Creep Along Weak Planes in Roof and How It Affects Stability

by

Mark K. Larson and Ryan G. Wade

National Institute for Occupational Safety and Health, Spokane, WA, USA

ABSTRACT

Researchers at the National Institute for Occupational Safety

and Health (NIOSH) are studying the time-dependent

response of rock stressed along weakness planes. The objective is to improve mine safety by reducing the number of

roof falls that cause injuries and fatalities to miners. 

Researchers conducted direct-shear tests on mudstone

overcored from a coal mine roof. Results showed frictional

strength weakens with displacement along the shearing

planes. Results of direct-shear creep tests also showed timedependent deformation. Test measurements were compared

to classical analytical models. Results suggest that risk of

roof collapse may be decreased through layout and support

design to reduce creep rates and thus slow progression

toward failure.

INTRODUCTION

It is an accepted fact that after the initial excavation of an

entry, most coal-measure rocks deform over time, even when

no mining is taking place nearby. This deformation is most

evident in the form of roof sag, floor heave, or pillar

dilation, but miners have observed shearing along bedding

planes and joints. Time-dependent deformation and strength

along joints significantly affect stand-up time of entries

(Fakhimi, 1992). In addition, time-dependent mechanisms

are evident in the timing of coal bumps. Thus, mine operators cannot ignore rock deformation over time when the risk

of a roof fall or a significant amount of entry closure or

encroachment are great during the life span of an entry.

NIOSH researchers are interested in learning how to design

entries and use support methods that will successfully arrest

or delay the onset of instability and resulting roof falls,

thereby preventing accidents and fatalities. In this regard, a

knowledge of the time-dependent properties of rock is

important. 

NIOSH researchers have conducted direct-shear, constantvelocity tests and direct-shear creep tests on mudstone cores

152 mm [6 in] in diameter. The cores were collected from

the roof of a western U.S. coal mine near a site where

Larson and others (1995) measured roof sag over time. Test

objectives were to measure friction and creep characteristics

of weak planes in the mudstone. The purpose of this paper

is to report upon and interpret the results of these tests for

engineers who design mine layouts. Simple rheological and

constitutive models are used to achieve this goal.

LITERATURE SURVEY

Creep behavior

Maranini and Brignoli (1999) conducted uniaxial, triaxial,

and hydrostatic tests (both standard tests and creep tests) to

characterize the behavior of Pietra Leccese, a massive

unfractured limestone. The predominant deformation mechanisms were crack propagation (at low confining pressures) and pore collapse (at higher stresses). During creep

tests, the collapse of pores caused lowering of the yield

stress, both in triaxial and hydrostatic configurations.

Price (1964) conducted bending and compressive creep tests

on various sandstones, a siltstone, and a nodular muddy

limestone. He showed that a Bingham-Voigt model adequately described results of the bending tests. Using the

results of Price’s bending tests on Pennant Sandstone,

Boukharov and others (1995) used rheological models for

each phase of creep and applied the models to describe

beam deflection over time. 

Price’s tests comprise the most extensive work done yet on

coal-measure rock. However, tests on other rocks should

not escape mention. Wawersik (1974) tested intact and

jointed rock specimens (Westerly Granite and Navaho Sandstone) in uniaxial and triaxial compression. Creep of the

rock was observed, particularly when water was present.

Very little creep was seen in a specimen with a clean, interlocked joint. Based on this, Wawersik concluded that the

creep behavior of jointed rock has the same character as that

of the intact material, but with a larger amount of strain. 

Considering Wawersik’s statement and the large strains

required to account for the amount of roof sag observed in

some coal mines, it is likely that creep in brittle coalmeasure rock occurs because of (1) microcracking along

weak bedding planes and (2) weakening of asperities of
(1)

(2)

joints. Because of the very friable nature of the mudstone

analyzed in this study along bedding, it appears reasonable

to conceptualize the shear plane in the mudstone as a

cohesive quasi-joint. For a joint, it is important to determine

frictional properties in addition to creep characteristics.

Amadei (1979) and Amadei and Curran (1980) conducted

direct-shear and triaxial tests on unfilled clean joints sawn

in specimens of sandstone, limestone, marble, and granite.

They reported that shear displacement was of the form

where A, B, and C are constants that depend on the ratio of

applied shear stress to peak shear strength (for constant

normal stress), properties of the intact rock, and joint surface

conditions, respectively.

Solberg and others (1978) conducted triaxial tests on

Westerly Granite with saw-cut joints filled with crushed

Westerly Granite. A confining pressure of 400 MPa (58,000

psi) was applied. They observed a correlation between differential stress and creep rate. Above a differential stress of

1,083 MPa (157,100 psi), primary and secondary creep were

followed by tertiary creep and violent slip.

Höwing and Kutter (1985) conducted a study of the effects

of joint filler on creep behavior. Creep velocity during the

primary phase followed a power law. Creep progressed

from the primary to the tertiary phase.

Friction laws

Bowden and Tabor (1964) defined the coefficient of friction

as the ratio between shear stress, , and normal stress, ,

in line with Amonton’s definition. The Coulomb law in

which is inherent joint cohesion and is coefficient of

friction is supported by Jaeger (1959) and by experiments of

Byerlee (1978). Other well-known definitions of frictional

strength are provided in Barton (1974) and Ladanyi and

Archambault (1970). 

Most other friction laws can be placed in one of three

classes: displacement weakening, velocity-dependent (velocity weakening), or normal-stress-dependent (normal stress

weakening).

The displacement weakening class includes laws such as

Patton’s (1966) bilinear model, Jaeger’s (1959) variation of

that model that provides a smooth transition between linear

segments, and Cundall and Hart’s (1984) continuously

yielding joint model that was described further by Cundall

and Lemos (1990). In the latter paper, a bounding shear

strength was used that was incrementally reduced as shear

displacement continued. 

Several researchers have suggested or used plasticity models

with a nonassociated flow rule to model joint friction and

implement a softening law (e.g., Michalowski and Mróz,

1978; Plesha 1987; Fakhimi, 1992; Lofti and Shing, 1994;

Mróz and Jarzbowski, 1994; Jarzbowski and Mróz, 1994;

Mróz and Giambanco, 1996). Softening is usually dependent on the amount of frictional work done.

Lippmann (1990) discussed the role of friction between a

coal seam and overlying and underlying rock layers in the

occurrence of translational coal bumps. Detonations, earthquakes, or other seismic events may generate waves along

interfaces and thus may convert static friction to sliding

friction.

Almost all research in velocity-dependent friction laws is

associated with the study of friction along faults. Dieterich’s

direct-shear experiments on granodiorite (1979) showed that

competing time, displacement, and velocity effects control

overall friction of a specimen, and so he proposed a simple

law. Others (Dieterich, 1981; Ruina, 1983; Rice, 1983; Rice

and Ruina, 1983) have proposed various state-variable friction laws. Generally, these laws describe a velocity-dependent friction with transitions over time between friction

levels. 

Only limited studies and discussions about the effects of

normal stress changes on friction have been published.

Results of some experiments do not show any effects of

normal stress history (Olsson, 1987b; Lockner and Byerlee,

1986), while others do (Hobbs and Brady, 1985; Olsson,

1985, 1987a, 1987b, 1988; Linker and Dieterich, 1986).

Given the nature of mining problems, velocity and normal

stress dependence are likely to be second-order effects.

Displacement dependence will likely be more significant.

APPARATUS AND EXPERIMENTAL PROCEDURE

All tests were carried out with a Gilmore direct-shear test

machine. Each of the two axes has a capacity of 1.334 MN

(300,000 lb) and is controlled through a servo-loop with an

MTS Teststar II controller. NIOSH engineers designed new

specimen boxes (figure 1) for 152-mm (6-in) diameter specimens to accommodate more instruments. Displacement

transducers were mounted on the sides of the specimen

boxes to measure shear displacement. The average of the
Figure 1.—Sketch of direct-shear test apparatus. 

Specimen frames are cut away near the specimen

for clarity.

two sensors was used as feedback during stroke-controlled

test segments.

Two classes of direct-shear tests were done. Constant-load

(normal and shear) tests were performed to measure shear

displacement over time. Constant-shear velocity tests were

done to measure deterioration of the applied shear force and

thereby infer reduction of friction on the shearing plane. For

one of the constant-shear velocity tests, the velocity was

changed suddenly in an attempt to measure any velocity

effects. No similar tests were performed to measure the

effect of changing normal loads.

Ends of the cores were not ground parallel because of the

fragile nature of the rock. The cores were sawn only when

the length exceeded the total height of the specimen frames

and the shear-plane gap (158.75 mm [6.25 in]). The diameter of the specimen cavity in the steel specimen frames

was 155.58 mm (6.125 in), which left a 1.6-mm (0.0625-in)

space between the rock and the frames. This space and any

space in the frames not taken up by a specimen were filled

with Hydrostone Super-X grout and allowed to cure overnight before testing began.

RESULTS

Creep tests

One constant-load, direct-shear creep test was conducted per

mudstone core specimen in the first series of tests. In all

cases, the first step of the test was to ramp the normal load

to the desired level over 60 sec. Next, the shear ram was

brought into contact with the specimen frames, and then

shear load was ramped to the desired level. The shear and

normal loads were held constant over several hours

(normally 48) before the shear and normal loads were, in

turn, ramped to zero.

Figure 2 shows shear displacement over time for six

specimens during the creep portion of the tests. Specimen

02, which failed 5 to 7 min after applying shear load, is also

shown in figure 3 with a zoomed-in time scale. This

specimen began to exhibit tertiary-phase creep (leading to

failure) before transient (primary phase) creep had faded

away. Transient creep was demonstrated by all specimens.

It is not possible to conclude that constant-rate (secondary

phase) creep was present because the duration of the creep

test was too short. However, the amount of roof sag over

time measured by Larson and others (1995) near the area

where these cores were collected suggested primary-phase

creep that was still dying out after 207 days. Figure 2 shows

no consistent correlation between creep rate and stress ratio

 or amount of creep and stress ratio.

Additional creep tests were begun, but the specimens failed

across the shear plane during ramping of the shear load.

Figure 4 shows shear stress versus shear displacement. The

 ratios for specimens 08, 09, 11, 13, 14, and

15 were 0.369, 0.336, 0.532, 0.942, 0.821, and 0.483,

respectively. The wide range of ratios suggests the variable

nature of the planes sheared. In some specimens, the plane

of shear may have been significantly weaker than in other

specimens. If the shearing planes are considered pseudojoints, then joint cohesion is much greater in some

specimens than in others.

Specimens 16 and 17 were subjected to several successive

creep tests under conditions of constant normal and shear

loads. In each test, the normal and shear loads were held

constant for 48 hr and then removed. Normal stresses for all

tests on specimens 16 and 17 were 2.068 and 1.379 MPa

(300 and 200 psi), respectively. Increasing levels of shear

stress were applied for each test (figures 5 and 6). Specimen

16 failed during the last test when the shear load was

ramped to 95% of normal load. While testing specimen 17

at a shear-to-normal load ratio of 0.90 (the first test at that

ratio), a power outage shut down the hydraulic system.

Shear displacement data from the tests suggests that load

relief caused by the power outage did not cause damage,

such as the formation of a crack. Therefore, specimen 17

was again tested at a stress ratio of 0.90. 

Figures 5b and 6b show the chronology of tests for the

respective specimens, including time breaks between tests.

Examination of figures 5 and 6 shows that the amount of

primary-phase creep was greatest when there was a period

of several hours where no loads were applied before the test.

Shear deformation was measured during several of these

relaxation periods. While not shown here, the sheardisplacement curves during relaxation have approximately

the same shape as the loading curves, but in the opposite

direction. When a creep test was started within minutes of

completion of the previous creep test, the amount and rate of

primary-phase creep were smaller than when a relaxation 
Table 1.—Successive shear force levels during creep tests where normal force was held constant

Test series Successive shear forces during creep segments expressed as a fraction of normal force, Fn

1 ( = 2.758 MPa) ...... 0.01, 0.05, 0.20, 0.35, 0.50, 0.65, 0.80, 0.90

2 ( = 1.379 MPa) ...... 0.01, 0.05, 0.20, 0.35, 0.50, 0.575, 0.65, 0.725, 0.80, 0.85, 0.90

3 ( = 4.137 MPa) ...... 0.01, 0.05, 0.20, 0.35, 0.50, 0.575, 0.65, 0.725, 0.80, 0.85, 0.90

period of several hours preceded the creep test.

Another series of creep tests was conducted on specimen 17

to characterize creep response at low levels of applied shear

stress. With normal stress held constant at 2.758 MPa (400

psi), five successive tests were conducted with the shear load

equal to 0.45Fn, 0.50Fn, 222 N (50 lb), 445 N (100 lb), and

667 N (150 lb). Subsequently, relaxation of shear displacement was measured for a couple of days. While the

accuracy of the applied shear loads is poor at such low load

levels, observations and measurements made while the test

was in progress suggest that the applied shear load was not

zero. Figure 7 suggests that shear displacement rates were

small but initially nonzero at low load levels. The relaxation

curve as displayed uses the beginning point as the datum for

convenience. The amount of displacement suggests that

some of the displacement locked in from the first two tests

(0.45 Fn and 0.50 F n) had not completely relaxed during the

low-level creep tests.

Three series of creep tests were conducted on specimen 17

to further characterize the effect of load levels and relaxation on shear displacement. During these series of tests,

normal load was maintained at 2.758, 1.379, and 4.137 MPa

(400, 200, and 600 psi) for the entire series. In each series,

the shear load was held constant for 48 hr, and then removed

for 48 hr. This process was repeated with the shear load

increased at each cycle. The sequential shear load levels for

each test series are described in table 1. Figure 8 shows

shear displacement over time during the entire first series.

The figure shows that unrecoverable shear displacement

took place at Fs = 0.65 Fn and above. 

Figure 9 shows results from the second series of tests in two

parts (separated by a dash-dot line) because a hydraulic

interlock stopped the test during the eighth creep segment.

The test series was resumed, starting with the seventh creep

segment. In these tests, unrecoverable strain was evident

when the shear load was as low as 0.35Fn. In running the

third series of tests, three hydraulic interlocks occurred,

stopping each test early in the series. Finally, the third series

was restarted from the beginning, and the entire series was

completed without a problem. Figure 10 shows shear displacement over time during the third series of tests.

Unrecoverable shear displacement is clearly evident when

the shear load was 0.20Fn and above.

Constant-Shear-Velocity Tests

Figure 11 shows applied shear stress with shear displacement for five constant-shear-velocity tests. Table 2 lists

normal stress and shearing displacement rates used for each

test. Shear stress increased linearly up to a peak load. In

three of the tests, the shear stress began to decrease quickly

almost immediately after reaching peak stress and then

continued to decrease with exponentially decaying rates. In

the other two tests, shear stress stayed near the peak value

for some time. Shearing was allowed to continue long

enough for exponential decay to be apparent in one of the

two tests. Results of the test with no applied normal load

suggested that an exponential decay of shear stress may be

typical even when normal stress is low.

Figure 12 shows results of a test on specimen 10. Normal

stress was not constant, but decreased nearly linearly because of a test template error. Changes in shear velocity

produced only very minor, if any, effects. The shear-stress

versus shear-displacement curve is very much like most of

the curves in figure 11. Frictional strength appears to be

dominated by displacement-weakening behavior. Cohesion,

or interlocking of asperities, may be responsible for those

instances in which high peak strength dropped off quickly

with increasing shear displacement.

Table 2.—Conditions of constant-rate, direct-shear tests

Specimen Normal stress Shearing displacement

rate

MPa psi mm/sec in/sec

01 . . . . . . 1.724 250 0.038100 0.001500

05 . . . . . . 1.724 250 0.009525 0.000375

06 . . . . . . 2.758 400 0.038100 0.0015

07 . . . . . . 0 0 0.038100 0.0015

10 . . . . . . 1.724 250 0.009525

0.038100

0.009525

0.002381

0.000375

0.001500

0.000375

0.000094

13 . . . . . . 2.758 400 0.009525 0.000375
Figure 13.—Rheological model used to examine behavior during creep

test

(5)

(3)

(4)

MODELS

A preliminary comparison with analytical models will

provide some insight into results of laboratory tests on

mudstone. Figure 13 shows elements of a rheological model

(essentially the same as that used by Boukharov and others,

1995) that may reasonably account for the deformation

measured. For this model, shear displacement may be

represented by 

where is shear displacement, is a strength above

which constant-rate creep takes effect, is time, is the

time when , is the Heaviside

step function (= 1 when its argument, , 0;

otherwise, = 0), and are stiffness parameters,

and and are viscosity parameters.

Figure 14 compares shear displacement over time from

figure 8 with model calculations using equation 3 with

estimated (only one creep curve was fitted) parameters. The

reader should note that the last term of equation 3 was reset

for each loading step, but previously accumulated displacements from that term were left in the total shear displacement. In the calculations, was 4.34315 MPa/mm

(16,000 psi/in), was 106.0232 MPa/mm (390,585.3

psi/in), was 6,251,726 MPat/mm (2.3031099 × 1010

psit/in), was 5,428,943 MPat/mm (2.000000 × 1010

psit/in), and was 1.600 MPa (232 psi)—58% of the

applied normal stress. For the figure, a seating displacement

of 0.01778 mm (0.0007 in) was assumed. Comparison of

the model curve with measured results suggests that transient

creep in the specimen may not have depended on shear

stress level as much as did transient creep in the model. The

model was able to capture the unrecoverable shear displacement above some level, similar to the measured result.

Displacement offsets were not always well simulated with

the stiffness in the model, suggesting a degree of

nonlinearity of the specimen in the elastic region. At higher

shear stresses, the shear stiffness began to soften. 

Figure 15 compares shear displacement over time from

figure 11 with model calculations using 

where is shear strength, is cohesive strength, and 

In equation 5, is friction angle, is residual friction

angle, is peak friction angle, is shear displacement

when , and is empirical constant. In the model

calculations, parameters were estimated was 2.758 MPa

(400 psi), was 2.413 MPa (350 psi), was 1°,

was 6.4°, and was 0.031496 mm-1. The shear stiffness in

the calculations for the loading portion of the curve was

2.8366 MPa/mm (10,450 psi/in). The model’s failing is that

the cohesion assumed the value of zero when the shear stress

reached the shear strength. However, cohesion in the

specimen did not reach zero as quickly. The jagged loss-ofcohesion effect actually may be the result of relatively large

asperities that were sheared off, although not all at once.

Perhaps a cohesion-like parameter may be appropriate if it

decreases exponentially with shear displacement instead of

going to zero suddenly when the shear strength is exceeded.

The absence of sharp peaks in some of the test results (in

figure 11) suggests that larger asperities may not always be

intact or present. It may be more appropriate to model such

behavior with a dilation angle that deteriorates with shear

displacement.
DISCUSSION

Results thus far suggest some points to be considered when

a mine operator is concerned about long-term stability of

entries. In this regard, the authors have assumed that joints

and planes of weakness play a dominant role in roof sag.

The similarities in creep behavior (transient creep) between

tested core and roof sag over time (Larson and others, 1995)

suggest that behavior measured in the laboratory is relevant

to the field. It is interesting to note that Larson and Maleki

(1996) measured constant-rate roof sag in a different part of

the mine where roof conditions were not as uniform.

Constant-rate deformation was pronounced at this second

measurement site. The differences in roof sag over time

suggests that a knowledge of creep properties and design

principles may be used to prevent collapse during the

service life of the opening. One way to do that is to design

entries so that constant-rate creep is reduced or entirely

avoided. This approach doesn’t preclude the possibility of

collapse, but if the amount of creep over time can be

reduced, the probability of collapse during an entry’s service

life decreases.

If the rheological model is valid (i.e., constant-rate creep

along weakness planes occurs only when shear stress is

above some strength ), then it may be possible to design

entries so that shear stress along bedding is maintained

below strength . This may be achieved with roof

support; however, care must be exercised in the case of bolts

and cable bolts so that applied shear stress does not exceed

the shear strength of the bolts (Signer and Lewis, 1998;

McHugh and Signer, 1999). Where shear stress is kept

below , roof sag would tend to stabilize unless transient

creep is large enough that might significantly decrease.

It is not known if is dependent on normal stress, but test

results suggest that its weakening is dependent on total shear

displacement or damage. Another possibility is that 

decreases by static fatigue (Larson, 1998), which is

suggested by the failure of specimen 02 (figure 3).

The combination of equations 4 and 5 seems a reasonable

approximation to shear strength. However, it may be appropriate to include in equation 4 a dilation angle that decreases

with shear displacement.

The next logical step is to write code for such constitutive

models (equations 3, 4, and 5) in a numerical model and

examine how well laboratory tests or measured roof sag

deformation can be simulated. Some of the unanswered

questions might be resolved by accomplishing this step.

CONCLUSIONS AND RECOMMENDATIONS

Comparing the results of direct-shear laboratory tests with

field measurements of roof sag suggests that knowledge of

characteristic creep behavior of planes of weakness in

mudstone can be useful in the design of stable long-term

entries so that roof collapse is avoided. This might be

accomplished by designing entries and support in such a way

to reduce the rate or avoid the onset of secondary-phase

creep. 

Primary-phase creep was seen along planes of weakness in

the mudstone even at low shear stresses, but unrecoverable

or secondary-phase creep only took place when shear

stresses were above a certain level. That strength decreased

with further testing of the specimen.

It is recommended that the models used in this report be

coded into a numerical model to investigate their applicability in laboratory tests and field case histories.

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