and the kerfcutting geometry; and a is the uniaxial compressive strength of the rock.

The resultant force on the cutter axle is:

Fresuiuim = [ Fr + Fn - ] -

= constant • O • W L • n • 2 ( D O C / d )

and the inclination of the resultant axle force from the normal direction r-given by equations [1-30] and [1-31]:

tan constant = Fr / Fn = ( DOC / d ) m -tan co/2

and therefore:

= acos co/2 = acos ( 1 - DOC / r ) / 2

26

1.3 TOOL CONFIGURATION AND TOOL RIMDIMENSIONS

Tool Configuration and Kerf Spacing

The procedure for cutterhead tool lacing design is discussed in detail inChapter 6.2. However, some aspects of tool configuration and its effect onsequential in-line kerf cutting with roller disk cutters are illustrated in Figure1-14.

ALTERNATIVE ROLLER DISK CUTTERCONFIGURATIONS

fff^x.Continuous disk ring cutters for use inmoderate to hard rock formations.

Studded dual row disk cutters for use inbrittle rock. Number of toolholdershalfed by use of 2 row cutters.

Studded dual row disk cutter configurationfor enhanced advance rates. Use of 2 toolrows per line potentially doubles netadvance rates.

Studded dual row disk cutterconfiguration with intermittent halftracking cutters for reducing the kerfspacing in hard or tough rock formations.

Figure 1-14. Alternative roller disk cutter configurations illustrating thevarious combinations of kerf spacing and tools per line commonly in usetoday.

27

Roller Cutter Kerf Cutting Geometry

Multiple carbide insert row or studded cone cutters totally dominate theraiseboring, boxhole and pipe-jacking tool market today; with 2 - 5 rows percutter being the most common. The use of carbide insert cutters reducesboth tool consumption and tool contact or wearflat area. Reduced toolcontact area results in lower tool cutting forces.

Steel disk cutters are typically used on tunnel boring machines. Single ordual row carbide insert cutters can sometimes be used on cutterheadsoriginally designed for single ring steel disk cutters. Studded Tri-Cone Bitsare used for rotary blasthole drilling in hard rock. Tri-Cone Bits or CherryButton cutters are sometimes used on large cutterheads as center cutters.

Some typical values for in-line roller disk kerf cutting are listed in Table 1-1and plotted in Figure 1-15 as a function of disk diameter for both face andgauge cutters. Gauge cutters have wider rims and thus more wear material soas to extend disk life in the outer gauge positions on a cutterhead to reducethe operational downtime represented by frequent cutter replacements inthese positions. The functional relationships between cutter diameter, kerfspacing, disk rim width and insert radius, as established in Chapter 2.5, havebeen used for creating the trendlines in Figure 1-15, i.e.

Kerf spacing S = constant d [2-28]Disk rim width W = constant • d3/2 [2-29]Insert diameter t = constant • d3/2 [2-30]

Table 1-1. Some typical values for in-line roller disk kerf cutting.

Disk/CutterDiameter

d

(mm)

LineSpacing

Sface

(mm)

RimWidthWface

(mm)

Constant Section Steel Disk Cutters254305394432483

54708288102

Studded Roller Disk Cutters254305360405

54706780

Multi-Row Roller Cone Cutters275300305305

31.5/6325.5/5123/5635/70

! i . V . V . ' . ' . ' . ' . ' . ' . ' . ' . ' ! " f f » " l ' i •••••• • • • • • • • • • • ' • ' • ' • •

11.112.714.5

RimWidth

(mm)

1117.219.522.5

Insert/StudDiameter

t

(mm)

15192529

17221919

28

Constant Section Disk Cutters

150

120

10090807060

_ 50

i. 40

30

25

20

15

10

yy -X

y i .

/

)/ >

/

Ap

/

/

/

Face Disk LineSpacing

Gauge Disk RimWidth

Face Disk RimWidth

100 150 200 250300 400 500 600

Disk Diameter, d (mm)

Studded Roller Disk Cutters

150

120

10090807060

-. 50

I 40

30

25

20

15

10

Multi-Row Cone Cutters

10090807060

E. 40

3025

20

15

10

y/

//

/

/

*/•

/

Y

i

/

k

//

//

>

y \i

/

/

/•

/

/

/

/

Row or LineSpacing

WC InsertDiameter

100 150 200 250300 400 500 600

Disk Diameter, d (mm)

Insert Row Spacing(for hard rock formations)

Kerf Spacing for Half Tracking Tools(for hard rock formations)

WC Insert Diameter

100 150 200 250300 400 500 600Disk Diameter, d (mm)

Figure 1-15. Scatter plot and trendlines of tool rim geometry and kerfspacing for in-line roller disk kerf cutting as a function of cutter diameter.

Note: Stud rim spacing RS = (0.7~> 1.3 ) • Sker/

29

2 A PHENOMENOLOGICAL MODEL FOR THECUTTING ACTION OF ROLLER DISK CUTTERS

2.1 INTRODUCTION

One of the research tools available to the design engineer is that branch ofapplied mathematics known as dimensional analysis. Usually a preliminarydimensional analysis of any experimental investigation discloses functionalrelationships between the measurable parameters involved that simplify theproblem and indicate the direction to be followed in the design of theexperimental programme. All similitude and model studies should be basedupon a dimensional analysis so that the results obtained can be applied to theprototype with confidence.

The fundamental dimensions of physical quantities in mechanics are usuallytaken as mass, length and time, and are denoted by M, L and T. Thedimensions of other physical quantities follow immediately from theirdimensions. For example, volume has the dimension L3; velocity has thedimensions LT'1; acceleration has the dimensions LT2; and force, defined asthe product of mass and acceleration by Newton's law, has the dimensionsMLT ~2. Thus mass, length and time have been expressed in terms of theprimary quantities, and secondary quantities have been expressed in terms ofthe primary quantities. There are no hard rules as to which measurablequantities should be considered the primary ones. In engineering mechanics,the primary quantities are often chosen as force, length and time.

The dimensions of various physical quantities encountered in mechanics aresummarized in Table 2-1, assuming that the primary quantities are eithermass, length and time or force, length and time. Some physical quantitiesare non-dimensional, for example strain, Poisson's ratio and angles. If aquantity is non-dimensional, this is indicated by the symbol 1 rather than 0as is often done.

The most important applications of dimensional analysis in engineering are:

M converting equations or data from one system of units to another8 developing relationships among variables9 systematising the collection of data and reducing the number of

variables that must be studied in any experimental programmeH establishing the principles of model design and assisting in the

interpretation of test data.

30

Table 2-1. Physical quantities and their dimensions.

Quantity

LengthAreaVolumeTimeMassVelocityAccelerationForceMass densityAngleAngular velocityPressure or stressWork or energyMomentumPowerMoment of inertia of an areaMoment of inertia of a massModulus of elasticityStrainPoisson 's ratioPorosityBulk modulus

Symbol

IAVt

mV

aF

P6 , <)>CO

p, o, iWmvPIIE

&YV

nK

DimensionsforM.L, T

LL2

L3

TMLT1

LT2

MLT2

ML3

1

T'

ML'T'2

ML2T'2

MLT 'ML2T3

L4

ML2

ML 'T'2

1

1

1ML 'T'2

Dimensionsfor F, L, T

LL2

L3

TFL'T2

LT 'LT2

FFL'T2

1

T'FL2

FLFTFLT 'L4FLT2

FL2

I

1

IFL2

2.2 CONDITIONS OF SIMILITUDE

Similarity analysis is a powerful engineering tool enabling full-scaleperformance to be predicted from small-scale experiments. For thisanalytical technique to be applicable, there must be exact similarity betweenthe model and its object. Furthermore, the method can be applied only to acomplete equation, and this equation must relate all the parameters ofrelevance to the system being described. Although the method does notprovide a description as complete as might be expected from a detailed puremathematical analysis, it is simple, and often more convenient to use.

The mathematical basis for dimensional analysis is founded on thefollowing two axioms. First, absolute numerical equality of quantities existsonly when the quantities have the same dimensions. Second, the ratio of themagnitudes of two like quantities is independent of the units used in theirmeasurement, provided the same units are used for both quantities.

31

The theory of dimensional analysis can be summarized by the BuckinghamTheorem, also known as the 7i-theorem which states:

"If any equation is dimensionally homogeneous, it can be reduced to arelationship among a complete set of dimensional products"

I.e. if a relationship exists where:

Pi = f(P2, Pi, ••• Pn) [2-1]

then an expression:

7tf = f'(n2, Ttj, ... 7 V k ) [2-2]

can be obtained where all 7t-terms are non-dimensional quantities and k isthe number of fundamental units. From the experimental standpoint, thefunction / ; is easier to establish than the function / .

2.2.1 Forming the Non-Dimensional Products

The matrix method has been used for obtaining the non-dimensional termssince a complete description of rock indentation by cutting tools involves alarge number of parameters. This method is particularly attractive insituations involving a large number of parameters since it facilitatescomputer analysis.

Given a set of n variables, pi, p2 , ••• pn , an infinite number of products ofpowers of these variables can be formed:

P? • Pi • - • P^ [2-3]

The exponents x, may have any positive or negative, integral or fractionalvalue including nil. The dimensions of these products of powers of variablesmay be found by replacing the symbols /?, with the symbols of itsdimensions and raising the symbols to the power Xj . For example, if the

y

variable /?, has the dimension M • • L' • T • , the dimension of P> isM ' : L' • T ' ' . Thus the general expression for the dimensions in[2-3] is:

• #A,X,+ /ljX2 + ...+ ^ X n TB,X, + B2X2 + ... + B,Xn yC ,X | + C2X2 + ... + CnXn

A non-dimensional product of powers is one whose exponents of thefundamental units M, L and T all vanish and which is designated by K andreferred to as a 7t-term.

32

Basic theory shows that each non-dimensional quantity is a product ofparameters p such that:

P/1 • P ? •... • px:

is dimensionless. In other words, if pi, p2, ... pn are the variables governing aphysical phenomenon, the exponents JC/( *2, ... xn can be found such thatequation [2-3] is dimensionless with all fundamental units cancelling out.To achieve this x;, x?. ••••*« must provide a solution of the linear equationsimplicit in:

£ rrij,, x, = 0i = /

[2-4]

where j = 1, 2, ... k and the corresponding m values are the dimensions ofthe parameters p. In the dimensional matrix, j is the number of rows and i isthe number of columns, being equal to the number of fundamental units andnumber of variables respectively.

Equation [2-4] can be expressed in open form suitable for conversion tomatrix notation:

m2

(p<)

x,

«/./ x,

m2 i Xi

(P2

X2

+ m,.2

+ m.22

)

X2 +

X2 +

(Pk)

Xk

mLkxk +

m2 k xk +

(Pk+i)

xk+i

ffl 1 k+1 Xk+1 +

Tt\2 jt+/ Xk+f "t"

(PM )

Xk+2

ml,k*2 Xk+2 +

ftl2.k+2 Xk+2 ~^~

(Pn

Xn

m,.nxn

m2,n Xn

= 0

mk +mk2x2+ mkkxk+

The above is referred to as equation set [2-4a].

The first part or the left hand side of equation set [2-4a] can be expressed asa product of two matrices:

m22 x2

Xk

or more generally M, , X, where:

ij , is the (/: • A:) matrix of m7,, J j = 1, 2, ... ki = 1, 2, ... k

j is the column vector of x, i.e. solution vector i = 1, 2, ... k.

33

Similarly, the second or right hand side of equation set [2-4a] can beexpressed as:

"I; , *+2

, k+2

ml,n

mk, n

xk+l

or more generally Nj,pXp where:

Nt p is the [ k • ( n - k ) ] matrix of m,, p 1 =1,2, ... k

p = 1,2, ... n - k

or p = k+1, k+2, ... n

Xp is the column vector of x on the right hand side.

Obviously equation set [2-4a] has many solutions but only n - k of these canbe linearly independent. To obtain exactly n - k linearly independentsolutions, k must be equal to the rank r of the matrix Mj , . This demandsthat the matrix Mj,; is non-singular.

The new form of equation set [2-4a] is now:

MjjXi =(-l)Nl.pXpXp [2-5]

Since the Mj , matrix is square and non-singular, the inverse matrix M ~'j ,exists. Pre-multiplication of the equation [2-5] by the inverse matrix yields:

M''j.i Mj,, Xi = (-1) M-'j.i Nt.p Xp

Further simplification gives:

X, = (-1) M-'j.i N,.p Xp

[2-6]

[2-7]

Equation set [2-4a] contains n unknowns to be solved from k independentequations. Therefore n - k unknowns must be chosen arbitrarily. Sincep = n - k on the right hand side of the equation set [2-4a] then the values ofthe corresponding x values on the same side of equation set [2-4a] can bechosen arbitrarily. This provides the opportunity to make the Xp columnvector a unity matrix.

Then equation set [2-7] becomes:

Xi = (-1)M-'j.i Ni.p [2-8]

which means the ith solution matrix for X is the /th column of the matrixproduct on the right hand side of equation set [2-8]. M ''j , has the order

34

( k • k ) and Nt, p has [k • ( n - k )]. There will therefore be n - k columns inthe matrix and so n - k solution vectors (i.e. non-dimensional quantities) asexpected.

By means of the above theorems we have shown that if there are n variablesand the rank of the dimensional matrix is r, there will be p dimensionlessproducts of exponents of the variables or rc-terms where p is given by:

p = n - r

Also a functional relation will exist among these 7t-terms that can berepresented as:

71/ = / ' ( n 2 , T C 5 , ... n n . k )

It should be noted that there are an infinite number of complete sets of n-terms because new complete sets can be formed from any given completeset. However, it is only necessary to find one complete set. Sometimes it isadvantageous to form several complete sets and to use the one that has thesimplest 7t-terms.

2.3 APPLICATION OF SIMILARITY ANALYSIS

The general steps in applying the theory to the design of prediction modelsare:

1. Determine the general nature of the simulation (mechanical asopposed to say chemical or electrical).

2. Select variables which are considered independent of each otherand which influence the process. This step can influence thefinal result in many ways. If an insufficient number of variablesare included, the final result, although correct, may contain somany n-terms that the functional relation is too difficult tointerpret or investigate.

3. Select the most appropriate fundamental units; in this case Mass[M], Length [L] and Time [T].

4. Express parameters arising from [2-2] in dimensional form (e.g.intact rock density as ML'3).

5. Establish the functional relationships between variables using adimensional method (in this case the matrix method). Ensurethat:

35

(a) each term is dimensionless( b ) the number of dimensionless terms are n - k( c ) each variable under [2-2] appears at least once.

6. Examine the resultant groups or TZ-terms for practical relevanceand physical significance.

7. If the n-terms do not have practical or physical significance,then thev must be manipulated by multiplication or division onewith another to produce terms having relevance. Otherwise it isnecessary to re-examine the parameters for completeness orchange the set of fundamental units.

2.3.1 Roller Disk Kerf Cutting of Rock

Rock indentation by roller disk cutters has been discussed in great detail inChapter 1.2. In addition, a comparison of experimentally and analyticallyderived results as to the cutting constant Q is presented in Chapter 4.4.

The next step in the design of prediction models for the kerf cutting processof rock is to include aspects such as kerf spacing, rock toughness and rockmass discontinuities into the functional relationships for roller disk cuttingas illustrated in Figure 2-1.

Following the listed stepwise approach in applying the theory ofdimensional analysis presented above and accepting that the simulation ispurely mechanical in nature; the physical parameters governing roller diskkerf cutting of rock may now be considered in detail as shown in Table 2-2.

36

ROLLER DISK IN-LINE KERFCUTTING OF ROCK

X X X Xs s s

Rock Indentation

- disk rim diameter

• disk rim width

- disk rim insert sizeand rim spacing

Kerf Cutting

- kerf spacing

- multiple tool passings

Rock Mass

• a

-Gic

- O and

Properties

or

Figure 2-1. Aspects of roller disk in-line kerf cutting process of rock thatcan be readily analysed by similarity methods.

37

Table 2-2. Physical parameters governing roller disk kerf cutting of rock.

Parameter

Disk normal forceDisk rolling forceIntact rock strengthIntact rock elasticityIntact rock densityIntact rock porosityCritical energy release rate of rockSpacing of discontinuitiesStrength of discontinuitiesOrientation of discontinuitiesDisk rim diameterDisk rim widthDisk rim contact areaKerf spacingDepth of cut

Symbol

FnFr

O

E

Pn

GIC

O

XadW

" con

sDOC

Dimensionsfor M, L, T

MLT2

MLT 2

ML'T2

ML'T2

ML3

IMT2

L

ML'1 T2

I

LLL2

LL

Reason/orInclusion

cutter loadcutter loadrock strengthrock strengthinertia of rockinertia of rockinertia of rockrock mass strengthrock mass strengthrock mass strengthtool geometrytool geometrycutting geometrycutting geometrycutting geometry

2 of the above 15 parameters are non-dimensional, leaving 13 dimensional parameters.Since the number of fundamental units is three (i.e. M, L and T) then n - k = 13 - 3 — 10non-dimensional groups are to be expected. The matrix method will be used to determinethe non-dimensional n-terms.

2.3.2 Forming the Dimensional Matrix

The dimensional matrix for the 13 dimensional parameters in Table 2-2 forroller disk cutting of rock is:

Acon p Fn Fr o GIC O E d W S DOC \Xj X2 X3 X4 X5 Xfy Xy X$ Xy XJQ X) \ X\2 X\^

1 - 1 1 1 1 1 -1

0 1 0 0 0 0 10 - 2 0 0 0 0 -2

LMT

m,m2

mt

200

-310

11-2

11-2

-1I-2

01-2

From this matrix it can be seen that the following independent parameterquotients are dimensionless:

Fr / Fn, d / VAcon, W / V A ^ , S / VAcon, DOC / VAcon, O / V A ^ , E / a, XI a [2-9]

The parametric quotients in [2-9] contain 8 of the 10 required non-dimensional 7r-terms, leaving 2 terms to be established. However, theremaining 71-terms must not include the parameters Fr, d, W, S, DOC, O, E,k since they are already represented in [2-9].

38

2.3.3 Forming the Unity Matrix and Remaining 7t-Terms

The revised dimensional matrix for roller disk cutting of rock from whichthe 8 parametric quotients have been excluded is:

LMT

m,m2

m.

Aeon

Xl

200

Px2

-310

FnXj

11

-2

ax4

-1I

-2 -2

The non-dimensional TT-terms yet to be established are given by thefollowing solution matrix in which the formation of the unity matrix iscarried out by using matrix algebra. The calculation procedure is as follows:

S subtract row 2 from row 1• divide row 3 with (-2 )• subtract new row 3 from old row 2• multiply new row 1 with ( 1/2 )• add new row 2 twice to new row 1.

The solution matrix is:

LMT

m,m2

m<

A•*»-COII

• * /

100

px2

010

FnXj

001

ax4

-I01

GXs

-1/201

The unity matrix shows that the rank r of the matrix is 3, thus we have 5 - 3or 2 7i-terms. In addition, the equations for the exponents x/, X2 and xj maybe rewritten by inspection of the modified matrix as in equation [2-4]:

LMT

Xl

X:

Xj

- x4

= 0+ x4

- 1/2

+ x5

• Xj —

= 0

0 =>=>=>

X/

X2

Xj

— + X4 +

= 0= - x4 - x

1/2

5

• X5

Substituting for JC/, X2 and xj in an equation of dimensional homogeneity asin equation [2-3] yields:

/ = L° M" 7"

= ( ?4 • Pi • Pj ) " • P". • (Pi -P'/2 • Ps' ) "

= [<*Km I F n I'4 ' [P ]" ' [ G , C • ^Ac, in / Fn \' [2-10]

39

2.3.4 Similarity and Scale Factors

The Buckingham Theorem is defined in general terms by equation [2-2];and can now be written for the roller disk kerf cutting of rock as:

n, = f'(n2, Kj, ... nl0,a,n) [2-11]

Each of the non-dimensional terms Ki to 7C/o in the Table 2-3 satisfies thisequation. The functional relation for the first 7t-term listed in Table 2-3 is:

Fn = a- Acon [2-12a]

The functional relationship for all parameters listed in Table 2-3 can now beexpressed as:

Fn = a Acon • / ( G,c • VAcon / Fn , ... X/o, a, n ) [2- 12b]

Equation [2-12b] can be modified by manipulating the listed non-dimensional terms in Table 2-3 as follows:

n6-(n7)-' = S/DOC

a-Acon/Fn = / ( S / D O C )

The relevance and physical significance of the found 7C-terms must beexamined; and practical functional relationships for roller disk kerf cuttingof rock be established for the design of prediction models.

Table 2-3. The non-dimensional set of K-terms for kerf cutting with rollerdisk cutters.

Original K-Terms Manipulated ft-Terms

= ( G , c / S ) / o

= d/DOC= W/DOC= S/DOC= DOC/O= O/S

712

7:4

n*

t «

Tim

= a Acon / Fn= G,c • VA.on / Fn= Fr/Fn= d / VACQ,,

= W / VA.O,,

= S/VA;On= DOC/VAcon= 0/VA.O,,

= E / a= X./o

7tp * \T^i )

It4 ' (iLy )

n5(K7y'n6-(n7Y'K7 • (U# )

«8 • fltfl ) "'

40

2.4 PRACTICAL USE OF THE NON-DIMENSIONALTC-TERMS

2.4.1 Functional Relationship between Normal Force, Depth of Cut andIntact Rock Strength

Based on the first rc-term in Table 2-3, the roller disk normal force can beexpressed as:

Fn = a Aam [2-12a]

Practical use of equation [2-12a] requires that the roller disk contact orfootprint area Acon be replaced by an expression which includes the diskdepth of cut DOC. The basic relationship between disk contact area and diskdepth of cut for constant section roller disk cutters has been establishedpreviously in Chapter 1.2 as:

A™ = constant • W • ( d • DOC - DOC 2 ) m

= constant • W • d m • DOC m [2-13]

The following practical expression for the relationship between Fn, a, d andDOC for the roller disk normal force can be found by substituting [2-13]into [2-12a] so that:

Fn#, = constant • a • Aconi • DOC m

= constant • a • W • d "2 • DOC "2 [2-14]

Thus, for a unit depth of cut (DOC =1.0 mm/pass), the disk normal forceFni represents the rock resistance to roller disk cutting; and is commonlyknown as the critical normal force. For constant section disk cutters it canbe expressed as:

Fn,.,, = constant • a • W • d m • 1.0 "2

= constant • C • W • d m [2-15]

and the roller disk normal force can then in general terms be expressed as:

Fn = Fn, • DOC m [ 1 -22] or [2-16]

This functional relationship has already been established in Chapter 1.2 asequation [1-22]. However, the functional relationship for roller disk cuttingincorporating the kerf spacing can now be carried out as the next step (aprocedure that is not readily done analytically).

41

2.4.2 Functional Relationship between Normal Force, Depth of Cut, IntactRock Strength and Kerf Spacing

Based on the 7t-terms in Table 2-3, the relationship between the roller disknormal force, depth of cut, rock specimen strength and kerf spacing can befound as:

Fn.2 = a - AC(m • [ s / V^,, , , f

= constant • a • W • d" 2 • D O C " 2 • ( S / D O C ) p '

Thus for a unit depth of cut, the disk normal force Fnj for constant sectionroller disk cutters can be expressed as:

Fn<: = constant • a • W • d1/2 • SPl [7-171

Due to dimensional homogeneity for equations [2-14] and [2-17] it followsthat:

Fn l > 2 / Fn#l = S3' / DOC "2

P) = 1/2 ; can be determined by statistical analysis of cutting data

The final expression for the functional relationship between Fn, DOC, o andS is:

Fn,2 = constant • o • W • d "2 • DOC m • S m [2-18]

= constant • o • W • d m - DOC • ( S / DOC ) m

2.4.3 Functional Relationship between Normal Force, Depth of Cut, IntactRock Strength and Degree of Rock Mass Fracturing

Based on the 7t-terms in Table 2-3, the relationship between the roller disknormal force, depth of cut, rock specimen strength and degree of rock massfracturing can be found as:

Pn = CT • A

= constant • a • W • d "2 • DOC "2 • [ O / DOC ]P ' • [ a ]P ' [2-19]

Thus, for a unit depth of cut, the disk normal force Fni for constant sectionroller disk cutters can be expressed as:

F n i-,3 = constant • CT • W • d "2 • O 3 j • a Pl [2-20]

42

Due to dimensional homogeneity for equations [2.14] and [2-20] it followsthat:

Fn l#3 / Fn #l = [On I DOC J or '

P2 = 1/2 ; can be determined by statistical analysis of cutting data

(^ ; indeterminable relationship; and must be determinedby statistical analysis of cutting data obtained fromfield cutting conditions

The final expression for the functional relationship between Fn, DOC, a, O

and a is:

Fn,, = O T W O ' W - d 1 / 2 ' D O C " 2 0 " 2 / ( a ) [2-21]

The NTH tunnel boring prediction model includes the effect of rock massfracturing as a combined fracture factor ks shown in Figure 3-9, i.e.

k, = ( constant* / Om ) • f (a)where f (a} is basically a trigonometric function based on the"void" area originating from rock fallouts in the face.

constant* - f (fracture aperture width and fracture strength }i.e. the effect of fracture types such as fissures, joints, markedindividual joints, mud seams and shears.

2.4.4 Functional Relationship between Normal Force, Depth of Cut andIntact Rock Toughness

Based on the second 7i-term in Table 2-3, the roller disk normal force can beexpressed as:

Fn = constant • G[C • VAcon

Fn,4 = GJC • ( constant • W • d m • DOC " 2 ) m [2-22]

Thus, for a unit depth of cut (DOC = 1.0 mm/pass), the critical disk normalforce Fni for constant section disk cutters can be expressed as:

Fn,.,4 = G,c • ( constant • W • d m • 1.0 m ) m

= G,c • ( constant • W • d m ) m

43

The roller disk normal force can then in general terms be expressed as:

Fn = Fn, • DOC "4

Combining Normal Force Relationships #2 and #4

The previously established relationships #2 and #4 for the roller disk normalforce Fn are:

Fn,2 = o • ( constant • W • d m • DOC "2 • S m ) ' [2-18]

Fn,4 = G,c • ( constant • W • d m • DOC m • S m) "2 [2-23]

Since a power function relationship between the roller disk cutting forcesand tool depth of cut exists, the correct function format for statisticalanalysis of multiple tool pass kerf cutting data is as follows:

Fn = / { o, G,c/S, constant- W • d "2 • DOC 1/2 • S "2 } [2-24]

= Fnn-DOC"* [2-25]

Fnn = rock resistance to in-line kerf cutting(not rock resistance to single pass disk indentation cutting)

b = kerf cutting exponent

A detailed discussion of this important finding is presented in Chapter 4.4.

44

2.5 ADDITIONAL FUNCTIONAL RELATIONSHIPS FORROLLER DISK CUTTING

Using the similarity analysis results in Table 2-3, additional relationships forroller disk cutting can be determined, i.e.

Cutter Coefficient k

The cutter coefficient k is a non-dimensional parameter from Table 2-3.This coefficient is readily understood as the rolling resistance of the disk,and is a function of the depth of cut, i.e.

k = Fr / Fn = tan aWum

= C, DOC1'2 [1-21] or [2-26]

Rock/Tool Interface Pressure

The rock/tool interface pressure is constant in the normal force direction andindependent of disk depth of cut since both the normal force and the diskfootprint area are a function of the depth of cut. This can be expressed as:

Orock interface — **^ ' ^ c o n

Cmckinlerface = COflStOnt • O • S ^ • O " 2 • / {(X} [2-27]

* / { D O C )

Relationship between Kerf Spacing and Disk Diameter

The ratio of kerf spacing to disk diameter can be expressed by the followingnon-dimensional expressions from Table 2-3 and the roller disk footprintarea:

(i) (d/VAcon) =1

(ii) ( S / VAcon) = 1

S = constant • d [2-28]

45

Relationship between Disk Tip Width and Disk Diameter

The ratio of disk tip width to disk diameter can be expressed by thefollowing non-dimensional expressions from Table 2-3 and the roller diskfootprint area:

(i) (d/VAcon) = 1

( ii) Acon = constant • W • d "2 • D O C m

(i) + ( ii) d2 = constant* • W • d m • \.0m

W = constant** • dV2 [2-29]

Relationship between Disk Insert Diameter and Disk Diameter

The ratio of stud insert diameter to roller disk diameter can be expressed as:

(i) ( t / W ) = 1

(ii) W = constant** • d V2

( i) + ( ii) t = constant*** • d m [2-30]

Example of Scaling Applications

The use of equations [2-28], [2-29] and [2-30] for scaling some selected kerfcutting parameters is shown in Figure 1-15.

46

2.6 SUMMARY OF FUNCTIONAL RELATIONSHIPS FORROLLER DISK KERF CUTTING ESTABLISHED INCHAPTERS 1 & 2

A short summary of the functional relationships for roller disk cutting ofrock based on tool indentation and similarity analysis of kerf cutting maynow be listed as:

Roller Disk Normal Force

Fn = Fn, DOC I / 2 ; for single tool pass cutting [1-22] or [2-16]

Fn = Fn, • DOC uh ; for multiple tool pass cutting [2-25]

Fn = constant • a • W • d m • DOC"2 • S l /2 • Om • f {a}

= constant a • W • d m • DOC • ( S / DOC ) m • O l /2 • / {a}

Fn, = constant 0 • W • d m- S l /2 • O m • f [ a ]

Roller Disk Kerf Cutting and Tool Design

k = Fr/Fn

= C, DOC"2 [1-21] or [2-26]

S = constant • d [2-28]

W = constant • dm [2-29]

t = constant dm [2-30]

Fn, = rock resistance to kerf cutting / disk tip geometry value

= critical normal force, i.e. the normal force at unity indentation

b = kerf cutting exponent

C, = cutter constant or cutter coefficient at unity indentation

a = dimension stress, i.e. UCS, BTS, E, c 2p, VHNR, ...

constant = proportionality constants to be determined by statistical analysis oflinear cutting test data and/or field cutting data

47

d = roller disk diameter

( S / DOC )"2 = relationship for kerf spacing to disk depth of cut

O "2 • / {a} = relationship for spacing and orientation of rock massdiscontinuities to the direction of advance

The final step in the design of prediction models for roller disk kerf cuttingof rock is to determine the listed constants representing the rock masscuttability by the normalisation of field cutting data-based on the functionalrelationships established in Chapters 1 and 2 using multivariate regressionanalysis due to the many variables required for normalising field cuttingdata.

The normalisation of linear roller disk cutting tests for individual tools isdiscussed in detail in Chapter 4.

48

3 ROCK MASS CHARACTERISATION

3.1 INTRODUCTION

Rock mass characterisation is a common field of study shared by the twomain fields of geotechnical engineering for rock excavation as illustrated inFigure 3-2; and forms the basis of geomechanical classification systems forrating amongst others:

• rock cuttability/drillability and tool life indicesS required ground support work.

The objective of geotechnical and structural rock mass characterisation workwith regard to rock cuttability is to develop optimal procedures for selectingcutting machines for a particular rock mass at a preinvestigation stage. Thebenefits are improved machine performance estimates, reliable machineselection and the capability to integrate new mining systems at the minefeasibility stage before the machine is installed.

The upper limits of efficient excavation of the main methods used forunderground excavation today are illustrated in Figure 3-1 as envelopecurves for the relationship between these methods and the rock massconditions characterised by fissure spacing and the strength of intact rockspecimens.

Eo

coQ.CO0)

0305

60

50

40

30

20

10 \-

50 100 150 200 250 300 350 400

Uniaxial Compressive Strength, UCS (MPa)

Figure 3-1. A generalised Rock Mass Cuttability Window or therelationship between rock mass conditions and the upper limits of efficientexcavation for the main methods used for underground excavation today.

49

ROCK MASSCHARACTERISATION

INTACT ROCK

Mineral constituentsprincipalauxiliary

accessoryLithology

grain size and shapetexture and cementation

anisotropypores and micro-fracturesweathering and alteration

Mechanical rock properties

strengthdeformability

hardnessfracture toughness

abrasivity

DISCONTINUITIES

Orientationstrike, dip and direction

of advance

Frequency, Spacing

Persistence

Surface propertiesroughness and coatings

Aperture, Openness

Infilling material

Genesis

beddingjoints

foliationschistosity and banding

STRESS

Initial stress

Stress around openings

Groundwater, gas

Seismic activity

shears

GEOMECHANICALCLASSIFICATION SYSTEMS

FOR ROCK EXCAVATION

Cuttability/DrillabilityBlastability

Blast-Rock Loadability/Pumpability of CuttingsBlast-Rock Assessment as Construction Material

Crushability/MillabilityTool Life IndicesGround Support

Figure 3-2. Relationship between rock mass characterisation andgeomechanical classification systems for rock excavation.

50

No universal or satisfactory method exists for rapid determination of rockmass cuttability. Generally, machine selection and performance estimationrelies on specialist advice based on limited geotechnical data. Manufacturesare unable to provide reasonable guarantees of performance and operatorscannot assess and compare the claims of different manufacturers. Auniversal procedure is required for rock mass cuttability estimation usingboth field and laboratory assessment methods.

Thus, the goal is the development of rock mass characterisation proceduresutilising common geotechnical and structural parameters to yield an index ofcuttability. Such a procedure may well follow a similar process to the wellknown Q and RMR classification systems for ground support and the NTHclassification system for tunnel boring performance prediction. It is intendedthat the procedure would help define the most appropriate machine for anapplication, the likely performance of the machine, likely machine power,weight and mechanical characteristics and possible tool failure modes(abrasive wear and/or impact damage). One aspect to be kept in mind is thata machine with high stiffness is required to excavate hard rock. This, in turn,means less mobility and flexibility. Innovative mine planning is needed, butmust respect these limitations whilst manufacturers need to improve thedesign of machines to enhance their potential.

The approach is to identify geotechnical and structural parameterscontrolling rock mass cuttability. Most mechanical tools break rock byindenting the rock surface. Hence the goals of basic or primary rockbreakage science and research projects are to:

• improve the understanding of the mechanisms of rock damageand rock failure caused by mechanical tools - by conducting aseries of experiments aimed at studying the effects of indentergeometry and rock micro-structure on failure behaviour

& improve the understanding of the mechanisms of rock damageand rock failure during rock cutting operations - by studying theeffects of cutterhead lacing and geometry, rock micro-structureand rock mass discontinuities on failure behaviour

B improve the understanding of the interaction between cutterheadlacing design, tool design and rock abrasivity on tool wear andtool breakage rates during rock cutting operations

M develop an understanding of how high velocity waterjets canreduce tool forces and enhance tool life during cuttingoperations.

51

3.2 ROCK MASS CHARACTERISATION

Before discussing specific mechanical properties of rocks, it is necessary todefine a rock and discuss some of its chemical and physical properties -particularly its structure, which may assist or resist a desired reaction. Rock,unlike steel which can be refined to consistent internal state before use, is anaturally occurring material and must be worked in its natural state. Certainsimplifying assumptions are justified to assist performance guidelines;others are not, and to a large extent the basis for all assumptions lies in thecomposition and structure of the rock mass.

Composition of Rocks

All rocks consist of an aggregate of mineral particles. The proportion ofeach mineral in the rock, together with the granular structure, the texture andthe origin of the rock serves as a basis for geological classification.

A mineral may be defined as an inorganic substance with consistent physicalproperties and a fixed chemical composition. With the exception of somecarbon forms, sulphur and a few metals, all minerals are chemicalcompounds, each containing two or more elements in fixed proportion byweight. Some elements are present in many minerals, the commonest beingoxygen and silicon, whilst others, including most of the precious and basemetals, form an insignificant proportion of the rocks in the earth's crust.

The way in which the composition of the earth's crust is dominated by eightelements is shown in Table 3-1. These elements comprise approximately99% of the earth's crust and together with other elements form twelvecommon minerals (Table 3-2) which make up 99% of all rocks in the earth'scrust. The remainder of the known rock-forming minerals, numbering over1 000, make up less than 1% of the earth's crust.

Table 3-1. The major chemical elements in the earth's crust.

Chemical Elements

OxygenSiliconAluminiumIronCalciumSodiumPotassiumMagnesium

(0)(Si)(Al)(Fe)(Ca)(Na)(K)

(Mg)

Weight Percent

46.4028.158.235.634.152.362.092.33

Volume Percent

94.040.880.480.491.181.111.490.33

52

Table 3-2. Mineralogical classification of the major rock-forming minerals.

Silicates TektosilicatesFeldspar Group

Phyllosilicates

Inosilicates

Nesosilicates

Carbonates Calcite GroupDolomite Group

Oxides Hematite Group

QuartzOrthoclasePlagioclase Series

Muscovite

BiotiteKaoliniteAmphibole Group

Hornblende

Pyroxene GroupAugite

Olivine Series

CalciteDolomite

Hematite

SiO2

KAlSi,O8

(Na,Ca)(Al,Si)AlSi2O8

KAl2(AlSiO,(,)(OH)2

K(Mg,Fe)3(AlSi30,o)(OH)4Al4Si4OI0(OH)8

NaCa2(Mg,Fe,Al)5(Si,AI)8O22(OH)2

(Ca,Mg,Fe,Al)(Al,Si)2O6

(Mg,Fe)2Si04

CaCO,CaMg(CO3 )2

Fe2O3

It can be assumed, therefore, that most if not all rocks encountered in miningand civil engineering, will consist of two or more of the minerals, each ofwhich has a particular set of physical properties which may affect theengineering properties of the rock as a whole. Properties such as thepreferred direction of cleavage and fracture, hardness and crystal structureused to define minerals can, however, under certain circumstancesdetermine the reaction of a rock to outside forces, particularly where largeamounts of a relatively soft mineral with marked fracture properties, such asmica or calcite, or of a particularly hard mineral, such as quartz, are present.

Some mineral properties relevant to an analysis of the mechanical propertiesof rock are listed in Table 3-3. Mineralogists use ease of scratching as thecriterion of hardness, rating it in terms of an empirical scale devised by theAustrian mineralogist Friedrich Mohs in 1822.

The Mohs' scale of hardness, consisting of 10 minerals from talc, thesoftest and equivalent to 1, through gypsum, calcite, fluorite, apatite,orthoclase, quartz, topaz, corundum, to diamond, the hardest and equivalentto 10, is based solely on the empirical property of one mineral to scratchanother. The hardness given for a mineral in Table 3-3 is that of a smoothclean surface, such as a crystal face or a cleavage plane. Minerals often havea superficial coating of weathered or altered material, and such coatings willgive a deceptively low hardness. Similarly, the apparent hardness of a fine-grained friable mass has no relation to that of a well-crystallised specimen;for example, hematite crystals show a hardness of 6, but much red earthyhematite can be scratched with a fingernail. Microindenter hardnessvalues, such as Vickers and Knoop, are a more accurate and useful methodof rating surface hardness.

53

Hardness is sometimes used as a strength criterion for rocks - a factor whichcan lead to serious discrepancies in some rocks. For instance a fibrous rock,such as gypsum or anhydrite, may have a relatively low hardness but a highbulk strength. Strength criteria for rating rock cuttability will be discussedlater in this chapter; but it can immediately be seen that silicates (quartz,feldspar, hornblende, augite, olivine) are considerably harder and hencestronger than any of the other common minerals except hematite. This isreflected to a certain extent in the mechanical properties of a rock - evenwhere the rock contains only a limited amount of the mineral.

Table 3-3. Properties of the major rock-forming minerals.

Mineral Hardness Density Fracture Structure

Quartz 7 2.65 No cleavage

Onhoclase 6 2.56 Good cleavage atright angles

Plagioclase

Muscovite

Biotite

Kaolinite

Hornblende

Augite

Olivine

Calcite

Dolomite

2

2

6

3

6

- 3

- 3

2

6

6

- 7

3

- 4

2.62

2.8

2.9

3.0

3.25

3.3

2.

2.

-2.76

-2.9

-3.4

L.6

-3.4

-3.55

-3.6

.71

85

Cleavage nearly atright angles - verymarked

Perfect singlecleavage

Perfect singlecleavage

No cleavage

Good cleavage at120°

Cleavage nearly atright angles

No cleavage

Three perfectcleavages

Three perfect

Hematite

cleavages

5.26 No cleavage

Trigonal; prismatic crystalsterminated by rhombohedrons;also massive, granular orcompact

Monoclinic; prismatic crystals,flattened or elongated; alsomassive, granular

Triclinic; prismatic crystals,flattened, also massive,granular

Monoclinic; usually in irregularplaty crystals; also massive,sometimes compact

Monoclinic; usually in regularplaty crystals

Triclinic; always in clayeymasses

Monoclinic; long prismaticcrystals, also columnar, fibrousor granular

Monoclinic; short prismaticcrystals; also massive, granular

Orthorhombic; usually massive,granular

Trigonal; scalehedral andrhombohedral crystals; alsomassive, granular or compact

Trigonal; small curvedrhombohedral crystals; alsomassive, granular

Trigonal; tabular crystals andmassive

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If roughly handled, crystals will break. If the broken surface is irregular, thecrystal possesses fracture, but if it breaks along a plane surface that isrelated to the structure, and parallel to a possible crystal face, then it hascleavage. Cleavage and fracture are expressions of the internal structure ofthe mineral. Cleavage occurs because of the variation in the strength of thebonds between different atoms. This is best illustrated by the layer silicates,of which mica is a familiar example. Chemical bonds are very strong withinthe silicon-oxygen layers, but the bonds between layers are weak, and solittle effort is needed to break them. Mica splits (cleaves) into thin sheets.The bond strength varies and so the degree of perfection of cleavage variesalso. Mica, for example, has a perfect cleavage; less perfect cleavages aredescribed as gooJ, poor or indistinct.

Geological Classification of Rocks

It is convenient to divide the rocks in the earth's crust into three differenttypes based on their origin, namely igneous, sedimentary and metamorphicrocks.

Magma is essentially a hot silicate melt (600-1200 °C), and is the parentmaterial of igneous rocks. Magmas and the formation of igneous rocks canbe observed in volcanic regions, but much magma solidifies within the crust,and the rocks thereby formed are later exposed at the surface by erosion orby earth movements - hence their classification as plutonic (intrusive),hypabyssal, or volcanic (extrusive); depending on the depth and rate of theircooling with its effect on their texture or crystal size.

Igneous rocks are also subdivided by their composition into acidic,intermediate, basic (mafic) and ultrabasic (ultramafic) rocks, depending onthe amount of silica in their composition as listed in Table 3-4. Animmediate observation is the relative high hardness of the mineralconstituents of all igneous rocks. The mica content tends to be small.

Sedimentation is, in fact, the result of the interaction of the atmosphere andhydrosphere on the crust of the earth. The original constituents of the crust,the minerals of igneous rocks, are more or less readily attacked by air andnatural waters. Having been formed at high temperatures, and sometimes athigh pressures as well, they cannot be expected to remain stable under thevery different conditions at the earth's crust. Silicates vary considerably intheir chemical stability. Susceptibility to chemical attack of common rock-forming minerals is in the order: olivine, augite and calcium feldspar >hornblende, biotite and sodium feldspar > potassium feldspar > muscovite >quartz.

Of the common minerals of igneous rocks, only quartz is highly resistant toweathering processes. All minerals tend to alter when attacked by the actionof oxygen, carbonic acid, and water; and new minerals are formed which aremore stable under the new conditions. The altered rock crumbles under the

55

mechanical effects of erosion, and its constituents are transported by wind,water, or ice and redeposited as sediments or remain in solution.

Table 3-4. Geological classification of the most common igneous rocks.

Texture

PLUTONIC(coarse grained)

HYPABYSSAL

VOLCANIC(fine grained)

Acidic> 66% silica

Granite

Micro-Granite

Rhyolite

Intermediate66 - 52% silica

Syenite

Micro-Syenite

Trachyte

Diorite

Micro-Diorite

Andesite

Basic< 52% silica

Gabbro

Diabase

Basalt

Ultrabasic< 45% silica

PeridotiteDunitePyroxenite

Principal Mineral Quartz Orthoclase Plagioclase Augite AugiteConstituents Orthoclase Plagioclase Hornblende Plagioclase Olivine

(Mica) (Mica) Orthoclase

Table 3-5. Geological classification of the most common sedimentary rocks.

Method ofFormation

Classification Rock Type Description Principal MineralConstituents

MECHANICAL Rudaceous Conglomerate Large grains in claymatrix

Various

Arenaceous Sandstone

Breccia

Medium round grains in Quartz, Feldspar,siliceous, calcareous or Mica, Calciteclay matrixCoarse angular grains inmatrix

ORGANIC

CHEMICAL

Argillaceous

Calcareous(siliceous,ferruginous,phosphatic)

Carbonaceous

Ferruginous

Calcareous(siliceous,saline)

Clay

Shale

Limestone

Coal

Ironstone

DolomiticLimestone

Micro-fine grained -plastic structureHarder - laminatedcompacted clay

Fossiliferous, coarse orfine grained

Impregnated limestone orclay (or precipitated)

Precipitated or replacedlimestone, fine grained

Kaolinite,Quartz, Mica

Calcite

Calcite, Iron Oxide

Dolomite, Calcite

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Sedimentary rocks can be subdivided into three main groups according totheir method of formation, namely those mechanically formed, those formedfrom organic remains and those chemically deposited.

From an engineering point of view, the most important sedimentary rocksare arenaceous (sand), argillaceous (clay) and calcareous (limestone)rocks. Typical arenaceous rocks consist of discrete fragments of minerals,usually quartz and feldspars, held together by a matrix of clay, calcite orhydrothermal quartz. Thus when a sandstone is broken, fractures follow theweaker clay or calcareous cement rather than propagating across the strongergrains. An argillaceous rock such as a shale consists of minute particles heldweakly together and comprising largely kaolinite. Calcareous rocks consistof organic remains or precipitates, mainly in the form of calcite.

Metamorphism is defined as the sum of the processes that, working belowthe zone of weathering, cause the recrystallization of either igneous orsedimentary rock material. During metamorphism the rock remainsessentially solid; if remelting takes place, a magma is produced, andmetamorphism passes into magmatism. Metamorphism is induced in solidrocks as a result of pronounced changes in temperature (200-800 °C),pressure, and chemical environment. These changes affect the physical andchemical stability of a mineral assemblage, and metamorphism results fromthe establishment of a new equilibrium. In this way the constituents of arock are changed to minerals that are more stable under the new conditions,and these minerals may arrange themselves with the production of texturesthat are likewise more suited to the new environment. Metamorphism thusresults in the partial or complete recrystallization of a rock, with theproduction of new textures and new minerals.

Heat, pressure, and action of chemically active fluids are the impellingforces in metamorphism. Heat may be provided by the general increase oftemperature with depth or by contiguous magmas. Pressure may be resolvedinto two kinds: hydrostatic or uniform pressure, which leads to change involume; and directed pressure or shear, which leads to change of shape ordistortion. Uniform pressure results in the production of granular, non-oriented structures; directed pressure results in the production of parallel orbanded structures. Uniform pressure affects chemical equilibria bypromoting a volume decrease, i.e. the formation of minerals of higherdensity. The action of chemically active fluids is a most important factor inmetamorphism, since even when they do not add or subtract material fromthe rocks they promote reaction by solution and redeposition. When theyadd or subtract material, the process is called metasomatism. Probably somedegree of metasomatism accompanies most metamorphism. Water is theprincipal chemically active fluid, and it is aided by carbon dioxide, boricacid, hydrofluoric and hydrochloric acids and other substances, often ofmagmatic origin.

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Two major types of metamorphism are commonly recognised: thermal orcontact metamorphism, and regional metamorphism. Contactmetamorphism is the type of metamorphism developed around bodies ofplutonic rocks. Here the temperature of metamorphism has been determinedmainly by proximity to the intrusive magma, which may also have given offchemically active fluids that stimulated recrystallization of the country rock.

Regional metamorphism, as the name implies, is metamorphism developedover large regions, often over thousands of square kilometres in the rootregions of fold mountains and in Precambrian terranes.

It has been established that the earth's crust is made up of 95% igneousrocks, 5% sedimentary rocks and an insignificant proportion of metamorphicrocks. This does not, however, give a completely true picture of the rockslikely to be encountered by engineering works in rock. The earth's crust maybe assumed to be from 30 to 50 km in thickness and virtually all majorworks take place in the top few kilometres which contain the major part ofthe sedimentary rocks. This means that the engineer working on the earth'ssurface or in near-surface mineral deposits must often contend with rockswhich are often sedimentary or metamorphosed. In addition, a highpercentage of these sedimentary rocks will be argillaceous, the majority ofthe remainder being arenaceous or calcareous.

Argillaceous rocks comprise mainly shales, normally closely bedded orlaminated, of two types; consolidated and cemented. The former arereasonably strong in a dry state, but weak when wet; the latter tend to haveintermediate strength under most conditions, but are easily deformed underload. The problems encountered in mining, tunnelling or foundation work insuch rock types are immediately apparent.

Table 3-6. Geological classification of the most common metamorphicrocks.

Classi-fication

Contact

Regional

Rock

Hornfels

QuartziteMarbleGneiss

Slate

Phyllite

Schist

Felsic Gneiss

Description

Micro-fine grained

Fine grainedFine to coarse grained

Medium -fine grained

Rock cleavage

Cleavage surfaces

Finely foliated

Coarsely foliated, banded

Principal MineralConstituents

Feldspar, Quartz, Mica

Quartz, FeldsparCalcite or Dolomite

Feldspar, Hornblende

Kaolinite, Mica

Mica, Kaolinite

Feldspar, Quartz, Mica

Feldspar, Quartz, Mica

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Rock Structure

It has been shown in the earlier sections that rocks are basically an aggregateof mineral particles. Many of the engineering properties of rocks to bediscussed in later sections depend on the structure of these particles and theway in which they are bonded together.

In materials science there are two accepted types of structural units fromwhich all solid bodies are formed - namely crystals and molecules. Theminerals which represent the basic rock structure normally take the form ofcrystals, but may exist as amorphous molecule aggregates (viz. silica).Crystals and molecules are formed from atoms - a crystal when the atomsare arranged in a stable three-dimensional pattern made up of units whichare repeated indefinitely in all dimensions. A molecule, on the other hand, isdefined as the smallest particle retaining the essential properties of thewhole and when in the role of the basic structural unit forms an amorphousmass held together by intermolecular bonds. This can be demonstrated mostclearly by considering the crystalline and amorphous forms of silica. In thecrystal form (quartz) there is a regular crystal lattice, made up of units, eachcomprising silicon atoms bonded to four oxygen atoms and oxygen atomsbonded to two silicon atoms. In the amorphous form the bonds are similarbut the structural pattern is destroyed.

In nature few minerals exist in pure macro-crystal form and few in a purelyamorphous form. Normally a mineral particle in a rock will consist of anaggregate of micro-crystals, held together by some form of ionic, atomic ormolecular bonding. In the rock these particles are cemented together by amatrix or by mechanical bonding at contact interfaces between grains. Thusthe ultimate strength of the rock will depend primarily on the strength of thematrix and the contact area between the grains; which since the matrix isalso a polycrystalline aggregate, means that rock strength (other factorsremaining constant) will be proportional to the contact area (grain size). Thebehaviour of the rock will also be affected by imperfections in the structuresuch as voids, micro-fractures, inclusions and weak particles.

Pore Space in Rock

Of all the physical characteristics of a rock which affect its mechanicalproperties, the most important is the presence of voids and micro-fracturesor pore spaces. All polycrystalline substances are comparatively porous - theamount of porosity depending on the type and structure of the rock.

Pore spaces are largely made up of continuous irregular capillary micro-fractures separating the mineral grains; the degree of porosity depending to alarge extent on the method of formation of the rock. Thus in the case ofigneous rock, a slowly cooling magma will render a relatively non-porousrock, whereas a rapidly cooling lava particularly associated with escapinggasses, will yield a porous rock such as a rhyolitic tuff. In the case of

59

sedimentary rocks, porosity depends largely on the amount of cementingmaterials present and the size, grading and packing of the granularconstituents. Some typical values for porosity, expressed in terms of thepercentage pore space to bulk volume, are given in Table 3-7.

Table 3-7. Bulk density and porosity of some common rock types.

Rock Type

Igneous RockBasaltGraniteRhyolite

Sedimentary RockLimestoneShaleSandstone

Metamorphic RockMarbleSlateGneissQuartzite

Bulk Density(g/cm3)

2.2-2.92.6-2.72.4 - 2.6

2.0 - 2.82.0 - 2.62.0-2.6

2.6-2.72.6 - 2.72.7 - 3.02.6 - 2.8

Porosity(%)

0.1 - 120.5- 1.54.0-7.0

0.5 - 355.0 - 301.5-35

0.5 - 3.00.1 -5.00.5- 1.50.1 -2.5

Bulk density p = M / V = Ms + Mv / ( Vs + Vv)

Porosity n = Vv • 100/V

Dry density pd = Ms / V

Density of solids ps = 100 pd / ( 100 - n )

where Vv and V are the volume of voids or pore spaces andbulk volume respectively, and Ms the mass of solidcomponents.

Rock Mass Discontinuities

A bed is a layer of rock deposited at the earth's surface and bounded aboveand below by distinct surfaces (bedding planes); these usually mark a breakin the continuity of sedimentation, i.e. a cessation of sedimentation, or aperiod of erosion, or a change in type or source of sediment. Beds arenormally sedimentary, but may also consist of volcanogenic material. Athickness in the range cm to m is normally implied. "Bed" is more or lesssynonymous with stratum, but the latter term is normally used only in theplural (e.g. Silurian strata). The simplest type of bedding geometry consistsof a set of parallel planes, representing a group of beds, or a formation, ofuniform thickness.

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Joints may occur in sets of parallel, regularly-spaced fractures and severalsets may occur in the same rock, giving a conspicuous blocky appearance toan outcrop. More commonly, however, joints are much less regular andsystematic. Where a recognisable joint set exists, it can usually be related insome way to the tectonic stresses and to the geometry of the rock bodycontaining the joints. For example, joint sets are frequently found bothperpendicular and parallel to the bedding in layered rocks. Theperpendicular joints may form two or more intersecting sets which bear asimple relationship to the regional folds.

"Unloading joints". Many joints are due to the release of "stored" stress.The weight of a great thickness of overlying strata causes deeply buried rockto be compressed. However, once the overlaying rock has been eroded, thisload pressure is reduced and the rock expands by the development oftensional joints which are often parallel to bedding surfaces in sedimentarystrata, or to the contemporary erosion surface in massive igneous rocks,where they are termed sheet joints.

Cooling joints. Another common cause of joint formation is the contractionwhich takes place in a cooling igneous body. Tabular igneous bodies, i.e.dykes and sills, frequently exhibit polygonal columnar jointingperpendicular to the cooling surfaces.

Shear zones. A shear zone is a zone of ductile deformation between twoundeformed blocks that have moved relative to each other. There are nodiscrete fracture planes in an ideal shear zone, although in practice there is acomplete gradation between a fault zone and a shear zone, with intermediatestages being represented by faulted shear zones.

Relationship between joints and regional deformation. Under favourablecircumstances, regular joint sets that occur regionally in various differentrock types can be related to a regional compression or extension in the sameway as folds. Since we can assume that shear stresses along the surface ofthe earth are zero, it follows that one of the principal stress axes will beapproximately vertical and the other two approximately horizontal. Thisleads to a simple threefold classification of fault sets based on the threepossible orientations of the stress axes as illustrated in Figure 3-3.

A fold is a structure produced when an original planar surface becomes bentor curved as a result of deformation. Fault sets result from brittledeformation that causes the rock to break completely along discrete planes.Folds, however, are an expression of a more ductile type of deformationwhich produces gradual and more continuous changes in a rock layer, bothin its attitude and internally, as the rock accommodates to changes in shape.

Three important observations may be made concerning the structures atdeeper crustal levels: folding is the typical mode of deformation rather thanfaulting; sets of new planar surfaces (cleavage, schistosity, etc.) arecommonly developed; and pervasive recrystallization under compression

61

results in the internal rearrangement of the rock texture producing a new"fabric" or structural texture. A foliation is a set of new planar surfacesproduced in a rock as a result of deformation. Foliation is a general termcovering different kinds of structure produced in different ways. Slatycleavage, schistosity, gneissose banding and sets of closely-spaced fracturesor fracture cleavage are all examples of foliation.

Types of foliation. The nomenclature of the various types of foliation israther confusing. This reflects the fact that the origin of such structures asslaty cleavage and gneissose banding, for example, was not fully understooduntil relatively recently. The term "cleavage" itself embraces structures ofvarious origin, the only common factor being the fissility which allows therock to be split along the foliation planes.

Slaty cleavage. This type of cleavage is best shown in fine-grained rockssuch as mudstones that have been deformed under very low-grademetamorphism. Consequently the nature of the internal changes in the rockthat have produced this penetrative fissility is not usually obvious at outcropor in hand specimen. Under the microscope, however, the nature of thecleavage becomes much clearer. The cleavage planes are then seen to be duepartly to the parallel orientation of flaky minerals such as muscovite andclay minerals, and partly to the parallel arrangement of tabular or lensoidaggregates of particles.

Normal Fault Sets

Thrust Fault Sets

Strike-Slip Fault Sets

J

Figure 3-3. Fault orientation in relation to principle stress and strain axesfor normal, thrust and strike-slip fault sets.

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Fracture cleavage. A fracture cleavage consists of parallel, closely-spacedfractures. Fracture cleavage is usually easy to distinguish from slatycleavage because it consists of discrete planes separated by slabs ofuncleaved rock, called microlithons. Displacement of the rock may often bevisible in thin section, showing that the planes are micro-faults. This type ofcleavage is formed under brittle conditions at low temperatures and istypical of deformed relatively strong rocks, e.g. sandstones and limestones.

Crenulation cleavage. This type of cleavage is caused, as the namesuggests, by small-scale folding (crenulation) of very thin layers orlaminations within a rock.

Schistosity. With increasing metamorphic grade, slates are transformed toschists by an increase in the size of the newly formed metamorphic minerals.In slates, the aligned flaky minerals that produce the slaty cleavage areinvisible to the naked eye, whereas in schists, the individual tabular crystalsof mica, hornblende, etc. are large enough to be visible in hand specimens.A foliation marked by the parallel orientation of such tabular minerals in ametamorphic rock with a sufficiently coarse grain size is called & schistosity.

A schistosity can be produced directly from a slaty cleavage merely by acoarsening of the grain-size, consequent on an increase in temperature.Crenulation cleavage may also pass into schistosity as a result of grain-sizecoarsening. Many schistose rocks show a combination of mineral alignment(true schistosity) and a tabular or lensoid arrangement, similar to that seen inmany slates, produced by compression, but on a larger scale.

Compositional layering is a characteristic feature of most gneisses and isoften termed gneissosity or gneissose banding. Gneisses are coarse-grainedmetamorphic rocks, typically quartzo-feldspatic in composition. Thedistinction between schists and gneisses is not clear-cut, and individualgeologists have their own preferences as to where the dividing line shouldbe drawn. Intensely deformed gneisses of sedimentary origin (paragneisses),when derived from sediments of mixed composition, e.g. greywackes orarkoses, are often very difficult to distinguish from those of igneous origin(orthogneisses). It cannot be assumed that the presence of a compositionalbanding necessarily indicates a sedimentary origin.

The formation processes of discontinuities in rock such as rock cleavage andfoliation in metamorphic rocks and cooling joints and fault sets in igneousrocks have a direct bearing on the properties of a fractured rock mass;characterised by fracture set aperture or openness, surface roughness,coating, infilling material, persistence and fracture set spacing and theireffect on rock stability, cuttability and blastability. In addition, when thephysical rock properties are directionally dependent, the rock is termedanisotropic. Typically, rocks with cleavage, fissility and especially foliationhave a marked degree of anisotropy. The anisotropy index Ia is perhaps themost important rock characteristic affecting rock blastability or ease of rockfragmentation by blasting.

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3.3 CLASSIFICATION OF ROCK MASS CUTTABILITY ANDDRILLABILITY

Indentation Cutting of Rock

Whilst geological classification of rocks based on origin, mineral contentand geological structure is useful in a general way for indicating certainstrength parameters and trends, such a classification provides littleinformation of immediate use to the engineer designing in or excavatingrock - who requires a functional geomechanical classification of rock massproperties for use as design and performance prediction criteria.

Where elastic deformation leads to failure, the material loses cohesion bythe development of a fracture or fractures across which the continuity of thematerial is broken. This type of behaviour is called brittle behaviour andgoverns the development of faults, joints and macro-fractures. Ductilebehaviour, in contrast, produces permanent strain that exhibits smoothvariations across the deformed rock without any marked discontinuities.Most rock materials are capable of exhibiting either brittle or ductilebehaviour depending on such factors as the size of differential stress,confining pressure, temperature, strain rate and pore-fluid pressure.

Brittle failure is typical of rocks at low confining pressure and lowtemperature. The pore-fluid pressure has the effect of reducing the shearstress required for slip, i.e. it reduces the shear strength of the rock since thedirect pressure between adjoining grains caused by the confining pressure iscountered by the effect of the pore-fluid pressure.

Most mechanical tools break rock by indenting the surface. Rock crushing,macro-fracture propagation and chip formation all occur under a loadedindentation tool; but the sequence, relationship and amount of each is largelyunexplored. Thus the parameters controlling rock cuttability or rockresistance to tool indentation can not be readily related to any singlemechanical rock property since the indentation process as illustrated inFigure 3-4 is a combination of the following failure modes:

8 initial tool indentation of rock surface with crushing andcompacting of rock material under the tool tip

• development of macro-fracture propagation patterns resultingin rock chip formation, chip loosening and stress release

• multiple pass cutting if chip loosening does not occur for everytool pass or load cycle

• efficient chip and fines removal so as to avoid recutting andrecompaction of broken material in the tool path.

Rock cutting or drilling is therefore the art of maximising chip formationand removal of rock material as cuttings; and not the development ofextensive macro-fracture propagation patterns under a tool. The influence ofrock mass discontinuities on rock mass cuttability is generally on a larger

64

scale than one individual tool; typically affecting several toolssimultaneously and the cutting performance of the cutterhead as a whole.The rock cutting process by indentation and the itemised elements of rockmass parameters affecting cuttability and drillability are summarised inTable 3-8.

The indentation force Fnis proportional to thetool tip contact area

Tool indentation depth,DOC

Chip loosening macro-fractures initiated by tooloff-loading; resulting inlarge chips loosening frombehind the roller disk

Approx. the same amount ofenergy is required to form ashallow or a deep chiploosening macro-fracture

Central macro-fracturesinitiated by tool onloading andoriginating from tool rim edges

1. Extent of macro-fracture growth from the 1st tool passing2. Extent of macro-fracture growth from the 2nd tool passing

3. Macro-fracture growth completed; resulting in chiploosening after the 3rd tool passing

Figure 3-4. Roller disk indentation of a rock surface with crushing underthe tool tip, induced macro-fracture growth patterns and consequent stagesof chip formation, chip loosening and stress release for multiple tool passcutting.

65

Table 3-8. Summary of the rock cutting processes by indentation and theitemised elements of rock mass characteristics affecting rock masscuttability and drillability.

Rock CuttingProcesses

Individual ToolIndentation

Chip Formationbetween AdjacentKerfs

CutterheadProduction Rates

Elements of RockCuttability/Driilability

* resistance to too)indentation(crushing)

* resistance to macro- * multi-pass cuttingfracture propagation * mixed faceconditions(toughness) * interaction between

* fatigue properties rock mass jointingand arrays of cuttingtools

Mineral Constituents * surface hardness * grain strength* grain anisotropy

Rock Specimen

* grain size and shape* intergranular

bonding orcementation strength

; aggregate surface * aggregate bulkhardness strengthdegree of * aggregate porosityweathering * grain orientation and

aggregate anisotropy

Rock Mass * rock mass fracturingproperties andorientation todirection of cutting

Mechanical Properties and Behaviour of Rock

Rock strength, or rock resistance to failure under load, is a mechanical rockproperty which is mainly dependent on the nature of the rock itself. Rockcuttability, on the other hand, depends not only on the rock, but also on theworking conditions or the cutting process itself (depth of cut, tool size,cutting speed, axial force, presence and extent of wetting, etc.). Therefore,the environment for rating of rock cuttability/drillability is continuouslychanging as rock excavation methods improve.

Systems for rating rock "cuttability and drillability" for specificcutting/drilling methods (such as percussive drilling, rotary drilling, dragtool and roller disk cutting etc.) have been developed resulting in separaterating systems for each method. These rating systems are not directlyinterconnected, making comparisons between different cutting/drillingmethods difficult. In addition, they tend to be outdated as cutting/drillingtechnologies develop.

A variety of apparatus and procedures have been developed for measuringmechanical rock properties. This has simplified the study of cutting/drilling

66

processes including the effects various mechanical rock properties and otherfactors have on rock cutting/drilling performance. Mechanical rockproperties may be grouped as follows:

/. Strength

2. Deformability

3. Hardness

4. Fracture Toughness

5. Coefficients of Friction

6. Crushability and MUlability

7. "Extractability"

Resistance to (bulk) failure underelementary stresses such as compression,tension or shearEffect of confining pressure, temperature,strain rates, pore-fluid pressure, specimensize, etc. on strength properties

Resistance to change of shape or volumeElastic and thermal expansion constants

Resistance to a local (surface) failure byindentation or scratching

Resistance to fracture propagation

Resistance to sliding of two bodies withplanar surfaces in contact

Resistance to comminution (reduction of asubstance to a powder)

Resistance to fragmentation and disruptionbv different extraction processes itemised asrock, cuttability, drillability, blastability,loadability of blast-rock and pumpability ofcuttings under certain "idealised" orstandard operating conditions

8. Abrasivity Ability of rock to induce wearmechanical tools and apparatus.

on

Most physical tests involve tabulation of a series of readings, withcomputation of an average said to be representative of the whole. Thequestion arises as to how representative this average is as the measure of thecharacteristic under investigation. Three important factors introduceuncertainties in the result:

• instrumentation and procedural errors• variations in the rock specimens being testedR representability of selected rock specimens for the rock

formation or zone under investigation as a whole.

The largest source of error in determining mechanical rock properties forrock formations or zones is without doubt the representability of the selectedrock specimens; rendering the quality of field work and specimen selectionof utmost importance.

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Methods for Rating Rock Mass Cuttability and Drillability

The following assessment of test methods for rating rock mass cuttabilityand drillability for performance prediction purposes is valid for the listedtypes of rock cutting tools:

• roller disk and studded roller disk cutters• rotary tricone bits• drag tools• percussive drilling bits.

Rock mass cuttability and drillability is in its simplest form defined asbeing a factor proportional to net cutting or net penetration rates, or specificcutting/drilling energy. However, the specific energy is closely linked to theapparatus or drilling equipment with which it has been determined. Anotherand perhaps more precise definition for rock cuttability is rock resistance totool indentation for a unit depth of cut, i.e. such as the critical normal forceFni for roller disk cutting or Ki for percussive drilling.

Several empirical test methods are in use today for rating rock masscuttability and drillability for performance prediction purposes. Thesemethods can be divided into the following groups:

f i) use of compiled historic performance data (generally net cutting ornet penetration rates) for a given cutting/drilling equipment and toolcombination by referencing net penetration rates to results obtainedin a standard rock type as a means of rating rock cuttability anddrillability. The most commonly used standard rock types are:

• Barre Granite• Dresser Basalt• Myllypuro Granodiorite.

(ii) use of compiled historic performance data including the utilisedpower levels for a given cutting/drilling equipment and toolcombination by correlating the specific cutting energy to mechanicalproperties of rock as a means of rating rock cuttability/drillability.The most commonly used mechanical rock properties are:

• Uniaxial compressive strength, UCS• Brazilian tensile strength, BTS• Point load index, Is.

( Hi) use of stamp tests based on impact loading and crushing of a confinedsolid or aggregated specimen of intact rock. Due to the impact loadingand crushing nature of stamp tests - they represent the relative energyrequired to break a given rock volume; thus allowing for thecutting/drilling performance or specific energy in the field to berelated to stamp test indice values. The most commonly used stamptests for rating drillability are:

68

• Drilling Rate Index, DRI• Protodyakonov Rock Hardness, /• Coefficient of Rock Strength, CRS• Rock Impact Hardness Number, RIHN.

Performance prediction models based on rock cuttability/drillabilityindices often include the effects of porosity and rock massdiscontinuities by incorporating correction factors or modifiers forthese rock mass characteristics using back analysis of experimentalfield performance data.

( iv) use of laboratory linear cutting tests for roller disk and drag toolcutting for rating rock cuttability. In addition, the prediction ofcutterhead forces as a function of net cutting rates in non-fracturedrock mass conditions can be made using analytical models bycombining linear cutting test results with cutterhead lacing designs.Refer to Chapters 4 and 5.

( v ) use of numerical simulation with finite element and particle flowcodes. Rock loading by roller disk cutters causes macro-fractures toinitiate from the corners of the tool rim and to propagate sidewardsand upwards in curved trajectories. Preliminary results also indicatethat a small shear load of around one tenth of the normal forcesignificantly modifies the stresses in the rock around the tool path.More importantly, for kerf cutting, tensile stresses may develop fromthe adjacent kerf; hence it is possible for macro-fracture propagationto occur from an adjacent kerf as well as from the kerf currently beingcut.

f vi ) analytical analysis and simulation of stress wave propagationcombined with bit indentation tests (static or dynamic K, values) toincorporate the dynamic nature of rock loading and bit indentationencountered in percussive drilling. An example of this method is theCASE programme developed by AB Sandvik Rock Tools.

Evaluation of Classification Systems for Rock Mass Cuttability andDrillability

The Drilling Rate Index DRI, as proposed by R. Lien in 1961, is acombination of the intact rock specimen brittleness value S20 and Sieversminiature drill-test value SJ. The test methods are described in detail inProject Report 13-90: Drilling Rate Index Catalogue. A qualitative rating ofDRI drillability scale is shown on the following page.

The SJ value is an expression for the aggregate rock surface hardness. Auseful correlation between SJ and the Vickers Hardness Number RockVHNR for determining the degree of rock weathering is shown in Figure 3-5(typical VHN values for minerals are shown in Table 3-16). The S20 valueincludes the effect of rock brittleness, and therefore, grain size and grainbonding strength. Unfortunately, rock porosity has a very small effect on the

69

brittleness value S2o- Field performance follow-up work on the FaeroeIslands in vesicular basalt has shown that porosity in the range of 3 - 12%has a considerable effect on both the critical normal force Fni and netpenetration rates for TBM's in addition to the degree of rock fragmentationby blasting.

1000900800700600500CO

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300

200

10090807060

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Rock with "bonding

Weatherec

zero"

rock

grain

J

Non-weathered rock

100 200 300 400 500 700 1000 1500

Vickers Hardness Number Rock, VHNR

Figure 3-5. Relationship between Vickers Hardness Number Rock VHNRand Sievers J -value for some common rock types.

70

Qualitative rating of the Drilling Rate Index is :

Rating

Extremely LawVery LowLowMediumHighVery' HighExtremely High

DRI

212837496586114

The brittleness value S20, when combined with the stamped rock specimenflakiness value f, is commonly used for assessing blast-rock suitability forroad and highway construction purposes and as crushed aggregates inasphalt and concrete.

A relationship between the unconfined or uniaxial compressive strengthUCS and the Drilling Rate Index DRI has been established for 80 paralleltests as illustrated in Figure 3-6 by grouping scatter plotted values accordingto rock type. The envelope curves clearly illustrate that when the uniaxialcompressive strength is used for rating rock cuttability/drillability - thefollowing should be noted:

• the cuttability of foliated and schistose (anisotropic) rock types suchas phyllite, micaschist, micagneiss and greenschist generally tend tobe underestimated

• the cuttability of hard, brittle rock types such as quartzite generallytend to be somewhat over-estimated.

In performance prediction models based on UCS rated rock cuttability,correction factors or modifiers for rock type are commonly used toincorporate the effect of rock "toughness". In addition, the compressional totensional strength (UCS/BTS) ratio can be used as a measure for rocktoughness. The following qualitative toughness rating used by Voest-AlpineBergtechnik for drag tool cutting is:

UCS/BTS Ratio

5:17,5:1

9:115:125:1 •

- 7,5:1- 9:1- 15:1- 25:1• 40:1

Qualitative Rating

Very ToughToughAverageBrittleVery Brittle

71

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Drilling Rate Index, DRI

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WO

55CD

a.

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300

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Limestone

Calcerous Shale

Garble |

20 30 40 50 60 70 80 90 100

Drilling Rate Index, DRI

300

200

100

Qua

j

12116

k sands one

^ L J Silt: tone

20 30 40 50 60 70 80 90 100

Drilling Rate Index, DRI

Figure 3-6. Relationship between the Drilling Rate Index DRI and uniaxialcompressive strength UCS for some common rock types.

However, the analysis and normalisation of linear cutting tests in Chapter4.4 shows that the UCS/BTS ratio relates poorly to rock cuttability for singletool pass roller disk cutting; indicating that perhaps the UCS/Gic ratio is abetter parameter for describing rock toughness and for predicting theoccurrence of multiple tool passing cutting.

The fabric of an intact rock specimen can be characterised as an aggregate ofbonded mineral particles of dissimilar size and strength. Random orientationof crystal grains increase the overall specimen strength and toughness on amacroscopic scale. One approach to assessing the effects of rock texture,grain size, grain bonding or cementation strength and porosity is to relaterock strength to the "bulk surface hardness" VHNR.

A relationship between the Brazilian tensile strength and the "bulk surfacehardness" VHNR has been established in Figure 3-7 by grouping scatterplotted values according to rock type. The envelope curves clearly illustratethe following:

72

basic or mafic rocks have very high tensile strength values relative totheir bulk hardness VHNR. These rock types are characterised by ahigh content of fibrous mineral grains, often randomly oriented, highmodulus of elasticity and Poisson's ratio v. Micro-fracturespropagate mainly through the relatively weak mineral grains; and theeffect of grain size is minimal.

acidic rocks such as felsic gneiss, granites and granodiorites havelower tensile strength values than quartzites. Quartzites are typicallyvery fine grained.

coarse grained granites and granodiorites have lower tensile strengthvalues than fine grained specimens, indicating an increasing amountof micro-fracture propagation along grain boundaries - and thusreduced toughness.

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Vickers Hardness Number Rock, VHNR

Fine grainedgranites andgranodiorites

Coarse grainedgranites andgranodiorites

100 150 200 300 400 600 8001000

Vickers Hardness Number Rock, VHNR

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Vickers Hardness Number Rock, VHNR

Figure 3-7. The relationship between the Brazilian tensile strength and the"bulk surface hardness" VHNR for some common rock types.

73

metamorphic and anisotropic rocks such as phyllites and micagneiss have very low tensile strength values. The strength reduction iscaused by micro-fracture propagation along crystal cleavages oralong grain boundaries - and not across the mineral grainsthemselves. Fracture propagation along mineral grain boundaries inlaminated rocks is enhanced when neighbouring mineral layers showlarge differences in elasticity and Poisson's ratios, i.e. typical forquartz and mica or chlorite layers in anisotropic rocks such asmicaschists and micagneiss.

increasing porosity dramatically reduces rock strength and toughnessdue to enhanced micro-fracture propagation from void to void.

Table 3-9. Protodyakonov classification of rock hardness.

Category Hardness Description of Rock RockLevel Hardness

f

I Highest The most hard, dense and tough quartzites and basalts. 20

II Very Hard Very hard granitic rocks, quartz porphyry, silicious 15schist, weaker quartzites. The most hard sandstones andlimestones

III Hard Granite (dense) and granitic rocks. Very hard 10sandstones and limestones. Quartz veins. Hardconglomerate. Very hard iron ore.

Ilia Hard Limestones (hard). Weaker granites. Hard sandstones, 8

marble, dolomite and pyrites.

IV Rather Hard Ordinary sandstone. Iron ore. 6

IVa Rather Hard Sandy schists. Schistose sandstones. 5

V Moderate Hard shale. Non-hard sandstone and limestone. Soft 4conglomerate.

Va Moderate Various schists (non-hard). Dense marl. 3

VI Rather Soft Soft schist. Very soft limestone, chalk, rock-salt, gypsum. 2Frozen soil, anthracite. Ordinary marl. Weatheredsandstone, cemented shingle and gravel, rocky soil.

Via Rather Soft Detritus soil. Weathered schist, compressed shingle and 1.5detritus, hard bituminous coal, hardened clay.

VII Soft Clay (dense). Soft bituminous coal, hard alluvium, 1.0

clayey soil

Soft sandy clay, loess, gravel. 0.8

Vegetable earth, peat, soft loam, damp sand. 0.6

Sand, talus, soft gravel, piled up earth, extracted coal. 0.5

Flowing Shifting sands, swampy soil, rare-fractioned loess and 0.3other rare-fractioned soils.

Vila

VIII

IX

SoftEarthy

DrySubstances

74

A comparative scale for rock resistance to breakage is the stamp test androck hardness ratio / proposed by M.M. Protodyakonov (Senior) in 1926. Itis primarily used in the CIS for assessing both rock drillability andblastability. Protodyakonov established the following relationship betweenthe relative rock hardness scale and the uniaxial compressive strength, i.e.

/ =0.1 UCS

Unfortunately the Protodyakonov rock hardness scale, as can be seen inTable 3-9, does not differentiate hardnesses of rocks extending beyond 200MPa. The US Bureau of Mines developed during the years 1968 - 1970 astamp test termed the Coefficient of Rock Strength CRS based in part on theProtodyakonov stamp test procedure for rating drillability. In addition,extensive drilling with two pneumatic percussive drills was carried outsimultaneously. A summary of rock specimen test results are shown on theusbm7684.xls file printout Appendix 2. The established relationship betweenthe coefficient of rock strength and the uniaxial compressive strength was:

CRS = 0.0065 UCS

Rock Mass Discontinuities

A rock mass is generally considered a linear elastic material in the absenceof specific information on rock mass discontinuities. Most rock formationsare fractured to some degree; where the fracture planes represent non-continuous structural elements in an otherwise continuous medium. Thestability of rock slopes and underground excavations are two areas ofgeotechnical engineering where the effect of intact rock properties isperhaps less dominant than the influence of rock mass discontinuities.

IntactRock

Joint Plane

/

11

/

/I111

\r

// /

i ,'I '; ,' /

I / /\ 1

Fractured Rock Mass Geotechnical Interpretation

Figure 3-8. Illustration of a typically fractured rock mass by a single set ofjoints; and a simplified geotechnical model consisting of regularly-spacedjoints of similar strength.

75

Structural mapping of rock formations includes the determination of rocktype and its distribution, degree of fracturing and rating of the predominanttypes of discontinuities. For practical use, this information must bestructured as specified by geotechnical classification systems designedspecifically for predicting rock mass behaviour with regard to structuralstability and excavation performance in rock.

When two or more intersecting fracture sets are present in a rock mass (referto Figure 3-3), an equivalent or "mean" fracture spacing based on theaccumulated volumetric fracture plane area is:

Omean =(Il/Oset)'

= (Ifracture area per m3 ) ' ' = [ m2 /m3 ]'

In the NTH tunnel boring performance classification system, fracture typesare grouped into four classes based on fracture strength (aperture oropenness, persistence, surface roughness and waviness, and infillingmaterial), i.e.

• Systematically fractured rock mass characterised by:• parallel-oriented joint sets (rated Sp)* parallel-oriented fissure sets (rated St)'foliation or bedding plane or parting sets (rated St)

• Non-fractured rock mass (rated St 0)• Marked single joints (rated ESP)• Shear zones - evaluation of necessary ground support work rather

than increased net excavation rates is required.

The combination of fracture type or fracture strength rating, fracture setspacing and fracture plane orientation to the tunnel axis forms the basis forthe rock mass fracture factor ks. The fracture factor ks for fissures andfoliation planes is shown in Figure 3-9.

TBM advance rates are more or less proportional to the fracture factor ks.However, unlike full-face tunnel boring machines, partial face cuttingmachines as the TM60 are typically equipped with a profile cutting controlsystem which maintains the tool depth of cut at a preset value. Thus thedegree of rock mass fracturing does not affect TM60 net cutting rates(unless the operator changes the set-point values) but results in reducedmean tool forces when excavating an increasingly fractured rock face.

76

o•2

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4.

3

2

1

0.36

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s,

Fissure FissureClass Spacing

IV 5 cm

- IV

I0

10 cm

20 cm40 cm

40 60° 80°

Angle between tunnel axisand planes of weakness, a

Figure 3-9. The fracture factor k, for full-face tunnel boring performanceprediction as a function of fissure class rating, the mean spacing betweenplanes of weakness and angle a, where : a = arcsin [ sinf • sin ( r - s ) ].

Friction of Mineral and Rock Surfaces

The study of friction is of significant importance in rock mechanics. Itseffects arise on all scales:

(i) the microscopic scale in which friction is postulated betweenopposing surfaces of minute Griffith cracks

(ii) a larger scale in which it occurs between individual grains orpieces of aggregate

( Hi) in friction on rock mass discontinuity surfaces in which theareas in question may vary from a few to very many squaremetres.

Suppose that two bodies with planar surfaces in contact of apparent area Aare pressed together by force G normal to the plane of contact, and the shearforce F parallel to the surface of contact necessary to initiate sliding on it ismeasured. The relationship between F and G may be written as:

F = fi-G [3-1]

where \x is called the coefficient of friction. \i depends on the nature of thematerials and wetting state of the surfaces in contact. \i might also beexpected to depend on A and G, but experiment has shown that, to areasonable approximation, it is independent of both these quantities; and isknown as Amonton's law. Dividing [3-1] by A, it becomes:

77

= an tan <p [3-2]

where an is the normal stress across the surfaces in contact, x is the shearstress across them necessary to initiate sliding, (p and is the friction angle.

Patton developed in 1966 a shear strength model based on experimentallaboratory data for shear of model joints with regular teeth. At normalstresses less than OT:

TP = en tan((pp+i)

and at normal stresses higher than CTT:

where:

<7T

cOn

<Pr

= C + on tan <pr

= C/ {tan ( (pp + i) - tan (pr }= shear stress intercept (cohesion)= normal stress in joint= peak friction angle= residual friction angle= angle of dilatancy

Patton's shear strength criterion is also a simple model for shear-normalstress behaviour of joints as illustrated in Figure 3-10.

COCD

COCD

v

Dilation yields a geo-metrical componentto the total resistance

T

Asperity failure yields ashearing component tothe total resistance

t

^ j — - • • • • ! " *

4Basic or residual frictionangle of a planar joint

Normal stress, O"n

Figure 3-10. Patton's bilinear criterion for shear strength of joints.

78

Results of friction measurements on minerals, natural shear surfaces of rockspecimens and rock mass discontinuities are listed in Tables 3-10, 3-11 and3-12.

The frictional force component on a drag tool sliding against rock is givenby \i- Fn, where \i is the coefficient of friction between rock and tool. Somecoefficients of friction are listed in Table 3-13.

Table 3-10. Coefficients of friction for some selected minerals.

Mineral

DiamondCorundum

QuartzFeldspar

Serpentine

Calcite

Biotite

Muscovite

Galena

Talc

Halite

M

0.100.40

0.11-0.190.110.620.14

0.31

0.430.600.360.70

Mnettal

0.42 - 0.650.460.290.680.13

0.23

0.16

Table 3-11. Coefficients of friction for natural shear surfaces of rockspecimens.

Rock

Sandstone

Marble

GneissQuartziteDiabase

Trachyte

Granite

M

0.51 -0.68

0.62 - 0.750.61 -0.710.48 - 0.670.64 - 0.95

0.63 - 0.680.60

fAvettal

0.61

0.61

0.560.60

79

Table 3-12. Coefficient of friction for natural rock mass discontinuities (noinfilling material).

Rock tan(<p+i)

Limestone 2.3 - 4.3Granite 2.6 - 3.1

Quartzite, gneiss and amphibolite 3.7 - 5.7

Table 3-13. Coefficient of static friction between steel and rock. Note: Staticfriction generally decreases with material surface hardness.

Materials Coefficient ofStatic Friction

Limestone/Steel 0.70 - 1.20Sandstone/Steel 0.50 - 0.70

Mudstone/Steet 0.30 - 0.60

Steel/Steel 0.19-0.35Steel/Steel (oiled) 0.08 -0.18

Steel/Steel (sliding) Multiply \i by 0.80

80

3.4 CHARACTERISATION OF TOOL CONSUMPTION

Classification of Wear-Types

Tool wear can be defined as microscopic or macroscopic removal or fractureof material from the working surface of a tool or wearflat by mechanicalmeans; in general any degradation that reduces tool life. Classification ofwear-types is based on the relative movement between the materials incontact, e.g. sliding, rolling, oscillation, impact and erosive wear.

Generally the tool wear encountered in rock cutting is a combination ofseveral ideal wear-types, in which some types of wear are more predominantthan others. Wear-types are influenced by several parameters, many ofwhich are interdependent, such as hardness and fracture toughness of wearmaterials, contact motion (e.g. sliding, impact), wearflat temperature andcontact stresses.

Tool wear is therefore a process in which the outcome is determined by thematerial properties of the tool tip, the rock mass, and the force-relatedinteractions on the contact surfaces of these materials. The wear capacity ofa rock mass, as illustrated in Figure 3-11, is a combination of:

• mineral constituents, i.e. size and hardness of mineral grains• strength and toughness of intact rock• tool depth of cut and cutting speed• occurrence of impact loading of tools (cutterhead bouncing, i.e.

cutting in broken rock and mixed face conditions or through shears)• type of cutting or contact motion in question (impacting, scraping,

rolling, grinding, etc.)• presence of coolants at the tool tip/rock interface• efficiency of cuttings and fines removal• strength, wear resistance and quality of the cutting tool

Various indices for tool life and wear rates are typically used as a measurefor the wear capacity of rock. Established relationships between indices fortool life and wear rates are mainly based on correlations with historic fieldperformance data for prediction of tool consumption in the field. However,when new laboratory methods are developed, relevant field data are oftennot available. As a consequence, relationships between new and old tool lifeand wear rate indices are often established so that previously reported fielddata can be used indirectly.

3.4.1 Classification of Wear Mechanisms

The importance of degradation mechanisms for cemented carbides may beclassified according to the scale of damage they cause, i.e. macroscopic andmicroscopic failure.

81

WEAR PROCESS OF ROCKCUTTING TOOLS

WEAR MATERIALSAND TOOL GEOMETRY

Bulk properties

sue effect on failure strengthfracture toughnessthermal conductivity

contiguity

Surface properties

hot hardnessdeformation hardening rates

Tool geometry and insertstructure

tool and tool tip geometriesstructure of insert

(e.g. DP carbide, PCD coatings)insert attachment to tool

MACROSCOPIC MICROSCOPICWEAR MECHANISMS WEAR MECHANISMS

ROCK MASSPROPERTIES

Intact rock

mineral constituentslithology

mechanical rock properties

Discontinuities

In situ stress conditions

Structural tool overload

structural overload and fatiguethermal shock and fatigueimpact shock and fatigue

Surface failure types

micro-ploughingmicro-cuttingmicro-fatigue

micro-cracking

Wear mechanisms

surface fatigueabrasive wearadhesive wear

tribochemical reactions

ROCK CUTTINGPROCESS

Occurrence of impact loading

(e.g. cutterhead bounce formixed face conditions)

Heat buildup of wearflat dueto applied cutting power

cutting speeddepth of cut

tool position on cutterheaduse of coolants

Wear modes and kerf profile strength

strength and frequency of asperitiesoccurrence of 2/3 body wearpresence of cuttings and fines

Flushing

removal of cuttingsand fines

CATASTROPHIC TOOLFAILURE RATES

TOOL WEARRATES

j

NET CUTTING/DRILLINGRATES

SERVICE LIFE OF TOOLS

Tool Life IndicesTool Wear Indices

Figure 3-11. Characterisation of rock cutting tool degradation and toolservice life.

82

3.4,2 Macroscopic Fracture and Structural Failure

Cemented carbides are a range of composite materials that consist of hardcarbide particles bonded together by a metallic binder. The proportion ofcarbide phase is generally between 70 - 97% of the total weight of thecomposite and its grain size averages between 0.4 - 14 fim. Tungstencarbide (WC), the hard phase, together with cobalt (Co), the binder phase,forms the basic cemented carbide structure from which other types ofcemented carbide have been developed. In addition to the straight tungstencarbide-cobalt compositions; cemented carbide may contain varyingproportions of titanium carbide (TiC), tantalum carbide (TaC) and niobiumcarbide (NbC). Cemented carbides which have the cobalt binder alloyedwith, or completely replaced by, other metals such as iron (Fe), chromium(Cr), nickel (Ni), molybdenum (Mo) or alloys of these elements are alsoproduced.

Structural overload and fatigue refer to macroscopic failure or degradationof the tool tip material structure caused by stresses induced in the bulk of thewear material. Voids and flaws in materials serve as fracture-initiation sitesdue to the stress concentrations at these sites. In cemented carbides, suchvoids or defects can result from inherent porosity resulting from incompletedensification during the sintering process; or they can form during service asa result of the stress history of the tool. In the presence of shear stresses,such as those caused by friction at a wearflat, microscopic voids cannucleate at WC grain boundaries due to the separation of WC grains fromthe Co binder and other WC grains.

The existence of a size effect on the failure strength of materials such astransverse rapture, tensile, compressive or shear strength for brittlespecimens is well known. As the specimen size is decreased, the averagefailure stress tends to increase, regardless of the failure criterion employed.This is due to the presence in all materials of a distribution of flaws varyingin number, size and severity, such as surface scratches or discontinuities,micro-fractures at grain boundaries and larger cracks both within the fabricand at bedding planes, and the existence of inclusions and pores. Thequantification of the size effect derives from the concept that there is adecreased probability of encountering and activating fracture-initiation sitesas the volume of material subjected to a given stress level decreases.

In the case of ductile materials (e.g. copper and mild steels) defect frequencyand mean size are important factors; whereas in the case of brittle materials(e.g. hardened steels and cemented carbides) the defect frequency above acertain size limits the strength. Based on statistical data, W. Weibull (1939)showed that the ratio of the failure strength a of two specimens withvolumes V/ and Vi respectively, is given by:

Pi/o> =(V,/V2)1/m

where the constant m is a factor derived from the spread in observed failure

83

stress levels and frequently labelled the Weibull or flaw density parameterassociated with the specimen volume. The variability of flaw densities hasbeen found to increase inversely with the value of m. High m-valuescorresponds to a small dependency on specimen volume with regard tofailure stress. Some typical m-values are:

Cemented carbide inserts m = 9Core drilled specimens of intact rock m = 5.6Large block specimens of intact rock m = 2

High quality cemented carbides are generally regarded as extremely defect-free materials. In practice, the internal stress distribution is complex and theWeibull theory only provides a partial description. However, the calculationof the fracture probability of a given cemented carbide composite for aknown stress distribution can be made.

Under high compressive stresses, and especially at elevated temperatures,plastic deformation of WC and Co grains occurs by slip, which is the lateraldisplacement of one plane of atoms relative to an adjacent plane. Micro-voids and micro-cracks are created during the slip process. Upon unloading,the compressive plastic deformation leads to the development of residualtensile stresses, which cause initiation of micro-fractures at voids,inclusions, and coarse WC grains. Once initiated, unstable fractures, whichpropagate in response to a static or single-impact load, tend to follow ratherstraight lines through the material in an intragranular fashion, i.e. throughpre-existing voids and flaws within grains. Stable fractures, which propagateduring cyclic loading, tend to follow grain boundaries in an intergranularmanner.

When specimens are exposed to external loads, static or dynamic,mechanical stresses arise within the material. In many instances, particularlywhen dealing with shock loading, both material strength and toughnessproperties must be considered simultaneously. This forms the background tothe term "toughness" that expresses a materials "ability to resist fracture",i.e. a complete separation of a specimen into at least two parts.

Toughness can be defined and determined in many ways. Modern fracturemechanics provides a means of explaining toughness as it deals with theconditions for micro-crack initiation and growth in non-homogeneousmaterials under stress and where the fracture toughness of the material isrepresented by its critical stress intensity factor KJC- An indirect methodcommonly used for determining the toughness of cemented carbides is thePalmqvist method where the sum of corner crack lengths for a Vickershardness indentation is used to derive the fracture toughness. The criticalstress intensity factor for cemented carbides can be expressed as:

K,c = 6.2 (HV50/IL)'/2 [MN/mm/

84

Toughness tests on cemented carbides show that the critical stress intensityfactor increases with Co content and WC grain size. The range for criticalstress intensity factors for the following materials is:

Cemented carbidesIntact rock specimens

K,c = 5-30MN/mJ/2

K,c = 0.05-3MN/m sn

Fracture toughness is substantially reduced at elevated temperatures. Due tothe reduction of fracture toughness with temperature, cemented carbidesmay exhibit a larger reduction in strength during cyclic loading at elevatedtemperatures.

Cemented carbides are classified as brittle materials since practically noplastic deformation precedes fracture. However, cemented carbides showlarge differences in toughness behaviour due to their microstructure. Thetypes of fracture seen are cleavage fractures in carbide grains, grainboundary fractures between carbide grains and shear fractures in the binder.Generally, the amount of cleavage fractures increases with increased grainsize and the amount shear fractures with increased binder content. Expressedas fracture energy, the major contribution is from the latter, i.e. the crackpropagation through the binder.

Thermal fatigue of cemented carbides is most noticeable in non-abrasiverocks since the low abrasive wear preserves more visual evidence of thermalcracks. These cracks penetrate deeply into the bulk of the material, run in anintergranular fashion, and branch readily. Fractures intersect, removing largeflakes of material and forming relatively steep angular craters. Once thisprocess has started, the tool rapidly becomes useless for rock cutting.

Figure 3-12. Illustration of Vicker's pyramidal indentation impression andresulting corner cracks used in the indirect Palmqvist method fordetermining the critical stress intensity factor Kicfor cemented carbides.

85

Wear resistance (a surface property) and toughness (a bulk property) are twocomplex properties, both of which provide a material the ability to withstanddestruction. A high wear resistance for cemented carbides can only beachieved if the demand for a high toughness is reduced and vice versa.However, both high wear resistance and high toughness can be achievedsimultaneously, provided these properties can be re-distributed. There aretwo ways of doing this: Dual Property (DP) cemented carbides or coatingsof highly wear resistant materials such as polycrystalline diamond (PCD) ona substrate of cemented carbide.

In highly fractured rock formations, mixed face conditions, or when toolbounce occurs; tools are subjected to impact shock and fatigue, which canbe far more destructive than thermal fatigue. Under these conditions,compressive shock waves in the tool are generated at the impact surface.These waves travel through the tool and reflect from free surfaces as tensilewaves, which have more destructive power and cause secondary cracks todevelop. Cracks propagate according to the fracture toughness of thematerial and the impact energy involved. High-velocity impacts causefractures to branch readily, leading to increased damage.

In an ideal case, tool life and tool wear rates are inversely proportional.However, the service life of tools is also determined by the structuraloverloading of tools and the occurrence and rate of catastrophic tool failures.The generalised distribution curve in Figure 3-13 for drag tool replacementson a cutterhead in service illustrates the increased sensitivity to tool impactfailures in harder rock formations as well as the detrimental effect ofincreased tool loading required to cut harder rock. However, conical dragtools are not as sensitive to catastrophic failures as radial drag tools.

O)O T3O to

CO ©

- oo~ Em o> ^=> in

O -c *2 £

"— ID3 o

J3 CO

03

5

1 O O C

Carbide Insert Wear

Carbide insert andBrazing Failures

Rock Strength

Figure 3-13. A generalised distribution curve as to the main reasons fordrag tool replacements on cutterheads in service as a function of rockstrength.

86

Catastrophic tool failures caused by impact loading are typically a result ofboth tool and cutterhead bouncing which occurs for an unfortunatecombination of rock mass structure, cutterhead lacing design, and selectedrotary speed. The impact forces on tools are caused by the striking action oftools when re-entering the kerf or harder portions of the rock structure;leading to progressive tool tip chipping and finally catastrophic failure ofcarbide inserts or disk rims. For single rowed carbide insert studded disks; aripple breakage effect of studs is often experienced. Some typical examplesof rock structure leading to reduced tool life due to impact loading are:

• fractured rock mass resulting in rock fallouts and voids in the face• variable rock structure hardness or mixed face conditions.

The origin and mechanisms behind tool bounce and cutterhead excitationfrequencies are described and illustrated in Chapter 5.7 Sequential Cuttingwith Domed Cutterheads. In addition, the severity of tool damage by impactloading is increased by the hardness ratio for mixed face conditions, i.e.VHNRminerai-2 / VHNRmmerai-i as illustrated in Figure 3-14 for some typicalexamples of variable rock structure hardness.

Banded rocksphyllites, mica schistsand mica gneiss

Rubble type rocksbackfills, brecciasand conglomerates

Intrusive rockssills, dykes andstringers

mica and chloritequartz and feldspars

weak matrix of lowstrength concretehard aggregates ofigneous rock

weak host rock of shalehard intrusions ofigneous rock

Figure 3-14. Illustration of variable rock structure hardness or mixed faceconditions typically leading to impact loading and shattering of especiallydrag tools.

87

3.4.3 Microscopic Fracture and Wear Mechanisms

Tool wear on the microscopic scale is the result of four basic wearmechanisms, i.e. surface fatigue, tribochemical reaction, adhesive andabrasive wear. Plastic deformation as such is generally not regarded as awear mechanism, but plays an important part in many wear processes.

Abrasive and adhesive wear mechanisms are assumed to dominate the toolwear process during the cutting of rocks containing minerals harder than thetool tip material. Surface fatigue wear mechanisms are only considered toplay a role if the wear rates are low; thereby allowing for the necessary timefor these processes to take place.

Wear due to surface fatigue is characterised by crack formation and theflaking of material caused by the repeated alternated loading of solidsurfaces. Repeated sliding contact of asperities on the surfaces of solids inrelative motion may result in surface fatigue on a microscopic scale.

Wear due to tribochemical reaction is characterised by the "rubbing"contact between two solid surfaces that react within a gaseous or liquidenvironment. The wear process takes place by the continuous removal andformation of new reaction layers; such as oxidation of WC grains on acontact surface or wearflat.

Adhesive wear, typical for conditions characterised by high temperaturesand high contact stresses, is defined as wear due to adhesive materialtransfer. Welding of contacting asperities followed by the breakage of thesejunctions and the subsequent removal of shorn particles from one surfaceand transfer of material to another.

Wear due to abrasion (or grooving) is defined as the displacement ofmaterial from a solid surface by hard protuberances, such as hardprotuberances on the rock surface (two-body wear) or hard particles in thekerf sliding along the surface (three-body wear) as illustrated in Figure 3-15.

Two-body Abrasion Three-body Abrasion

Tool

Figure 3-15. Illustration of two- and three-body abrasive wear. Micro-cutting is thought to be the main mechanism behind two-body wear,whereas three-body wear is related to the mechanism of micro-ploughing.

88

In-line kerf cutting tools such as roller disk cutters are typically subjected tothree-body wear. Two-body wear gives rise to wear rates one to two ordersof magnitude higher than three-body wear.

A subdivision of three-body wear can be made based on mineral grainhardness and rock hardness (strength) relative to the tool tip materialhardness, i.e.

• for mineral grains which are harder than the tool tip materialand the rock matrix; the hard abrasive grains will be pressedand bedded into the weaker rock matrix or the crushed andcompacted rock powder in the tool path. The top of these hardmineral grains will protrude from of this surface as abrasiveasperities.

B for relatively weak mineral grains and rock matrices comparedto the hardness of the tool tip material - wear by abrasion is notlikely to occur.

• for relatively hard mineral grains and rock matrices comparedto the hardness of the tool tip material; the hard abrasivemineral grains are pressed and bedded into the tool cuttingsurface and form a protective layer against abrasive action fromthe rock surface.

The effect of some of these phenomena on tool life are clearly illustrated inFigure 3-25.

Some Aspects of Abrasive and Adhesive Wear

Abrasive and adhesive wear mechanisms make up the greater part of thetotal wear encountered by tools sliding across abrasive rock surfaces. Weardue to sliding abrasion can be divided into four basic material failure types;i.e. micro-ploughing, micro-cutting, micro-fatigue and micro-cracking asillustrated in Figure 3-16.

Micro-ploughing, micro-cutting and micro-fatigue are the dominant types ofmaterial failure in ductile materials such as steel. In an ideal case, micro-ploughing due to a single pass of one abrasive particle does not result in anydetachment of material from a wearing surface. A prow is formed ahead ofthe abrading particle and material is continually displaced sideways to formridges adjacent to the micro-groove produced. During micro-ploughing,material loss can however occur, since many abrasive particles actsimultaneously or in succession. Material is then ploughed aside repeatedlyby the passing particles and thus break off by fatigue. Micro-cracking isrelated to brittle materials like cemented carbides.

89

abrasive grain

Figure 3-16. The four basic types of material failure for abrasive wear.

Failure mechanisms also vary with the shape of asperities due to thedifferences in contact surface stress regimes. It has been found thatcompressive stresses prevail when the asperity attack angle a is small andtensile stresses prevail when the attack angle is large. Asperities with smallattack angles gives rise to abrasive wear by micro-ploughing and asperitieswith large attack angles result in micro-cutting. The attack angle a in Figure3-17 is related to the ratio of micro-cutting to micro-ploughing. The criticalattack angle Oc is the angle at which micro-cutting and micro-ploughingcontribute equally to the total wear process. The critical attack angle isdependant on both the cutting conditions and the tool tip material.

!

o"5.25

Relative Attack Angle a / a c

Figure 3-17. Ratio of micro-cutting to micro-ploughing as a function of theabrasive asperity attack angles.

90

One of the principal properties of metallic materials required to resistabrasive wear is surface hardness. Studies of tool wear rates show thatabrasive wear mechanisms are a function of the relative hardness of thematerials with sliding contact. It has been established that one material willscratch another provided the difference between their respective surfacehardnesses is greater than ~ 20%.

Abrasive wear can be divided into types, i.e. soft and hard abrasive wear.

Soft Abrasive Wear Hrock/Htoot < 1.2

Wear rates are relatively low and do not depend greatly on the actualhardness ratio. Soft abrasive wear for cemented carbides occurs when theabrasive particles (e.g. quartz at room temperature) which are softer thanWC grains yet harder than the Co binder preferentially remove the Cobinder, leaving the WC particles free to be dislodged from the structure.Thus, in the absence of thermal effects, soft abrasive wear rates arerelatively low.

The interaction between abrasive particles and the surface of WC-Cocomposites depends on the relative hardness and size of the particles and theseparate phases of the composite. Abrasive particles that are softer than theWC grains but harder than the Co grains (such as quartz at roomtemperature) preferentially remove the Co binder from the surface layers.Small particles in this category remove Co through a ploughing actioninvolving plastic deformation of the Co grains. Larger particles that aresofter than WC tend to bridge between adjacent WC grains; in this case, Cois preferentially removed by extrusion as WC grains are rocked back andforth by friction with the sliding particles. The plastic strain experienced byCo grains during either of these processes causes the formation of voids andcracks in the surface layers. Once initiated, surface fractures propagatebecause of impact shock or fatigue.

The significant role of binder removal in the wear of WC-Co composites bysoft abrasives is illustrated by tests in which specimens were chemicallyetched to remove Co and then abraded on sandstone. Although Co wasremoved to a depth below the surface of only 0.2 (xm (about 5% of the WCgrain diameter), the wear rate was found to be an order of magnitude greaterthan that of similar unetched specimens. Thus, Co removal is found to bethe controlling factor in initiating surface cracking and abrasive wear ofWC-Co by soft abrasives. Because Co softens with temperature and thus ismore easily deformed and removed, wear should accelerate at elevatedtemperatures. Tests show that preferential removal of Co also accelerateswear by hard abrasives. Fractures having their origin in abrasion may bepropagated by thermal fatigue occurring on a macroscopic scale. It is alsoknown that the initiation of thermal stress cracks is sensitive to surfacefinish (which is severely degraded by abrasion).

91

Hard Abrasive Wear HroCk/ Htooi > 1.2

Wear rates increase significantly and become very sensitive to the hardnessratio. Hard abrasive wear for cemented carbides occurs when the abrasiveparticles harder than WC grains strike the composite and fracture WCgrains on impact. This action causes a large degree of plastic deformationas the particles cut grooves or craters into the wearflat surface, formingvoids and residual stresses that lead to additional fragmentation of WCgrains.

Silicates typically cause most of the abrasive wear on rock cutting tools. Arange of room-temperature Vickers hardness values for some selectedmaterials are:

M feldspars 730 ... 800 kgf/mm 2

» quartz 1060kgf/mm2

& cast iron and steels 200... 750 kgf/mm "

M WC-Co mining grades 800 ... 1700 kgf/mm 2

• polycrystalline diamond, PCD 4500... 7000 kgf/mm 2

Both rock and tool tip materials are often inhomogeneous on the scale ofhardness testing and may consist of several components of varying hardness.The "aggregate surface hardness" of rock and wear materials are averagedvalues based on the hardness of their components. However, somecomponents influence the aggregate hardness more than others:

• Carbides in steel, for example, have a significant effect on the wearresistance of steel cutting tools, but do not influence the overallcomposite material hardness since they are too small to be significantfor the Vickers microindentation hardness.

• Quartz would be considered a soft abrasive relative to WC-Cocomposites. Yet the wear of rock cutting tools in quartzitic rockoccurs rapidly in a manner consistent with that produced by hardabrasives. This behaviour suggests that thermal effects are important.With increasing temperature, the hardness of the wearflat drops morerapidly than that of quartz; thereby increasing the HnKk /Htoni ratio.Furthermore, quartz particles may not attain the same temperaturerise as the tool tip due to the limited period of time that individualquartz particles are subjected tofrictional heating.

Thus, the relative hardness between tool tip materials and rock mineralgrains is insufficient to describe their behaviour in a wear system. This ispartly true due to the different nature of rock and tool materials, and theirmechanical response in hardness testing and wear systems.

92

^_____ homogeneous wear materialsen \ f—~~~ e.g. hardened steels(S9)

composite wear materials'» • e.g. cemented carbides

Hardness Ratio, H r o c k /H t o o |

Figure 3-18. Abrasive tool wear rates as a function of the relative hardnessratio, Hrock /HWoi of the materials in contact. Refer also to Figure 3-25.

One final aspect of abrasion is the finding that, in the presence of rockpowder or debris during cutting, WC-Co wear is an order of magnitudegreater than that produced during abrasion on a clean surface. This is causedby extremely small quartz particles (0.1 |lm) that are produced duringcutting, which are more efficient in removing Co than are large, fixedabrasive particles. Tool life may be improved by directing waterjets in frontof the tool. This may partly be because of improved removal of cutting finesas well as reduced tool loads that result in lower wearflat temperatures.

Adhesive wear contributes to the total wear when the wearflat temperatureand contact stresses are high enough to weaken the tool tip material so thatthe cutting tool is worn by hard abrasives. The ability to retain hardness athigh temperature, or hot hardness, is a function of the WC-Co compositestructure. WC grain hardness is not appreciably affected by the temperaturesreached during normal cutting operations. Critical hardness losses resultwhen the Co binder absorbs sufficient heat to transform it into the plasticrange where deformation and creep of WC-Co composites readily occurs.Sintered cobalt within cemented carbides melts at approx. 1350 °C. Bearingthis in mind and due to the presence of asperities, localised peak contacttemperatures may be as high as 2000 °C.

For wearflat temperatures below a threshold limit, WC-Co composites inrock cutting experience wear of the type produced by soft abrasives; while athigher temperatures, tool wear is accelerated and occurs by mechanismsassociated with hard abrasives and adhesion.

The temperature at which tool tip materials first start to weaken is called thecritical temperature Tcntjcai and the corresponding tool cutting velocityVcnticai- The critical velocity is affected by several factors such as tool tipgeometry, tool tip material properties (especially WC grain size since coarse

93

WC grains improve thermal conductivity and thus enhance the transfer ofheat away from the wearflat), use of waterjets for cooling and rock wearcapacity as illustrated in Figure 3-19.

13

/ I/ i

/ t

adhesive wearmechanisms

abrasive wearmechanisms

v critical T ° o 1 Velocity

Figure 3-19. Typical trendline for tool wear rates for sliding motion contactas a function of tool cutting velocity.

WC-Co wearresistance

Predominantwearmechanisms

WC-Cobehaviour

Wearflattemperature

High

Soft Abrasive

Hrock /H,ool<1-2

* Co binderworn away;followed byloss of WCgrains

* occurrence

of surfacefatigue wearmechanisms

(or corresponding ,cutting velocity)

Moderate

Hard Abrasive

Hroc* /H,oo,>1-2

* deformationhardening ofwearflat,followed byrupture of WC

grains

i

J50 °C - 500'cr i

Low

Adhesive

* hot-hardnessreduction ofwearflatresulting inlow surface

layer wearresistance

°C - 700tical

ExtremelyLow

Tribochemicalreaction

* plasticdeformationand creep

* p» hinrlAri o Dinuer

flow followedby Co

depletion inwearflat

* oxidation ofWC-Coaccelerates

°C

Figure 3-20. Generalised summary of the behaviour and wear resistance ofcemented carbides as a function of temperature.

94

3.4.4 Classification of Tool Wear Modes for Sliding Wear

Additional rock cutting process parameters which influence tool wear ratescan be divided into two groups; one group controlling the tool cutting forcesand another group which influences the response of the rock/tool tip contactsurfaces.

The surface or profile of the kerf (or tool path) cut into the rock is a crucialfactor when classifying tool wear modes. The kerf profile strength is definedas its resistance to the crushing. The kerf profile strength is characterised bythe rock material strength and the tool path profile geometry, which in turndepend on rock composition and texture.

When a load is applied to the rock through the tool tip, the kerf profile willbe deformed, first elastically, then plastically and finally fail. As the kerfprofile deforms, the actual contact area between rock and tool tip increases.With an increase in deformation or contact area, the stiffness of the profilewill increase and the actual contact stresses decrease. The profile deformsuntil the applied load becomes equal to the force resisting deformation.

The kerf profile strength depends on several factors; such as rock materialstrength properties, overall profile geometry or roughness and the strength ofasperities.

The geometry and frequency of asperities also affect the strength of the kerfprofile. The shape of asperities affect their strength; e.g. steep and sharpasperities are more sensitive to crushing than blunt asperities.

crushed asperity tip

A A'Bock

F F F Fi i IT T i T

4 Mimmmm.

2F 2F

Figure 3-21. Sharp asperities in the kerf profile are more sensitive to tipcrushing than broad based asperities. In addition, a larger spacing ofasperities increases the loading of individual asperities.

95

However, sharp asperities in one cutting direction may be broad and flatasperities in another direction, e.g. mica grains. The shape should thereforebe related to the direction of cutting. An increase of asperity spacingincreases the load per asperity and therefore to a reduction of the profilestrength. Angular asperities cause tensile stresses whereas rounded asperitiesinduce compressive stresses in the wearflat, Figure 3-17. Failuremechanisms typical for abrasive wear are determined by the shape of theasperities, tool tip material properties and whether two- or three-body wearprevails.

Strength of rock material?,. The kerf profile asperities consist of rockmaterial and may therefore be related to the rock material strength.However, asperities generally consist of individual mineral grains of adifferent strength than the aggregate rock specimen; and thus the strength ofasperities may also be independent of the bulk strength of the rock. In bothcases the stresses imposed on the asperities by a cutting tool are distributedinto the rock beneath the asperities. The rock beneath the asperities reactsupon loading according to its material strength (which may be a function ofthe grain frame and cementation matrix for sedimentary rock types) andthereby kerf profile strength is influenced by the rock bulk strength.

Stiffness of rock material. Rock material is an aggregate of mineral particles.The various mineral types all have different strength and stiffness, and inaddition, are anisotropic in most cases. The average stiffness of the differentmineral constituents determines the stiffness of the rock specimen. If theamount of stiff minerals is so large that they form a skeleton, the less stiffminerals do not influence the stiffness of the rock. The stiffness of the kerfprofile is determined by the stiffness of the rock and the kerf profilegeometry.

The effect of strain rate on rock stiffness and strength. Rock stiffness as wellas rock strength increases with strain rate. Rock strength determined at veryhigh (impact) strain rates may be a factor two larger than the strengthdetermined at lower (standard test) strain rates. Above a certain strain ratethe effective strength does not increase further.

Hardness of mineral grains. Mineral grains which during cutting are harderthan the tool tip material are termed abrasive. An abrasive mineral grain incontact with the wearflat of a cutting tool may either break, penetrate thetool wearflat or the kerf (or rock) matrix.

The wear process of rock cutting tools can be characterised by the threewear modes as described and illustrated in Figure 3-22 for a sliding contactmotion - depending on the magnitude of the contact stresses relative to thekerf profile strength. The cutting mode, scraping or cutting, affects the wearmodes by influencing the tool cutting forces and the contact area betweenthe wearflat and kerf (rock) surface. The wear capacity of rock changes asthe wear modes change; thus rock abrasivity is not an intrinsic physicalrock property.

96

Model

Asperities remain intact(2-body wear redominates);high contact stresses maydevelop due to a smallcontact area; and relativelyhigh wearflat temperaturesoccur favouring adhesivewear with deep penetrationof asperities into the toolwearflat resulting in highrates of wear.

Mode II

Some of the asperities arecrushed (2-body wear and 3-body wear both occur);lower contact stressesdevelop than in Mode I dueto a larger contact area;lower wearflat temperaturesoccur than in Mode I withless penetration of asperitiesinto the tool wearflatresulting in a lower rate ofwear than in Mode I.

Modem

Most asperities are crushed(3-body wear redominates);low contact stresses developdue to a relatively largecontact area compared toModes I and II; relativelylow wearflat temperaturesoccur with a shallowerpenetration of asperities intothe tool wearflat resulting ina lower rate of wearcompared to Modes I and II.

Figure 3-22. The wear process of rock cutting tools charaterised by wearmodes. Arrows indicate the mean tool cutting force levels.

The formation of chips during rock cutting causes the cutting forces tofluctuate. The normal and cutting tool force components are not constantduring a length of cut, but increase to a maximum until a large chip isformed; after which the forces fall back to a minimum value. If the area ofcontact between tool and rock are considered to be constant - then thecontact stresses at the wearflat vary accordingly.

The variable contact stresses result in different wear modes during theformation of rock chips. Figure 3-23 illustrates how the kerf profileresponds to the stresses on the wearflat as a function of time. If the stressesacting on the kerf profile asperities become larger than the strength of theseasperities, the asperities are crushed.

Studies of tool wear show that wear rates increase for low tool loads anddecrease for higher tool loads. This behaviour can be explained by a changeof wear mode (two-body wear to three-body wear) which takes place whenthe kerf profile strength is exceeded. Since the change of wear mode isaccompanied by a deepening of the kerf in the rock by a cutting tool, it isassumed that the rate of wear changes as a result of the contact stressesexceeding the strength of the abrasive asperities.

97

A summary of wear mechanisms, wear modes, rock mass and tool serviceconditions affecting tool consumption in rock cutting is presented inTable 3-14.

Table 3-14. Summary of wear mechanisms, wear modes, rock mass and toolservice conditions affecting tool consumption.

WearMechanisms

Wear TypesDrag ToolsSteel DiskStudded DiskPercussive Bits

Fatigue

* thermal* surface &

thermal* thermal

Abrasion

* sliding* rolling, sliding* rolling, sliding* sliding

Adhesion

* adhesive* adhesive

StructuralOverload

* impact* impact* impact* impact

Rock Mass ConditionsSoft rock conditions

Rock types composed ofminerals of widely varyingindividual grain hardness

Mixed face and brokenground conditions, andcutting through shears

* self sharpeningwear of steeldisk rims

* emery wheelwear of steeldisk rims 2

* catastrophicfailure ofinserts, steeldisks andbearings due toimpactingcaused bycutterheadbouncing3

Tool Service ConditionsTool tip * thermal fatigue and snakeskinmaterial formation on carbide inserts

* disk rim mush-rooming ofsteel diskcutters 6

Tool depth of cutShallowIntermittentDeep

* Wear Mode I (2-body wear)* Wear Mode II (2 and 3-body wear)* Wear Mode III (3-body wear)

Tool cutting forcesVery high * surface fatigue and

disk rim chipping ofsteel disk cutters s

Cutting velocity

Waterjetcooling

* abrasive wearforv < vcrilicai

* adhesive wearforv > vcritical

* waterjet cooling used to arrestadhesive wear

98

Extension of Table 3-14:

One example of thermal fatigue is the development of "snake skin" whichleads to premature breakage of cemented carbide inserts on percussive drillbits. Another example of thermal fatigue resulting in poor life of drag toolsis the cutting of low-abrasive rocks such as limestones.

The excessive wear experienced on steel disks when cutting in rock typessuch as mica schist and mica gneiss is an example of a wear type termed the"emery wheel wear" effect.

Catastrophic failure of carbide inserts, steel disks and cutter bearings dueto impacting caused by mixed face conditions, an unfortunate cutterheadlacing design, or imbalanced cutterhead running characteristics or mis-matched machine stiffness to cutterhead bounce excitation frequencies.

The excessive steel disk rim side wear experienced when cutting soft rockssuch as shales is an example of a wear type termed the "self sharpeningwear" effect due to tempering of disk steel and loss of disk rim workhardening.

An example of surface fatigue is disk "rim chipping" of highly stressedsteel disks when cutting in hard rock.

An example of insufficient steel disk rim hardness relative to tool servicestress levels is disk "rim mushrooming" resulting in severely deformeddisk rims.

The wear rate of cemented carbide during percussive drilling in hard rocksthus seems to be dependent on two factors:

(i) the rate of formation of the hardened surface layer(ii) the rate at which it wears away

The target is to establish a balance between wearflat deformation hardeningand surface layer wear rates to obtain optimum insert life. In percussivecontact with the rock, the crystal structure of cobalt changes from cubic tohexagonal and deformation hardens; thus increasing insert wear resistanceduring service. The numerous micro-cracks which develop on the nowbrittle wearflat surface are not worn away due to the increased wearresistance (or low rock abrasivity) - and merge into a highly destructivemacro-fracture structure driven by cyclic loading and thermal fatigueknown as "snake-skin "; resulting in premature insert failure.

99

peak stress peak stress

4 -/»(sf

crushing of kerf profile-<-"*-' • • • rock strength

(00)

55kerf profile strength

oo

Time

Figure 3-23. Contact stresses in a wearflat typical for drag tool cutting as afunction of time. The stress fluctuations are caused by the formation andloosening of rock chips. Wear Mode I predominates within the low stresszones A; and Wear Mode HI predominates within the high stress zones B.

3.4.5 Methods for Rating the Wear Capacity of a Rock Mass

Parameters for characterising and quantifying properties of intact rockspecimens may be divided into two groups:

(i) Physical rock properties such as grain size, density and porosity.These parameters describe insintric rock properties, which areinherent only to the rock itself.

( i i) Mechanical rock properties such as strength, deformability,hardness, toughness, wear capacity, etc. These properties areinfluenced by the method of testing.

Tool consumption is dependent on the following wear process parameters:

Tool Tip Material

M carbide grade wear resistance to thermal and surface fatigue• carbide grade resistance to catastrophic failure due to

structural overload, thermal shock and shatteringM carbide insert size, shape, and arrangement of attachment to

toolholder.

KerfProfile

fragment size and strength of kerf rock powder (both dependenton mineral grain surface hardness)

100

tool indentation depth (defines both the tool/rock contact area,i.e. where wear takes place and which abrasive wear modepredominates)effect of rock cutting mode (relieved/unrelieved cutting) on toolforce levels.

Tool Service Conditions

8 actual cutting velocity relative to the critical velocity vcnucaiforthe selected tool tip material

• presence of tool tip cooling (waterjets etc.)• cut length per cutterhead revolution for drag tools• occurrence of structural overloading of tools and cutterhead

bouncing8 general handling of tools during transport, tool change, etc.

The most common laboratory methods used for determining the wearcapacity of rock specimens are:

• (Rosiwal Mineral Abrasivity Rating)• Wear Index F• CERCHAR Abrasivity Index, CAI• Vickers Hardness Number Rock, VHNR

• Cutter Life Index, CLI (a combination of the Abrasion Value,AV and Sievers miniature drill-test value, SJ)

• Goodrich Wear Number• Hardgrove Grindability Index.

Rosiwal Mineral Abrasivity Rating

A relative abrasivity rating for minerals based on grinding tests wasintroduced in 1916 by A. Rosiwal where the mineral specimen volume lossrelative to corundum was used as an abrasivity rating, i.e.

Rosiwal = 1000 volume loss corundum / volume loss mineral specimen

Typical Rosiwal abrasivity ratings for some common non-weatheredminerals without impurities are listed in Table 3-16.

Wear Index Ffor Drag Tool Cutting

The Wear Index F proposed by J. Schimazek and H. Knatz in 1970 was as aresult of pin-on-disk wear tests on carboniferous rock from the coal miningdistricts in Germany. The Wear Index F is linearly related to pin wear rates;and increases with relative mineral abrasivity, mean quartz grain size and

101

tensile strength of the rock specimen, i.e.

F = Q -D-Z-10'2 [3-3]

Q = equivalent quartz percentage [ % ]D = mean quartz grain size I mm ]Z = Brazilian tensile strength [ MPa ]

The equivalent quartz percentage takes both the amount of and relativemineral grain abrasivity to quartz into consideration. The Rosiwal mineralabrasivity rating as used by Schimazek and Knatz for determining theequivalent quartz percentage is:

CarbonatesMica, chlorite, clayFeldsparsQuartz

3%4%

30 - 33%100%

Determination of the equivalent quartz percentage for a typical sandstone isexemplified in the following table:

Mineral Mineral Content Equivalent Quartz Percentage

QuartzFeldsparCarbonateMica, clay

639

3

25

63 • 1.0 =9 0.32 =3 0.03 =

25-0.04 =

63.03.00.11.0 => 67.1

The relationship between the Wear Index F and the CERCHAR AbrasivityIndex, CAI for the Saar Coal District in Germany has been established as:

CAI = 0.6+3.32 F

The Wear Index F has been successfully used in very fine grained andporous sedimentary rocks in Central Europe. Unfortunately, use of the WearIndex F in coarse grained metamorphic and igneous rocks leads to highlymisleading results; and the Wear Index F was consequently modified byG. Ewendtin 1989.

102

CERCHAR* Abrasivity Index, CAI

CERCHAR is an acronym for the Centre a"Etudes et Recherches desCharbonnages de France.

The CERCHAR scratch test for rating rock wear capacity was introduced in1971. It is defined as follows: a pointed steel pin with a cone angle of 90° isapplied to the surface of a rock specimen, for approx. one second, under astatic load of 7 kgf to scratch a 10mm long groove. This procedure isrepeated several times in various directions always using a fresh steel pin.The abrasivity index is obtained by measuring the resulting steel pinwearflat diameter d in millimetres using an average value of 3 - 6 scratchtests depending on the variability of the individual scratch test results:

CAI = 10 • I d wear1iat / n

Steel pin volume loss is proportional to the pin wearflat diameter as d3, andtherefore to the abrasivity index as CAI3. The pin steel is specified byCERCHAR only as having 200 kgf/mm2.

Typical CERCHAR abrasivity ratings for some common non-weatheredminerals without impurities are listed in Table 3-16.

The abrasiveness of a rock specimen is not necessarily the same as theaggregate abrasiveness of its mineral constituents; factors such as grain sizeand angularity, grain cementation and degree of weathering, etc. all have aneffect on the wear capacity of rock.

The main sources of error when performing CERCHAR scratch tests are:

HI Scratch tests should be performed on natural failure surfaces.Scratch tests carried out on smooth surfaces (cut or polished)tend to promote steel pin skating resulting in low indice values.

Some rocks are so hard that the tool is unable to "cut" a 10 mmgroove without skating. The steel pin is blunted at the beginningof the scratch, and does not interacted proper with the rock overthe length of the scratch to form a genuine abrasion wearflat.

When testing hard rocks it is therefore necessary to examine thespecimen after each scratch to ensure that the tool has bitten intothe rock, rather than just skated over the surface. Precautionsshould be taken when attempting to measure non-symmetrical orlopsided wearflats. Typically, these measurements should bediscarded.

• Over-representation of one mineral type or individual grainalong the 10mm long groove leading to a pronounced scatteringof scratch test results. This effect is typical for very coarse

103

grained rocks such as augen gneiss and rapakivi granite.

& In anisotropic and banded rock such as mica gneiss withcentimetre thick layers of quartz, a representative abrasivityvalue for this laminated rock type is difficult to assess.

9 In the case of weak and non-abrasive rocks (CAI < 0.7), indicevalues are relatively undifferentiated. Some rocks are so weakthat no detectable wear can be seen on the steel pin at the end ofa scratch test.

The CERCHAR Abrasivity Index scale ranges from 0 to 7. Typical indiceranges for some common rock types are given in Table 3-15.

The following relationship between the CERCHAR Abrasivity Index, CAIand Vickers Hardness Number Rock, VHNR for non-weathered rocks hasbeen established for CAI > 0.7 as:

CAI = VHNR/145

Table 3-15. CERCHAR Abrasivity Index CAI for some common rock types.

Rock Type CAI

Igneous RockBasalt 1.7 - 5.2Diabase 3.8 - 5.4Andesite 1.8 - 3.5Diorite/Syenite 3.0 - 5.6Granite 3.7 - 6.2

Sedimentary RockLimestone 0.1- 2.4Sandstone " 0.1-2.6Sandstone2' 2.3 - 6.2

Metamorphic RockPhyllite 1.3 - 4.3Mica schist and mica gneiss 1.8 - 5.0Felsic gneiss 3.7 - 6.3Amphibolite 2.8 - 3.7Quartzite 4.8 - 7.3

!) with carbonate and/or clayey cementation of mineralgrains

2) with SiO2 cementation of mineral grains

104

Vickers Hardness Number Rock, VHNR

A simplified approach to rating rock wear capacity is the use of rock surfacehardness or mineral microindentation hardness. The most commonly useddiamond tipped microindenters are Vickers (a square based pyramid) andKnoop (an elongated based pyramid). Most systematic studies of oreminerals have employed Vickers microhardness determination and thistechnique has been widely adapted in ore microscopy.

The hardness number is defined as the ratio of the applied indenter load(kilogramme force) to the total (inclined) area of the permanent impression.Microindenter hardness tests on minerals normally employ loads of 100 ...200 gf; resulting in indentations with diagonal lengths of 5 ... 100 urn. Forprecise results, the load employed should be stated since VHN valuesobtained are not independent of load. For comparison, test loads andnotation used for rating cemented carbides are:

Test Test Load Notation for Metal Testing

HV05

HV30

Hot hardness ratingHardness ratingK/c determination

500 gf30 kgf50 kgf

The rock matrix is typically inhomogeneous on the scale of testing and mayconsist of several minerals of widely varying individual grain hardnesses.The Vickers Hardness Number Rock VHNR or the "surface hardness" of therock is an aggregate value based on the weighted hardness values of itsmineral constituents, i.e.

VHNR = I( VHNj % mineralj/100) [kgf/mm2/

VHNR = Vickers Hardness Number Rock [kgf/mm2]

% mineralj = percentage content of mineral j in rock specimen [ % ]

VHNj - Vickers Hardness Number for mineral j [kgf/mm2]

Typical mean values for the Vickers (VHN) and Knoop Hardness Numbers,Rosiwal and CERCHAR Abrasivity Indices for a selection ofnon-weathered rock-forming minerals without impurities are listed inTable 3-16.

105

Table 3-16. Typical mean values for Vickers (VHN) and Knoop HardnessNumbers, Rosiwal and CERCHAR Abrasivity Indices for a selection of non-weathered rock forming minerals.

Mineral

corundum

quartz

garnet

olivine

hematite

pyrite

plagioclase

diopside

magnetite

orthoclase

augite

ilmenite

hyperstene

hornblende

chromite

apatite

dolomite

pyrrhotite

fluorite

pentlandite

sphalerite

chalcopyrite

serpentine

anhydrite

calcite

biotite

galena

chalcocite

chlorite

gypsum

talc

halite

sylvite

Chemical Composition

A12O3

SiO2

Fe-Mg-Al-Mn-Ca-Cr silicates

(Mg,Fe)2SiO4

Fe2O3

FeS2

(Na,Ca)(Al,Si)AlSi2O8

CaMgSiA,

Fe3O4

KAlSi3O8

Ca(Mg,Fe,Al)(Al,Si)2O6

FeTiO3

(Mg,Fe)SiO3

NaCa2(Mg,Fe,Al)5(AI,Si)8O22(OH)2

(Mg,Fe)Cr2O4

Ca,(PO4 )3(F,C1,OH)

CaMg(CO3 )2

Fe,.xS

CaF2

(Fe,Ni)9S8

(Zn,Fe)S

CuFeS2

Mg6Si4O,0(OH)8

CaSO4

CaCO3

K(Mg.Fe)3(AlSi3O10)(OH)2

PbS

Cu2S

(Mg,Fe,Al)6(Al,Si)4O10(OH)8

CaSO42H2O

Mg3Si401()(0H)2

NaCl

KC1

Vickers

2300

1060

1060

980

925

800

800

800

730

730

640

625

600

600

600

550

365

310

265

220

200

195

175

160

125

110

85

65

50

50

20

17

10

Knoop

1700

790

560

395

163

0.8

85

32

12

Rosiw

al

1000

141

52

7.3

4.3

4.08

0.85

0.82

CE

RC

HA

R

5.7

4.7

4.7

4.4

3.1

3.3

1.9

0.8

0.3

0

106

3.5 SOME ADDITIONAL ASPECTS OF TOOLCONSUMPTION

Cutting Rock with Drag Tools

When extending the application area or performance of cutting tools such asdrag tools through the introduction of new tool designs and cementedcarbide grades, the main items of rock cutting to be considered are:

Tool depth of cut

• shallow depths of cut result in adhesive wear, especially in hardand abrasive rock

• large depths of cut result in structural overload, especially forradial picks in hard rock.

Counter-measures against adhesive wear

• by introducing waterjets to prevent or reduce the occurrence ofadhesive wear mechanisms due to heat build-up in the tool tip

S by introducing more wear resistant insert materials such ascoarse grained cemented carbides with improved hot-hardnessproperties or PCD coatings on cemented carbide inserts

• use of VSD cutterhead motors to maintain cutting velocitiesbelow VCriticai.

Counter-measures against structural overload

M use of VSD cutterhead motors to reduce the effect of cutterheadbouncing and impact shattering of tool tips and impacthammering damage to toolholders

• use of well balanced cutterheads, stiff booms and cutting controlsystems to regulate tool depth of cut so as to reduce cutterheadbouncing

S use of conical tools is less sensitive to structural overloadingthan radial picks.

Drag tool wear rates are highly dependent on tool cutting velocities due tofrictional heating originating at the rock/tool tip interface. Critical cuttingvelocities refer to the corresponding tool wearflat thermal threshold valueswhere adhesive wear commences. These threshold values are readilydetermined as the knee-point on drag tool wear rate/cutting velocity graphs,Figure 3-19. The relationship between drag tool wear rates and tool cuttingvelocities can be expressed as:

107

Tool Cutting Velocity Tool Insert Wear Rates

Under critical v < vmtKai Abrasive wear mode WR - ffva'6J

Over critical v > v(T,,,(.,,, Adhesive wear mode WR = f f v 3 0 /

Critical cutting velocities (or critical wearflat temperatures) for cementedcarbide inserts are dependent on the:

B wear capacity of rock8 carbide grade hot-hardness and thermal conductivity (indirectly

WC grain size and Co content)& effective cooling of the tool tip wearflat by waterjets where the

frictional heating originates.

Cutting Rock with Roller Disk Cutters

When extending the application area or performance of cutting tools such asroller disks through the introduction of new tool designs, steel qualities andcemented carbide grades; the main items of rock cutting to be consideredare:

Tool depth of cut

S shallow depths of cut result in disk rim tip wear• large depths of cut result in structural overload of disk rims;

especially when using large diameter disk cuttersffl large depths of cut result in premature stud shearing due to the

large stud protrusion from the disk required to obtain thesedepths of cut

M large depths of cut result in excessive steel disk rim wear due todisk ploughing in soft rock. This wear mode is called self-sharpening wear and is characterised by excessive steel diskrim side wear due to tempering and loss of disk rim workhardening.

Counter-measures to reduce tool consumption

H the effect of self-sharpening wear can be contained by usinglarge diameter cutters with blunt rims so as to reduce theploughing-like action of the disk rim in soft rock. Typically, verywide constant section disks are used in these conditions

S the emery wheel wear effect can be reduced by using more wearresistant tools, i.e. studded cemented carbide roller disk cutters.

S the steel disk rim chipping effect can be reduced by lowering thenormal force level per disk or use of tougher steels

S the disk rim mushrooming effect can be reduced by usingimproved heat treated steels

108

8 the general trend has been to increase disk diameter in hard andabrasive rock to enhance tool life. The problem with largediameter disk cutters is the elevated cutter loads required tomaintain acceptable depths of cut and the ability of the machinestructure to accommodate these high loads. Typically, smalldiameter disk cutters require significantly lower cutting forcesthan large diameter disks, but tool life is also significantly lower

5 in extremely abrasive rock; the trend has been to use cementedcarbide insert studded roller disk cutters. However, largecemented carbide inserts are more sensitive to structuraloverload and prone to premature failure including the ripplebreakage effect for single row studded disk cutters .

Counter-measures against structural overload

6 use of VSD cutterhead motors to maintain cutting velocitiesbelow Vcriticui and reduce cutterhead bouncing

M use of well balanced cutterheads and cutting control systems toregulate tool depth of cut so as to reduce cutterhead bouncing.Cutterhead bouncing typically occurs when operating in mixedface conditions or shears resulting in impact shattering of diskrims and impact load damage to bearing surfaces resulting infrozen bearings.

3.5.1 Laboratory Studies of Disk Cutter Life for Off-Line Kerf Cutting

Some interesting findings as to off-line roller disk kerf cutting (disks do notroll in a previously cut kerf or tool path, but do have an adjacent kerf intowhich chips can break free) are the Bochum Micro-Disk Lathe Cutting Testresults.

The micro-disk lathe cutting data and normalised test results are shown onthe bochum35.xls file printout in Appendix 3, i.e.

Disk normal force Fn = Fn,, • ( DOC • S / 3 )"2

Frii i = rock resistance to off-line kerf cutting

= critical normal force [kN/disk]

Disk weight loss WLM = WLM,, ( DOC S / 3 )

WLM| i = rock wear capacity for off-line kerf cutting

= critical weight loss [mg/m]

109

Correlations between the rock wear capacity values for micro-disks WLMnversus rock abrasivity indices for the Bochum Rock Suite gave thefollowing ranking with regard to goodness of fit:

8 VHNRS CA1 for "Rough Surfaces "S Wear Index F (The traditional Wear Index F values proved

basically useless for prediction purposes due to the importancegiven to rock specimen mean quartz grain size in equation13-3]).

The Rock Cuttability Window for Intact Rock in Figure 3-24 is a scatterplot of rock wear capacity versus rock resistance to off-line kerf cutting withmicro-disks. The Bochum Rock Suite Cuttability Window for Intact Rockclearly illustrates that:

• rock resistance to off-line kerf cutting of intact rock relatespoorly to the uniaxial compressive strength UCS

8 rock wear capacity of intact rock has a markedly larger range ofvariation than rock resistance to off-line kerf cutting.

2.0

"3)

o(0aAoaa>

uo

K

Ur£mi

Sandstone^j j \1 !

sai

/

/,1

}

LiQ

V\

1 V

fAIr

/ T *•

/

1 t{

\ .idstone -W

>ne

iss

~-« Gabbrc

uart.zile

Basalt

t i c

i/P

*J

1.0

0.80.70.60.50.4

0.3

0.2

0.1

0.080.070.060.05

1 2 3 4 5 6 7 8 910

Rock Resistance to Kerf Cutting, F n ^ (kN/disk)

Figure 3-24. The Rock Cuttability Window for Intact Rock for the Bochum0 35 mm Micro-Disk Off-Line Lathe Cutting Tests.

110

3.5.2 Field Studies of Disk Service Life for In-Line Kerf Cutting

The following factors which determine disk service life when rated inm3/cutter must be considered when normalising field data:

• disk rim wear resistance and amount of wearable material ondisk rims

• type of cutting mode, i.e. in-line kerf cutting (TBM's) and off-line cutting for sweeping cutterheads (Robbins Mobile Miner)

• rock powder wear capacity on disk rims for in-line kerf cutting• rock surface hardness, which indirectly determines where disk

rim wear will take place, i.e. at the tip, sides or bothM rock mass fracturing and/or mixed face conditions• cutterhead curvature and diameter8 well balanced cutterhead design so as to avoid individual disk

over-loading, i.e. taking the following into consideration:• number and positioning of disk cutters on the cutterhead• frequency of cutter bearing failures, disk slippage from the

cutter body or hub, disk rim chipping, etc.& net advance rates.

The relationship between disk service life and tunnel boring machine netadvance rates is given by:

' m 3 = (KD2/4) (Lh/N) AR [m3/cutter]

Lh = cutter disk life in hours [ h/cutter ]D = cutterhead diameter [ m ]N - number of tools on the cutterheadAR = net advance rate [ m/h ]

The relationship between disk life and rock surface or microindentationhardness shown in Figure 3-25 illustrates that it is necessary to take both themineral type, mineral content and the relative distribution of weak to strongminerals in a rock specimen into account to determine the "effective" timedependent wear capacity of kerf rock powder. Weak mineral fragments arecrushed and compacted to such an extent that harder mineral fragmentsbecome over-exposed in the kerf rock powder resulting in excessive toolwear as illustrated in Figure 3-26. This enhanced wear mechanism is termedthe "emery wheel wear" effect; and becomes more pronounced as thecontent of weaker minerals, such as mica, calcite and even amphibolerelative to stronger minerals such as feldspars and quartz increases. The"emery wheel wear" effect is clearly illustrated in Figure 3-25 for steel diskcutting for tunnel boring in phyllites, micaschists and micagneiss.

I l l

o

100 200 300 500

J Vesicular basalt

Greenstone & greenschist

Arkosite

Granite & felsic gneiss

Quartzite

1000

MAmmmmmm

= % mica + 'MA <15%35%

15%< MA< MA

MA

Vo amphibole

< 35%< 45%> 45%

Vickers Hardness Number Rock, VHNR

Figure 3-25. Envelope curves for 15 1/2" steel disk service life Li,(hours/cutter) as a function of Vickers Hardness Number Rock VHNR forRPM = ( 38/D ), TBM diameter 0 3.5 m and rock type.

Compaction pressure Compaction pressure

Asperity forceon wearflat

Movingresultant

Asperity forceon wearflat

Figure 3-26. The principle relationship between the compaction pressure ofkerf rock powder by a cutting tool and rock powder fragment size on theresulting asperity force and direction on a wearflat.

112

Table 3-17. Example of disk life normalisation based on cutterhead toolreplacements. In practice the illustrated procedure is made by PC software.

Cutterhead Diameter, D

Tools per Line, TPL

Cutterhead Rotary Speed

Net Advance Rate, NAR

0,5 m

1

38RPM

2,0 m/h

Location

on

Cutterhead

Center

Gauge

Cutting hours

Tunnel meters

Toolholder

Number

Ni

1234

0

0

Disk Life, LK

(hours/disk)

50 50100

75 |

50 | 50

50

100

50

75

I100

200

50

100

150

300

50

5075

I200

400

50

I50

10050

75

250

500

50300

600

Location Tool- Kerf Disk Relative Disk Life Disk Disk Disk

on holde Radius Replace- Disk Life Life Life Life

Cutterhead N, R, ments LN L^ LM LMI

(mm) IM, Ru (h/disk) (km/disk) (m/disk) (m3/disk)

Center

Gauge

Total

Average

1

2

3

4

50

125

200

250

6

3

4

6

0,79

1,58

1,19

0,79

50

100

75

50

35,8

179,1

214,9

179,1

100

200

150

100

0,79

8,25

11,49

7,07

625 19 4,35 1200 2686,1 2400 117,81

156,25 4,75 1,089 63,16 141,37 126,32 6,20

FORMULAE FOR AVERAGE VALUES

FOR THE CUTTERHEAD

= ( Z I M , / N ) / Z M ,

= N/I(1/LJ

f

Hi-avg

CONTROL

= 156.25/250

= 0.625

= 4 - 3 0 0 / 1 9

= 63.16

= 1 ( 2 J I R , R P M - 6 0

N/Z(1/LJLBNAR

= 7iR2 -Ln , -NAR/N

k,.avg =0.625 • 2n • 0.250 • 38 • 60 • 63.16/1000

= 141.38

= 4 - 6 0 0 / 1 9

= 126.32

= p - 0 . 2 5 2 - 6 0 0 / 1 9

= 6.20

Note The average relative life for the cutterhead, 1.089, is the parameter used as a basis for thecutterhead diameter correction factor kj - incorporating the effect of reduced life for center andgauge cutters.

113

3.6 ROCK CUTTABILITY WINDOWS

One of the main objectives for testing rock specimens, apart from fieldfollowup work for rating jobsite rock mass cuttability and machineperformance, is to visualise a generalised geotechnical "excavator workarea" or rock cuttability window for the evaluation of rock cuttingproductivity and economic excavation range of rock by tunnellingmachinery.

The Rock Cuttability Window for Intact Rock as illustrated in Figure 3-27is a scatter plot of rock wear capacity versus rock strength for rockspecimens tested during the TM60 R&D Programme. In essence, Figure3-27 is a scatter plot of rock surface hardness versus rock bulk strength.

<o0>

'352

<

O

WO

6

5

A

*

A

0

I Micro-fissured Rock 1

j

•L-L n

Rock |

: «A; j

yT A

• •

Anisntrnpir |

D D

XY

•

X ••

"A _/<

y

Ultramafic |

y*y

/o•

A

X

X

a

V•

Serpentinite P1Serpentinite P3

AmphiboliteBiotite SchistBiotite GneissRhyolitic Tuff

GranitePegmatiteFelsic Gneiss

DolomiteGeneral Trendline

50 100 150 200 250 300 350 400

Uniaxial Compressive Strength, UCS (MPa)

Figure 3-27. The Rock Cuttability Window for Intact Rock - a scatter plotof rock wear capacity versus the bulk strength of rock for rock specimenstested during the TM60 R&D Programme.

114

There is a self-evident trendline illustrating that rock wear capacity increaseswith rock bulk strength and mineral surface hardness. However, there aresome important exceptions as noted in Figure 3-27 such as:

• ultramafic rocks characterised by relatively high bulk strengthbut low rock wear capacity values. Ultramafic rocks haverelatively high bulk strength values since fractures primarilypropagate through mineral grains; and not along grainboundaries

S anisotropic rocks characterised by low bulk strength but highrock wear capacity values. Anisotropic rocks have relatively lowbulk strength values due to fracture propagation primarilyalong planes of schistosity. This effect is especially pronouncedfor uniaxial compression tests of rock specimens.

• porous rocks characterised by low bulk strength but high rockwear capacity values. These rock types have relatively lowstrength values due to rapid fracture propagation originating atand radiating from voids in the rock matrix when in stress; thusenhancing the cuttability or drillability of intact rock.

• micro-fractured igneous rocks characterised by low bulkstrength but very high rock wear capacity values. Observationsshow that this micro-fracturing seldom, if ever, enhances therock cuttability or drillability of intact rock. The phenomenon istypical for Pre-Cambrian granites, granodiorites and felsicgneisses in the Fenno-Scandian Shield.

• weathered and decomposed rocks characterised by low bulkstrength and low rock wear capacity values due to chemicalalteration of the mineral grains.

115

4 LINEAR CUTTING TESTS

4.1 LINEAR CUTTING TEST APPARATUS

Most mechanical tools used by excavators to break rock do so by indentingthe rock surface, i.e.

roller disk cutters (with wedge-shaped or constant section disks)studded or carbide insert roller disk cuttersrotary tricone bitsdrag toolspercussive drilling bits.

The distinguishing characteristic of an indentating roller cutter is that thedisk penetrates in a direction more or less perpendicular to the rock surfacebeing cut, in contrast to a drag tool, which travels parallel to the surface thatis being cut.

In its simplest form, an indentation tool is thrust into a surface normally, sothat it either displaces material by some kind of plastic flow or compaction,or else forms a crater by brittle fracture. The cutting process progresses bymoving the tool forward to a fresh surface during the interval betweensuccessive loading cycles due to these indentation craters (bit indexing forpercussive bits); so that a line of indentations or craters is formed. If thecraters are very closely spaced, a continuous path, kerf, or groove is created.At the same time the rock between an adjacent and previously cut kerf isloosened as large chips. This chip loosening process can be studied in detailusing high-speed photography of linear cutting tests.

The objective of rock cuttability studies is to develop a model to predict thecutting forces acting on an indenting tool from a knowledge only of rockmass properties, tool tip and kerf geometries, and depth of cut. If thisobjective is met, then in conjunction with the knowledge gained fromcutterhead and machine configuration work, it will be possible to designexcavators with optimized rock breakage operations and minimized machinemass.

The Linear Cutting Machine, LCM

The LCM is a laboratory test apparatus designed to provide data for theevaluation of rock cuttability and kerf cutting processes so as to makeaccurate performance estimates for various mechanical excavators; such astunnel boring machines, raiseboring and boxhole machines, mobile miners,continuous miners and roadheaders. LCM's have been used extensively overthe last two decades to predict excavator field performance in a wide rangeof rock types and to generate data for the optimal design of cutterheads;including tool design, kerf spacing, cutterhead tool lacing design and

116

cutterhead force and torque balancing.

The LCM test apparatus is capable of simulating field cutting conditions byenabling the testing and performance assessment of full sized cutters underoperating conditions encountered in the field. The LCM can generate theentire range of cutter loads and depths of cut experienced on an excavatorwhile allowing the testing and evaluation of different kerf spacings, depthsof cut, cutting velocities, use of waterjets and other operational parameterswhich may influence excavator performance in the field.

However, the use of linear cutting tests is somewhat limited in that only theeffects of intact rock properties on rock mass cuttability can be evaluated.The effects of rock mass jointing properties such as type, frequency andorientation, and mixed face conditions on rock mass cuttability can not beevaluated by linear cutting tests. In addition, these properties often have onlya minor effect on an individual cutting tool, whilst for cutting with multiplearrays of tools, i.e. a cutterhead, their effect on rock mass cuttability can besignificant.

A schematic illustration of a LCM test apparatus is shown in Figure 4-1.Basically, a LCM incorporates a large, stiff reaction frame onto which a testcutter and a load cell assembly are mounted. The load cell monitors andmeasures the forces acting on the cutter in the three mutually perpendiculardirections, i.e. normal, side and rolling.

_ ____ Side ForceRolling Force

Normal Force

Rock breakage is effected when the cutter is pressed against the rocksurface. In brittle rock, the loading causes the region immediately under thecutter to be crushed; at a later point in the loading cycle tensile cracksinitiate from the edges of this crushed zone and these propagate either to therock surface or to an adjacent, previously cut kerf or groove, to form rockchips.

117

n Feed Cylinder

DOC Spacers

_LL

3D Load Cell

Cutter Saddle

/ • t Cutter Spacing Cylinder

Sled

M

Pass 1

Pass 6

Depth of Cut

Kerf Spacing

Figure 4-1. Schematic view of a Linear Cutting Machine.

The normal force is the cutter axle force component perpendicular to therock surface, and is the force required to indent/crush the rock at therock/tool tip interface. This force is used to determine the excavator thrustrequirements to achieve a given rate of advance. The rolling force acts in thedirection of cutter travel, parallel to the surface being cut. These cutter axleforce components are used for calculating machine torque and powerrequirements. The side force acts perpendicular to the direction of travel inthe plane of the surface being cut. Its primary use is in determining theoverturning moments imposed on a cutter during excavation. The generatedside forces also play a minor role in cutterhead balancing and the mainthrust bearing life expectancy.

118

It should be noted that all three force components acting on a disk cutter arerelated to each other. In general, the rolling force directly follows the normalforce fluctuations, but at a much lower magnitude. The side force displaysan opposite trend to the normal force whereby it increases when the normalforce experiences a sudden drop after the formation of large chips. Ingeneral, for roller disk cutters, the rolling force is approx. 10% of the normalforce. The ratio of rolling to normal force, also known as the cuttercoefficient, increases with tool depth of cut. This is the reason whymechanical excavators usually become torque and power limited whenexcavating softer rock formations where significant tool depths of cut can bemaintained. The reverse is true for hard rock excavation where the excavatorthrust capacity is usually reached first, making the system thrust limitedrather than torque limited.

As illustrated in Figure 4-1, the LCM rock sample is held within a structuralframe box featuring a tapered cross-section to provide sample confinementduring testing to prevent splitting of the rock sample. The sample box ismounted on a sled riding on a pair of rails. A servo-controlled hydraulicactuator capable of generating a wide range of cutting velocities is used tomove the sample box under the cutter. Rock samples are cast in concretewithin the sample boxes and allowed to cure for about a week prior totesting. After curing, the sample box is mounted onto the machine sled.

Cutting tests are conducted with a constant tool depth of cut, i.e. cutter diskpenetration is held constant and the forces required to maintain thispenetration are measured. The depth of cut is set by inserting metal spacersbetween the load cell assembly and the main cross-frame of the machine.

After placement in a LCM, the surface of the rock sample surface ispreconditioned by taking several passes with a cutter at fixed kerf spacingsand depths of cut. This serves two purposes. First, the preconditioningcreates a damaged rock surface as is typical for in-line kerf cutting andrepresentative for field cutting conditions where the cutters operate on asurface damaged by their previous passings. Secondly, data recorded duringthe preconditioning passes provide insight as to the level of forces to beexpected for different depths of cut. This information is then used toformulate a test matrix regarding the selection of kerf spacings and depths ofcut to be used for actual testing and data recording.

Prior to the start of recorded cutting tests, the load cell is calibrated byloading the cutter using a hydraulic actuator and measuring the load celloutput voltage. A computer-based data acquisition system is used to recordand analyze the cutter axle forces measured by the triaxial load cellassembly. The system is typically programmed to scan each force channel ata rate of 1000 readings per second (sampling rate 1000 Hz), providingseveral thousand measurements for each cut made across the rock samplesurface.

Once a test is completed, the recorded data is analyzed by computer to

119

produce a test summary containing information on average, minimum andmaximum cutting forces, ratio of forces, specific cutting energy and otherrelevant test data. If desired, the system can also generate trace printouts ofindividual cutting forces; thereby illustrating their variation with time andthe dynamic behaviour of rock failure and chipping along the tool path.Such information is useful when analyzing and evaluating machinevibrations for three-dimensional balancing of cutterheads.

No data is recorded for cutter travel less than approx. 150 mm away fromthe sample ends. The purpose is to avoid any potential end-boundary effectson the cutting forces. Micro-switches programmed in line with this selecteddata window are utilized to start and stop the data acquisition system. Inaddition, the side cuts for each pass are excluded from the data base toeliminate potential side-boundary effects.

Once a particular test is completed, the rock surface is again preconditionedby taking several passes at the desired kerf spacing and depth of cut for thenext recorded test series. This is necessary to eliminate any effects of theprevious test settings.

In addition, the roller disk itself can be instrumented with strain ortemperature gauges to enable more detailed studies of rock/tool tip interfacephenomenon.

4.2 PERFORMANCE PREDICTION MODELLING OFROLLER DISK CUTTING

The basic principles for scaling laboratory and field roller disk cutting datahave been presented in Chapter 2; A Phenomenological Model for theCutting Action of Roller Disk Cutters.

For roller disk cutting, the normal force, Fn was found to be proportional tothe disk rim contact area AcOn (or footprint area); thus enabling the followingfunctional relationships to be established for in-line kerf cutting:

Fn = constant-C- Acon • S*" • 0 s2 • / { a } [2-12b]

Pi = (32 = 1/2 ; the actual scaling exponent can bedetermined by multivariate regressionanalysis of the entire cutting data base

Acon = constant • W • d m • D O C m [2-13]

Consequently, by substituting equation [2-13] into [2-12b], the roller disknormal force can be expressed as a function of tool depth of cut, disk rimand kerf cutting geometry, and rock mass strength as:

Fn = constant a • W • d m • DOC m • S "2 • O m • / { a } [2-18/2-21 ]

120

4.3 PERFORMANCE PREDICTION MODEL FOR ROLLERDISK CUTTING

Linear Roller Disk Cutting Test Data Normalisation

The recorded linear cutting test data for a given rock/tool combination canbe reduced to two cutting test constants, i.e.

Fn, _iinear = rock cuttability/disk rim constant or critical normal forceC = cutter constant

These two cutting test constants summarize and describe the whole rollerdisk cutting process, albeit only for one individual linear cutting disk. Theexpressions required for scaling and normalizing the recorded linear rollerdisk cutting test data are:

Normal Force Fn = Fn,.|inear • DOC 1 / 2 [4-1]

Fn,.,inear = constantUnedr- c • W • d m • S m

Rolling Force k,inear = Fr / Fn = CXAineM • D O C m [4-2]

Power Demand Pdemund = Fr • v

Specific Energy SE = Pdemand / ( DOC • S • L / 1000 2 )

= k Fn- v / ( D O C S - v • 6 0 2 / 1 0 0 0 2 )

( S • 6 0 2 / 1 0 0 0 2 ) [4-3]

Published linear cutting test data from the Colorado School of Mines, UKTransport and Road Research Laboratory and Anglo American Corporationhave been compiled and the data normalized in accordance to the aboveexpressions. This work is included in Appendix 1 as Excel file printouts.

Performance Prediction Model for Linear Roller Disk Cutting

A summary of the cutting test constants, Fni.|jnear and Ci-unear , fromAppendix 4 are listed in Tables 4-1 and 4-2. The linear cutting test constantshave, for ease of comparison, been scaled to a standard disk rim and in-linekerf cutting geometry, i.e.

d = 432mm, W = 12.7mm, S = 76.2mm and DOC = 1.Omm/pass

121

Table 4-1. A summary of the cutting test printouts in Appendix 4.

Exel file Rock Type Compr. Tensile Density Porosity Drilling Disk Disk KerfStrength Strength Rate Diam. Width Spacing

UCS BTS p n Index d W S(MPa) (MPa) (g/cm3) (%) DRI (mm) (mm) (mm)

1.4" Micrcbochum35bochum35bochum35bochum35bochum35bochum35bochum35

> Disk Off-Line Lathe TestsBasaltGabbroGneiss/PGneiss/NGraniteQuartziteSandstone

5" Mini Disk Testshdrk51hdrk52hdrk53zimchr51zimchr52tivcan51

Felsic GneissNoriteNoriteChromite OreSerpentiniteWelded (Rhyolitic) Tuff

7 7/8" Disk Testsgresand1shagran1

SandstoneGranite

12" Disk Testsfennl Norite

15.5" Disk Testsholslim 1holslim2daksand2

Holston LimestoneHolston LimestoneDakota Sandstone

17" Disk Testsbersand 1bersand2indilimlindilim2lesbas1Iesbas2Iesbas3Iesbas4colosprlcolospr2colorg 1colorg2colorg3colorg4colorg5franrid 1franrid2peolpeo2

Berea SandstoneBerea SandstoneIndiana LimestoneIndiana LimestoneBasaltVesicular Basalt (NAB)Vesicular Basalt (MAB)Vesicular Basalt (HAB)Colo. Spring GraniteColo. Spring GraniteColo. Red GraniteColo. Red GraniteColo. Red GraniteColo. Red GraniteColo. Red GraniteWelded (Rhyolitic) TuffWelded (Rhyolitic) TuffColo. Red GraniteGranodiorite

400168181180170180165

269297297

60165

50155 1

254 1

118 1118 152

46464444

9,9

3,50,8

1,9

0,10,13,9

1,11,15,25,2

188 14,997 12,991 1

111144144138 1138 1138 1138 1138 1

1,97,97,87,81,7U1,71,71,7

86 14,795 1

138 11,51,7

221 13,1

2,77

2,352,63

2,92

2,682,68

2,112,112,342,34

2,622,62

2,292,28

2,71

14,80,4

0,20,2

19,119,112,512,5

7?

0,60,6

8,68,6

0,3

282020

50

7272

434742544444

5151

42

Note: DRI values from the same location, but seperate specimen

35353535353535

127127127127127127

200200

305

394394394

432432432432432432432432432432432432432432432432432432432

6,48,28,28,28,2

15,715,7

9,4

12,7011,0511,05

12,7019,0512,7019,0512,7012,7012,7012,7012,7012,7012,7012,7012,7012,7012,7011,413,712,70

12,70

batches

3333333

19,0519,0519,0519,0519,0519,05

76,276,2

19,05

76,276,276,2

76,276,276,276,276,276,276,276,276,276,276,276,276,276,276,276,276,276,276,2

122

Table 4-2. A summary of the cutting test printouts in Appendix 4.

Exel file Peak/MeanForceRatio

Peak/MeanForceRatio

Frpeal/Fr

Peak/MeanForceRatio

* speak' ^ s

1.4" Micro Disk Off-Line Lathe Testsbochum35bochum35bochum35bochum35bochum35bochum35bochum35

5" Mini Disk Testshdrk51hdrk52hdrk53zimchr51zimchr52tivcan51

3,192,092,071,571,63

7 7/8" Disk Testsgresand 1shagran1

12" Disk Testsfennl

15.5" Disk Testsholslimlholslim2daksand2

17" Disk Testsbersand 1bersand2indilimlindilim2lesbas 1Iesbas2Iesbas3Iesbas4colosprlcolospr2colorg 1colorg2colorg3colorg4colorg5franrid 1franrid2peolpeo2

2,011,872,211,861,892,212,282,061,86

4,223,103,111,801,80

2,622,953,023,002,902,422,412,142,25

24,00

6,2118,00

9,006,275,874,573,045,79

13,61

Sdev/MeanRatio

^*nt I-.sdev

Critical EstimateNormal FormulaeForce

Fnll/Fnl, (kN/disk)

0,470,380,350,290,31

5,813,423,624,183,725,092,83

22,5822,3626,2314,435,48

13,67

19,2360,40

43,07

71,1672,0524,80

22,4825,8922,8334,5479,9656,0347,4350,3891,6075,5661,4976,5360,1572,3675,1541,2742,9173,59102,95

Fnll-Est(kN/disk)

23,9620,6526,46

5,3414,70

21,4066,35

40,20

57,3549,9021,99

23,4135,1222,3933,5995,6849,3646,3156,4973,2873,2870,2370,2370,2370,2370,2339,3952,2370,23112,47

CutterConst

c,

0,0900,0780,0770,0790,0810,078

0,0600,068

0,057

0,0510,0390,056

0,0420,0450,0420,0380,0320,0380,0430,0430,0460,0470,0450,0350,0440,0450,0460,0450,0540,0400,037

EstimateFormulae

C|-Esl

0,0800,0800,0800,0800,0800,080

0,0640,064

0,052

0,0450,0450,045

0,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,0430,043

Specific! Energy

SE-ESI

(kWh/m3)

29,525,329,516,66,5

15,6

4,214,9

35,9

13,110,15,1

3,44,33,54,79,47,87,47,9

15,313,010,29,89,6

12,012,66,88,5

10,613,9

123

These scaled cutting test constants are shown on the following graphs as a:

( i ) scatter plot of the scaled critical normal force Fnu^iinear (or standardcuttability resistance) versus the uniaxial compressive strength, UCS.

(ii) scatter plot of the cutter constant, C\.\imar versus disk diameter, d.

i76

linea

r (

U,

rce,

ou.

Nor

mal

ao

200

150

100

80

60

50

40

30

20 Ai

y

•

. 1/>

<

* 10

o10 20 30 40 50 6080 100 150 200250300

Uniaxial Compressive Strength, UCS (MPa)

Figure 4-2. Scatter plot of the scaled critical normal force Fnn.76imear (orstandard cuttability resistance) versus the uniaxial compressive strengthUCS; for d = 432 mm, W = 12.7mm, S = 76.2 mm and DOC = 1 mm/pass.

ucaV,coow0)

o

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

_ ^ _ _»

• i^ t

Ir100 200 300 400 500 600

Disk Diameter, d (mm)

Figure 4-3. Scatter plot of the cutter constant, Ci-imear versus disk diameter, d.

124

Finally, the presented cutting test constant prediction equations [4-4] and[4-5] for linear roller disk cutting were determined by linear regression ofthe listed constants in Tables 4-1 and 4-2.

Normal Force

Rolling Force

Fllll-761inear

*-l-linear

= 0.00195 UCS W ( d S / 76.2 ) 1/2

= 0.0433 ( 432 / d ) 1/2

[4-4]

[4-5]

Example of Prediction Model Application

Rock Type GranodioriteUniaxial compressive strength, UCS 141 MPaBrazilian tensile strength, BTS 9.1 MPaBulk density, p 2.69 g/cm3

Young's modulus of elasticity, E 67.7 GPaPoisson's ratio, v 0,27Drilling Rate Index, DPJ 46Cerchar Abrasivity Index, CAI 5.9Vickers Hardness Number Rock, VHNR 780

Mineral Content Percentage (thin section)Quartz 34 %Plagioclase 32 %Orthoclase 20 %Biotite 14 %

Disk Cutting GeometryDisk diameter, d 127 mm (5")Disk rim contact width, W 8.2 mmKerf spacing, S 25 mm

Table 4-3. Prediction of mini-disk performance for DOC = 5 mm/pass inGranodiorite.

Critical normal force FnHinear = 0.00195 • 141 8.2 ( 127 25 / 76.2 ) m

Normal force

Cutter constant

Cutter coefficient

Rolling force

Specific energy

F r i n ^ = 14.6 • 5 m

CMinear = 0.0433 • ( 432 /127 ) m

k,inear = 0.080 5 m

Fr,inear = 0.179 32.6

SEiineal = 0.080 14.6 / ( 1 • 25 6 0 2 / 10002 )

= 14.6kN/disk

= 32.6kN/disk

= 0.080

= 0.179

= 5.82kN/disk

= 13.0kWh/m 3

125

4.4 RELEVANCE OF LCM TEST CUTTING RESULTS TOFACE CUTTING PERFORMANCE

The linear cutting test constants Fni i-76iinear and Ci_iinear, combined with thecutterhead tool lacing design, can be used to predict partial or full facecutting performance as exemplified in Chapter 5.6. However, the followingparameters and their effects on cutting performance must be considered:

8 linear cutting rig stiffness3 recorded cut lengthS in-line kerf cutting modes.

Effect of Linear Cutting Rig Stiffness

Hydraulic rams are the most common method of providing thrust ontunnelling machines as well as linear cutting rigs. However, due to thecompressibility of mineral oil, hydraulic systems are flexible and the axialstiffness of cylinders is reduced as the stroke is increased.

The hydraulic stiffness for individual tools mounted on a cutterhead can beexpressed as:

Hydraulic stiffness per tool = n A • K/(N • L)

where: n is the number of thrust cylinders working on the cutterheadA is the cross-sectional area of one cylinderN is the number of tools on the cutterheadL is the distance between the cylinder head and the piston faceK is the bulk modulus of the hydraulic oil (typical bulk modulusfor mineral oils with no entrained air taken as 1700 N/mm2).

Typical hydraulic stiffness range for TBM cutterheads is 500 - 5000 kN/mmdepending on the piston face position in the cylinder, and correspondingly20 - 200 kN/mm for individual tools on the cutterhead. Typical hydraulicstiffness range for individual drag tools mounted on boom supportedcutterheads for lightweight roadheaders is 2 -15 kN/mm.

The linear cutting test constants for Gregory Sandstone are presented inTable 4-4. The results show that the linear cutting rig stiffness has apronounced effect on the cutting performance of roller disk cutters, i.e. asthe stiffness decreases, both the rolling and normal forces acting on the diskand the specific energy increase.

The effect of machine stiffness on normal forces can be stipulated, i.e.

Fn = f{ ( Hydraulic Stiffness ) •"*}

126

Table 4-4. Linear cutting test constants in Gregory Sandstone (for detailsrefer to the gresand 1 .xls file printout in Appendix 4).

Linear Rig Stiffness Cutter Constant(kN/mm) C,.Unear

Critical Normal Force Specific EnergySE 76llnear

147.621.5

0.05980.0664

19.2330.23

4.197.32

The observed increase in cutter axle forces and specific energy withdecreasing machine stiffness can be explained by studying the normal forcetime traces. Figure 4-4 shows that the normal force curves consist of a seriesof peaks and troughs; with the variations becoming more smooth withdecreasing stiffness. In a stiff machine the load builds up to a peak at whichrock failure occurs and a chip is formed; it then falls back to near zerobefore building up again to another peak. In the case of a soft machine thesame peak normal force is required to cause a chip to form, but in betweenchip formation, the tool is held in contact with the rock by the spring-likeaction of the soft machine.

Thus, the peak normal force is near independent of machine stiffness, as isthe case in stiff and soft testing machines, but the mean normal forceincreases with decreasing stiffness.

In addition, the experimentally determined cutter constants are 11% lowerthan the analytically determined cutter constants in Chapter 1-2; asillustrated below for the standard disk diameter rim of d = 432mm:

100

^ 80

1 6040

20

0100

80

I 6°*"" 40

20

Stiffness = 21.5 kN/mm, DOC = 8 mm, S = 40 mm

Stiffness = 147.6 kN/mm, DOC = 8 mm, S = 40 mm

Time (seconds)

Figure 4-4. Typical normal force traces in Lindley Sandstone.

127

Experimentally C,.linear = 0.0433 •( 432 / d ) m [4-5]

Analytically k = (DOC / d ) m [1-20]

C,,inear = ( 1 / 432 ) m • (432 / d ) m

= 0.0481 ( 4 3 2 / d ) ' / 2

Effect of Recorded Cut Length

The scatter of the experimentally determined cutter constant values, as canbe seen in Figure 4-3, increases with disk rim diameter. This increase inscatter may be due to the relatively shorter recorded cut lengths for the largediameter disks; thus resulting in the formation of relatively fewer large chipsand consequently fewer force peaks over the recorded length of cut.

The effect of insufficient recorded cut length for large diameter linear diskcutting tests may also be the explanation for the linear relationship foundbetween the critical normal force (or standard resistance to roller diskindentation) Fnn-76]inear and the uniaxial compressive strength UCS inequation [4-4]. Both TBM and raiseboring field performance followup workshows that Fnu-76iinear is typically a function of UCS3/4.

As opposed to linear drag tool cutting test results, the peak to mean toolforce ratios for in-line kerf cutting with roller disks listed on the lintestl.xlsfile printout in Tables 4-1 and 4-2 seem to vary little with rock cuttability orkerf cutting geometries. Typical values for the roller disk peak/mean forceratios are:

Normal Force Ratio Fiipeak / Fri^-an ~ 2.0Rolling Force Ratio F r ^ / F r , , ^ = 3 . 0

In addition, the normalization of linear roller disk cutting data shows that theUCS/BTS ratio relates poorly to the critical normal force Fnn.76ijnear. Thisratio is deemed to be of importance for drag tool cutting where it representsa rating of rock toughness. It should be noted that the variation of theUCS/BTS ratio increases with decreasing rock strength as illustrated inFigure 3-7. Drag tool cutting is typically used in low strength, low abrasiverock.

Effect ofln-Line Kerf Cutting Modes

Kerf spacing has a pronounced effect on how the rock between adjacent (notnecessarily neighbouring) kerfs breaks out as chips. The resulting cuttingmodes are termed as the single tool pass or multiple tool pass cutting modes.

128

Single Tool Pass versus Multiple Pass Tool Cutting

Kerf (groove) deepening is the result of multiple tool pass cutting, i.e. whenthe kerf spacing between adjacent cutting tools is too great for the depth ofcut taken during each tool pass to allow the rock between the adjacent toolpaths to break out, then the kerf will be progressively deepened bysuccessive tool passes until breakout occurs. Breakouts will occur when theinduced lateral fracture development required to form chips from thematerial between two kerfs is completed. Kerf deepening is therefore acondition described by insufficient induced lateral fracture lengthpropagation per tool pass as illustrated in Figure 3-4.

Kerf deepening occurs in face cutting operations as a result of toolsoperating under conditions other than those defined by optimum S/DOCratios, i.e.

(i) for low or insufficient machine thrust causing a lower thandesirable depth of cut to be achieved

( ii) insufficient tool strength to maintain the desirable depth of cut( Hi ) hard bands of rock in the face causing a local reduction in depth of

cut(iv) for a badly worn or broken tracking tool causing an effective

increase in kerf spacing for neighbouring tools.

Disk ring

Chip loosening

Lateral fracturepropagation

Adjacent kerf

Crushed and compactedrock powder

W> chips from the 1st tool passingO chips from the 2nd tool passing

Figure 4-5. Kerf formation and chipping at the face.

129

Kerf Deepening and Specific Energy

Specific energy, i.e. the energy required to excavate a unit volume of rock, isused as a basis for comparing the relative efficiencies of selected kerfspacings for linear cutting tests. When the cuttings produced over therecorded length of cut are collected and weighed, the actual specific energyrequired for a cut is:

SEactual = Fr • length of cut I ( weight of cuttings per cut I p ) [4-6]

The average specific energy for a particular pass varies considerably fromcut to cut. This suggests that on some cuts, where a high specific energy isrecorded, kerf deepening occurs since the yield of cuttings is fairly small;whilst on other passes, where a low specific energy is recorded, the kerfdepth has been sufficiently developed to allow breakouts to adjacent kerfs tooccur with a correspondingly larger yield of cuttings.

However, the specific energy is also defined by the cutting test constants, i.e.the calculated specific energy is:

SEcalculaKd = C,,inear • Fn,,inear/ ( S • 60 2I 1000000 ) [4-7]

= constant • CMinear • Fnn.lineiir/ ( S "2 • 602/ 1000000 ) [4-8]

When the specific energy SEactuai is plotted against the kerf spacing to depthof cut ratio, the graph typically reveals a minimum value for the specificenergy; as can be observed for the linear cutting tests in Gregory Sandstoneand Shap Granite (refer to the gresandl.xls and shagranl.xls file printoutsin Appendix 4).

The specific energy is not a function of tool depth of cut, but( kerf spacing ) ' / l as expressed by equation [4-8]. When the two expressionsfor specific energy, i.e. equations [4-6] and [4-8] are equal, this pointcorresponds to the "optimum" kerf spacing for a given tool/rockcombination as illustrated in Figure 4-6.

In-Line Kerf Cutting Modes and Prediction Model Upbuilding.

Kerf spacing for linear cutting tests can be readily varied so that an optimumS/DOC ratio can be found. However, for face or field cutting conditions, nooptimum kerf spacing can be determined since the cutterhead tool lacing isfixed and the rock mass cuttability varies as the tunnel progresses.

The effect of sub-optimal kerf spacing for face cutting conditions manifestsitself as multiple tool pass cutting as shown in Table 4-5.

130

CO

1IUJ

>iS><DUJO

•5

(0

Underbreaking

Single tool pass cutting

Multiple tool pass cutting

\\ \

" • • •

^ S pJ^ODtil

• \

Hum

•

SEactual

SEcalculated

Kerf Spacing to Depth of Cut Ratio, S/DOC

Figure 4-6. Determination of the optimum kerf spacing.

Table 4-5. Effect of cutting modes on chip width and thickness, tool passesand cutterhead advance rates.

Chip Width Tool Passes Cutterhead Advance Rates

Single Tool Pass CuttingW c h i p = S k e r f ( S P R / T P L ) m = l AR = D 0 C n m a . • SPR R P M 6 0 / 1 0 0 0

Multiple Tool Pass CuttingWchip = Skerf m = Tchip / DOCnmax AR**= DOCnmax TPL RPM 60 / 1000

for underbreaking; Tchtp ^typical for partial face drag tooled cutterheads operating in soft rockand for linear roller disk cutting teststypical for full face roller disk tooled cutterheads operating in hardrock with sub-optimal kerf spacing.

131

Multiple tool pass cutting therefore has a pronounced effect on cutterheadadvance rates. Equation [4-1] applies to linear disk cutting tests and singletool pass cutting; not multiple tool pass cutting common for face cuttingconditions where multiple disk arrays are simultaneously in contact with therock. This situation is described by equation [2-25] as a generalizedexpression or envelope type curve for the mean normal force developed inChapter 2.2 for constant section roller disk cutters, i.e.

Fn = / { o, G,c / S, constant • W • d m • DOC m • S "2 } [2-24]

Fn = Fn,, • DOCl/b [2-25]

Fn,, = / { o, G,c / S, constant • W • d "2 • S m }

= rock resistance to multiple pass in-line kerf cutting* rock resistance to single pass disk cutting

b = kerf cutting exponent

The kerf cutting exponent b is the factor in the generalized expression [2-25]which represents the chipping frequency; in other words how many times acutterhead must rotate to achieve a sufficient number of tool passes for acomplete breakout of rock between kerfs at the face as illustrated in Figure4-5.

The following functional relations have been developed in Chapter 2:

Fn = a • constant • W • d m • DOC m • S m [2-18]

Fn = G,c • ( constant • W • d m • DOC m • S m ) m [2-23]

The generalized expression [2-25] used for normalizing field data thereforerepresents a link between these two expressions. Field performancefollowup work has shown that a relationship exists between the kerf cuttingexponent b and the critical normal force Fni . In addition, the disk tipdullness or rather disk rim width has a significant effect on the kerf cuttingexponent b.

Field performance followup work for tunnel boring and raise boringmachines show that the typical range for the kerf cutting exponent b is for:

Studded Roller Cone Cutters 1.5 < b < 3.5

Constant Section Disk Cutters 1.5 < b < 4.5

The principle reasons for the variation of the kerf cutting exponent b arelisted in Table 4-6.

132

Table 4-6. Effect of cutting modes on cutterhead performance and the kerfcutting exponent b in equation [2-25] exemplified for constant section diskcutters.

Tool CuttingMode

Exponent Description of the In-Line Kerf Cutting Process

Single Pass b < 2 Under breaking; characterized by excessive lateralfracture propagation relative to indentation depth andthe volume of rock removed. The kerf spacing shouldin principle be increased.

Single Pass b = 2 Optimum kerf spacing and in-line roller disk kerfcutting conditions for constant section disk cutters.

Multiple Pass b > 2 Kerf deepening; characterized by insufficientinduced lateral fracture propagation relative toindentation depth. However, in hard rock formations,this can also be an indication of insufficient diskindentation depth as illustrated in Figure 4-7. Thekerf spacing should in principle be reduced.

OO

o

u

a.0)

O

Kerf cutting controlledby rock resistance todisk indentation

Envelope Curve [2-25]

Kerf cutting controlled byrock resistance to lateralfracture propagation

Normal Force, Fn (kN/cutter)

Figure 4-7. Illustration of the three different depth of cut predictionequations established for roller disk cutting with constant section diskcutters.

133

The effect of in-line kerf cutting modes has been exemplified for constantsection disk cutters in Table 4-6. A summary of the ideal case conditionvalues for the kerf cutting exponent b for other types of roller cutter disk rimgeometries are listed in Table 4-7.

The roller disk rim contact area Aeon can be used for comparison of thenormal forces obtained for kerf cutting by various disk rim geometries suchas studded and constant section disk cutters.

Table 4-7. Summary of the ideal case condition values for the kerf cuttingexponent b for some typical roller cutter disk rim geometries given singletool pass cutting; and the resulting expressions for the disk normal force Fn.

Disk Type Exponent Normal Force for Single Pass Cutting

. 3/2 c 3/2Pristine Wedge-Shaped Disks b = 2/3 Fn = o • constant • tan p/2 • d • DOC3/2 • S

Studded Disks withHemispherical InsertsStudded Disks withTapered Inserts

b = 1 Fn = o constant • t DOC S / d

b = 2 Fn = a • constant W L • d 1/2 DOC "2 S m

Constant Section Disk Cutters b = 2 Fn = a constant • W d m • DOC m • S m

Constant Section Disk Cutters b = 4 Fn = G,c- ( constant • W d 1/2 • DOC m S " 2 ) "2

134

TOOL AND CUTTERHEAD FORCES ON DOMEDAXIAL ROTATION MACHINES

Axial rotation machines for cutting and boring are devices that rotate acutting head about the axis of advance. In the drilling and excavation of rockand other materials; this category of machine includes items such as rotarydrills, augers, tunnel boring machines, raiseborers, Marietta miners andsome snow ploughs.

This chapter deals with the geometry, motion and forces of axial rotationmachines tooled with roller disk cutters. The intention is to provide a digestof theory for describing the rock cutting process in detail and provide a basisfor performance prediction modelling of in-line roller disk kerf cutting.

5.1 TOOL PATHS, DEPTH OF CUT AND CUTTERHEADADVANCE RATES

Tool Paths for the Sump Cutting Mode

As a cutterhead rotates at a constant angular frequency / and simultaneouslyadvances at a constant axial rate AR, any tool on the cutterhead at a givenradius R\ will follow a helical path around a circular surface of radius R j asillustrated in Figure 5-1.

= 27i * f

Pitch A

Advance Rate AR

Figure 5-1. The helical tool path for axial rotation machines.

135

The Cartesian description of the helix is usually given in parametric form fortool i as:

X; = Rj cos <p

Yj = R] • sin cp

Z, = A R ( t / 6 0 2 ) - 1000

Xj, Y|, Z| = coordinates for tool i at time t

where co is the angular velocity ( to = 2K • f ), (p the total cutterhead rotationangle (cp = cot), and / = ( RPM / 60 ) the angular frequency.

The helix pitch A, or advance per cutterhead revolution is:

A = AR/( / -6O 2 / lOOO)

= AR/ (RPM-60 /1000)

The helical path length Sj is:

Si = ( ( P / 2 : r ) - [ ( 2 7 t R i )2 + ( A ) 2 ] 1 / 2

= <pRr [ 1 + ( A / 2 T c R i ) 2 ] " 2

and the helix angle Pi, defined at a given point as the angle between thetangent to the helix of radius Rf and the tangent to the concentric circle ofradius Ri passing through the same point, is:

tan Pi = vadvance / vro[atlon = A / ( 2TI • Rj)

These relations describe the motion of fixed cutting tools (drag tools), or themotion of roller cutter bearing.

Tool Depths of Cut and Cutterhead Advance Rates

The cutterhead advances by the helix pitch A during each revolution. Thus,for a given rotary speed, the cutterhead advance rate will be:

AR = A RPM-60/1000

The sector between two consecutive cutterhead revolutions or tool pathsrepresents the material cut by one tool pass. Tool depth of cut thereforeequals the helix pitch A, and is independent of the cutterhead rotationalangle cp, i.e.

DOCrw = A

The above discussion is only valid if there is only one tool at each axiallocation (line) on the cutterhead. With more tools evenly spaced at eachaxial location; TPL such trajectories must be drawn to represent the cutting

136

pattern. However, the shape of the freshly cut sector does not change, butthe depth of cut per tool now takes the following form:

DOCnmax = AR/(TPLRPM-60/1000) [5-1]

Equation [5-1] applies to the cutting of materials where chipping betweenadjacent kerfs does not necessarily take place for every tool pass, i.e.

• in metal cutting• in rock cutting where kerf (groove or tool path) deepening

occurs and multiple tool pass cutting is required to allow therock between adjacent kerfs to break out as chips.

Equation [5-2] applies to the cutting of materials where chipping betweenadjacent kerfs does take place for every tool pass, i.e.

DOCrw = AR / ( { 360 / AAPscrolls line } RPM -60 / 1000 )= AR / ( SPR • RPM • 60 / 1000 ) [5-2]

Kerf (groove) deepening can generally be avoided by selecting a kerfspacing that is not too large. The validity and importance of equations [5-1]and [5-2] for both linear and field cutting tests are discussed in Chapters 4and 6.

5.2 CUTTING WITH DOMED AXIAL ROTATIONCUTTERHEADS

Typical for kerf cutting of rock with axial rotation cutterheads is that the:

B individual tool depth of cut is dependent on toolholder locationon the cutterhead

B individual tool cutting forces are dependent on toolholderlocation on the cutterhead

• cutterhead lacing design must incorporate the two abovementioned factors

8 individual tool forces do not vary with cutterhead rotaryposition - but are dependent on tool depth of cut, kerf spacingand cutterhead tool configuration

M actual kerf spacing is a function of cutterhead advance rate, toolline spacing and tools per line for the sump cutting mode.

The principle cutterhead forces are the sum of the generated individual toolcutting forces. Since the principle tool cutting forces Fn, Fr and Fs vary withtoolholder location on a domed cutterhead; an average cutterhead mean toolforce must be determined to simplify field performance followup andprediction modelling work.

137

The variation of depth of cut and cutting forces for individual tools due tocutterhead doming is illustrated in Figure 5-2; and the principle cutterheadforces in Figure 5-3.

Toolholder #N

DOCnm a x ,Fnm a x

tiltj> DOCn., Fn.

tilt i ,.•~ Fn. • cos tilt.

tthrust

Figure 5-2. Generation of individual tool depth of cut and cutting ftorces.

Note: Tool normal forces drop significantly towards the cutterheadperiphery due to cutterhead doming and reduced individual tooldepth of cut in the normal force direction.

138

5.3 CUTTING FORCES ON DOMED AXIAL ROTATIONCUTTERHEADS

Individual Tool Forces for Linear Roller Disk Cutting

The cutting forces generated by individual tools during linear cutting testsare a function of the following parameters:

• tool depth of cut, DOC• tool path or kerf spacing, S* tool cutter constant, C[_nneai

• rock cuttability/tool tip constant or critical normal force, Fni.unear-

The functional relationships between these parameters for linear roller diskkerf cutting have been established in Chapter 2.4 as:

Normal force

Rolling force

Fn

Fr = k= C

Fn

J -linear

t DOC m

• D O C m •

• S m

Fn

[2-18]

[1-21]

Individual Tool Depths of Cut on Domed Cutter heads

The actual depths of cut for individual tools mounted on a cutterhead are acombination of cutterhead advance rates, cutterhead doming and tool lacingdesign. The direction of the tool normal force is always defined as equalingthe direction of tool penetration.

Max tool depth of cut D O O w = AR / ( TPL • RPM • 60 / 1000 )

Individual tool depth of cut DOCnj = DOCn,™* • sin tiltj= DOC,inear ; given tiltj = 90°

Mean tool depth of cut DOCn^an = 1 DOCn, / N= Z D O G w • sin tilti / N= DOCnmax • SINTM

Note: The depth of cut for individual tools in the normal force directionDOCni decreases towards the cutterhead periphery due to cutterheaddoming and resulting toolholder tilt angles.

The dome factor SINTM equals the tilt angle for the mean cutterheadtool, i.e.

SINTM = I sin tilts / N = sin tilt „,,,,

139

Individual Tool Cutting Forces on Domed Cutterheads

The cutting forces generated by individual tools mounted on a cutterheadcan now be expressed as a function of tool depth of advance, kerf spacing,toolholder mount or tilt angle and tools per line.

Depth of advance DOAnmax = AR / ( RPM 60 / 1000)

DOCrii = DOAnmax • sin tilt; / TPL

Normal force Fn, = Fn,.|inear • (DOAnmax • sin tilt; / TPL) m • (Snj / Snmax )"2

Fr, = k| • Fn,Rolling force

Side force Fs, = (DOAnmax • cos tilt: / T P L ) ' " • (Sn, / Snmax)\ l /2

Mean Tool Forces for Domed Cutterheads

The mean tool forces for domed cutterheads can now be expressed as:

Mean kerf spacing Snmean = I Sns / N

Mean normal force Fnmean = Z Fn, / N

Fnmean = I Fn,.linear • ( DOAnmax • sin tilt, / TPL ) m • ( Sn; / S n ^ ) m IN

Mean rolling force Frmean

Frmean

Fn m a x • SINTM m •

Z Fri / N

Sn m

= ^ l -

I kj • Fni / N

CMinear • ( DOAnmax • sin tilt, / TPL ) m • Fn, / N

r n

m

l-mean '

Mean side force Fsmean = £ Fs, / N

F s ^ = I Fni. l inear • ( DOAnmax • cos tilt, / TPL ) m • ( Sn i / Snmax ) m I N

= F n m a x • C O S T M lu • ( I Snmax)

The following relationship has been found to apply for well designed axialrotation cutterheads on TBM's for individual tool line spacings:

140

«n2tilti [5-3]

Snmean = Sn^SINTM 2

Cutting Test Constants for Domed Cutterheads

The relationship between the rock cuttability/tool tip constants aredetermined by the cutting mode and cutterhead tool lacing design. Thisimplies for domed axial rotation cutterheads with variable line spacing andtool density that the critical normal force relationships are:

Fnm a x = Fn, DOAnm a x m = F n , . ^ • DOCnm a x

m • T P L

Fnmean = I Fn, • ( DOAnm a x • sin tilt;) m • ( Sns / Sn m a x ) m IN

m TPL m ( S n / Snmax ) m= Fn,.mean • DOCnm e a n

m • TPL m • ( Sn m e a n / Sn

= n, • DOQjneur " = Fni. l i n e a r • DOC]jnear

Fn,/TPL' / 2 = Fn,.max = Fn,.mean = Fn,.linear / T P L m

Using the same procedure as for the critical normal force, the followingrelationships can be found for the cutter constant:

kmax = C, • ( D0An m a x / TPL ) m • Fnmilx = C,.max • DOAnm a x m • Fnm a x

kmean = I C, • ( DOAn m M • sin tilt; / TPL ) "2 • Fllj / N

= C, • ( DOAnm e a n / TPL ) m • F r w = C , . ^ , , • DOA n m e a n m • Fn

DOC| j n e a r • r r i | j n e a r = C\.ylneaI- DOC| j n e a r

Ci/TPL = Ci.m a x = C i . m e a n = Ci. linear / T P L

The cutting test constants are determined by normalizing cutting test data;and constitute the basis for prediction modelling of axial rotation machineperformance, i.e.

M Fn/.unear and C'i-unear from linear cutting testsM Fni-,nean and Ci.mean from field cutting tests

141

5.4 THE PRINCIPLE CUTTERHEAD FORCES

The main cutterhead forces are represented by the machine thrust forceust, cutterhead side force Fsjde and cutterhead torque Tdemand, i.e.

Cutterhead thrust I Fz = 0

* c y l i mylinder

* thrust

thrust

Side forces ZFside

FS1,ide

Cutterhead torque

T• • k motor

1 demand

Rn

: r1 thrust

: ^"cylinder ' ^ P ' A C y | j n ( j e r

: Z Fn; • sin tilt,: Z Fn^jnea, • ( DOAnj / TPL ) m • ( Sn, / Sn

: N • Fnmean • ( Snmean / S n m x ) m • SINTM:)

m-sin tilt,

= N • ( /

= 0

Z ( Fnj • cos tilt j • cos APj - Fri • sin APj)

S ( Fnj • cos tilt j • sin APj + Fri • cos AP,)

0 for a wandering or eccentric runningcutterhead. Refer to Chapter 6.3 for adetailed analysis of cutterhead side forces.

2* 1 centerline ~ "

= 1 demand

= Pmo l o r-60/(2JtRPM)

= ( 1/2 - Z Frj) • 2Rmean ; refer to Figure 5-3= kmean(Fthrust/SINTM )R m e a n

1/9

IN • rTroea

Z R, / N

/ olljnax )

f " ) T demand = Z Fr, • Ri

= Z kj • Fn,.,inear • ( DOAn, / TPL ) m • ( Sn j // J>nmax )

= IN • ) • K

w ) m • R,

Cutterhead power Pdemand = Z Frj Vj

Pdemand = Z Kj • F n j . i j n e a r • (

= N • Fr^n • ( S1i/TPL)1 /2-(Sn i/Snmax)1 /2-Vj

\ 1/2

Specific energy

SE

142

t = "demand ' ( Acutterhead '

I Fri • vi / ( DOCni • Stii • \, • 60 2 / 10002 )

C l-l ,ne ar

DOAnmeim / TPL) • Snmean • 60 2 / 1000

\ l / 2

Tmotor

side

thrust

DOCnr

Figure 5-3. The principle cutterhead forces acting on domed axial rotationcutterheads.

143

5.5 BALANCING OF INDIVIDUAL TOOL NORMALFORCES AND LINE SPACINGS

The above expressions regarding the distribution of individual cutting toolforces on cutterheads include the effects of both tool tilt angles and linespacings. The next step is to relate the rock cutting done by each individualtool to the cutterhead lacing design; i.e. match individual tool normal forcesto individual line spacings so as to avoid localized overloading of individualtools on the cutterhead. Localized tool overloading typically results inpremature disk and bearing failures and unnecessarily frequent toolreplacements in these toolholder positions.

To equalize neighbouring tool normal forces; line spacings should bemodified in the following way:

F n i

=

Fn,+I Fn, r > /Sn i + 1sin

Sn, = Sn i +1 • ( s i n tilt f / sin tilt j +1 ) ' [5-4]

Equation [5-4] is used as a guideline for cutterhead lacing design for tunnelboring and raiseboring machines. The relevance of this design criteria hasbeen verified numerous times by cutterhead tool replacement followupprofiles in the field.

5.6 SUMMARY OF PREDICTION EQUATIONS FOR AXIALROTATION MACHINES TOOLED WITH ROLLER DISKCUTTERS

Net advance rate

Net cutting rate

Depth of advance

Critical normal force

Cutter constant

Individual tools

AR = DOAnmax RPM • 60 / 1000

NCR = Acuuerhead • AR

DOAnmax = DOC,inear • TPL = DC-Cn,™ • TPL

Fill-mean = FOl-max = Fni.linear / T P L

I-mean — ^—l-max — *— I -l inear' 1 * L-

DOAn, = DOArw • sin tilt;

Fn, = Fn,.linear • ( DOAn; / TPL ) "2 • ( Sni / S n m )

SE, = Fr, / (( DOAn, / TPL ) • Sn; • 602 /1000 2 )

144

Mean tool = DOAnm a x SINTM

= I Srii / N

. 1/2Fnmean = F n m a x • S I N T M • ( Snmean / S n m a x ,

e a n • D O A n m e a n " 2 • ( S n ^ n / S n m a x ) ш

F r m e a n

Cutterhead F,hrast

1 demand

1 4 mean

"demand

= к™

= N-

= N-

= / •

= N-

an * ^ " m e a n

„«an • D O A n m e a n

m • Fn r a

Fnmean • ( S n ^ ^ / S n ^ u

Fr^-CSn«

R ™

• Tdemand ' R P ^

an/Snmax

4/60

te an

)

) m -

) • « .

R

vr

SE = Pdemand NCR

Examples of application as to cutterhead and individual roller disk cuttingforce predictions are enclosed on the file printouts, i.e.

• curforcl.xls for individual tool and cutterhead forces given TPL = 1 inpages 163 and 164

• cutpredl.xls for cutterhead performance prediction given TPL = 1 inAppendix 5

• cutpredl.xls for cutterhead performance prediction given TPL = 2 inAppendix 6.

5.7 SEQUENTIAL CUTTING WITH DOMEDCUTTERHEADS

Concentric and Sequential Cutting with Axial Rotation Machines

The most effective sequence of cuts which can be made by cutting tools is aseries of "relieved" cuts where each cut is made adjacent to a preceding cutat a predetermined spacing small enough to substantially reduce the toolforces compared with an isolated (i.e. unrelieved) cut made to the samedepth. Although relieved cutting is the most common and desirable type ofcut, many machines have tools arranged in such a way that more complexforms of cut are made.

145

The use of scrolled tool vanes or lines in concentric and sequential rockcutting as illustrated in Figure 5-4 is an attempt to ensure relieved cutting forindividual tools whilst maintaining a well balanced cutterhead with smoothrunning characteristics.

For varying tool density across the cutterhead:

TPLmean = X disks or carbide insert rows / I kerfs

SPR = ( 360/AAP s c r o l l s per line)

SPR = 2TPL = 2

Scroll #2

Scroll #2

AAPtools

Scroll #1

AAP.tools

. . . . - - Scroll #1

Figure 5-4. Concentric and sequential in-line kerf cutting with 2 scrolledtool vanes.

146

Cutterhead Constants for Domed Axial Rotation Machines

Cutterhead constants are used as practical input parameters for cutterheadlacing design and performance prediction models. The itemized effects ofcutterhead geometry and tool lacing taken into account are:

• dome factors SINTM and COSTM• mean tool tilt angle, tiltmean• mean tool torque radius, Rmean

• mean tool torque radius factor, /• mean tool kerf spacing, SnmeanS starts per revolution, SPR• tool density or tools per line,

Cutterhead constants are readily determined on spreadsheets for a givencutterhead profile geometry and tool lacing pattern. The effect of cutterheadlacing design is illustrated in the cutforcl.xls file printout in pages 163 and164 using the established rock cutting prediction equations for eachindividual tool mounted on a cutterhead.

Individual Tool and Cutterhead Bouncing for Sequential Cutting

Individual tool bouncing is caused by the following mechanisms asillustrated in Figure 5-5:

(i) Inability of a tool to cut variable rock hardness formations to aconstant depth of cut; resulting in transient tool peak loading.

(ii) Tool hammering when re-entering the tool path after passing througha void. Voids are created by fallouts along intersecting joints andfissures in the tunnel face (heading).

( Hi) The recutting of chips and fallouts on the tunnel invert (especially infractured rock) also initiates tool bouncing.

Cutterhead bounce frequency and cutterhead bounce amplitude forsequential cutting is a combination of:

• individual tool bouncing• bounce amplitude for individual cutters decreases as roller cutter

diameter increases; and denoted as the "buggy wheel" effectS differential angular position AAP of the tracking tool in the

adjacent kerfa cutterhead rotary speed RPM® the adverse effect of peak or transient tool loading due to tool

bouncing is enhanced for cutterheads with low hydraulicstiffness; refer to Chapter 4.4.

147

Cutterhead bouncing is readily illustrated for the sump cutting mode as inFigure 5-6. Cutterhead bounce frequencies originate as follows:

S individual tool bouncing occurs for tools a,b in line i• the tracking tools a,b in line i + 1 bounce individually after a

given time At = ( 60 / RPM ) • ( AAP / 360 ) resulting in acutterhead excitation frequency / = 1 / At.

• >„ DOC

hard layer

DOC

joint

rock fallout

* DOC

Figure 5-5. Individual tool bounce mechanisms.

148

The cutterhead bounce frequency / functions as an excitation frequency forboom and machine body vibrations. This excitation frequency can not beeliminated and must be designed away from the natural boom or machinefrequency. There are two controllable design variables that affect cutterheadexcitation bounce frequencies, i.e.

* cutterhead RPM (advantage with variable speed drive electricalmotors)

• differential angular position AAP of tracking tools in theadjacent kerfs

Example of Application - Hydra Tools Intl. Cutterhead #24

Natural boom frequency /boom = 6 Hz(Measured by impact hammer tests)

Cutterhead excitation frequency /excitation = l / { ( 6 0 / 7 ) - ( 7 . 5 / 3 6 0 )}

= 5.6 H z

A A P

Figure 5-6. Illustration of cutterhead bouncing mechanisms for sumpingwith axial rotation machines.

149

Actual Tool Path or Kerf Spacing for the Sump Cutting Mode

The effective tool path or kerf spacing is illustrated in Figure 5-7 for thetransitional tool positions on a cutterhead. However, the found expressionsapply to all tool positions on a domed cutterhead including:

• forward mounted tools with AL = 08 side mounted tools with AR = 0.

The effective tool path or kerf spacing increases with DOAnmax; but isindependent of cutterhead rotary speed.

A L + DOCnmax TPL360

AR

The actual or effective individual tool kerf spacing can be found using thefollowing expressions for the tool path helix angle /?:

tanDOCnmjxTPL(p/360

27t-R,-<p/360

AL + DOCn mM • TPL cp/360

advance

Snt

AR + S,

Snt = AR +AL + DOCm a • TPL • (p I 360

tan/3sin ft

150

AR

360

" A L<PDOCnmax TPL -—max 3 6 Q

kerf

v rotation

vadvance

Figure 5-7. The actual kerf spacing for domed axial rotation cutterheads.

151

Cutterhead Profiles and Coning Geometry for Axial Rotation Machines

Cutterheads are in principle built with cross-sectional profiles characterizedas:

( i) domed heads; with the coning commencing from the centercutters

( ii) flat-faced heads; with the coning commencing just prior to thegauge cutters

The difference in cross-sectional profiles between these two cutterhead typesis illustrated in Figure 5-8.

Concentric and sequential in-line roller disk kerf cutting is illustrated inFigure 5-4. The doming of cutterheads is an attempt to maintain relievedcutting for individual tools by introducing a corrective coning angle CA asillustrated in Figure 5-9. "Optimum" cone angles are dependent onanticipated cutterhead advance rates and tool lacing patterns, i.e.

ADOC = A • ( AAP / 360) = DOCnmai • TPL • ( AAP / 360 )

tan CA; = ADOC / Sn, = DOCn^ • TPL • (AAP / 360 ) / Sni

tilt,+1 = 90° -1=1

Gauge cutters are typically mounted with tilt angles of 20°±10° oncutterheads for tunnel boring machines. Large diameter cutterheads tend tohave flat cross-sectional profiles and small diameter cutterheads can be both.Small diameter cutterheads tooled with large diameter disk cutters tend to bemore difficult to design due to the limited space available for toolholderplacement on the cutterhead shell.

Table 5-1. Cutterhead coning angles as a function of tool depth of advanceand tool lacing design; i.e. shown for TPL = 2, AAP = 90° and Sn = 50 mm.

DOAnmax = DOCnmax TPL tan CA CA(mm/rev) (°)

5 0.025 1.4310 0.050 2.8315 0.075 4.29

Note: Cutterheads designed for cutting hard rock (smaller depth ofadvance) tend to be flat-faced. However, when tunnelling in brokenrock, domed cutterheads generally run more smoothly.

152

L max-flat

L max-dome

Figure 5-8. Typical cross-sectional profiles for the two main cutterheadtypes used on axial rotation machines.

AAP

1b 1a" P2a'

2b

2a,b

1b •cAr1a 2a'

Sn

ADOC

AR

tilt1ab = 90°= 90°- CAi

= 90°- 2-CA,i+1

Figure 5-9. Effect of tool depth of advance on cutterhead coning angles.

153

6 CUTTERHEAD TOOL LACING DESIGN

6.1 TOOL LACING DESIGN PARAMETERS

The following factors must be taken into account when positioning cuttingtools across a cutterhead shell:

• structural considerations so that sufficient space for toolholderattachment to the shell, bolt-holes for lifting, water-way connections,etc. is ensured

• smooth running characteristics by minimizing cutterhead oscillationsso as to reduce peak and eccentric loading of gearboxes and drivemotors

• a balanced cutterhead tool configuration so as to avoid localizedoverloading of individual tools. In practical terms, this means that acutterhead tooled with roller disk cutters should develop a"triangular" cutter replacement followup profile. In addition, afterreplacing worn tools, excessive protrusion of individual tool tipsshould be avoided by replacing tools in neighbouring lines as well.

• design the cutterhead bounce excitation frequency away from theboom or machine body natural frequency range.

The first factor requires that tools be well distributed over the availablecutterhead shell area - rather than just concentrated along a few spokes. Thesecond requires that there should be no unbalanced moments at any point onthe cutterhead. The third requires the use of domed and scroll-vanedcutterheads with variable tool line spacings for sequential cutting.

A balanced distribution of tools over a cutterhead can be achieved byarranging the following tool positioning or lacing design parameters in aplanned fashion:

• radial tool spacing, AR• axial tool spacing, AL• angular tool spacing, AAP• tool density or tools per line, TPL.

However, the effect of these tool and tool path positioning parameters onrock chipping, cutting performance and tool life must be understood withregard to:

sequential and relieved cuttingtool density, tool forces, tool depth of cut and cutterhead advancetool tilt angles and kerf spacingkerf deepening and chipping frequencycutterhead tool replacement profiles.

The expression cutting tool has been used deliberately in this chapter sincethese considerations apply to both drag tool and roller disk cutterhead toollacing designs.

154

Radial Tool Spacing, AR

Cutterhead tool lacing design is based on toolholders set at various radii insuch a way that the tools, for the sump cutting mode, sweep out a concentricset of kerfs. These kerfs are separated by ribs of uncut material. Thus, only alocal force is applied to 15 - 25% of the rock surface for the extraction of thewhole face. The uncut ribs are removed indirectly, either by lateraloverbreak to the side(s) of the tools, or by the eventual formation of anunstable rib after several tool passes (i.e. kerf or groove deepening).

A uniform radial line spacing can be maintained for flat-faced cutterheads.However, for domed cutterheads, the individual line spacing must be seen inrelation to the tool tilt angles to maintain evenly distributed individual toolnormal forces.

*& chips from the 1st tool passingO chips from the 2nd tool passing

Figure 6-1. Kerf formation and chipping at the face.

Axial Tool Spacing, AL

Tools are often offset relative to each other in the axial direction (refer toChapter 6.2) with the result that the face being cut has a concave profile.This can yield a number of advantages, including lateral stabilization of thecutterhead, potential for relieved cutting, special design of center toolplacement and convenience of cuttings removal.

The center section of a cutterhead is sometimes placed in front of the maincutterhead itself, e.g. the pilot bit on a boxhole machine cutterhead. Analternative is to have the center of the cutterhead recessed, thereby reducingthe workload of the central tools (center cutters, sumpers, etc.). For thetraverse cutting mode, these recessed sumpers are not in contact with therock - thereby eliminating unnecessary pick wear on axial type cutterheadsfor roadheaders.

155

Angular Tool Spacing, AAP

In a simple arrangement where tools are arrayed along two or more spokesas in Figure 6-2, it is obviously desirable to have the radial spokes atuniform angular spacings. On each of the n spokes there is a resultant of therolling (cutting) force Fr acting at a radius R, and the sum of the momentsabout the center of the head, nRFc, equals the applied cutterhead torque T.

With an equal angular spoke spacing 2n/n, the moments sum to zero for allpoints on the cutterhead, and there is no tendency for turning about otherthan the central axis. With irregular angular spacings, as is generally not thecase for flat-faced cutterheads, there is a tendency for eccentric running.

If simple radial tool spokes are inconvenient for structural purposes or inhard rock formations where a more evenly distributed axial load on thecutterhead shell is desirable, then the individual tools can be dispersedacross the head as spirals, scrolls or vanes, such that the angular spacingsremain uniform at any given radius as illustrated in Figure 6-3. This will notdisturb the balance of moments.

AAP

Figure 6-2. Example of balanced tool arrays for 3 starts per revolution andan angular spacing of2n/3.

Figure 6-3. Typical 3-spoked and 3-scroll-vaned cutterheads,.

156

Tool Density or Tools per Line, TPL

Tool density is perhaps the least appreciated lacing design parameter. Theeffect of cutting with more than one tool per line is illustrated in Figure 6-4.

The effect of tool density on cutterhead lacing design is best illustrated bythe tool strike grid concept; as shown in Figure 6-5 for a traversing barreltype cutterhead used on continuous miners. A wrap or scroll angle has, forsimplicity, not been included in the drawings. The parameter tools per lineTPL affects the tool strike grid, and therefore the chip width and thicknessof rock broken off between neighbouring (not necessarily adjacent) kerfs;i.e.

Single Pass CuttingMultiple Pass Cutting

( SPR / TPL )Wchl

hll, ~ Skerf

Typical tool density values for roller cutter tooled hard rock TBMcutterheads:

SPR = 2 (tool vanes scroll with an angular tool spacing of typically 45°)TPL = 1

Typical tool density values for drag tooled medium to heavy dutyroadheader cutterheads:

SPR = 2-8 (depending on cutterhead diameter)TPL = 1-3

L__l Uncut area

CZH Area cut once

WZM Area cut twice

Figure 6-4. Effect of cutting with more than one tool per line TPL as afunction of the cutterhead rotation angle for axial rotation cutterheads.

157

CASE 1 - Single Array

Pick strike "grid"

t 'MM'-f- • • •

for cp = 90

1 revolution

1 revolution

S S S

CASE 2 - Dual Array

Pick strike "grid"for <p - 90°

1 revolutionf f

f I

s s s

CASE 3 - Modified Dual Array

Pick strike "grid"for <p = 90°

1 revolution

Direction of Cut

SPR = 1PPL= 1SPR/PPL = 1

DOCnmax

DOCn max

TR * 1000RPM

DOCn,

DOCn,

Direction of Cut

SPR = 2PPL = 2SPR/PPL = 1

TR * 1000SPR * RPM

SPR = 2PPL = 1SPR/PPL = 2

D omitted pick positions

TR * 1000DOCn

DOCn

m a x " SPR * RPM

Figure 6-5. The tool strike grid for traversing barrel type cutterheads usedon continuous miners illustrating the effects of starts per revolution SPRand tools per line TPL on chip dimensions.

The use of complex cutterhead lacing design patterns leads to:

II increased cutterhead sumping or traversing rates by increasingtools per line. Tools per line TPL has the same effect asincreasing tool passes or "cutterhead RPM's" with regard toadvance rates

9 the use of starts per revolution SPR is a systematic way ofomitting tool positions from the cutterhead so as to reduce thetotal number of tools on the cutterhead.

158

The effect of tool density on individual tool and cutterhead forces and torqueare shown in Table 6-1.

Table 6-1. Relative cutterhead force and torque requirements as a functionof tool density for roller disk cutting given RPM = 1.

Tools perRowTPL

12312

CutterheadAdvance

AR

11122

IndividualTool

DOCnmax

11/21/32I

IndividualTool

J**/f ** **max

l0.7070.5771.414

1

CutterheadForce''thrust

11.4141.7321.414

2

CutterheadTorque* demand

11122

• given Fnmax = FnrfDOAn^/TPL)'" = Fn,

6.2 THE STEPWISE TOOL LACING DESIGN PROCEDURE

The basic rock cutting and tool lacing parameters which must be taken intoaccount if a balanced cutterhead tool lacing design is to be achieved are:

Rock Cutting Parameters Cutterhead Design Parameters

DOCni

rock cuttability/tool tip constantsFnh Frh Fs,

tiltj, CAiAP,TPL, SPR

Cutterhead tool lacing therefore consists of an optimized combination of thefollowing parameters:

toolholder tilt angleline spacingtools per linetool starts (spokes or scrolled vanes) per revolutiondensity of spirals towards the center and periphery of the cutterheadangle between two tracking tools in adjacent kerfstorque peak load smoothening by introducing scrolled tool vanes.

Since tool path lengths increase with tool radii, and thus the requirement fortool replacements; there are in principle two ways to compensate for thisuneven tool replacement requirement on cutterheads so as to obtain a flattool replacement profile for drag tooled cutterheads. This is typicallyachieved by:

159

S introducing more tools to the cutterhead periphery by decreasingline spacings towards the periphery or by increasing the numberof tool starts towards the periphery

8 use of larger tools (more wear material) for peripheral tools.

The procedure for designing scroll-vaned cutterhead tool lacing designpatterns in a stepwise fashion is illustrated in Figure 6-6.

STEP1

TPL = 1SPR = 1N = 6

STEP 5

CenterTPL = 2SPR = 2

PeripheryTPL = 6SPR =6

THE STEPWISE TOOL LACING DESIGNPROCEDURE

STEP 2

STEP 3

TPL = 2

SPR = 2

N =12

A AP= 90°

STEP 4

STEP 6

CutterheadBounceControl

AAP

Dummy scroll of"empty" toolboxes

AAP

Figure 6-6. Illustration of the stepwise cutterhead tool lacing designprocedure.

160

STEP 0 Select cutterhead coning start point. Startup tool tilt angles aregiven by the "optimized" cutterhead cone angles for relievedcutting as shown in Chapter 5.7:

tan CA, = DOCnmax • ( AAP / 360 ) / Sri;

tilt, = 90° -

STEP 1 Line spacings must be adjusted according to toolholder tiltangles to equalize the normal forces between neighbouring linesas shown in Chapter 5.5:

Sumping with full face and partial face machines

Sn; = Snmax • sin tiltj

=> line spacings are reduced towards the periphery

Cutterheads for full face tunnelling machines are designed withcompromise rather than "optimum" face line spacings since themachines will operate in varying rock mass conditions throughouttheir useful lives.

Traversing with partial face machines

Srij = Sn^x • cos2 tilt;

=> line spacings are increased towards the periphery

Cutterheads for partial face tunnelling machines such as the axialtraverse type for roadheaders use both the sump and traversecutting modes; and are therefore based on a compromise withregard to tool lacing design to suit both these cutting modes.

The axial tool spacing AL* can be found by selecting tool radiiARj startup values:

ALj = ( Sni2 - ARi2) m

Finally, as a check, the startup tool tilt angles from STEP 0should ensure that tools are mounted perpendicular to the cutrock surface:

tan tilt. = AR,/ALj

Should this condition not be met; then the startup tilt anglevalues for tool radii AR; must be changed - thus creating aniteration process for this lacing design step.

161

AR J

i +1

i+3

STEP 2 Select number of tools per line, TPL.

STEP 3 Select number of tool starts (spokes, arrays scrolled-vanes) perrevolution SPR.

STEP 4 Introduce a tool scroll vane (wrap or spiral) angle to enhancesmooth running characteristics.

STEP 5 Introduce intermittent tool vanes due to:

H lack of space for toolholders at the center of thecutterhead

8 bring about a more balanced cutterhead toolreplacement profile (by reducing peripheral toolworkloads and thereby reduce tool replacements inthe periphery for sumping type cutterheads).

STEP 6 Check cutterhead bounce properties as shown in Chapter 5.7with regard to:

B cutterhead excitation frequencies generated bycutting

• natural boom or machine body frequency.

Note: The difference between spoked and scroll-vaned cutterheads are:

162

f i) tools in a start line for spoked cutterheads cut therock at equal depths - but not sequentially

(ii) spoked cutterheads have poor smooth runningcharacteristics for cutting in fractured rock andmixed face conditions.

STEP 7 CUTTERHEAD CONSTANTS

The cutterhead lacing design can be summarized by a fewcutterhead constants which are readily calculated onspreadsheets. The constants are used for predicting individualtool and cutterhead forces and torque versus cutterhead advancerates.

Sumping with full face machines

• tool density or tools per line TPL• tool starts per revolution SPR» mean tool torque radius Rmean = I Rt IN• mean tool tilt angle tiltmean= arcsin SINTM• mean radius factor / = Rmm IR^• mean line spacing Sn^an = £ Sn; / N• dome factor SINTM = I sin tilt; / N

<•! '

Sumping with partial face machines

• TPL - tool density or tools per line• Vsump - total volume of the sump• Snsump - function of line spacing, AAP, SPR and

sump advance rates• Rsump - function of tools in cut, i.e. cutterhead depth

in the sump• SINTM and COSTM - doming factors which are a

function of cutterhead depth in the sump

Traversing with partial face machines

• TPL - tool density or tools per line• mean tool attack position for:

* L,rav - distance from cutterhead tip to mean tool* Rtrav - torque radius of mean tool* tiltmean - mean tool tilt angle

* Atrav - active cutterhead coverage area* Sntrav - mean kerf spacing• NT,™ - number of tools in cutm SINTM and COSTM - doming factors

163

6.3 CUTTERHEAD FORCES AND TORQUEEQUALIZATION ON DOMED AXIALROTATION CUTTERHEADS

The procedures for cutterhead tool lacing design must take the followingfactors into account, i.e.

• the tool lacing geometry must suit the rock mass cuttability sothat the generated individual tool forces remain within the toolstrength specifications

M a well balanced cutterhead with regard to rotational torque, i.e.• no eccentric loading• peak torque load smoothing

S minimize the effect of cutterhead bounce on machine vibrations• a well balanced cutterhead tool replacement profile. The

importance of this aspect increases disproportionately with rockhardness and abrasivity.

The balancing of forces and moments acting on a cutterhead is based on thesummed effect of the individual tool forces and their location on thecutterhead as shown on Figure 6-7.

The Principle Cutterhead Forces

Z Fz, = 0 Fz = Z Fri; • sin tilt;

Z Fxj = 0 Fx = Z ( Frii • cos tilt; • cos AP, - Fr, • sin AP : )

Z Fyi = 0 Fy = Z ( Fri; • cos tilt; • sin AP, + Fr; • cos AP;)

where: F ^ = Fz

Fside = (Fx2 + Fy2)1 / 2

The Principle Cutterhead Moments

I Mzi = 0 Mz = I ( Fxj • Yi - Fy, • X,)

Z Mx; = 0 Mx = I ( Fyj • Zi - FZJ • Yj)

Z My, = 0 My = Z ( Fx, • Z> - Fz* • X, )

where: X; = Rj • cos APj

Tdemand =

164

iFnl * costilt I • cos API

— • X

Figure 6-7. Individual tool forces and location on a domed cutterhead.

The objective of cutterhead force and torque balancing is to ensure non-eccentric loading situations and smooth running characteristics byminimizing or eliminating the:

B principle non-axial forces, i.e. Fx = Fy = 0• principle non-axial moments, i.e. Mx = My = 0M oscillating cutterhead loads, i.e. the principle cutterhead force

and moments Fx, Fy, Mx, My are, in addition to the stationarytool positioning angle APj, a function of the cutterhead rotationalangle 9 (or rather 9 + APj) and thus the source of oscillatingcutterhead loads.

The practical use of the cutterhead force and torque balancing equations areshown on the following cuttorql.xls file and as graphs printouts in Figures6-8.

165

Cutterhead

Cutterhead Diameter, DNumber of Cutters, NDisk Diameter, dCutterhead Rotary Speed

Cutterhead Rotation Angle, <p

Principle Force and Torque Balancecuttorql.xls/A. Lislerud

2,90 m Max Depth of Cut, DOCnmax 7,11 mm/rev20 Critical Force, Fnlmax

368 mm Cutter Constant, Clmax7,9 RPM Max Line Spacing, Snmax

360"

51,4 kN/cutter0,0511 mm"2

88,9 mm

Cutter Tool# Radius

i Ri ARi

(mm) (mm

123456

7

89

101112

131415

1617181920

58

142227

316405494

583

672761

850939102711161198

1279

13511402142814431448

857Rmean

588485

8989

8989

89

8989898989

8181

725125155

1448Rmax

Note

ALi

(mm)

0000000000000-5-8

-25-38-64-38-25

•203

Lmax

TiltAngle

tilti

(°)

90909090

909090

90

90909090

908267

50372717

17

Angular Tool TipPosition Coordinates

APi Xi Yi Zi

(°) (mm) (mm) (mm)

01800

180

922450

180

922600

18092

270340

144

70288

7215

58-142227

-316-14

-209583

-672-27

-148939

-1027-390

1202

-1093

4804411432

-1186

0

000

405-448

0

0

760

-83700

1116-1198

-437

794

1318-1358

176-830

0

0000

00

00

0000

-5-13

-38

-76-140-178-203

LineSpacing

Sni sin (tilt

(mm)

5884858989

8989

8989

8989898981

8277

646841

26

78Snmean

1,001,001,00,00,00,00,00

,00

,00

,001,001,001,00

0,990,92

0,77

0,600,450,290,29

0,87

LineSpacing

i) Sni-theo

(mm)

89898989

898989

89

89

89

898989

8775

52321888

72 <

IndividualTool Tool

Depth Norm,of Cut, Force,DOCni Fni

(mm/ (kN/rev) cutter)7,1

7,17,17,17,17,1

7,1

7,17,1

7,17,17,17,17,06,5

5,4

4,33,22,12,1

111

133134137

137137137

137137

137137137

137

131126

111

90815040

S,16 2378SINTM DOCn £

mean

Design line spacings Sni are not well matehedto the theoretical Sni-theo line spacings.

Fni

166

Cutter#

1234567891011

12

13141516

17

181920

IndividualTool

RollingForce, Fri

(kN/cutter)15,14

18,1318,2718,6718,6718,67

18,6718,67

18,67

18,6718,67

18,6718,6717,7016,4713,29

9,507,443,712,95

309,3I Fri

Individual IndividualTool Tool Lateral

Torque ForceFri-Ri Fn( • cos (tilt i

(kNm/cutter)

0,88

2,58

4,155,907,57

9,2310,8912,55

14,21

15,8717,5319,1920,8521,2021,07

17,96

13,3210,625,354,27

235,2Z Fri • Ri

(kN/cutter)

0,00

0,00

0,000,000,00

0,000,00

0,00

0,00

0,000,000,000,0018,1749,2471,63

71,77

72,1748,14

38,26

Force

) Fxi

(kN/cutter)

0,00

0,000,000,00

-18,6616,930,000,00

-18,66

18,390,000,00

-18,6617,7051,91-65,76

15,62

29,3747,33-29,65

45,8I Fxi

Components

Fyi Fzi

(kN/cutter)15,14

-18,1318,27

-18,67-0,65-7,8918,67

-18,67

-0,65

-3,2418,67

-18,67

-0,65-18,17-1,36

31,3570,69

-66,349,55

-24,36

-15,1IFyi

(kN/cutter)111,

133,134,137,137,137,137,137,

137,

137,137,

137,137,1129,3116,085,4

54,1

36,814,7

11,7

2196,7ZFzi

Torque Components

Mxi Myi Mzi

(kNm/cutter)

0,00

0,000,000,00

-55,4961,360,000,00

-104,19

114,670,000,00

-152,90154,9250,76-69,00

-76,64

59,19-4,2914,66

-6,9

IMxi

(kNm/cutter)-6,49

18,92

-30,4843,341,94

28,61-79,8992,07

3,64

20,22

-128,63140,815,34-0,09

-140,07

95,83-27,12

-20,33-29,4919,90

8,0I Myi

(kNm/cutter)-0,88

-2,58-4,15-5,90-7,57

-9,23-10,89

-12,55

-14,21

-15,87

-17,53-19,19-20,85-21,20-21,07

-17,96

-13,32-10,62-5,35-4,27

•235,2

ZMzi

DOCni = DOCnmax • sin tilt iFni = Fnlmax-(DOCni-Sni/Snmax)A0.5Fri = Clmax • DOCniA0.5 • Fni

ARi = Ri+1 - RiALi = Li+1 - LiSni = (ARiA2 + ALiA2 )A0.5

Sni-theo = Snmax • sinA2 (tilt i )Xi = Ri • cos APiYi = Ri-sin APiZiFx = Z ( Fni cos (tilt i ) • cos APi - Fri • sin APi)Fy =• Z (Fni cos (tilt i ) • sin APi + Fri • cos APi)Fz = ZFni • sin (tilt i )

Mx = Z ( Fyi • Zi - Fzi • Yi)My = Z ( Fxi • Zi - Fzi • Xi)Mz. = Z ( Fxi • Yi - Fyi • Xi)

Fthrust = ZFziFside = ( FxA2 + FyA2 )A0.5

Tdemand = ZMzi

167

15.0

-~ 10.0

-15.0

Cutterhead Rotation Angle (°)

360

Cutterhead Rotation Angle (°)

Figure 6-8. The principle non-axial cutterhead forces and moments as afunction of the cutterhead rotation angle (p.

168

FIELD PERFORMANCE PREDICTION

Rock breakage is effected when a cutting tool is pressed against the rocksurface. In brittle rock, the loading causes the region immediately under thetool to be crushed, and at a later point in the loading cycle, tensile cracksinitiate from the edge of this crushed zone and propagate either to the rocksurface or to an adjacent, previously cut kerf to form rock chips.

The ultimate goal for rock excavation prediction modelling is thedevelopment of rock mass characterisation procedures utilizing commongeotechnical and geological structural parameters to yield an index of rockmass cuttability. Such a procedure may well follow a similar process to thewell known Q and RMR geomechanical support classification systems orthe NTH rock mass classification system for rating tunnel boringperformance. The model(s) would help define the most appropriate machinefor an application, the likely performance of the machine, likely machinepower, weight and mechanical characteristics, likely cutting toolperformance, consumption and possible failure mode (abrasive or adhesivewear, or impact damage).

Structuring Principles of Performance Prediction Models

A wide variety of performance prediction methods and principles are used indifferent countries and by various machine manufacturers. Most of thesemethods are based on one or two mechanical properties of intact rock asinput parameters (e.g. uniaxial compressive strength and CERCHARAbrasivity Index), whilst others are based on a combination ofcomprehensive laboratory and field cutting data.

In general, methods for predicting net cutting rates are based on one or moreof the following principles:

• selective field trials combined with site characterisationincluding items such as sampling of intact rock specimens andface/wall mapping

• small scale laboratory testing (linear cutting tests)* full scale laboratory testing (cutterhead cutting tests)81 empirical/statistical methods based on field performance data• theoretical models such as dimensional analysis, FEM analysis.

Contrary to percussive rock drilling, full scale field testing is seldom afeasible option for cutting and boring machine performance prediction. Fullscale laboratory rock cutting tests are carried out at the:

S Colorado School of Mines, Earth Mechanics Institute (TBM andraiseboring cutterheads)

B USBM Pittsburgh Research Center (Continuous Miners).

169

In brief, the most advanced machine prediction models contain elements ofall five principles. However, common to all machine performance predictionmethods is that field work with regard to rock sampling and tunnel mappingare key issues. If the sampling of intact rock or face/wall mapping is notrepresentative of the actual tunnelling conditions, prediction estimates canand will not be reliable.

On the basis of the current state of rock mechanics modelling; the followingaspects regarding performance prediction model upbuilding should be keptin mind:

( i) A model is a simplification rather than an imitation of reality. It is anintellectual tool that has to be designed or chosen for a specific task.

(ii) The design of the model should be driven by the questions that themodel is supposed to answer rather than by the details of the systemthat is being modelled. This helps to simplify and control the model.

( Hi) It might even be appropriate to build a few simple models rather thanone complex model; the simple models would either relate to differentaspects of the problem or address the same questions from differentperspectives.

f iv j The aim should not be to attempt to validate a model but to gainconfidence in it and modify it in use. One's approach to the modelshould be like that of a detective rather than a mathematician.

First, a simple model is built and exercised in a conjectural way. The resultsalmost always suggest new ways of obtaining data or new ways ofinterpreting available data. New data, in turn, suggest improvements to themodel or ideas for new models. Implementing these improvements leads torequirements for new data or insights, and so on. The whole process may betermed "adaptive modelling".

To summarize; performance prediction models required for mechanizedrock excavation are:

B rock mass cuttability/drillability and abrasivity8 net cutting and net advance ratesB tool consumption8 machine utilisationB individual tool forces, cutterhead forces and moments• cutterhead tool lacing design• cutterhead bouncingS tunnelling costs.

Some of these topics lie within the scope of this report.

170

The flow and linkups of field data collection required for the upbuilding ofperformance prediction models for mechanical rock excavation areillustrated in Figure 7-2. The use of cutting control and monitoring systemson tunnelling machines as illustrated in Figure 7-1 has greatly increased theavailability of in situ cutting data. However, one of the major drawbacks ofcomputer based data acquisition systems is the lack of inexpensive butsophisticated software for reducing the large amounts of sensor generateddata to a comprehensive and readily usable source of information forpractical field follow-up work.

OVERVIEW OF CUTTING CONTROL

AND MONITORING SYSTEMS

ROCK

ITUNNELLINGMACHINE

ACTUATORS SENSORS

! CONTROL STRATEG

I SIGNAL PROCESSING

DATA LOGGING

DATAOFF-LOADING

GEOLOGY AND \GROUND SUPPORTS-INFORMATION ;

OPERATORDISPLAY/INPUTS

MANAGEMENTREPORTS

Figure 7-1. Flow chart for machine monitoring, cutting control andperformance data acquisition.

171

FIELD FOLLOWUP CHART

Excavation SiteCharacterization

TunnellingMachinePerformance

Tunnel SizeTunnel AlignmentFace/Wall MappingIntact Rock Material TestingIn Situ Rock StressGround Support Measures

Net Advance RatesTool LifeTool Replacement ProfilesCutter head BouncingMachine Utilisation

Station No.or

Tunnel Zone

Net Cutting and Net Advance Rates

• cutterhead forces versus net cuttingrates and rock mass characterisation

• net advance rates versus net cuttingrates for partial face machines

• individual tool force distribution andcutterhead tool lacing design

Tool Consumption and Tool Life

• tool life versus tool type, toolgeometry and rock masscharacterisation

• cutterhead RPM's (VSD)• cutterhead tool replacement profiles• occurrence of cutterhead bouncing

Machine Utilisation

• itemized operational unit times• scope of ground support work

Figure 7-2. Field followup chart for matching site characterization andmachine performance.

Face/Wall Mapping

• rock mass distribution• rock mass jointing

• type• orientation• frequency

• shears, mudseams, ...

Testing of Intact Rock Specimens

mineralogyrock strengthrock surface hardnessporositycuttability/drillabilityabrasivity

172

8 TERMINOLOGY

The terms and expressions used in this report to describe essentially similarcomponents or functions of rock cutting machines may vary with theindustry or country in which the machine is built or used, or with thetechnical background of the people using the terms.

8.0 GENERAL EXPRESSIONS

Kinematics deals with the inherent relationships defined by the geometryand motion of the machine and its cutting tools - without much reference tothe properties of the material being cut. Dynamics deals with the forcesacting on the machine and its cutting tools - taking into account machinecharacteristics, operating procedures and material properties. Energeticsdeals largely with the specific energy relationships that are determined frompower considerations involving forces and velocities in various parts of thesystem - taking into account properties of the materials being cut.

A simplified classification of excavators based on the characteristic motionsof the major machine element and the cutting tools categorises machines astransverse rotation, continuous belt, axial rotation, or planers; while theaction of cutting tools is divided into parallel motion and normal-indentation.

Transverse rotation devices turn about an axis that is perpendicular to thedirection of advance; as in circular saws. The category includes equipmentsuch as bucket-wheel trenchers and excavators, rotary-drum pavementgraders, coal shearers, roadheaders, continuous miners and booms withripping heads, some rotary snow ploughs, and some cutterheads fordredging. In addition, the Robbins Mobile Miner represents a special formof transverse rotation devices, i.e. the sweeping of a rotating wheel-typecutterhead. Continuous belt machines represent a special form of transverserotation devices in which the rotor has been changed to a linear element; asin chain saws. The category includes "digger chain" trenchers, ladderdredges, coal saws, shale saws, and similar devices. Axial rotation devicesturn about an axis that is parallel to the direction of advance; as in drills. Thecategory includes equipment such as rotary drills, augers and shaft-sinkingmachines, tunnel and raiseboring machines, corers, Marietta Borers, andcertain types of snow ploughs. Planing devices only use a horizontaltranslation movement; as in carpentry planes. The category includesequipment such as coal ploughs, asphalt planers and some snow ploughs.

A few excavators and some operations do not really fit this classification.For example, certain roadheaders and ripping heads sump in by axialrotation and produce largely by traversing; and there may be some questionas to the classification of tunnel reamers and tapered drill bits.

173

Boring machines are generally large full-face (full bore) excavators;typically equipped with an axial rotation cutterhead with either drag tools,disk cutters or studded roller cone cutters depending on the properties of thematerials being cut.

Cutting machines are generally partial face machines; typically equippedwith a transverse rotation or an axial rotation cutterhead and equipped withdrag tools.

There are four basic cutterhead modes of operation, i.e. sumping,traversing, sweeping and planing. These modes of operation are listed forthe most common excavator categories in the following table:

Cutterhead Modeof Operation

Sump

Traverse

Sweep

Plane

Axial Rotation

1 +2

2

TransverseRotation

(3) + 4 + 6

4 + 5+7

3 + 6

ContinuousBelt

8

8

Planing

9

1. Tunnel and raiseboring machines, Marietta Borers, reamers, ...2. Roadheaders with axial rotation cutterheads (in-line cutterheads)3. Roadheaders with transverse rotation cutterheads (milling

cutterheads), ...4. Continuous miners, bolter miners, ...5. Coal shearers,...6. Robbins Mobile Miner7. Wohlmeyer type machines8. Trenchers,...9. Coal ploughs, asphalt planers, ...

8.1 CUTTING TOOLS

Cutting tools are the actual cutting elements attached to a cutterhead. Thetool attachment device on a cutterhead shell is termed a toolholder, or:

S pickbox - for drag tools• saddle - for roller cutters

On domed cutterheads the toolholder mount angle relative to the cutterheadrotation axis is the toolholder tilt angle.

174

Pickboxes must be skewed inwards for a pick tip to run in the intended line(due to pick tip protrusion u ahead of the radial distance between cutterheadand pickbox centerlines). Thus, pick skew angles decrease with kerf radii.However, pick skewing in the chip loosening direction must also be ensuredfor point attack picks, so as to enhance pick rotation in the toolholder.

Parallel-motion tools operate with a planing action which moves the toolparallel to the surface that is being cut. This category includes tools such ascarbide-tipped drag tools (roadheaders, continuous miners, coal ploughs andsoft-rock tunnel boring machines), hard faced teeth (large augers), steelcutting blades (ice drills), and diamond tipped tools (core drilling).

The term drag tool (bits in the US and picks in the UK) is used for the twoprinciple types of parallel-motion tools; namely point attack or conical tools(which rotate in the toolholder) and radial tools which do not.

Normal-indentation tools in the present context is limited to the varioustypes of roller cutters that are thrust into the surface being cut by highnormal forces. More generally, the category would also include bits forpercussive drilling.

The term roller cutter is used for all types of unpowered cutters that workprimarily by means of a rolling action indentation. Examples of such devicesare wheel-type glass cutters, tricone bits for rotary drilling, disk cutters,studded disk cutters, steel-toothed disk cutters, studded roller cone cutters,etc.

Cutter radius is taken as the radius to the extreme tip of a continuous diskrim, the studs, or teeth.

Inserts, studs, or buttons, are hard projections, usually of cemented carbide,set into the disk rim or cutter cone frustum.

Stud protrusion is taken as the radial distance between the tip of the studand the disk or cone perimeter.

The rim edge angle of a roller disk cutter is the apex angle for the part of thetool that penetrates the rock, i.e. the cross section of the rim. The half-angleis denoted by p, so that the total wedge angle is 2p\ However, the mostcommonly used roller cutter rim geometry today are disks with constantsection rims.

175

8.2 CUTTERHEADS FOR AXIAL ROTATION MACHINES

For axial rotation machines, the cutterhead is the complete rotor whichrevolves about the central axis of the hole, shaft or tunnel that is beingbored. Its diameter corresponds to that of the bore. Thus fox full-face tunnelboring machines it is the face plate onto which the cutters are attached. Onpartial-face machines, it is the boom mounted rotating shell onto whichdrag tools are attached. Some excavators have two or more booms and/orcutterheads, e.g. Marietta Borers.

Reamers are devices that increase the diameter of an existing pilot holeusing a tapered cutterhead to attack the hole walls continuously; or they mayconsist of a series of annular boring heads that cut out a set of discrete steps,each larger in diameter than the preceding one. Some raiseborers and tunnelboring machines fall into this category.

The advance axis is the central axis of the hole that is being bored, and theaxis about which the cutterhead rotates.

Net penetration rate or net advance rate is the speed at which thecutterhead advances in the axial direction.

The rotational velocity of a cutterhead is its angular velocity GO (radians perunit time), but it is often expressed as angular frequency f (revolutions perunit time).

The absolute tool speed for a given point on a disk rim is the velocity of thatpoint relative to the rock, taking into account the components of motion dueto both rotation and penetration, i.e. it is the time derivative of the tooltrajectory. In the case of fixed tools (drag tools), it is equivalent to "surfacemeters per minute". Tool speeds vary with the radius of the tool on thecutterhead; at the periphery of the head, where speeds are highest, tangentialvelocity derived from rotation alone is usually a good approximation. In thecase of roller cutters, the velocity of the center of the roller is typically takenas the "tool speed" although indentation velocity of the rim is more directlyrelevant to cutting.

The trajectory of a fixed cutting tool, or the trajectory of a fixed part of aroller cutter, is the helical path traced relative to fixed axes (relative to therock) as the cutterhead advances. The cutting trajectory for a roller cutter isthe path traced relative to the rock by a given point on the disk rim; itapproximates a cycloid or epicycloid superimposed on a helix.

The helix pitch A (as described by the cut tool path) is the cutterheadadvance for one complete revolution in the axial direction.

176

The helix angle at any given radius Rj on a cut helical tool path is the slopeangle defined by fj = atan ( A /

A tracking tool follows one or more identical tools set at the same radius onthe cutterhead. If there are n tracking tools at a given radius, they arenormally uniformly spaced with an angle 2K I n between their positions. Themost commonly used term for expressing the number of tracking tools istools per line, i.e. TPL = n.

Angular position AP refers to the angular spacing of cutting tools relative toa given tool.

The most effective sequence of cuts which can be made by cutting tools is aseries of "relieved" cuts where each cut is made adjacent to a preceding cutat a predetermined spacing small enough to substantially reduce the toolforces compared with an isolated (i.e. unrelieved) cut made to the samedepth. The use of scrolled tool vanes or lines in concentric kerf cutting is anattempt to ensure sequentially relieved rock cutting for individual toolswhilst maintaining a well balanced cutterhead with smooth runningcharacteristics.

Center cutters are tools set at or near the cutterhead axis of rotation. Tooltrajectory helix angles approach 90°, and the tools must progress directlyinto the rock in the axial direction with cutter rotation approaching nil. Thisfrequently leads to tool skidding and reduced tool service life.

Skidding of roller cutters, especially for coned roller cutters is almostunavoidable, when non-tilted roller cutters of standard design are attached toflat-faced cutterheads at different radii. Skidding has a detrimental effect ondisk and cutter life, since it gives rise to facet wear of the disk rim - andultimately frozen or locked cutter bearings.

Gauge or peripheral tools are the tools set at the full radius of the bore.They have to cut the corner or angle that marks the transition from face tohole wall.

Cutting with constant penetration with roller cutters means that the normaldistance between the axle and the (smooth) rock surface remains constant asthe roller cutter travels, so that the depth of cut does not vary. For constantpenetration operation, the mountings of the roller cutter must be stiff.

Cutting with constant thrust with roller cutters means that the normalcomponent of the cutting force remains constant as the roller cutter travels.In reality, constant thrust is virtually unattainable in brittle materials (therequirements are perfect compliance and zero inertia).

The compliance of a tool in any given direction is the tool deflectiondivided by the applied force. Compliance is the reciprocal of stiffness (forcedivided by deflection).

177

8.3 ROCK CUTTING MODES

A pit, or crater, made by an indenter is usually taken to be the cavity thatremains when the indenter is withdrawn and loose fragments have beenremoved. In brittle materials this cavity is usually larger than the volume ofthe indenter that penetrated; partly due to rock breakage to the sides, andpartly due to rock crushing under the tip of the indenter.

A normal-indentation tool is a device that forms a pit, crater or kerf in therock surface by penetrating in a direction more or less perpendicular to thesurface. The indentation process may involve:

a brittle failure, with formation of loose rock fragments or chipstowards the free surface

B ductile yielding, with displacement of material towards the freesurface

• compaction of a readily compressible material.

A kerf or tool path is the slot gorged out in the rock face by a cutting tool.Parallel kerfs swept out by adjacent tools are separated by ridges or ribs ofrock yet to be broken up as chips.

A kerf made by a roller cutter is the channel, often irregular, left afterpassing of the cutter. As in the case of a crater, the cross-sectional area of akerf in brittle material is usually greater than the cross-sectional area of therim of the roller cutter that penetrated the rock. For drag tool cutting inbrittle materials a kerf usually has sloping sides resulting from overbreak.

Overbreak is the rock removed as chips on the unrelieved side of a cut.

Underbreak is the rock removed as chips below the level of tool tippenetration.

The depth of cut for an indenting tool is the distance from the starting rocksurface to the tip of the indenter, measured normal to the surface.

Kerf spacing describes the shortest distance between two cut kerfs or toolpaths traced in the rock face. The tool line spacing describes the shortestdistance between circles described by individual tools on a freely rotatingcutterhead.

Relieved cutting is an expression characterising the rock breakage along thecut tool path by chipping towards an adjacent kerf from a preceding cut. Thepreceding cut enhances the process of chip formation and loosening.

Unrelieved cutting is an expression characterising the rock breakage alongthe cut tool path by chipping where no preceding or adjacent kerf is present(or the spacing to the adjacent cut is too large to enable any interaction);

178

resulting in breakout angles typical for the tool, rock type and depth of cutas used for the specific cut.

Single-Pass cutting is an expression for relieved rock cutting characterisedby continuous rock breakage by chipping along the cut tool path.

Multi-Pass cutting is an expression for unrelieved rock cuttingcharacterised by discontinuous rock breakage by chipping along the toolpath, i.e. necessitating multiple tool passes (or cutterhead revolutions) toremove all the rock (ridges) between adjacent kerfs as chips.

Kerf profiling, kerf deepening or overcoring is the process resulting fromunrelieved cutting where little or no lateral chipping has occurred onprevious tool pass(es) towards the adjacent kerfs, and the kerf is deepenedinto a groove.

Chipping is the process where the growth of lateral macro-fractures extendsto neighbouring kerfs or macro-fractures generated by previous tool passesin the neighbouring kerfs resulting in the formation and loosening of rockfragments as chips.

Chipping frequency relates to the number of tool passes (or cutterheadrevolutions) required to remove the rock (ridges) between kerfs as chips.

Yield is the volume of rock excavated per unit distance of cut.

In-Line cutting is an expression characterising rock cutting where the toolsalways pass in previously cut kerfs or tool paths (typical for full-facemachines such as tunnel and raiseborers with concentric kerfs in the face).The crushed and compacted rock material remaining in the kerf obviouslyaffects the transfer of tool forces to the rock during the next tool pass.

Off-Line cutting is an expression characterising rock cutting where the toolsin principle never pass in previously cut kerfs or tool paths (typical forsweeping cutterheads such as the Robbins Mobile Miner and millingcutterheads for roadheaders).

Undercutting is an expression characterising rock cutting where the toolsattack the rock at an inclined angle - thus utilising an additional free face toenhance chip formation and loosening under the tool (as opposed to lateralchipping typical for in-line and off-line kerf cutting). The distance from theadditional free surface to the kerf or tool path is now taken as the kerfspacing. If this distance is so large that macro-fracture growth originatingfrom the tool contact area does not extend to this free surface; the rock isthen removed by wedging of the cut groove. This rock cutting method istermed Cut & Break. Undercutting was first introduced with the Wohlmeyermachine equipped with drag tools.

179

8.4 CUTTING FORCES AND SPECIFIC ENERGY

The principle cutterhead forces are the sum of the individual tool cuttingforces. Since the principle tool cutting forces Fn, Fr and Fs vary withtoolholder location on a domed cutterhead; an average "mean tooV force forthe cutterhead must be determined so as to simplify field performance andprediction modelling work.

The thrust force is the average force applied to the cutterhead in thedirection of the advance to maintain a prescribed advance rate.

Tool forces or cutting forces are the forces generated by the individualcutting tools on a cutterhead to maintain a prescribed depth of cut.

The individual tool cutting forces are either resultant forces, or componentsof the resultant force at some specified stage of tool penetration. For simpleindenters the cutting force is usually the direct thrust, more or less normal tothe surface.

The cutting forces are usually measured at the axle of a roller cutter, anddefined in terms of orthogonal components parallel and normal to thesurface and direction of cutter travel, i.e.

Mean normal force The average normal force Fn imposed on acutting tool to maintain a given depth of cut.The mean normal force is proportional to thetool contact area (or foot print area) forsingle-pass tool cutting.

Mean rolling force The average rolling force Fr imposed on aroller cutter to maintain a given depth andarises mainly from the rolling resistance of thecutter.

Mean side force The average side or lateral force Fs imposedon a cutting tool. This force, albeit generallysmall, manifests itself typically in relievedcutting operations when large chips areformed.

The ratio of the major tool force components, i.e. the ratio of the radial tothe tangential tool force component is:

8 cutting coefficient k = Fc / Fn for drag tools8 cutter coefficient k = Fr /Fn for roller cutters

180

The specific energy of an indentation tool is the work put into theindentation process per unit of material displaced. Alternatively, for acontinuous uniform process it is the power input for indentation divided bythe volumetric displacement rate. The dimensions of specific energy areenergy per unit volume, which is the same as force per unit area (e.g. J / m 3

= N / m 2 ). This parameter can be regarded as an indication of the cutting"efficiency" - which includes the effects of rock cuttability and drillability,toolholder and cutterhead compliance and kerf spacing.

8.5 ROCK MASS CUTTABILITY AND WEAR CAPACITY

Most rock mass formations are fractured to some degree; where the fractureplanes represent non-continuous structural elements in an otherwisecontinuous medium {intact rock).

Rock mass cuttability and drillability is its simplest form defined as being afactor proportional to net cutting or net advance rates, or specificcutting/drilling energy. However, the specific energy is closely linked to theapparatus or drilling equipment with which it has been determined. Anotherand perhaps more precise definition for rock cuttability is rock resistance totool indentation for a unit depth of cut, i.e. such as the critical normal force

for roller disk cutting or Ki for percussive drilling.

Rock resistance to tool indentation is the generated tool normal force for agiven tool indentation depth (generally taken as 1 mm/pass or 1 mm/rev/start)for a standard cutting tool geometry and kerf spacing. This rockcuttability/tool tip constant is commonly denoted as the critical normalforce Fnj.

Tool wear is defined as microscopic or macroscopic removal or fracture ofmaterial from the working surface of a tool or wearflat by mechanicalmeans; in general any degradation that reduces tool service life.

Tool wear rate is measured as tool weight, volume or height loss per cut orrolled distance.

The wearflat on cutting tools or studs is the abraded area of the tool tip.

Tool service life is measured in cut or rolled distance. However, tool servicelife in cutting hours per tool is a more practical unit of measure.

Tool consumption is the reciprocal of tool service life.

181

8.6 LIST OF ABBREVIATIONS

Uniaxial compressive strengthBrazilian tensile strengthPoint Load IndexYoung's modulus of elasticityPoisson's ratioDensityCritical energy release rateCritical stress intensity factor

Joint spacingJoint orientationStrikeDipAzimuth

Tungsten carbideCemented carbideVickers hardness for metals

Drilling Rate IndexBrittleness ValueSievers J Value

ucsBTSIsEV

PG,cKIC

0as/r

weWC/CoHV

DRIS20

SJ

[MPa][MPa][MPa][GPa]

[g/cm3][J/m2]

[MN/m3/2 = MPa • m"2]

[m]

n

[kgf/mm2]

Protodyakonov Rock Hardness /

Rosiwal Abrasivity Rating RosiwalWear Index F FCERCHAR Abrasivity Index CAIVickers hardness number (minerals) VHNVickers hardness number rock VHNR

[kgf/mm2][kgf/mm2]

Disk diameterDisk radiusDisk rim widthStuds on a disk rimAngular stud spacingStud rim spacingStud protrusion

Depth of cutHelix pitchLine spacingKerf spacingTool contact area

Mean normal forceMean rolling forceMean cutting forceMean side forceCritical normal forceKerf cutting exponent

drWn6 =RS =

P

DOCASline

Skerf

FnFrFcFsFn,b

[mm][mm][mm]

271 / n [°]2rcr / n [mm]

[mm]

[mm/pass or mm/rev/tool][mm/rev]

[mm][mm]

[mm2]

[kN/disk or kN/row or kN/pick][kN/disk or kN/row or kN/pick]

[kN/pick][kN/disk or kN/row or kN/pick][kN/disk or kN/row or kN/pick]

182

Cutter coefficientCutting constantTool cutting velocityCritical tool cutting velocitySpecific energy

Tools on cutterheadCutterhead rotary speedTool radius on cutterheadTool line number

k = Fr/Fn = C, • DOC l/2

C,v [m/s]Vcntical [m/s]

SE [2.78107 • kWh/m3 = J/nv = N/m2]

NRPM

[m]

Radial tool spacingAxial tool spacingLongitudinal tool spacingAngular tool spacingTools per line

Cutterhead rotation angleTool rotation angleTool path helix angleTool tilt angleSkew angleClearance angleRake angle

Cutterhead advance rateNet cutting rateCutterhead torqueCutterhead powerCutterhead thrustCutterhead side force

Tool wear ratesTool consumptionTool service lifeTool service life

ARALAZAAPTPL

Ptilt,

ARNCRTPf" thrust

F.side

WR

atari ( A / 27lR,)

atari ( AR, / AL;)

atari ( u I Rj)

[mm][mm][mm|

[m/h][nr/h]ikNm]

[kW][kNJ[kN]

[mg/mj[tools/m3][mVtool]

[hours/tool or meters/tool]

Conversion Factors

lkg

1 MPa

1 bar

1 kN

= 9.81 N= 0.4536 lb

= 1 N/mm2

= 1 • 106N/m2

= 145.14 psi

= 0.1 MPa

= 0.00445 lbf

1 kWh/m3 = 0.976 HPh/yd3

183

SUMMARY AND CONCLUSIONS

A summary of the main items in this study on mechanical rock cutting byroller cutters are:

B phenomenological model based on similarity analysis for rollerdisk cutting

& review of rock mass properties which affect rock cuttability andtool life

H principles for linear and field cutting tests and performanceprediction modelling

S review of cutterhead lacing design procedures and principles

In detail, the mechanics of cutting and boring are presented in Chapter 1. Aphenomenological model based on similarity analysis for the cutting actionof roller disk cutters is presented in Chapter 2. Rock mass properties whichaffect rock cuttability and tool life are presented in Chapter 3. The principlesof linear test cutting machines and prediction modelling of roller diskcutting based on linear cutting test and field trial results are presented inChapter 4. A procedure for calculating individual tool and cutterhead forcesis presented in Chapter 5, followed by a presentation of cutterhead toollacing design in Chapter 6, including some aspects of field performanceprediction modelling in Chapter 7.

As a conclusion of this study, the following items have been carried out:

• construction of a test rig• field tests proposed and started up8 the study results can be used to improve the performance

prediction models used to assess the feasibility of differentmechanical excavation techniques at various repositoryinvestigation sites.

184

LITERATURE

Autio, J. & Kirkkomäki, T. 1996. Boring of full scale deposition holesusing a novel dry blind boring method. Report POSIVA-96-07, Posiva Oy,Helsinki and similar report in SKB's (Svensk Kärnbränslehantering AB)report series Projekt Rapport PR 96-21.

Baker, W.E., Westine, P.S. and Dodge, F.T. (1973). Similarity Methods inEngineering Dynamics. Hayden Book Company Inc.

Bieniawski, Z.T. (1984). Rock Mechanics Design in Mining andTunnelling. A.A. Balkema, p 272.

Blindheim, O.T. (1979). Bergarters borbarhet. Borbarhetsprognoser fortunnelanlegg. Dr ing avhandling, Geologisk Institutt, NTH, p 406.

Ewendt, G. (1989). Erfassung der Gesteinsabrasivität und Prognose desWerkzeugverschleißes beim maschinellen Tunnelvortrieb mitDiskenmeißeln. Bochumer geologische und geotechnische Arbeiten, Heft33,p88.

Fenn, O., Protheroe, B.E. and Joughin, N.C. (1985). Enhancement ofRoller Cutting by Means of Water Jets. Chapter 21, RETC Proceedings,Vol.1, 1985.

Gertsch, R.E. (1993). Tunnel Boring Machine Disk Cutter Vibrations.Colorado School of Mines, MSc Thesis, p 144.

Gertsch, R.E. and Özdemir, L. (1991). Performance Prediction ofMechanical Excavators in Yucca Mountain Welded Tuffs from LinearCutter Tests. CSM/Sandia National Laboratories, Albuquerque, NewMexico, SAND91-7038.

Hoek, E. and Bray, J.W. (1977). Rock Slope Engineering. Institution ofMining and Metallurgy, London, p 402.

Jaeger, J.C. and Cook, N.G.W. (1971). Fundamentals of Rock Mechanics.Chapman and Hall Ltd., p 515.

Lislerud, A. (1990). Hard Rock Tunnel Boring. Sandvik Rock DrillingDays, Sandviken, October 1990, pp 49-70.

Mason, B. and Berry, L.G. (1968). Elements of Mineralogy. W.H.Freeman and Company, p 550.

185

Manttari, MJ. (1997). Laboratory Scale Rock Drillability Tests. LicentiateThesis, Helsinki University of Technology, p 131.

NTH (1988). Project Report 1-88: Hard Rock Tunnel Boring. University ofTrondheim, p 183.

NTH (1990). Project Report 13-90: Drillability - Drilling Rate IndexCatalogue. University of Trondheim, p 179.

Obert, L. and Duvall, W.I. (1967). Rock Mechanics and the Design ofStructures in Rock. John Wiley & Sons, Inc., p 650.

Rostami, J. (1992). Design Optimization, Performance Prediction andEconomic Analysis of Tunnel Boring Machines for the Construction of theProposed Yucca Mountain Nuclear Waste Repository. Colorado School ofMines, MSc Thesis, p 248.

Sandvik Hard Materials (1997). Understanding Cemented Carbide. H-9100-ENG, p20.

Schmidt, R.L. (1972). Drillability Studies. Percussive Drilling in the Field.USBM Report of Investigations 7684.

Snowdon, R.A., Ryley, M.D., Temporal, J. and Crabb, G.I. (1983). TheEffect of Hydraulic Stiffness on Tunnel Boring Machine Performance. Int. J.Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 20, No. 5, pp 203-214.

TVO 1992. Final Disposal of Spent Fuel in the Finnish Bedrock, TechnicalPlans and Safety Assessment. Helsinki. Teollisuuden Voima Oy. ReportYJT-92-31-E.

186

APPENDICES

Appendix 1. Excel file printouts of Disk Contact Angle Formula,2 pages

Appendix 2. Excel file printouts of Coefficient of Rock Strength versusUnaxial Compressive Strength, 1 page

Appendix 3. Excel file printouts of Skewed and Off-Line Micro-DiskLathe Cutting Tests, 2 pages

Appendix 4. Excel file printouts of Normalized Linear Roller DiskCutting Tests, 44 pages

Appendix 5. Excel file printouts of Tool and Cutterhead Forces forSumping Cutterheads (1), 1 page

Appendix 6. Excel file printouts of Tool and Cutterhead Forces forSumping Cutterheads (2), 1 page

Disk Contact Angle w Formulaecontangl.xls/A. Lislerud

nQ.><

Disk diameter, dDisk radius, rDisk edge width, W

Actual disk contact angleApprox. disk contact angleActual chord lengthActual disk contact arcApprox. disk contact arc

Actual disk edge contact areaApprox. disk edge contact area

Actual disk indentation areaApprox. disk indentation areaIndentation depth at resultant force attack pointIndentation depth ratio, p

Mean disk edge indentation depth

Approx. resultant force attack angleActual cutting coefficientApprox. cutting coefficient

305 mm152.5 mm

10 mm

or co1 = atan ((d-DOC - DOCA2 )A0.5 / (r - DCco' = acos ( ( r - DOCco = ( 360/rc )•( DOC/d )A0.5Lchord = 2 • (d-DOC - DOCA2 )A0.5Lore' = Ttdio / 360Larc = (d-DOC )A0.5

Aeon'= Wjidco/360Aeon = W( d-DOC )A0.5

Aindenf = 7irA2< co/360 ) - 1 / 2 ( r - DOC )•( d-DOC - DOCA2 )A0.5Aindent = rA2( p-DOC / d )A0.5 - 1 / 2 ( r - p-DOC )•( d-p-DOC )A0.5DOCresultant = p D O C

0.75

DOCmean = Aindent' / ( 1 /2 • Lchord )

toresultant = acos ( ( r - ( 1 - p )DOC) / r )k' = tan coresultantk = ( DOC / d )A0.5

Max DiskIndentation

Depth

DOC(mm)

0.10.5123456789101112131415

ActualDisk

Approx.Disk

Contact ContactAngle

co1

(°)2.084.646.579.2911.3813.1514.7116.1317.4318.6419.7820.8621.9022.8823.8324.7425.63

AngleCO

O2.074.646.569.2811.3713.1214.6716.0717.3618.5619.6920.7521.7622.7323.6624.5525.41

ActualDisk

Approx.Disk

Contact ContactArcLarc'

(mm)5.512.417.524.730.335.039.242.946.449.652.655.558.360.963.465.868.2

ArcLarc

(mm)5.512.317.524.730.234.939.142.846.249.452.455.257.960.563.065.367.6

ActualDisk

Approx.Disk

Contact ContactAreaAeon'

(mm2)55.2123.5174.7247.2302.9350.0391.5429.1463.8496.1526.5555.2582.7608.9634.1658.5681.9

AreaAeon

(mm2)55.2123.5174.6247.0302.5349.3390.5427.8462.1494.0523.9552.3579.2605.0629.7653.5676.4

Mean DiskIndentation

Depth

OOCmean(mm)0.0690.3360.6701.3382.0062.6763.3474.0184.6915.3646.0396.7147.3908.0688.7469.42510.105

DiskIndentationDepth Ratio

DOCmean/OOC

0.6910.6720.6700.6690.6690.6690.6690.6700.6700.6710.6710.6710.6720.6720.6730.6730.674

ActualDisk

Approx.Disk

ndentation indentationArea

Aindenf/2(mm2)

0.182.065.8216.4330.1646.3964.7685.05107.07130.68155.78182.27210.07239.12269.35300.71333.16

AreaAindent/2(mm2)

0.182.015.6716.0429.4745.3763.4183.36105.04128.34153.14179.35206.92235.77265.84297.10329.49

ResultantForce Attack

Angle

coresultant

o1.042.323.284.645.686.577.348.048.699.299.8510.3910.9011.3811.8512.3012.73

DiskContact

Angle Ratio

axesultant/w

0.5000.5000.5000.5000.4990.4990.4990.4990.4990.4980.4980.4980.4980.4980.4970.4970.497

ActualCuttingCoeff.

k'

0.01810.04050.05730.08120.09950.11510.12880.14130.15280.16360.17370.18330.19250.20130.20980.21800.2260

Approx.CuttingCoeff.

k

0.01810.04050.05730.08100.09920.11450.12800.14030.15150.16200.17180.18110.18990.19840.20650.21420.2218

Mean Value 2/3 1/2

NO

Coefficient of Rock Strength versus Uniaxial Compressive Strengthusbm7684.xis/A. Lislerud

GeologicName

Negaunee Iron FormationBanded Grey Gneiss

Rib Hill QuartziteWelded Tuff

Dneta Member, Prairie du Chien FormatiorDneta Member, Prairie du Chien Formatior

Sioux QuartziteSioux Quartzite

Rockville Quartz MonzoniteSt Cloud Gray GranodioriteWarman Quartz Monzonite

Dneta Member, Prairie du Chien FormatiorBiwabik Iron FormationBiwabik Iron FormationBiwabik Iron Formation

Duluth Gabbro

Duluth GabbroBad River Dolomite

GabbroNegaunee Iron Formation

Drillability Studies. Percussive Drilling in the

CommercialName

Humboldt Iron SilicateHornblende SchistGranite PegmatiteWausau QuartziteWausau Argillite

Winona DolomiteMankato Stone

New Ulm QuartziteJasper QuartziteRockville GraniteCharcoal Granite

Diamond Gray GraniteDresser Basalt

Shiely LimestoneMt. Iron TaconiteAurora TaconiteBabbit TaconiteBabbitt Diabase

Ely GabbroTrap Rock

AnorthositeEly Gabbro

MarblePrimax Gabbro

Iron Ore

Location

Humboldt, Mich.Randville, Mich.Randville, Mich.

Wausau, Wis.Wausau, Wis.Winona, Minn.Mankato, Minn.New Ulm, Minn.Jasper, Minn.

Cold Spring, Minn.St. Cloud, Minn.

Isle, Minn.Dresser, Wis.

St. Paul Park, Minn.Mt. Iron, Minn.

Hoyt Lakes, Minn.Babbitt, Minn.Babbitt, Minn.

Ely, Minn.Tofte, Minn.Tofte, Minn.

Duluth, Minn.Grandview, Wis.

Mellen, Wis.Palmer, Mich.

Field.

TensileStrength

(psi)20801080123025102620600910225029501300185017804020820

4330316041103550215073015001990101018101680

USBM Ri 7684

CompressiveShore HardnessStrength

(psi)5955029600127503165031400138001780022250437002200028950243504080014200513505240051850533002960098001870026500181502505032050

(ScleroscopeUnits)

767688100725249669291878881358083869089439175528265

Density

(g/cm3)3.502.992.632.642.732.622.602.612.632.652.662.652.992.483.363.073.122.992.852.682.712.912.852.933.33

R.L, Schmidt

Static Young'Modulus

(10**6-psi)11.114.65.910.57.6

7.45.89.49.69.89.313.16.215.713.313.011.712.98.512.29.211.614.810.0

: PoissonRatio

0.130.240.070.070.23

0.270.140.030.260.250.230.290.280.190.160.220.240.280.280.270.270.260.270.23

pen

di

'sCoefficientof*Rock Strength •

CRS2.391.640.770.782.280.470.450.751.010.841.210.822.860.571.472.622.842.441.210.640.732.110.681.021.28

Conversion Factor '{MPa} = 0.006889-{psi} Coefficient of Rock Strength, CRS USBM modified version of the Protodyakonov test

Skewed and Off-Une Micro-Disk Lathe Cutting TestsErfassung der Gesteinsabrasivitat und Prognose des Werkzeugverschleisses beim maschinellen Tunnelvortrleb mlt Diskenmeissein.Bochumer Geologlsche und Geotechnische Arberten. Heft 33, 1989.G. Ewendt

bochum35.xls/A. Uslerud

Q.

Disk DiameterDisk Rim AngleDisk Tip RadiusDisk Steel HardnessCutting Speed

35 mm70°

2.0 mm60HRC

0.17 m/s

Rock Type ~~KeT?—Depth Cutting B 5 5 TSpacing of Ratio Normal

Cut Force

Critical Standard Mean—Weight Weight Weight Mean Critical Standard Mean Uniaxial—Point Youngs—TIcEiTi CERCHAR—CERCHAR—W5a7"Normal Critical Value Loss Loss Loss Value Weight Critical Value Compress. Load Modulus Hardness Abrasivlty Abrasivity IndexForce Normal Control' Loss Weight Strength Index Rock "Smooth" "Rough"

Force LossFnl Fnll Fnll WLM WLM3 WLM3 WLM3 WIM1 WLM11 WLM11 UCS IsSO E VHNR CAI CAI F

(kN/dlsk) (kN/dlsk) (kN/disk) (mg/m) (g/m*) (g/m*) (g/m*) (mg/m) (mg/m) (mg/m) (MPa) (MPa) (GPa) (kgf/mm') (N/mm)S

(mm)DOC(mm)

S/OOC Fn(kN/dlsk)

BasaltBasaltBasaltBasaltBasalt

GabbroGabbroGabbroGabbroGabbroGabbroGabbroGabbroGabbroGabbro

Gneiss/PGneiss/PGnelss/PGneiss/PGneiss/PGneiss/P

Gneiss/NGneiss/NGneiss/NGneiss/NGneiss/NGneiss/N

GraniteGraniteGranite

33666

3336669121212

366699

336699

336

0.20.30.30.60.6

0.30.60.90.30.60.90.90.30.60.9

0.30.30.60.90.60.9

0.3060.60.90.60.9

0.30.60.3

15.010020.010.010.0

10.05.03.320.010.06.710.040020.013.3

10.020.010.06.715.0100

10.05.010.06.715.010.0

10.05.020.0

2.753.554625.755.70

2.002.743.222.923.754.414574.135.156.25

2.302.653.734.564.796.09

2.883,724.235.175.035.87

2.043.133.38

6 ) 56.488.437.427.36

3.653.543.395.334.844.654.827.546.656.59

4.204.844.824.816.186.42

5.264.805.465.456.496.19

3.724.046.17

6.156.485.965.255.20

3.653.543.393.773.423.292.783.773323.29

4.203.423.413.403.573.71

5264.803863.853.753.57

3.724.044.36

5.81

3.42

3.62

4.1S

0.140.230.420.950.88

0.030.040.040.070.070.150.160.140.200.40

0.060.120.210.250.340.63

0.150.290.420.820.500.92

0.380.480.28

301254235267244

32211539182419392737

687061526377

16116011514792114

426268158

233256233264244

33221539192820392837

676758466378

16716111715293114

422267156

246.1

28.0

63.1

133.7

0.7000.7671.4001.5831.467

0.1000.0670.0440.2330.1170.1670.1780.4670.3330.444

0.2000.4000.3500.2780.5670.700

0.5000.4830.7000.9110.8331.022

1.2670.8000.933

0.7000.7670.7000.7920.733

0.1000.0670.0440.1170.0580.0830.0590.1170.0830.111

0.2000.2000.1750.1390.1890.233

0.5000.48303500.4560.2780.341

1.2670.8000.467

0.738

0.084

0.18!

0.401

11.8 77.9 770 2.8 3.4 1.1

168

181

180

7.9

2.4

7.5

56.5

49.2

41.2

687

748

748

3.5

4.2

4.2

4.1

5.2

5.2

3.3

2.4

7.4

• o

GraniteGraniteGranite

QuarfziteQuartziteQuartzlteQuartzite

SandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstone

Sandstone #2Sandstone #2

669

3666

333666999121212

99

0.60.90.9

0.30.30.60.9

0.30.60.90.30.60.90.30.60.90.30.61.2

0.60.9

1006.710.0

10.020.010.06.7

10.05.03,320.010.06.730.015.010.040.020.010.0

15.010.0

3.504.825.58

3.424.274.785.68

1.532.032.392.323.023.373.153.924.353.514.805.52

3.043.58

4 525.085.88

6.247.806.175.99

2.792.622524.243.903.555.755.064.596416.205.04

3.923.77

3.203.593 40

6.245.514.364.23

2.792.622523.002.762.513.322.922.653203.102.52

2.272.18

3.72

5.09

2.83

2.22

0.650.891.45

0.750.591.361.98

0.030.070.100.050.090100.110.180.230.080.160.40

0.290.31

181164179

833325377367

363738282620413331232228

5338

181165179

833328378367

333937282519413328222228

5438

1.0830.989

189.3 1.611

2.5001.9672.267

357.4 2.200

0.1000.1170.1110.1670.1500.1110.3670.3000.2560.2670.2670.33329.6

0.48346.0 0.344

0.5420.4940.537 0.568

2.5000.9831.1331100 1.072

01000.1170.1110.0830.0750.0560.1220.1000.0850.0670.0670.083 0.089

0.1610.115 0.138

170 7.2 55.2 869

180 10.4 58.5 1060

3.2

2.8

5.2

4.9

16.7

4.0

Q.

165 6.0 34.6 4.5 5.1 1.5

Data Normalisation

Prediction Model

Comments

= WLM'(Fnll /Fn)"2

Fnl =Fn/DOC**l/2Fnll = Fn / (DOC' (S /3 ) ) " l / 2 = Fnl / (S/3 )"l/2

"Contror = WLM " 1000 / (DOC • S)WLM1 = WLM / DOCWLM11 = WLM/(DOC'S/3)

Fn = Fnll * (DOC* S/3)" ' l /2Fnll = rock cuttability/dtek tip constant

WLM =WLM11 * ( D O C ' S / 3 )WLH = WLM ' v * 3600

= WLM11 * ( DOC ' S / 3 ) • v * 3600WLM3 = WLM" 1000/(DOC'S)

= WLM11 * 1000/3WLM 11 = rock abrasivity/ disk tip constant

Gneiss/F = disk penetration parallel to foliationGneiss/P> = disk penetration normal to foliationSandstoi = artificial "laboratory" rockCAI-Rou = measurements on natural failure surfaces

(mg / m)(mg / h)

(g / m3)

is)

CSM Linear Cuffing Tests

Source

File

Rock TypeUniaxia] Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width. W

Tamrock Technology CenterArne Lislerud

MSc Thesis, Jamal Rostami, CSM

bersandl.xls

Berea Sandstone46.2MPal. lMPa

"Wedged" Constant SectionRobbinsA30581432mm (17")12.7mm (0.5")

na.x-p-

KerfSpacing

S(mm)76.276.2152.4152.4

DiscPenetration

DOC(mm)25.438.125.438.1

Overall Average Mean

CuttingRatio

S/DOC

3.02.06.04.0

MeanNormal

Fn(kN/disc)

121.8155.4139.8183.1

MeanRolling

Fr(kN/disc)

20.241.533.547.6

CuttingCoefficient

k

0.16600.26720.24000.2600

CuttingConstant

Cl

0.03290.04330.04760.04210.0415

CriticalNormal

Fnl(kN/disc)

24.1625.1727.7329.66

CriticalNormalFnl1-76

(kN/disc)24.1625.1719.6120.9822.48

SpecificEnergy

SE(kWh/m3)

2.903.972.412.28

Coefficient of Rock Strength versus Uniaxiai Compressive Strengthusbm7684.xls/A. Lisierud

GeologicName

Negaunee Iron FormationBanded Grey Gneiss

Rib Hill QuartziteWelded Tuff

Dneta Member, Prairie du Chien FormatiorDneta Member, Prairie du Chien Formatior

Sioux QuartziteSioux Quartzite

Rockville Quartz MonzoniteSt Cloud Gray GranodioriteWarman Quartz Monzonite

Dneta Member, Prairie du Chien FormatiorBiwabik Iron FormationBiwabik Iron FormationBiwabik Iron Formation

Duluth Gabbro

Duluth GabbroBad River Dolomite

GabbroNegaunee Iron Formation

Driliability Studies. Percussive Drilling In the Field.

CommercialName

Humboldt Iron SilicateHornblende SchistGranite PegmatiteWausau QuartziteWausau Argillite

Winona DolomiteMankato Stone

New Ulm QuartziteJasper QuartziteRockville GraniteCharcoal Granite

Diamond Gray GraniteDresser Basalt

Shiely LimestoneMt. Iron TaconiteAurora TaconiteBabbit TaconiteBabbitt Diabase

Ely GabbroTrap Rock

AnorthositeEly Gabbro

MarblePrimax Gabbro

Iron Ore

Location

Humboldt, Mich.Randville, Mich.Randville, Mich.

Wausau, Wis.Wausau, Wis.

Winona, Minn.Mankato, Minn.New Ulm, Minn.Jasper, Minn.

Cold Spring, Minn.St. Cloud, Minn.

Isle, Minn.Dresser, Wis.

St. Paul Park, Minn.Mt. Iron, Minn.

Hoyt Lakes, Minn.Babbitt, Minn.Babbitt, Minn.

Ely, Minn.Tofte, Minn.Tofte, Minn.Duluth, Minn.

Grandview, Wis.Mellen, Wis.

Palmer, Mich.

TensileStrength

(psi)20801080123025102620600910225029501300185017804020820

4330316041103550215073015001990101018101680

•

USBM Ri 7684

CompressiveShore HardnessStrength

(psi)5955029600127503165031400138001780022250437002200028950243504080014200513505240051850533002960098001870026500181502505032050

(ScleroscopeUnits)

767688100725249669291878881358083869089439175528265

Density

(g/cm3)3.502.992.632.642.732.622.602.612.632.652.662.652.992.483.363.073.122.992.852.682.712.912.852.933.33

R.L. Schmidt

Static Young'Modulus

(10**6-psi)11.114.65.910.57.6

7.45.89.49.69.89.313.16.215.713.313.011.712.98.512.29.211.614.810.0

:Poisson'Ratio

0.130.240.070.070.23

0.270.140.030.260.250.230.290.280.190.160.220.240.280.280.270.270.260.270.23

pendi

^Coefficient of *Rock Strength •

CRS2.391.640.770.782.280.470.450.751.010.841.210.822.860.571.472.622.842.441.210.640.732.110.681.021.28

Conversion Factor '{MPa} = 0.006889> {psi} Coefficient of Rock Strength, CRS USBM modified version of the Protodyakonov test

Skewed and Off-Line Micro-Disk Lathe Cutting TestsErfassung der Gesteinsabrasivitat und Prognose des Werkzeugverschleisses beim maschinellen Tunnelvortrieb mit Diskenmeisseln.Bochumer Geologische und Geotechnische Arbeiten, Heft 33, 1989.G. Ewendt

bochum35.xls/A, Lislerud

Disk Diameter 35 mmDisk Rim Angle 70 °Disk Tip Radius 2.0 mmDisk Steel Hardness 60 HRCCutting Speed 0.17 m/s

"a

a.x

Rock Type Kerf Depth CuttingSpacing of Ratio

Cut

Critical StandardNormal CriticalForce Normal

ForceFnl Fnll

(kN/disk) (kN/disk)

Mean Weight WeightValue Loss Loss

Fnl 1 WLM WLM3(kN/disk) (mg/m) (g/m')

Weight Mean Critical Standard Mian Uniaxial Point Youngs Vickers CERCHAR CERCHAR WearLoss Value Weight Critical Value Compress. Load Modulus Hardness Abrasivity Abrasivity Index

Control' Loss Weight Strength Index Rock "Smooth" "Rough"Loss

WLM3 WLM3 WLM1 WLM11 WLM11 UCS ls50 E VHNR CAI CAI F(g/m') (g/m') (mg/m) (mg/m) (mg/m) (MPa) (MPa) (GPa) (kgf/mm') (N/mm)

S(mm)

DOC(mm)

S/DOC

MeanNormalForce

Fn(kN/disk)

BasaltBasaltBasaltBasaltBasalt

GabbroGabbroGabbroGabbroGabbroGabbroGabbroGabbroGabbroGabbro

Gneiss/PGneiss/PGneiss/PGneiss/PGneiss/PGneiss/P

Gneiss/NGnelss/NGneiss/NGneiss/NGneiss/NGneiss/N

GraniteGraniteGranite

33666

3336669121212

366699

336699

336

0.20.30.30.60.6

0.30.60.90.30.60.90.90.30.60.9

0.30.30.60.90.60.9

0.30.60.60.90.60.9

15.010.020.010.010.0

10.05.03.320,010.06.710.040.020.013.3

10.020.010.06.715.010.0

10.05,010.06.715.010.0

0.3 10.00.6 5.00.3 20.0

2.753.554.625.755.70

2.002.743.222.923.754.414.574.135.156.25

2.302.653.734.564.796.09

2.883.724.235.175.035.87

2.043,133.38

6.156.488.437.427.36

3.653.543.395.334.844.654.827.546.656.59

4.204.844.824.816.186.42

5.264.805.465.456.496.19

3.724.046.17

6.156.485.965.255.20

3.653.543.393.773.423.292.783.773.323.29

4.203.423.413.403.573.71

5.264.803.863.853.753.57

3.724.044.36

5.81

3.42

3.62

4.18

0.140.230.420.950.88

0.030.040.040.070.070.150.160.140.200.40

0.060.120.210.250.340.63

0.150.290.420.820.500.92

0.380.480.28

301254235267244

32211539182419392737

687061526377

16116011514792114

426268158

233256233264244

33221539192820392837

676758466378

16716111715293114

422267156

246.1

28.0

63.1

133.7

0.7000.7671.4001.5831.467

0.1000.0670.0440.2330.1170.1670.1780.4670.3330.444

0.2000.4000.3500.2780.5670.700

0.5000.4830.7000.9110.8331.022

1.2670.8000.933

0.7000.7670.7000.7920.733

0.1000.0670.0440.1170.0580.0830.0590.1170.0830.111

0.2000.2000.1750.1390.1890.233

0.5000.4830.3500.4560.2780.341

1.2670.8000.467

0.738 440 11.8 77.9 770 2.8 3.4 1.1

0.084

0.189

0.401

168

181

180

7.9

2.4

7.5

56.5

49.2

41.2

687

748

748

3.5

4.2

4.2

4.1

5.2

5.2

3.3

2.4

7.4

NJ

10.06.710.0

10.020.010.06.7

10.05.03.320.010.06.730.015.010.040.020.010.0

15.010.0

3.504.825.58

3.424.274.785.68

1.532.032.392.323.023.373.153.924.353.514.805.52

3.043.58

XIX)tt>

Q.t—•X

GraniteGraniteGranite

QuartziteQuartziteQuartziteQuartzite

SandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstoneSandstone

Sandstone #2Sandstone #2

669

3666

333666999121212

99

060.90.9

0.30.30.60.9

0.30.60.90.30.60.90.30.60.90.30.61.2

0.60.9

4.525.085.88

6.247.806.175.99

2.792.622.524.243.903.555.755.064.596.416.205.04

3.923.77

3.593.40

6.245.514.364.23

2.792.622.523.002.762.513.322.922.653.203.102.52

2.272.18

3.72

5.09

2.83

2.22

0.650.891.45

0.750.591.361.98

0.030.070.100.050.090.100.110.180.230.080.160.40

0.290.31

181164179

833325377367

363738282620413331232228

5338

181165179

833328378367

333937282519413328222228

5438

1.0830.989

189.3 1.611

2.5001.9672.267

357.4 2.200

0.1000.1170.1110.1670.1500.1110.3670.3000.2560.2670.2670.333

0.4830.344

29.6

46.0

0.5420.4940.537 0.568

2.5000.9831.1331.100 1.072

0.1000.1170.1110.0830.0750.0560.1220.1000.0850.0670.0670.083 0.089

0.1610.115 0.138

170 7.2 55.2 869

180 10.4 58.5 1060

3.2

2.8

5.2

4.9

16.7

4.0

165 6.0 34.6 4.5 5.1 1.5

Data Normalisation

Prediction Model

Comments

= WLM * ( Fnl 1 /Fn) "2

Fnl =Fn/DOC" l /2Fnll = F n / ( D O C * ( S / 3 ) ) " l / 2 = Fnl / (S / 3 ) " l / 2

"Control' = WLM * 1000 / ( DOC * S )WLM1 = WLM / DOCWLM11 = WLM/ (DOC 'S /3 )

Fn =Fnll * ( D O C * S / 3 ) " l / 2Fnl 1 = rock cuttability/disk tip constant

WLM = WLM11 * ( DOC * S / 3 )WLH = WLM " V * 3600

= WLM11 * (DOC * S / 3 ) * v* 3600WLM3 =WLM* 1000 / ( D O C ' S )

= WLM11 * 1000/3WLM 11 = rock abraslvify/ disk tip constant

Gneiss/F = disk penetration parallel to foliationGneiss/r> = disk penetration normal to foliationSandstoi = artificial "laboratory" rockCAI-Rou = measurements on natural failure surfaces

(mg / m)( m g / h )

(g / m3)

ts j

CSM Linear Cutting Tests

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

Tomrock Technology CenterArne Lislerud

MSc Thesis, Jamal Rostami, CSM

bersandl .xls

Berea Sandstone46,2MPal. lMPa

"Wedged" Constant SectionRobbins A30581432mm (17")12.7mm (0.5")

X)- an>CLI—

X

KerfSpacing

S(mm)76.276.2152.4152.4

DiscPenetration

DOC(mm)25.438.125.438.1

Overall Average Mean

CuttingRatio

S/DOC

3.02.06.04.0

MeanNormal

Fn(kN/disc)

121.8155.4139.8183.1

MeanRolling

Fr(kN/disc)

20.241.533.547.6

CuttingCoefficient

k

0.16600.26720.24000.2600

CuttingConstant

Cl

0.03290.04330.04760.04210.0415

CriticalNormal

Fnl(kN/disc)

24.1625.1727.7329.66

CriticalNormalFnl1-76

(kN/disc)24.1625.1719.6120.9822.48

SpecificEnergy

SE(kWh/m3)

2.903.972.412.28

CSM Linear Cutting Tests Tamrocic Technology CenterArne Lislerud

>-anQ.

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

bersandl.xls

Berea Sandstone46.2MPal.lMPa

"Wedged" Constant SectionRobbinsA30581432mm (17")12.7mm (0.5")

KerfSpacing

S(mm)76.276.2152.4152.4

DiscPenetration

DOC(mm)25.438.125.438.1

Overall Average Mean

CuttingRatio

S/DOC

3.02.06.04.0

MeanNormal

Fn(kN/disc)

121.8155.4139.8183.1

MeanRolling

Fr(kN/disc)

20.241.533.547.6

CuttingCoefficient

k

0.16600.26720.24000.2600

CuttingConstant

Cl

0.03290.04330.04760.04210.0415

CriticalNormal

Fnl(kN/disc)

24.1625.1727.7329.66

CriticalNormalFnll-76

(kN/disc)24.1625.1719.6120.9822.48

SpecificEnergy

SE(kWh/m3)

2.903.972.412.28

t-o

CSM Linear Cutting Tests Tamrock Technology CenterArne LislerucS

XIXI0!

Q.

X

4=-

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

bersand2.xls

Berea Sandstone46.2MPal. lMPa

Constant SectionRobbinsAM1724432mm (17")19.05mm (0.75")

KerfSpacing

S(mm)76.276.2152.4152.4

DiscPenetration

DOC(mm)25.438.125.425.4

Overall Average Mean

CuttingRatio

S/DOC

3.02.06.06.0

MeanNormal

Fn(kN/disc)

156.8166.0159.4165.5

MeanRoiling

Fr(kN/disc)

27.642,339.446.3

CuttingCoefficient

k

0.17600.25460.24720.2800

CuttingConstant

Cl

0.03490,04120.04910.05560.0452

CriticalNormal

Fnl(kN/disc)

31.1126.9031.6232.83

CriticalNormalFnil-76

(kN/disc)31.1126.9022.3623.2225.89

SpecificEnergy

SE(kWh/m3)

3.964.042.833,32

-p-

0>zsQ,X

Rock TypeCompressive Strength (MPa)Tensile Strength (MPa)

Disk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Colorado Red Granite137.811.7

Robbins A30581432(17")12.7(0.5")0.254

Test Cut Cut Ratio Mean Mean Mean Critical Critical Cutter Cutter SpecificCut Depth Spacing Normal Roll Side Thrust Thrust Coeff. Constant Energy

# DOC S S/DOC Fn Fr Fs Fnl Fnl 1-76 k e l SE(mm/pass) (mm) (kN/disk) (kN/disk) (kN/disk) (kN/disk) (kN/disk) (kWh/m3)

1234567

1.912.543.183.815.086.357.62

76.276.276.276.276.276.276.2

39.930.024.020.015.012.010.0

99.796.4111.9121.0128.5147.2159.1

5.026.078.3011.4414.0319.1822.27

2.172.933.243.524.478.5813.60

72.1360.5062.7662.0057.0158.3957,65

72.1360.5062.7662.0057.0158.3957.65

0.05040.06300.07420.09450.10920.13030.1399

0.03640.03950.04160.04840.04840.05170.0507

9.8.9.10101110

587151.95.07.01.65

Overall Average Mean 61.49 0.0453

-P-

X I

TestCut

#

PeakNormalFnpeak

(kN/disk)

PeakRoll

Frpeak(kN/disk)

PeakSide

Fspeak(kN/disk)

RatioNormal

Fnpeak/Fn

RatioRoll

Frpeak/Fr

RatioSide

Fspeak/Fs

X-P-

1234567

200.9194.3236.8247.3261.5283.1305.5

17.0417.5122.9528.5831.7443.4449.90

26.1029.8835.8238.9740.3546.5656.58

2.022.022.122.042.041.921.92

3.392.882.772.502.262.262.24

12.0310.2011.0611.079.035.434.16

Overall Average Mean 2.01 2.62 9.00

Data Normalization

Prognosis Model

Conversion Factors

Comments

FniFoi lkc lSESE

FnFniFr

{KN}{MPa}{kWh/m3}

(0

= Fn/(DOC)**l/2= Fn/(DOC*(S/76.2))**l/2= Fr/Fn . .= k/(DOC)**l/2= (Fr/3600)/(DOC*S/1000000) {kWh/m3}= Fr*1000/(DOC*S) {MJ/m3}= Fn11*(DOC*S/76.2)**1/2= rock cuttability/disc tip constant= Fn*cr(DCC)**1/2

= 0.004445*{lb}= 0.006889*{psi}= 0.976*{hph/yd3}

peak value = overall peak (max) value for an individual cut sequencerock seems to "soften" as higher loads are applied

-p-

Illlil

Rock TypeCompressive Strength (MPa)Tensile Strength (MPa)

Disk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Colorado Red Granite137.811.7

RobbinsA30581432(17")12.7(0.5")0.254

Test Cut CutCut Depth Spacing

# DOC S(mm/pass) (mm)

Ratio MeanNormal

S/DOC Fn(kN/disk)

Mean Mean Critical Critical Cutter Cutter SpecificRoll Side Thrust Thrust Coeff. Constant EnergyFr Fs Fnl Fnll-76 k cl SE

(kN/disk) (kN/disk) (kN/disk) (kN/disk) (kWh/m3)242526273132

1.912.543.183.815.086.35

63.563.563.563.563.563.5

33.225.020.016.712.510.0

10/.3116.4126.0128.6150.3164.6

4.585.017.009.4813.7018.58

3.564.702.488.239.1414.01

77.6273.0270.6565.8766.6865.33

85.0379.9977.3972.1673.0471.57

0.04270.04300.05560.07370.09120.1129

0.03090.02700.03120.03780.04040.0448

10.498.639.6310.8811.8012.80

a>Q.

x'

Overall Average Mean 76.53 0.0353

n>Q.X

TestCut#

242526273132

Overall

PeakNormalFnpeak

(kN/disk)193.3204.7228.1246.4296.5318.1

PeakRoll

Frpeak(kN/disk)

17.7017.4221.7724.1232.5742.93

Average Mean

PeakSide

Fspeak(kN/disk)

26.2329.2128.6737.2439.5250.83

RatioNormal

Fnpeak/Fn

1.801.761.811.921.971.931.87

RatioRoll

Frpeak/Fr

3,863.483.112.542.382.312.95

RatioSide

Fspeak/Fs

7.376.2111.564.524.323.636.27

Data Normalization

Prognosis Model

Conversion Factors

Comments

Fnl = Fn/(DOC)**l/2Fnl 1 = Fn/(DOC*(S/76.2))**1 /2k = Fr/Fnc l = k/(DOC)**l/2SE = (Fr/3600)/(DOC*S/1000000) {kWh/m3}SE =Fr*1000/ (DOC*S) {MJ/m3}

Fn = Fn l l *(DOCS/76.2)"1 /2Fn 1 = rock cufrability/disc tip constantFr =Fn*cl*(DOC)** l /2

{kN} = 0.004445*{lb}{MPa} = 0.006889*{psi}{kWh/m3} = 0.976*{hph/yd3}

(i) peak value - overall peak (max) value for an individual cut sequence(li). rock seems to "soften" as higher loads are applied

liiili

Rock TypeCompressive Strength (MPa)Tensile Strength (MPa)

Disk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Colorado Red Granite137.811.7

RobbinsA30581432(17")12.7(0.5")0.254

TestCut

#

91011121314

CutDepthDOC

(mm/pass)1.912.543.183.815.086.35

CutSpacing

S(mm)50.850.850.850.850.850.8

Overall Average Mean

Ratio

S/DOC

26.620.016.013.310.08.0

MeanNormal

Fn(kN/disk)

72.578.889.892.7106.0120.8

MeanRollFr

(kN/disk)3.975.006.958.4611.1614.47

MeanSide

Fs(kN/disk)

3.364.573.845.858.6812.35

CriticalThrust

Fnl(kN/disk)

52.4749.4350.3747.4747.0247.92

CriticalThrust

Fnl1-76(kN/disk)

64.2660.5461.7058.1357.5858.6960.15

CutterCoeff.

k

0.05480.06350.07740.09130.10530.1198

CutterConstant

cl

0.03960.03980.04340.04680.04670.04760.0440

SpecificEnergy

SE(kWh/m3)

11.3710.7611.9512.1412.0112.46

XICD

CL

00

4?

TestCut#

91011121314

Overall

PeakNormalFnpeak

(kN/disk)160.4177.7196.6208.6233.7259.9

PeakRoll

Frpeak(kN/disk)

14.1316.5821.0123.8629.2240.44

Average Mean

PeakSide

Fspeak(kN/disk)

23.1827.6829.7733.3542.4048.18

RatioNormal

Fnpeak/Fn

2,212.262.192.252.202.152.21

RatioRoll

Frpeak/Fr

3.563.323.022.822.622.793.02

RatioSide

Fspeak/Fs

6.906.067.755.704.883.905.87

a>Q.x"-ft-

Data Normalization

Prognosis Model

Conversion Factors

Comments

Fnl = Fn/(DOC)**l/2Fnll =:Fn/(DOC*(S/76.2))**l/2k = Fr/Fnc l = k/(DOC)**l/2SE = (Fr /3600) / (DOC*S/1000000) { kWh/m3}SE = Fr*1000/(DOC*S) {MJ/m3}

Fn =Fn i r (DOC*S/76.2) " l /2Fnl = rock cuttability/disc tip constantFr = Fn*cT(DOC)** l /2

{kN} = 0.004445*{lb}{MPa} = 0.006889*{psi}{kWh/m3} - 0.976*{hph/yd3}

( i ) . . peak value = overall peak (max) value for an individual cu t sequence(ii) rock seems to "soften" as higher loads are appl ied

^^^^|gS|S£HS

Rock TypeCompressive Strength (MPa)Tensile Strength (MPa)

Disk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Colorado Red Granite137.811.7

Robbins A30581432(17")12.7(0.5")0.254

Test Cut Cut Ratio Mean Mean Mean Critical Critical Cutter Cutter SpecificCut Depth Spacing Normal Roll Side Thrust Thrust Coeff. Constant Energy# DOC S S/DOC Fn Fr Fs Fnl Fnll-76 k cl SE

(mm/pass) (mm) (kN/disk) (kN/disk) (kN/disk) (kN/disk) (kN/disk) (kWh/m3)33343536373839

1.271.912.543.183.815.086.35

38.138.138.138.138.138.138.1

30.019.915.012.010.07.56.0

62.573.979.987.895.4107.3120.5

3.045.095.257.168.8111.6314.33

1.742.044.207.107.8712.0815.22

55.4853.4450.1349.2148.8747.6047.83

78.4675.5770.8969.5969.1167.3167.64

0.04860.06890.06570.08160.09240.10840.1189

0.04310.04990.04120.04580.04730.04810.0472

17.4519.4315.0716,4216.8616.6916.45

TJft)ZSQ.

Overall Average Mean 71.22 0.0461

o

>X)T)D

TestCut#

33343536373839

Overall

PeakNormalFnpeak

(kN/disk)117.4132.3146.4172.9186.5193.9217.7

PeakRoll

Frpeak(kN/disk)

12.5821.0316.3118.2221.9127.1132.40

Average Mean

PeakSide

Fspeak(kN/disk)

12.9214.4018.6326.0129,2636.2341.17

RatioNormal

Fnpeak/Fn

1.881.791.831.971.961.811.811.86

RatioRoll

Frpeak/Fr

4.144,133.112.542.492.332.263.00

RatioSide

Fspeak/Fs

7.437.064.443.663.723.002.704.57

Data Normalization

Prognosis Model

Conversion Factors

Comments

Fnl =Fn/(DOC)^l/2Fnll = Fn/(DOC*(S/76.2))** 1 /2k = Fr/Fnc l • = k/(DOC)**l/2SE = (Fr /3600)/ (DOC*S/1000000) {kWh/m3}SE =Fr*1000/ (DOC*S) {MJ/m3}

Fn = Fnl 1*(DOC*S/76.2)**l/2Fnl = rock cuttability/disc tip constantFr =Fn*cl*(DOC)**l /2

{kN} = 0.004445* {Ib}{MPa} = 0.006889*{psi}{kWh/m3} = 0.976*{hph/yd3}

(i) peak value = overall peak (max) value for an individual cut sequence(it) rock seems to "soften" as higher loads are applied

"D

iiiili iiill iliiilii

Rock TypeCompressive Strength (MPa)Tensile Strength (MPa)

Disk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Colorado Red Granite137.811.7

Robbins A30581432(17")12.7(0.5")0.254

TestCut

#

1617181920212223

CutDepthDOC

(mm/pass)0.641.271,912.543.183.815.086.35

CutSpacing

S(mm)25.425.425.425.425.425.425.425.4

Overall Average Mean

Ratio

S/DOC

39.720.013.310.08.06.75.04.0

MeanNormal

Fn(kN/disk)

42.447.157.863.872.880.895.3115.9

MeanRollFr

(kN/disk)1.602.423.934.816.107.309.0712.43

MeanSide

Fs(kN/disk)

5.013.514.046.708.8911.2416.6125.79

CriticalThrust

Fnl(kN/disk)

52.9941.7941.8240.0340.8041.4142.2845.99

CriticalThrust

Fnll-76(kN/disk)

91.7872.3972.4369.3370.6771.7273.2379.6675.15

CutterCoeff.

k

0.03770.05140.06800.07540.08380.09030.09520.1073

CutterConstant

cl

0.04720.04560.04920.04730.04700.04630.04220.04260.0459

SpecificEnergy

SE(kWh/m3)

27.3420.8422.5020.7120.9820.9519.5321.41

Q.

x'

XIX}

TestCut

#

1617181920212223

Overall

PeakNormalFnpeak

(kN/disk)84.194.7111.2124.5142.4146.3169.3197.4

PeakRoll

Frpeak(kN/disk)

7.348.4611.3613.2915.3717.7520.8227.48

Average Mean

PeakSide

Fspeak(kN/disk)

13.5414.3217.8921.4826.2429.4238.5251.09

RatioNormal

Fnpeak/Fn

1.982.011.921.951.961.811.781.701.89

RatioRoll

Frpeak/Fr

4.593.502.892.762.522.432.302.212.90

RatioSide

Fspeak/Fs

2.704.084.433.212.952.622.321.983.04

X

Data Normalization

Prognosis Model

Conversion Factors

Comments

Fnl = Fn/(DOC)**l/2Fnli = Fn/(DOC*(S/76.2))**l/2k = Fr/Fnc l = k/(DOC)**l/2SE = (Fr/360G)/(DOC*S/1000000) {kWh/m3}SE = Fr*10Q0/(DOC*S) {MJ/m3}

Fn =Fn1l*(DOC*S/76.2r*1/2Fnl = rock cuttabiiity/disc tip constantFr =Fn*cr(DOC)**l/2.

{kN} = 0.004445* {Ib}{MPa} = 0.006889*{psi}{kWh/m3} = 0.976*{hph/yd3}

(i) peak value = overall peak (max) value for an individual cut sequence(ii) rock seems to "soften" as higher loads are applied

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

(V

X

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

colosprl.xls

Colorado Spring Granite143,9MPa7,8MPa

"Wedged" Constant SectionRobbins A30581432mm (17")12,7mm (0,5")

KerfSpacing

S(mm)69.969.969.969.9

DiscPenetration

DOC(mm)

2.53.85.16.4

Overall Average Mean

CuttingRatio

S/DOC

27.518.313.811.0

MeanNormal

Fn(kN/disc)

147.7165.5193,9220.1

MeanRolling

Fr(kN/disc)

10.913.719.927.1

CuttingCoefficient

k

0.07370.08300.10280.1232

CuttingConstant

Cl

0.04620.04250.04560.04890.0458

CriticalNormal

Fnl(kN/disc)

92.6484.8086.0187.34

CriticalNormalFnll-76

(kN/disc)96.7688.5789.8391.2291.60

SpecificEnergy

SE(kWh/m3)

17.0314.3415.6016.98

-p-

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerucl Q,

X-P-

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

colospr2.xls

Colorado Spring Granite143,9MPa7,8MPa

"Wedged" Constant SectionRobbinsA30581432mm (17")12,7mm (0,5")

KerfSpacing

S(mm)69.969.969.969.969.969.969.9

DiscPenetration

DOC(mm)2.543.815.086.357.628.8910.16

Overall Average Mean

CuttingRatio

S/DOC

27.518.313.811.09.27.96.9

MeanNormal

Fn(kN/disc)

134.8140.9164.9174.3195.8191.4230.1

MeanRolling

Fr(kN/disc)

10.8512.1415.5119.8425.5327.7738.97

CuttingCoefficient

k

0.08050.08620.09410.11380.13040,14510.1694

CuttingConstant

Cl

0.05050.04410.04170.04520.04720.04870.05310.0472

CriticalNormal

Fnl(kN/disc)

84.5972.1873.1569.1670.9364.1972.19

CriticalNormalFnl1-76

(kN/disc)88.3675.3976.4072.2474.0867.0475.4075.56

SpecificEnergy

SE(kWh/m3)

16.9912.6712.1412.4313.3212.4215.25

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

Q.

X

-P-

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

daksand2.xls

Dakota Sandstone51,5MPa3,9MPa

Constant SectionRobbinsA21530394mm (15,5")11,05mm (0,435")

KerfSpacing

S(mm)76.276.2101.6101.6

DiscPenetration

DOC(mm)12.719.112.719.1

Overall Average Mean

CuttingRatio

S/DOC

6.04.08.05.3

MeanNormal

Fn(kN/disc)

77.6120.698.1130.9

MeanRolling

Fr(kN/disc)

17.028.519.630.1

CuttingCoefficient

k

0.21930.23610.19970.2299

CuttingConstant

Cl

0.06150.05410.05600.05270.0561

CriticalNormal

Fnl(kN/disc)

21.7727.6327.5429.99

CriticalNormalFnl1-76

(kN/disc)21.7727.6323.8525.9824.80

SpecificEnergy

SE(kWh/m3)

4.885.454.224.32

-p-

Anglo American Corp. Linear Cutting TestsTamrock Technology Center Arne Lislerud

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTSPoisson's Ratio, vDensity, p

Enhancement of Roller Cutting by Means of Water JetsChapter 21, RETC 1985O. Fenn, B. Protheroe & N.C. Joughin

fennl.xls

Norite254MPa11.9MPa0.232.92g/cm3

Cutter TypeCutter Diameter, dDisk Tip Radius, tDisk Tip AngleDisk Tip Contact Width, WCutting SpeedWaterjetsLinear Rig Stiffness

Wedged305mm (12"1.5mm105°9.4mm0.6m/sunassistedlOOOkN/mm

KerfSpacing

S(mm)

15306090

Depthof CutDOC(mm)

2222

CuttingRatio

S/DOC

7.515.030.045.0

MeanNormal

Fn(kN/disk)

51.273.9116.7141.1

MeanRolling

Fr(kN/disk)

5.766.638.118.32

CuttingCoefficient

k

0.11250.08970.06950.0590

CuttingConstant

Cl

0.07950.06340.04910.0417

CriticalNormal

Fnl(kN/disk)

36.2052.2682.5299.77

CriticalNormalFnll-19

(kN/disk)40.8041.6446.5045.90

SpecificEnergySE-calc

(kWh/m3)53.3330.6918.7712.84

1530456090

44444

3.87.511.315.022.5

79.2107.2127.4144.4188.4

10.3512.8414.4614.9617.91

0.13070.11980.11350.10360.0951

0.06530.05990.05680.05180.0475

39.6053.6063.7072.2094.20

44.6342.7141.4540.6843.34

47.9229.7222.3117.3113.82

T3

ro3CL

x'

Overall Average Mean 0.0572 43.07

-P-

i ^ ^ f e l ^ f e i ^ 'Rock TypeLocality

Test Cut #Compressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAI

Disk TypeDisk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Paintbrush TuffFran Ridge TsW2, Nevada Test Site

Average86.314.72.294.23

Constant SectionRobbinsA30581432(17")11.43 (0.45")0.254

8,9,10,1153.315.7

2.2764.28

12,13,14,15129.714.3

2.3043.93

16,17,1875.914.1

2.2914.47

lislerud;

x'-R-

TestCut#

89101112131415161718

Overall

CutDepthDOC

(mm/pass)5.087.6210.1612.705.087.6210.1612.705.087.6210.16

CutSpacing

S(mm)76.276.276.276.2101.6101.6101.6101.6127.0127.0127.0

Average Mean

Ratio

S/DOC

15.010.07.56.020.013.310.08.0

25.016.712.5

MeanNormal

Fn(kN/disk)

100.0132.7138.9156.4113.2113.6142.6177.8116.4135.2144.3

MeanRollFr

(kN/disk)8.9416.5819.9824.1910.6916.4023.6128.5812.2616.7819.18

MeanSide

Fs(kN/disk)

4.1512.4912.3117.223.409.0111.5715.335.695.075.77

CriticalThrust

Fnl(kN/disk)

44.3548.0843.5643.8850.2341.1744.7549.8951.6648.9645.28

CriticalThrust

Fnl1-76(kN/disk)

44.3548.0843.5643.8843.5035.6538.7543.2140.0137.9335.08

AverageMean

Fnl1-76(kN/disk)

44.97

40.28

37.6741.27

CutterCoeff.

k

0.08940.12490.14390.15470.09440.14430.16550.16070.10530.12410.1329

CutterConstant

cl

0.03970.04530,04510.04340.04190.05230.05190.04510.04670.04500.0417

AverageMean

cl

0.0434

0.0478

0.04450.0453

•p-

-p-

Appendix 19

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IS 8Q.

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:^anrid2;xls/A;; LJsSerud: •

fD

Q.X-p-

Rock TypeLocality

Test Cut #Compressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAl

Disk TypeDisk CodeDisk Diameter (mm)Disk Width (mm)Cutting Speed (m/s)

Paintbrush TuffFran Ridge TsW2, Nevada Test Site

Average 33,34,3595.3 68.011.5 12.82.28 2.2594.20 4.43

Constant SectionRobbinsAM1723432(17")13.72(0.54")0.254

28,29129.714.3

2.3043.93

31,3288.27.5

2.2674.25

TestCut#

333435282942303132

Overall

CutDepthDOC

(mm/pass)5.087.6210.165.087.6210.165.087.6210.16

CutSpacing

S(mm)76.276.276.2101.6101.6101.6127.0127.0127.0

Average Mean

Ratio

S/DOC

15.010.07.5

20.013.310.025.016.712.5

MeanNormal

Fn(kN/disk)

112.1127.0152.9115.0134.6163.7122.0128.8137,9

MeanRollFr

(kN/disk)15.6420.5929.3814.7919.7422.8414.7518.4121.34

MeanSide

Fs(kN/disk)

4.556.398.534.536.496.310.082.903.47

CriticalThrust

Fnl(kN/disk)

49.7246,0147.9551.0048.7751.3554.1346.6643.26

CriticalThrust

Fnl1-76(kN/disk)

49.7246.0147.9544.1742.2444.4741.9336.1433.51

AverageMean

Fnl1-76(kN/disk)

47.89

43.63

37.2042.91

CutterCoeff.

k

0.13960.16210,19220.12870.14660.13950.12090,14290.1547

CutterConstant

cl

0.06190.05870,06030.05710,05310.04380.05360.05180.0485

AverageMean

cl

0.0603

0.0513

0.05130.0543

O

TestCut

#

333435282942303132

Overall

SpecificEnergy

SE(kWh/m3)

11.229.8510.547.967.086.156.355.284.59

PeakNormalFnpeak

(kN/disk)234.4282.1393.8265.6334.3374.3278.7301.4260.2

Average Mean

PeakRoll

Frpeak(kN/disk)

33.9447.9085.4935.6852.4254.6435.7643.5543.42

PeakSide

Fspeak(kN/disk)

21.3329.6357.1925.9033.3935.725.7331.8125.59

RatioNormal

Fnpeak/Fn

2.092.222.582.312.482.292,282.341.892.28

RatioRoll

Frpeak/Fr

2.172.332.912.412.662.392.422.372.032.41

RatioSide

Fspeak/Fs

4.694.646.705.725.145.6671.6310.977.3713.61

Data Normalization

Prognosis Mode!

FnlFni lk .c lSESE

FnFnlFr

= Fn/(DOQ**l/2= Fn/(DOC*(S/76.2))**l/2= Fr/Fn= k/(DOC)**1/2= (Fr/3600)/(DOC*S/100000Q)= Fri000/(DOC*S)

= Fnll*(DOC*S/76.2)**l/2- rock cuttability/disc tip constant= Fn*cl*(DOC)" l /2

Conversion Factors

Comments

{kWh/m3}{MJ/m3}

{kN} = 0.004445*{lb}{MPa} = 0.006889*{psi}{kWh/m3} = 0,976*{hph/yd3}

(i) peak value = overall pea! (max) value for an individual cut sequence(ii) rock seems to "soften" as higher loads are applied

X>a>a.x

TRRL Linear Cutting Tests Tamrock Technology Centergresandl.xls Arne Lislerud

-a

3Q.

X

Source The Effect of Hydraulic Stiffness on Tunnel Boring Machine PerformanceR.A. Snowdon, M.D. Ryley, J. Temporal and G.I. CrabbInt. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 20, No. 5, pp. 203-214, 1983

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTSBulk Density, pPorosity, n

Gregory Sandstone50MPa3.5MPa2.35g/cm314.8%

Cutter TypeCutter Diameter, dDisk Tip Radius, tDisk Tip AngleDisk Tip Contact Width, WLinear Rig Stiffness

Wedged200mm (7 7/8")2.5mm80°15.7mmVariable

KerfSpacing

S(mm)

30609012050100150200

NominalDepth of Cut

DOC(mm)

666610101010

Overall Average Mean

ActualDepth of Cut

DOC(mm)

6.06.06.06.010.010.010.010.0

CuttingRatio

S/DOC

5.010.015.020.05.010.015,020.0

MeanNormal

Fn(kN/disk)

23.637.257.558.436.466.3109.9120.2

for Stiffness 147.6kN/mm

MeanRolling

Fr(kN/disk)

3.55.48.08.27.413.120.422.5

CuttingCoefficient

k

0.14830.14520.13910.14040.20330.19760.18560.1872

CuttingConstant

C1

0.06050.05930.05680.05730.06430.06250.05870.05920.0598

CriticalNormal

Fnl(kN/disk)

9.6315.1923.4723.8411.5120.9734.7538.01

CriticalNormalFnl1-76

(kN/disk)15.3617.1121.6019.0014.2118.3024.7723.4619.23

SpecificEnergy

SE-calculated(kWh/m3)

5.44.24.13.24.13.63.83.1

SpecificEnergy

SE-measured(kWh/m3)

5,83.03.76.24.52.14.55.5

X)XIfD

O.X

KerfSpacing

S(mm)

30609012050100150200

NominalDepth of Cut

DOC(mm)

666610101010

Overall Average Mean

ActualDepth of Cut

DOC(mm)

6.47.16,27.411.110.110.112.6

for Stiffness 21

CuttingRatio

S/DOC

4.78.514.516.24.59.914.915.9

.5kN/mm

MeanNormal

Fn(kN/disk)

31.059.296.1127.658,297.9182.1202.0

MeanRolling

Fr(kN/disk)

4.99.714.823.712.425.339.845.4

CuttingCoefficient

k

0.15810.16390.15400.18570.21310.25840.21860.2248

CuttingConstant

Cl

0.06250.06150.06190.06830.06390.08130.06880.06330.0664

CriticalNormal

Fnl(kN/disk)

12.2522.2238.5946.9117.4730.8157.3056.91

CriticalNormalFnl 1-76

(kN/disk)19.5325.0435.5137.3821.5726.8940.8435.1330.23

SpecificEnergy

SE-calculated(kWh/m3)

7.16.37.47.46.27.07.35.0

SpecificEnergy

SE-measured(kWh/m3)

6.74.96.48.66.13.17.510,2

INJ

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAI

Disk Diameter (mm)Disk Width (mm)Disk HardnessCutting Speed (m/s)

Felsic GneissOnaping Mine, Sudbury2699.92.77

127(5")8.2 (0.32")HRB 57 (steel disk used for lab testing only)0.254

X )

a.

TestCut#

MD01MD02MD03MD04MD05MD06MD07MD08MD09MD10Overall

CutDepthDOC

(mm/pass)0.6351.2701.9051.2701.5241.9052.5401.9052.5403.175

CutSpacing

S(mm)19.0519.0519.0538.1038.1038.1038.1050.8050.8050.80

Average Mean

Ratio

S/DOC

30.015.010.030.025.020.015.026.720.016.0

MeanNormal

Fn(kN/disk)

20.0427.7234.9442.7641.2944.0047.9744.5648.9051,91

MeanRollFr

(kN/disk)1.742.774.054.774.634.925.985.736.837.80

MeanSide

Fs(kN/disk)

0.411.072.221.100.742.041.56-0.802.240,52

CriticalThrust

Fnl(kN/disk)

25.1524.6025.3137.9433.4531.8830.1032.2930.6829.13

CriticalThrustFnll

(kN/disk)25.1524.6025.3126.8323.6522.5421.2819.7718.7917.84

AverageMeanFnii

(kN/disk)

25.02

23.58

18.8022.58

CutterCoeff.

k

0.0870.1000.1160.1120.1120.1120.1250.1290.1400.150

CutterConstant

cl

0.10880.08880.08410.09900.09090.08110.07830.09310.08770.0843

AverageMean

cl

0.0939

0,0873

0.08840.0896

-p--p-

TestCut#

MD01MD02MD03MD04MD05MD06MD07MD08MD09MD10Overall

SpecificEnergy

SE(kWh/m3)

39.9131.8531.0327.3822.1618.8517.1716.4514.7113.43

PeakNormalFnpeak

(kN/disk)85.3379.61104.83145.19117.05138.44148.91120.42165.31164.26

Average Mean

PeakRoll

Frpeak(kN/disk)

12.1311.9014.7519.4918.1317.5724.9025.6123.0728.52

PeakSide

Fspeak(kN/disk)

10.9016.6316.2318.1119.8621.3026.6128.2433.9041.67

RatioNormal

Fnpeak/Fn

4.262.873.003.402.833.153.102.703.383.163.19

RatioRoll

Frpeak/Fr

6.984.293.644.093.913.574.164.473.383.664.22

RatioSide

Fspeak/Fs

26.6815.507.3016.4026.8110.4217.03

-35.1415.1680.7024.00

SdevNormalFn-sdev

(kN/disk)11.7313.0015.2518.8319.1720.7521.8619.0924.1124.93

SdevRoll

Fr-sdev(kN/disk)

1.161.522,062.342.442.483.052.943.564,08

SdevSide

Fs-sdev(kN/disk)

1.832.683.314.615.054.875.717.227.737.89

SdevNormal

Fnl-sdev(kN/disk)

14.7211.5411.0516.7115.5315.0413.7213.8315.1313.99

SdevNormal

Fnll-sdev(kN/disk)

14.7211.5411.0511.8110.9810.639.708.479.278.57

Mean SdevNormal

Fnll-sdev(kN/disk)

12.44

10.78

8.7710.67

-oXI0>a.x-B-

Data Normalization

Prognosis Model

Conversion Factors

Statistics

Comments

Fnl =Fn/(DOC)**l/2Fnl 1 = Fn/(DOC*(S/19.05))** 1/2k =Fr/Fnc l =k/(DOCr*l /2SE =(Fr /3600) / (DOC*S/1000000) {kWh/m3}SE =Fr*1000/ (DOC*S) {MJ/m3}

Fn = Fnl 1*(DOC*S/19.05)** 1/2Fnl • = rock cuttability/disc tip constantFr =Fn*cl*(DOC)** l /2

{kN} = 0,004445*{lb}{MPa} = 0.006889*{psi}{kWh/m3} = 0.976*{hph/yd3}

standard deviation means that 68,3% of the observations are within the range (x+-sdev)

(i) peak value = overall peal (max) value for an individual cut sequence(ii) rock seems to "soften" as higher loads are applied

X3

a>3Q.

x"

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAI

Disk Diameter (mm)Disk Width (mm)Disk HardnessCutting Speed (m/s)

NoriteOnaping Mine, Sudbury297

127(5")6,4 (0.25")

0.254

TestCut

#

MD42MD44MD46MD41MD43MD45MD36MD38MD40MD35MD37MD39

Overall

CutDepthDOC

(mm/pass)1.9052.5403.1751.9052.5403.1751.9052.5403.1751.9052.5403.175

CutSpacing

S(mm)19.0519.0519.0525.4025.4025.4038.1038.1038.1050.8050.8050.80

Average Mean

Ratio

S/DOC

10.07.56.013.310.08.020.015.012.026,720.016.0

MeanNormal

Fn(kN/disk)

32.7637.9142.0537,8543.2048.2346.0652.3552.6843.0451.3958.00

MeanRollFr

(kN/disk)3.304.925.813.675.396.744.756.797.654.426.418.35

MeanSide

Fs(kN/disk)

1.172.393,731,632.694.101.39

-0.173.370,553.615.11

CriticalThrust

Fnl(kN/disk)

23.7423.7823.6027.4227.1027.0733.3732.8529.5631.1832.2532.55

CriticalThrustFnll

(kN/disk)23.7423.7823.6023.7523.4723.4423.6023.2320.9019.1019.7519.93

AverageMeanFnll

(kN/disk)

23.71

23.55

22.58

19.5922.36

CutterCoeff.

k

0.1010,1300.1380.0970.1250,1400.1030.1300.1450.1030.1250.144

CutterConstant

cl

0.07300.08140.07750.07030.07830.07850.07470.08130.08150.07440.07820,0808

AverageMean

cl

0.0773

0.0757

0.0780

0.07780.0775

-P--P-

Appendix 27

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x'

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAI

Disk Diameter (mm)Disk Width (mm)Disk HardnessCutting Speed (m/s)

NoriteOnaping Mine, Sudbury297

127(5")8.2 (0.32")

0.254

TestCut

#

MD48MD50MD52MD47MD49MD51Overall

CutDepthDOC

(mm/pass)1.9052.5403.1751.9052.5403.175

CutSpacing

S(mm)19.0519.0519.0525.4025.4025.40

Average Mean

Ratio

S/DOC

10.07.56.013.310.08.0

MeanNormal

Fn(kN/disk)

37.8543.1148.3542.7345.9949.35

MeanRollFr

(kN/disk)4.065.186.414.945.526.69

MeanSide

Fs(kN/disk)

1.492,393.722.693.243.74

CriticalThrust

Fnl(kN/disk)

27.4227.0527.1430.9628.8627.70

CriticalThrustFnll

(kN/disk)27.4227.0527.1426.8124.9923.99

AverageMeanFnll

(kN/disk)

27.20

25.2626.23

CutterCoeff.

k

0.1070.1200.1330.1160.1200.136

CutterConstant

cl

0.07780.07540.07440.08380.07530.0761

AverageMean

cl

0.0759

0.07840.0771

ro

Appendix 29

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CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

ft

CL

x'

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

holsliml.xls

Holston Limestone118,6MPalOJMPa

"Wedged" Constant SectionRobbins A30580394mm (15,5")12,7mm (0,5")

KerfSpacing

S(mm)

DiscPenetration

DOC(mm)

CuttingRatio

S/DOC

MeanNormal

Fn(kN/disc)

MeanRolling

Fr(kN/disc)

CuttingCoefficient

k

CuttingConstant

Cl

CriticalNormal

Fnl(kN/disc)

CriticalNormalFnll-76

(kN/disc)

SpecificEnergy

SE(kWh/m3)

76.276.2101.6101.6101.6101.6

6.48.93.85.17.68.9

12.08.626.720.013.311.4

172.1193.8142.7186.5242.1284.7

24.631.115.021.730.336.1

0.14310.16020.10520.11620.12500.1268

0.05680.05370.05390.05150.04530.0425

68.2864.9973.1282.7687,7295.49

Overall Average Mean 0.0506

68.2864.9963.3371.6775.9782.6971.16

14.1412.7310.7811.6610.8611.11

o

4?

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

>x>0)DQ.X

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

holslim2.xls

Hoiston Limestone118,6MPalaiMPa

Constant SectionRobbinsA21530394mm (15,5")11,05mm (0,435")

KerfSpacing

S(mm)76.276.2101.6101.6

DiscPenetration

DOC(mm)

6.48.96.48.9

Overall Average Mean

CuttingRatio

S/DOC

12.08.616.011.4

MeanNormal

Fn(kN/disc)

174.9211.1205.5266.4

MeanRolling

Fr(kN/disc)

13.324.419.138.8

CuttingCoefficient

k

0.07610.11540.09320.1455

CuttingConstant

Cl

0.03020.03870.03700.04880.0387

CriticalNormal

Fnl(kN/disc)

69.4170.8181.5389.36

CriticalNormalFnil-76

(kN/disc)69.4170.8170.6177.3972.05

SpecificEnergy

SE(kWh/m3)

7.649.998.2411.92

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

x>

a.x

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

indiliml.xls

Indiana Limestone44MPa5.2MPa

"Wedged" Constant SectionRobbins A30581432mm (17")12.7mm (0.5")

KerfSpacing

S(mm)76.276.2152.4152.4

DiscPenetration

DOC(mm)25.438.125.438.1

Overall Average Mean

CuttingRatio

S/DOC

3.02.06,04.0

MeanNormal

Fn(kN/disc)

120.8140.5168.8182.7

MeanRolling

Fr(kN/disc)

26.532.536.648.3

CuttingCoefficient

k

0.21950.23170.21670.2644

CuttingConstant

Cl

0.04360.03750.04300.04280.0417

CriticalNormal

Fnl(kN/disc)

23.9622.7633.5029.60

CriticalNormalFnl1-76

(kN/disc)23.9622.7623.6920.9322.83

SpecificEnergy

SE(kWh/m3)

3.803.112.632.31

X)

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

X

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

indilim2.xls

Indiana Limestone44MPa5.2MPa

Constant SectionRobbinsAM1724432mm (17")19.05mm (0.75")

KerfSpacing

S(mm)76.276.2152.4

DiscPenetration

DOC(mm)25.438.125.4

Overall Average Mean

CuttingRatio

S/DOC

3.02.06.0

MeanNormal

Fn(kN/disc)

189.7207.4230.9

MeanRolling

Fr(kN/disc)

37.443.945.6

CuttingCoefficient

k

0.19730.21140.1973

CuttingConstant

Cl

0.03910.03430.03920.0375

CriticalNormal

Fnl(kN/disc)

37.6333.6045.82

CriticalNormalFnl1-76

(kN/disc)37.6333.6032.4034.54

SpecificEnergy

SE(kWh/m3)

5.374.203.27

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

3Q.

X

-p-

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

lesbasl.xls

Lesotho Basalt187,5MPa14,9MPa

"Wedged" Constant SectionRobbinsA30581432mm (17")12,7mm (0,5")

KerfSpacing

S(mm)

DiscPenetration

DOC(mm)

CuttingRatio

S/DOC

MeanNormal

Fn(kN/disc)

MeanRolling

Fr(kN/disc)

CuttingCoefficient

k

CuttingConstant

Cl

CriticalNormal

Fnl(kN/disc)

CriticalNormalFnl1-76

(kN/disc)

SpecificEnergy

SE(kWh/m3)

69.969.989.789.789.7

1.32.51.32.53.8

55.027.570.635.323.5

86.0124.096.5136.8171.0

3.65.64.16.210.5

0.04150.04480.04210.04500.0615

0.03680.02810.03740.02820.0315

76.3577.8085.5985.8387.60

79.7481.2678.9079.1380.76

11.188.699.907.508.55

Overall Average Mean 0.0324 79.96

-P--P-

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

ftDCLi — •

X

-p-

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

Iesbas2.xls

Lesotho Basalt - NAB97,2MPa12,9MPa

"Wedged" Constant SectionRobbins A30581432mm (17")12,7mm (0,5")

KerfSpacing

S(mm)69.969.969.989.789.7

DiscPenetration

DOC(mm)3.817.3712.453.817.37

Overall Average Mean

CuttingRatio

S/DOC

18.39.55.623.512.2

MeanNormal

Fn(kN/disc)

108.2123.9187.0114.9191.3

MeanRolling

Fr(kN/disc)

7.4313.5824.988.33

21.41

CuttingCoefficient

k

0.06860.10960.13360.07250.1119

CuttingConstant

Cl

0.03520.04040.03790.03710.04120.0384

CriticalNormal

Fnl(kN/disc)

55.4545.6452.9858.8570.47

CriticalNormalFnl1-76

(kN/disc)57.9247.6755.3454.2664.9756.03

SpecificEnergy

SE(kWh/m3)

7.767.337.986.779.00

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

3

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

Iesbas3.xls

Lesotho Basalt - MAB91,3MPall,9MPa

"Wedged" Constant SectionRobbins A30581432mm (17")12,7mm (0,5")

KerfSpacing

S(mm)

DiscPenetration

DOC(mm)

CuttingRatio

S/DOC

MeanNormal

Fn(kN/disc)

MeanRolling

Fr(kN/disc)

CuttingCoefficient

k

CuttingConstant

Cl

CriticalNormal

Fni(kN/disc)

CriticalNormalFnll-76

(kN/disc)

SpecificEnergy

SE(kWh/m3)

69.969.969.989.789.7

3.817.3712.453.817.37

18.39.55.6

23.512.2

88.2123.3163.5102.3134,8

6.2416.4526.377.1417.25

0.07070.13340.16130.06980.1280

0.03620.04910.04570.03580.0471

45.2045.4246.3252.4149.66

Overall Average Mean 0.0428

47.2147.4448,3848.3245.7847.43

6.518.888.425.817.25

ON

CSM Linear Cutting Tests Tamrock Technology CenterArne Lislerud

IDDI—.X

Source

File

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeCutter Diameter, dCutter Edge Width, W

MSc Thesis, Jamal Rostami, CSM

Iesbas4.xls

Lesotho Basalt - HABl l l . l M P a7,9MPa

"Wedged" Constant SectionRobbins A30581432mm (17")12,7mm (0,5")

KerfSpacing

S(mm)

DiscPenetration

DOC(mm)

CuttingRatio

S/DOC

MeanNormal

Fn(kN/disc)

MeanRolling

Fr(kN/disc)

CuttingCoefficient

k

CuttingConstant

Cl

CriticalNormal

Fnl(kN/disc)

CriticalNormalFnl1-76

(kN/disc)

SpecificEnergy

SE(kWh/m3)

69.969.969.989.789.7

3.817.3712.453.817.37

18.39.55.623.512.2

101.1125.7141.5117.0154.1

7.5315.4622.018.52

20.92

0.07450.12300.15560.07280.1357

0.03820.04530.04410.03730.0500

51.8046.3040.0959.9356.78

Overall Average Mean 0.0430

54.1048.3641.8755.2452.3450.38

7.868.347.036.938.79

VjO

•e-

Polyethylene Oxide (PEO) Tests

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Rock Surface Hardness, VHNR

Colorado Red GraniteLyons, Colorado13811.72.62858

Disc TypeDisc Diameter (mm)Disc Width (mm)Cutting Speed (m/s)

peol.xIs/A. Lislerud

Robbins AM 1723432(17")12,7(0.5")0.254

XI

n>Q.

x

TestCut

#

57

10,11,15Overall,

CutDepthDOC

(mm/pass)6.35012.7006.350

CutSpacing

S(mm)

114.30114.3057.15

Average Mean

Ratio

S/DOC

18.09.09.0

MeanNormal

Fn(kN/disc)210.24305.37180.46

MeanRollFr

(kN/disc)17.7844.4520.00

CriticalThrust

Fnl(kN/disc)

83.4385.6971.61

CriticalThrust

Fnl1-76(kN/disc)

68.1269.9682.6973.59

CutterCoeff.

k

0.08460.14560.1108

CutterConstant

cl

0.03360.04080.04400.0395

SpecificEnergy

SE(kWh/m3)

6.808.5115.31

PeakNormalFnpeak

(kN/disc)492.95594.30339.60

PeakRoll

Frpeak(kN/disc)

39.5691.1242.67

RatioNormal

Fnpeak/Fn

2.341.951.882.06

RatioRoll

Frpeak/Fr

2,232.052.132.14

Linear Mini-Disk Cutting Tests in SerpentiniteDCL

x'

Mechanized Mining of Narrow Chrome Seams3rd Intl. Symp. on Mine Mech. and AutomationL, Ozdemir & D. Magaisa

zimchr52.xls/A. Lislerud

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAI

Disk Diameter (mm)Disk Width (mm)

SerpentiniteGreat Dyke, Zimbabwe60

127(5")8.2 (0.32")

TestCut#

dmp-2sdmp-3sdmp-4sdmp-5sdmp-6sdmp-7s

CutDepthDOC

(mm/pass)2.543.815.082.545.087.62

CutSpacing

S(mm)25.425.425.450.850.850.8

Overall Average Mean

Ratio

S/DOC

10.006.675.0020.0010.006.67

MeanNormal

Fn(kN/disk)

12.2112.7914.4213.0119.6921.23

MeanRollFr

(kN/disk)1.602.402.321.683.744.17

MeanSide

Fs(kN/disk)

0.451.501.20-0.540.012.16

CriticalThrust

Fni(kN/disk)

7.666.556.408.168.747.69

CriticalThrustFnll

(kN/disk)6.635.675.545.005.354.71

AverageMeanFnll

(kN/disk)

5.95

5.025.48

CutterCoeff.

k

0.1310.1880.1610.1290.1900.196

CutterConstant

cl

0.08220.09610.07140.08100.08430.0712

AverageMean

cl

0.0832

0.07880.0810

Appendix 4.

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M::M<U'::;:::ti!i:i.?

iitfl'i fotlffi JJI:

ioiii: 3::i>O-::

Linear Disc Cutting Tests in Charcoal Grey GranitePolyethylene Oxide (PEO) Tests peo2.xls/A. Lisierud

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Rock Surface Hardness, VHNR

GranodioriteSt. Cloud, Minnesota22113.12.71758

Disc TypeDisc Diameter (mm)Disc Width (mm)Cutting Speed (m/s)

RobbinsAM1723432(17")12.7(0.5")0.254

TestCut

#

CutDepthDOC

(mm/pass)

CutSpacing

S(mm)

Ratio

S/DOC

MeanNormal

Fn

MeanRollFr

(kN/disc) (kN/disc)

CriticalThrust

Fnl(kN/disc)

CriticalThrust

Fnl1-76(kN/disc)

CutterCoeff.

k

CutterConstant

cl

SpecificEnergy

SE(kWh/m3)

PeakNormalFnpeak

(kN/disc)

PeakRoll

Frpeak(kN/disc)

RatioNormal

Fnpeak/Fn

RatioRoll

Frpeak/Fr

2224263338

6.3503.1753.1756.3506.350

114.3057.1557.1557.1557.15

18.018.018.09.09.0

225.80176.02181.35225.36232.91

23.569.339.3324.8924.00

89.6198.78101.7889.4392.43

73.16114.07117.52103.27106.73

0.10430.05300.05150.11050.1031

0.04140.02980.02890.04380.0409

9.0214.2914.2919.0518.37

468.50324.93320.48426.28395.16

55.5628.0024.4555.5652.01

2.071.851.771.891.70

2.36

2.232.17

XI0>

Q.

x'

Overall Average Mean 102.95 0.0370 1.86 2.25

Data Normalization Fnl =Fn/(DOC)**l/2Fnl 1 - Fn/(DOC*(S/76.2))**1 /2k =Fr/Fnc l . = k/(DOC)**1/2SE = (Fr/3600)/(DOC*S/1000000 { kWh/m3}SE = Fr*1000/DOC*S) {MJ/m3}

Prognosis Model Fn = Fnl 1 *(DOC*S/76.2)**1 /2Fnl = rock cuttability/disc tip consiFr = Fn*c1*(DOC)**l/2

Conversion Factors {kN} = 0,004445* {Ib}{MPa} - Q,006889*{psi}{kWh/m3] = 0,976*{hph/yd3}

CSM Linear Cutting Tests

Source

File

Note

Rock TypeUniaxial Compressive Strength, UCSBrazilian Tensile Strength, BTS

Cutter TypeCutter CodeDisk Diameter, dDisk Edge Width, W

Tamrock Technology CenterArne Lisierud

Alcove Excavator for the Yucca MountainExperimental Study Facility.Earth Mechanics Institute, CSMJ.E. Friant, E. Ronnkvist & L. Ozdemir

tivcan.51.xls

Data taken from graphs

Tiva Canyon Welded (Rhyolitic) Tuff165,4MPa

Rounded tipCSM Minidisk127mm (5")8,2mm

XI

x>fD

Q.

X

KerfSpacing

S(mm)76.276.276.2

DiskPenetration

DOC(mm)1.912.543.53

Overall Average Mean

CuttingRatio

S/DOC

39.930.021.6

MeanNormal

Fn(kN/disk)

39.540.552.6

MeanRolling

Fr(kN/disk)

4.825.026.79

CuttingCoefficient

k

0.12200.12400.1290

CuttingConstant

Cl

0.08830.07780,06870.0782

CriticalNormal

Fni(kN/disk)

28,5925.4128.0127.34

CriticalNormalFnll-19

(kN/disk)14.2912.7114.0013.67

SpecificEnergy

SE(kWh/m3)

9.207.217.01

>x>

Linear Mini-Disk Cutting Tests in Chromite OreQ.

X

Mechanized Mining of Narrow Chrome Seams3rd Intl. Symp. on Mine Mech. and AutomationL. Ozdemir & D. Magaisa

zirnchr51 .xls/A. Lislerud

Rock TypeLocalityCompressive Strength (MPa)Tensile Strength (MPa)Density (g/cm3)Cerchar Abrasivity Index, CAI

Chromite OreGreat Dyke, Zimbabwe

TestCut

#

dmp-lcdmp-2cdmp~3cdmp-4cdmp-5cdmp-6cdmp-7cOverall >

Disk Diameter (mm)Disk Width (mm)

Cut CutDepth SpacingDOC

(mm/pass)1.272.543.815.082.545.087.62

Average Mean

S(mm)25.425.425.425.450.850.850.8

i

Ratio

S/DOC

20.0010.006.675.0020.0010.006.67

MeanNormal

Fn(kN/disk)

16.2021.5926.3246.2245.4551.7571.68

127(5")8.2 (0.32")

MeanRollFr

(kN/disk)1.352.344.678.985.159.1116.41

MeanSide

Fs(kN/disk)

0.04-0.293.595.234.860.360,76

CriticalThrust

Fnl(kN/disk)

14.3813.5513.4820.5128.5222.9625.97

CriticalThrustFnll

(kN/disk)12.4511.7311.6817.7617.4614.0615.90

AverageMeanFnll

(kN/disk)

13.40

15.8114.43

CutterCoeff.

k

0.0830.1080.1770.1940.1130.1760.229

CutterConstant

cl

0.07390.06800.09090.08620.07110.07810.0829

AverageMean

cl

0.0798

0.07740.0787

•a

a.

TestCut

#

dmp-lcdmp-2cdmp-3cdmp-4cdmp-5cdmp-6cdmp-7c

SpecificEnergy

SE(kWh/m3)

11.6310.0813.4019.3311.099.8111.78

PeakNormalFnpeak

(kN/disk)27.4636.1844.0166.3563.5087.22104.48

Overall Average Mean

PeakRoll

Frpeak(kN/disk)

2.834.458.3814.929.3316.2225.17

PeakSide

Fspeak(kN/disk)

3.085.9810.0415.0310.6614.4916.44

RatioNormal

Fnpeak/Fn

1.701.681.671.441.401.691.461.57

RatioRoll

Frpeak/Fr

2.101.901.791.661.811.781.531.80

RatioSide

Fspeak/Fs

77.00-20.622.802.872.19

40.2521.6318.02

SdevNormalFn-sdev

(kN/disk)6.526.748.8010.5212.8216.4516.26

SdevRoll

Fr-sdev(kN/disk)

0.720.921.862.651.933.454.58

SdevSide

Fs-sdev(kN/disk)

1.823.243.845.483,127.858.13

SdevNormal

Fnl-sdev(kN/disk)

5.794.234.514.678.047.305.89

SdevNormal

Fn 11-sdev(kN/disk)

5.013.663.904.044.934,473.61

Mean SdevNormal

Fnll-sdev(kN/disk)

4.15

4.334.23

|actors::

Fnl: Fryj 1

af ;

:=Fn/(DOC)**l/2

^Ei-FgcM^

" :- ;• ; ;= r o c k e u f f a b i l i t y / d i s Q : t i p - c o p i s t a n t ; :3BB;::;:"~'"•:: • ^•^:^:-,\;-i:~:i£;:;,~u.^=~>,:»§;Ss:FBM"(D0C:f*l/2;s

;!i oslsippMglJ;-i:£;:•: ^ ^je:yj'g|fcn-TO^

; i ; peak value = : overqll peai <rac^ vgfUQfQr an; individual cut s; to-"soften" as higherldads-are;applled:.::: : : : ;;;; •••;;;;';::\£:zEr:.

Tool and Cutferhead Forces for Sumping Cufterheadscutpredl .xls/A. Lisleruc!

Cutterhead Diameter, DCutterhead Radius Factor, fNumber of Cutters, NTools per Line, TPLStarts per Revolution, SPRDisk Rim Diameter, dDisk Rim (Constant Section) Width, W

2.90 m Max Line Spacing, Snmax0.592 Mean Line Spacing, Snmean

20 Cutterhead Rotary Speed1 Dome factor, SINTM1 Rock Type

310 mm Uniaxia! Compressive Strength, UCS11.6 mm Critical Normal Force, Fnl -linear

Cutter Constant, Cl -linear

88.9 mm77.8 mm

7.9 RPM0.866

Limestone120 MPa

51.4 kN/disk0.0511

Max Depthof Cut

DOCnmax(mm/rev/tool)

123456789101112131415

Mean Depthof Cut

DOCnmean(mm/rev/tool)

0.871.732.603.464.335.206.066.937.798.669.5310.3911.2612.1212.99

Max Depthof AdvanceDOAnmean

(mm/rev)0.871.732.603.464.335.206.066.937.798.669.5310.3911.2612.1212.99

Net AdvanceRateAR

(m/h)0.470.951.421.902.372.843.323.794.274.745.215.696.166.647.11

Net CuttingRateNCR

(m3/h)3.16.39.412.515.718.821.925.028.231.334.437.640.743.847.0

Mean NormalForce

Fnmean(kN/disk)

44.763.377.589.5100.1109.6118.4126.6134.2141.5148.4155.0161.3167.4173.3

CuttingCoefficient

kmean

0.04760.06730.08240.09510.10640.11650.12590.13450.14270.15040.15780.16480.17150.17800.1842

Mean RollingForce

Frmean(kN/disk)

2.14.36.48.510.612.814.917.019.221.323.425.527.729.831.9

ThrustForceFthrusf(kN)783.21107.61356.51566.31751.21918.42072.12215.12349.52476.62597.52713.02823.82930.43033.2

CutterheadTorque

Tdemand(kNm)34.268.4102.6136.7170.9205.1239.3273.5307.7341.8376.0410.2444.4478.6512.8

CutterheadPower

Pdemand(kW)28.356.684.8113.1141.4169.7198.0226.2254.5282.8311.1339.4367.6395.9424.2

SpecificEnergy

SE(kWh/m3)

9.039.039.039.039.039.039.039.039.039.039.039.039.039,039.03

IDDQ.

x'

Tool and Cufferhead Forces for Sumping Cutterheadscutpr©d2.xls/A. Lislerud

Cutterhead Diameter, DCutterhead Radius Factor, fNumber of Cutters, NTools per Line, TPLStarts per Revolution, SPRDisk Rim Diameter, dDisk Rim (Constant Section) Width, W

2.90 m Rock Type0.592 Uniaxial Compressive Strength, UCS

40 Critical Normal Force, Fnl -linear2 Cutter Constant, Cl -linear2 Max Line Spacing, Snmax

310 mm Mean Line Spacing, Snmean11.6 mm Cutterhead Rotary Speed

Dome factor, SINTM

Limestone120 MPa

51.4 kN/disk0.0511

88.9 mm77.8 mm

7.9 RPM0.866

Max Depthof Cut

DOCnmax(mm/rev/tool)

123456789101112131415

Mean Depthof Cut

DOCnmean(mm/rev/tool)

0.871.732.603.464.335.206.066.937.798.669.5310.3911.2612.1212.99

Max Depthof AdvanceDOAnmean

(mm/rev)1.733.465.206.938.6610.3912.1213.8615.5917.3219.0520.7822.5224.2525.98

Net AdvanceRateAR

(m/h)0.951.902.843.794.745.696.647.588.539.4810.4311.3812.3213.2714.22

Net CuttingRateNCR

(m3/h)6.312.518.825.031.337.643.850.156.462.668.975.181.487.793.9

Mean NormalForce

Fnmean(kN/disk)

44.763.377.589.5100.1109.6118.4126.6134.2141.5148.4155.0161.3167.4173.3

CuttingCoefficient

kmean

0.04760.06730.08240.09510.10640.11650.12590.13450.14270.15040.15780.16480.17150.17800.1842

Mean RollingForce

Frmean(kN/disk)

2.14.36.48.510.612.814.917.019.221.323.425.527.729.831.9

ThrustForceFthrust

(kN)

1566.32215.12713.03132.73502.53836.74144.24430.34699.04953.25195.05426.05647.55860.76066.4

CutterheadTorque

Tdemand(kNm)68.4136.7205.1273.5341.8410.2478.6546.9615.3683.7752.0820.4888.8957.11025.5

CutterheadPower

Pdemand(kW)56.6113.1169.7226.2282.8339.4395.9452.5509.0565.6622.2678.7735.3791.8848.4

SpecificEnergy

SE(kWh/m3)

9.039.039.039.039.039.039.039.039.039.039.039.039.039.039.03

a.x'ON

LIST OF REPORTS 1(2)

LIST OF POSIVA REPORTS 1997, situation 12/97

POSIVA-97-01 Model for diffusion and porewater chemistry in compacted bentoniteTheoretical basis and the solution methodology for the transport modelJarmo LehikoinenVTT Chemical TechnologyJanuary 1997ISBN951-652-026-X

POSIVA-97-02 Model for diffusion and porewater chemistry in compacted bentoniteExperimental arrangements and preliminary results of the porewaterchemistry studiesArto Muurinen, Jarmo LehikoinenVTT Chemical TechnologyJanuary 1997ISBN 951-652-027-8

POSIVA-97-03 Comparison of 3-D geological and geophysical investigation methodsin boreholes KI-KR1 at Aanekoski Kivetty site and RO-KR3 at KuhmoRomuvaara siteKatriina LabbasHelsinki University of TechnologyMaterial Science and Rock EngineeringJanuary 1997ISBN 951-652-028-6

POSIVA-97-04 Summary Report - Development of Laboratory Tests and the Stress-Strain Behaviour of Olkiluoto Mica GneissMatti Hakala, Esa HeikkilaLaboratory of Rock EngineeringHelsinki University of TechnologyMay 1997ISBN 951-652-029-4

POSIVA-97-05 Radionuclide solubilities at elevated temperatures - a literature studyTorbjorn Carlsson, Ulla VuorinenTechnical Research Centre of FinlandJuly 1997ISBN 951-652-030-8

POSIVA-97-06 Surface complexation modelling: Experiments on sorption of nickel onquartz, goethite and kaolinite and preliminary tests on sorption ofthorium on quartzEsa Puukko, Martti HakanenUniversity of HelsinkiDepartment of ChemistryRadiochemistry laboratorySeptember 1997ISBN 951-652-031-6

LIST OF REPORTS 2(2)

POSIVA-97-07 Diffusion and sorption of HTO, Np, Na and Cl in rocks and mineralsof Kivetty and OlkiluotoVesa Kaukonen, Martti HakanenUniversity of HelsinkiDepartment of ChemistryLaboratory of RadiochemistryAntero LindbergGeological Survey of FinlandOctober 1997ISBN 951-652-032-4

POSIVA-97-08 Regression methodology in groundwater composition estimation withcomposition predictions for Romuvaara borehole KR10Ari Luukkonen, Juhani Korkealaakso, Petteri PitkanenVTT Communities and InfrastructureNovember 1997ISBN 951-652-033-2

POSIVA 97-09 Dissolution of unirradiated UO2 fuel in synthetic saline groundwater •Experimental methods and preliminary resultsKaija OllilaVTT Chemical TechnologyDecember 1997ISBN 951-652-034-0

POSIVA 97-10 Application of surface complexation modelling: Nickel sorption onquartz, manganese oxide, kaolinite and goethite and thorium on silicaMarkus Olin, Jarmo LehikoinenVTT Chemical TechnologyDecember 1997ISBN 951-652-035-9

POSIVA 97-11 FEPs and scenarios - Auditing of TVO-92 and TILA-96 againstInternational FEP databaseTimo Vieno, Henrik NordmanVTT EnergyDecember 1997ISBN 951-652-036-7

POSIVA 97-12 Principles of Mechanical ExcavationArne LislerudTamrock Corp.December 1997ISBN 951-652-037-5