DrillingRoy Rathner and Arne Lislerud

� well planned operations and correctly selected rigs yield low cost drilling

� technically good drilling (good drill settings) and correctly selected rigs yields low cost drilling

� straight hole drilling yields safe and low cost D&B operations

Agenda for drilling operations

The most common drilling methods in use

� bits

� drill string

� boom or mast mounted feed

� TH or DTH hammer / Rotary - thrust

� drill string rotation and stabilising systems

� powerpack

� automation package

� drilling control system(s)

� collaring position and feed alignment systems

� flushing (air, water or foam)

� dedusting equipment

� sampling device(s)

Drilling consists of a working system of:

� bit face and skirt design

� button shape, size and carbide grade

� shanks, rods, tubes, …

� grinding equipment and its location

Selecting drilling tools

� avoid excessive button wear (rapid wearflat developm ent)

=> select a more wear resistant carbide grade or d rop bit RPM

� avoid button failures (due to snakeskin development or too aggressive button shapes)

=> select a less wear resistant or tougher carbide grade or spherical buttons

=> use shorter regrind intervals

Guidelines for selecting cemented carbide grades

PCD ?48 DP65

Selecting button shapes and cemented carbide grades

R48

Robust ballistic buttons48

S65

Spherical buttonsDP65

Optimum bit/rod diameter relationship for TH

Thread Diameter Diameter Optimumcoupling bit size

R32 ∅∅∅∅44 ∅∅∅∅32 ∅∅∅∅51

T35 ∅∅∅∅48 ∅∅∅∅39 ∅∅∅∅57T38 ∅∅∅∅55 ∅∅∅∅39 ∅∅∅∅64T45 ∅∅∅∅63 ∅∅∅∅46 ∅∅∅∅76T51 ∅∅∅∅71 ∅∅∅∅52 ∅∅∅∅89GT60 ∅∅∅∅82 ∅∅∅∅60 ∅∅∅∅92GT60 ∅∅∅∅85 ∅∅∅∅60/64 ∅∅∅∅102

Optimum bit/guide or pilot (lead) tube relationship for TH

Thread Diameter Diameter Optimumcoupling bit size

T38 ∅∅∅∅55 ∅∅∅∅56 ∅∅∅∅64T45 ∅∅∅∅63 ∅∅∅∅65 ∅∅∅∅76T51 ∅∅∅∅71 ∅∅∅∅76 ∅∅∅∅89GT60 ∅∅∅∅85 ∅∅∅∅87 ∅∅∅∅102GT60 ∅∅∅∅85 ∅∅∅∅102 ∅∅∅∅115

� drill steel component life

� bit regrind intervals

� bit replacement diameter

� component discard analysis

� costs in € per drm or m 3

Jobsite KPI’s for drill steel

Example of drill steel followup for MF-T51

Shanks

MF-T51 rods

100

Bit service life (drm)

Rod

and

sha

nk s

ervi

ce li

fe (d

rm)

Spread in data due to cal-

culations in drmand not in rdm

50 1000400 10000200 2000

1000

100

10000Short holes

Long holes

2000

4000

20000

4000600

6000

400

600

200

16000

Trendlines for bit service life

102 4 61 2004020 10060

1000

2000

600

400

200

100

4000

6000

10000

20000

Siever’s J Value, SJ

Max

bit

serv

ice

life

(drm

/bit)

Limestone

Dolomite

Granite

Quartzite

Rotary Drilling - Ø311mm / Std.

DTH *

Tophammer *

* Bit service life highly dependenton regrind intervals – regard curveas a top limit value

Bit regrind intervals, bit service life and over-drilling

10000100010020 40 60

Bit service life (drm)

Bit

regr

ind

inte

rval

s (d

rm)

2000

1000

2

10

100

4

86

200

400

40

20

200 400 2000 4000

Premature button failures

d d

d/3 d/3

600

60

� bending of drill string - leads to premature tube failure

� hardrock drilling or bit service life < 1750 drm - leads to poor tube life

� jerky drill string rotation - leads to an unstable bit which initiates drill-hole deviation

Tube drilling for TH – avoid:

2 x R/C jaws for tubes

Guide plate for tubes

2 x slot plates with cut-outs for larger

tube diameters

Flushing housing for tubes

Centraliser jaws for tubes

Mechanics of percussive drilling

Percussive drilling

���� Down-the-hole, DTHStress waves transmitted directly through bit into rock

���� TophammerStress wave energy transmitted through shank, rods, bit, and then into rock

Basic functions

���� percussion - reciprocating piston used to producestress waves to power rock indentation

���� feed - provide bit-rock contact at impact

���� rotation - provide bit impact indexing

���� flushing - cuttings removal from hole bottom

���� foam flushing - drill-hole wall stabilisation

FEED

PERCUSSION

CUTTINGS

FLUSHING

ROTATION

Flushing of drill-cuttings

Insufficient air < 15 m/s

� low bit penetration rates� poor percussion dynamics� interupt drilling to clean holes� plugged bit flushing holes� stuck drill steel� ”circulating” big chip wear

Too much air > 30 m/s

� excessive drill steel wear� erosion of hole collaring point� extra dust emissions� increased fuel consumption

Correction factors

� high density rock� badly fractured rock

(air lost in fractures- use water or foam tomud up hole walls)

� high altitude(low air density)

� large chips requireadditional air as well

Flift

G

Flift

G

Foam flushing – an aid for drilling in caving material

Burst of inhole water

Time consumption for 2 holes

5

10

15

20

25

0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00 1:26:24 1: 40:48 1:55:12

Time (h:min:s)

Hol

e de

pth

(m)

tough holenormal hole

drilling uncoupling

tube #2 back to carousel

rock found with tube #5

hole ready - 22 minhole ready -1h 46min

uncoupling

Chip formation by bit indentationand indexing

Spray paint applied between bit impacts

Chipping around the button footprint areas

Button footprint area

Ø76mm bit

Direction of bit rotation

How rock breaks by indentation

ubutton

Fbutton

ubit

Vcuttings

Abutton footprint

Fbutton

ubit

Volume of cuttings

Energy used for rock breakage

1

ubit

k1Energy lost as elastic rock deformation

Indentation with multiple chipping

Drop in button force indicates elastically

stored energy in rock released by chipping

0

40

80

120

160

200

0 5 10 15But

ton

For

ce (

kN)

Indentation (mm)

y = 0.2376x0.5019

R² = 0.95150123456

0 200 400 600 800

Inde

ntat

ion

(mm

)

Indentation Energy (Nm)

chipping while on-loading

chipping after off-loading

k1 = 30 kN/mm for on-loading

k2 = 112.5 kN/mm for off-loadingγ = k1 / k2 = 0.267

Energy transfer efficiency η related to rock chipping

No energy retained in rock after off-loading for γ = 1.0(all elastic energy in rock returned to drill strin g)

Button resistance, k 1 / N (kN/mm)

η = Wrock / Wincident

= ηimpedance · ( 1 – γ )

ηimpedance-max ≈ 0.90

106 20

0.10

0.20

0.06

0.40

0.60

1.00

γ=

k1

/ k2

8

0.80

10040 60

static bit testspercussive drilling

6 8

How does this apply to practical drilling?

“Poor” drilling situation- chipping after off-loading- potential for severely reduced drill steel life- correct choice of bit design and size?- sufficient bit regrinding (resharpening)?

“Good” drilling situation- chipping during on-loading- potential to achieve max drill steel service life

10 4020 10060

Button resistance, k 1 / N (kN/mm)

0.10

0.20

0.06

0.40

0.60

1.00

γ=

k1

/ k2

0.80

static bit testspercussive drilling

“Hopeless” drilling situation- no bit advance rate for γ = 1.0

Energy transfer efficiency η related to impedance matching

ubutton

Fbit

1

k1 = bit indentation resistance (kN/mm)

ηηηη impedance

k1

Feed force

2 · LpistonLpiston

� strain gauge measurements on rods/tubes while drill ing

� numerical modelling

=> the tell-tale items we are looking for:

How do we study drill string energy transfer issues?

Time, t (ms)

Str

ess

in r

ods,

σ

(MP

a) inci

dent

wav

e

bit m

ass

… etc.

1stte

nsile

1stco

mpr

essi

ve

1stγ

refle

ctio

n

Energy transfer chain – video clip cases

cavity

bit face bottoming – caused by:

■■■■ drilling with too high impact energy■■■■ drilling with worn bits i.e. too low button protrus ion

bit / rock gap – i.e. underfeed

“perfect” bit / rock match

Energy transmission through threads

Energy transfer can be divided into:

���� energy transmission through the drill string- optimum when the cross section throughout

the drill string is constant- length of stress wave- weight of bit

���� energy transmission to rock- bit indentation resistance – k 1- bit-rock contact

The most critical issue in controlling stress waves is to avoid high tensile reflection waves.

Tensile stresses are transmitted through couplings by the thread surfaces - not throughthe bottom or shoulder contact as in the case for c ompressive waves.

High surface stresses combined with micro-sliding r esult in high coupling temperatures andheavy wear of threads.

Compressive wave →→→→

←←←← Tensile wave

Feed force rquirements

From a drilling point of view From a mechanical poin t of view- to provide bit-rock contact - compensate piston moti on

- to provide rotation resistance - compensate linear m omentum of stress waves in rodsso as to keep threads tight

Feed forceRod force

Stress waves in rod (MPa)

Piston movement (mm)

Matching drill settings to site conditions

Rock hardness

Button count and size( and bit size )

Same bit in 2 different rock types or quarries

k1-good rockk1-soft

k1-soft k1-good rock

ηηηηsingle pass

BPR ratio}

Feed ratio( p feed / pperc. )

ubutton

Fbit

1k1-soft

Drilling in variable rock mass conditions

k1-void ≈≈≈≈ 0

k1-good rock

k1-joint < k1-good rock

k1-good rock

k1-hard layer > k1-good rock

Total overfeed(feed speed control)

OK(ratio set here)

Overfeed

OK

Underfeed

Actual feed conditions

Situation =>k1-soft k1-good rock

Feed ratio( p feed / pperc. )

ηηηηsingle pass

BPR ratio

k 1-g

ood

rock

k 1-h

ard

laye

r

k 1-jo

int

k 1-v

oid

}}

� drilling capacities in drm/ph or drm/eh

� production capacity in drm/shift

� avg. percussion pressure

� fuel consumption l/eh

� drill steel consumption & costs

� drill-hole straightness

� geological conditions

� costs in € per drm or m 3

Jobsite KPI’s for drilling operations

Predicting bit penetration rates - TH

Rock drillability, DRI

20 30 40 50 60B

it pe

netr

atio

n ra

te (

m/m

in)

0.4

0.8

1.2

1.6

70

0.6

1.0

1.4

1.8

HL1060T 102 mm 4”HF1560T 115 mm 4.5”HL1010 102 mm 4”

HL650T 76 mm 3”HL810T 89 mm 3.5”HF810T 89 mm 3.5”HL1560T 115 mm 4.5”

HL510/HLX5 76 mm 3”HL710 89 mm 3.5”

� rock mass drillability, DRI� percussion power level in rods (tubes)� bit diameter and type

���� hole wall confinement of gauge buttons� goodness of hole-bottom chipping

���� bit face design and insert types���� drilling parameter settings (RPM, feed)

� flushing medium and return flow velocity

Predicting bit penetration rates - DTH

� rock mass drillability, DRI� percussion power of hammer� bit diameter and type

���� hole wall confinement of gauge buttons� goodness of hole-bottom chipping

���� bit face design and insert types���� drilling parameter settings (RPM, feed)

� flushing medium and return flow velocity

Rock drillability, DRI

20 30 40 50 60

Bit

pene

trat

ion

rate

(m

/min

)0.2

0.6

1.0

1.4

70

0.4

0.8

1.2

1.6

5” RH550 (M50) 140 mm 5.5”6” RH550 (M60) 165 mm 6.5”

3” RH550 (M30) 89 mm 3.5”4” RH550 (M40) 115 mm 4.5”6” RH550 (M60) 203 mm 8”

8” RH550 (M85) 251 mm 7/8”

Gross drilling capacities (drm/h)

Bit penetration rate, BPR 2 (m/min)N

et d

rillin

g ca

paci

ty (d

rm/ h

our)

0.6 0.8 1.0 1.2 1.4 1.6 1.8

10

20

30

40

50

60

70

� time for rig setup and feed alignment per drill-hol e

� collaring time through overburden or sub-drill zone

� drill-hole wall stabilisation time (if required)

� rod handling times (unit time and rod count)

� bit penetration loss rate percentage i.e.���� rods and couplings 6.1 % per rod���� MF rods 3.6 % per rod���� tubes 2.6 % per tube

� effect of percussion power levels on:���� bit penetration rates���� drill steel service life���� drill-hole straightness

� time for tramming between benches, refueling, etc.� effect of operator work environment on effective

work hours per shift� rig availability, service availability, service and

maintenance intervals

Poor net drilling capacities for:���� very broken rock���� terrain benches - winching���� very low or very high benches���� very poor collaring conditions

Typical breakdown of longterm rig usage and capacities

Shift time, 100 %

Mechanical availability, 80 - 90 %

Machine utilisation, 60 - 80 %

Net drilling time, 40 – 60 %

Bit penetration time

engine hours

percussion hours(30 - 60 % of engine hours)

net drilling hours

shift hours

Rod handlingHole stabilisationReposition rig and feedBit change…

Shift changeLunchBlast downtimeSet out pattern…

Daily serviceScheduledmaintenanceBreakdowns…

Set out TIMTrammingRefuelingNew set rods…

Limestone Quarry – Drilling Report DI550 / Ø140mm

Company: XXXX Drillmaster: XXXX

1. Net drilling time 43,0 ---> 39,5 Net drilling time (drm/ph) - percussion hours2. Moving : 10,7

3. Total 1+2 53,7 ---> 31,6 Gross drilling time (drm/h) - incl. time for moving on bench

4. No-productive time 6,1h Waiting: hRe-dress: h Maintenance: 4,1hRe-fuel: h Repair: 2,0hTotal: h Total: 6,1h

5. Driving time 4,3h

6. Shift time 3-5 70,50 ---> 24,1 drm /shift hour(wihout breaks)

Efficiency (NG) : 76% Availability: 89%

Oper. ratio (eh/sh) : 80%7. Fuel consumption

Total consumption: 3131,0 L ---> 1,84 l/drill meter---> 53,98 l/engine hour

Can we drill straight holes?

Ventilation Shaft, Olkiluoto Nuclear Power Plant

Shaft diameter, Section I Ø6.5 m

Shaft length 15 m

Rock type Quartz Diorite

Contour hole size Ø60 mm

Contour hole charging 80 g/m det. cord

Contour hole spacing 0.4 m

Contour row burden 0.7 m

� floor humps

� poor loading conditions, uneven floors

� poor walls

� unstable walls

� difficult 1 st row drilling

� flyrock

� safety issue

What happens when we shoot holes that look like spaghetti?

� blowout of stemming

� safety, dust, toes, …

� blast direction

� quality of floors and walls

� shothole deflagration / misfires

� safety

� locally choked muckpiles (poor diggability)

� good practise

� max. drill-hole deviation up to 2 – 3 % forproduction drilling

Drill-hole collar positions

Drill-hole positions at hole bottom

� understand the many issues leading to drill-hole de viation

� technically good drill string

� technically good drill rig, instrumentation, …

� motivate the drillers!

How do we go about drillingstraighter holes?

Sources of drilling error

1. Collar position

2. Hole inclination and direction

3. Deflection (bending)

4. Hole depth

5. Omitted or lost holes

6. Shothole diameter (worn out bits)

Accurate drilling gives effective blasting

4

4

2

5

3

1

Examples of drill-hole deviation

Directional error for Ø89 mm retrac bit /

T45 in granite

Drill string deflection caused by gravitational pull orsagging of drill steel in

inclined holes in syenite

Examples of drill-hole deviation

Deflection with and without pilot tube for Ø89 mm DC retrac bit / T51 in micaschist

Floor hump due to explosives malfunction -

caused by drill string deflection

� bits loose diameter due to gauge button wear

� typical diameter loss for worn out bits is ~ 10%

� diameter loss effect on drill patterns

Diameter new bit Ø102mm

Diameter worn out bit Ø89mm

Diameter loss ( 102 – 89 ) / 102 = 12.8%

=> Drill pattern too big ( 102 / 89 ) 1.6 = 24%

Shothole diameter error control

Drill-hole diameter, d (mm)

50 100 150 20070 300 400

10

7

5

70

15

20

25

50

30

Dril

l pat

tern

, SB

(m

2 )

Better blastability

100

50 100 150 20070 300 400

10

7

5

70

15

20

25

50

30

Better blastability

Finer Finer fragmentation

100

� use tape, optical squares or alignment lasers for measuring in collar positions

� use GPS or total stations to measure in collar positions

� collar positions should be marked using painted lines – not movable objects such as rocks etc.

� completed drillholes should be protected by shothole plugs etc. to prevent holes from caving in (and filling up)

� use GPS guided collar positioning devices e.g. TIM-3D

Collar position error control

Difficult 1 st row drilling

� Rock type limestone, 1.6 Mtpa

� Bench height 32 m

� Bit Ø115 mm guide XDC

� Drill steel Sandvik 60 + pilot tube

� Hole-bottom deflection < 1.5 % or 0.5 m

� Gross drilling capacity 67 drm/h

� Drill pattern 4.5 x 4.8 m 2 (staggered)

� Sub-drill 0 m (blasted to fault line)

� Stemming 2.8 m

� No. of decks 3 ( stem between decks 1.8 m)

� Deck delays 25 milliseconds

� Charge per shothole 236 kg

� Explosives ANFO (0.95 & 0.85 g/cm 3)

� Powder factor 0.34 kg/bm 3

Lafarge Bath Operations, Ontario

Hole depth error control

Set-point values for TIM 2305

laser level

quarry floor levelsub-drill level

bench top level

inclination

b

a

c

c - alaser height

Remaining drill length = c - a(at 1st laser level reading)

Total drill hole length = c - a + b

Inclination and directional error control

quarry floor levelsub-drill level

bench top level

inclination

Set-point values for TIM 2305✓ inclination✓ blast direction projection✓ distant aiming point direction

(new aiming point readingrequired when tracks are moved)

blast direction

How bit face designs enhance drill-hole straightness

�

Feed

When the bit first starts to penetrate through the joint surface on the hole bottom - the gauge buttons tend to skid off this surface and thus deflect the bit.

More aggressively shaped gauge inserts (ballistic / chisel inserts) and bit face gauge profiles (drop center) reduce this skidding effect by enabling the gauge buttons to “cut” through joint surfaces quickly - thus resulting in less overall bit deflection.

How bit skirt designs enhance drill-hole straightness

�

Feed

As the bit cuts through the joint surface - an uneven bit face loading condition arises; resulting in bit and drill string axial rotation - which is proportional to bit impact force imbalance.

A rear bit skirt support (retrac type bits) reduces bit and string axial rotation by “centralizing” the bit.

Other counter measures:- longer bit body- add pilot tube behind bit- lower impact energy- rapid drilling control system reacting

to varying torque and feed conditions

� select bits less influenced by rock mass discontinuities� reduce drill string deflection by using guide tubes, etc. � reduce drill string bending by using less feed force� reduce feed foot slippage while drilling - since this causes a misalignment

of the feed leading to excessive drill string bendi ng� avoid gravitational effects which lead to drill string sagging when drilling

inclined shot-holes ( > 15 ⁰ )� avoid inpit operations with excessive bench heights

Drill-hole deflection error control

δ

Feed foot slippage δδδδoccurs at this point

∆∆∆∆L

Prior sub-drill zone

Dril

l-hol

e de

flect

ion,

∆∆ ∆∆L

Drill-hole length, L

∆∆∆∆L = ƒ ( L 3 ) for δδδδ ≠≠≠≠ 0

∆∆∆∆L = ƒ ( L 2 ) for δδδδ ==== 0

Drill-hole deflection trendlinesin schistose rock

Stabile drilling direction

perpendicular to fissures along schistosity or

bedding planes

Relatively stabile drilling

direction parallel to fissures

along schistosity

Fissures along schistosity or

bedding planes

� optimum bit / rod diameter relationship� insert types / bit face and skirt

� spherical / ballistic / chisel inserts � normal bits � retrac bits � drop center bits� guide bits

� additional drill string components� guide tubes / pilot (lead) tubes

Selecting straight-hole drilling tools - TH

Drill pattern at quarry floor

1 2

37

3

4 5 6

39 36 3533

31

78 9 1011

12

30 2928

2726

1314 15

25 24

16 17 18

23

20

2221

19

1 2

38

3 4 5 6

39 36 3534

3332 31

78 9

37

10 11 12 13 14 15 16

30 29 28 27 26 25 24 23 2221

20

17 18 19

Bench toe

Bench crest H = 33 m

Drill-hole collar positionsDrill-hole positions at quarry floor

Bench height 33 m

Hole inclination 14 °°°°

Drill steel Ø76 mm retrac / T45

Drill pattern 2.5 x 2.75 m 2

Rock type Granitic gneiss

3234

Drill pattern at quarry floor

1 2

37

3

4 5 6

39 36 3533

31

78 9 1011

12

30 2928

2726

1314 15

25 24

16 17 18

23

20

2221

19

1 2

38

3 4 5 6

39 36 3534

3332 31

78 9

37

10 11 12 13 14 15 16

30 29 28 27 26 25 24 23 2221

20

17 18 19

Bench toe

Bench crest H = 33 m

Drill-hole collar positionsDrill-hole positions at quarry floor

Clustered shothole areas / Risk of dead pressingVacant shothole areas / Risk of toe problemsSmall burden areas / Risk of flyrock

Bench height 33 m

Hole inclination 14 °°°°

Drill steel Ø76 mm retrac / T45

Drill pattern 2.5 x 2.75 m 2

Rock type Granitic gneiss

3234

Vertical projection of Row 1181716151413121110987

34 m

32 m

28 m

24 m

20 m

16 m

12 m

8 m

4 m

0 m

- 3 m

2019654321

2.7 2.72.72.72.92.82.72.72.83.02.72.72.92.7

2.73.12.82.82.2

3.41.75.92.23.72.92.43.52.63.72.721.64.16.13.4

1.1 1.1

� direction of deviation can not be “predicted”

� magnitude of deviation can be predicted

Prediction of drill-hole deviation errors

Rock mass factor, k rock� massive rock mass 0.33� moderately fractured 1.0� fractured 2.0� mixed strata conditions 3 .0

Bit design and button factor, k bit

� normal bits & sph. buttons 1.0� normal bits & ball. buttons 0.70� normal X-bits 0.70� retrac bits & sph. button 0.88� retrac bits & ball. buttons 0.62� retrac X-bits 0.62� guide bits 0.38

Drill-hole Deviation PredictionpredH=33.xls/A. Lislerud

Location Bench H = 33mRock type Granitic gneissBit type Retrac bit

Bit diameter (mm) dbit 76

Rod diameter (mm) dstring 45

Guide tube diameter (mm) dguide / No No

Total deflection factor kdef 1,34

rock mass krock 1,30

drill-string stiffness kstiffness 0,138

bit wobbling kw obbling 0,592

guide tubes for rods kguide 1,000

bit design and button factor kbit 0,88

constant krod 0,096

Inclination and direction error factor k I + D 47,8

Drill-hole deviation predictionDrill-hole Drill-hole Drill-hole Drill-hole Drill-holeLength Inc + Dir Deflection Deviation Deviation

L ∆∆∆∆L I + D ∆∆∆∆Ldef ∆∆∆∆Ltotal ∆∆∆∆Ltota l / L(m) (mm) (mm) (mm) (%)9,3 444 116 459 4,9

13,4 640 241 684 5,117,6 840 415 937 5,321,7 1036 631 1213 5,634,1 1628 1559 2254 6,6

� drill string startup alignment

� bit will follow a joint if at sharp angle to bit pa th

� drill string stiffness and “tube” steering behind bit

� deviation increases with impact energy

� button shape, bit face and bit body design

� drilling with dull buttons (worn bits)

� bit diameter checks when regrinding

� feed foot slippage while drilling

� removal or controlled drilling through prior sub-dr ill zone

� drilling control systems, i.e.

- applied feed, torque and percussion dynamics

� operator motivation!

Factors affecting drill-hole deviation

Wall control drillingMacon Quarry, GA

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Sorted Hole "Number"

Hol

e de

viat

ion

from

co

llar

loca

tion,

∆

L (

m)

Presplit Production

Excessive deviation due to feed foot slippage

DP1500 - Ø87mm Tubes - 24.5m Bench - Ø140mm Presplit

Wall control drillingMacon Quarry, GA

∆L % ∆x = ∆y α β

Max error 0.45 m 1.8 0.32 m ( ≈ 2d ) 0.75°°°° 12.0°°°°Median error 0.15 m 0.6 0.11 m ( ≈ d ) 0.25°°°° 4.2°°°°

∆x = error parallel to wall - lesser importanceα = atan ∆x / H

∆y = error perpendicular to wall is of greater importa nceto extent of blast damage in backwalls

β = atan ∆y / S

∆x

∆L = ( ∆x2 + ∆y2 )1/2

∆y

H

α

S

β

Wall control D&BChadormalu Iron Mine

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