Workplace 

Safety and Health

Department of Health and Human Services

Centers for Disease Control and Prevention

National Institute for Occupational Safety and Health

RI REPORT OF INVESTIGATIONS/2004

9662

Evaluation of Instrumented Cable Bolts

in Cement Grout to Determine Physical

and Numerical Modeling Properties
Report of Investigations 9662

Evaluation of Instrumented Cable Bolts in Cement

Grout to Determine Physical and Numerical Modeling

Properties

By Lewis Martin, Doug Milne, Marc Ruest, and Rimas Pakalnis

U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES

Centers for Disease Control and Prevention

National Institute for Occupational Safety and Health

Spokane Research Laboratory

Spokane, WA

April 2004
This document is the public domain and may be freely copied or reprinted.

Disclaimer: Mention of any company or product does not constitute endorsement by NIOSH.

ORDERING INFORMATION

Copies of National Institute for Occupational Safety and Health (NIOSH)

documents and information

about occupational safety and health are available from

NIOSH–Publications Dissemination

4676 Columbia Parkway

Cincinnati, OH 45226-1998

 FAX: 513-533-8573

 Telephone: 1-800-35-NIOSH

(1-800-356-4674)

 E-mail: pubstaft@cdc.gov

 Web site: www.cdc.gov/niosh

DHHS (NIOSH) Publication No. 2004-140
CONTENTS

Page

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Introduction ................................................................................... 2

Laboratory tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Calibration tests on ungrouted cable .............................................................. 3

Pull tests on grouted cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Test interpretation: Load versus strain for grouted cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Comparison of standard and new SRL cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Interpretation of load profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Load profile matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Split-pipe test results from FLAC .................................................................. 7

Model boundary conditions and material properties .................................................... 8

Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Final calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

ILLUSTRATIONS

1. Instrumented king wire with gauges and connecting cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Instrumented cable grouted in steel pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3. Pull-test apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4. Calibration curve for instrumented cable bolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

5. Displacement pull tests ..................................................................... 4

6. Graph of measured and calculated strains for three gauges in pull test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

7. Collar load plotted against A, microstrain (load profile curve) and B, distance from head of cable (load 

 correlation curve) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

8. Load profile matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

9. Pull test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

10. Idealized measured load versus distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

11. FLAC model and boundary conditions ......................................................... 9

12. Axial behavior of FLAC cable element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

13. Illustration of conceptual fully bonded reinforcement .............................................. 9

14. Grout material behavior for cable elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

15. Ultimate bound strength in kilonewtons per meter as a function of grout quality and rock modulus at 40 mm1

 of slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

16. Plot of load distribution in cable at applied load of 22 kN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

17. Plot of shear force at grout-cable interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

18. Load distribution at applied loads of 44 and 117 kN for kbond values of 1 e8

, l e9, and 1 e10 N/m•m . . . . . . . . . 12

19. Load distribution at applied loads of 44 and 117 kN for sbond values of 180, 190, and 200 kN/m . . . . . . . . . . . 12

20. Plot of laboratory loads and modeled cable loads at 44, 89, 133, and 178 kN . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

TABLES

1. Theoretical load and deformation measured for different cable instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Cable properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3. Grout properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

cm centimeter m•m meter per meter

GPa gigapascal mm millimeter

kN kilonewton MPa megapascal

kN/m kilonewton per meter N newton

kN/min kilonewton per minute N/cm newton per centimeter

m meter 0 microstrain
EVALUATION OF INSTRUMENTED CABLE BOLTS IN CEMENT GROUT 

TO DETERMINE PHYSICAL AND NUMERICAL MODELING PROPERTIES

By Lewis Martin,1 Doug Milne,2 Marc Ruest,3 and Rimas Pakalnis4

ABSTRACT

Whereas many researchers and mine engineers have conducted tests on cable bolts using various grouts,

water:cement ratios, and physical modifications of the cable to determine the load-carrying characteristics of

a bolt, few studies have been conducted on cable bolts fitted with internal instruments. Those studies that have

been done have concentrated on cable response averaged over significant (6.1 m) cable lengths. Researchers

at the Spokane Research Laboratory (SRL) of the National Institute for Occupational Safety and Health in

Spokane, WA, are investigating the physical properties of cable bolts by replacing the conventional king wire

with a modified king wire on which strain gauges have been installed. 

A numerical analysis was performed to match laboratory results. Loads calculated by the model were then

compared to loads measured in the laboratory on 1.83-m-long cables grouted into two 0.91-m-long pull-tube

assemblies. Load along the cable was monitored with 20 strain gauges installed along the length of the cable.

This paper documents test results on these modified cable bolts. The instrumented cable bolt provided

reproducible point measurements of cable load as opposed to load measurements averaged over long cable

lengths. Such point measurements can assist in interpreting the influence of cable confinement, grout quality,

rock mass stiffness, and other factors. The instrumented cable bolt is a practical field and research tool because

it can predict point loading along the cable.

The instrument has been successfully field tested at FMC's Granger Mine, Granger, WY; the Meikle Mine,

Carlin, NV; the Stillwater Mine, Nye, MT; and the Getchell Mine, Golconda, NV. By monitoring load and

displacement of the rock mass using these instrumented bolts, more-effective ground support can be selected

and installed, which will lead to safer working conditions for miners.

1

Mechanical engineer, Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA. 2

Mining engineer and associate professor, University of Saskatchewan, Saskatoon, SK. 3

Mining engineer, Itasca Consulting Group, Inc., Minneapolis, MN.

4

Mining engineer and professor, University of British Columbia, Vancouver, BC.
2

Figure 1.—Instrumented king wire with gauges and

connecting cable.

Figure 2.—Instrumented cable grouted in steel pipe.

INTRODUCTION

Many researchers and mine engineers have conducted a large

array of tests to determine the effects of various grouts,

water:cement ratios, and physical “enhancements” (Garford

bulbs, buttons, birdcage configurations, nut cages, etc.) on the

load characteristics of cable bolts (Goris 1990). A limited

number of studies have looked at load distribution along a cable

bolt. However, tests with instrumented cable bolts installed

inside steel pipes have been conducted only with extensometertype internal instruments (Hyett and Bawden 1997) and externally mounted strain gauges (Chekired et al. 1997; Choquet

and Miller 1987; Goris et al. 1993; Windsor and Worotniki

1986).

Well-tested commercial instruments, such as the Tensmeg

and the SMART cable, exist for measuring load on cable bolts.

The Tensmeg is a 60-cm-long, externally mounted strain gauge,

while in the SMART cable, the king wire has been replaced by

an extensometer having internal wires anchored along the cable

and attached to potentiometers within the electrical head. The

difference in displacement between anchors is used to calculate

average strain, which is then related to load via cable stiffness.

Strain is defined as change in length over distance. Therefore, a strain gauge measures the change in length (deformation)

along some object of previously fixed length. As this length

increases, the sensitivity of the strain gauge decreases. The

anchor spacings within a SMART cable are usually no less than

1 m, and load and strain are averaged over this length. 

The Spokane Research Laboratory (SRL) of the National

Institute for Occupational Safety and Health (NIOSH) has developed a new instrumented cable bolt (figure 1) (patent

6,311,564) in which the original king wire has been replaced

with a strip of steel (ribbon cable) to which strain gauges have

been attached (figure 2). Because of their low cost and small

size, many strain gauges can be installed along the cable to get

a better understanding of load distribution. 

This cable bolt is 1.8 m long and 15.8 mm in diameter and

has an ultimate strength of 258 kN. Twenty strain gauges are

positioned at 7.6-cm intervals along two sides of the replacement king wire. The cable is then inserted into two 0.9-m-long

sections of thick- walled (8.55 mm) steel pipe (so that 10 gauges

are in each pipe section) and grouted with Type I/II portland

cement at a water:cement mixing ratio of 0.35:1.

The main advantage of the new instrument is that cable axial

elongation can be measured over a short distance, thereby providing an accurate estimate of load over a small (approximately

13 mm) length of cable. That is, as the grout transfers axial load

to the cable, the strain gauge on the king wire reads elongation

in microstrain. Using Hooke's Law, strain can be converted back

to load. The instrument has the potential to provide more information than can be obtained from existing cable load monitoring

devices. It also provides valuable insights into cable support

behavior.
3

Figure 3.—Pull-test apparatus.

Figure 4.—Calibration curve for instrumented cable bolt.

LABORATORY TESTS

The instrumented SRL cables have a modified geometry and

therefore required calibration to determine their behavior.

Therefore, pull tests were conducted to compare load to strain

along the embedded cable. These tests followed the procedure

developed by Goris (1990), and the test apparatus (figure 3) was

the same one used by Goris and Conway (1987) during a testing

program at the U.S. Bureau of Mines.

Methods of estimating cable load are based on cable stiffness

using the equation— 

P = K × 0, (1)

where P = cable load, kN

K = cable stiffness, kN/(mCm)

and 0 = cable strain, microstrain.

Manufacturer's specifications state that the common K value

is 28,410 kN/(mCm) for a seven-strand cable. Thus calculating

P using K is accurate for the elastic deformation range of a cable

and is valid up to about 0.8% strain, or 227 kN (K = P ÷ 0).

CALIBRATION TESTS ON UNGROUTED CABLE

To understand the deformation behavior of a grouted cable,

it is first necessary to determine the behavior of free (ungrouted)

cables. 

To conduct these tests, the king wires in five conventional

cables were replaced with instrumented king wires to create the

new cables. The cables were then loaded to 178 kN of pull,

which is the maximum load for elastic cable deformation, to

obtain a calibration curve for each gauge (figure 4).

If a cable bolt is deforming, all measured strains on each

strand should be the same. Therefore, a simple approach to

determining the stiffness of a six-strand instrumented cable is to

assume that the king wire carries one-seventh of the cable load,

which would give a stiffness of 24,500 kN/(m•m) for a sixstrand cable.

The slope of load-versus-microstrain in figure 4 shows the

stiffness of the instrumented cable. The instrumented king wire

on the SRL instrumented cable did not carry appreciable load.

The drift observed was largely due to the length of the lead wire

connecting the individual gauges and was taken into account

through the use of an average calibration curve (figure 4).

Calibration test 3 indicated an instrumented cable stiffness

that ranged between 21,528 and 25,264 kN/(m•m) at an applied

load of 178 kN, which brackets the expected stiffness for a

standard cable with one strand removed (or six-sevenths of the

standard seven-strand stiffness). A range in values of measured

stiffness may be due to differential movement between a king

wire and the six external cable strands. A second source of

variation may be the position of individual strain gauges with

respect to the cable strands. That is, higher strain (lower stiffness) may correspond to gauges positioned directly under a

cable strand where slip between the instrumented king wire and

the cable strands is unlikely.

PULL TESTS ON GROUTED CABLE

A large database of results from pull tests exists for conventional cables grouted in steel pipes with cement grouts. The

load-to-deformation behavior of standard seven-strand cables

can be obtained from cable manufacturers.

Three “split-pipe” pull tests were conducted on three instrumented cables that had been grouted into steel pipes. These

tests were intended to duplicate crack dilation in underground

mine environments and to provide a load profile for the bolt

(figure 5).
4

Figure 5.—Displacement pull tests.

Continuous readings of load, strain, and displacement in the

cable bolt were taken throughout the test at a load rate of

2.2 kN/min. Load readings were collected electronically from

a load cell within the test machine. To verify that the readings

from the test apparatus were correct, displacement readings

were also obtained from a micrometer attached to the pull tubes

and an LVDT on the machine.

At 28 days of grout curing, the first pipe was pulled apart,

and the resulting load, displacement, and strain at various points

along the cable were measured. An average grout compressive

strength of 57 MPa was achieved at 28 days. The second and

third tests were conducted after 30 days. The tests were run on

all three samples until the cable-grout bond failed. In all three

tests, the grout failed before the cable; however, the cables were

all undergoing plastic deformation.

Figure 5 shows pull-test results plotted as applied load in

kilonewtons versus displacement in centimeters. In each test, the

maximum applied load was 200 kN, which is the yield point of

the instrumented cable. The plotted displacements are the total

displacements measured with LVDT’s at the free ends of the

cable.

TEST INTERPRETATION: LOAD VERSUS STRAIN FOR GROUTED CABLE

Deformation-based estimates of cable load relate load to

deformation by simply dividing deformation by monitored

distance to approximate strain and multiplying the result by

cable stiffness. This gives an average load or strain along the

measured length.

Substantial work has been conducted looking at load

distribution along fully grouted bolts (Hyett et al. 1996). In this

study, a simplified approach was taken to interpret behavior on

the instrumented cable based on observed cable response. The

gauges installed 76.2 cm from the load point did not show

significant loading until a load of approximately 156 kN had

been applied. The gauges at 38.1 cm showed loading at

approximately half of 156 kN, or 78 kN. This load transfer rate

can be expressed as C, the ratio of loaded cable length to applied

load. Therefore, the load at which each strain gauge will start

to deform can be estimated as follows:

Po = Lo/C (2)

where Po = applied load required to initiate deformation

 of strain gauge, N

Lo = distance of strain gauge from applied load or

 point of dilation, cm

and C = ratio of cable length-to-applied load.

Thus, C = 76.2 cm /156 kN = 4.89 × 10-1 cm/kN.

After a strain gauge on the cable has started to take load, any

additional load will increase strain on the gauge directly. Strain

will be related to the increase in load based on K (cable stiffness), or -24,019 kN/(m•m) [six-sevenths of 28,410 kN/(m•m)

—the common value for standard seven-strand cable] for the

six-strand cables used in this research. 

Based on the load transfer rate and cable stiffness, theoretical

strain-versus-load curves (figure 6) were calculated for three of

the gauges monitored in pull test 2. There was reasonably good

agreement between measured and theoretical strains for the

gauge at 76.2 cm and excellent agreement for the gauge at 38.1

cm. At high strain values, measured microstrain exceeded

theoretical microstrain because the cable had exceeded the 0.8%

elastic strain limit. The good agreement for the gauges at 76.2

and 38.1 cm suggests that the basic approach for calculating a

constant load transfer rate for instrumented cables is reasonable.

Agreement was not as good between measurements and theory

for the gauge at 68.6 cm. It appears that the instrumented king

wire was being pulled past the outer cable strands, which would

result in low strain readings well before the cable could be

expected to carry load. Slip of the instrumented king wire at 68.6

cm would explain the lower-than-expected strain values when the

gauge should be loaded (figure 6). This gauge is close to the free

end of the cable, and it is possible that untwisting of this end

contributed to the lower-than-expected strains at this location.

Additional data from tests at the Noranda Technology Centre

(NTC), Montreal, Quebec, in 1992 (Milne et al. 1992) support

this interpretation. In these experiments, a pull test was done on

a 0.91-m-long grouted cable on which strain gauges had been

bonded to the external cable strands at 15.2-cm spacings. The

load-versus-microstrain graph had a form similar to the curves

from the SRL tests (figure 6), and the load transfer rate was

approximately 2.28 × 10-1 cm/kN. A maximum load of only

112 kN was applied to the cable because most of the externally

bonded strain gauges and wires had failed at this load. The SRL

approach of protecting the gauges and wires in a replacement

king strand is a more practical situation.
5

COMPARISON OF STANDARD AND NEW SRL CABLE 

All approaches for measuring load in cable bolts are based on

the principle of measuring deformation over a fixed length and

relating the amount to cable stiffness. As the length of the

measured distance increases, the accuracy of the estimate of

cable strain at a given point may decrease. 

It was assumed that load along a grouted cable is driven by

dilation of a crack. That is, as a crack expands or lengthens, then

cable load increases. Values estimated from SRL tests of sixstrand cables are K (on six-strand cables) = 24,019 kN/(mCm)

and C (on grouted cables) = 4.89 × 10-1 cm/kN. These values

were used in the following analysis. Distances of 91 and 183 cm,

which are the typical distances used for monitoring load on

conventional cables, were assumed.

Using the load and strain distributions proposed above, load

estimates obtained from using various fixed lengths can be

compared, as shown in table 1. Table 1 also shows estimates of

load at different base lengths for strain gauges installed at

various distances from a single dilating crack. A similar

qualitative comparison was proposed by Windsor (1992);

however, no values were provided. Windsor states that "A

discontinuous load profile in a cable is very difficult to measure

properly and requires both discrete measurements (i.e., short

base length 'cells') and integrated measurements (i.e., long base

length 'gauges')." 

Table 1 is based on property values used during tests of the

SRL instrumented cable. Conventional cables with different

grout properties would exhibit different behavior. If several

cracks were dilating and loading a grouted cable, much less

discrepancy among the different loads would be predicted.

INTERPRETATION OF LOAD PROFILE

Collar load plotted against recorded microstrain at individual

gauge locations is shown in figure 7A, while load profile along

the length of the cable at different collar loads is shown in figure

7B. Figure 7B also shows the strong correlation between

predicted (Eq. 2) and actual loads. When critical load at the

collar (x - 0) exceeds 5,204 N × distance of the gauge from the

collar (in centimeters), the gauge will commence sensing load

so that every incremental change of collar load will equal a

similar increase in load on the gauge. This implies that a gauge

positioned 25.4 cm from the collar will sense load only when the

collar load exceeds 25.4 × 2,043 N/cm, or 51,908 N. When

collar load increases from 51,908 to 56,356 N, the gauge at 25.4

cm will sense the incremental load of 4,448 N. Another

observation is that the slope of collar load versus microstrain as

recorded by the individual gauges parallels the slope of a free

cable after a "critical load" has been exceeded (figure 7A).

Table 1.–Theoretical load and deformation measured for different cable instruments

Actual cable

 load, N

Cable length, loaded on

each side of crack, cm

Calculated crack

dilation, cm

Load based on fixed

length, N

Load measured at various distances of SRL

gauge from crack, N

 91 cm 183 cm 0 cm 30.5 cm 45.7 cm 61 cm

22,240 11.2 0.01 2,668 1,334 22,240 0 0 0

44,480 21.8 0.04 10,675 5,337 44,480 0 0 0

88,960 43.7 0.15 42,700 21,350 88,960 222,680 0 0

133,440 65.5 0.36 86,736 48,038 133,440 71,168 40,477 12,899

177,920 87.1 0.64 131,216 84,957 177,920 115,648 84,512 53,376

Figure 6.—Graph of measured and calculated strains for three gauges in pull test 2.
6

Figure 7.—Collar load plotted against A, microstrain (load profile curve) and B,

distance from head of cable (load correlation curve).

LOAD PROFILE MATRIX

Figure 8A shows the critical collar load required before individual gauges on the standard seven-strand cable and the SRL

instrumented cable sensed load at various embedment lengths

(Goris et al. 1993). The number of wires in contact with the

grout is the same for both types of cable. The slopes of the two

cables are similar, as would be expected since slope is largely a

function of the bond strength of the wire in contact with the

grout.

In figure 8B, it is assumed that a gauge is positioned every

7.6 cm along the cable. A load of 0 N at the gauge infers a

possible load increase of 2.04 kN/cm. Therefore, on the graph,

gauges positioned 1.2 m apart indicate a load of 125 kN at point

x ~ 76.2 cm, as do the gauges at 15.2 and 137.2 cm. These

figures are based on the assumption that there is a single crack.

Alternatively, a gauge located at point x ~ 76.2 cm and

indicating a load of 0 N negates this possibility. However, an

interpreted load of 62 kN is possible if a crack were positioned

midway between the gauge at 15.2 cm and the gauge at 76.2 cm.
7

Figure 8.—Load profile matrices. A, Load versus embedment length. 

Squares indicate data points. B, Load matrix graph.

This method should be employed when estimating predicted

load on a crack using measurements recorded in situ and projecting these measurements to the interpreted location of the

crack. This situation is presented in table 1 and shows that it is

critical to interpret loading based on measured conditions rather

than relying on a single load reading or an average of loads.

SPLIT-PIPE TEST RESULTS FROM FLAC

Strain measured by the strain gauges is related to load on the

cable bolt by the stiffness determined from the calibration. The

results from the laboratory experiment are provided in terms of

measured strain at 7.6-cm intervals along the length of the cable

versus applied load to the cable. A plot of applied load-versusmeasured microstrain for the first experiment is shown in figure 9.

It is convenient to compare load measured on the instrumented cable and load calculated by Itasca's (2000) computer

code Fast Lagrangian Analysis of Continua (FLAC) to

determine increments of applied load. For the purpose of this

analysis, laboratory-measured and FLAC-calculated loads were

compared at 22.2-kN increments. Because the experiment was

symmetrical on both sides of the split, it was assumed that the

gauges measured identical loads at identical distances away

from the split. It was therefore valid to average loads for each of

the three tests. In total, six data series for load-versus-applied

load were averaged to provide one "idealized" data set to

compare with FLAC results (figure 10).
8

Figure 9.—Pull test 1.

Figure 10.—Idealized measured load versus distance.

MODEL BOUNDARY CONDITIONS AND MATERIAL PROPERTIES

The geometry and boundary conditions for the FLAC model

are illustrated in figure 11. In the model, the cable is represented

as a series of elements attached at nodes, and the split pipe is

represented by two rows of zones. The two rows of zones are

"split" at the model's center by detaching the grid points so that

both ends of the pipe are free to separate without lateral

constraint. The grout bonding the cable to the pipe is implicit in

the cable bolt logic. To simulate pulling the split pipe apart, a

velocity boundary was applied to both ends of the model. This

is analogous to a laboratory test in which each end of the pipe

is pulled apart at a constant rate. 

The behavior of the FLAC cable element is a function of the

behavior of the steel cable (axial behavior) and of the grout-steel

cable interface (shear behavior). Because it is slender, the cable
9

Figure 11.—FLAC model and boundary conditions.

Figure 12.—Axial behavior of FLAC cable element

(adapted from Itasca 2000.) Yield = tensile strength,

E area = Young’s modulus, and ycomp = cross-sectional

area.

10ln(1 2 / )

2

t D

G kbond

+ ≈ π

Figure 13.—Illustration of conceptual fully bonded reinforcement (adapted from Itasca 2000).

element does not offer any resistance to bending. A simple

linear relationship between applied strain and the resulting force

describes the axial behavior of the steel. The cable can

theoretically take load in either compression or in tension, but

in the following analysis, only tensile behavior is relevant. 

Figure 12 schematically illustrates cable axial behavior. The required properties for the cable are its tensile strength, Young's

modulus, and cross-sectional area (labeled "yield," "E area," and

"ycomp," respectively, in the figure). The assumed dimensions and

properties for the cable are summarized in table 2. For the purpose

of this experiment, yield strength was not relevant because the

applied load was kept below the yield strength of the cable. 

Shear behavior plays an important role in how a cable is

loaded when the grid is displaced. It is through the grout-cable

interface that grid displacement induces load in the cable via

shear stress. The shear behavior of the grout is represented as a

spring-slider system at the cable nodes (figure 13). 

Table 2.—Cable properties

Property Model input

Area . . . . . . . . . . . . . . . . . . . . . . . . 1.826 e-4 m2

Young’s modulus .............. 128 GPa

Yield . . . . . . . . . . . . . . . . . . . . . . . . 220 kN

The properties that describe grout (see figure 14) are bond

stiffness (kbond) and shear strength (sbond). Bond stiffness

determines the load applied to the cable through the grout as a

result of shear displacement between the grout and the cable. It

is usually calculated from field pull-out tests, but such data are

not available for the current laboratory setup. The FLAC manual

provides the following guideline for choosing kbond (Itasca

2000).

(3)

where G = shear modulus of the grout, 

t = radial distance between the cable and the pipe

 wall, 

and D = inside pipe diameter. 

For the split-pipe model, a shear modulus of 0.35 w:c grout

and a Poisson’s ratio of 0.20 are calculated from the upper and

lower bounds of Young's modulus of groups using the properties

shown in table 3, or 6 e9

 to 8 e9 N/(mCm).

In previous numerical analyses of pull tests (Ruest 1998),

kbond was found to be closer to 3.5 e8

 N/(mCm), which is one

order of magnitude lower than the value calculated with

equation 3. In the current analysis, the importance of kbond was

assessed by evaluating the cable's response in the range of 1 e8

to 1 e10 N/(mCm).
10

Figure 14.—Grout material behavior for cable elements (adapted from Itasca 2000). A,

Grout shear strength criterion; B, grout shear force versus displacement.

Figure 15.—Ultimate bond strength in kilonewtons per meter as a function of grout

quality and rock modulus at 40 mm of slip (Hutchinson and Dieterichs 1996). The

value of kbond is 1 e8

 to 1 e10 N/(mCm), and the value of sbond is 180 to 210 kN/(mCm).

Table 3.—Grout properties

Property Value 

Water:cement ratio. . . . . . . . . . . . . . . . . 0.35

Poisson's ratio . . . . . . . . . . . . . . . . . 0.2

kbond (Young's modulus) . . . . . . . . . 6 e9

 - 8 e9 N/(mCm)

After Hutchinson and Diederichs 1996.

Shear strength determines maximum shear stress in the grout

before it begins to slip. Hutchinson and Diederichs (1996) have

published values for maximum shear stress (referred to as bond

strength) as a function of the Young's modulus of the host rock. An

equivalent rock modulus for the experimental pipe assembly is

found using the following equation (Hutchinson and Diederichs

1996).

(4)

where Er = rock modulus,

νR = rock Poisson’s ratio, 

dBH = borehole diameter,

EP = pipe modulus,

νP = pipe Poisson’s ratio,

di = pipe inside diameter,

and do = pipe outside diameter.

With the equivalent rock modulus, the value for sbond is

determined from the plot of rock modulus versus ultimate bond

strength (figure 15) (taken as sbond), also provided by

Hutchinson and Diederichs (1996). { } 2 2

2 2

(1 ) (1 2 )

2 ( )

(1 ) i p p i o

p o i

R BH

r

d d d

E d d

d

E

+ − +

− = +ν ν ν
11

Figure 16.—Plot of load distribution in cable at applied load of 22 kN.

It is well known that increases and decreases in confinement

will influence cable bolt behavior. FLAC attempts to account for

this effect by relating confinement on the bolt to maximum shear

strength. Increases in confinement are followed by increases in the

shear strength of the grout according to the strength criterion

defined by the parameter sfriction and the grouted perimeter

(perimeter). In the calibration presented below, no confinement

on the cable was modeled (since no confinement was applied to the

pipe in the laboratory experiment), and therefore these parameters

were irrelevant to the final solution. Thus, only bond stiffness and

grout shear strength were varied. The value of kbond is 1 e8

 to 1

e10 N/(mCm), and the value of sbond is 180 to 210 kN/(mCm).

MODEL RESULTS

Once the model was constructed and the boundary

conditions applied, the reaction forces at the modeled pipe ends

were monitored as the two sides were pulled apart. Once the

applied load reached one of the 22-kN increments, load on the

cable at 7.6-cm intervals was recorded. The plot in figure 16 shows cable load distribution as calculated by FLAC for

an applied load of 22 kN. The plot shows that maximum load

is located at the pipe split and that the distribution is

symmetrical about the model center. Figure 17 is a plot of

shear force at the grout-cable interface. Because the pipe is

displaced in both directions, shear forces are negative on the

right-hand side of the split and equal but positive on the lefthand side.

Figure 18 is a plot of the averaged laboratory results and the

FLAC calculated cable loads for 44- and 117-kN load increments at kbond values of 1 e8

, 1 e9, and 1 e10 N/(mCm). The

plot indicates that the shape of the FLAC cable curves is very

similar to the shape of the idealized laboratory curves for each

of the kbond values tested, with the lowest stiffness apparently

providing the best match with laboratory results. High loads

were observed at the split, but decreased with distance from

the split. The magnitude of the load at the cable split must be

equal to the applied load, but this is not reflected in the plotted

data since load is an average across the element. 

In each case, the model underpredicts load in the cable at

7.6 cm (near the pipe center). Improvement diminishes with

changes in stiffness. The conclusion from this analysis is that,

although a reasonable estimate of cable load distribution can be

obtained using the previously published equation for kbond, a

better estimate is obtained using

(5)

Figure 19 shows a plot of load distributions for the modeled

cable at applied loads of 44 and 117 kN for sbond values of

180, 190, and 200 kN/m. These values are within the range

estimated using Hutchinson and Diederichs' ultimate bond

strength plot (figure 10). Only a small amount of variability is

apparent in the model results within the range. Note, however,

that the ultimate pull-out load will depend on this parameter.

For the modeled cable to sustain a load of 178 kN as in the

laboratory, a minimum sbond of 200 kN/m is required.

FINAL CALIBRATION

Figure 20 is a plot of the FLAC-calculated cable loads compared to laboratory-determined load distributions at applied loads

of 44, 89, 133, and 178 kN. The kbond and sbond values used

to obtain these results were l e8

 N/(mCm) and 200 kN/m, respectively, as determined from the parametric analysis above. The

plot shows that there is very good agreement between laboratory

loads and the loads predicted by FLAC. The load at the split is

underpredicted by FLAC, and the difference becomes more

significant as load increases. The difference is explained by

realizing that the modeled grout remains perfectly intact for the

duration of the simulation. In the laboratory tests, the grout

deteriorates at the split as the confinement offered by the second

pipe is removed. This condition can not be simulated by FLAC.

The reader is reminded that the load at the split is necessarily

equal to the applied load and that this is not reflected in the data

set because no element appears in the model exactly at the split.

100 ln(1 2 / )

2

t D

G kbond

+ ≈ π
12

Figure 17.—Plot of shear force at grout-cable interface.

 Figure 19.—Load distribution at applied loads of 44 and 117 kN for sbond values

of 180, 190, and 200 kN/m.

 Figure 18.—Load distribution at applied loads of 44 and 117 kN for kbond values

of 1 e8

, 1 e9, and 1 e10 N/(mCm).
13

 Figure 20.—Plot of laboratory loads and modeled cable loads at 44, 89, 133, and

178 kN.

CONCLUSIONS

CABLE

Pull-test results confirmed that the stiffness of the SRL sixstrand cable paralleled that of a standard seven-strand cable,

which would ensure that measured strains would also be the

strains measured on an adjacent standard cable. The SRL cable

can provide a source of reliable point measurements, which can

help with evaluations of the effects of cable confinement, grout

quality, and rock mass stiffness, among other factors. 

The instrumented cable bolt is a unique field and research

tool that shows significant potential for improving understanding of the load deformation behavior of grouted cables.

Using measured load distribution along a cable will make it

possible to (1) predict point loading and load transfer rate along

a cable and (2) calculate the stiffness of a grouted cable. The

behavior of the SRL six-strand instrumented cable bolt largely

parallels the behavior of a standard seven-strand cable in the

elastic range; however, this result should be further confirmed

in the field. 

As mentioned by Windsor (1992), the behavior of a grouted

cable bolt needs to be assessed over both short and long intervals. The SRL cable provides insights into how a cable

responds to load by measuring loads over short intervals. This

tool has the potential to enhance understanding of the overall

interaction of cables, rock, and grout.

MODEL

In this investigation, a laboratory split-pipe test on the SRL

six-strand instrumented cable bolt was modeled using the continuum code FLAC. Laboratory boundary conditions were reproduced, and modeled cable loads were compared to laboratorymeasured cable loads under a variety of grout conditions. Cable

properties were kept constant for the calibration, since these are

generally well known.

The important conclusion from this analysis is that model

parameters can be determined on the basis of engineering principles and published data independent of laboratory results. Although the FLAC cable element is simple, model results indicate

very good agreement with the independently determined SRL

cable load results. The most significant discrepancy between the

two tests was with the 7.6-cm-interval sensor, where modeled

cable loads were consistently lower than the laboratory-derived

cable loads. The difference between results is either because the

grout quality in the model was not reproduced at the split, or

because the modeled grout did not reproduce failure and deterioration at the split resulting from cable pull-out. The analysis

presented above did not test how FLAC accounts for the effects

of confinement, since appropriate data are not available.

It was found that the best agreement between the model and

the laboratory experiment was obtained with a grout stiffness

(kbond) of 1 e8

 N/(mCm) and a maximum shear strength

(sbond) of 200 kN/m.
14

REFERENCES

Chekired, M., B. Mokrane, and H.S. Mitri. 1997. CTMD: A New Cable

Tension Measuring Device.. Presentation at 99th annual meeting of CIM,

Vancouver, BC, April 27-30, 1997, Paper WAM2-El.

Choquet, P., and F. Miller. 1987. Development and Field Testing of a

Tension Measuring Gauge for Cable Bolts Used as Ground Support.

Presentation at 89th annual meeting of CIM, Toronto, ON, May 3-7, 1987,

Paper No. 43, 19 pp.

Goris, J.M. 1990. Laboratory Evaluation of Cable Bolt Supports. U.S.

Bureau of Mines Report of Investigations 9308, 23 pp.

Goris, J.M., T.M. Brady, and L.A. Martin. 1993. Field Evaluation of Cable

Bolt Supports, Homestake Mine, Lead, SD. U.S. Bureau of Mines Report of

Investigations 9474, 28 pp.

Goris, J.M., and J. P. Conway. 1987. Grouted Flexible Tendons and Scaling

Investigations. Paper in Improvement of Mine Productivity and Overall

Economy by Modern Technology. 13th World Mining Congress (Stockholm,

Sweden). Balkema, v. 2, pp. 783-792.

Hutchinson, J.D., and M. Diederichs. 1996. Cablebolting In Underground

Mines. Bitech Publishers, Ltd., Richmond, BC. 406 pp.

Hyett, A.J., and W.F. Bawden. 1997. Development of a New Instrumented

Cable Bolt to Monitor Ground Support Loads in Underground Excavations.

Presentation at 99th annual meeting of CIM, Vancouver, B.C., April 27-30,

1997, Paper WAM2-E3.

Hyett, A.J., M. Moosavi, and W.F. Bawden. 1996. Load Distribution along

Fully Grouted Bolts, with Emphasis on Cable Bolt Reinforcement.

International Journal for Numerical and Analytical Methods in Geomechanics,

vol. 20, pp. 517-544.

Itasca Consulting Group, Inc., Minneapolis, MN. 2000. FLAC (Fast

Lagrangian Analysis of Continua), Version 4.0.

Milne, D., A. Gendron, and R. Hamilton. 1992. Cable Bolt Research Summary

Report. Internal report, Noranda Technology Centre, Montreal, Quebec.

Ruest, M. 1998. Back Analysis of Instrumented Hanging Wall Cable Bolt

Reinforcement at Complexe Bousquet. M.Sc. (Eng.) thesis, Queen's University,

England.

Windsor, C.R. 1992. Cable Bolting for Underground and Surface

Excavations. Paper in Rock Support in Mining and Underground Construction:

Proceedings of the International Symposium on Rock Support (Sudbury, ON,

June 16-19, 1992). Balkema, pp. 349-376.

Windsor, C.R., and G. Worotnicki. 1986. Monitoring Reinforced Rock

Mass Performance. Paper in Proceedings of the International Symposium on

Large Rock Caverns (Finland). Pergamon, pp. 1087-1098.