A THESIS SUBMlTTED IN CONFORMITY WITH THE REQUIWMENTS FOR THE DEGREE OF ASTER OF APPLIED SCIENCE GRADUATE DEPARTMENT OF CIVIL ENGINEERNG

UNIVERSITY OF TORONTO

O Copyrisht by Paul B. Tomory 1997

395 Wellington Street 395, rue Wellington Ottawa ON K I A ON4 Ottawa ON K I A ON4 Canada Canada

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Split set' fiction stabilizer bolts are used by many underground mining operations in North

Arnerica for temporary and long-term support. In order to develop a rational design procedure

for this type of ground support, an extensive compilation of pull test results fiom a wide range

of mines throughout North America has been assembled and analyzed. To assist mine

engineers in the design process, a set of practical considerations and recomrnendations has

been developed. These include a set of charts quanti@ng the influence of various factors on

the effectiveness of Split Sets as well as the results of a statistical analysis used to find

significant trends and relationships in the available information. For the purposes of design,

the anticipated range, or distribution, of the strength of Split Sets has been determined for a

wide range of initial conditions, which include rock mechanics and operational parameters. A

case study is presented illustrating the use of the results in a probabilistic anaIysis, yielding a

percentage value for the reliability of support, or the probability of failure, rather than a single

value for the factor of safety. The information presented will assist rnining engineers in

designing safer and more efficient ground support with Split Sets.

' Tlic Split Set name is a tradcinark of Iiigersoll Rand

1 would like to thank Professor Murray Grabinsky, my supervisor, for his assistance and

support over the last year and a half, and Dr. José Carvalho of Golder Associates in

Mississauga for his encouragement and advice and for helping to organize the project from its

earliest stages. 1 would like to express my gratitude to the Natural Sciences and Engineering

Research Council of Canada (NSERC) and Golder Associates for providing financial support

and, in the case of the latter, allowjng me the use of thejr facilities, through the NSERC

Industnal Post-Graduate Scholarship (IPS) program.

1 would like also to express my sincere thanks to Reginald Hammah of the Rock Engineering

Group for his generous help and patience durhg the preparation of the statistical portion of

this thesis.

Thanks also to Doug Morrison of Golder Associates in Sudbury for his timely and practical

advice and comments and to Professor John Curran for inviting me to participate in the

proj ect .

1 would also like to acknowledge the participation of many individuals from various mining

companies in the background research for this thesis; without their valuable contributions this

project could not have been completed. They are listed at the end of chapter two. In

particular, 1 would like to thank Dan Haller of Tngersoll-Rand in Sudbury for his much-needed

advice in the earIy portions of rny research. Thanks also to Chuck Steed (Golder Associates,

Mississauga) and Dr. Evert Hoek for their practical suggestions, and especially to Dr. James

Scott for his advice, CO-operation and insightfûl commentary.

Title Page

Abstract

Acknowledgements

Table of Contents

List of Tables

List of Figures

1 INTRODUCTION

2 FACTORS INFLUENCING THE EFFECTIVENESS OF SPLIT SET FRICTION STABlLlZER BOLTS

2.0.0 Summary

2.1 .O Introduction

2.2.0 Split Sets and pull Testing

2.2.1 Description of Study

2.3.0 Factors Associated with Rock Type

2.3.1 Rock Classification

2.3.2 Variation in Pull-out strength with Rock Type

2.4.0 Factors Associated with Installation

2.4.1 Installation Quality

2.4.2 Drive Time

2.4.3 Slot Closure

2.4.4 Bit Size

2.5.0 Strength Development

2.5.1 Load Reaction Curves

2.5.2 Split Set Deformation

2.5.3 Load Development with Time

2.5.4 Steel Failure

2.5.5 Solt Length

2.6.0 Recommendations for Design

2.6.1 Range of Application

2.6.2 Determining Bond Strength

2.7.0 Conclusions

1

l i

iii

iv

vi

vii

3 STATISTICAL ANALYSE OF SPlLT SET PULL TEST DATA 37

3.0.0 Summary 37

3.1 .O Introduction 38

3.2.0 Description of Data Set 39

3.3.0 Statistical Analysis 43

3.3.1 Linear Regression 43

3.3.2 Residuals Analysis 44

3.3.3 Results and lnterpretation 45

3.4.0 Recommendations and Conclusion 5 1

4 PROBABlLlTY ANALYSIS OF GROUND SUPPORT USING SPLIT SET BOLTS, A CASE STUDY 54

4.0.0 Summary 54

4.1 .O Introduction 55

4.2.0 Description of Design Situation 57

4.2.1 Wedge Stability Analysis 57

4.2.2 Supporting Unstable Wedges 60

4.3.0 Deterministic Sensitivity Analysis 62

4.4.0 Probabilistic Analysis 69

4.5.0 Conclusions 77

5 RECOMMENDATIONS AND CONCLUSIONS 79

REFERENCES 8 1

APPENDIX A UNlTS CONVERSIONS 82

APPENDlX 6 LISTING OF SAS PROGRAM USED IN THE STATISTICAL ANALYSE 83

APPENDIX C LIST OF ALL PULL TEST DATA FOR SPLIT SETS 88

APPENDIX D AUTHORIZATION LETTERS 98

LIST OF TABLES

TABLE 2-1 Split Set specifications 6

TABLE 3-1 95% prediction intervals for SS39 pull-out strength 48

TABLE 4-1 Joint combinations fonning unstable wedges 58

TABLE 4-2 Summary of design variables in deterministic analysis 65

TABLE 4-3 Summary of design variables in probabilistic analysis 74

Figure 2-1

Figure 2-2

Figure 2-3

Figure 2-4

Figure 2-5

Figure 2-6

Figure 2-7

Figure 2-8

Figure 2-9

Figure 2-1 0

Figure 2-1 1

Figure 2-12

Figure 2-i3

Figure 2-14

Figure 2-15

Figure 2-1 6

Figure 2-1 7

Figure 2-1 8

Figure 2-1 9

Figure 2-20

Figure 3-1

Figure 3-2

Figure 3-3

Figure 3-4

Typical load-deformation curve for a pull test on a Split Set

Histogram showing the distribution of pull-out strengths

Relationship between Rock Mass Rating and pull-out strength

Histograms showing the distribution of pull-out strength for different rock types

Relationship between drive time and pull-out strength

Relationship between drive time, rock type and pull-out strength

Relationship between bit size and pull-out strength

Relationship between bit size, rock type and pull-out strength

Load reaction curve showing response of a support system to excavation boundary displacement

Load-deformation curve for a pull test carried out on a 5 ft, SS39 immediately after installation

Load-deformation curves obtained in tests carried out on various support elements

Load development with time for SS33 bolts in laminated rocks

Load development with time for SS33 bolts in competent rocks

Load development with time for SS39 bolts in several rock types

Histogram showing the distribution of pull-out strengths for tests immediately and 1 to 3 weeks after installation i n laminated rock

Histogram showing the distribution of pull-out strengths for tests immediately and 1 to 3 weeks after installation i n cornpetent rock

Load-deformation curves for three pull tests carried out at different times on the same 5 f t SS39

Relationship between bolt length and pull-out strength

Histograms showing the distribution of pull-out strengths for SS33 and SS39 bolts

Histograms showing the distributions of immediate pull-out strength for different rock types and bit sizes.

Histograms showing the distributions of each analysis variable

Simple linear regression model

Plots of equations 6, 7, 8 and 9 showing the relationship between SS39 pull-out strength and bit size for the different rock types

Plots of equations I O and 11 showing the relationship between SS33 pull-out strength and time from installation for the competent and laminated rocks.

Figure 4-2

Figure 4-3

UNWEDGE analysis, perspective view of wedge

UNWEDGE analysis for unstable wedge supported by 4 ft Split Sets on a 4x4 ft pattern

Variation in factor of safety with friction angle for different groundwater pressure conditions

Figure 4-4

Figure 4-5 Variation in factor of safety with increasing lateral acceleration for different support configurations

Figure 4-6

Figure 4-7

Variation in factor of safety with increasing wedge size

Variation in factor of safety with increasing Split Set bond for four different support configurations

Factor of safety for four support configurations assurning a bond strength of 0.6 tonslft for eight separate cases

Figure 4-8

Factor of safety for four support configurations assurning a bond strength of 0.8 tonslft for eight separate cases

Figure 4-9

Factor of safety for four support configurations assurning a bond strength of 1 .O tonslft for eight separate cases

Figure 4-1 0

Figure 4-1 1 Distributions and characteristics of the random input variables used in an @RlSK probabilistic analysis

Figure 4-12

Figure 4-1 3

Resulting probability density function for the factor of safety

Reliability of support for four support configurations assuming a mean Split Set bond strength of 0.8 and 1.0 tonslft

Figure 4-14 Plot relating rnean factor of safety and reliability of support for about 80 separate @RISK analyses

... Vlll

INTRODUCTION

When designing support for underground mining excavations, a common problem

encountered by mine engineers is the lack of reliable and specific information conceming rock

mass behaviour and rock-support interaction, and especially under particular conditions. With

this problem in mind, a research project was carried out in order to obtain actual test-based

information conceming the performance of one particular type of supporting element - the

Split Set friction stabilizer bolt. With this information, the factors which influence the

performance, or capacity, of the bolt can be analyzed and the effects quantified.

The research focused on Split Sets, which along with Swellex is one of the rnost common

types of friction bolt, because bolt effectiveness can be measured by means of a simple pull

test, wherein a jackinç load is applied to an installed element. Upon loading, Splits Sets almost

always fail by slipping at an easily identified and measured load, called the pull-out strength,

or slip load. This simple yet effective way of measuring bolt performance made the Split Set

an obvious candidate for being the subject of field-based research. The aims of this thesis,

therefore, were to identie and analyze the factors which influence Split Set effectiveness, as

measured by a pull test, and to provide çround support designers with reasonable estimates

(and ranges) of Split Set capacity under different mining conditions.

Rather than provide single values for Split Set capacity for different conditions, it was thouçht

more practical to sugçest rançes, or distributions, to account for the natural variations which

will occur in any rock mass, reçardless of the deçree of control. In addition, with the current

L A U ~ U 111 I ubn G ~ L ~ I G G I 1 1 1 5 4 w 4 y 11 U I I ~ a ~ V I G I c I I a i l b G VII L I I G LI a u l u v i l a l UCLCI IIIIILISLIC, L ~ C I L U I UL

safety approach for stability towards probabilistic analyses, there is a need for reliable

empirically-derived information concerning the distribution, or range, of values which certain

input variables, such as Split Set capacity, may assume.

The objective of this study was to identifL trends in the field data of Split Set pull-out

strengths with regard to rock mechanics and operational parameters. This was accomplished

by means of both a manual (spreadsheet) graphical approach to the analysis of the data as well

as a more rigorous statistical approach. Relationships between bond strength and key

parameters were identified and plotted using the spreadsheet and equations were generated by

means of a statistical software tool. A secondary objective was to demonstrate the usefûlness

of probabilistic analyses which account for the inherent uncertainty present in many design

situations, especially in rock engineering.

The layout of this thesis is straightfonvard and is based on three self-contained journal or

conference papers which were, or have yet to be, submitted or presented. Chapter two deals

with factors that influence the effectiveness of Split Set friction stabilizer bolts. The

information gathered in the research phase was analyzed by means of a spreadsheet program

and relationships were identified and plotted. Chapter two will be submitted to a journal for

publishing. Chapter three deals with the statistical aspects of the data and builds upon the

information presented in chapter two. The identified trends are quantified by equations that

allow prediction of means and confidence intervals for Split Set strength in various mining

conditions. This chapter will also be submitted, separately, for publishing. Chapter four

discusses the applications of probabilistic analysis and compares it to traditional deterministic

approaches to stability analysis. In it, the results described in chapters two and three are

applied to a specific design scenario. Chapter four has already been presented at and published

in the proceedings of a technical conference.

FACTORS INPLUENCING THE EFFECTIVENESS OF SPLIT SET FRICTION STABILIZER BOLTS*

Many underground mining operations use Split Set friction stabilizer bolts for rock support.

Currently, however, little has been done to quanti@ the effects of various rock mechanics and

operational parameters on the capacity of frictional support systems. The strençth of Split

Sets is usually measured by means of a pull test wherein a jacking force is applied to the bolt

and a slip load is obtained. In order to evolve a rational design procedure for this type of

support, an extensive database of over 900 pull test results from more than 50 mines

throughout North Arnerica has been assembled and analyzed. Associated relevant rock

mechanics parameters (rock type and quality) and operational details (drilling method, bit size,

drive time, time to pull test) were also obtained, as completely as possible, for each test.

Analysis of the information has yielded several charts that relate pull-out strength to relevant

parameters and simple statistical analyses were conducted where necessary. Quantified

distributions for pull-out strength were also produced for several operating conditions. The

factors that most significantly affect bolt strength have been identified and specific applications

to design are discussed. The information presented will assist mining ençineers in designing

safer and more economic support usinç Split Sets.

* This cliapter will appear as a journal article entitled 'Factors Influcncing tlie EîTcclivcncss of Split Set

Friction Stabilizer Bolts'.

In the design process for underground excavations, the amount of information concerning

rock mass behaviour and rock-support interaction is often of a limited nature. As such, one of

the most significant obstacles encountered in rock engineering is the lack of good information.

With this problem in mind, a research project was carried out in order to obtain actual test-

based information concerning the performance of a particular type of supporting element - the

friction bolt.

During the initial phases of this study, it was thought that information could be gathered on

both Swellex and Split Sets, the two most common types of friction bolt. Aithough the

effectiveness of both bolt types oiten is measured by means of a pull test, two major factors

restricted the scope of the study to Split Sets: first, the limited availability of Swellex pull test

results; and second, a Swellex pull test, more oflen than not, measures the breaking strength

of the steel, rather than the actual frictional performance of the bolt. Splits Sets, on the other

hand, almost always fail by slipping at an easily identified and measured load, called the pull-

out strength, or slip Ioad.

There is a current trend in rock engineering away from a sole reliance on the traditional

deterministic factor of safety approach for stability towards probabilistic analyses which

account for the inherent uncertainty associated with many of the design variables. Hoek et al.

(1995) give an excellent introduction to the assessment of acceptable risks in design and also

to probabilistic stability analyses. In order to perform probability analyses succesfûlly (see

companion paper, Tomory et al., 1997 - Chapter Four), actual data is required to quanti@ the

distribution of the design variables and to calibrate the analysis.

The objective of this study is to identi@ trends in the field data of Split Set pull-out strengths

with regard to rock mechanics and operational parameters. This will be accomplished by

means of a graphical approach to the analysis of the data. Relationships between bond

strength and key parameters will be identified and plotted. Later work will focus on the

statistical aspects of data analysis.

Split Set friction rock stabiiizers were developed by Scott (1977) and are manufactured and

distributed by the Split Set Division of Ingersoll-Rand. The bolt, consisting of a slotted high-

strength steel tube with a face plate, is installed by driving it into a slightly undersized hole.

Frictional anchorage, along the entire length of the bolt, is provided by the radial sprinç force

generated by compression of the tube. Splits Sets are used for a wide variety of mining

applications throughout many mines worldwide.

The pull test is the method which is commonly used for determining the effectiveness of Split

Set fiiction stabilizers. Bolts are tested at any time afier installation by applying a load to the

pull collar and increasing it until the bolt slips. A typical load-deformation curve for a pull test

is shown in Fig. 2- 1 .

Loaddefomation curve for pull test

O 0.1 0.2 0.3 0.4 0.5 0.6 0 7 0.8 0.9 1

Delorm ation (Inches)

Figure 2-1. Typical load-deformation curve for a pull test on a Split Set friction stabilizer.

The first part of the curve represents the elastic deformation of the steel and the seatinç of the

test apparatus and the bolt. The initial slip load, which is the load at which the bolt firsts

moves in its hole, is considered to be the bolt's pull-out strençth (in the case of the example

shown, the pull-out strençth is 7.5 tons). Once slippaçe has beçun, the load remains constant

as shown.

W 1 1 d u

the Split Set and the rock, the size of the drill hole into which the bolt is installed, the

characteristics, properties and type of the rock, the time elapsed between bolt installation and

pull test, the quality of installation and other less significant factors. Some of these, such as

rock type, drilling bit size and time to test are easily obtained. Others, such as contact area and

installation quality are either very difficult to determine or are not readily quantifiable.

The pull test should not necessarily be viewed as a definitive measure of a bolt's capacity but

rather as an index test, one that can give a reasonably good idea of the bolt's expected

performance. An analysis of the effectiveness of Split Sets bolts can only be successfùl if the

many factors which influence bolt behaviour are considered along with an interpretation of

pull test results.

2.2.1 Description of Study

As part of the background research for this paper and others, an extensive database of over

900 pull test results was compiled from about 50 mines throughout North Arnerica,

representing a very wide range of ground conditions and applications. An effort was made to

obtain detailed information, for each individual test, about the general conditions and about

several parameters which influence bolt effectiveness. If possible, information was gathered on

the following: bolt type (i.e. SS33, SS39 or SS46; see Table 2- l), bolt length, drilling bit size,

drive time, driver equipment, time elapsed from installation to test, rock type, rock quality

(RMR), specific bolt application and pull-out, or slip load. Some of this information will be

discussed subsequently in greater detail. The full data list is given in Appendix C.

Split Set Specifications b l i t Set rnodel SS33 SS39 SS46 1 Nominal outer diameter Bolt lengths Capacity of steel, average Ca~acitv of steel. minimum

33mm 0.9 to 2.4

Table 2-1. Split Set specifications. After Split Set Division, Ingersotl-Rand Company.

10.9 tonnes 7.3 tonnes

1.3 in. 3 to 8 ft. 12 tons 8 tons

39mm 0.9 to 3.0 12.7 tonnes 9.1 tonnes

1.5 in. 3 to 10 ft. 14 tons 10 tons

46mm 0.9 to 3.6

- -

1.8 in. 3 to 12 ft.

16.3 tonnes f 3.6 tonnes

18 tons 15 tons

- - - - - - - . . =--- - - - -J - - r - --- ---- =--' --- ------O--- "-- - . . - J -- - - - - - - - - - - -------

is to divide the pull-out load (normally measured in tons) by the length of the bolt (measured

in feet) to obtain a value in tons/foot. This measure is reasonable because it can be assumed

that bond strength is developed along the entire length of the bolt. Fig. 2-2 shows a histogram

and an initial statistical analysis of the pull-out strength values (in tonslft) for al1 test results

collected in this study. Imperia1 measurements are used in this study because the vast majority

of mines use them and almost al1 mines measure pull-out strengths in tons and bolt lengths in

feet. Metric conversions are provided in Appendix A.

Histograrn of al1 pull test results

250 1 I

'1 l Mean 1.09 Standard Deuation 0.46

Sample Variance 0.21 Skewness 2.1 2

8?2!$ z=?zF z Pull-out strength (tonsm)

Figure 2-2. Histograrn showing the distribution of pull-out strengths for al1 data collected

study.

As can be seen, the histogram closely resembles a normally distributed random variable with

some degree of skewness. The mean pull-out strength is 1-09 tonslft with a standard deviation

of 0.46. It is beyond the scope of this paper to discuss the characterization of this distribution

and the more involved statistical aspects of the sample set and its subsets; these will be

considered in a later paper.

..w a..".., 3'""' ".'V 7 . .. "' * .a. - - Y.."..." ..WC " Y "Y..".""."" .+Y ...Y " V I A... ...Y Y . " C . . V U C . V . . .V.

Split Set pull-out strengths in specific probabilistic stability analyses because it includes al1 test

results representing a very wide range of conditions. The test results can be broken down into

more specific design applications, based on, for instance, rock type andlor drill bit size, so that

more accurate and representative distributions can be determined.

2.3.1 Rock Classification

Given the very Iimited nature of the information available concerning rock type and quality at

many of the sites where the pull tests were conducted, it was impossible to appIy any of the

more involved rock mass classification or strength charac-terization systems to al1 the data.

Many of these require fairly good knowIedge of the condition and nature of the joints,

groundwater conditions and of the strength of the rock mass (i.e. Hoek-Brown, GSI, m, Q, etc.. .). For many of the test results collected in this study, such information was simply not

available. The information from the various mine sites varied in detail; some of the mines kept

fairly good records of rock type and quality while others simply noted the rock types and

perhaps a brief qualitative description. For instance, RQD or RMR was available for some but

not al1 of the rock types encountered in the study. In any case, çiven a certain number (about

300) of test results where the RMR of the rock was known, there was no observable

relationship between RMR and pull-out strength (see Fig. 2-3).

Figure 2-3. Relationship between Rock Mass Rating and pull-out strength. Each point in the

plot represents approximately 10 pull tests; i.e. often several tests were conducted in one

location where a single value for RMR was recorded.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - J - - ------- ,---Q ------- - - - - m m - - r - - - - - - - - - - - - - - - factors, the data was analyzed in terms of bit size, rock type and time to test. There were no

observable trends which could clariFy the plot.

For the purposes of classifiing the rock types encountered in this study, the classification

system of Terzaghi (1946), with some modifications, was found to be the most appropriate.

Rock types can be divided into four very broad categories based on easily identifiable physical

characteristics which dominate rock mass behaviour. These categories are summarized below:

Laminated rocks. This category includes crystalline or metasedimentary rocks which are

strongly laminated or foliated; including schists, laminated arçillites, shafes and other hard

laminated rocks. The individual laminations usually have moderate to little or no resistance

against separations along the boundaries between them and surface spalling is common. The

laminations may or may not be weakened by transverse jointing. The values for RMR are

typically around 50, ranging from about 25 to 65.

Comoetent rocks. These include intact and weakly to moderately jointed crystalline and hard

sedimentary rocks; including granite, gabbro, rhyolite, quartzite, hard sandstones, dolomite,

hard limestones and others. The blocks between joints are locally grown together or so

intimately interlocked that vertical walls do not require lateral support. In rocks of this type,

bursting and spalling may be encountered. The RMR values are above 50, typically ranging

from 60 to 80.

Altered, weathered or brokeri rocks. These include weathered crystalline rocks, rock in

shear zones, certain ores, cemented gravels and others. The structure of these rocks is blocky,

seamy or crushed, consisting of generally intact fragments which are entirely separated from

each other and imperfectly interlocked. In such rocks, vertical walls require lateral support.

Rock mass deformations are usually by block movement. The values for RMR are below 50.

, - - - - - - - - - - - - - , . - - - - - - , - - - - - - - - - - - - - - , - , - - - - , - - - - - - - - -

and others. This category includes those rocks which Terzaghi describes as squeezing and

swelling. Squeezing rock slowly advances into the excavation without perceptible volume

increase (stress driven) while swelling rocks move into the excavation chiefly on the account

of expansion (chernical process). Rock mass deformations are generally plastic. For the

purposes of this study, permafrost-affected rocks were included in this category. The values

for RMR range from 20 to 60.

2.3.2 Variation in Pull-out Strength with Rock Type

For the four different rock types described above, a significant amount of variation in the

distribution of pull-out strengths was observed. Normalized histograms showing the

occurrence of values for pull-out strength, as a percentage of the total number of pull tests in

each rock type category, are shown in Fig. 2-4.

Distribution of pull-out strengths for lamlnated rocks

Dlstrlbution of puil-out strengths for competent rocks

-.- . . . , . . . . . , . . , . . . . o ~ ~ q w ~ ~ ~ q ~ ~ n ~ c o n

0 0 0 0 r r r r N N N N %

Dldribution of pull-out strengths for aitered rocks

Distribution of pull-out strengths for soft rocks

Figure 2-4. Normalized histograms showing the distribution of pull-out strengths for the four

different rock types, al1 test results.

A T V C Y CI~UC LA.- U A Y L . S V U L I V B ~ ~ ~ AU. V V B ~ ~ ) I Y L Y ~ L C U~IU VAL I v w n a UA Y 51 w u p r u IIIWI Y L I ~ I I L I J ~ 8 1 ~ 8 8 L L I ~

ones for laminated and altered rocks. Additionally, the former two could be more easiIy

characterized as normally distributed random variables. The mean pull-out strength for

competent rocks is 1.12 tonslft, with a standard deviation of 0.46, while the mean for soft

rocks is 0.75 tonslft, with a standard deviation of 0.38.

For altered rocks, there appears to be a wide range of values for pull-out strength with two

distinct peaks, one at 1.0 and one at 1.6 tonslft. Upon close examination of the test results,

there is no readily apparent reason for this. Both peak groupings include rocks of similar type,

in similar conditions and installed in similar-sized holes. Bond strength development with time

is also not the cause of the second peak because the great majority of the results (for altered

rocks) were of pull tests conducted immediately after bolt installation. A possible explanation

for the second peak is that many of the test results in that group were for bolts installed in

highly stressed (and fractured) ore zones where the hole was drilled with an undersize bit.

In the case of laminated rocks, pull-out strengths of 0.8 to 1.4 tons/ft are common. However,

this broad range of values can be attributed to the marked development of bond strençth with

time exhibited by bolts installed in laminated rocks (many of the tests were conducted days or

weeks after bolt installation). Thus, the distribution for pull-out strengths in laminated rocks

(as shown in Fig. 2-4) is not as wide as it may appear initially. The issue of bond strength

increase over time is discussed in a later section.

2.4.1 Installation Quality

The installation of Split Set stabilizers is a fairly straight-fonvard procedure and can be

performed easily by trained personnel. The diameter of the bit should be measured and the

length of the hole should be at least two inches longer than the bolt. Since Split Sets are

driven through a pounding action, it is essential that the end edge of the bolt be flared over the

ring by the driver tool to achieve proper contact of the ring to the roof plate. The bolts should

not be overdriven but placed tightIy against the rock so that a slight deformation in the roof

plate is visible.

Other installation factors affecting bolt capacity are hole roughness and curvature. Crooked or

rough holes do not adversely affect the performance of a Split Set, but rather they increase the

anchorage and hence the pull-out strength .

2.4.2 Drive Time

A practical method for determining the quality of an installation without a pull test is to

measure the lençth of time required to hlly drive the bolt against the rock; in other words, the

drive time. The drive time is dependent on the friction that must be overcome by the driving

tool to insert the bolt tùlIy. A longer drive time is indicative of greater friction between the

rock and the bolt surface and conversely a shorter drive time indicates less friction. As a

result, there is a direct relationship between drive time and immediate capacity (rock

movements over time may give bolts with otherwise low drive times higher bond strengths).

Bolts that require a çreater amount of work energy to install, as manifested by hiçher drive

times, will have a hiçher pull-out strength when tested. As such, for each particular driver

type, because the work energy delivered by different drivers is different, there should be a

- - b- - - r - - - - - U . observed for several driver types in the collected data. For example, Fig. 2-5 shows the

relationship between drive time and immediate pull-out strength for the commonly used

Jackleg driver.

Figure 2-5. Relationship between drive time and pull-out strength for a Jackleg driver with

SS39 bolts. The line has been fitted using Iinear regression techniques.

The scatter of the data points can be, to some extent, attributed to such factors as differing bit

size or rock type, as shown in Fig. 2-6 for the latter; there was insuficient data to observe

properly the effect of bit size on drive time. In general, however, the scatter is what could be

anticipated from a data set composed of information from a very wide range of sources. The

relationships appears to be linear. A trend line was produced for each usinç linear regression

in order to show a mean relationship between drive time and pull-out strength.

nwlr xype ana arive urne, DJJJ

- - - LaMnated rocks

- - Corqxknt rocks

Ç o f t rock,

Drlve (lm* (m)

Figure 2-6. Relationship between drive time, pull-out strength and rock type for a Jackleg

driver with SS39 bolts. The lines have been fitted using linear regression.

One further, though unquantifiable, reason for the scatter of the points in Fig. 2-5 is that the

pneumatic line pressure is not necessarily a fixed quantity. At sites where the tool is fùrther

from the main compressor unit, there will naturally be a lower pressure available for bolt

driving. If the operating pressure was known at the bolt installation sites, which was not the

case for the tests in this study, then a somewhat more accurate relationship between drive time

and pull-out strençth could be obtained.

The drive tirne can be a very practical and easy indication of installation quality. Once the

characteristic drive time vs. pull-out strength plot for a driver type is known (such as the ones

shown in Figs. 2-5 and 2-6), then a simple measurement of the drive time can give a good

day-to-day measure of installation quality.

2.4.3 Slot Closure

Split Sets are one of the only support fixtures where a miner can visually observe the quality

of installation. By shining a light down the length of the tube, a miner can observe the degree

narrower the slot, the higher the anchorage. Scott (1 996) reports that if the slot is closed 1/16

of an inch, then there is full rock-metal contact around the Split Set. If the slot is the same size

as before installation, then the hole is larger than the Split Set and there is zero or near-zero

anchorage.

With slot closure, the Split Set bolt is deformed beyond the yield point and into the cold

working portion of a stress-strain curve. Anchorage, or bond strength, is produced by the

reaction of the spring-like Split Set against the walls of the drill hole. If the bolt is removed,

and the steel unloaded, there will be some amount of spring-back, typically around 1/32 of an

inch on the diameter of an SS39 bolt.

2.4.4 Bit Size

To achieve proper slot closure and to develop bolt anchorage, the hole should be drilled with

a bit of a diameter slightly less than that of the Split Set (Le. 1.3 in. for SS33 and 1.5 in. for

SS39). Since the bolts are deformed plastically upon insertion in the hole, the bit size is not

overly critical. If Split Sets were designed to be loaded only in the elastic range of the steel,

then the hole size would be supercritical and it would prove impracticai, if not impossible, to

drill holes within appropriate tolerances.

Given that the hole size should be sliçhtly smaller than the diameter of the bolt, there will still

be variations in bond strength with different bit sizes for different rock types. The diameter of

the drill hole will not always be the same as the diameter of the drill bit used to do the drillinç.

For instance, there will be a significant degree of overbreak in holes drilled in sofi or broken

rocks while holes drilled in more competent rocks will have a diameter closer to the actual bit

size. As a result, bond strength will Vary for the same drilling bit size in different rock types.

For example, if the hole for an SS39 bolt (diameter of 1.5 in.) in weathered or broken rock is

drilled with a 1.438 in. bit, the developed bond strength will be lower, because of greater

overbreak in the hole, than the strençth developed in a same size hole in stronger rock.

The variation in pull-out strength with bit size for al1 SS39 bolt test results, regardless of rock

type, is shown in Fig. 2-7. As can be seen, there is a trend of decreasing pull-out strength with

increasing bit size. To further analyze the relationships between bit size and pull-out strength,

the type and quality of the rock in which the hole was drilled must be considered.

tnlluence of blt size, SS39

2.5 5

1.3 1.35 1.4 1.45 1.5 1.55 1.6

8Ï i ize (in.)

Figure 2-7. Relationship between bit size and pull-out strength for al1 SS39 test results

(numbering over 450). The results are plotted in error bar form for the five most common bit

sizes (1.35, 1.375, 1.438, 1.5 and 1.538 in. sizes). Each bar represents the distribution of test

results for its particular bit size. The bars are centred on the mean, with each extremity

positioned one standard deviation on either side of the mean.

The relationship between bit size and pull-out strength for the four different rock types is

shown in Fig. 2-8. By plotting the data in this form, a clarification of the error bar plot in Fig.

2-7 is obtained.

As can be seen, competent rocks are the most sensitive to the size of the drillinç bit. This is

attributable to the çeneral nature of the rock; it is not easily deformed or broken. Due to

minimal overbreak, the actual hole diameter in such rocks is close to that of the drillinç bit

and, as such, a fairly clear relationship between anchoraçe and bit size can be observed.

bond strength are not significant.

Influence of Mt size for difkrent rock types 5539

I

C o m p e t e n t r o c k s

- Altered rocks - ~Laminated rocks

. . . - . . . Ço(t rocks

Bit mizs (in.)

Figure 2-8. Relationship between bit size and pull-out strength for al1 SS39 test results for the

four different rock types. The trend lines shown were fit to the data using second order

regression.

For laminated rocks the influence of bit size on pull-out strength is not as pronounced. For

these, breakaçe and movement of the rock mass during and imrnediately after hole drillinç and

bolt insertion combine to lessen the influence of bit size on bond strençth. In particular, shear

movements alonç lamination or foliation planes cause a çeneral increase in bolt anchoraçe by

introducing a confining stress.

The pull-out strength, in the case of altered, weathered or broken rocks and sofl rocks,

appears to be influenced by bit size to an intermediate deçree. For these rock types, overbreak

during drilling is a greater concern. However, the effects of overbreak are mitiçated, to

varying degrees, by deformations of the mass durinç and after drilling and installation. These

deformations, whether plastic or alonç fractures can cause closure of the rock mass around

the bolt, increasinç confinement.

2.5.1 Load Reaction Cumes

The response of a support system to excavation boundary dispIacement can be described by a

load reaction curve, as shown in Fig. 2-9.

support rec

Figure 2-9. Load reaction curve showing the response of a support system to excavation

boundary displacement. Frorn Scott, 1989 (reprint of ground reaction curve developed by

Deere and Peck).

During mininç, a certain amount of deformation occurs ahead of the advancinç face of the

tunnel. According to Hoek et al. (1 999, at the face itself, approximately on third of the total

radial deformation has already occurred and this deformation cannot be recovered. In

addition, there is always a stage in the excavation cycle in which there is a çap between the

face and the closest installed support element. Hence, fùrther deformation occurs before the

support becomes effective. The total initial displacement, or rock mass relaxation,

corresponds to section OB on the horizontal axis in Fiç. 2-9.

to prevent this initial load relaxation and rock movement. As such, it is important to install

support which possess adequate stiffness to allow ground strength to become fùlly developed

as shown in the figure. In some conditions where excessive movements are expected, Split

Sets can be an effective mode of support because of their deformation characteristics.

2.5.2 Split Set Deformation

When installed, a Split Set bolt has a certain anchorage or bond strength. When a load is

applied, the initial deformation, up to the total bond strength developed, will be that of the

steel yielding in the elastic range and of the test apparatus seatinç itself As the load on it

reaches or exceeds the total available bond strength, the bolts will slip a small amount and

açain be capable or supporting a load equal to the available bond strength. This process can

continue indefinitely, with the bolts alternately sticking and slipping at a more or less constant

load. The results of a load-deformation test carried out on an SS39 installed in hard shale by

Scott (1977) are presented in Fig. 2-10. They demonstrate that there is no loss of bond

strength with bolt slippage in the hole.

Loaddeformaiion curve for pull test

Figure 2-10. Load-deformation curve for a pull test carried out on a 5 ft. SS39 immediately

after installation. The bolt was loaded until initial slippage, unloaded and reloaded twice and

then pulled out of the hole for a a full 0.5 inches. Note that an approximately constant load of

7.5 tons was reached. From Scott, 1977.

be their chief advantage. This allows the botts to adapt to extensive ground movements while

maintaining a certain constant load level; other types of bolts under identical conditions would

rupture because of their higher stiffness. Fig. 2-1 1 shows a comparison of load-deformation

curves for vanous support elements including Split Sets.

uasmlbrdowd

expauioaMl- If3 ~dl.mccnrOmfLbdi 0 150-

l)ipe SS 39 Split Set mbili~s

Figure 2-1 1. Load-deformation curves obtained in tests carried on various support elements.

High strength reinforced concrete with a uniaxial compressive strength of 60 Mpa was used

for the test blocks and holes were drilled with a percussion rig to simulate in-situ rock

conditions. From Stillborg, 1994

2.5.3 Load Development with Time

As deformations occur over time in the rock mass surroundinç an excavation, there is an

increase in the confininç stress on supporting elements. Split Sets not only demonstrate

sticWslip behaviour as discussed, but they also yield and adjust to the load reaction curve with

- - - - - - - - - - - 2 ----- ------ a - - ' --- -- - ------ ---. --- - . , O - - - - - - - - - - - - - - - - , - - - - - - - - - - - - - y---,

is developed between the rock and the bolt with tirne. As the system reaches equilibrium, and

the ground strength becomes fully developed, the load in the supporting elements reaches a

maximum.

This is confirmed by pull tests carried out on SS33 bolts days, weeks and months afler

installation that show higher than average values for pull-out strençth. Load development

varies with rock type, as shown in Figs. 2-12 and 2-13, which plot puII-out strength against

time for laminated and competent rocks respectively. Note that these results represent the

mean of al1 tests, so they incorporate al1 results, regardless of bit size. The plots couId be

firther broken down into a series of curves representing different bit sizes.

Load development in Iaminated rocks, SS33 bolts

1 0.70 . O 10 20 30 40

Time frorn lnstallatlon to pull test (days)

Figure 2-12. Load development with time for SS33 bolts installed in larninated rocks. The

cunre was fit using second order regression.

There was not enouçh data available in this study for obsewinç load development with time in

soft or altered rocks. There was also insuficient data to consider load development in SS39

bolts but presumably the general trends would be identical.

O 20 40 BO 80 100 120 140

f lm e from lnstallatlon to pull test (days)

Figure 2-13. Load developrnent with time for SS33 bolts installed in competent rocks. The

curve was fit with second order regression.

These figures can be compared with earlier results published by Scott (1980) and shown in

Fig. 2-14. It should be noted that Figs. 2-12 and 2-13 illustrate Ioad development in SS33

bolts while Fig. 2- 14 shows the same for SS39 bolts. In al1 cases (in Figs. 2- 12, 2-1 3 and 2-

14), the pull-out strength increases with time. The rate of increase depends on the rock type.

- Uranium; wet shale Copper; shale

- Uranium; sandstone

Days afler installation

Figure 2-14. Load development with time for several different rock types. The pull-out load is

given in tons for 5 ft. long SS39 bolts. From Scott (1 980).

tend to cause shearing along lamination sudaces. These movements produce slight offsets in

the Split Sets which increase the anchorage or bond strength. In such conditions, the amount

of sticwdip behaviour is diminished and a greater degree of lock-up occurs due to shearing.

Note that in Fig. 2-1 3, for laminated rocks, there is a 70% increase in load over a 45 day

period. The load appears to level off to a maximum after about 40 days. A similar rate of load

development can be observed in Fig. 2-14 for the case of the copper mine shale, a laminated

rock.

Where Split Sets are installed in competent rocks, the rate of load development is not as

pronounced and it appears to be more uniform. In such rocks, load development is caused by

mass deformations which tighten the rock mass around the bolt rather than by shearing.

A cornparison of the distributions obtained in tests performed immediately after installation

and in tests performed seven to twenty one days after installation in laminated rocks is shown

in Fig. 2-15. Note that since the distributions are normalized histoçrams, an aççregate

distribution would not be the same as the distribution shown in Fig. 2-4 for laminated rocks.

Also note that the mean value for pull-out strength is 30% hiçher for the tests conducted one

to three weeks after installation. Essentially, the distribution curve for pull-out strençths

moves to the right with tirne. The broad range of values obtained for pull-out strengths for

laminated rocks, as shown in Fig. 2-4, can thus be attributed to the development of load with

time in Split Sets. Fiç. 2-1 6 shows a similar pair of distributions for competent rocks. As with

the load developrnent curves, these histograms include test results including al1 bit sizes. The

result is an inherent spread of the results.

Summary Statiçtics lmmediate tests

Mean 1 .O2 Siandard Deviation 0.39

Sample Variance 0.1 5 Skewness 1.59

7 10 21 day tesis Mean 1.32

Siandard Deviafion 0.27 Sarnple Variance 0.07

Skewness 0.40

[ 45.0 ,

I ~ u l ~ o u t strength (tonsnt1

imrnediate tests

Figure 2-15. Normalized histograms showing the distribution of pull-out strengths for tests

perfonned immediately and between a week and three weeks on SS33 Split Sets installed in

laminated rocks.

l ime eiïed distributions for puilout strengths (competent rocks)

0 > 7 days tests

Summary Statistic lm rnedlate tests

h a n 0.98 Standard Dewation 0.23

Sample Variance 0.05 Skewness 0.25

>7 days tests Mean 1.16

Standard Dewation 0.35 Sample Variance 0.1 2

Skewnnss 3 38.

" f X 2 " L a Puli-out strength (tonslft)

Figure 2-16. Normalized histograms showing the distribution of pull-out strengths for tests

performed immediately and after more than a week on SS33 Split Sets installed in competent

rocks.

As shown, a significant amount of load development will occur in Split Sets installed in

laminated rocks. In addition, Scott (1996) indicates that similar behaviour can be expected in

highly stressed ground. In these cases, movements along cracks or shearing planes which

intersect the length of the bolt produce offsets which may lead to the bolt locking up.

Excessive lock-up or load development is not necessarily desirable since one of the reasons

for Split Set use is that they yield with the rock mass in a controlled manner. If the loads reach

high enough values then failure of the steel will occur. This should not be allowed to happen

because it could result in an uncontrolled failure of the excavation. For Split Sets to rnaintain

their yielding behaviour, the load developed over time should remain less than the failure load

of the steel; which is, on average, 12 tons for SS33 bolts and 14 tons for SS39 bolts or as a

minimum, 8 tons for the SS33 and 10 tons for the SS39.

I Load-deformation curve for several pull tests over time

test aRer 3 months

1 O 0.05 0.1 0.15 0.2 0.25 0.3 O35 0.4 0,45 0.5 deform atlon (Inches)

Figure 2-17. Load-deformation curves for three pull test carried out on the same 5 ft. SS39

bolt in hard shale: at the time of installation, at 19 days and at 3 months. From Scott, 1977.

Fig. 2-1 7 shows the load-deformation curves for three separate pull tests conducted on the

same SS39 bolt: at the tirne of installation, at 19 days and at 3 months. Each test shows a

progressive increase in ancnorage witn rime; rrom 3 . ~ 3 Cons, IO I U . L ~ tons ana tnen to iz

tons. Again, these tests were conducted on bolts installed in a hard shale in an area showing

significant rock deformation caused by stress. After three months, a load greater than the

minimum steel breaking load has been developed in the Split Set. This is still acceptable, but

fbrther load development will cause the steel of the bolt to break, potentially causing an

uncontrolled failure of the support element and possibly also the excavation if progressive

overloading of bolts in the pattern occurs.

In the case of SS39 bolts, an ultimate tensile strength of 14 tons is available. If the bolt is

installed in a highly stressed rock, or in a laminated rock, where large deformations are

expected, it will be necessary to install the bolt at a Iow initial anchoraçe of as low as, Say, 2

tons for a 5 ft. bolt. In this way, 12 tons of effective support capacity are available in the Split

Set during the period of rock mass relaxation on the load reaction curve. Thus, when the

ground strength becomes fùlly developed and the support is fùlly effective, there will be a load

in the Split Set near to but not exceeding the steel failure load. If the Split Set were installed

with an initial anchorage of 6 or 7 tons, then the strength available for Ioad development is

less and bolt overloads may occur. As a result, it is very important to be able to predict, with a

fair degree of accuracy, the loads which can be anticipated under certain conditions.

In laminated rocks, where the observed load development reaches 1.7 tonslft, bolt lengths

should be limited to 5 A. for the SS33 and 6 fi. for the SS39 if installed under normal drilling

conditions. This lençth limit, however, could be increased if the bolts are installed in larger

diameter holes where the initial anchorage is lower.

2.5.5 Bolt Length

The effect of bolt length on pull-out strength was also considered. Althouçh it has been

suggested that longer-lençth bolts (longer than 6 fi.) are more prone to lock-up than shorter

ones, the same was not found in this study. As shown in Fiy. 2-18, for SS39 bolts, there may

even be a decrease in the bond strength with increasinç bolt lençth. Nevertheless, there are

Figure 2-18. Relationship between bolt length and pull-out strength for SS39 bolts.

To account for the possibility that there may be underlying trends in Fig. 2-18 caused by

different factors (as was the case for the bit size vs. pull-out strength relationship), the data

was analyzed by separating, in turn, the points into the bit size, rock type and tirne to test

groups used earlier. There were no observable trends which couId dari@ the plot.

2.6.1 Range of Application

Before making any specific comments concerning the anticipated strength of Split Sets, some

general considerations rnust be addressed and the range of applicability of Split Sets must be

defined.

Split Sets should never be expected to carry large loads. On the contrary, they are designed to

yield in a controlled fashion under comparatively limited loads. This is their chief advantage.

However, the limited load-carrying capacity of Split Sets does preclude their exclusive use in

some applications (high-modulus rock, for instance). Nevertheless, in these situations, they

can be employed in conjunction with stiffer elements, such as resin-çrouted rebar, to provide

an effective means of supporting an excavation. Additionally, in conditions where the primary

mechanism of excavation support is suspension of the rock mass, Split Sets are not an

effective means of support. In these cases, cables, resin-grouted rebar and point-anchor bolts

are more suited to the task.

Split Sets are particularly good for supporting rock where high stress and strain levels are

encountered. Stress relaxation and movement of the rock mass around the excavation, and in

particular if the rock is brittle, produce offsets in the Split Sets, increasinç their anchorage. If

these conditions are expected then Split Sets should be installed at a low initial anchorage to

allow it to reach maximum deformation without steel failure. As discussed earlier, the same

holds true for Split Sets installed in laminated rocks.

In hard, brittle rocks where surface spalling is a problem, Split Sets can be a very effective

means of retaining the broken pieces of rock in place. AIthough this condition does not

represent a major stability concern, broken pieces should be kept in place to prevent

progressive spalling and unravelling. In these situations, Split Sets are best installed with wire

initiation.

In rockburst situations, Split Sets have the advantage of yielding under constant load, which

enables them to restrain broken rock which would otherwise be ejected from the face. In these

situations, where other, stiffer, support elements may fail, Split Sets can move up to several

feet in their hole without failing. In such events, Split Sets act as dynamic dampers,

transferring the burst energy to pull-out force. Split Sets are used widely in burst-prone

ground in both the United States and South Africa. However, progressive burstinç may be a

problem for Split Sets because, afier each successive burst, a certain deçree of lock-up occurs.

The bolts would then be locked in so tightly that either steel failure occurs or the plate is

ripped off the head of the bolt. In these situations, an alternating pattern of Split Sets and

resin-grouted rebars has been found to be effective.

A major concern associated with Split Sets is their usefùl life span. They are susceptible to

corrosion and in some severely corrosive groundwater conditions, they can becorne ineffective

after a period of seven or eight months or even as little as two months. In less corrosive

environments, life spans of two to six years are common. Galvanized and stainless steel Split

Sets are available for use in permanent excavations. Split Sets are well suited to temporary

support applications, such as shafi sinking, where support is required only for a few days until

the advance of the permanent concrete liner.

2.6.2 Determining Bond Strength

For the purposes of design and analysis (conventional or probabilistic), several

recommendations can be made with regard to the bond strençth which Split Sets could be

expected to develop in specific rock types and for specific drilling bit sizes.

Firstly, it should be noted that the strençth developed in SS33 and SS39 bolts appears to be

very similar (rneasured in tonslft), as shown in Fig. 2-19. In general, the distribution for the

instance, there appears to be a slightly greater proportion of test results yielding higher pull-

out strengths (in the range of 1.8 to 2.2 tonslfi) for the SS39. This can be attributed to the

fact that many of the tests in that range were performed on bolts installed in undersize holes

(Le. 1.375" holes). Nevertheless, general conclusions which are drawn for SS39 bolts should

hold also for SS33 bolts.

Distribution of pulleut strengths for 5533 and SS39

Figure 2-19. Normatized histograms showing the distribution of pull-out strengths for SS33

and SS39 bolts. The sample site is 475 test results for the SS39 and 374 for the SS33.

For the purposes of determining what value of bond strength to use in a deterministic stability

analysis or which distributions to assign in a probabilistic analysis, Fig. 2-20 provides a quick

and easy reference, provided that the drillinç bit size and the rock type are known.

The distributions shown in Fig. 2-20 are for SS39 bolts. Distributions for SS33 bolts should

be qualitatively similar, i.e. a 1.3 inch bit for the SS33 corresponds rouçhly to the 1.5 inch bit

for the SS39.

ROCK TYPE

1.375" bit

W N V)

k m

t .438" bit

1 . S bit

1.538" bit

competent JO, I

~ndndmt data

Figure 2-20. Histograms showing the distribution of immediate pull-out strength for different

rock types and bit sizes. Note that the sample sizes are not al1 the same and that there was

not enough data in some circurnstances to produce histograms. Al1 histograms are for SS39

bolts.

As is shown, the distributions of pull-out strength values for al1 rock types shift to the leR

progressively with increasing bit size. The mean values for each distribution are plotted as

curves in Fig. 2-8. Note that the distributions presented in Fig. 2-20 are for pull tests

conducted irnmediately or very sooii afier installation (less than 6 hours). To account for load

-

distributions with time.

Several concerns need to be met during the ground support design process; first, that the

installed Split Set possesses sufficient bond strength immediately afier installation to support

the excavation; second, that load development with time does not cause rupture of the steel (if

support is intended for a period longer than several days). An optimum solution must be

found.

An example of a simple design method is as follows:

1. The first step is to identiQ the length of time for which the Split Set is intended to provide

support (i.e. is the design scenario temporary sidewall support in a shafi sinking operation

or is it long-term support for burst-prone gound, etc.. .)

2. The second step is to identie the rock type and refer to the load development charts and

distributions to çet an idea of what anchorage increases are expected in the design time

frarne. (see Fiçs. 2- 12 to 2- 16).

3. Establish a desired initial bond strength which will not result in long-term steel failure.

4. Knowing rock type and the desired initial anchorage, the fourth step is to recommend a

drilling bit size based on the distributions shown in Fig. 2-20 or the generalized curves

shown in Fig. 2-8.

5. Having established the expected value or distribution of bond strençth, the next step is to

specie a boltinç pattern, with a density that is suficient to support expected loads.

6. M e r bolt installation has beçun, design assumptions can be compared to actual

performance values using Figs. 2-5 and 2-6 if drive times are measured or to periodic pull

test resuits.

The distributions presented in this paper form the basis for the data to be used in a

probabilistic analysis. In such an analysis, uncertainty is taken into account and a resulting

support reliability (expressed in terms of percentage) can be determined. An example of such

an analysis is presented in Tomory et al. (1 997).

One of the primary benefits from an undertaking such as the one presented in this paper is that

the findings are derived empirically from actual field test data. As mentioned in the

introduction, one of the key obstacles in rock engineering design is a çeneral lack of

information concerning rock mass behaviour and rock-support interaction. The current

research has attempted to address the latter of the two by considering the effects of various

factors on the bond strength of a particular type of supporting element - the Split Set.

The two most important factors governing the immediate strength of installed Split Sets are

rock type and bit size. Additionally, with time after installation, the strength increases at

different rates for different rock types. Figures have been presented in this paper that should

enable mine engineers to determine the expected value of pull-out strengths given bit size and

rock type and time elapsed after installation. The result should be safer, more efficient and

more economical support designs for Split Set applications.

For example, given a certain rock type, ground support designers can refer to the relationships

presented in the various figures of this report to determine the anticipated bond strength for

bolts installed in holes of various sizes. Additionally, bolt load, or bond strençth, development

has been analyzed and can be factored into drilling bit selection if there is a final desired long-

term load for the Split Set. Finally, Simple indications of strençth can be obtained by

measuring the drive time and referrinç to the chart provided in this paper.

The results presented in this paper are ideally suited to probabilistic analyses where

distributions for Split Set bond strençth can be defined for many operatinç conditions. For

instance, if rock type, drilling bit size and time after installation are known, there are several

distributions which could be applied. Further discussion on the probabilistic and statistical

aspects of the data presented herein will be discussed in subsequent chapters.

Pinairy, it 1s the h o p 01 the authors that hirther studies, sirnilar to this one, will be undertaken

for other types of ground support. In this report, only the Split Set bolt has been considered,

partly because it is perhaps the supporting element with the most easily quantified and

measured strength. Nevertheless, comparable studies considering resin-grouted bolts, cable

bolts, mechanically-anchored bolts and al1 other types of supporting elements would be

welcome additions to the rock engineering and ground support design process.

The results presented in this chapter would not have been possible without the CO-operation of

many mine and rock mechanics engineers throughout the North Arnerican rnining industry.

The author gratefully acknowledges the participation of the following individuals and

companies in this study:

Fred Bailey, Nanisivik Mines Ltd.; Peter Barber, Barrick Gold Corporation, Holt-McDermott; Ian Clegg, Falconbridge Ltd., Lockerby Mine; Dan Crackel, Echo Bay Minerais, Kettle River Operations; Donald Gagnon, Stewart Mining Products; John Henning, Barrick Gold Corporation, Bousquet Complex; Lorne Herron, Atlas Copco Construction and Mining; Tom Landsberg, Ingersoll-Rand, Split Set Division; Serge Lévesque, MSV Resources Inc.; Gary McSporran, Cominco Ltd., Sullivan Mine; Eric Nelson, Inçersoll-Rand; Mark OdelI, Newmont Gold Company; Brian O'Hearn, lnco Mines Research; Garnet Parcher, Placer Dome Canada Ltd., Detour Lake Mine; Randy Reichert, Cominco Ltd., Polaris Operations; Joel Rheault, Homestake Mining Company, Eskay Creek Mine; Pierre Rocque, Kinross Gold Corporation, Kirkland Lake; Daniel St. Don, Stillwater Mining Company; Tim Sandford, Placer Dome Canada Ltd., Dome Mine; Shawn Seldon, Falconbridge Ltd., Kidd Mining Division; Mike Stahl, Homestake Mining Company; John Stalcup, Asarco Inc., Mission Complex.

In particular, the author would like to acknowledçe Dan Haller of Inçersoll-Rand in Sudbury

for his advice and for providing pull test results from many Canadian mines. Thanks also to

Chuck Steed and Doug Morrison of Golder Associates (Mississauga and Sudbury

respectively) for their advice and to Evert Hoek for his commentary. Finally, special thanks to

James Scott for his advice, CO-operation and insightfül commentary during the research of this

paper and for providinç over 300 pull test resuks from a large number of American mines.

STATISTICAL ANALYSIS OF SPLIT SET PULL TEST DATA*

Split Set fiction stabilizer bolts are used widely by mines throughout North Arnerica for

temporary and long-term support. Currently, however, little has been done to quanti@ the

effects of various rock mechanics and operational parameters on the capacity of these

supporting elements. A detailed statistical analysis of the information contained in a database

of over 900 pull test results from many different mines has been performed and the results are

presented here. The capacity of Split Sets can be expressed as a set of equations incorporating

influencing factors such as rock type, drilling bit size, bolt type and time from installation.

These equations were obtained by employing a software package which uses linear regression

techniques to characterize the data. The presented information should allow mine designers to

more confidently assess the effectiveness of support systems usinç Split Sets during the design

phase. The results demonstrate the eficacy of statistical analysis tools in the analysis and

characterization of available information. However, the results also show that the success of

statistical analyses are contingent on the availability -of accurate and reliable information from

the field.

- This cliaptcr will appear as a journal article cntitlcd 'Statistical Cliaractcrimtion of Rcsults frorii Pull Tcsls Perfonned on Split Sct Friction Stabilizcr Bolts'.

The chief aim of this chapter is to provide mine designers with reliable results from statistical

analyses to aid in the process of designing support using Split Sets for underground

excavations. The analyses were carried out on the information collected concerninç the

effectiveness of Split Set bolts. This same information was used as the basis for earlier, more

simple analyses using a spreadsheet. The results of this chapter cornplement those presented

earlier in this thesis by verieing the principal conclusions. The statistical analyses were carried

out in order to identi@ and quanti@, by means of models, or equations, the trends and

relationships apparent with regard to the various rock mechanics and operational parameters

which influence the capacity of Split Sets.

A description of the data set is followed by a report on the nature of the statistical analysis and

a discussion of the results. Equations are presented which mode1 the capacity of SS33 and

SS39 bolts in terms of rock type, bit size and time from installation to pull test. These

equations provide mean values for capacity which can then be used in subsequent stability

analyses. The reliability, or the confidence with which these values are predicted, are also

discussed. The chapter concludes with a series of recommendations detailing the requirements

of more successful statistical analyses.

For the statistical analysis described in this chapter, the same set of pull test results that was

analyzed in the preceding chapter was used. This data set consists of 909 separate records,

each containing information concerning several variables. The complete list of pull test results

is given in Appendix C. For each pull test, information was obtained, where possible, about

bolt type, bolt length, bolt diameter, bit size, drive time, driver type, time from installation to

pull test, rock type, rock class, RMR and pull-out strength. In most cases the records are not

complete, i.e. they do not al1 contain information about al1 the items listed above. This made

statistical analysis of the data more dificult, necessitating several assumptions (to be discussed

subsequently).

Based on the results of the manual analysis presented in the previous chapter, it was decided

to include only the following variables in the statistical analysis:

i) pull-out strength (measured in tondfout)

ii) bit size (measured in inches)

iii) bolt diameter (Le. bolt type, measured in inches)

iv) rock class (according to classification presented earlier, Le. Terzaghi, 1946)

v) time from installation to pull test (measured in days)

In chapter two, variables such as RMR and bolt length were found not to have an appreciable

effect on the pull-out strength of Split Sets and, as such, were excluded from a statistical

analysis. Drive time and driver type were also not included, in this case because they are not

causative factors, but rather they serve as indicators of bond strength during the installation

process. Additionally, al1 records containing recorded bit sizes greater than 1.55 inches were

discarded because they represent atypical conditions (e.g. special cases involvinç severely

squeezing rock where large hole sizes were required to make installation possible).

Initially it was intended to develop a mode1 or models which would establish the relationship

between pull-out strength and the other four variables, namely bolt diameter, bit size, rock

class and time to pull test. However, due to nature of the data where there was insutficient

had to be separated for the two bolt types. The reasons for this twofold lack of data are

readily apparent. SS33 bolts are used almost exclusively by Canadian mines whereas SS39 are

employed, for the most part, in American mines. Canadian mines perform a large number of

pull tests on Split Sets at various times after installation to monitor strençth development and

also to ver@ that the Split Sets have an adequate capacity at any one time. As a result there is

an abundance of information concerning the strength development of SS33 bolts. The same

does not appear to be the case, for whatever reason, in the United States; Splits Sets are

tested almost always imrnediately or very soon after installation. As for information about bit

size for tests on SS33 bolts, there simply is not enough variation in the use of different bit

sizes to allow for a valid statistical analysis. In fact, more than 80% of the tests on SS33 bolts

where bit size was known, it was reported to be the standard 33 mm (1.3 inch) drilling bit.

Additionally, many SS33 records lacked bit size. For SS39 bolts, there was excellent

information availabte concerning different bit sizes.

In order to characterize the population distributions for the variabies included in the analysis,

the raw data was analyzed univariately (one variable at a time) for each individual variable.

Histograms of the distributions and important quantities such as means, variances and

skewness were computed for each variable and are shown in Fig. 3-1. A brief explanatory

note concerning each distribution for the univariate analysis is warranted:

i) Pull-out strength, al1 test results. This is the same histogram shown in the previous

chapter. It shows the distribution of pull-out strençths, measured in tonslfoot to account

for different lençths, for al1 test results, reçardless of bolt type, bit size, time to pull test,

etc.. . This distribution is skewed somewhat to the riçht because of those results from tests

performed at Iater times when some strength development has taken place.

ii) Rock class, al1 test results. This is provided sirnply to çive an idea as to the numbers

involved for the different rock types, as per the classification system used earlier. The

distribution shown reveals the total number of pull tests results frorn the different rock

types and also breaks the numbers down into the two bolt types. Note that laminated rocks

are class L; altered, weathered or broken rock are class A; competent rocks are class C and

sofl rocks are class S.

1 Pullout strength. al1 test results Rock class, al1 test results

-

O -3 results W ES39 results

Mean 1.0 Standard M a t i o n 0.4

Sample Variance 0.21 Skewness 2.12

Puliout stmngth ( t M )

Pullout strength, SS33 bolts 120 1 1

1 Pullout strength, SS39 bolts 1

- 1 Summary ~tatistics] 1

Summary Statistic Mean 1.14

Standard üeviation 0.52 Sample Variance 0.27

SkANness 1.92

- v q q ~ ~ m ~ w ~ r n ~ c r c r N N d d S

Pullout stmngth (tondi¶)

Mean 1 .O6 Standard Deviation 0.39

Sample Variance 0.15 Skewness 2.32

a X ~ ~ ~ ~ ~ ~ 2 8

Pullout strength (lonsflt)

Bit site, 5539 Tirne to pull test, SS33 bolts

Mean 12. Standard deviation 22. Sample Variance 498.

Mean 1.44 Standard Oevjation 0.102

Sample Variance 0.01

O = R E i S X Z ~ Z 8 ~ P R ~ ~ ~ ~ a Tlms from lnstallatlon to pull test (days)

Figure 3-1. Histograms showing the distributions of each of the analysis variables.

the first histogram. It shows the distribution of pull-out strengths for SS39 bolts and

appears to be skewed to the right.

iv) Pull-out strength, SS33 bolts. This histogram is the second component of the first

histogram. It shows the distribution of pull-out strengths for SS33 bolts and its values

appear to be more tightly grouped than those for the SS39 test results.

v) Bit size, SS39 bolts. This plot is shown in order to demonstrate the breakdown of bit sizes

used to drill holes for SS39 bolts. Again, the distribution is meaningfùl only in that it shows

that the majority of holes are drilled with 1.375 and 1.5 inch drill bits. The other

predorninant drill bit sizes are 1.438 and 1.538 inch. Bit sizes çreater than 1.55 were

ignored in the statistical analysis.

vi) Tirne to pull test, SS33 bolts. The skewness of the distribution of values for time to pull

test can be attributed to the manner of data collection rather than as being inherent to the

variable, i.e. most pull tests are performed immediately afier bolt installation and fewer and

fewer tests are carried out on Splits Sets as time elapses.

In each of the data çroups, there were some outlying points. These are points which are

relatively far from the majority of the other points and which have the potential to bias the

final regression equations. To avoid outlying points from overly influencing subsequent

regression analyses, the skewed variables could have been transformed (by applying a power

transformation to each point, e.g. by taking the square root or by squaring the value of each

point) or have had long tails removed with the aim of obtaining approximate syrnmetry in the

distribution. However, these measures were not implemented for the reason that this analysis

was done to show, in very simple terms, the potential of statistical methods in solvinç the

problems of estimatinç the capacity of Split Sets.

3.3.V 3 1 A 113 1 I L A L ANAL Y SIS

3.3.1 Linear Regression

The statistical analysis for this study was performed using SAS, a statistical software package.

SAS can be used to perform a wide range of statistical analyses, including, arnong others,

linear regression. In the current study, techniques of linear regression were applied in building

models. See Appendix B for a listing of the SAS program written for this analysis.

Regression analyses are used in statistics to establish relationships between variables. The

objective of a regression model is to relate one variable, the dependent variable, in this case

pull-out strength, to one or more independent variables. The regression model can be used to

describe, predict or control the dependent variable, given particular values for the independent

variables. Both quantitative and qualitative variables can be employed in a reçression model.

A linear regression model is one in which the regression equation expresses the dependent

variables as a linear iùnction in the coefficients of the independent variables. The independent

variables themselves may not be linearly related to the dependent variable, but their

coefficients must be linearly related to it.

One of the aims of this study, as mentioned earlier, was to learn which reçressor

(independent) variables were important in explaining the variations observed in the pull-out

strençth of Split Sets (dependent variable). Based on the physical meaning of the variables and

the results of the manual analysis presented in the previous chapter, the variables bit size, rock

class, time to pull test and bolt diameter (representing bolt type), were used. Of these, only bit

size and time to pull test were used as quantitative variables; the rest were used as qualitative,

or categorical, variables.

As a result of the screeninç of the variables in chapter two, the aims of the statistical analysis

were to establish a relationship between pull-out strençth and bit size and time to pull test for

L 1 1 b L W U L U I L I b . 1 W L I L L V W I \ WLU.?rlUL.. A I V I V Y I W., Y W W U Y Y V ...W. v r i u v .,ri--- --i- .---- cl ---

size for SS33 bolts and insufficient information on the effect of time to pull test on the pull-

out strength of SS39 bolts, the data set had to be split into two along these lines: namely, by

bolt type. It is assurned that the behaviour of the two bolt types (SS33 and SS39) with time

are very similar and that the results of the statistical analysis on the effect of time on the pull-

out strength of SS33 bolts can be applied to SS39 bolts. In other words, in arriving at a final

relationship predicting the pull-out strength of SS39 bolts as a function of bit size, rock type

and tirne, some data from SS33 test results was used. This assumption is very reasonable

based on the cornparison in chapter two of strength development curves for SS33 bolts with

previously published material concerning time effects in SS39 bolts (see chapter two). In

addition, it should be noted that there was insufficient information to consider the effects of

time on the strength development of SS33 (and thus SS39) bolts installed in A and S class

rocks (altered and soft rock categories).

As the final results of the statistical analysis it was possible to arrive at an incomplete group of

equations sets: one set relating pull-out strength with time for SS33 bolts (for C and L class

rocks), one set relating pull-out strength with bit size for SS39 bolts (al1 bit sizes and al1 rock

classes) and a final equation proposed for SS39 bolts. The final equation beinç proposed,

accounting for al1 variables, holds only for SS39 bolts installed in competent and laminated

rocks.

3.3.2 Residuals Analysis

A check of the assumptions underlying linear regression can be performed by analyzing

residuals. Residuals can be described simply as the differences between predicted and

observed values of the dependent variable. See Myers (1990) and Bowerman and O'Connel1

(1990). Residuals were analyzed for the purposes of detecting departures from the basic

assumptions of linear regression, narnely (see Fig. 3-2):

i) correct hnctional form (the regression equation correctly captures the order of the

equation, e.g. linear, quadratic, etc. ..)

distributed about predicted values - the regression line - at each data point).

iii) constant variance (the variance of the distribution of the observed dependent variable

values at each data point is the same).

Figure 3-2. Simple Iinear regression model showing assumptions of constant variance and

normal populations of error. From Myers, 1990.

To veriS, the assumption of correct functional form, the plots of residuals against the

predicted values were used. Since these plots did not exhibit much curvature, it can be

concluded that the models obtained from the analysis have the correct functional forms.

Diagnostic plots to determine if model assumptions appeared reasonable included plots of

histograms of ordinary residuals. All of the histoçram plots of the residuals except for the

HAT diagonals (a measure of the leverage, or moment, of each data point) exhibited

reasonable bell-shapes (shapes similar to that of normal distributions) and symmetry. A

symmetrical and bell-shaped residual histogram indicates that the assumption of normal

populations of error holds approximately.

Plots of the residuals against predicted values were used to determine whether or not the

assumption of constant variance for the models was credible. If the assumption of constant

points about the zero-residual line. There was little noticeable fanning-in or fanning-out of the

residuals except for the data sets which had very few sample points (e.g. SS39 bolts, rock

class S) and it can be said therefore that this assumption was reasonable. The violations can be

attributed to the very small number of sample points available in the small data sets.

The fourth assurnption of linear regression, that of independence, could not be verified

because the data was not time ordered.

3.3.3 Results and Interpretation

The data set was then analyzed by means of a SAS program (see listinç in Appendix B). A

reasonable mode1 describing the pull-out strength of Split Sets as a function of bolt diameter

(indicating bolt type), rock class and bit diameter is:

Yi = P o + P l x i + P ~ X ; + PtCl.i 'B4'2.i 'P5'3.i

+ P6Ai + B,Aix i + P8Aix: + p9AiCl, ixi + B , o A i C 2 . i ~ i + p,,AiC3,,xi

+ B,,A,C,,X: + P , , A ~ C ~ , ~ X : + P , ~ A , c , ~ x :

Where xi is the bit size (in inches). The effects of rock class and bolt diameter (type) are

modeled using dummy variables A, Ci, Cz, C3. These variables are detined as follows:

f 1 if bolt diameter is 1.5 inches)

A = 10 othenvise

1 if rock class is A c l = { O othenvise

1 if rock class is C c2 = { O othenvise

1 if rock class is L c3 = { O othewise

1) For an SS39 in class A rock:

3) For an SS39 in class L rock:

U l I L L I L U A Y Y U U L I V I A J A V I U U d J V V l C J VU11 U b I l l L b l l b U \rU311J V U J W U U A 1 L 1 1 b b A U L I I ~ I b 3 J l lU WAI UUVVb,

but because of insuficient information on bit sizes, the results will not be reliable.

The coefficients, pj, obtained from the SAS analyses for the above equations are:

Po = -2.777 p4 = -0.603 = 12.835 P12 = 1.292

pl = 6,062 ps = -0.158 p9 = -1.739 Pl3 = 0.924

PZ = -2.3 72 P b = 31.762 Pie = -1.132 P14 = 0.770

P3 = -0.188 fi7 = -40.496 pli = -1.063

This translates into the following prediction models for the SS39 (where xi is the bit size):

1) For rock class A (altered, weathered or broken rock):

y , = (-2.777 - 0.1 88 + 3 1.762) + (6.062 - 40.496 - 1.739)~ + (-2.372 + 12.835 + 1.292)~:

= 28.797 - 36.1 73xi + 1 1.755~: (6)

2) For rock class C (competent rock):

y i = (-2.777 - 0.603 + 3 1.762) + (6.062 - 40.496 - 1 .063)~~ + (-2.372 + 12.835 + 0.924)~:

= 28.382 - 35 .566~~ + 1 1.387~: (7)

3) For rock class L (laminated rock):

y = (-2.777 - 0.1 58 + 31.762) + (6.062 - 40.496 - 1.063)~~ + (-2.372 + 12.835 + 0.770)~:

= 28.827 - 35 .497~~ + 11.233~: (8)

4) For rock class S (sofi rock):

y , = (-2.777 + 3 1.762) + (6.062 - 40 .496)~~ + (-2.372 + 12.835)~:

= 28.983 - 3 4 . 4 3 4 ~ ~ + 10.463~:

These equation models give the bond strength (or more appropriately, the pull-out strençth)

of SS39 bolts for different bit sizes and rock types. They are shown graphically as lines in Fiç.

3-3.

I - - - - Atered rocks

- Larrinated rock

0.00 ! I 1.300 1.350 1 . a 1.450 1.500 1.550

Bit size (inches)

Figure 3-3. Plots of equations 6, 7, and 8, showing the relationship between SS39 pull-out

strength and bit size for the different rock types.

Class A rock

Class C rock

Class L rock

Class S rock

Lower 95% mediction intenral prediction interval -1

Table 3-1. 95% prediction intervals for SS39 pull-out strength (in tonslft) for different bit sizes

and rock types.

Also computed for these models were the 95% prediction intervals at different values of bit

size. These results are given in Table 3-1. As can be seen, the prediction intervals are not

good, meaning that the confidence in the mode1 equations is low. In most cases, the difference

reliability, of the mode1 equations. Nevertheless, the prediction intervals do indicate that bond

strength decreases with increasing bit size and differs for different rock types. Note that these

prediction intervals refer to equations 6 to 9 which provide mean values of bond strength.

To improve the confidence intervals, more data would be required where accurate records are

kept. It proved dificult to analyze the existing information with SAS because of the

incomplete nature of the pull test records. Nevertheless, a successful preliminary evaluation

has been made and later work could fiirther refine the presented results.

For SS33 bolts, where there was enough information to consider strength developrnent with

time, the data was divided into subsets based on rock class. There was suscient information

to consider the effects of time on strength developrnent for competent and laminated rocks

(i.e. classes C and L). The equations establishing the relationship between pull-out strength

and time for SS33 bolts are given below (where t; is the time between bolt installation and the

pull test, in days):

1) For rock class C (competent rock):

y = 1.02 + O.OMt,

2) For rock class L (laminated rock):

y = 1.03 7 + 0.03 8ti -.00006t:

These equations are plotted in Fig. 3-4. Note that the plotted results compare favourably with

Figs. 2-12 and 2-13 in chapter two which plot the results of the manual analysis of the data

concerninç strençth development with tirne in competent and laminated rocks.

- - e- --- - = Cornpetent rock - Laminateci rock

O 20 40 60 80 100 120

Tirne from installation to pull test (days)

Figure 3-4. Plots of equations 10 and 11, showing the relationship between SS33 pull-out

strength and time from installation to pull test for competent and laminated rocks.

If it is assumed that the strength development with time in SS39 bolts is similar to that

experienced by SS33 bolts, then equations 10 and 1 1 can be applied to the SS39 equations

modeling the effects of bit size on pull-out strength for rock types C and L (i.e. equations 7

and 8) as follows (subscripts denote equation numbers):

1) For rock class C (competent rock):

~ , , ( t ime = x) bit size and time) = tir bit size) (12) F,, (time = O)

2) For rock class L (laminated rock):

FI, (time = x) bit size and time) = tir bit sire) (13) FI, (time = O)

The primary conclusion which can be drawn from the analysis presented in this chapter is

either that there is insuficient and incomplete information available to more accurately mode1

the capacity of Split Sets or that the effectiveness of Split Sets cannot accurately be predicted.

Fortunately, it would seem that the former is the case. Although there were over 900 pull test

results available for the analysis, the record of information was incomplete or inadequate in

most cases. In other words, details concerning al1 the relevant parameters were not available

for al1 pull test records. For instance, in many cases, only the pull-out strength and one other

parameter were recorded (e.g. bit size or rock type or RMR, etc.. .).

Although valuable equations modelling the capacity of Split Sets have been developed from

the statistical analysis presented in this chapter, there is still an apparent lack of consistent

information gathering and performance monitoring occurring in the mines. The size of the

prediction intervals, or the degree of confidence in rnost of the predicted values for bolt

capacity are unsatisfactory. In order to narrow the confidence intervals and allow for the

development of more reliable models and equations, mine operators must take better records

in the field. A simple yet consistent note of such details as bit six, rock type, description of

rock quality and other items at each pull test location will enable statistical analyses such as

the one presented in this chapter to arrive at more accurate and truly representative results.

For example, a typical record of a pull test on a Split Set may include the following

information:

i) bolt type (SS33, SS39 or SS46)

ii) bolt length

iii) actual bit diameter

iv) rock type and RMR

v) note on the condition of rock (broken, intact, wet, etc.. .)

vi) drive time and driver type

vii) location of bolt (back, wall)

viii) elapsed time between installation and pull test

ix) note on unusual conditions

In addition, mine designers may want to perform a greater number of pull tests, especially at

Iater times, so that a more complete and tùndamental understanding of the behaviour of Split

Sets may be gained and that a complete assessment of the factors which influence the

effectiveness of Split Sets be the result.

Despite the inadequacies revealed in the information, this study has nevertheless allowed for a

fairly detailed analysis of Split Set bolt performance. The factors which influence bolt capacity

have been identified and some models quantifjing the effects of these various factors have

been proposed. The equations presented should allow mine designers to assess the anticipated

capacity of Split Sets in specific situations.

PROBABILITY ANALYSIS OF GROUND SUPPORT USING SPLIT SET BOLTS, A CASE STUDY*

Traditionally in underground mines, the acceptability of ground support designs have been

assessed on the basis of a single value for the Factor of Safety. However, in many areas of

rock engineering there is a growing trend towards risk-based analyses which provide a range

of values for the Probability of Failure. A comparison between conventional and probability

analyses of temporary ground support in a shafl reveals that the support design has a Factor of

Safety of 1.5 and that, under most conditions, there is a Probability of Failure of about 5-10%

(or alternately, a Reliability of go-%%). The analysis also shows how sensitive the design is to

variations in parameters such as joint orientation and joint friction angle, water pressure and

rockbolt performance. This kind of analysis can lead to a much better understandinç of the

importance of the factors which influence stability and can provide a much more realistic

assessment of support design and performance. We hope that a broader application of this

approach to ground support in underçround mines will eventually lead to a greater acceptance

in the industry of probabilistic analyses and of terms such as Probability of Failure and

Reliability of Support.

-- -

This cliapter was prescntcd as 'Probability Analysis of Ground Support' at thc CIM 13'" Atinual Mine Operators' Conference in Sudbury, Ontario, Feb 16-20, 1997 and printcd in its procccdings. The autliors werc P.B. Toinory (University of Toronto, Civil Engineering), J. Canrallio (Goldcr Associates, Mississauga) and D. M. Morrison (Goldcr Associates, Sudbuq). Scc Appendis D for autliorization lctters.

In the mining industry there is a trend away from traditional subjective and experience-based

decision making processes towards a more forma1 process of objective risk assessment and

decision analysis. Assessing the performance and identifjing the risks associated with several

alternatives provides a means of evaluating the most cost-effective and efficient solution. A

probabilistic analysis is an example of this type of evaluation.

Nowhere in the field of mining engineering is this probabilistic approach more appropriate

than in the field of rock mechanics which deals with the naturally complex and ofien

unpredictable behaviour of a rock mass subjected to mining-induced stresses. Traditionally,

the approach to designing support systems that control rock mass deformation has been to

develop an understanding of the anticipated failure mechanism and to design a ground support

system to control the failure process and prevent collapse. The design is usually very

conservative in that conservatism is included either explicitly in the support desiçn or

implicitly in the failure mechanism. This approach has two advantages; firstly, it is relatively

simple and secondly, the strength:load ratio gives the 'factor of safety' as a measure of the

stability of the system. However, there are disadvantages; first, this approach is expensive and

results in most areas of the mine having much more support than is actually necessary for

stability and second, that the factor of safety gives an unrealistic measure of the reliability of

the support system which can result in a false sense of security.

A probabilistic approach to support design examines the variations in the critical parameters

that control the behaviour of the rock mass as well as the parameters that control the

performance of the ground support elements. Toçether, these can provide a realistic

assessment of the reliability of the ground support system and result in a more cost-effective

support desiçn.

In order to introduce the idea of a probabilistic approach to çround support desiçn, a very

simple reinforcing elernent, the Split Set friction stabilizer, was selected because it has only

V L L Y ui i L i V U i yu. Uiii".Vi, uviii. --. -,, - - - -- - - -- - - - - - - - - Y

mechanically-anchored bolts and grouted rebars have many more parameters, most of which

are difficult to assess. Since the Split Set bolt is generally only used in the walls of

excavations, the mining situations that could be considered were limited to an excavation such

as a shaft where the issues of roof support could be ignored.

For the purposes of comparing conventional and probabilistic analysis methods, the case of a

hypothetical mine shaft in jointed ground is considered. The 28 ft diameter shafi is excavated

through a moderate to heavily jointed norite mass by conventional means. With the advance of

the permanent concrete liner, the walls of the shafi at the working levei are exposed only for

two or three days. The problem is to determine the support, if any, which is required to

contain any instabilities which may anse in the exposed section of the shaR wail before the

concrete liner is placed. In situations where the support is required on a temporary or short-

term basis, Split Sets are commonly used because of their relative ease of installation and low

cost.

Three or four predominant joint sets are identifiable, includinç two sub-orthogonal joint sets

with dips ranging from 20" to 80°, typically about 60' (joints with dip direction of 45" and

3 15" or 45" and 235"), a set of low angle joints (dip/dip direction of 5/180) and a set of sub-

vertical joints (W270). Al1 joints have a spacing of approximately 1 m. The shaft is in a low

stress environment.

Owing to the jointed nature of the rock mass, the main instabilities which need to be

accounted for are gravity-driven wedge-type failures. The UhrWLDGE prograrn was used to

determine the location and size of potentially unstable wedçes in the shaft sidewall.

4.2.1 Wedge Sta bility Analysis

Since there are several possible çroups of three for joint orientations which can be entered

into UNWEDGE, the first step was to run the program for al1 likely joint combinations and to

decide which joint combinations produce the most critical wedçes. In decidinç which wedge

represented the worst case, some reasonable judgements were made. For instance, wedges

weighing much less than one tonne, wedges which were extremeIy heavy and larçer than the

not reasonably form were ignored.

The joint groups (Table 4-1) which yielded the most potentially unstable wedges were the

ones formed by the intersection of two sub-orthogonal joints with a low angle joint

(combinations 1, 2 and 3), and the ones formed by the intersection of two sub-orthogonal

joints with a sub-vertical joint (combinations 4, 5 and 6). Joints sets are given in the form

dipldip direction.

Combination 1 * 51180 40/45 4013 15

Combination 2* 511 80 60/45 6013 1 5

Combination 3 * 511 80 70/45 7013 15

Combination 4 851270 40/45 4011 35

Combination 5 85/270 60/45 601135

Combination 6 85/270 70/45 70/135

Table 4-1. Joint combinations forming unstable 1

others are the sub-vertical joint group).

wedges ( * den otes low angle joint group,

Note that in Table 4-1, the only difference between combinations 1, 2 and 3 is the dip of the

two sub-orthogonal joint sets. These three represent essentially the same scenario, differing

onIy in that they take into account the variability of the dip of the sub-orthogonal joint sets.

The same can be said for combinations 4, 5 and 6.

The output from a typical U W E D G E analysis is shown in Fiçs. 4-1 and 4-2. Note that a

maximum of six wedçes can be formed, of which any or al1 could be unstable.

NO

WEDCE

FORIIED

W e d g e 0 1 13 S.Tons

May s l i d c on J1 J 3

35/276 68/13S

U c d g r U 2 1 3 S.Tons Slides o n

53 60/135

S.F.=0.33

U e d g e U 3

NO UEDCE FORMED

W e d g e U 4 13 S.Tons Slides on

J2 6 8/845

S.F.dd.33

May r l i d e on 52 JI

i W 0 4 5 85/270

U e d g e U 6

NO UEDCE FORMED

Figure 4-1. UNWEDGE analysis showing the four possible wedges which can form with joint

sets 851270, 60145 and 6011 35.

In the case shown, the wedge-forming joints are 85/270, 60145 and 601135 (combination 5)

and the critical wedge is #4. In addition, for this case, a low friction angle of 30" was used for

al1 joint surfaces, no cohesion was attributed to any joint surface, no çroundwater pressure

was considered and no effects of cfamping due to stresses çenerated around the shaft were

considered.

As can be seen, the worst case wedge in this scenario is one with a mass of 13 tons and an

unsupported factor of safety of 0.33. This wedge is the most dangerous of al1 unstable wedges

of al1 joint combination scenarios for our particular shaft problem. Consequentiy, a support

design which effectively controls this wedge will also be effective for al1 other unstable

wedçes.

b U s e arrow k e ~ s CCESCY to oxi t)

U e d g e b 4 13 Tonnes

I

-

Figure 4-2. UNWEDGE analysis, perspective view of wedge .

4.2.2 Supporting Unstable Wedges

Since the wedçe in question has a factor of safety less than one, some form of support will be

required. In this analysis, it was decided that Split Set friction stabilizers would be used

exclusively. The program UWEDGE has the capability to deal with friction bolts, and it

requires that the user enter the expected bond strength of the bolt in tons/fi. This parameter is

the most important when designing ground support with Split Sets. The purpose of using

UNWEDGE is to give a preliminary estimate of what bolt lençths should be used (i.e 4 ,5, 6 ft

Split Sets, etc.) and at what spacing they should be installed (Le. a 4x4 ft or 6x6 fi pattern,

etc.) to effectively contain potentially unstable wedges.

An U W E D G E analysis of the wedge in question, supported by 4 ft Split Sets on a 4x4 A

bolting pattern, is shown in Fig. 4-3. Thus, a 4x4 A pattern of 4 ft Split Sets should be

--- y--..- -- "-Fr-a - --- --a-=---- -. --- ---- ------ ----. .---W. - ---- ----- , --- ---- - - ----

strength of 0.8 tonslft, a friction angle of 30" for al1 joint surfaces, no joint cohesion and no

water pressure. The factor of safety has been increased to 1.48 from 0.33 by the installed

support.

-- I I I

RESULTS W e d g e I B 4 13 S . T a n s

M a y slidc on J2

68/045 S.F.=1.48

P a t t e r n Bolt Spac i ng

4 . 8 f t x 4 . 8 f t Lensth 4. Bart

B o l ts normal t o houndaru

USE P A C E U P & DOWN

TO Z O O M

JSE l R R O W KEYS 10 ROTIITE

Figure 4-3. UNWEDGE analysis for unstable wedge supported by 4 ft Split Sets on a 4x4 ft

pattern.

This design, however, cannot be viewed as entirely satisfactory because it fails to account for

the possibility of variations in water pressure, joint friction angle and cohesion, Split Set bond

strength and lateral blast-induced accelerations. In order to arrive at a desiçn for ground

support which does take these factors into consideration a more detailed analysis must be

conducted.

To account for the variations in bolt performance and strength conditions, the same wedge

was re-analyzed for several different support scenarios using an EXCEL spreadsheet. Water

pressure, joint friction, joint cohesion, lateral acceleration and wedge size were al1 varied

individually and in combination to observe the effects on the supported factor of safety.

Fig. 4-4 shows the variation of the factor of safety with increasing values of friction angle for

three separate groundwater pressure conditions. Note that even a minimal water pressure has

a fairly siçnificant effect on the factor of safety. In the case where somewhat severe

groundwater conditions are expected, the prescribed support of 4 fi Split Sets on a 4x4 fi

pattern would be inadequate. However, it is unlikely, even in the case of bad groundwater

conditions, that a sustained water pressure would develop on the interna1 wedge faces without

drainage occurring along the dayliçhting joints.

È 2 - - IC 1 1.5 - - ici O

I - . s O 2 0.5 - - w

Friction angle, degrees

Figure 4-4. Graph showing the variation in factor of safety with friction angle for three

different groundwater conditions. Note that w is the water pressure in tonneslrn2 and c is

joint cohesion, also in tonneslm2. The wedge is supported by 4 ft Split Sets on a 4x4 ft

pattern, assuming a bond strength of 0.8 t/ft.

- -o. . - ---- ..- ---- . ------ '-- --- ---- ---- '- '- -----, ..---- ' - - - - V I - - - - 3 - 1 - - - 1 - - - - - - - - - - - - - - - - - - - - - - -

support configurations. This estimates the response of the support to blast-induced horizontal

forces. In reality, for a shaft sinking cut, the vertical component of the blast-induced force

would be greater in magnitude (but less significant for wedge stability) than the horizontal

component .

Late ral acce le ration (fraction of g)

+4ft SS, 4x4

+6ft SS, 6x6

+ 6ft SS, 4x4

- FS=l

Figure 4-5. Graph showing the variation in factor of safety with increasing lateral acceleration

(given as a fraction of g) for three different support configurations (al1 assuming a Split Set

bond strength of 0.8 ffft). The acceleration is in the horizontal direction trending towards the

centre of the shaft. Water pressure and cohesion are zero in this case.

Another important factor is the variation which may occur in the expected wedse size. The

dip of the two sub-orthogonal joints varies from 20" to 80°, with a predominance of joints

dipping at 60°, but the analyses have been restricted to the wedge formed by the joints dipping

at 60". Fiç. 4-6 shows the results of an analysis performed by varyinç the dip of the sub-

orthogonal joints sets across their fidl potential range for several çroundwater pressure

conditions. As the dip of the sliding joint increases, so do the weight and size of the wedge.

As can be seen in the çraph, in the case of zero water pressure, al1 but the Iargest potential

wedge sizes can be safely supported by 4 fi Split Sets on a 4x4 fi pattern (althouçh the factor

of safety may not be high enouçh in the case of the heaviest wedge). The lines are not smooth

steps with increasing wedge size.

üip of the joint along whkh wedge rlMes

Figure 4-6. Graph showing the variation in factor of safety with increasing wedge size for a

support design of 4 ft Split Sets on a 4x4 ft pattern, assuming a bond strength of 0.8 t/ft.

Results are given for two scenarios (w is in tonnes/m2).

The effect of varying the bolt bond strength is shown in Fig. 4-7. The increase iri the factor of

safety from 0.6 t/ft to 1.0 tlfi is considerable and demonstrates that the bond strençth of Split

Sets is a very important design parameter.

Consequently, to design effective and efficient ground support, it is necessary to have a çood

idea of the range of bond strengths that can be developed in various rock types and çround

conditions. The results presented in earlier chapters of this thesis give reasonably good initial

estimates for the expected means and distributions of Split Set bond strençth for several

different rock types, and for drilling with several different bit sizes. Additionally, the increase

in mean bond strençth with time has been demonstrated and can be incorporated into a

probabilistic analysis if required.

0.5 0.6 0.7 0.8 0.9 1 1.1

Split Set bond strength (tift)

-+-411 SS, 4x4

+6ft SS, 4x4

-611 SS, 6x6

&BI1 SS, 6x6

Figure 4-7. Graph showing the variation in factor of safety with increasing Split Set bond

strength for four different support configurations. In al1 cases water pressure and cohesion

are zero.

Table 4-2 shows cases A through H, eight different scenarios where friction angle, cohesion,

water pressure and laterai acceleration are varied. The unstable wedçe can now be analyzed

for several different scenarios to observe the effect on the factor of safety.

Table 4-2. A summary of the design variables which define cases A through H. All cases are

CASE A

for the same wedge (the one formed by joints 851270, 60145 and 601135). Water pressure and

cohesion are denoted by w and c while alpha refers t o the horizontal acceleration as a

Design variables phi (deg) w (tlm2) c(tim2) alpha (%g:

30 O O O

percentage of g (acceleration due to gravity).

Factor of safety

without support

0.33

In Figs. 4-8,4-9 and 4-10, the four most commonly used support configurations for Split Sets

are placed along the x-axis of the graphs, fi-om left to right, in order of increasing

effectiveness. Note that 4x4~4 refers to a 4x4 fi pattern of 4 fi Split Sets, 4x4~6 refers to a

4x4 pattern of 6 fi Split Sets and so on. The three graphs show the same situations but for

different Split Set bond strengths (Le. Fig. 4-8 assumes a bond strength of 0.6 tlft; Fig. 4-9, a

bond strength of 0.8 t/fi and Fig. 4-10, a bond strength of 1.0 t/A). These analyses were

carried out to fùrther demonstrate the importance of bond strength and account for the

possibility of the bolts developing less than expected which is normally around 1 ton/A).

For the majority of scenarios, the wedge in question can be supported with a factor of safety

greater than one (only three points lie below the FS=l line in Fig, 4-8 and only one point in

Fig. 4-9).

I Bond strengîh = 0.6 UR

Figure 4-8. Graph showing the factor of safety for four support configurations assuming a

Split Set bond strength of 0.6 Uft (which is a low estimate) for eight separate cases (denoted

by A through H and described in Table 4-2).

bond strength is assumed be only 0.6 t/ft (Fig. 4-8), then only a 6x6 ft pattern of 8 ft Split Sets

and a 4x4 fi pattern of 6 ft Split Sets are adequate for ALL scenarios (if FS>1 S).

Nonetheless, even with a low value for bond strength, a 4x4 pattern of 4 A Split Sets and a

6x6 A pattern of 6 fi Split Sets are adequate for some of the less severe design situations.

If it is assumed that the bond strength is 0.8 t/ft (Fig. 4-9), al1 but one of the factors of safety

are greater than one and rnost are greater than 1 . S . In this case, the 4x4 fi pattern of 4 fi Split

Sets is adequate only for the less severe design situations and the 6x6 ft pattern of 6 A Split

Sets is good for al1 but the two most severe cases (again assuming that FS must be >1 S).

It should be noted that al1 but one of the design scenarios (case G) assume a very conservative

value of 30" for the friction angle. In most actuat situations, the friction angle will be hiçher

than this and, consequently, so would the factors of safety.

Bond drongth = 0.0 UR

Figure 4-9. Graph showing the factor of safety for four support configurations assuming a

Split Set bond strength of 0.8 tlft for eight separate cases (denoted by A through H and

described in Table 4-2.

safety are greater than 1.5 indicating that even a 4x4 ft pattern of 4 fi Split Sets should be

adequate for al1 but the most severe circumstances.

Note that each point in the graphs shown in Figs. 4-8 to 4-10 represents a single factor of

safety stability calculation for the unstable wedge in the shaft sidewalf.

l Bond rbrngth = f.0 UR

Figure 4-10. Graph showing the factor of safety for four support configurations assuming a

Split Set bond strength of 1.0 Uft (which is the value recommended by lngersoll Rand) for

eight separate cases (denoted by A through H and described in Table 4-2).

So, it has been shown how sensitive the design is to variations in parameters such as water

pressure, joint friction ançle, joint cohesion, lateral acceleration, water pressure, bond strength

and design configuration. In the next section, the results of a probabilistic analysis of the same

factors will be presented in the context of the same design situation, i.e. an unstable wedge in

a vertical shaft.

An important issue in designing ground support is determining the appropriate values which

should be used for analysis. There is a certain degree of uncertainty associated with al1 of the

design parameters which, unfortunately, cannot be taken into account by a conventional

stability analysis.

One approach which can be used to deal with uncertainty is a parametric analysis which

considers a wide range of possibilities in a conventional deterministic analysis in order to

demonstrate the sensitivity of the design. As has been shown, the factor of safety is not

necessarily a fixed or known quantity if it is accepted that there will be some variation in the

design parameters and/or if the assumed design parameters do not conform to actual in-situ

ground conditions. The factor of safety can be quite sensitive to changes in the value of the

assurned design conditions.

A probabilistic analysis assigns a range of values to each input parameter, in the forni of a

distribution, in order that the reliability of the design, expressed as a percentage, can be

determined. This can be accomplished by assigning a distribution tùnction to each input

parameter (as in Fig. 4- 1 1).

Consider the case of an unstable wedçe in the shaft sidewall, this time in the context of a

probabilistic analysis usinç @ISK, which is an add-in program for EXCEL. The wedçe in

question is the same one that was analyzed earlier by deterministic means (i.e. the one formed

by joint sets 851270, 60145 and 6011 35) . The first step is'to assign a likely range of values, or

distributions, to the random input variables. The distributions which were chosen are

illustrated in Fig. 4-1 1.

A brief discussion of each of the plots is warranted to demonstrate the reasoning behind the

choice of the probability distribution fùnctions.

1. Friction angle - A truncated normal distribution has been assumed for this variable. The

mean is assumed to be 30". The standard deviation of 7.5" implies that 68% of the friction

angle values fall between 22.5" and 37.5". The distribution is truncated by a minimum

value of 10" and a maximum of 65" which have arbitrarily been chosen as the extreme

values represented by a smooth slickensided surface and a fresh, rough tende fracture

surface.

0.00 0.10 0.20 0.30 0.40 0.50

L I t a r i acçahrallon ratio (of g)

4 0.0 0.5 1.0 1.5 2.0 2.5

Jolnl cohrrlon. 1m.slm2

0.2 0.4 0.6 0 8 1 1.2 1.4

g i l t Sd bond strmgth, t o n d

@RISK random variables Assurned distribution mean stdev min max joint cohesion truncated normal 1 0.4 O 30 friction angle truncated normal 30 7.5 1 O 65 alpha truncated exponential 0.08 O 0.5 water pr. truncated normal 0.3 0.3 O 10 Split Set bond strength truncated normal 0.8 0.13 0.2 1.4

Figure 4-11. Distributions and characteristics of the random input variables used in an

@RISK probabilistic analysis.

2. Joint cohesion - A value of 1 tonne/m2 has been chosen for the mean of this truncated

normal distribution, with a standard deviation of 0.4 tonne/m2. In order to allow for the

wide range of possible joint cohesive strengths the minimum and maximum values used to

truncate the normal distribution are O and 30 tonne/m2 respectively.

3. Lateral acceleriition ratio (of g) - This random variable is described by a truncated

exponential distribution because, in general, low-magnitude (usually insignificant) events

are very frequent as compared to larger ones. This variable is used to describe both blast-

induced forces and natural seismicity. The mean is assumed to be 0.08 (Le. 8% of g) with a

minimum of O and a maximum of OS.

4. Water pressure - The water pressure is assigned a tmncated normal distribution with a

mean of 0.3 tonne/m2, a maximum of 10 tonne/m2 and a minimum of zero. Note that in

this case the truncation is more significant than for the friction angle and the cohesion

variables. This is to approximate that, in most cases, the water pressure will be low, with a

mean around 0.3 tonne/m2.

5. Split Set bond strength - As mentioned earlier, this is the most significant design variable

and, as such, it is important to assign to it a realistic distribution. The assumed distribution

is a truncated normal with a mean value of 0.8 tonslft, a standard deviation of 0.13, a

maximum of 1.4 and a minimum of 0.2. These numbers for Split Set bond strength are

appropriate for a jointed rock mass such as the norite in this case study, as based on

results presented earlier (see Section 2.3.2)

Although it would may have been valid to use 1 .O tordfi as the design mean for a probabilistic

anafysis owing to the moderate to heavily jointed nature of the norite, it was decided to use a

conservative mean value of 0.8 tonslft. This is to account for the possibility of any bit size

beinç used for drilling and to assure immediate shafl stability. More detailed results for

analyses assuming mean values of 0.8 and 1 .O tons/ft are presented later.

of 4 A Split Sets on a 4x4 A pattern, an @MSK simulation was carried out with 10000

iterations on the factor of safety calculation. In other words, each of the above distributions

were sarnpIed and the problem was solved 10000 separate times. The resulting factor of safety

distribution is plotted in Fig. 4-12.

It should be noted that Fig. 4-12 represents only the case described in Fig. 4-1 1 supported by

4 ft bolts on a 4x4 A pattern. A different distribution for the factor of safety wili be obtained

for analyses with different input parameters (distributions) and for different support

configurations.

O 0.5 1 1.5 2 2.5 3 3.5

Factor of safety

Figure 4-12. Resulting probability density function for the calculated factor of safety. The

reliability of the support, given by the ratio of the area under the curve for FS>1 divided by

the total area under the curve, is approxirnately 92%. Alternately, there is an 8% risk of failure.

From the statistical tables produced by @RISK it was determined that the probability of

failure for this wedçe is approximately 8% or, to use more appropriate lançuage, the support

has a reliability of 92%. This value (reliability) is given by the ratio of the area under the

distribution curve for FS>I divided by the total area under the distribution curve.

----- '-- --- --- -- , ----- ------- -- r - -r------ y - - r - ---- - -,

acceleration and Split Set bond strength parameters described in Fig. 4-1 1, a 4x4 ft pattern of

4 A Split Sets would fail to support the wedge 8 times out of 100 in the lifetime of the shafi.

This is a small but not negligible risk of failure which should be considered acceptable if the

support for the wedçe is intended only for a short period of tirne, i.e. until the concrete liner is

placed two or three days later.

Most importantly, it must be noted that, in this case, the mean value for the factor of safety is

1.55, slightly higher than the value of 1.50 which was the result of a conventional

deterministic factor of safety analysis. Thus, for this case, if a factor of safety of 1.5 is

considered acceptable, then an 8% risk of failure should also be considered acceptable.

A series of probabilistic analyses were carried out using W S K for a number of difTerent

situations. The results are shown in Figs. 4-13 (a & b), which are laid out in a fashion similar

to that used in Figs. 4-8, 4-9 and 4-10, where support effectiveness is plotted on the vertical

axis (this time in terms of reliability of support, rather than factor of safety) and the different

support configurations are on the horizontal axis. Fig. 4-13a shows the results for probabilistic

analyses using a nean Split Set bond strength of 0.8 tons/ft and while Fig. 4-13b shows the

results for a mean bond strength of 1 .O tons/ft.

It should be noted that each point on the graphs in Fig. 4-13 represents a probabilistic analysis

similar to that summarized by Fiçs. 4-1 1 and 4-12. In other words, each point in Fiç. 4-13 has

a distribution for the factor of safety from which the reliability of support can be calculated

(Le. reliability of support equals the area under the factor of safety distribution curve to the

right of FSW divided by the total area under the curve).

As with the deterministic results plotted in Figs. 4-8, 4-9 and 4-10, Fiçs. 4-13a and 4-13b plot

the results for several different design scenarios. However, in this case, the scenarios are

described by mean and standard deviation values as well as distribution type, not just by a

fixed value as was the case for the deterministic analysis. For each scenario, the input mean

A, B, E and F correspond to the scenarios described by the same categories in the

deterrninistic analyses surnmarized in Table 4-2. A slightly different set of scenarios were used

in the probabilistic analyses in order that the effects of distribution, mean and standard

deviation could be observed.

- - . .- - -

J 30 7.5 0.6 0.3 16 1 O K 40 10 O O O 1 0.44

'in al! cases cohesion is zero

Design variables

Table 4-3. A summary of the random variables which define the seven design scenarios. Al1

cases are for the same wedge (the one forrned by joints 851270, 60145 and 601135). Water

pressure is denoted by w while alpha refers to the horizontal acceleration as a percentage of

g (gravity).

Factu of safety

Thus, each plotted line in Fiç. 4-13 shows how the reliability of the design changes with

support configuration for a particular design scenario (al1 for the case of the same unstable

wedçe).

ICASE* phi (deg) stdev w (llm2) stdev alpha (%g: *ait ~ u p p n

For instance, in Fig. 4-13a, for case E, the reliability of support increases from 92% to 98%

when the support configuration is changed from a 4x4 fi pattern of 4 A Split Sets to a 6x6 ft

pattern of 6 ft Split Sets. Given the very short exposure time to the possibility of wedge

failure, the 6.5% increase (98/92) in reliability may be dificult to justie compared to the

increase in the cost of additional support.

Having described a probabilistic analysis and observed that it yields values for the reliability of

support, expressed as a percentaçe, as well as a value for the mean factor of safety, the next

step is to compare a broad range of values.

4 x 4 ~ 4 6~6x8 6 6 x 8 4 x 4 ~ 6

Support Design O s t M

4 x 4 ~ 4 6 6 x 6 6 ~ 6 x 8 4 x 4 6

Support üerign 1.M

Figures 4-13 (a &b). Plots showing the reliability of support for four support configurations

assuming a Split Set bond strength of 0.8 tonslft and 1.0 tonslft respectively. Six separate

cases are analyzed and described in Table 4-3. Note that 4 x 4 ~ 4 refers to a 4x4 ft pattern of 4 ft

Split Sets, 4 x 4 ~ 6 refers to a 4x4 pattern of 6 f t Split Sets and so on.

A plot relatinç the mean factor of safety and the reliability of support obtained for about 80

different 6iJRISK probability analyses is shown in Fig. 4- 14. As with Fig. 4- 1 3, each point in

this plot describes a probability analysis similar to that described by Figs. 4-1 1 and 4-12. In

other words, each point in Fiç. 4-14 has a distribution curve for the factor of safety from

which a reliability and a mean can be obtained. Each individual analysis (each point) in Fig. 4-

14 represents I O 000 recalculations of a stability problem. (i.e. the same set of random

variable distributions, but not necessarily the same sampling, and the same support

configuration for each recalculation). As such, Fiç. 4-14 is the result of 800 000 separate

deterrninistic stability analyses.

Factor of safety

Figure 4-14 Plots relating sample mean factor of safety and reliability o f support for about 80

separate @RISK probabilistic analyses. The reliability o f support is given by the ratio of the

area under the factor of safety's probability density function cuwe for FS>l divided by the

total area under the curve. The sample mean is the centre of gravity of the same cuwe. The

single point indicated by the open circle corresponds to the example shown in Fig. 4-13 (Le.

FSz1.55, Reliability=92%)

The points in Fiç. 4-14 represent an entire set of analyses of unstable wedçes in the shaft

sidewall. They are the result of a very wide range of analyses where variations in joint friction,

joint cohesion, water pressure, lateral acceleration, Split Set bond strength, support

confiçuration, bolt lençth and wedçe size are taken into account. Fig. 4-14 can be described as

the characteristic curve for the case of wedge instability in a vertical shaft (çiven the jointing

described earlier).

Usinç reçression techniques, a curve can be fitted to the set of points in Fiç. 4-14 and direct

correIations between factor of safety and reliability can be obtained.

Two methods of stability analysis have been presented. The conventional sensitivity analysis

was able to determine the effect of variations in some of the parameters which control the

rock mass behaviour and the performance of the reinforcing elements. Essentially, each of the

solutions was the result of a single calculation, with different values for the various parameters

being used each tirne, resulting in a range of values for the factor of safety. For instance, the

results showed that a ground support system of 4 A Split Sets on a 4x4 ft pattern with a bond

strength of 1 .O tons/ft would have controlled al1 but the most severe wedge problems.

The analysis of a simple mining situation has demonstrated the value of a probabilistic

approach to ground support. By using a probabilistic analysis, it was possible to carry out a

very large number of calculations determine the reliability of the support design. In one case of

a 4x4 A pattern of 4 A Split Sets, the reliability was 92%. This could be increased to 98% if

the bolting configuration was changed to a 6x6 A pattern of 6 f t Split Sets. The increased cost

of the longer bolts can be considered in terms of the effect that it has on the total cost of the

shafi development as compared to the small increase in the reliability of the çround support

system.

It is not possible to develop a mining situation with zero risk of injury; the objective is to have

the risk 'as low as reasonably achievable'. The risk of an event such as a ground fa11 can be

defined as the product of the likelihood (or probability) of the occurrence and the

consequences of the occurrence. In the case of the temporary shaft support, the consequence

of a wedge failure is a serious injury or a fatality. However, the exposure time to this risk is

extremely small, less than two days. If the same 4x4 fi pattern of 4 ft Split Sets, were the final

tonç-term support for the excavation, then the exposure to a wedge failure 8 out of 100 times

over several years clearly would be unacceptable. A similar risk over a two day period is not

unreasonable.

deterministic analysis. Frorn the characteristic reliability curve for the shaA problem, a factor

of safety of 1 .O is equivalent to a reliability of 50%. A factor of safety of 1.5 is equivalent to a

reliability of about 87%. A factor of safety of 1.3 which is normally acceptable for temporary

support systems is only 70% reliable.

It has been demonstrated that a probabilistic analysis can easily be accomplished using

commercially available software and provides a realistic assessment of the effectiveness of the

ground support system. As the trend towards risk assessment and decision analysis continues,

the mining industry will have to corne to terms with terms such as 'probability of failure7 and

'the reliability of support'. The use of the term 'factor of safety' should be discontinued

because it says nothing about the safety of a particular situation and because it has M e to

contribute to a thorough understanding of the quality of a ground support systern. While a

reliability of 92% does not sound as comforting as a factor of safety of 1.5 both these figures

describe the saine situation. However, the reliability factor of the support system is a much

more meaningfùl measure of the support design.

RECOMMENDATIONS AND CONCLUSIONS

One of the primary benefits from an undertaking such as the one presented in this thesis is that

the findings are derived empirically from actual field test data. As mentioned in the

introduction, one of the key obstacles in rock engineering design is a general lack of

information concerning rock mass behaviour and rock-support interaction. The current

research has attempted to address the latter of the two by considering the effects of various

factors on the bond strength of a particular type of supporting element - the Split Set.

Although valuable conclusions with regard to the performance of Split Sets have been drawn

from the field data, there is still an apparent lack of consistent information gatherinç and

performance monitoring occurrinç in the mines. As was discussed in the chapter dealing with

statistical analysis, in some of the situations analyzed in this paper, the deçree of confidence in

many of the relationships or in the predicted values for bolt capacity are not hiçh. In order to

narrow the confidence intervals and allow for more efficient design, mine operators must take

better records in the field. For Split Sets, a simple yet consistent note of such details as bit

size, rock type, description of rock quality and other items at each pull test location will

enable analyses such as the one presented in this thesis to arrive at results and design

guidelines incorporating a higher degree of reliability. For instance, although more than 900

pull test results were gathered, fewer than 350 of thern were what could be called an adequate

record of the relevant factors. In many cases, as has been discussed, this prevented the

complete anaIysis of the factors that influence the effectiveness of Split Sets. Nevertheless,

allow engineers to arrive at safer and more efficient support systems.

Consistent record keeping should be extended to al1 forrns of ground support so that fùture

research, of the type presented in this thesis, can analyze with accuracy the performance of

various support systems. For each type of ground support, the measure of effectiveness must

be identified (in the case of the Split Set, the pull test) and the factors which influence the

capacity of the support must be identified. Once recognized, these factors should be quantified

to the extent that observations can be made which will be usefùl in the context of an analysis

(such as bit size, rock type and time for Split Sets).

If the result of this thesis is that better records are kept with reçard to the factors influencing

the effectiveness of Split Sets, then perhaps future work can tùrther refine and fil1 the gaps in

the results of this thesis. More importantly though, future work could, and should, concentrate

on other types of ground support which are more commonly used, and in situations of greater

risk, than Split Sets. Such research should involve first the gathering of as much information

concerning field andlor laboratory test results on the capacity of a particular support type as

possible, followed by an analysis which identifies relevant parameters and quantifies their

effects on bolt capacity. Research could be extended to analyzing the effectiveness of more

than one supportinç element at a time, that is, to account for pattern installation and also to

the performance of two or more supporting elements in combination (for instance, Split Sets

are often used in an alternating pattern with resin-grouted steeI bars).

The results concerning the effectiveness of Split Sets presented in this thesis should enable

mine engineers to determine the expected value of pull-out strençths çiven bit size and rock

type and time elapsed after installation. The application of the results of this thesis, including

the observations made with reçard to the performance of Split Sets and also the use of the

results in probabilistic analyses, should have the outcome of safer, more eficient and more

economical support designs using Split Sets.

1. Bowerman, B. L. and O'Connell, R. T., 1990, Linear Statistical Models, second edition,

PWS-KENT Publishing Company, Boston.

2. Hoek, E., Kaiser, P.K. and Bawden, W.F., 1995, Support of Underground Excavations in

Hard Rock. A.A. Balkema, Rotterdam.

3. Myers, R. W., 1990, Classical and Modern Regression With Applications, second edition.

Duxbury Press, Belmont, California.

4. Scott, J.J., 1977, Friction Rock Stabilizers - A New Rock Reinforcement Method. AIME-

SME Annual Meeting, Atlanta.

5. Scott, J.J., 1977, Testing of Friction Rock Stabilizers. AIME-SME Annual Meeting,

Atlanta.

6. Scott, J.J., 1980, Interior Rock Reinforcement Fixtures - State of the Art. 21" U S .

Symposium on Rock Mechanics, University of Missouri- Rolla.

7. Scott, J.J., 1989, Roof Bolting - A Sophisticated Art. Reprint from COAL (Auçust, 1989).

8. Scott, J.J., 1996, unpublished memorandum on the manner in which Split Set friction rock

stabilizers support rock.

9. Stillborg, B., 1994, Professional Users Handbook for Rock Bolting. 2nd ed., Clausthal-

Zellerfeld, Transtech Publications (cited in Hoek et al., 1995).

lO.Terzaghi, 1946, Rock Defects and Loads on Tunnel Supports, Rock Tunneling With Steel

Supports (eds. Proctor, R.V. and White, T.L.) 1, pp. 17-99. Commercial Shearinç and

Stamping Company, Youngstown, Ohio (cited in Hoek et al., 1995).

1 l.Tomory, P.B., Carvalho, J. and Morrison, D.M., 1997, Probability Analysis of Ground

Support. CIM, 13'" Annual Mine Operators' Conference, Sudbury.

Some Imperia1 units have been used in this paper because they are used almost universaliy by

mine personne! and are familiar. Some relevant metric conversions are presented below:

1 foot = 0.3048 metres

1 ton = 0.909 1 tonnes

1 ton/ft= 2.98 tonnedmetre

LISTING OF SAS PROGRAM USED IN THE STATISTICAL ANALYSIS

options ls=120 ps=85; data pullout;

infile 'c:\regpaul\regpaul. dat'; input test 1-3 type$ 7-1 1 length 14-17 boltd 22-25 bitd 32-37 dt 42-46 driver% 49-68 tpt 70-

73 rock$78- 101 class$ 102- 1 O4 rmr 1 12- 1 1 8 cap 120- 125 tonsi? 132-1 3 5;

bitdnew = bitd**(1/3); tptnew = tpt**(l/3); if tpt gt O then tptnew = tpt; if class = 'A' then c l =l ; else c 1 =O; if class = 'SI then c2= 1 ; else c2=0; if class = 'LI then c3=1; else c3=O;

if boltd = 1.5 then a=l; else a=O; if bitd gt 1.55 then delete;

run;

proc chart; vbar bitd bitdnew tpt tptnew;

run;

proc univariate data=pullout plot; var bitd tpt tonsft;

run;

proc corr data=pullout; mn;

mode1 tonsfi= c l c2 c3 a bitd bitd*bitd a*bitd a*bitd*bitd c l *a*bitd c2*a*bitd c3*a*bitd cl*a*bitd*bitd cZ*a*bitd*bitd c3*a*bitd*bitd /P CLM CU;

output out=reset 1 r=resid; mn;

proc plot data=reset 1 ; plot resid*bitd / VREF=O; plot tonsfi*bitd;

run ;

data ss39; set pullout; if type ne 'ss39' then delete;

if class = 'A' then c l = 1 ; else cl =O; if class = 'S' then c2=1; else c2=0; if class = 'LI then c3= 1 ; else c3=0;

if bitd gt 1.55 then delete; run;

data ss39-A; set ss39; if class ne 'A' then delete;

run;

proc print data=ss39_A; run;

proc glm data=ss39-A; mode1 tonsfi = bitd bitd*bitd /P CLI; output out=residA r=resA p=predA h=hiiA rstudent=tiiA student=riiA;

run;

proc plot data=residA; plot (resA hiiA tiiA riiA) * predA;

run;

proc chart data=residA; vbar resA hiiA tiiA riiA/levels=5;

run;

set ss39; if class ne 'C' then delete;

run;

proc pnnt data=ss39-C; mn;

proc glm data=ss39-C; model tonsfi = bitd bitd*bitd /P CLI; output out=residC r=resC p=predC h=hiiC rstudent=tiiC student=riiC;

run;

proc plot data=residC; plot (resC hiiC tiiC riiC) * predl;

nin;

proc chart data=residC; vbar resC hiiC tiiC riiCAevels=5;

run;

data ss39-L; set ss39; if class ne 'L' then delete;

run;

proc pnnt data=ss39 - L; run ;

proc glm data=ss39-L; model tonsfi = bitd bitd*bitd /P CLI; output out=residL r==resL p=predL h=hiiL rstudent=tiiL student=riiL;

run;

proc plot data=residL; plot (resL hiiL tiiL riiL) * predl;

run;

proc chart data=residL; vbar resL hiiL tiiL riiL/levels=S;

mn; - - - - - - - - - -

data ss39-S; set ss39; if class ne 'S' then delete;

run;

proc print data=ss3 9 3 ; mn;

proc glrn data=ss39-S; model tonsft = bitd /P CLI; output out=residS r r e s S p=predS h=hiiS rstudent=tiiS student=riiS;

run ;

proc plot data=residS; plot (resS hiiS tiiS riiS) * predS;

run;

proc chart data=residS; vbar resS hiiS tiiS riiS/levels=S;

run;

data ss33; set pullout; if type ne 'ss33' then delete; if class ne 'Cl and class ne IL' then delete; if cIass = 'C' then x = 1 ; else x = 0;

proc glm data=ss33; model tonsfi = x tpt x*tpt tptrtpt x*tpt*tpt; output out=ss33res i-resid;

run;

proc plot; plot resid*tpt / VREF=O;

run;

data ss33L; set ss3 3; if class ne IL' then delete;

run;

proc glm data=ss33L; model tonsfi = tpt tpt*tpt; output out = ssLres I-res;

run;

plot res*tpt / VREF=O; plot tonsfi*tpt;

run;

data ss33C; set ss33; if class ne 'Cl then dejete;

run;

proc glm data=ss3 3 C; model tonsfi = tpt tpt*tpt; output out = ssCres r=res;

run;

proc plot datazsscres; plot res*tpt 1 VREF=O; plot tonsft*tpt;

run;

LIST OF ALL PULL TEST DATA FOR SPLIT SETS Test test number

TY Pe Split Set type

TPT time from installation to pull test (days)

Rock type rock type Length bol! length (ft) Class classification according to Terzaghi (1 946), see chapter 2 Boit dia bol! diameter (in) Bit size driiling bit size (in)

RMR Rock Mass Rating

Cap pullout strength, or slip load, (tons) DT drive time (s) tons/ft pullout strength, capacity divided by bolt length, (ton*)

Tert Type 1 si39 2 si39

Length Bolt dia Bit size DT (s) Driver 7 1.5 26 7 1.5 17 7 1.5 15 7 1.5 18 7 1.5 15.9

T PT (d) O O O O O O O O O O O O O O O O O O O

Rock type CIass C

RMR Cap. (tons) 6.4

hi&& id. irantone ~ghty rd. irantcns Nghty id. iromtona Nghty fa. i m a m Nghty id. iromlone Hghiy id. IraMone Nghty M. iranlons Nghty Id. Irmslone Nghiy Id. Irmsiono Nghly Id. iro<Klw# NghEl fd. lrmslone NpNy fd. Irot%lcne Nghty fol. Irom(ont Nghly fd. Iromtone highty fd. Iromtone ~gtuy rd. (ronacne Nghty Id. iromlont Nghly fd. Iraisione tirfJy Id. ironsion NgNy Id. iraisione tigiùy fd. Imsione NQWj fd. iiaisione NghEl fd. lronsiont tigiùy Id. ironsicne tigiùy fd. iionslone Ngiùy Id. ironslone Nghty Id. lromlone NOhly fol. ironslone NgNy Id. iraisione higiùy rd. irwisione Nghty Id. lromlont Nphly Id. ironsione highty fol. lronsiont hi# Id. lronslone Nghty fd. lronsicne Ngiùy Id. Ironsiw tighly toi. iromlw higiùy Id. lronslone Ngiùy Id. ironslm Ugiùy Id. irwlone Nghty Id. ironsiont Nghly Id. ironslone hi# fci. lronsim Ngiùy foi. ironsionc tighiy fd. lronslone N# Id. ironUMK t i m fd. lronslone N m Id. ironslone

Id. Lrmslonc NG (6. iraislw tiphly foi. ironsicne N m fd. IrO(K1one NpNj fd. ironsime Ngiùy Id. ironstone N#Uy Id. irmsicne MpNy Id. ironstone

1, r ==.S.# a ,.a 8 .s . r io dir-y v yiiii.2 b =.a I . IV

178 ss33 3 1.3 1.26 O glni ie C 2.5 0.83 179 sr33 3 1.3 1.26 O g l r i l e C 3 1.W 180 sr33 1 1.3 1.26 O ganils C 1 1 .00 181 sr33 5 1.3 1.30 59 grsirite C 4.5 0.40 182 si33 5 1.3 1.27 59 -nits C 6 1.20 183 sr33 5 1.3 1.27 59 ~ d l s C 5 1.00 184 sr33 5 1.3 1.22 59 eanile C 6.75 1.35 185 ss33 3 1.3 1.26 59 granite C 4 1.33 186 si33 3 1.3 1.26 59 p n i t a C 4 1.33 187 sr33 1 1.3 1.28 59 m ~ l e C 1 1.00 1.98 sr39 5.5 1.5 1.44 12 SlGmoQ. HBMW O meiamorphicsadlmril C 6 1.09 189 sr39 5.5 1.5 1.44 8 SIGmod. HBMSO O mclimorphiciedmni C 5 0.91 140 ss39 5.5 1.5 1.44 18 SlGmod. HBMSO O m c i i ~ c s u % m C 6.5 1.18 191 ss33 5 1.3 1.25 14 Jacldca O Uered basal C 65 6 1 .20

O Uersd basal O ilercd basal O U a e d basai O alered brrrll

196 1 4 3 5 1.3 1.26 14 ~acldsl) O i lered basal C 65 5.25 1.05 197 sr33 4 1.3 1.27 11 JbckkaMklo~sr O wunile C 50 4 1.00 198 sr33 4 1.3 1.27 10 Jackk&I&r O &nile C 50 3.5 0.88 199 5333 4 1.3 1.27 8 J.clrka*lopa O symiie C 50 3.75 0.94 MO s s f 4 1.3 1.27 10 Jaddemoper O syudie C 50 3.875 0.97 201 sr33 4 1.3 1.25 O syenile C 50 3.5 0.88 202 si33 4 1.3 1.27 O mie C 50 4.5 1.13 203 si33 5.75 1.3 1.252 9 J a c W O suww m i l e 29 3.5 0.61

~addep JacHeg Jackieg

Tamrock H320 Tamock H320 T a d H320 Tamock H320 Tsmock H320 Tamrock H320 Tamrock H320 Tamrock H320

Jsckieg Jackkg Jicklag Jackkg Jacldeg

- 7 . .

WIY Write s w r y pyrite supary Write Limirutled Odiisl Limnaied sCM4 bnJMItd -SI lrmhSted WSI bminaled sctist LimlMled W r t L i n J ~ l e d L im t~ led XtiSI bmnaled a r t bmtnaled sctisi hmirmted XNSI lsminmted xhirt h m i M t d xhiSI b n J ~ l s d -SI lrminalsd schirt bmnaled %chiSI kimnaled sctirt bminatsd *SI bmnaled sctisl b h ~ k d h m i ~ l e d SdliIt !aminalad whirt W M k d XhiQ bminited Xhisl laminaled schlrt kimineled W r t h m i ~ l s d whiSl M n r l e d W r t *mnited xhirt krdneled xhist b m i ~ l s d WSI bminaled Sdlist inminalcd M s l bmnaled schisi bminaled schisi laminaled sctisl laminelcd Wsl bminaled schirt b m ~ k d Schia iarnnelcd XhiU inmnaled schist laminaled whisl bmlnaied schisI inmnaled &SI brnnaled sehiSI bhnated xhisl kminated schisl lamirutcd schisl lsmnaled schisi bminaled xhisi hmnated xhirl

258 ss33 5.75 1.3 37 lamnalcd seNsi L 40 8 1.39 259 ss33 5.75 1.3 1.256 14 Jackleg O ma fic A 3.5 0.61

~acMeg O maiic Jickkg O chohlic gccnsione JocMeg O choritic greenslow JacMeg O chdritic preenslons

O lak O t l k O t i k O t l k O t i k

JacMeg O tak Jacldeg O talc Jackleg O tak Jackkg O t i k Jackieg O tak

SMy lmcrtone slky lmertone

1.5 siRy imestone 1.375 siIy Cmertona 1.5 s i b imeaone 1.625 sib imestone 1.375 YRy imstone 1.375 sir# limeStone 1.375 siRy Wmedone 1.375 *Iy limeStone t ,375 m I y imestare 1.375 imrione 1.375 siRy imestone 1.5 sily imertonc 1.5 JIy imertone 1.375 massive cak-sikale 1.375 massive cale-silicate 1.375 qwrtz. seiecile. dolorn'le 1.375 quartz. sereclle. doIociille 1.375 quam. screclle. dolomite 1.375 quartz. screclte. dolomllc 1.375 qwrlz. serecile. dolomlle 1.375 quartt. sertci~e. ddomik 1.375 massive dorilc 1.375 aiarU. serccile. dolomilc 1.375 massive diorile 1.375 WlphidiC S l lSw~ 1.375 utphide s i l s w 1.375 siky lmestone 1 .5 10 marUe 1.5 9 mrbie 1.5 10 mrMe 1.5 11 rnarbie 1.5 24 puartzitehllrtwie 1.5 28 qwrtzitehilstone 1.5 quatlzilehi#slnne 1.5 marbic 1.5 made 1.5 made 1 .5 made 1.5 marblc 1.5 srpiIlile 1.5 argutie 1.5 ladite

unalcred &bte unallercd rhyolle unalefed rhyolte unalered myolle uialcred W k t e unaileicd rhydite uiaiiered m i e l ~ l e r e d mydrle milered rtrjdile

=Y amcd myolle A c44-n 0.53 570 akered mydle A c44-54 0.59 571 atered m y d h A c44-54 0.59 572 ancrca myoile A ~44.54 0.59 573 aleied mydle A s44-54 0.59 574 akercd myoïle A c44-54 0.59 575 alered mydlc A <44-54 0.59 576 akercd r i W l e A 144-54 0.59 577 l - rdshe A c44-50 0.62 578 mudslonc A c44-5.5 0.62 579 mdrllme A c44-58 0.62 580 mdslone A ~ 4 4 5 8 0.62 581 InUdslOrm A <44-58 0.62 582 mudstons A c44-50 0.62 583 Mont A s44-58 0.62 584 midslm A c44-58 0.62 585 mudnone A c44-58 0.62 586 massive *de C 7585 0.91 587 massiva +de C 7585 0.91 588 massive W d e C 7545 0.91 589 massiw C 7585 0.91 590 mslive %&rd& C 75-65 O 91 591 mssive rgN& C 75-85 0.91 592 mpssive supN& C 7585 0.91 593 ~ U S J V S *de C 75-85 0.91 594 msstve sgN& C 7585 0.91 595 massiw %&rd& C 7585 0.91 5% masdva rrlpNde C 7585 0.91 597 massive C 7585 0.91 598 massive suiphide C 7585 0.91 599 ~ ~ 3 9 S 4.1 0.51

Sloper Jackkg Jicldeg Jackkg Jackkg Jacldcp MW83 Ji- MW83 Jicldeg MW83 Jicldeg MW83 Jiddeg MW83 Jackkg MW83 Jacidep Hydmstii 200 Hydrastar 200

Tamrock Jwnbo Jackkg Jackkg Hybesiir 200 Hydrastar 200 Tamrock Junba Tamrock JviiDo Tamrock Jvnbo GD 83

AC Bdec AC 8oUcc çiopar

=eOer Sopn sopn

MW 83 MW 83 MW 83 GD 83 GD 83 MW 83 MW 83 MW 83 MW 83 MW 83 MW 83

GD 83

GD 83 C a m ûfil C a m ûfil C a m DiII C a m DiII Hydrastu ZOO HyaisiU m Hydndu m Hydreslir 200 JR300

Tamock W u Tamock ûotu Tamock ûotu Hydrarlir 200 JOY JOY Hydiislii m 83 Jaeldep 83 Jacideg 83 Jacldeg 83 Jacideg Tamock Bdcc Tamock W u Tamock W u Tamrock W c r Tamock ûottr Tamock Botu Tamoek W u GD 83 GD 83 GD 83 Jarvis Chrk Jarvis Chrk Jaivlr Clark Joy Joy GDIJC GD 83

500s ha- 500s ha-

JOY JOY Hydrestar 100 Hydrastar 200 Hydtastar 200

IR 300 IR 300 IR 300 GD JD GD JD GD JD GD JD GD JD

Jackleg Jackleg Jackleg Jachkg GD 83

"" "" GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 Temock Jvnbo GD 83 GD 83 GD 83

GD 83 GD 83

GD 83 GD 83 GD 83 GD 83 GD 83 lsckkp Jackkg MW 83 MW 83 J i c w q Jacklep Jeckkg GD 83 GD 83 GD 83 Toyo Jackkg Toyo Jac#sg GD 83 GD 83 GD 83 GD 83 Jackleg Jackkg Jackkg Jackkg

GD 83 GD 83 GD 83 GD 83 T imock Tamrock Tsmocf GD 83 GD 83 GD 83 GD 83 GD J a c k g GD Jscldcg GD J a c k p JOY J w JOY JOY JOY JOY Jacklep Jacklep Jackkp Jacklep

Jackkg Jacldeg

GD HPR-1 GO HPR-1 GO HPR-1 GD HPR-1 GD HPR-1 Jecldeg Jackkg Jackkg Hydraslar 200 Hydaslar 200 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83 GD 83

AUTHORIZATION LETTERS FOR PREVIOUSLY PUBLISHED MATERIAL

This Appendix includes three letters of authorization for previously published material.

Chapter 4 of this thesis was presented as a talk and conference paper entitled 'Probability

Analysis of Ground Support' at the CIM 13' Annual Mine Operators' Conference in Sudbury,

Ontario, Feb 16-20, 1997. The authors were P.B. Tomory (University of Toronto, Civil

Engineering), J. Carvalho (Golder Associates, Mississauga) and D. M. Morrison (Golder

Associates, Sudbury). Authorization letters are included here from Dr. Carvalho, Mr.

Morrison and also from Mr. Charles Graham, who was the coordinator of the technical

program at the conference.

Galbraith Building 35 St. George St., Toronto M5S 1A4

Dr. Joe Carvalho Golder Associates 21 80 Meadowvale Blvd. Mississauga, Ontario, L5N 5 S3

Dear Dr. Carvalho:

I m compkting a ;ilas;er7s thesis at the U ~ d e i s i t ' 0fTo~9iitü ciîtitled 'Aiialysis of Split Set Bolt Performance'. 1 would like to allow inclusion of the following material in the thesis and permission for the National Library to make use of the thesis (i.e., to reproduce, loan, distribute, or sel1 copies of the thesis by any means and in any form or format). .

These nghts will in no way restrict publication of the material listed below in any other form by you or others authonzed by you.

1 would like to reprint, as one chapter in my thesis, 'Probability Analysis of Ground Support', which we CO-authored for the C M 13' Annual Mine Operators' Conference in Febmary.

If these arrangements meet with your approval, please sign this letter where indicated below and return it to me in the enclosed retum envelope. Thank you for your assistance in this matter.

Yours sincerely,

PERMISSION G ~ D FOR THE USE REQUESTED ABOVE

A &W -fkph‘L \8/‘q Print name Date I

r aui. 1 uiiiui y

Dept. of Civil Engineering Galbraith Building 35 St. George St., Toronto M5S 1A4

Mr. Doug Mmison Golder Associates 423 Wzstmount Avenue, Unit H Sudbury, Ontario, P3A 528

Dear Mr. Momson:

1 am completing a master's thesis at the University of 'Toionto entitled 'Analysis of Split Set Bolt Performance'. I would like to allow inclusior: of the following material in the thesis and permission for the National Library to make use of the thesis (i.e., to reproduce, loan, distribute, or seli copies of the thesis by any means and in any form or format).

These rights will in no way restrict publication of the material listed below in any other form by you or others authorized by you.

I would like to reprint, as one chapter in my thesis, 'Probability Analysis of Ground Support', which we CO-authored for the CIM 13' Annual Mine Operators' Conference in February.

If these arrangements meet with your approval, please sign this letter where indicated below and return it to me in the enclosed return envelope. Thank you for your assistance in this matter.

Yours sincerely, n

Paul Tomory. U

PERM~ssIoN GRANTED FOR THE USE REQWCSTED ABOVE

Y "Y.. V a . V L . -. -a- a--------- u

Galbraith Building 35 St. George St., Toronto M5S 1A4

Mr. Charles Graham CM, Sudbury Brmch 74 Balsam Street, Suite 100 Box 661, Copper ClifF, Ontario POM 1NO

Dear Mr. Graham:

i am completing a master's thesis at the University of Toronto entitled 'Analysis of Split Set Bolt. Performance'. 1 would iike to allow inclusion of the following material in the thesis arrd permission for the National Library to make use of the thesis (i.e., to reproduce, loan, disiribute, or seil copies of the thesis by any means and in any form or format).

These rights will in no way restnct publication of the material listed below in any other forrn by you or others authorized by you.

1 would like to reprint, as one chapter in my thesis, 'Probability Analysis of Ground Support', which Doug Momson and I presented at the CIM 13" Annual Mine Operators' Conference in February.

If these arrangements meet with your approval, please sign this letter where indicated below and return it to me at the address above. Thank you for your assistance in this matter.

Yours sincerely,

Paul Tomory.

PERMISSION GRANTED FOR THE USE REQUESTED ABOVE

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