Shear Origin of Tension in Excavation-Induced Fractures

Brian G. White

Steve Iverson

Mark Larson

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

ABSTRACT

The authors hypothesize that excavation-induced extension fractures are caused by elastic shearing displacement that

in turn causes tension oblique to a propagating shear zone. Such extension is manifested as tension on scales larger

than that of microcracks. En echelon fracture patterns are a common result. FLAC modeling confirmed that localized

tension is created near the corners of mine openings. In the model, tension was concentrated at the leading edge of

a simulated fracture in a pattern that could promote the formation of an en echelon fracture. Particle Flow Code

models confirm progressive formation of en echelon tensile failures with distance from an opening. The elastic

displacements and the resulting fractures facilitate reduction in applied load at the expense of shear deformation and

lateral dilation. Understanding the mechanics of fracture and deformation is vital for designing more effective ground

support practices, a major objective of ground control research being conducted at the Spokane Research Laboratory

of the National Institute for Occupational Safety and Health. 

1 INTRODUCTION

Excavation-induced extension fractures are common in both deep hard-rock mines and coal mines

and in shallow mines in weak rock. Such fractures

play a major role in roof falls, support failures, and

rock bursts. However, the mechanics of their

formation is not well understood despite a century of

consideration.

The mechanics of extension fracture formation

first received widespread attention during the

1960's. In one of a number of important papers from

that period, Fairhurst and Cook (1966) commented

that these fractures form parallel to the direction of

maximum compression and “represent the principal

mode of macroscopic fracture in brittle rock.” They

stated that “such failure may be explained on the

basis of the extension of Griffith flaws . . ., [which]

provides in general principle the most satisfactory

explanation of brittle rock failure.” Emphasis on the

formation of macroscopic excavation zone extension

fractures from extendingGriffithflaws has continued

to the present, despite no observational evidence for

such a mechanism (Lajtai et al., 1990) and the known

capability of several materials, such as glass, to fail
despite a lack of development of microcracks at

conditions near failure (Swanson, 1986). Several

other mechanisms for the formation of microcracks

have been proposed (e.g., Kemeny and Cook, 1991),

but the mechanical basis for the transition from

microcracks (microscopic to submicroscopic fractures) to macrofractures (typically decimeter- to

meter-long fractures) has not been clearly identified.

Fairhurst and Cook (1966) also suggested that

extension microfractures first form an “incipient

cleavage” and that the cleavage develops into macrofractures through macroscale buckling. This idea

appears to have captured little attention. Instead, the

emphasis has remained on the development of

macrofractures as individual entities that grow from

tension generated on a microscale at fracture tips.

In contrast to these prevailing ideas, White (2002)

proposed that fracture initiation and elongation are

caused by elastic displacement involving combined

shear and dilation. According to White, these

displacements create macroscale regions of tensile

stress, suggesting that Fairhurst and Cook were

fundamentally correct in proposing that macrofractures are ultimately the result of macromechanics.

However, in White’s proposal, the requisite macromechanics primarily involve shearing displacement

ratherthan buckling, and excavation-induced macrofractures are both initiated by and propagate from

such displacement. This paper expands upon this

hypothesis to describe the formation of fractures.

Although this paper emphasizes the formation of

fractures in underground hard-rock mines, the

mechanism described should be active in all excavation settings that cause localized strain concentrations of sufficient magnitude to cause fracturing.

Since clay has often been used in laboratory investigations of fractures (e.g., Cloos, 1955), soil exposed in trenches and soil cuts may also initially fail

through fracturing. Hence, the mechanism described

here is applicable to trenches, roadcuts, and pit

walls, as well as excavation damage zones involving

roofs, ribs, and pillars. Other rock behavior that may

also be directly related to fracture zones formed

through this process include strain-type rock bursts,

destressing by blasting, squeeze of mine openings,

coal mine gob development and subsidence, and

major mine seismicity.

A well-developed understanding of the mechanics

of fracturing and deformation is vital for designing

more effective ground support practices and for

developing and carrying out more effective research

programs directed toward this end. Reduction of rock

failure injuries is a major objective of ground control

research currently being conducted at the Spokane

Research Laboratory of the National Institute for

Occupational Safety and Health (NIOSH).

2 PRIMARY AND SECONDARY FRACTURES

Carter et al. (1991) categorized extension fractures

that form in the vicinity of circular openings as either

primary or remote. “Primary” fractures form close to

the opening and include fractures that lie parallel to

the edges of the opening, which is the fracture type

considered by Fairhurst and Cook (1966). “Remote”

fractures form at some distance from circular openings and do not trace the shape of the opening, they

apparently result from a larger-scale change in

conditions caused by the presence of the opening.

A series of papers have documented themechanics

of formation of remote fractures about circular

openings. Prior to the widespread use of continuum

modeling, Hoek (1964) used photoelastic film to

demonstrate the presence of remote areas of tension

about a circular opening. Hoek and Brown (1980)

found that an isolated “tension fracture” would form

in each region of tension. Carter et al. (1991)

successfully modeled these areas of tension using

ANSYS, a finite-element program created by

Swanson Analysis Systems, Inc., Canonsburg, PA.1

However, in laboratory demonstrations of fracture

development, Carter et al. noted that each initial

remote fracture was succeeded by a second fracture

parallel to and offset from the previous fracture in an

en echelon pattern. Since en echelon fractures are

typically interpreted as indicating the presence of

shearing displacement, these patterns suggest that

shearing displacement played a role in development

of the fractures. 

Fakhimi et al. (2002) repeated this exercise with

circular holes using Itasca Consulting Group’s

Particle Flow Code (PFC) modeling program and

1The mention of specific products and manufacturers

does not imply endorsement by the National Institute

for Occupational Safety and Health
testing the equivalent laboratory specimens under

confining pressure. In the test, narrow faults formed

at an oblique angle to the direction of greatest stress,

confirming that shear was involved in deformation

at remote sites. The PFC model showed a narrow

zone of abrupt change in displacement trajectories

corresponding closely to the line of faulting in the

sample. Fakhimi et al. noted that displacement along

this zone involved shear. Hence, both continuum

and PFC modeling and laboratory experience

confirm the involvement of shearing displacement

and macroscopic tension in the development of

remote fractures about circular openings. 

3 EN ECHELON EXTENSION FRACTURE

ZONES

Observations in mines (White, 2002), in the

laboratory (Peng and Johnson, 1972; Carter et al.,

1991), and in geologic field studies (Segall and

Pollard, 1983) indicate that extension fractures are

commonly arranged in en echelon sets. White

(2002) described the site of a face strain rock burst

in a hard-rock mine and called attention to closely

spaced fractures concentrated at the periphery of the

burst cavity. White concluded that these fractures

were arranged in an en echelon distribution, with

each fracture extending only part way across the

face. This pattern contrasted with that proposed by

Fairhurst and Cook (1966), that fractures should

extend entirely across the face. White noted the

similarity of the fractures to ones seen in laboratory

samples when sample ends were restrained against

expansion. He also noted that the fractures

resembled those involved in hourglassing of pillars

(as inferred from Fairhurst and Cook, 1966) and in

roof failures in a western U.S. longwall coal mine.

Here, we note that en echelon fracture zones are also

common geologic structures, both in the form of

joints or joint zones and as the host structures for

gash veins.

Field and laboratory observations emphasize that

en echelon fracture zones are characterized by shearing displacement having a consistent direction with

respect to the pattern of fractures. For example, rock

bolts are systematically bent where they cross these

fractures zones (White, 2002), geologic markers are

displaced (White and Whyatt, 19992), and zones of

en echelon fractures in laboratory samples are activated as faults that cut across individual fractures

(Peng and Johnson, 1972). In an rare opportunity to

examine roof fractures along the length of a crosscut,

Terrill and VandelKraats (1997) and Francke et al.

(1997) identified en echelon fractures that were

integral to faults that extended upward toward the

center of the opening from opposite edges of the

roof. “Shear ruptures,” which are mining-induced

faults documented in South African gold mines (Gay

and Ortlepp, 1979), also involve extension fractures

distributed en echelon along faults that have the

usual orientation with respect to the sense of displacement on the fault. We have seen numerous

examples of brecciation, comminution, and faulting

in both mining-induced en echelon fracture zones in

the deep mines of the Coeur d’Alene Mining District

and in geologic joint zones, supporting the view that

shearing is fundamental to the mechanics of formation and function of these fracture zones.

Field observations suggest that the fracture zones

are probably initiated near the corners of rectangular

mine openings. Continuum models consistently

identify regions of concentrated normal and shear

stress (Hoek and Brown, 1980) and high extension

strain (Stacey, 1981) at these locations. The

additional fractures that define the fracture zone

evidently form in succession within a propagating,

oblique zone of high shear strain that extends

progressively deeper and away from the opening.

These observations imply that shearing is involved in

the formation of primary as well as remote fractures.

The interpretation that shear is involved in the

formation of en echelon fractures suggests that the

fractures somehow resulted from distortion that takes

place prior to fracturing. We note that simple shear

causes extension between two opposite corners of

deformed reference rectangles, or parallelograms.

Furthermore, such extension increases continuously

as shearing displacement increases. Stacey (1981)

noted that high extension strain favors rock failure,

although he did not provide an explanation for why

2White and Whyatt (1999) noted that zones of closely

spaced mining-induced fractures often show evidence

of shearing as manifested in offsets in geologic markers

such as veins. These fracture zones are now interpreted

as being composed of en echelon fractures.
fractures formed. For remote fractures, extension

(and shear) apparently proceeds until tension is generated. Since primary fractures also form en echelon

zones, it is reasonable to speculate that these also

result from local tension generated by shear.

4 TENSILE ORIGIN OF PRIMARY

FRACTURES

Conventional continuum models typically use

fairly large modeling elements that yield consistent,

reasonable results that satisfy our major interests.

But, unlike models of remote fractures about circular openings, continuum models of rectangular

openings generally do not identify tensile regions.

On the chance that small areas of tension may be

concealed by usual models having coarse element

meshes, we modeled progressively narrower elements near the corner of a rectangular opening using

the computer program FLAC (Fast Langrangian

Analysis of Continua) (Itasca, 1993). 

We first constructed a continuum model and

initialized a mesh with a 2:1 ratio of horizontal to

vertical stress at the center of the grid. Gravity

effects were accounted for. For convenience, the

stress levels were set unrealistically high (414 MPa

horizontal compressive stress and 207 MPa vertical

compressive stress [60,000 and 30,000 psi, respectively]), but only linear elastic behavior was

allowed. Therefore, significant ground distortion

was likely, despite an absence of strain softening

from the microfracturing that characterizes deformation in actual rock. We removed zones to form a

rectangular opening 6.1 m wide by 4.3 m high ( 20

by 14 ft) at the center of the grid and monitored the

effects of excavation. Boundaries were placed 18 m

(60 ft) from the opening to minimize their influence

near the opening. To see if we could find tension

that would otherwise be hidden, the grid size was

kept small; zone size was 7.6 m wide by 7.6 cm high

(3 by 3 in). However, for 0.6 m (2 ft) above the

opening, zone height was reduced to 1.9 cm (0.75

in). 

Figure 1A shows principal stresses as hatch

marks in the upper left roof of the opening. Two

areas of tension are identified; these areas are shown

more clearly in a contour plot of least principal

stress (figure 1B). For clarity, the tensile areas are

traced by lines drawn freehand. The location with

the greatest tensile stress (about 35% of the applied

horizontal stress of 207 MPa (30,000 psi) is located

in the roof about 13 cm (5 in) from the corner and

close to the skin of the opening. If tensile stress at

this location exceeds tensile strength, formation of a

tension fracture is guaranteed. In our example, the

calculated tension exceeds the tensile strength of all

rock types. Hence, an origin of primary fractures

from physical tension is a reasonable interpretation.

In another FLAC simulation, a “glued” interface

(in which opposite nodes were not allowed to

separate from each other) traversed the model 7.6 cm

(3 in) above the opening. Thin elements were placed

below the interface and above the horizon of the

opening, and the same internal stresses and boundary

conditions were applied as in the example above.

Figure 1C shows contours of least principal stress

and the location of the glued interface. This view is

enlarged in comparison to figure 1B so that the rib is

located 6.4 cm (2.5 in) to the left of the edge of the

plot. Similar tensile zones are present to compare to

the case of no interface, except that the right tensile

zone is slightly higher. We suggest this occurred because we initialized the interface with no normal

stress. Even so, the result is close enough to the continuum case to consider them practically equivalent.

The interface was then “unglued” from 7.6 to 23

cm (3 to 9 in) to the right of the rib line to simulate

a fracture parallel to the edge of the opening. Figure

1D shows the contours of minimum principal stress

along with the location of the unglued portion of the

interface (shown by x’s connected by lines). Ungluing the interface caused the tensile zone to extend

further above and to the right. The greatest tensile

stress above the interface is 1.7% of the maximum

applied stress, or 5 MPa (720 psi). Figure 1E shows

results with the unglued portion extending from 7.5

to 53 cm (3 to 21 in) to the right of the rib and

indicates that the area of tension expands upward and

advances to the right as the simulated fracture is

extended. The maximum tensile stress above and to

the right of the fracture was about 8% of the

maximum applied stress, or 30 MPa (5000 psi). This

indicates that the likelihood of an en echelon fracture

forming increases as the simulated fracture grows.
Figure 2A

Figure 1.—Stages in crack formation. A, Top left, Principal stresses in the upper left roof of the opening shown as hatch

marks; B, top right, minimum principal stress. Tensile regions are highlighted by hand. The region of greatest tension

is nearest the corner; C, center left, “glued” interface (in which opposite nodes were not allowed to separate from each

other) 7.6 cm (3 in) above the opening. Interface is progressively unglued in subsequent figures; D, center right,

interface “unglued” from 7.6 to 23 cm (3 to 9 in) to the right of the rib line to simulate a fracture parallel to the edge of

the opening; E, bottom left, Interface unglued from 7.5 to 53 cm (3 to 21 in) to the right of the rib. Note that region of

tension expands upward as the simulated fracture is extended, favoring formation of an en echelon fracture.
We also duplicated this exercise with PFC2D

(Itasca, 1999). A test was designed to simulate conditions along one side of a rectangular mine opening

using the biaxial test simulation provided by Itasca

(Itasca, 1999). To simulate a rock mass, circular

particles were generated in a tightly packed assemblage and bonded together using parallel bonds.

These bonds acted like glue and had stiffness and

strength properties in both normal and shear. Table

1 lists the important input parameters used in the

simulation. 

Table 1. PFC Input parameters. 

Input Value

Particle radius (minimum,

maximum)

3.00e-4, 4.98e-4 m

Mean particle density 2360 kg/m3

Bond strength 200 MPa

Standard deviation 0.5e6 MPa

Modulus of elasticity 49e9 MPa

Confining pressure 1 MPa

Deviator stress application rate 0.2 m/sec

Block width 80.e-3 m

Block height 150.e-3 m

Notch width 40.e-3 m

Notch height 70.e-3 m

Walls were used to constrain the margins.

Confining stress was applied to all margins except

part of one side, which was left constrained by

negligible confining stress so as to simulate the margin and corner of a mine opening. A deviator stress

was then applied to the upper and lower walls.

The block compressed elasticallyuntil the particle

bonds began to fail. The response of the block to the

applied deviator stress was then monitored from the

progression of bond failures (figure 2) and from a

graphical representation of deviatory stress versus

strain (figure 3). The elasticity compared well with

the input modulus. Bonds between particles failed

either by tension or shear, but tensile failures

dominated.

Initial bond failures were located just below the

corner and near the free vertical surface (figure 2).

Failuresthen progressed diagonallydownward about

30° from the free surface in a series of four elongatFigure 2.—Failed bonds at an advanced stage of block

failure. Tensile failures are gray, shear failures black.

Elongated en echelon clusters of tensile failures progressed from the upper left to the center of the block and

finally merged into a continuous shear zone. Failures in

the right half of the block progressed upward from the

lower right corner and resulted from corner effects not

related to the en echelon progression on the left. 

ed clusters of tensile failures arranged in an en

echelon pattern. Discrete, individual fractures were

not immediately evident, possibly reflecting a

limitation of the method or of the input parameters

used. In figure 2, the block is shown at a point in the

simulation where extensive failure had occurred and

where part of each individual cluster of tensile

failures had been knitted together into a continuous

shear zone. Two of the en echelon clusters near the

sidewall ultimately merged into one discrete fracture

that then propagated some distance below the

corner. A deeper cluster also created a long discrete

fracture. Failures in the right half of the block

propagated upward from the lower right corner.

These failures were attributed to corner effects not

directly related to the failures in the left half of the

block.

Figure 3 shows deviator stress and confining

pressure on the block versus sample strain during

the simulation. The initial steep slope indicates 
Figure 3.—Deviatory stress-strain diagram showing initial

elastic response and ultimate failure.

Figure 4.—Distribution of normal stresses after extensive

deformation (black) showing destressed caused by

fracture m echanism. 

elastic compression, which is followed by instability

and eventual failure. The lower line indicates the

slight increase in confining pressure as the side

walls locked as confining pressure was applied and

deviator stress added.

In a separate plot showing the distribution of

normal stresses after extensive deformation (figure

4), it is evident that the region adjacent to the

opening became substantially de-stressed as a result

of displacement involved with the fracturing. Destressing and dilation of rock about openings as a

result of fracturing in the excavation deformation

zone are well known. Here the cause of de-stressing

and dilation is identified as the fracture-forming

mechanism; that is, shearing displacement and the

resulting fractures facilitated reduction in applied

load at the expense of shear deformation and lateral

dilation. White (2002) pointed out that such

behavior may have major significance with respect

to ground support practices involving placement of

rock bolts. 

Both FLAC and PFC modeling identified an

initial tensile region near the corner and close to the

surface of simulated, rectangular mine openings.

FLAC suggested a mechanical reason for initiation

of subsequent en echelon fractures as a result of

redistribution of tension, and PFC verified the progression of en echelon fractures along a developing

shear zone. The FLAC model indicated that the

initial deformation of the rock and the appearance of

tension did not involve the creation of microfractures, indicating that these are not essential elements

of rock fracturing. However, microfractures would

soften rock in areas of high shear strain and thereby

concentrate strain and promote the formation of

additional macrofractures at a lower level of stress

than was used in the FLAC models.

5 SUMMARY

Based on these results, the following conclusions

were reached.

• Elastic rock deformation about excavations

generates local regions of tension.

• Tensile areas become sites of individual fractures,

which must, therefore, be caused substantially by

this tension.

• Tension is caused by elastic shearing

displacement, which results in extension oblique

to the plane of shearing.

• Fracture propagation redistributes tension in such

a way as to cause the formation of en echelon

fractures.

• Microcracks are not essential for the development

of macrofractures, although microcracks would

promote further deformation and therebypromote

macrofracturing.

• Elastic displacement and the resulting fractures

facilitate reduction in applied load at the expense
of shear deformation and lateral dilation, which has

ground support implications.

• The mechanism described is probably active

about excavations in both soil and rock. 

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