Workplace Workplace 

Safety and Health 

Department of Health and Human Services

Centers for Disease Control and Prevention 

National Institute for Occupational Safety and Health 

RI 9662 

REPORT OF INVESTIGATIONS/2004 

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 
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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

1

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

Doug Milne,2

2

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

Marc Ruest,3

4

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

3

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

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. 
2 

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. 

Figure 1.—Instrumented king wire with gauges and 

connecting cable. 

Figure 2.—Instrumented cable grouted in steel pipe. 

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 

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. 

Figure 3.—Pull-test apparatus. 

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). 

Figure 4.—Calibration curve for instrumented cable bolt. 

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). 
Figure 5.—Displacement pull tests. 

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Continuous readings of load, strain, and displacement in the di

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

2 kN/min. Load readings were collected electronically from 

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

om the test apparatus were correct, displacement readings 

ere also obtained from a micrometer attached to the pull tubes 

nd an LVDT on the machine. 

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

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

ong the cable were measured. An average grout compressive 

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

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

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

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

l undergoing plastic deformation. 

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

lonewtons versus displacement in centimeters. In each test, the 

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

the instrumented cable. The plotted displacements are the total 

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

ble. 

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 

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

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.–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 

91 cm 183 cm 

Load measured at various distances of SRL 

gauge from crack, N

 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 

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). 
 

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 

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. 

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. 

Table 2.—Cable properties 

Property Model input 

Area ..........

Young’s modulus 

Yield . . . . . . . . . .

.............. 

.............. 

.............. 

2 1.826 e-4 m

128 GPa 

220 kN 

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 a

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

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

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). 

s a 2 πG kbond ≈ (3) 

10 ln(1 + 2 t / D)

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. 

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). 

E 2E s

p (do 

2 − di 2 ) (4) r = 2 (1+ν )d d (1+ν ){(1− 2ν )d + d 2 

R BH i p p i o }

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 

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

Hutchinson and Diederichs (1996).

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). 
 

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

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 t

of the kbond values tested, with the lowest stiffness apparently s

providing the best match with laboratory results. High loads 

were observed at the split, but decreased with distance from l

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 s

data since load is an average across the element. r

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 

s better estimate is obtained using 

2πG kbond ≈ (5) 100 ln(1+ 2t / D) 

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 

o obtain these results were l e8

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

plot shows that there is very good agreement between laboratory 

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

underpredicted by FLAC, and the difference becomes more 

ignificant as load increases. The difference is explained by 

ealizing 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 

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

11 
12 

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

 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). 

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

of 180, 190, and 200 kN/m.
 

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 

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