Figure 1.—Instrumented king wire with gauges and

connecting cable.

FLAC Simulation of Split-Pipe Tests on an Instrumented Cable Bolt

Marc Ruest

Itasca Consulting Group, Inc., Minneapolis, MN, USA

Lewis Martin

Spokane Research Laboratory, National Institute for Occupational Safety and Health

Spokane, WA, USA 

ABSTRACT

A new instrumented cable bolt has been developed by the National Institute for Occupational Safety and Health at

the Spokane Research Laboratory in Spokane, WA. Although various instruments are available to measure load

distribution and magnitude along a grouted cable, this instrument is innovative in that it uses strain gauges internal to the

cable as load-measuring sensors. The instrument has been successfully tested in the field at FMC’s Granger Mine,

Meikle Mine, and Getchell Mine. 

A “split-pipe” laboratory pull test was performed on each of three cable bolts instrumented with the new device. Each

test consisted of grouting a 1.83-m-long cable in two 0.91-m-long sections of schedule 80 pipe. A numerical analysis

was then performed in which laboratory boundary conditions were simulated and model properties derived from textbook

guidelines. The loads calculated by the model were then compared to the measured loads.

INTRODUCTION

Researchers have conducted a large number of experiments on cable bolts to determine their load characteristics for

different grout types, grout ratios, and cable configurations (Garford bulb, buttons, birdcage, nut cage, etc.). However,

published data are limited on studies of instrumented cables that would provide additional information on loading

mechanics (Hyett and Bawden 1997; Choquet and Miller 1987; Goris et al. 1993; Chekired et al. 1997). 

The Tensmeg and the SMART cable are two commercially available instruments used to interpret load along a cable

bolt. The Tensmeg sensor is a 60-cm-long, externally mounted strain gauge. Multiple Tensmegs are fixed along the

cable length to obtain the cable loads at those locations. In the SMART cable, the king wire is replaced by an

extensometer with internal wires anchored along the cable and attached to potentiometers within the electrical head. The

difference in displacements between anchors is used to calculate average strain, which is then related to load by cable

stiffness.

This study presents the results of “split-pipe” tests conducted on a new instrumented cable bolt developed at the

Spokane Research Laboratory (SRL). The sensors for this instrument are positioned along the length of a king wire that

replaces the steel king wire inside a regular seven-strand

cable. The replacement king wire is a strip of steel having

strain gauges attached along its length and remolded to a

cylindrical shape with epoxy (patent 6,311,564) (Fig. 1).

The main advantage of the SRL instrument is that cable

stretch is measured over a short distance and can therefore

provide an accurate estimate of load over a small (approximately 13 mm) length of cable. Because of their low cost,

many strain gauges can be installed along the cable to get a

better understanding of load distribution.
Figure 3.—Pull-test apparatus

EXPERIMENTAL SET-UP AND METHODOLOGY

Three split-pipe tests were conducted. The split-pipe assembly simulates the opening of a crack in a supported rock

mass. An instrumented cable with 20 equally spaced gauges was grouted within each pipe assembly (Fig. 2). During the

simulation, two 0.91-m-long pipes were pulled apart using a hydraulic load frame, and the reaction loads and pipe

displacements were monitored. As the pipes were displaced, the grout transferred axial load to the cable and the strain

gauges fixed inside the king wire gave a microstrain reading to a data acquisition system. The data provided a measured

load profile along the instrument for a given pipe displacement and resulting reaction load. 

Figure 2.—Instrumented cable grouted in steel pipe.

TEST SET-UP

The first instrumented split-pipe test was conducted 28 days after pouring the sample, and the second and third tests

were conducted at 30 days. The mixing ratio of 0.35 water to Type I/II portland cement was used for the grout, achieving

an average compressive strength of 57 MPa at 28 days. The instrumented cables were constructed using 15.8-mm

diameter, seven-strand conventional cables with breaking strengths of approximately 258 kN. Conventional cables were

chosen due to the large database of experimental results available for this cable type. The tests were run on all three

samples until the cable slipped and the cable-grout system could no longer hold the loads. 

The pull-test apparatus was built to prevent the tubes from twisting during the tests. The test apparatus was one used

by Goris during his testing program at the Bureau of Mines (Fig. 3). Centralizing fixtures were welded to the pipe at each

end and in the middle, but were not attached to the bolt. End caps

with holes were placed on the bottom ends of the pipes while grout

was poured into the tubes. A vibrator was attached to the pipes,

and a tamping rod was used during pouring to rid the system of

entrapped air. A bead welded to the inside of the pipes prevented

slippage at the grout-pipe interface (Goris and Conway 1987). 

CALIBRATION

Tensile tests are used to determine a cable’s characteristic loadversus-strain curve. The slope of the elastic portion of the curve

is referred to as “cable stiffness,” which is required to convert

microstrain readings from the gauges in the instrument to a load

measurement. The average cable stiffness for the six-strand SRL

cable was calculated to be 23,370 kN/m/m. This compares to a

stiffness of 28,000 kN/m/m for a standard seven-strand cable. The

reduced stiffness was due to the absence of a load-bearing steel

king wire.
Figure 4.—Pull-test 1.

Figure 5.—Idealized measured load versus distance.

SPLIT-PIPE TEST RESULTS

The strain measured by the strain gauges is related to the load in 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-versus-measured microstrain for the first

experiment is shown in Figure 4. It is convenient to compare load measured on the instrumented cable and load calculated

by FLAC for increments of applied load. For the purpose of this analysis, the laboratory-measured and FLAC-calculated

loads are compared for applied loads at 22.2-kN increments. Because the experiment was symmetrical on both sides of

the split, we can assume that the gauges measured identical loads at identical distances away from the split. It is therefore

valid to average the load measured on both sides for each of the three tests. In total, six data series for load-versusapplied load were averaged to provide one “idealized” data set to compare to the FLAC results (Fig. 5). 

MODEL BOUNDARY CONDITIONS

AND MATERIAL PROPERTIES

The geometry and boundary conditions

for the FLAC model are illustrated in Figure 6. 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 grout bonding the

cable to the pipe is implicit in the cable

bolt logic. To simulate the pulling apart of

the split pipe, a velocity boundary was

applied to both ends of the model. This is

analogous to pulling each end of the pipe

at a constant rate in the laboratory. The

two rows of zones are “split” at the

model’s center by detaching the gridpoints

so that both ends of the pipe are free to

separate without lateral constraint.
Figure 6.—FLAC model and boundary conditions.

Figure 7.—Axial behavior of FLAC cable

element (adapted from Itasca 2000).

Figure 8.—Conceptual illustration of fully bonded

reinforcement (adapted from Itasca 2000).

The behavior of the FLAC cable element is

a function of the steel’s behavior (axial

behavior) and the behavior of the grout-steel

interface (shear behavior). Because it is slender, the cable element does not offer any resistance to bending. The axial behavior of the

steel is described by a simple linear relationship between applied strain and resulting force.

The cable can theoretically take load in either

compression or in tension, but in the following

analysis, only the tensile behavior is relevant.

Figure 7 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” in the figure, respectively). The assumed dimensions and

properties for the cable are summarized in Table 1. For the purpose of

this experiment, the yield strength is not relevant since the applied load

was kept below the yield strength of the cable.

TABLE 1.—Cable properties

Property Model input

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

Young’s modulus ............ 128 GPa

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

Shear behavior plays an important role in how the 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 stresses. The

shear behavior of the grout is represented as a spring-slider system at

the cable nodes (Fig. 8). The properties that describe the grout with

reference to Figure 9 are its bond stiffness (kbond) and its 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).

Eq. 1 10 ln(1 2 / )

2

t D

G kbond

+ ≈ π

In this equation, G is the shear modulus of the grout, t is

the radial distance between the cable and the pipe wall, and

D is the inside pipe diameter. Therefore, for this split-pipe

model and the shear modulus of 0.35 w:c grout (calculated

from upper and lower bounds of Young’s modulus obtained

from Hutchinson and Diederichs [1996] and a Poisson’s ratio

of 0.20), the starting value for kbond is bounded by 6e9 and

8e9 N/m/m. In previous numerical analyses by the senior

author, kbond was determined from the results of pull tests

performed at Complexe Bousquet in Quebec (Ruest 1998).

kbond was found there to be closer to 3.5e8 N/m/m, one

order of magnitude lower than calculated using the equation
Figure 9.—Grout material behavior for cable elements (adapted from Itasca 2000). A, Grout

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

Figure 10.—Ultimate bond strength (in kN/m) as a function of grout quality

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

value of kbond is 1e8 to 1e10 N/m/m, and the value of sbond is 180 to 210

kN/m/m.

above. In this analysis, the importance of kbond was assessed by evaluating the cable’s response in the range of 1e8 to

1e10 N/m/m.

Shear strength determines the maximum shear stress in the grout before it begins to slip. Hutchinson and Diederichs

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).

Eq. 2 { } 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

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 in

Figure 10 (taken as sbond), also provided by

Hutchinson and Diederichs (1996). 

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 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 are irrelevant to the final solution. Thus,
Figure 11.—Plot of load distribution in cable at applied load of 22 kN.

Figure 12.—Plot of shear force at grout-cable interface.

only bond stiffness and grout shear strength were varied. The value of kbond is 1e8 to 1e10 N/m /m, and the value of

sbond is 180 to 210 kN/m/m.

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, the load

on the cable at 7.6-cm intervals was recorded. The plot in Figure 11shows cable load distribution as calculated by FLAC

for an applied load of 22 kN. The plot shows how the maximum load is located at the pipe split and that the distribution

is symmetrical about the model center. Figure 12 is a plot of the 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 opposite in sign

on the left-hand side.

Parametric Analysis of kbond and

sbond

Figure 13 shows a plot of the averaged laboratory results and the FLAC

calculated cable loads for 44- and 117-

kN load increments for kbond values

of 1e8, 1e9, and 1e10 N/m/m. 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 for the laboratory

results. High loads were observed at

the split and 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 the load is

an average across the element. In each

case, the model underpredicts the 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

Eq. 3 100 ln(1 2 / )

2

t D

G kbond

+ ≈ π

Figure 14 shows a plot of load distributions for the model 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 (Fig. 10). There is only a small amount of variability in the model results within the range. Note, however,

that the ultimate pull-out load will depend on this parameter. For the model cable to sustain a load of 178 kN as in the

laboratory, a minimum sbond of 200 kN/m is required.
Figure 14.—Load distribution at applied loads of 44 and 117 kN for sbond values

of 180, 190, and 200 kN/m.

Figure 13.—Load distribution at applied loads of 44 and 117 kN for kbond values

of 1e8, 1e9, and 1e10 N/mCm.

Final Calibration

Figure 15 provides a plot of the FLAC-calculated cable loads compared to the laboratory-determined load distributions for applied loads of 44, 89, 133, and 178 kN. The kbond and sbond values used to obtain these results were 1e8

N/m/m and 200 kN/m, respectively, as determined from the parametric analysis above. The plot shows that there is very

good agreement between the laboratory loads and the loads predicted by FLAC. The load at the split is underpredicted
Figure 15.—Plot of laboratory loads and model cable loads at 44, 89, 133, and 178 kN.

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, the grout deteriorates at

the split as the confinement offered by the other pipe is removed. This 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 there is not an element included in the model exactly at the split.

CONCLUSIONS

In this investigation, a laboratory split-pipe test on the SRL instrumented cable bolt was modeled using the continuum

code FLAC. Laboratory boundary conditions were reproduced, and model cable loads were compared to laboratorymeasured cable loads for a range of model grout properties. The cable properties were kept constant for the calibration,

since these are generally well known.

The important conclusion from this analysis is that the model parameters were determined based on engineering

principles and published data, independent of the laboratory results. Although the FLAC cable element is simple, the

model results indicate very good agreement with the independently determined SRL cable loads. The most significant

discrepancy between the two tests was at the 7.6-cm sensor where model cable loads were consistently lower than the

laboratory cable loads. The difference between results is either because the grout quality in the model was not reproduced

at the split, or because the model grout did not reproduce failure and deterioration at the split due to cable pull-out. The

analysis presented above does not test how FLAC accounts for the effect of confinement since appropriate data were not

available.

It was found that the best agreement between the model and the laboratory experiment was obtained with a grout

stiffness (kbond) of 1e8 N/m/m and a maximum shear strength (sbond) of 200 kN/m.

REFERENCES

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CIM conference, Vancouver, BC, April 27-30, 1997. Paper WAM2-E1.

CHOQUET, P., and MILLER, F. 1987. Development and field testing of a tension measuring gauge for cable bolts used as ground
support. Presentation at 89th CIM conference, Toronto, ON, May 3-7, 1987. Paper 43, 19 pp.

GORIS, J.M., BRADY, T. M., and MARTIN, L.A. 1993. Field evaluation of cable bolt supports, Homestake Mine, Lead, SD. U.S.

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underground excavations. Presentation at 99th CIM conference, Vancouver, BC, April 27-30, 1997. Paper WAM2-E3.

ITASCA CONSULTING GROUP, INC., Minneapolis, MN. 2000. FLAC (Fast Lagrangian Analysis of Continua), Version 4.0.

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Queen’s University.