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EFFECTS OF FAR-FIELD SHEARING DEFORMATION ON FRACTURING AROUND 

AN UNDERGROUND OPENING 

By M. K. Larson, B. G. White, and S. R. Iverson 

Spokane Research Laboratory, National Institute for Occupational Safety and Health, 

 Spokane, WA 

ABSTRACT 

 Researchers at the National Institute for Occupational Safety and Health (NIOSH) are 

investigating the causes and mechanisms of roof failure in underground mines. It is expected that 

a better understanding of these causes and mechanisms will lead to better layout and support 

designs that will help prevent accidents and fatalities associated with fall of ground. Two 

numerical experiments were conducted by NIOSH researchers using the Fast Lagrangian 

Analysis of Continua (FLAC) computer modeling program with a strain-softening continuum to 

simulate fracture zones. Two models, one of a round hole in a plate and one of a rectangular 

opening, were constructed and boundary conditions were applied to simulate far-field shear. The 

Particle Flow Code in Two Dimensions (PFC2D) computer program was used to look at the 

effects of far-field shear in generating fractures around an underground opening, but these 

models are preliminary until boundary conditions, strengths, and stiffnesses are matched to the 

FLAC models. Results showed that shear zones propagated from the opposite corners of 

openings in directions that appeared to be determined by opening shape and far-field stress. 

Tensile failures also formed and extended away from these shear zones. The consistent direction 

of shear deformation with respect to far-field shear provides a plausible explanation for preferred 

directions of shear as seen in geologic environments. 

INTRODUCTION 

 Fairhurst and Cook (1966) proposed a roof-rib failure mechanism in which parallel, stressinduced microcracks form parallel to the roof or rib line. Stress around the opening causes these 

microcracks to increase in length. The length of these fractures decreases with distance from the 

opening, and, in the event of a roof fall or rock burst, their ends define a limit of breakage that is 

concave to the surface. Diederichs (2003) illustrates a zone of fractures with the same geometry 

as fractures described by Fairhurst and Cook (1966). However, White (2002) examined failure 

around an underground opening and concluded that the closely spaced fractures describe by 

these authors did not extend through the entire volume of fallen rock, but were limited to near the 

periphery of the breakout. Other examples are cited in White et al. (2003) that support this 

assertion. 

 Terrill and VandeKraats (1997) observed similar features in a salt mine after the fractured 

roof was excavated by a roadheader. They noted that fractures first formed near corners, and then 
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either took the form of a fault that angled upward toward the centerline of the roof or more often, 

a zone of en echelon fractures that angled over the opening. Zones of both faults and en echelon 

fractures displayed a component of slip. The alternating appearance of faults and en echelon 

fractures and their similar displacements suggested that both structures were closely related, an 

idea that was also considered by Peng and Johnson (1972). 

 Using the observations of Terrill and VandeKraats (1997), White et al. (2003) concluded that 

a fundamental pattern of fracturing around rectangular underground openings involves dilatory 

shear zones that originate near the corners of openings and propagate obliquely away from these 

corners to intersect the vertical centerline of the opening, as seen in figure 1. 

Figure 1.─ Representative cross section showing fracture patterns in halite roof (modified from Terrill and VandeKraats 1997: figure 6). 

 Larson et al. (1995), Larson and Maleki (1996), and Larson (2003) describe roof failures in 

the roof of a coal mine in which the immediate rock above the coal seam was a carbonaceous 

mudstone containing weak bedding planes. Failure typically occurred over time near the upper 

corner on the downdip side of the roof, creating a zone of failure. This failure zone then began to 

extend over the entry. Larson et al. (1995) and Larson (2003) surmised that, over time, much of 

the deformation might become concentrated along the weak planes as a result of far-field shear 

driving forces along these planes. A dip of 16o at one of the two sites studied added credence to 

this hypothesis. The question arises as to whether typical far-field shear deformation resulting 

from shear stress or shear ride can cause zones of shear and tensile fracturing to extend in a 

preferred direction (for example, fracturing on only one side of an opening). 

PREVIOUS MODELS 

 White et al. (2003, 2004) conducted numerical experiments with two computer modeling 

codes: Fast Lagrangian Analysis of Continua (FLAC) (Itasca Consulting Group, 1993) and 

Particle Flow Code (PFC2D) (Itasca Consulting Group, 1999). Continuum modeling with FLAC 

using very small elements under far-field compressive stresses of 68.95 MPa (10,000 psi) 

horizontally and 34.47 MPa (5,000 psi) vertically identified a small but significant zone of 

tension near each corner of the roof following excavation of the opening. The effects of a crack 
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parallel to the opening were simulated by removing an element at that position and extending the 

“crack” (figure 2). The result was that the tension zone migrated, staying above and near the end 

of the crack, but peak tension decreased in magnitude. This pattern suggests that another crack 

might form above and be offset from the first crack and that propagation of such a system of 

cracks would eventually stop. 

Figure 2.─Portion of FLAC model showing least principal stress near corner of rectangular opening using stress 

conditions and rock properties approximating those of the Coeur d’Alene Mining District. Untextured pattern along 

edge of opening reflects tension. A, Initial model. Tension reaches 24 MPa (3,480 psi) near corner, but 1.4 MPa (200 

psi) maximum along edge of roof farther from corner. B, C, D, Least principal stress for simulated fracture created by 

removing progressively longer row of narrow elements. B, Removal of element containing highest stress in A. A 

region of tension extends diagonally upward to second site of concentrated tension. C, D, Third and fourth tension 

sites revealed as simulated fracture extends to right, tensile regime expands, and tension sites at end of simulated 

fracture move with progressive extension of fracture (White et al. 2004:figure 3). 
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 Discrete-element modeling with twodimensional particles using PFC2D, in 

which an isotropic stress was applied to all 

walls (or external boundaries), was done 

next. The opening was then excavated and 

vertical load increased (figure 3). Figure 4 

shows the formation of several en echelon 

cracks. While boundary conditions do not 

represent the effects of excavation, they 

may represent further loading of an opening because of nearby mining. 

 While both the FLAC and PFC2D

modeling experiments showed a possible 

cause for the initial formation of en 

echelon zones and the possibility that additional loading could cause propagation 

of faults or en echelon fractures, it was not 

clear what caused the extension of such fracture zones in the absence of loading (that is, 

fracturing resulting from mining of the opening) and what the mode of failure was. In the case of 

the coal mine described, far-field shear ride is a likely cause. The rest of this paper examines the 

effects of far-field shearing on fracturing and identifies modes of failure and where failure 

occurs. It is a work in progress with results to date presented. 

NUMERICAL EXPERIMENTS 

 Two experiments were conducted with FLAC models to examine the effects of far-field 

shearing. The first experiment used a round hole in a plate. The second experiment used a 

rectangular opening. One material type was used in each experiment. Material softening was 

used to simulate the loss of strength because of fracturing. Additional models were run with 

PFC2D to examine the capabilities of particle modeling to simulate fracturing. 

Hole-in-a-Plate Experiment 

 FLAC was used to examine fracturing caused by far-field shear around a circular opening. In 

this case, a mesh was mapped around a circular opening and joined to form a “glued” joint in the 

vertical plane down from the opening. Strain softening was used to simulate the effects of 

fracturing, and no dilation was assumed. Figure 5 shows graphically the assumed deterioration of 

(1) cohesion and friction with plastic shear displacement hardening/softening parameter ps e and 

(2) tensile strength with plastic tensile displacement hardening/softening parameter pt e . These 

are defined in incremental form as— 

Figure 3.—PFC model in which margins of rectangular 

block of particles are loaded and a rectangular area excavated to simulate cross section of corner of mine opening. 

Horizontal load is gradually increased so progressive 

failure can be observed (White et al. 2004:figure 4). 
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Figure 4.—Stages of progressive failure of square-corner model. A, Early stage of bond failure, identified as short 

lines. The first clustered failures occur at site X and spread downward; subsequent failures began and spread 

upward from site Y. Complete detachment along lower part of zone ultimately forms a fault. B, Velocity vectors 

(displacement from previous modeling step) during formation of wing crack a-b. Vectors indicate shear and 

dilational components along fault portion and also along wing crack. C, Velocity vectors as wing crack a-b 

reaches its fullest extent. A new cluster of failures (site of diverging vectors in offset position c) defines early stage 

of first en echelon fracture. Note scattered distribution of these early failures at this site. D, E, Velocity vectors 

indicate new en echelon fracture d-c-e and sites of initiation of two subsequent en echelon fractures f and g. In D, 

fault zone propagates to fracture d-c-e and activates it as a wing crack. Each long extension fracture propagates 

through a series of individual bond failures at fracture tips. Particles not shown in E (White et al. 2004:figure 5).
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( ) ( ) ( ) 2

1

2

3

2 2

1 2

1

2

1

2

1

⎭

⎬

⎫

⎩

⎨

⎧ ∆ = ∆ − ∆ + ∆ + ∆ − ∆ ps

m

ps ps

m

ps

m

ps ps e e e e e e (1) 

and pt pt e e ∆ = ∆ 3 , (2) 

where ps e ∆ 1 and ps e ∆ 3 are the incremental maximum and minimum principal plastic shear strains, 

respectively, pt e ∆ 3 is the incremental minimum principal plastic tensile strain, and 

( ) ps ps ps

me e e 1 3 3

1 ∆ = ∆ + ∆ . (3) 

 The softening functions shown in figure 5 were chosen to represent (1) the immediate loss of 

tensile strength at the moment of fracturing, (2) a quick loss of cohesive strength, which occurs 

at a slower rate than does the loss of tensile strength, and (3) a gradual deterioration of friction to 

a residual value. Peak strength values were chosen to represent a moderate to strong sedimentary 

or igneous rock. 

 Localization and softening behavior are somewhat mesh-dependent (Rice 1976; Fakhimi and Fairhurst 1994). Fakhimi and Fairhurst 

(1994) used an idea from Bazant 

and Pijaudier-Cabot (1988) of a 

nonlocal continuum in which stress 

at a point is a function of a weighted average of strains near that 

point. Characteristic size of the 

averaging zone is an important 

issue (Bazant and Pijaudier-Cabot 

1987), but experiments done by 

Zietlow and Labuz (1998) suggest 

that characteristic size is related to 

grain size and fabric of the rock. In 

this paper, FLAC models did not 

use a nonlocal continuum model. 

However, mesh size was small (19.6 by 9.5 mm [0.77 by 0.37 in] near the opening) and therefore 

not much larger than the typical grain size of several rock types. 

 A vertical compressive stress of 41.37 MPa (6,000 psi) and a horizontal compressive stress 

of 20.68 MPa (3,000 psi) were applied to the boundaries. Before applying shear stress to the 

boundaries, some shear yielding occurred on the sides at the position of greatest tangential 

compressive stress (figure 6A). In addition, minimal tensile yielding occurred in the vertical 

plane at the bottom of the opening but not at the top, probably because of the presence of the 

“glued” joint at the bottom. 

Figure 5.─Strength versus plastic strain functions assumed for FLAC 

experiments
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 A shear stress of 20.68 MPa (3,000 psi) was applied to the boundaries. Figure 6 shows model 

results. Figure 6B shows elements yielding at the end of the experiment and elements that had 

yielded in the past. Shear failure was largely localized in tight zones. Prominent shear failure 

zones extended from the upper right wall of the hole upward to the top boundary and from the 

lower left wall of the hole downward to the lower boundary. Figure 6C, D, and E shows the 

contours of cohesive, tensile, and frictional strengths, respectively. A less prominent shear failure 

zone was localized as if it extended away from the hole as a continuation of the prominent shear 

zones. Specifically, a less prominent shear zone extended from the upper right wall of the hole 

and downward and to the right until it met the right boundary. Another less prominent shear zone 

extended from the lower left wall of the hole and upward and to the left until it met the left 

boundary. Figure 6D shows that tensile failures occurred within the localized shear zones, but 

also extended from these zones, mostly in the direction perpendicular to the direction of tension. 

Figure 6F shows the proximity of areas of tension to zones that had yielded in tensile mode, 

indicating a potential for further tensile yielding with additional far-field shearing. 

 PFC2D will be used in the future to conduct these experiments and compare results with those 

of the FLAC models. Before proceeding, however, tests must be conducted to match particle 

contact and bond properties to elastic and strength properties of the FLAC continuum material. 

In the meantime, a preliminary experiment was run to examine capabilities. 

 A 4-m- (13-ft-) diameter hole was cut in a 12- by 12-m (39- by 39-ft) plate during the 

construction phase. Outside boundary walls were moved automatically as if in a servo-controlled 

test machine until the average stress on each wall was 6 MPa (870 psi). Next, the upper and 

lower walls were moved inward until the average stress was 205.6 MPa (29,820 psi). Average 

confining pressure was maintained at 6 MPa (870 psi). Figure 7 shows the expected system of 

diagonal cracks that intersected the hole from the upper left to the lower right. A companion 

fracture system appears to be developing at the lower left and upper right corners. These results 

are similar to results obtained by Fakhimi et al. (2002) in both their physical experiment and a 

numerical simulation with PFC2D.

 In a subsequent run of the model, vertical stress was only applied to 143.9 MPa (20,870 psi), 

while average stress on the sidewalls was maintained at 6 MPa (870 psi). At this stage, bond 

failures had not begun. Finally, the upper and lower walls were slowly rotated clockwise about 

their midpoints until displacement at the corners was 12.5 cm. Figure 8A shows a tensile crack 

extending from about 1:30 (as seen on a clock) upward and a little to the right. Failure zones of 

shear and tension begin around 4:00 and 10:00 and extend upward and to the right on the right 

side of the model and downward and to the left on the left side of the model. On the right side, 

the failure zone was not continuous, but a bridge formed between fracture zones where loading 

was able to continue (see figure 8B) 

Rectangular Opening Experiment 

 This experiment was designed to examine the effects of mining a rectangular opening under 

conditions of preexisting shear stress caused by far-field shear. First a model was constructed 

with FLAC without far-field shear stress as a control. Vertical and horizontal compressive 

stresses of 41.37 and 20.68 MPa (6,000 and 3,000 psi), respectively, were applied at the bound- 
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Figure 6.─Results of hole-in-a-plate experiment with shear stress applied 

to boundaries. A, Yield state of each element before application of 

boundary shear stress; B, yield state of each element after application of 

boundary shear stress; C, contours of cohesive strength showing location 

of cohesive softening; D, contours of tensile strength showing location of 

tensile softening; E, contours of friction angle showing location of friction 

softening; F, contours of minimum principal stress showing location of 

tensile zones. Boundary conditions shown in B apply also to C, D, E, and 

F.
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aries and initialized in every element. The strain 

softening constitutive law with the same softening 

functions used in the hole-in-a-plate problem 

(figure 5) was incorporated into the model. A 6.1-

by 4.3-m- (20- by 14-ft) opening was excavated in 

five stages to minimize the shock of removing 

confining forces suddenly. A nonlocal continuum 

model was not used because elements were small 

(7.62 by 7.62 cm [3 by 3 in]). 

 Figure 9 shows results of that model. Each 

stage of excavation produced a successively larger 

excavation, which is a reasonable approximation 

of a typical blasting sequence. Failure in shear 

extended from near the corner of each opening at 

a 45o angle to the roof and ribs, with the greater 

amount of failure extending into the ribs (figure 

9A). Cohesion and friction softening coincided 

with the zone of shear (figure 9B and D) and also 

indicated previous softening from earlier excavation stages of the same shape. Tensile failures extended from these shear failure zones, primarily 

Figure 7.─Hole-in-a-plate experiment with 

horizontal confining and vertical deviatoric 

stress showing bond breakage according to 

failure mode. 

Figure 8.─Particle bond breakage resulting 

from far-field shear in hole-in-a-plate experiment. A, Bond breakage by mode of failure; B, 

contact forces. 
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Figure 9.─Results of rectangular-opening model with no far-field application of 

shear stress. A, Yield state of each element; B, contours of cohesive strength 

showing location of cohesive softening; C, contours of tensile strength showing location of tensile softening; D, contours of friction angle showing location 

of friction softening; E, contours of minimum principal stress showing location 

of tensile zones. Boundary conditions shown in A also apply to B, C, D, and E
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Figure 10.─ Results of rectangular-opening FLAC model with far-field application of 

shear stress. A, Yield state of each element; B, contours of cohesive strength showing 

location of cohesive softening; C, contours of tensile strength showing location of 

tensile softening; D, contours of friction angle showing location of friction softening; E, 

contours of minimum principal stress showing location of tensile zones. Boundary 

conditions shown in A also apply to B, C, D, and E.
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above and below the openings, but not intersecting, as 

indicated in figure 9C. However, the minimum principal 

stress was tensile adjacent to the tensile failure zones, 

indicating the potential for further failure if more 

deviatoric stress were to be applied (figure 9E). 

 The model was rerun in FLAC with the same applied 

vertical and horizontal stresses. A shear stress of 13.79 

MPa (2,000 psi) was applied at the boundaries and 

initialized in every element before excavation. Figure 10 

shows results of the model. Instead of symmetrical shear 

zones at each corner of the opening, shear failure zones 

extended from opposite corners in roughly the same 

shape as appeared in the hole-in-a-plate model (figure 

10A). However, the shear zones did not extend as far 

from the opening, probably because the boundaries were 

farther away (18.3 m [60 ft]), and the amount of applied 

shear stress was lower than in the hole-in-a-plate model. 

Also, the shear zones seem more prominent in the rib 

rather than above and below the opening (figures 10A, 

B, and D). Tensile failure zones took off from the shear 

zones, running largely parallel with the opening (figure 

10C). Figure 10E shows tensile zones adjacent to tensile 

failure zones, suggesting the probable extension of 

tensile zones with further shear loading. 

 A PFC2D model of the rectangular opening was 

constructed without first matching particle and bond 

properties and bond strengths to the FLAC continuum 

material. Applied horizontal and vertical stresses were 

68.9 and 34.5 MPa (10,000 and 5,000 psi), respectively. 

The opening dimensions and distance to boundaries 

matched the FLAC model. 

 The left and right boundaries were rotated clockwise 

22 cm (8.66 in) maximum at the corners, at which point 

fracture patterns were well developed for the level of 

parallel bond strength used (200 MPa [29,000 psi] with 

a standard deviation of 0.5 MPa [73 psi]). Figure 11A

shows bond-breakage results of the PFC2D model. A tensile crack set originated near the upper 

left and lower right corners and extended diagonally at 45o to the roof line. These tensile cracks 

were absent in the FLAC model, but differences should be expected when boundary conditions, 

strengths, and stiffness of the material are not matched between FLAC and PFC2D models. 

Additional zones in which bonds broke in both tensile and shear modes appeared near the lower 

left and upper right corners and extended away from the opening just above horizontal on the left 

and below horizontal on the right. Moreover, within these zones, one can see possible en echelon 

Figure 11.─Results of PFC2D model 

with rectangular opening. A, Parallel 

bond breakage according to tensile 

and shear modes of failure; B, contact 

forces, both compressive and tensile. 
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distribution of bond breakage, though such formation is not clear. Given the small number of 

bond breakages directly above and below the opening, it is not hard to imagine further extension 

of the shear/tensile fractures angling over and below the openings from the existing shear/tensile 

crack set. Figure 11B shows contact forces. The location of tension and the contrast between 

much compressive force and little compressive force indicate the potential for shear/tensile crack 

extension above and below the opening. 

DISCUSSION 

 The foregoing experiments had a few minor deficiencies. The far-field boundaries of the 

hole-in-a-plate model were too close to the opening so that boundary effects around the hole 

were not eliminated. The PFC2D particle stiffnesses and bond strengths were not calibrated to 

FLAC models having selected elastic and strength properties so that model conditions would be 

similar. Far-field shear stresses were not applied in the same way as in the FLAC models. 

Therefore, the PFC2D model results only illustrate capabilities. 

 The PFC2D model results (figures 7 and 8) suggest that en echelon fracturing might be 

simulated, but careful tests must verify this suggestion. It appears from figure 8 that FLAC 

models are not likely to reflect distinct en echelon fractures, but rather will localize failure to a 

narrow band in which both shear and tensile failures occur. These bands can be considered either 

a coalescence of microcracks or regions of en echelon fractures. 

 Softening appears to be a reasonable way to represent fracturing with a FLAC model. 

However, one could argue that fractures could be better simulated if cohesion loss proceeded 

more quickly upon yielding—perhaps as quickly as the tension loss. 

 The presence of far-field shear ride caused preferential fracturing or yielding. Instead of the 

symmetrical yielding seen in figure 9, shear and tensile fracturing or yielding originated at two 

opposite corners of a rectangular opening instead of from all four corners. Similar localized shear 

zones appear both in the hole-in-a-plate model and the rectangular opening model, but the 

direction of prominent shear failure seemed to be affected by the shape of the rectangular 

opening when compared to shear failure around the circular opening. Examination of previous 

modeling results suggests that the applied horizontal-to-vertical stress ratio may also have an 

effect on the direction of prominent shear failure. 

CONCLUSIONS 

 Far-field shear ride causes failure or yielding in preferential directions. Fracturing is no 

longer symmetrical around an underground opening. The results of the model experiments may 

not always directly relate to en echelon fracturing, but relevant features are present, such as a 

fracture zone propagating over and under an opening at an acute angle to the surface. Therefore, 

the results are likely to be relevant to zones containing en echelon sets of fractures. The models 

suggest the presence of both tensile and shear fracturing, although the FLAC model suggests that 

those zones may be adjacent to each other around a rectangular opening. Shape of the opening 
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and direction of far-field major and minor principal stresses appear to affect the direction of 

prominent shear failure, but more tests need to be conducted to assess cause and effect 

accurately. 

REFERENCES 

Bazant, Z.P.,and G. Pijaudier-Cabot. 1987. Measurement of characteristic length of non-local 

continuum. Report 87-12/498m, Center for Concrete and Geomaterials, Northwestern 

University. 

Bazant, Z.P., and G. Pijaudier-Cabot. 1988. Non-local continuum damage, localization instability 

and convergence. J. Appl. Mech., V. 55, pp. 287-293. 

Diederichs, M.S. 2002. Stress-induced damage accumulation and implications for hard rock 

engineering. In Mining and Tunnelling Innovation and Opportunity, NARMS-TAC 2002, 

Hammah et al. (eds.). Toronto: University of Toronto, V. 1, pp. 3-12. 

Fakhimi, A., and C. Fairhurst. 1994. A model for the time-dependent behavior of rock. Int. J. 

Rock Mech. Min. Sci. & Geomech. Abstr., V. 31, No. 2, pp. 117-126. 

Fakhimi, A., F. Carvalho, T. Ishida, and J.F. Labuz. 2002. Simulation of failure around a circular 

opening in rock. Int. J. Rock Mech. Min. Sci., V. 39, No. 4, pp. 507-515.

Fairhurst, C., and N.G.W. Cook. 1966. The phenomenon of rock splitting parallel to the direction 

of maximum compression in the neighborhood of a surface. In Proceedings of the First Congress 

on the International Society of Rock Mechanics, (Lisbon, Portugal, Sept. 25-Oct 1, 1966). 

Lisbon, Portugal: Nat. Lab. of Civil Eng., V. 1, pp. 687-692. 

Itasca Consulting Group, Inc. (Minneapolis, MN). 1993. Fast Lagrangian Analysis of Continua 

(FLAC), User’s Manual. 

Itasca Consulting Group, Inc. (Minneapolis, MN). 1999. PFC2D Particle Flow Code in 2 

Dimensions, User’s Guide. 

Larson, M.K., C.L. Stewart, M.A. Stevenson, M.E. King, and S.P. Signer. 1995. A case study of 

a deformation mechanism around a two-entry gate road system involving probable timedependent behavior. In Proceedings of the Fourteenth International Conference on Ground 

Control in Mining, S. Peng (ed.) (Morgantown, WV, Aug 1-3, 1995). Morgantown, WV: West 

Virginia University, pp. 295-304. 

Larson, M.K., and H. Maleki. 1996. Geotechnical factors influencing a time-dependent 

deformation mechanism around an entry in a dipping seam. In Proceedings of the Fifteenth 

International Conference on Ground Control in Mining, Ozdemir, L., K. Hanna, K.Y. Haramy, 

and S. Peng (eds.), (Golden, CO, Aug 13-15, 1996). Golden, CO: Colorado School of Mines, pp. 

699-710. 
15

Larson, M.K.. 2003. Time-dependent deformation and shear strength along weakness planes in 

the roof of a coal mine. Ph.D. Thesis, University of Minnesota, 238 pp. 

Peng, S.S., and A.M.Johnson, 1972. Crack growth and faulting in cylindrical specimens of 

Chelmsford granite. Int. J. Rock Mech. Min. Sci., V. 9, pp. 37-86. 

Rice, J.R. 1976. The localization of plastic deformation. In Theoretical and Applied Mechanics.

W.T. Koiter (ed.). Amsterdam: North-Holland, pp. 202-220. 

Terrill, L.J. and J.D. VandeKraats. 1997. Case study of conditions observed during the removal 

of a highly fractured roof beam in bedded halite. In Proceedings, 16th Conference on Ground 

Control in Mining, S. Peng (ed.) (Morgantown, WV, Aug. 5-7, 1997). Morgantown, WV: West 

Virginia University, pp. 235.242. 

White B.G. 2002. Shear mechanism for mining-induced fractures applied to rock mechanics of 

coal mines. In Proceedings, 21st International Conference on Ground Control in Mining, S. 

Peng, C. Mark, A.W. Khair, and K. Heasley (eds.) (Morgantown, WV, Aug. 6-8, 2002). 

Morgantown, WV: West Virginia University, pp. 328-334. 

White, B., S. Iverson, and M. Larson. 2003. Shear origin of tension in excavation-induced 

fractures, In Proceedings for Soil and Rock America 2003 and 39th Rock Mechanics Symposium, 

P. J Culligan, H. H. Einstein, and A. J. Whittle (eds.) V. 1, pp. 909-916. 

White, B.G., M. Larson, and S.R. Iverson. Origin of mining-induced fractures through 

macroscale distortion. In press. Gulf Rocks 2004: Rock Mechanics Across Borders and 

Disciplines, 6th North American Rock Mechanics Symposium (Houston, TX, June 5-10, 2004). 

Zietlow, W.K., and J.F. Labuz. 1998. Measurement of the intrinsic process zone in rock using 

acoustic emission. Int. J. Rock Mech. Min. Sci., V. 35, No. 3, pp. 291-299.