Conference PaperPDF Available

Numerical simulation of acoustic emission in rocks using FEM/DEM

  • Geomechanica Inc.


Content may be subject to copyright.
1.1 AE simulation Techniques
Several modelling methodologies have been adopted to simulate the AE activity associated with
the failure processes of brittle rocks. Tang et al. (1997) first discussed the simulation of AE
based on elastic continuum damage mechanics and implemented their theory in a finite-element
code named RFPA (Tang et al., 1997). Hazzard & Young (2000) developed a technique to dy-
namically quantify AE using a bonded particle DEM model. The technique was further im-
proved by Hazzard et al. (2002), Hazzard & Young (2002) and Hazzard & Young (2004). Simi-
lar to DEM models, lattice models were adopted to describe the mesoscopic behavior of brittle
and quasi-brittle materials (Zapperi et al., 1997, Alava et al., 2006); Models that deal with AE
emitted from a pre-existing crack propagating in an elastic medium were discussed, among oth-
ers, by Hirose & Achenbach (1991). Despite the broad use of AE in experimental rock mechan-
ics and in in-situ monitoring, not much other progress has been made in the past decade in this
research area probably due to the complexity in modelling the various interacting aspects asso-
ciated with material failure and AE emission.
1.2 Principles of FEM/DEM
The combined finite/discrete element method (FEM/DEM) is an numerical method pioneered
by Munjiza et al. (1995) that simulates multiple interacting deformable bodies by directly solv-
ing Newton’s equations of motion. In this study, a two-dimensional FEM/DEM code, namely
Y-Geo (Mahabadi et al., 2012), is used to simulate the AE phenomena in a synthetic rock. The
FEM/DEM technique combines the advantage of discrete element methods (DEM) to capture
the interaction and fracturing of different solids with finite element method (FEM) to describe
Numerical simulation of acoustic emission in rocks using
Q. Zhao, A. Lisjak, G. Grasselli
Department of Civil Engineering, University of Toronto, ON, Canada
Q. Liu
Department of Physics, University of Toronto, ON, Canada
ABSTRACT: Acoustic emissions (AE) are stress waves released by localized inelastic defor-
mation events during the progressive failure of brittle rocks. Although several numerical meth-
ods have been developed to simulate the deformation and damage processes of rocks, only a
limited number have been capable of providing quantitative information regarding the associ-
ated acoustic activity. FEM/DEM is a numerical tool that simulates material failure by explic-
itly modelling fracture nucleation and propagation using cohesive elements. Seismic informa-
tion is extracted with a newly developed algorithm based on the monitoring of internal
variables in the proximity of propagating cracks. Several simulation cases were analyzed, in-
cluding a point source model, a wing crack propagation model, and a circular excavation
model. Simulated AE were cross-analyzed by travel-time inversion, spectral analysis, and fre-
quency-magnitude statistics. These preliminary results demonstrate the capabilities of
FEM/DEM as a tool to numerically simulate seismicity associated to the rock failure process.
their elastic deformation (Munjiza, 2004). As shown below, FEM/DEM is capable of simulat-
ing crack propagation and the corresponding particle motions.
The fundamental governing equation can be expressed as:
where M is the mass matrix of the system,
22 /tx
is the second order derivative of displace-
ment, and R is a nodal force vector which includes external loads, interaction forces between
bodies, deformation forces, viscous damping forces, and the crack bonding forces.
In order to simulate the initiation and propagation of fractures, dedicated four-noded cohe-
sive elements, named as crack elements (Fig. 1), are inserted between each pair of triangular
elements. The failure processes are modeled in FEM/DEM following principles of non-linear
elastic fracture mechanics (Dugdale, 1960, Barenblatt, 1962). Crack elements are enabled be-
tween all adjacent triangular pairs, thus arbitrary fractures can be captured within the con-
straints imposed by the original mesh topology.
Figure 1. Implementation of crack elements. (a) Behaviour of crack elements under given nodal forces; (b)
exaggerated mesh structure after the introduction of crack elements. The FEM/DEM mesh is developed
based on a FEM mesh generated using a Delaunay triangulation scheme.
An important aspect illustrated in Figure 1b is that the model is meshed by the common De-
launay triangulation scheme, which has great advantage of avoiding formation of triangles with
small included angles (Sloan, 1987). The resulted mesh has relatively high quality (Shewchuk,
1996), and most importantly, elements do not have a preferred orientation which could result in
an anisotropic orientation of the generated crack elements.
The three modes of cracking can be simulated as follows:
1. Mode I (i.e. opening mode) fracturing is simulated through a cohesive crack model based
on the Fictitious Crack Model originally proposed for concrete by Hillerborg et al. (1976).
When the opening between two triangular elements reaches a critical value (op), which is
related to intrinsic tensile strength, the normal bonding stress is gradually reduced until a
residual opening value (or) is reached (Fig. 2a).
2. Mode II (i.e. sliding mode) fracturing is simulated by a slip weakening model which re-
sembles the model from Ida (1972). The critical slip (sp) corresponds to the intrinsic shear
strength (fs) which is calculated according to the Mohr-Coulomb criterion:
ns cf
where c is the internal cohesion, ϕ is the internal friction angle, and σn is the normal stress
acting across the fracture surface. While slip approaches sr, the tangential bonding stress is
gradually reduced to the residual value
gradually as shown in Fig. 2b
(Mahabadi et al., 2012).
3. Mode I-II (i.e. mixed mode) fracturing is defined by a coupling criterion between crack
opening and slip. As illustrated in Figure 2c, this mode describes a combination of shear
and tensile deformation, and the failure criterion is defined by
Figure 2. Constitutive behavior of crack element. (a) Mode I (opening mode), the crack element start to
yield when normal stress reaches ft and breaks at critical opening Or; (b) Mode II (sliding mode), the crack
element yields under peak shear stress fs and breaks at critical shear distance Sr where the residual shear
stress fr is applied even after the breakage; (c) Graphic representation of the coupling relationship between
crack opening and crack slip for Mode I-II, the mixed mode.
where o is opening distance and s is slipping distance.
The shapes of the curves for mode I and mode II are based upon experimental complete
stress-strain curves obtained for concrete in direct tension (Evans & Marathe, 1968, Munjiza et
al., 1999). The specific fracture energy values GIc and GIIc are related to the areas under these
curves through:
cdooG )(
src dsfsG ])([
From an energetic point of view, strain energy is stored during the elastic deformation of the
triangular elements, and once the material intrinsic strength is overcome, the release of the
strain energy begins along with the initiation of a new fracture. Released energy is consumed by
the fracturing process itself through GIc and GIIc. If sliding occurs, part of the energy is dissi-
pated by frictional work. The excess of elastic strain energy is radiated as kinetic energy in the
form of AE. Two types of approaches are used to capture and analyze the synthetic AE: internal
monitoring of AE sources and seismogram interpretation.
2.1 Model Description
In this section, a simple model is used to validate the ability of FEM/DEM in simulating wave
propagation. The simulation results are analyzed based on seismograms and wavefield snap-
A vertical point source is excited at the left bottom corner of a homogeneous sample by a
Ricker wavelet function with duration is 0.015 s with a center frequency of 200 Hz. The model
is a 50 × 100 mm homogeneous sample, which is meshed into 13852 triangular elements with
an average size h = 1 mm. Material properties for this simulation are listed in Table 1. No
damping is applied to preserve the waveform, and absorbing boundaries are used at margins of
the model to prevent reflections. The absorbing boundary condition is accomplished by imple-
menting the solution proposed by Lysmer & Kuhlemeyer (1969), and further information can be
found in Mahabadi et al. (2012).
Table 1. Rock Sample Properties for the Wave Propagation Simulations in Section 2
Parameter Unit Value
Density, ρ kg/m3 2300
Young’s modulus, E GPa 3
Poisson’s ratio, υ - 0.29
Internal friction angle, ϕ degree 35
Internal cohesion , c MPa 15
Tensile strength, ft MPa 3
Mode I fracture energy, GIc J/m2 2.0
Mode II fracture energy, GIIc J/m2 10
Damping coefficient, μ kg/m
s 0
Normal contact penalty, pn GPa 30
Tangential contact penalty, pt GPa 3
Fracture penalty, pf GPa 15
Sample-platen friction coefficient, k - 0.1
2.2 Simulation Results
The propagation of the wave front simulated by FEM/DEM can be observed in Figure 3a,
where the four-quadrant distribution of the velocity field is clearly shown at early times. Assess
the accuracy of the AE wave simulation by FEM/DEM, a model with the same geometry and
properties but without introducing crack elements, is tested first (Fig. 3b). When crack elements
are not introduced, the simulation is essentially a time explicit FEM. Moreover, a similar for-
ward simulation is carried out using the spectral-element method (SEM) for comparison pur-
pose (Fig. 3c). The SEM method is essentially an FEM with high polynomial order and thus
more accurate, and it is recognized as the most popular FEM method in global and regional
seismology (Komatitsch & Vilotte, 1998, Komatitsch et al., 2004, Komatitsch et al., 2005,
Shearer, 2009). The software package SPECFEM2D developed based on SEM is used for com-
Wavefields presented by these methods share a high degree of similarity, which indicates
that the FEM/DEM algorithm is capable of simulating seismic wave properly. Although the
general trend of the wavefield produced by FEM/DEM is quite accurate, significant amount of
noise exists around the source area (Fig. 3a), due to scattering induced by the yielding of crack
elements. As mentioned in section 1, each pair of triangular elements is bonded together by a
crack element and, due to the violent stress change induced by the source excitation, crack ele-
ments yield (but do not break in this example) and hence oscillate between varying stress condi-
tions. This behaviour generates noise in the near-source region. Another disadvantage associ-
ated with the crack elements is that their elastic behaviour modifies the overall stiffness of the
material and results in lower wave speed. This effect could be minimized by increasing the pen-
alty values of the elements. Overall, the time difference could be optimized to be within 10-2 ms
range, which is considered accurate for most scenarios.
The recorded seismograms by a receiver at the center of the sample are plotted for three
above methods (Fig. 4). Although the first arrivals from FEM and SEM simulations agree with
each other well, the cause of the difference in peak times needs to be investigated in future re-
The results discussed above demonstrate the ability of FEM/DEM in modelling AE wave
propagation simulations, and this could be useful to simulate laboratory tests where AE waves
are generated by transmitters attached to a sample (Hardy, 2003). Moreover, AE are mostly as-
sociated with fracturing processes which, although providing a powerful passive way to monitor
internal variations of rocks in the field (Lockner, 1993), are very difficult to simulate numeri-
cally. The most significant advantage of FEM/DEM is its ability to simulate the entire process
of fracture growth. Using the validated AE analysis method as shown in section 2, a fracturing
propagation induced AE example is given in the next section.
Figure 3. Comparison of the wavefields (x-component) modeled by FEM/DEM and SEM at same time
frames. (a) FEM/DEM model with introducing crack elements; (b) FEM/DEM model without crack ele-
ments implementation; (c) SEM model. Note that absorbing boundaries are not perfect, and reflections
from the corners and edges sometimes interfere with the original wave fields.
Figure 4. Comparison of the P-wave seismograms modeled by FEM/DEM and SEM. FEM here refers to
the simulation by FEM/DEM without introducing crack elements. First arrivals calculated by FEM and
SEM are almost identical at 0.034 ms, and a time difference Δt = 0.003 ms is observed for the first arri-
val of FEM/DEM simulation result. The seismogram produced by FEM/DEM algorithm is not as smooth
as those by the continuum algorithms due to interaction effects at the contact between particles.
3.1 Model Description
The major body of the model is a 50 × 100 mm (Fig. 5a) homogeneous sample containing an
inclined flaw located at the center of the sample. Two platens compress the sample at a constant
rate of 0.05 m/s. The sample is discretized by a Delaunay triangulation scheme with an average
size h = 0.7 mm. Material properties for the sample are the same as in Table 1 except for the
damping coefficient, which is set to be twice the critical damping (Equation 6), c = 7.4 × 103
s. Moreover, absorbing boundary conditions are not applied, and receivers are placed on
both sides of the sample to record synthetic seismograms.
3.2 Internal Monitoring of Simulation Results
Figure 5a shows the crack propagation simulation results, and the broken crack elements clus-
tering in two macroscopic fractures originating from the tip of the diagonal flaw. The nuclea-
tion of every crack is associated with an acoustic event which is then monitored in FEM/DEM
by numerically assessing the following parameters: (i) source location, (ii) fracture mode, (iii)
initiation time, and (iv) seismic energy and magnitude.
3.3 Seismic Analysis and Comparisons with Internal Monitoring Results
Seismic analyses are performed on vertical and horizontal-component synthetic seismograms
recorded by receivers on both sides of the rock sample.
Figure 5c illustrates the horizontal-component synthetic seismograms recorded as particle ve-
locities for receivers on the right-hand side of the sample (numbered as receivers 0-10). Wave-
lets occur before 1 ms are induced by the impact between platens and the sample, and it is
damped out before first-arrival of the earliest AE event at about 1.8 ms. Four groups of AE
events can be observed from the seismogram as listed in Table 2, where a group may consist
several sub-events which are considered to be associated with the propagation of a continuous
fracture. Since several sub-events occur close in time, not all of them can be identified from the
seismogram, and only the first event in each group can be analyzed in practice.
Figure 5. (a) Geometry of the model and fracture propagation results from internal monitoring of
FEM/DEM. Receivers are placed on both sides of the sample (indicated by dots); (b) Zoomed-in view of
the fracture propagating area, where AE sources recorded by internal monitoring are denoted by circles,
and inverted source locations are indicated by two crosses; (c) Seismograms recorded by receivers placed
at the right-hand side of the sample (Lisjak et al., 2013).
Table 2. Event Groups and Their Time Ranges
Group number Time range
0 [1.8, 2.2]
1 [4.1, 5.0]
2 [5.8, 6.6]
3 [8.0, 8.2]
A travel time inversion of hand-picked first arrivals is done for group 1 and group 2 to locate
the AE sources, and theoretically, the inverted locations would be the initial points of the frac-
ture propagation. Inverted AE sources are at the center of the crosses shown in Fig 5b, while the
location errors of the inversions in mm scale are given by the sizes of the crosses. Note the in-
verted AE locations for group 1 and 2 are consistent with the initiation of wing cracks from the
tips of inclined center flaw from FEM/DEM modelling.
Two types of amplitude reduction effects can be observed from synthetic seismograms in
Figure 5c, geometrical spreading and numerical damping attenuation, in which numerical damp-
ing is chosen to be twice the critical damping (μc) calculated from
where h=0.7 mm is the characteristic element size, ρ is density, and E is Young’s modulus. In
calculating the numerical damping, each element is considered as a mass-spring-dashpot sys-
tem. Damping is applied to dissipate the noise induced by the oscillation of platens. Increasing
the damping value will reduce the AE amplitudes and attenuate more high frequency content.
Specifically, the damping is most significant for frequencies
i.e. frequency contents above 60 kHz will suffer considerable attenuation.
Figure 6a, b shows the synthetic seismograms and their frequency spectra recorded by re-
ceivers 0-4 at time interval 8 ms-8.2 ms. According to these spectra, the AE activities have en-
ergy primarily concentrated around 10 kHz, while higher frequency contents are mostly attenu-
ated. With increasing travel distance (from receiver 4 to 0), the amplitudes of waves are
significantly reduced.
The frequency range of the recorded seismograms are is significantly lower than the lab test
results which usually range between 100 kHz to 2000 kHz (Lockner, 1993). Several factors may
be considered to explain the inability of capturing high frequency contents in FEM/DEM. Nu-
merical damping is one of the important reasons, as it not only decreases the amplitude but also
damps out high frequency content as shown in Figure 6a. Moreover, the frequency content of
source time functions is related to the sizes of seismic sources and their estimated rup-
ture speeds. In this example, rupture speed value is low, which results in a quasi-
dynamic AE behavior in the FEM/DEM simulations. Although seismic energy is emit-
ted upon failure, the low rupture speed indicates that most released energy is dissipated
as fracture energy within the fracture propagation zone.
Figure 6. (a) Synthetic seismograms recorded by receivers 0-4 for time interval 8 ms-8.2 ms; (b) Frequen-
cy spectra of the seismograms recorded by receivers 0-4 for time interval 8 ms-8.2 ms.
The FEM/DEM algorithm exhibits great potential in assessing the stability of an underground
structure by combining mechanical behaviour simulation with the analysis of recorded AE
events. An example of simulation of damage around an unsupported circular excavation is
shown here in Figure 7. The rock mass is a horizontally layered clay shale formation, and the
axis of the circular tunnel parallel to the bedding planes. Tunnel liner is not applied to allow the
full development of the Excavation Damaged Zone (EDZ). The excavation induced AE activity
is plotted in Figure 7 with associated magnitude indicated by different colors.
Figure 7b depicts the frequency-magnitude distribution of the excavation induced AE. Ac-
cording to the Gutenberg-Richter relationship (Gutenberg & Richter, 1956), in logarithmic
coordinates, the relationship between AE magnitude and occurrence frequency becomes linear
as described by
bMaN log
where N is the number of AE events with magnitude larger than M, a and b are constants, and
the slope of the linear portion, b value, could be estimated from the plot. The b value is related
to the geological setting and can help to improve the efficiency of operation. The relatively
large b value (b = 2.4) agrees with the fact that majority of the simulated AE events are planar
fractures parallel to the horizontal and vertical stresses (Downie et al., 2010).
Figure 7. (a) Spatial distribution of AE events and associated magnitudes of the simulated damage induced
by excavation; (b) Frequency-magnitude plot of the recorded AE events and the estimated b value.
In this study, we analyzed the numerical simulation of AE using the FEM/DEM algorithm. Ex-
ample in section 2 validated the ability of FEM/DEM in capturing general wave propagation
against a specifically developed synthetic seismogram simulator (SEM), while examples in sec-
tion 3 and section 4 took advantage of the discrete representation of materials in FEM/DEM to
obtain seismic information associated with the propagation of a fracture and the development of
a damage zone around a circular excavation. Simulations results show promising potential of
FEM/DEM in AE studies.
When compared with SEM, the FEM/DEM method needs many improvements before being
used as a pure seismic wave simulator. Producing realistic high frequency AE contents is also a
key feature that needs to be developed, while eliminating the scattering from crack elements
could improve the simulation quality significantly. Although not perfect in AE simulation,
FEM/DEM can properly simulate AE and fracturing at the same time, which are of great inter-
ests to engineers, and can provide the correlation between AE and mechanical behavior which
has a great implication for engineering the rock mass.
Numerical simulations of AE have been studied for decades in analyzing rock failure
processes, and the method discussed in this study provides a tool to quantitatively assess the
microcracking activities as well as the associated AE. In future studies, the validated
FEM/DEM AE modelling technique will be used to obtain further insights into the mechanics
of rock failure with potential applications ranging from laboratory scale to engineering scale
processes (e.g. underground excavations, petroleum and geothermal reservoirs). Moreover, a
three-dimensional version of the FEM/DEM code is currently under development, and the AE
simulation approach will be adopted.
ALAVA, M. J., NUKALAZ, P. K. V. V. & ZAPPERI, S. 2006. Statistical models of fracture. Advances in
Physics, 55, 349-476.
BARENBLATT, G. 1962. The mathematical theory of equilibrium cracks in brittle fracture. Advances in
applied mechanics, 7, 104.
DOWNIE, R., KRONENBERGER, E. & MAXWELL, S. Using Microseismic Source Parameters To
Evaluate the Influence of Faults on Fracture Treatments: A Geophysical Approach to Interpretation.
SPE Annual Technical Conference and Exhibition, 2010.
DUGDALE, D. S. 1960. Yielding of Steel Sheets Containing Slits. Journal of the Mechanics and Physics
of Solids, 8, 100-104.
EVANS, R. H. & MARATHE, M. S. 1968. Microcracking and stress-strain curves for concrete in tension.
Matériaux et Construction, 1, 61-64.
GUTENBERG, B. & RICHTER, C. F. 1956. Earthquake magnitude, intensity, energy, and acceleration
(second paper). Bulletin of the Seismological Society of America, 46, 105-145.
HARDY, H. R. 2003. Acoustic emission/microseismic activity: Volume 1: Principles, Techniques and
Geotechnical Applications Lisse, Balkema.
HAZZARD, J. F., COLLINS, D. S., PETTITT, W. S. & YOUNG, R. P. 2002. Simulation of unstable fault
slip in granite using a bonded-particle model. Pure and Applied Geophysics, 159, 221-245.
HAZZARD, J. F. & YOUNG, R. P. 2000. Simulating acoustic emissions in bonded-particle models of
rock. International Journal of Rock Mechanics and Mining Sciences, 37, 867-872.
HAZZARD, J. F. & YOUNG, R. P. 2002. Moment tensors and micromechanical models. Tectonophysics,
356, 181-197.
HAZZARD, J. F. & YOUNG, R. P. 2004. Dynamic modelling of induced seismicity. International
Journal of Rock Mechanics and Mining Sciences, 41, 1365-1376.
HILLERBORG, A., MODÉER, M. & PETERSSON, P. E. 1976. Analysis of crack formation and crack
growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete
Research, 6, 773-781.
HIROSE, S. & ACHENBACH, J. D. 1991. Acoustic-Emission and near-Tip Elastodynamic Fields of a
Growing Penny-Shaped Crack. Engineering Fracture Mechanics, 39, 21-36.
IDA, Y. 1972. Cohesive force across the tip of a longitudinal-shear crack and Griffith's specific surface
energy. Journal of Geophysical Research, 77, 3796-3805.
KOMATITSCH, D., LIU, Q., TROMP, J., SÜSS, P., STIDHAM, C. & SHAW, J. H. 2004. Simulations of
ground motion in the Los Angeles basin based upon the spectral-element method. Bulletin of the
Seismological Society of America, 94, 187-206.
KOMATITSCH, D., TSUBOI, S. & TROMP, J. 2005. The spectral-element method in seismology. In:
NOLET, G. A. L., A. (ed.) The Seismic Earth. Washington DC: AGU.
KOMATITSCH, D. & VILOTTE, J. P. 1998. The spectral element method: An efficient tool to simulate
the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of
America, 88, 368-392.
LISJAK, A., LIU, Q., ZHAO, Q., MAHABADI, O. K. & GRASSELLI, G. (2013). Dynamic simulation of
acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis. Submitted.
LOCKNER, D. 1993. The Role of Acoustic-Emission in the Study of Rock Fracture. International
Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30, 883-899.
LYSMER, J. & KUHLEMEYER, R. L. 1969. Finite Dynamic Model for Infinite Media, Journal of the
Engineering Mechanics Division.
MAHABADI, O., LISJAK, A., MUNJIZA, A. & GRASSELLI, G. 2012. YGeo: A New Combined
FiniteDiscrete Element Numerical Code for Geomechanical Applications. International Journal of
Geomechanics, 1, 153.
MUNJIZA, A. 2004. The Combined Finite-Discrete Element Method, John Wiley & Sons, Ltd.
MUNJIZA, A., ANDREWS, K. R. F. & WHITE, J. K. 1999. Combined single and smeared crack model
in combined finite-discrete element analysis. International Journal for Numerical Methods in
Engineering, 44, 41-57.
MUNJIZA, A., OWEN, D. & BICANIC, N. 1995. A combined finite-discrete element method in transient
dynamics of fracturing solids. Engineering computations, 12, 145-174.
SHEARER, P. M. 2009. Introduction to Seismology, New York, CAMBRIDGE UNIVERSITY PRESS.
SHEWCHUK, J. 1996. Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator.
Applied computational geometry towards geometric engineering, 203-222.
SLOAN, S. W. 1987. A Fast Algorithm for Constructing Delaunay Triangulations in the Plane. Advances
in Engineering Software and Workstations, 9, 34-55.
TANG, C. A., CHEN, Z. H., XU, X. H. & LI, C. 1997. A theoretical model for Kaiser effect in rock. Pure
and Applied Geophysics, 150, 203-215.
ZAPPERI, S., VESPIGNANI, A. & STANLEY, H. E. 1997. Plasticity and avalanche behaviour in
microfracturing phenomena. Nature, 388, 658-660.
... Then, this technique was improved by introducing moment tensor calculation by tracking the change in contact force at the time bonds broke, which is referred to as the moment tensor model (MTM) 27 . In addition to the FEM and DEM, there are other AE simulation models, such as the static lattice model 28 , continuum fracture mechanics model 29 , quasidynamic monitoring kinetic energy model 30,31 , deviatoric strain rate model 32 and Voronoi element-based explicit numerical manifold model 33 . Among the aforementioned models, MTM based on DEM has been widely used in simulating AE benefiting from the ability of DEM to explicitly represent fractures and bond failure of rocks and excellent applicability of MTM to quantitatively characterize AE 34-37 . ...
Full-text available
Acoustic emission (AE) characterization is an effective technique to indirectly capture the failure process of quasi brittle rock. In previous studies, both experiments and numerical simulations were adopted to investigate the AE characteristics of rocks. However, as the most popular numerical model, the moment tensor model (MTM) cannot be constrained by the experimental result because there is a gap between MTM and experiments in principle, signal processing and energy analysis. In this paper, we developed a particle-velocity-based model (PVBM) that enabled direct monitoring and analysis of the particle velocity in the numerical model and had good robustness. The PVBM imitated the actual experiment and could fill in gaps between the experiment and MTM. AE experiments of marine shale under uniaxial compression were carried out, and the results were simulated by MTM. In general, the variation trend of the experimental result could be presented by MTM. Nevertheless, the magnitudes of AE parameters by MTM presented notable differences of more than several orders of magnitude compared with those by the experiment. We sequentially used PVBM as a proxy to analyse these discrepancies and systematically evaluate the AE characterization of rocks from the experiment to numerical simulation, considering the influence of wave reflection, energy geometrical diffusion, viscous attenuation, particle size and progressive deterioration of rock material. The combination of MTM and PVBM could reasonably and accurately acquire AE characteristics of the actual AE experiment of rocks by making full use of their respective advantages.
... FDEM simulated seismic activity has been analyzed using two approaches: (1) internal monitoring of the node motions during crack propagation and (2) seismic source inversion of the simulated seismograms ( Lisjak et al., 2013;Grasselli et al., 2012). The latter approach is limited to models with simple geometry and stress conditions, and in this study, we further develop the former approach to obtain more insight into the fracturing process. ...
Full-text available
The purpose of this paper is to present Y-Geo, a new numerical code for geomechanical applications based on the combined finite-discrete element method (FDEM). FDEM is an innovative numerical technique that combines the advantages of continuum-based modeling approaches and discrete element methods to overcome the inability of these methods to capture progressive damage and failure processes in rock. In particular, FDEM offers the ability to explicitly model the transition from continuum to discontinuous behavior by fracture and fragmentation processes. Several algorithmic developments have been implemented in Y-Geo to specifically address a broad range of rock mechanics problems. These features include (1) a quasi-static friction law, (2) the Mohr-Coulomb failure criterion, (3) a rock joint shear strength criterion, (4) a dissipative impact model, (5) an in situ stress initialization routine, (6) a material mapping function (for an exact representation of heterogeneous models), and (7) a tool to incorporate material heterogeneity and transverse isotropy. Application of Y-Geo is illustrated with two case studies that span the capabilities of the code, ranging from laboratory tests to complex engineering-scale problems.
Full-text available
Inhomogeneous materials, such as plaster or concrete, subjected to an external elastic stress display sudden movements owing to the formation and propagation of microfractures. Studies of acoustic emission from these systems reveal power-law behaviour. Similar behaviour in damage propagation has also been seen in acoustic emission resulting from volcanic activity and hydrogen precipitation in niobium. It has been suggested that the underlying fracture dynamics in these systems might display self-organized criticality, implying that long-ranged correlations between fracture events lead to a scale-free cascade of `avalanches'. A hierarchy of avalanche events is also observed in a wide range of other systems, such as the dynamics of random magnets and high-temperature superconductors in magnetic fields, lung inflation and seismic behaviour characterized by the Gutenberg-Richter law. The applicability of self-organized criticality to microfracturing has been questioned,, however, as power laws alone are not unequivocal evidence for it. Here we present a scalar model of microfracturing which generates power-law behaviour in properties related to acoustic emission, and a scale-free hierarchy of avalanches characteristic of self-organized criticality. The geometric structure of the fracture surfaces agrees with that seen experimentally. We find that the critical steady state exhibits plastic macroscopic behaviour, which is commonly observed in real materials.
This supersedes Paper 1 (Gutenberg and Richter, 1942). Additional data are presented. Revisions involving intensity and acceleration are minor. The equation log a = I/3 − 1/2 is retained. The magnitude-energy relation is revised as follows: log E = 9.4 + 2.14 M – 0.054 M^2 (20). A numerical equivalent, for M from 1 to 8.6, is log E = 9.1 + 1.75 M + log (9-m) (21). Equation (20) is based on log (A_0/T_0) = -0.76 + 0.91 M – 0.027M^2 (7) applying at an assumed point epicenter. Eq. (7) is derived empirically from readings of torsion seismometers and USCGS accelerographs. Amplitudes at the USCGS locations have been divided by an average factor of 2 1/2 to compensate for difference in ground; previously this correction was neglected, and log E was overestimated by 0.8. The terms M2 are due partly to the response of the torsion seismometers as affected by increase of ground period with M, partly to the use of surface waves to determine M. If MS results from surface waves, MB from body waves, approximately M_S – M_B = 0.4 (M_S – 7) (27). It appears that MB corresponds more closely to the magnitude scale determined for local earthquakes. A complete revision of the magnitude scale, with appropriate tables and charts, is in preparation. This will probably be based on A/T rather than amplitudes.
Stress waves, known as acoustic emissions (AEs), are released by localized inelastic deformation events during the progressive failure of brittle rocks. Although several numerical models have been developed to simulate the deformation and damage processes of rocks, such as non-linear stress-strain behaviour and localization of failure, only a limited number have been capable of providing quantitative information regarding the associated seismicity. Moreover, the majority of these studies have adopted a pseudo-static approach based on elastic strain energy dissipation that completely disregards elastodynamic effects. This paper describes a new AE modelling technique based on the combined finite-discrete element method (FEM/DEM), a numerical tool that simulates material failure by explicitly considering fracture nucleation and propagation in the modelling domain. Given the explicit time integration scheme of the solver, stress wave propagation and the effect of radiated seismic energy can be directly captured. Quasi-dynamic seismic information is extracted from a FEM/DEM model with a newly developed algorithm based on the monitoring of internal variables (e.g. relative displacements and kinetic energy) in proximity to propagating cracks. The AE of a wing crack propagation model based on this algorithm are cross-analysed by traveltime inversion and energy estimation from seismic recordings. Results indicate a good correlation of AE initiation times and locations, and scaling of energies, independently calculated with the two methods. Finally, the modelling technique is validated by simulating a laboratory compression test on a granite sample. The micromechanical parameters of the heterogeneous model are first calibrated to reproduce the macroscopic stress-strain response measured during standard laboratory tests. Subsequently, AE frequency-magnitude statistics, spatial clustering of source locations and the evolution of AE rate are investigated. The distribution of event magnitude tends to decay as power law while the spatial distribution of sources exhibits a fractal character, in agreement with experimental observations. Moreover, the model can capture the decrease of seismic b value associated with the macrorupture of the rock sample and the transition of AE spatial distribution from diffuse, in the pre-peak stage, to strongly localized at the peak and post-peak stages, as reported in a number of published laboratory studies. In future studies, the validated FEM/DEM-AE modelling technique will be used to obtain further insights into the micromechanics of rock failure with potential applications ranging from laboratory-scale microcracking to engineering-scale processes (e.g. excavations within mines, tunnels and caverns, petroleum and geothermal reservoirs) to tectonic earthquakes triggering.
A technique is presented to simulate seismicity in brittle rock under stress using a distinct element numerical modelling code. Itasca Consulting Group's particle flow code is used to model rock deformation, damage and the resulting seismicity. With this code, rock is represented by thousands of individual particles bonded together at points of contact. Seismicity results when bonds break under high local stresses and stored strain energy is released as kinetic energy. A full 3D formulation that enables the calculation of seismic event locations, magnitudes and mechanisms (moment tensors) is presented. A simulation of an axial compression test on a granite core sample is used to test the modelling technique. The source parameters of the acoustic emissions produced by the model are considered realistic when compared with similar experiments conducted in the laboratory. The technique is then tested on a field-scale problem by applying the algorithms to the 2D mine-by tunnel excavation simulation (Potyondy and Cundall, Int. J. Rock Mech. Min. Sci., this issue). Seismicity produced by the model is compared to actual seismicity recorded in the field and it is shown that locations, magnitudes and mechanisms match reasonably well. The similarities between the modelled and recorded seismicity provide confidence that the model is behaving in a realistic way. It is then shown how the model could be used to examine the details of the mechanisms behind the recorded seismicity by direct observations of particle forces and motions at the seismic sources.
—The mechanism of Kaiser effect was studied with the aid of a damage model for rock. Recognizing that the AE counts are transient elastic waves due to local damage of the rock, the quantitative relation between AE counts and statistical distribution of the local strength of the rock has been established. Subsequently, according to Damage Theory, an expression for Kaiser Effect under uniaxial stress state was derived from the model. This is found to be in good agreement with the experimental results.
Microseismic monitoring during hydraulic fracturing treatments has confirmed that hydraulic fractures are much more complex than might have been assumed even a few years ago, when conventional fracture models were considered adequate. Analysis of diagnostic pump-in tests and mining tunnels has shown that fracture complexity exists in both the near-wellbore and far-field regions of the fracture. Also, microseismic monitoring and interpretation have shown that even fractures initiated in the same wellbore during successive stages can have distinctly different characteristics. Evaluating the effectiveness of hydraulic fracture treatments using microseismic events is challenging. The most common techniques attempt to correlate production with the dimensions of the microseismic clouds and volume estimates based on the density of microseismic events. Geophysical interpretation has shown that microseismic activity recorded during fracturing treatments can sometimes be associated with existing geological structures such as faults. It is possible to examine the frequency of the microseismic event magnitudes during a fracturing treatment and determine if microseismic events are being produced by the failure of the existing rock fabric, or activation of existing geologic structural features, which might be detrimental to well performance. The resulting frequency-magnitude distributions can then be correlated to observed fracture geometries. We show that it is possible to use microseismic magnitude to identify whether faults are influencing the observed dimensions of the microseismic event cloud. We also show that it is possible to use microseismic magnitude values to evaluate fracture behavior in real-time applications, allowing stimulation engineers to modify individual stage treatment designs as the specific situation dictates. The potential benefits to both stimulation cost and production results will also be discussed.
- A bonded-particle model is used to simulate shear-type microseismic events induced by tunnel excavation in granite. The model represents a volume of granite by an assembly of 50,000 individual particles bonded together at points of contact. A plane of weakness is included in the model and this plane is subjected to increasing shear load while the normal load across the plane is held constant. As shear stress in the model increases, bonds begin to break and small acoustic emissions (AE) result. After enough bonds have broken, macro-slip occurs across the large portions of the fault in an unstable manner. Since the model is run dynamically, seismic source information can be calculated for the simulated AE and macro-slip events. This information is compared with actual results obtained from seismic monitoring around an underground excavation. Although the modelled events exhibit larger magnitudes than the actual recorded events, there are many similarities between the model and the actual results, namely the presence of foreshocks before the macro-slip events and the patterns of energy release during loading. In particular, the model provides the ability to examine the complexity of the slip events in detail.