A Tensile Model for the Interpretation of Microseismic Events near Underground Openings

Abstract

For small-scale microseismic events, the source sizes provided by shear models are unrealistically large when compared to visual observations of rock fractures near underground openings. A detailed analysis of the energy components in data from a mine-by experiment and from some mines showed that there is a depletion of S-wave energy for events close to the excavations, indicating that tensile cracking is the dominant mechanism in these microseismic events.
In the present study, a method is proposed to estimate the fracture size from microseismic measurements. The method assumes tensile cracking as the dominant fracture mechanism for brittle rocks under compressive loads and relates the fracture size to the measured microseismic energy. With the proposed method, more meaningful physical fracture sizes can be obtained and this is demonstrated by an example on data from an underground excavation with detailed, high-quality microseismic records.

Full text

International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–1145
Quantification of rock mass damage in underground excavations
from microseismic event monitoring
M. Cai
a,
*, P.K. Kaiser
a
, C.D. Martin
b
a
Geomechanics Research Centre, Mirarco Inc., Laurentian University, Sudbury, Ontario, Canada P3E 2C6
b
Department of Civil & Environmental Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
Accepted 19 October 2001
Abstract
Rock mass damage assessment is required for many applications in rock engineering practice including support design,
contamination transport control, stope design, amongst others. While various methods such as displacement measurement, seismic
refraction, and direct observation using borehole camera have been used, relatively few efforts have been made to use microseismic
monitoring to quantify the rock mass damage. From laboratory tests, it is well known that microseismic events are indicators of
fracturing or rock damage as the rock mass is brought to failure at high stress. By capturing the microseismic events, underground
excavation induced rock mass degradation or damage can be located but can the amount of damage in terms of changes to strength
or deformation properties be measured?
In the present study, a method of characterizing rock mass damage near excavations based on microseismic event monitoring is
developed and a damage-driven numerical model is presented that takes the microseismic data as input to determine the damage
state described by fracture density. The approach is built on the discovery that a realistic crack size corresponding to a seismic event
can be established by applying a tensile cracking model instead of the traditional shear model, commonly used in earthquake
analysis. The rock mass is softened by the introduction of cracks and this is simulated by a micro-mechanics based constitutive
model. The material property input for the model are Young’s modulus, Poisson’s ratio of the intact rock, and information obtained
from the monitoring of microseismic events such as the location and the source size of each event calculated from source parameters.
Using data from the Atomic Energy of Canada Limited Mine-by Experiment, this model has been verified by investigating
the linkage between microseismicity, rock mass damage and ground deformation. It is found that when damage related softening
based on microseismic data is considered, predicted rock mass displacements are in good agreement with extensometer
measurements. r2002 Elsevier Science Ltd. All rights reserved.
1. Introduction
The initiation, accumulation and growth of stress-
induced cracks or fractures in rock causes rock or rock
mass damage. It is well known that rocks loaded in
testing machines and rock masses that are stressed near
underground excavations emit detectable acoustic or
seismic signals, and seismic monitoring techniques have
been used to locate damage in rock engineering practice
[1–3]. By incorporating source location and source
parameter estimates, it is now possible to visualize the
development of microseismic events in 3D space [4].
Sophisticated seismic monitoring systems can today
accurately record the ground motions caused by the
deformations at a seismic source and such systems are
now found at many mines, particularly in deep mines
[5,6]. Seismic signals emanating from earthquakes have
been studied for decades by seismologists [7]. More
recently, this accumulated knowledge has been applied
to study mining induced seismicity [8]. The nuclear
waste industry has carried out several large-scale in situ
experiments over the past 15 years to assess the
excavation disturbed zone (EDZ) or extent of fracturing
that forms around openings in brittle rocks [9]. Two of
these more recent experiments (Atomic Energy of
Canada Limited (AECL’s) Mine-by Experiment at the
Underground Research Laboratory (URL) [10] and
SKB’s Zedex Experiment [11]) used microseismic
monitoring to quantify this fracturing. Since the seismic
*Corresponding author. Tel.: +1-705-675-1151; fax: +1-705-675-
4838.
E-mail address: mcai@nickel.laurentian.ca (M. Cai).
1365-1609/01/$ - see front matter r2002 Elsevier Science Ltd. All rights reserved.
PII: S 1365-1609(01)00068-5

events are closely related to the damage or fracturing of
the rock, excavation induced rock mass degradation or
damage can thus be measured rather than predicted [12].
Based on these seismic monitoring results, it is possible
to develop a damage-driven numerical model to follow
the rock mass degradation process. Damage-driven
models are models where the material characteristics
are gradually changed as more damage information
becomes available. By taking the current state of rock
mass damage into account, it is possible to predict with
numerical models the actual stress distribution around
the excavation. Furthermore, it is possible to forecast
subsequent seismically active zones. Based on such
numerical analyses tracking the degradation process, it
is possible to make sound engineering judgment and to
develop proper ground control measures.
The location of the seismic event front is directly
related to the current active excavation face and to zones
of failing ground where the stress exceeds the rock
strength and the rock is deformed passing yield limit.
With focused seismic systems, it is possible to accurately
locate seismic source on the order of o0.5 m [13]. This is
sufficient for practical purpose when the dimension and
the size of damage zones around underground excava-
tions used in civil and mining engineering are consid-
ered. However, the source dimensions given by
traditional source models, which are based on shear
failure models [14,15], are unrealistically large when
compared to the size of visually detectable cracks or
fractures near excavations. In situ observations of rock
mass damage do not agree with source sizes calculated
from these models [16]. Contrary to natural earthquakes
in which the rock mass failure is mainly attributed to
slip along pre-existing faults, stress-induced rock mass
fracture process near underground openings is at least in
part governed by extension cracking [16,17]. We recently
proposed a model based on tensile fracturing mechan-
ism and energy conservation consideration to estimate
the source dimension of microseismic events near
excavation walls [16]. The source dimension estimated
from the proposed model is more in keeping with field
observations and has lead to the development of the
damage-driven numerical model presented here which
uses seismic data to quantify damage and its effect on
the rock’s deformation properties.
In conventional damage models, the damage is
represented in the form of effective stress [18]. A damage
law, which describes the variation of damage parameters
relative to the change of stress or strain imposed on the
material, needs to be defined for such models but it is
usually a difficult task to find suitable damage laws for
rock masses under complex loading conditions. In a
damage-driven model, the damage is measured rather
than predicted and the consequence of rock mass
damage (e.g., tunnel convergence) is tracked. For
example, we can operate microseismic systems to
measure the microseismic activity, use appropriate
source models to determine the damage parameters,
and then take the damage parameters as input in
calculations to obtain stress or displacement pattern.
This process is interactive and the nonlinear response of
rocks can be simulated by an integrated modeling
approach.
At low in situ stress conditions, the failure of rocks is
often controlled by persistence natural fractures or
joints. As the in situ stress magnitude increases, natural
fractures becomes clamped and failure of rocks is then
increasingly dominated by new stress-induced fractures,
frequently growing parallel to the boundary of under-
ground openings [19]. This is one of the most obvious
characteristics of damage near excavations in hard
rocks. The stress-induced fractures are primarily parallel
to the maximum principal stress around the openings.
For example, in deep underground mines in South
Africa, where the vertical in situ stress is much higher
Stres s-ind uced f rac tur es
(a)
(b) (c)
Fig. 1. Stress-induced fracturing near underground openings in a high
stress environment. The fractures are parallel to the sidewalls because
the major principal stress is parallel to the surface: (a) schematic; (b)
field observation at URL showing fractures in the v-notch; (c) field
observation at URL showing fractures in the sidewall (Photos courtesy
AECL).
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–11451136

than the horizontal stress, fractures parallel to the
sidewalls are commonly observed (Fig. 1a). At the URL
(Fig. 1b and c), surface parallel fractures are encoun-
tered near the notch as well as on the flat sidewalls. As a
result, the rock mass is subjected to directional damage
and the material properties of the damaged rock are
anisotropic in such cases.
In the present study, a method to characterize the
rock mass damage based on microseismic monitoring is
developed and a damage-driven numerical model for
rock mass behavior simulation is presented. Softening of
the rock mass due to fracturing is considered by a
constitutive model based on micro-mechanics. The
damage-driven model takes the microseismic monitoring
information as inputs to determine the damage state
(fracture density) of the rock mass and the resulting
anisotropic softening. The model has been implemented
into FLAC, and data from the AECL’s Mine-by
Expriment tunnel has been used to validate the model.
It is found that when softening based on microseismic
data is considered, better predictions of radial deforma-
tion measured by extensometers can be achieved.
2. Microseismicity and rock damage
2.1. Brittle failure of rocks and microseismicity
Fault slips, rock fracturing and blasting cause
straining and displacement of the failing rocks at high
velocity and acceleration. The released energy moves
through the rocks as strain waves which can be recorded
by seismic monitoring systems. Large seismic events are
usually caused by fault slip and microseismic events
caused by extensile rock fracturing are characterized by
popping sounds and normally are not associated with
violent features. Fault slip produces both p-wave and s-
wave, with the amplitude of the s-wave being greater
than that of the p-wave [20]. On the other hand,
extensile rock fracturing produces predominantly p-
waves [21]. The focal mechanisms related to these
microseismic events are different from that of natural
earthquakes.
The failure of brittle rocks in the laboratory has been
extensively studied [22,14,23–25]. Two characteristic
stress levels are identified: (1) crack initiation at stress
levels of approximately 0.3–0.5 times the peak uniaxial
load [14,23]; (2) onset of fracture coalescence at stress
levels of approximately 0.7–0.8 times the peak strength
[24,25]. The in situ damage initiation threshold for the
URL Mine-by experimental tunnel is approximated by a
constant-deviatoric stress criterion which is about 1/3 of
the unconfined compressive strength of the rock [26]. It
is seen from these experimental investigations that the
fracture formed under stable conditions are mainly
mode-I extension fractures, formed parallel or sub-
parallel to the major principal stress. These
features must be considered when processing and
interpreting microseismic data recorded near under-
ground openings.
Diederichs [17] used the particle flow code (PFC) [27]
to explore the damage initiation process in simulated
samples of Lac du Bonnet granite. It was demonstrated
that despite high applied confining stress of up to
5 MPa, internal tension (perpendicular to the direction
of compressive stress) in excess of 6 MPa was locally
observed when the maximum compressive stress applied
reached 100 MPa [19]. This simulation provides clear
evidence for the underlying process of tensile failure in a
highly confined state.
2.2. Microseismic events at AECL’s Mine-by Experiment
The main objective of the Mine-by Experiment was to
study processes involved in progressive failure of brittle
rock and the development of excavation-induced da-
mage around underground openings. Rock mass beha-
vior and damage developments were monitored around
a 3.5 m diameter test tunnel excavated parallel to s2
(Fig. 2), using a non-explosive technique by parallel hole
drilling. Extensive state-of-the-art geomechanical and
geophysical instruments, including extensometers, con-
vergence arrays, triaxial strain cells and an acoustic
emission/microseismic (AE/MS) monitoring systems,
were installed prior to the start of excavation to monitor
the complete mechanical response of the rock mass
surrounding the tunnel. The details of the project are
presented in an extensive report by Read and Martin
[28].
Microseismic
Accelerometer
Test
Tunnel
Room
405
Room
413
Borehole
4.6-m-diameter
Shaft
Room 409
Scale
5 m
60
11
45 MPa
In Situ
Stress
Fig. 2. Location of the microseismic triaxial accelerometers distrib-
uted around the 3.5-m-diameter test tunnel at URL [28].
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–1145 1137

An array of 16 triaxial accelerometers was installed to
monitor excavation-induced seismicity near the advan-
cing face (see Fig. 2). The accelerometers, with a
frequency response from 50 Hz to 10 kHz (73 dB), were
grouted in place at the end of diamond-drilled bore-
holes. The array was designed for focal sphere coverage
and a source location accuracy of about 70.25 m near
the center of the tunnel. The function of the system was
to evaluate the physics of fracturing associated with the
development of a damaged zone around the tunnel. The
sequencing of the construction schedule for the test
tunnel provided about 12 h of quiet time for monitoring
after the initial perimeter drilling and about 12 h of quiet
time for monitoring after mechanical breaking of the
rock stub at the tunnel face. Over 25,000 events were
detected and some 3500 events (or 14%) were source
located [10]. Most microseismic events clustered in the
areas where spalling eventually occurred from a v-
shaped notch (Fig. 1b). The difference in event numbers
in the roof and floor was attributed to the confining
pressure provided by the weight of the tunnel muck in
the floor (Fig. 3). Acoustic emissions (AE) were also
recorded in one sidewall (Fig. 3); the same event
distribution was assigned to the opposite side resulting
in 390 AE events. AE events are very small seismic
events and only the locations of the events are available
(no source parameters). It is therefore impossible to
relate the AE events to fracture sizes and only the
microseismic events recorded by the accelerometer array
are considered in the source parameter study.
To estimate the rock mass damage from the
microseismic measurements, a 3.5-m thick slice (ap-
proximately one tunnel diameter long between chainage
21.03 and 24.59 m) was chosen for analysis. 804 seismic
event source centers are located in this region
(Fig. 3) and the radiated seismic energy ranges from
10
6
to 101J.
It is observed from the microseismic monitoring that
almost all events were recorded in the regions of
maximum tangential compression stress, not in the
sidewall where global tensile stress is expected. As has
been demonstrated by numerical model simulation
[19,17], local tensile stresses perpendicular to the
maximum compressive stress can be generated, indicat-
ing a tensile cracking mechanism for these microseismic
events in a globally compressive stress field.
2.3. Interpretation of microseismic data
Data provided by modern microseismic systems offer
extensive information about the location and mode of
failure. Microseismic event locations identify seismically
active regions and microseismic parameters provide
insight into the magnitude, the shape, the deformation,
the energy released and the stress change of the events
within that region.
For the purpose of damage characterization, it is
necessary to obtain the location and the size of the
source. With this input, it is then possible to calculate
the fracture or crack density, which in turn can be used
to describe the softening of the rock mass (lowering of
the deformation moduli due to fractures). In the
following, it is assumed that there is a unique associa-
tion between a microseismic event and the fracture
dimension. Once the seismic source dimension
or a fracture length is obtained, the fracture density
can be estimated if it is further assumed that the
fractures are parallel to the local maximum stress
direction.
Traditionally, the interpretation of the small-scale
microseismic events is based on earthquake seismology
[29,30,15], assuming that the fractures form by shear slip
[39,21]. The source dimension defined by the shears-slip
model is given by [20]
r0¼Kcb0
2pfc
;ð1Þ
where Kcis a constant depending on the source model,
b0is the s-wave velocity in the source area and fcis the
corner frequency of the s-wave. For Brune’s [29] source
model, only s-waves are considered and the constant Kc
is set equal to 2.34, a constant that is independent of the
angle of observation. The radii given from Brune’s
model for the URL microseismic data vary from 0.21 to
2.69 m and the diameter distribution is shown to scale in
Fig. 4. These fractures would not form in the cross
MS events
AE events
Notch
R=1.75m
Fig. 3. Locations of AE/MS events.
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–11451138

sectional plane but rather in a plane perpendicular to
the cross-section plane and parallel or sub-parallel to the
excavation boundary. According to a shear model, the
fractures should be aligned in the maximum shear stress
direction and then should be inclined to the tunnel wall,
and in many cases should intersect the tunnel wall. It
can be seen from the figures that the source dimensions
are very large relative to the excavation size. Many large
deep seated events are found in areas of little visual
damage. Hence, this image of damage is inconsistent
with visual observation of rock mass damage. In other
words, the source sizes provided by the conventional
shear models [29,15] are unrealistically large [16,20].
Detailed analysis of the energy components at the
URL and some mine openings showed that there is a
depletion of s-wave energy, indicating that tensile
fracturing is dominant in small-scale microseismic
events. Hence, a tensile model was developed for the
interpretation of microseismic events near underground
openings [16]. The method assumes tensile fracturing as
the dominant fracture mechanism for brittle rocks under
compressive loading and relates the fracture size to the
measured microseismic energy. This model implies that
the measured seismic energy is a portion of the total
radiated energy and this energy component is equal to
the difference between the elastic strain energy change
and the surface energy. The elastic strain energy is
calculated from the model by putting a flat crack in an
infinite solid under a uniform far-field stress. It is further
assumed that the stress on the crack is zero after
fracturing such that the driving tensile cracking stress is
equal to the far-field confining stress. The crack size
estimated from this model depends on the surface energy
and on the normal stress at the point of crack formation.
The derivation can be found in [16] and the resulting
source size equation is:
8ð1n2Þs2
n
3Ea3þ2pgsa2þE0¼0;ð2Þ
where snis the stress normal to the crack, Eand nare
Young’s modulus and Poisson’s ratio of the rock
respectively, ais the half-length of the crack, gsis the
specific surface energy, and E0is the energy imbalance.
This approach led to more realistic source sizes when
compared to field observations, than those determined
by traditional shear slip models. Assuming seismic
efficiency of 1%, a factor which takes into account the
energy loss due to propagation, the distribution of
fracture radii is shown in Fig. 5. The fracture sizes are
reasonably sized as there is a good visual agreement of
the extent of event clustering in the notch region. Again,
these fractures are not oriented in the cross-section plane
but, according to the model, are parallel to the major
principal stresses at the event locations. This direction is
more realistic than the direction in the maximum shear
stress direction for the shear-slip model, which are not
supported by field observation. An image of the oriented
fracture distribution from the tensile model is presented
in Fig. 6. Here, the fractures are oriented in the direction
of maximum principal stresses. The few large fractures
are attributed to the fact that the event centers are very
R=1.75m
Fig. 4. Fracture size distribution from Brune’s model. Sources are
plotted to scale as disks rotated into the drawing plane (perpendicular
to the actual source) [16].
R=1.75m
Fig. 5. Fracture sizes from the tensile model, shown as circles rotated
into the cross-section plane.
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–1145 1139

close to the zero stress contour line (shown in Fig. 6 as a
dashed line).
Since not all events were recorded, the actual crack
density is much higher. For the purpose of damage
modeling, it was assumed that damage is proportional
to the number and size distribution of the recorded
events. This fracture size distribution constitutes the
most important part of the damage-driven numerical
models as it allows to define the rock mass damage
parameters such as fracture density, crack tensor, and
cluster index [12]. By combining the field microseismic
monitoring data with this new quantitative means of
characterizing rock mass damage it is now possible to
drive the damage model in an active manner. Because
the cracking happens in a preferred direction, the
resulting rock mass behavior is anisotropic and an
anisotropic softening model which takes the input
parameters derived from microseismic monitoring data
into account is needed to properly simulate the
degradation process near excavations.
3. Softening of rock masses due to damage
3.1. Micro-mechanics based constitutive model of
damaged rock
The evaluation of the overall elastic parameters of a
rock mass containing fractures has been the subjects of
research by many investigators [31–36]. Knowing the
relevant fracture information, i.e. size, number, and
orientation, it is possible to determine simple but
rigorous and computationally effective means for
estimating the stiffness or compliance matrix of frac-
tured rock based on the micro-mechanics.
Let us consider a rock mass containing many
fractures under a stress-prescribed boundary condition.
A representative volume element with volume Vis
chosen and the average stress and strain are defined as
%
sij ¼1
VRVsij dV
%
eij ¼1
VRVeij dV;ð3Þ
where the over bar indicates a volume averaged
quantity. Following the procedure introduced by Horii
and Nemat-Nasser [34], the average strain and average
stress relationship for rocks containing fractures are
obtained as
%
eij ¼Cijkl
%
skl þ1
2VZSc
ð½uinjþ½ujniÞdSð4Þ
where Cijkl is the compliance tensor of the intact rock,
Scdenotes fracture surface, niis unit normal vector of
the fracture; and [ui] denotes the displacement jump
across the fracture surface. The second part in Eq. (4) is
the fracture-induced additional strain which is derivable
from the displacement jump along the surface of each
fracture. The existing fractures around an underground
opening will experience an unloading state in most cases
and it is reasonable to assume that the overall response
is elastic at a given damage state. In this case, the
constitutive relation can be represented by the constant
effective elastic compliance tensor %
Cijkl ;which is
defined by
%
eij ¼ðCijkl þCp
ijkl Þ%
skl ¼%
Cijkl
%
skl ;ð5Þ
where %
Cp
ijkl is the fracture-induced compliance tensor.
When evaluating the overall behavior of a fractured
rock mass, it is important to take the interaction effect
between fractures into consideration. Cai and Horii [35]
proposed a efficient method for this purpose. They
calculate the fracture induced additional strain by
putting the fracture into a solid with the effective
material properties given by the non-interaction solu-
tion. The results of the effective moduli obtained in this
manner are in good agreement with experimental data
[36].
Without losing generality, standard 6 6 engineering
notion is used in the following discussion. The
constitutive equations are
%
ei¼%
Cij
%
sj;i;j¼1;2;3;y6:ð6Þ
In a two-dimensional setting, we have %
e1¼%
e11;%
e2¼
%
e22;%
e6¼2%
e12;%
s1¼%
s11;%
s2¼%
s22;%
s6¼%
s12:For a
fracture of half-length a;the displacement jumps are
R=1.75m
60MPa
11MPa
σn=0
Fig. 6. Fractures oriented in the cross-section plane.
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–11451140

calculated from
½u0
1¼4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2x2
pEs0
6;
½u0
2¼4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2x2
pEs0
2;ð7Þ
where Eis the Young’s modulus of the intact rock; and
the prime denotes a local coordinate system. Following
the process described by Cai and Horii [35], for a rock
mass with Nrandomly oriented fractures (Fig. 7a), the
fracture density is o¼Npa2=Vand the compliance
matrix of the fractured rock mass is obtained as
½%
Cij ¼1
E
1þa0n0
1þa00
sym:2ð1þnÞþ2a0
2
6
43
7
5;ð8Þ
where a0¼oð1þoÞ:The above compliance matrix is
for plane stress and the compliance matrix for plane
strain is obtained by replacing Eby E=ð1n2Þand nby
n=ð1nÞ:Note that random fracture interaction has
been considered above and the resulting effective
material properties are isotropic.
In a rock mass with fractures parallel to the X-axis, as
shown in Fig. 7b, the total compliance matrix for plane
stress problems is obtained as [35]
%
Cij

¼1
E
1n0
1þ2oa10
sym:2ð1þnþob1Þ
2
6
43
7
5;ð9Þ
where
a1¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ2o
2½ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ2o
pþ1þo
r;
b1¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
2½ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þ2o
pþ1þo
r:ð10Þ
The effective material properties in this case are
anisotropic. The compliance matrix for plane strain is
again obtained by replacing Eby E=ð1n2Þand nby
n=ð1nÞ:It is seen that the deformation properties
depend on the damaged state of the rock mass. In the
approach presented here, the fracture density is
obtained from microseismic measurements as explained
earlier.
3.2. Implementation and model verification
Because FLAC [37] has a powerful built-in program-
ming language, FISH, which allows the user to
implement new constitutive models, it was chosen as
the tool for the implementation of the damage-driven
constitutive model for brittle rock masses. The isotropic
softening model (Eq. (8)) and the orthotropic softening
model (Eq. (9)) were implemented into FLAC. The
material property inputs are Young’s modulus, Pois-
son’s ratio of the intact rock, and information related to
the microseismic events such as the location and
the source size of each event. The fracture density
is computed based on these microseismic source
parameters.
The implementation of the numerical model was
verified through the analysis of a hollow cylinder with
radially anisotropic moduli (see insert in Fig. 8). r1and
r2are the inner and outer radii of the cylinder,
respectively. The cylinder is subjected to a uniform
pressure ðp2Þat the outer boundary. The analytical
solution can be found in Ewy and Cook [38].
Only a quarter of the problem is considered with
Ey¼E;Er¼E=ð1þ2oa1Þ;nyr¼nfor the radially
anisotropic medium. The parameters used in the
calculation are: E¼65 GPa, n¼0:25;r1¼1:75 m,
r2¼31:5m, p2¼7:071 MPa, and the fracture density
is assumed to be o¼0:2 throughout the cylinder.
Fig. 8 presents a comparison of stress results from
FLAC and the analytical solution for plane stress
conditions, showing very good agreement. The stresses
for non-softening case (o¼0;isotropic) are also shown
X
Y
(a)
X
Y
(b)
Fig. 7. Fracture distribution in rocks: (a) randomly oriented fractures;
(b) unidirectionally distributed fractures.
r/r
1
1234567891011121314151617181920
Normalized stress
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
σ
t
/p
2
(Analytical)
σ
r
/p
2
(Analytical)
σ
t
/p
2
(FLAC)
σ
r
/p
2
(FLAC)
σ
t
/p
2
σ
r
/p
2
θ
r
1
r
2
p
2
θ
r
E
r
E
Anisotropic
Isotropic
Isotropic
Anisotropic
σ
r
/p
2
σ
t
/p
2
Fig. 8. Normalized stresses from the FLAC model and the analytical
solution of a hollow cylinder with radially anisotropic moduli (the
solution for the isotropic case is shown for comparison).
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–1145 1141

for comparison. The radial stress ðsrÞfor the anisotropic
softening case is always smaller than that of the case
without non-softening, and the tangential stress ðstÞfor
the anisotropic softening case is lower near the inner
wall and larger at the outer boundary than that of the
non-softened case.
4. Analysis of Mine-by Experiment
4.1. FLAC model and input parameters
The grid used for the Mine-by Experiment simulation
is a radial grid with a square shaped boundary contain-
ing 1728 elements. The outer boundary, which is about
17 times the excavation diameter is 60 60 m wide. A
close-up view of the grid and the corresponding
extensometer boreholes is presented in Fig. 9. In reality,
the major principal stress is inclined at 151. For the
analysis, the grid in Fig. 9 was rotated 151clockwise so
that the major and minor principal stresses are
horizontal and vertical, respectively. The horizontal
stress is s1¼60 MPa, the vertical stress is s3¼11 MPa,
and the stress parallel to the opening axis is
s2¼45 MPa. The Young’s modulus and Poisson’s ratio
of the intact rock are 65 GPa and 0.25, respectively. The
input parameters for microseismic events are the
location of events, seismic energy and specific surface
energy.
4.2. Discussion of results
The fracture density distribution calculated from the
fracture geometry shown in Fig. 5 is presented in
Fig. 10. A spherical representative volume element
(RVE) was chosen with a radius of 0.44 m for the
contouring. The nine largest events, whose radii range
from 0.26 to 0.56 m, were excluded because they were
assumed to be generated by unrealistic near zero stress
predictions [16]. The gradual increase of the fracture
density near the notch surface indicates that damage is
intense near the notch surface, which agrees well with
the field observation of progressive failure in the
compression zones. Because non-blasting excavation
technique was used, the damage in the rock mass was
induced entirely from the stress change, and captured by
the microseismic monitoring system.
In the present study, the tensile softening zone near
the sidewall was considered and represented by the zone
defined by the AE events and the fracture density in this
zone was determined by back analysis using results of
extensometers located in the tensile zone. The fracture
density in this tensile zone is assumed to be uniformly
distributed. From parametric study, it was found that
-3.500
-2.500
-1.500
-.500
.500
1.500
2.500
3.500
-3.500 -2.500 -1.500 -.500 .500 1.500 2.500 3.500
90
0
315
Extensometers
5
7
8
Fig. 9. FLAC grid and the locations of extensometers. The grid was rotated 151clockwise to align principal stress directions with horizontal and
vertical axis of model.
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–11451142

the softening of the tensile zone greatly affects the
response of rock mass in this region but has little effect
on the rock mass response in the compression (notch)
region.
As previously noted, the rock mass in the notch
region is softened by fractures distributed in the
direction parallel to the maximum stress, resulting in
the anisotropic softening of the rock mass. The
directions of principal stresses in the rock mass differ
at different points so that the principal elastic directions
are not the same at different points in space. This
directional variation of principal elastic direction is
properly simulated in the FLAC model with the adopted
anisotropic constitutive model. Knowing the fracture
density distribution in space, the distribution of elastic
constants can be readily obtained. It is interesting to
note that rock mass damage is mostly concentrated in
the roof. This is reported by the non-symmetric notch
formation. The rock deformation modulus is small in
the direction perpendicular to the notch boundary.
The numerical simulation results were then compared
to measurement of the extensometers located as shown
in Fig. 9. In this manner, the adopted approach can be
indirectly validated, i.e., rock mass damage character-
ized by the tensile interpretation model for the micro-
seismic events. In the field, little rock damage would be
visually identified beyond the back of the notch [28]. The
kind of damage simulated here cannot be seen using
borehole cameras. However, displacement measure-
ments as instruments measuring the accumulated effect
of damage are ideal instruments for this purpose. The
results for extensometers 5 and 8 near the notch are
presented in Figs. 11 and 12. ‘‘No softening’’ represents
the case in which the fracture density is zero everywhere.
As can be seen from the results, when softening based on
the microseismic data is considered, better model
predictions are obtained. The damage-driven model
provides better predictions of displacement magnitudes
and distribution along the measurement lines.
As stated above, the stress-induced fractures around
the opening have a preferred orientation, in the direction
of maximum compressive stress and the resulting rock
mass, hence properties are anisotropic. The result
presented in Fig. 13 compares the isotropic and aniso-
tropic softening results for Extensometer 7 near the
sidewall. In the isotropic case, fractures are assumed to
Extensometer 5 (90
o
)
Radius / Excavation Radius
0123456789101112
Radial Displacement (mm)
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
Measured
No softening
Anisotropic softening
Fig. 11. Radial displacement responses from the anisotropic softening
model compared to results from measured and non-softening model
for extensometer 5.
Extensometer 8 (315
o
)
Radius / Excavation Radius
0123456789101112
Radial Displacement (mm)
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Measured
No softening
Anisotropic softening
Fig. 12. Radial displacement responses from the anisotropic softening
model compared to results from measured and non-softening model
for extensometer 8.
Fig. 10. Fracture density (o) distribution around the opening. The
density shown is calculated from the microseismic event data presented
in Fig. 5.
M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 1135–1145 1143

be oriented in a random fashion with the fracture
density distribution shown in Fig. 10. The larger
departure from measurement results suggests that rock
mass softening near the opening is not isotropic but
anisotropic.
Compared to the initial modeling study to interpret
extensometer measurements [28], the present approach
overcomes several disadvantages. In the previous study,
the elastic model was modified to obtain better
predictions by lowering the modulus beyond the notch
tips, by using ubiquitous joints to simulate a unidirec-
tional reduction in tensile strength in region where
s3ost;and by reducing the shear modulus for region
where s3ost:The reduction in modulus had to be
defined in an arbitrary manner and the softening based
on the condition of s3ostlimited the softening effect to
the tensile region only (side walls), ignoring softening of
the notch region. By the approach presented here, the
arbitrariness of assigning reduced elastic modulus is
eliminated by using quantitative data from microseismic
event monitoring and by taking directional cracking or
induced anisotropy properly into account. As a result of
the combined effect, much better agreement of model
predictions and field measurements is achieved.
5. Conclusions
Microseismic measurements provide quantitative in-
formation about damage location, extent and magni-
tude as well as possible failure progression in the rock
mass. It is imperative to make better use of microseismic
monitoring data not only qualitatively but also quanti-
tatively. The quantitative approach presented here relies
on the extensile microseismic source model to provide
fracture dimensions.
Based on an appropriate source model, representative
rock mass damage parameters can be determined from
the microseismic data. Traditional source models are
based on a shear slip concept, producing unrealistic
source dimensions when compared to observable crack
or fracture size. To arrive at a realistic fracture size for a
damage-driven numerical model, a microseismic event
interpretation model based on a tensile cracking
mechanism was adopted. A damage-driven numerical
model has been developed and implemented using
FLAC. The input parameters for this damage-driven
model are mechanical properties for the intact rock and
parameters derive from the microseismic measurements
such as the locations and source sizes of the events.
Even if there are still many issues to be resolved
before seismic source parameters can be correctly
related to damage parameters, the present study opens
the door for interactive modeling with damage-driven
models. Practically, if captured microseismic data is
updated regularly in the numerical model, nonlinear
rock mass behavior can be simulated. Because fractures
developed near the underground opening have preferred
orientation, the rock mass, softened by the stress-
induced fractures, will behave like an anisotropic
material with directional deformation properties. The
developed model defines the orientation of deformation
moduli based on the principal stress direction at each
point.
The study of the AECL’s Mine-by Experiment rock
mass response has shown that the interpretation of
extensometer can be significantly improved when soft-
ening based on the microseismic data is considered,
especially when anisotropic softening of rock mass is
taken into account.
Future research needs to address inherent weakness
derived from incomplete microseismic data records and
should address the application of damage-driven models
to rock mass strength modeling.
Acknowledgements
This work has been supported by a strategic research
grant of the Natural Science and Engineering Research
Council (NSERC) of Canada on the Mitigation of
Violent Failure Processes in Deep Excavations. The
authors wish to thank V!
eronique Falmagne and Mark
Gutberlet for their contribution to this project. The
authors are also grateful to Dr. Neil Chandler of AECL
for providing detailed data for this investigation.
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Extensometer 7 (0
o
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Radius / Excavation Radius
0123456789101112
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1.5
2.0
2.5
3.0
3.5
4.0
Measured
Isotropic softening
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model compared to results from measured and isotropic softening
model for extensometer 7.
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