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Excavation-induced fault instability: Possible causes and implications for seismicity
Tunnelling and Underground Space Technology 92 (2019) 103041
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Excavation-induced fault instability: Possible causes and implications for seismicity Kang Duana, Yinlin Jib, Nuwen Xuc, Zhijun Wand, Wei Wub,
T
⁎
a
School of Civil Engineering, Shandong University, Jinan, China School of Civil and Environmental Engineering, Nanyang Technological University, Singapore c State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, China d Key Laboratory of Deep Coal Resource Mining, School of Mines, China University of Mining and Technology, Xuzhou, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Underground excavation Stress evolution Fault instability Discrete element method
Fault rupture and associated seismicity have been reported frequently in underground excavation. The mechanism that drives the human-induced geohazards still eludes explanation, and uncovering this mechanism relies heavily on our understanding of the failure characteristics of fractured rock. We carried out the triaxial compression testing and discrete element modelling on intact and fractured granite samples to consider the controllable change of the angle β between the maximum principal stress orientation and pre-existing fracture orientation and to interpret the complicated mechanism of fault rupture adjacent to rock excavation. Our results show that the reduction of the angle β leads to the failure pattern of fractured samples changing from the tensile failure of rock matrix to the shear failure along pre-existing fractures. This transition results in relatively small b value, as small magnitude AE events decrease in the rock matrix and large magnitude AE events concentrate along pre-existing fractures. The change of b value in the pre-peak stage is independent to the angle β, implying the challenge in rock failure prediction. Our study also indicates that fault rupture adjacent to rock excavation is due to the changes of magnitude and orientation of principal stresses, and the associated seismicity is likely dependent on the portions of rock matrix and fractures involved in the failure process.
1. Introduction Multiple lines of evidence indicate that excavation activities perturb the stress equilibrium of rock masses, presumably resulting in the shear rupture of nearby faults (Snelling et al., 2013; Wu et al., 2017; Yang et al., 2018). Although fault instability is primarily induced by the unloading activities, it is also controlled by geological conditions (e.g., in-situ stress, rock type, fault geometry and distribution). One notable example was the Jinping II hydropower station project in China, in which fault reactivation was frequently reported due to the excavationinduced disturbance on pre-existing faults in highly stressed rock masses (Zhang et al., 2013; Xu et al., 2016; Manouchehrian and Cai, 2018). Fig. 1 illustrates an activated fault recognized at the periphery of an excavated tunnel after a seismic event with a Richter magnitude of 2.0 occurred on November 28th, 2009 (Xu et al., 2016). The in-situ stress is obtained from Zhang et al. (2013). After the tunnel excavation, the in-situ stress was not subjected to any change in the far-field region. However, the radial stress at the tunnel perimeter approached zero, and the maximum principal stress became vertical (Cai, 2008). The changes
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of principal stress magnitude and orientation from the far-field region to the tunnel boundary indicated stress evolution along the fault. Consequently, one portion of the fault close to the tunnel was collapsed, but the other portions remained stable. Understanding the mechanism of excavation-induced fault instability is critical for optimizing excavation strategies in underground projects. The complicated process of rock collapse and associated seismicity is dependent not only on the change of principal stress orientation with respect to unvaried fault orientation, but also on the portions of rock matrix and faults involved in this process. Because the excavation activities can modify stress distribution near the tunnel boundary, the principal stresses may rotate to accommodate the change in stress state (Yin and Rogers, 1995). The stress rotation also influences the magnitude and orientation of the stresses acting on nearby faults. Meanwhile, the change of the angle between the maximum principal stress orientation and pre-existing fault orientation may lead to fault reactivation from unfavorable orientation with damage in rock matrix to favorable orientation slipping along discontinuous planes. Our capability of acquiring the tempo-spatial characteristics of rock
Corresponding author. E-mail address: [email protected] (W. Wu).
https://doi.org/10.1016/j.tust.2019.103041 Received 29 January 2019; Received in revised form 6 April 2019; Accepted 12 July 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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method can simulate realistic rock with pre-existing fractures and mimic AE events during rock failure (Cundall and Strack, 1979; Ivars et al., 2008). The objective of this study is to investigate the possible causes and associated seismicity of excavation-induced fault instability. Because stress rotation is difficult to simulate in laboratory experiments, we maintain the maximum principal stress orientation in triaxial compression tests and change the inclination angles of single fractures in granite samples. The intact and fractured granite samples are collected from the same geological area, but may exhibit different matrix and fracture behaviours. The DEM model is thus used to simulate the effect of inclination angle change on the failure process of a fractured sample with fixed matrix and fracture properties. The evolutions of AE event, moment tensor and b value are also studied to interpret the seismic events during the failure process. 2. Experimental study We carried out a suite of triaxial compression tests to investigate the effect of the angle between the maximum principal stress orientation and pre-existing fracture orientation on the failure process of fractured samples. We used the Bukit Timah granite sourced from the central region of Singapore Island. The typical mineralogy of this light-grey and medium-grained granite includes 60–65% feldspar, 30% quartz, as well as 5–10% biotite and hornblende (Zhao, 1996). The bulk density, water content, porosity and P-wave velocity of the granite were 2660 kg/m3, 0.07%, 0.26% and 5900 m/s, respectively, which were measured based on the suggested methods proposed by the International Society for Rock Mechanics (ISRM, 2007). We collected two fractured samples and an intact sample from 51.4 mm diameter granite cores at similar depths. The lengths of the two fractured samples were 100 mm and 120 mm, respectively. The intact sample was 100 mm long without visible surface cracks and used as a comparison. Because the orientation of the maximum principal stress was not variable in the experimental setup, we selected one granite sample containing single pre-existing unopened fracture with 45° inclination angle and the other containing similar fracture configuration with 63° inclination angle. The angle between the maximum principal stress orientation and pre-existing fracture orientation was defined as β. Thus, the corresponding β for the two fractured samples were 45° and 27°, respectively. We used the MTS rock mechanics test system to conduct the triaxial compression tests and the SAMOS AE monitoring system to record AE events. The MTS test system is able to supply an axial load up to 2600 kN accurate to ± 0.3% and a confining pressure up to 140 MPa accurate to ± 0.3%. The axial and circumferential extensometers attached on the central part of a granite sample measure the axial and radial deformation, respectively, with an accuracy of ± 0.2%. The acoustic emission system enables data transfer at speeds up to 132 Mb/ s, and covers frequencies ranging from 1 kHz to 400 kHz. We used three piezoelectric sensors to detect AE events at a sampling rate of 1 MHz, and maintained both pre-amplitude gain and amplitude threshold values at 40 dB to compensate for ambient noise. For each triaxial compression test on a granite sample, we increased
Fig. 1. Evolution of principal stresses along a pre-existing fault from the farfield region to the periphery of an excavated tunnel in the Jinping Ⅱ hydropower station project. σ30 is the maximum principal stress. (modified from Zhang et al. 2013).
failure can improve our understanding of excavation-induced rock collapse and associated seismicity. The instantaneous failure rate and invisible cracking process of rock are the major barriers to the direct observation of rock failure characteristics. Acoustic emission (AE) is an effective approach to monitor the brittle failure of rock due to its high sensitivity, real-time measurement, and source localization capability (Lockner, 1993). The rapid release of strain energy stored in rock produces elastic waves, known as AE events, which directly reflect crack development. The AE events monitored from laboratory-scale rock failure are similar to the seismic waves generated from natural earthquakes (Amitrano, 2003) and explain the occurrence of earthquake aftershock sequences (Scholz, 1968). The AE events can also be used to illustrate crack nucleation and propagation (Lockner, 1993; He et al., 2010). However, the AE events recorded from laboratory experiments cannot distinguish different types of cracks, which are important to identify the portions of rock matrix and fractures involved in the failure process. Shear cracks likely concentrate along favorably oriented fractures, whereas tensile cracks mainly distribute in rock matrix (Jouinaux et al., 2001). Therefore, we employ the discrete element method (DEM) to identify shear and tensile cracks. The numerical
Table 1 Micro-parameters used to represent the intact and fractured granite samples. The micro-parameters of particle, parallel bond and smooth joint are calibrated based on the triaxial compression tests on the intact sample and fractured sample with β = 27°. Particle property
Value
Parallel bond property
Value
Smooth joint property
Value
Contact modulus (GPa) Ratio between normal and shear stiffness of particle Coefficient of friction Particle radius ratio Minimum particle radius (mm)
46.5 1.86 0.50 1.66 0.2
Parallel bond modulus (GPa) Ratio between normal and shear stiffness of parallel bond Tensile strength of parallel bond (MPa) Shear strength of parallel bond (MPa) Parallel bond radius ratio
46.5 1.86 239 ± 23.9 239 ± 23.9 1.0
Normal stiffness (GPa/s) Shear stiffness (GPa/s) Friction coefficient Dilation angle (°) Tensile strength (MPa) Cohesion (MPa) Friction angle (°)
800 800 0.82 0 32 32 40
2
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Fig. 2. (a) Intact sample and two fractured samples with (b) β = 45° and (c) β = 27° after the triaxial compression tests under 20 MPa confining pressure. The diameter of all the samples is 51.4 mm, and the heights of the intact sample and fractured samples with β = 45° and 27° are 100 mm, 100 mm and 120 mm, respectively.
stiffness was equal to the shear stiffness, and subsequently varied the tensile strength, cohesion and friction angle to fit the magnitude of the peak stress. Finally, we adjusted the friction coefficient to match the residual strength in the post-peak stage. For the fractured sample with β = 45°, we simply altered the dip angle to obtain the DEM model. Additionally, we considered two fractured samples with β = 60° and 35°, which were not available in the experimental study, to assess the overall changes of deviator stress and crack number as a function of β . In the DEM model, strain energy is released when the bonds break, and seismic source information can be simultaneously tracked. We adopted a validated technique proposed by Hazzard and Young (2002, 2004) to calculate moment tensor in the bonded particle model. This technique sums the components of force changes at neighboring particle contacts to obtain the elements of moment tensor matrix:
the confining pressure to 20 MPa and the deviator stress at an axial displacement rate of 0.001 mm/s. After the failure of the sample, the confining pressure and axial displacement rate were maintained until the residual stress became stable. We simultaneously monitored AE events during the test. The confining pressure was used to simulate the stress level at potential excavation sites in Bukit Timah formation and also considered as an intermediate stress level to study the mechanical properties of rock from the Jinping II hydropower station project (Jiang et al., 2016). The axial displacement rate was applied to perform a quasi-static compression test and to avoid the rate-dependent effect on rock behaviors. 3. Numerical model As selecting rock samples containing pre-existing fractures with similar configurations and desired inclination angles was very challenging, we used the two-dimensional particle flow code (PFC 2D) based on DEM to further study the effect of the angle between the maximum principal stress orientation and pre-existing fracture orientation on the failure process of fractured samples. Rock samples were represented by bonded particle models, which were assemblies of rigid particles bonded at their contacts (Potyondy and Cundall, 2004). Each contact was bonded through a set of elastic springs with constant normal and shear stiffness. The movement of particles followed Newton’s second law, and the interaction between adjacent particles was based on forcedisplacement law. The geometrical and mechanical properties of the DEM models were the same as those used in the experimental study. The intact sample consisted of 20,694 particles following the uniform size distribution with Rmin = 0.2 mm and Rmax/Rmin = 1.66, where R is the radius of particles. The micro-parameters used to represent the sample are listed in Table 1. The micro-parameters of particles and parallel bonds were calibrated based on the triaxial compression test on the intact sample under 20 MPa confining pressure, following the calibration process recommended by Itasca (2010). In the fractured samples, to represent pre-existing fractures, we used a series of continuous smooth joint contacts dipping at desired angles to the sample axis in the bonded particle models (Ivars et al., 2008; Duan et al., 2018). The micro-parameters of smooth joint contacts were calibrated to reproduce the mechanical properties of the fractured sample with β = 27°. We first chose the stiffness of smooth joint contacts by assuming high tensile strength and cohesion (e.g., 100 MPa) to fit the slope of the stress-strain curve. We then assumed that the normal
Mij =
∑ ΔFi Rj S
(1)
where ΔFi is the ith component of force change, Rj is the jth component of the distance from event centroid to contact point, and S is the surface involved in the event. The moment magnitude is then calculated based on the eigenvalues of moment tensors. 4. Results and discussion 4.1. Experimental results Fig. 3 shows the triaxial compression test results of the intact and fractured samples under 20 MPa confining pressure, in terms of deviator stress, cumulative AE count and AE energy rate. The three samples experience similar pre-peak behaviors. The deviator stresses increase linearly until the peak stresses are reached. For the intact sample, the high deviator stress increases slowly before the peak value appears likely owing to the generation and interaction of induced cracks. The intact sample breaks accompanied by both the tensile and shear failure occurred in the rock matrix (Fig. 2a). The residual strength of the intact sample is relatively high due to the mechanical interaction of randomly formed cracks. However, pre-existing fractures significantly degrade the stiffness and strength of fractured samples and affect the post-peak behaviors. The fractured sample with β = 45° exhibits both the shear failure along the pre-existing fracture and the tensile failure in the rock matrix (Fig. 2b). The residual strength is relatively low as the pre-existing fracture partially dominates the postpeak behavior. The failure of the fractured sample with β = 27° is 3
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Fig. 4. Deviator stress as a function of axial strain obtained from the experimental and numerical tests on the intact and fractured samples with β = 27°, respectively, under 20 MPa confining pressure.
cracks. For the fractured sample with β = 45° (Fig. 3b), the cumulative AE count also jumps at the peak stress and slightly increases in the postpeak stage due to the mechanical interaction of limited tensile failure in the rock matrix. The fractured sample with β = 27° exhibits the lowest AE energy rate at the peak stress and nearly constant cumulative AE count in the post-peak stage, indicating that the shear failure along the favorably oriented fracture releases negligible strain energy. 4.2. Numerical results The DEM model evaluates the tensile and shear failure modes of parallel bonds and smooth joints, respectively, to identify the portions of rock matrix and fractures involved in the failure process. Fig. 4 shows that the DEM model can replicate the strength and stiffness of both the intact sample and fractured sample with β = 27°. The DEM model can also reproduce the general trend of deviator stress, in terms of sudden drop and residual strength. All the cases shown in Fig. 5 indicate that the deviator stress in the pre-peak stage gradually increases from zero to the peak value, implying that both the intact and fractured samples experience elastic deformation. Very few cracks appear in this stage. When the deviator stress approaches the peak value, a slight increase of crack number emerges in the intact sample and fractured samples with β = 60° and 45°. Most of the cracks are formed by the tensile failure of parallel bonds in the model, suggesting the cracks likely initiate in the rock matrix. After that, the deviator stress drops, and the number of cracks jumps simultaneously. In the fractured samples with β = 35° and 27°, a little number of cracks appear in the pre-peak stage. The shear failure of smooth joints in the model dominates the post-peak stage, indicating limited damage in the rock matrix. The failure modes of parallel bonds and smooth joints in the five cases are further analyzed in Fig. 6. The crack numbers obtained from different failure modes at the peak stress and the end of the post-peak stage exhibit that the majority of induced cracks appears when the peak stress is reached, which align with the results of AE energy rate monitored in the experimental study (Fig. 3). For the intact sample, approximately 90% of the parallel bonds fail in tension (Fig. 6a). In the fractured sample with β = 60°, the tensile failure of parallel bond also dominates the failure process, and the shear failure of smooth joint is relatively insignificant. However, for the fractured sample with β = 45° (Fig. 6c), a considerable amount of the shear failure of smooth joint occurs at the post-peak stage. With further decrease of β , the shear failure of smooth joint becomes the dominant failure mode (Fig. 6d and e). For all the fractured samples, both the shear failure of parallel bond
Fig. 3. Results obtained from the triaxial compression tests on (a) the intact sample and fractured samples with (b) β = 45° and (c) β = 27° under 20 MPa confining pressure.
induced along the pre-existing fracture (Fig. 2c). The favorably oriented fracture shows the lowest residual strength and no obvious damage in the rock matrix. The result of AE events aligns with the measurement of deviator stresses and the observation of failure patterns. The vertical axis scale of cumulative AE count shown in Fig. 3a is much greater than those given in Fig. 3b and c. Fig. 3a shows that the cumulative AE count of the intact sample slowly increases in the pre-peak stage, and suddenly jumps when the peak stress appears. This observation confirms our above explanation that the pre-peak non-linear deformation is mainly associated with the generation and interaction of induced cracks. After that, the cumulative AE count still increases with occasional jumps of AE energy rate, due to the mechanical interaction of randomly formed 4
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Fig. 5. Numerical results of deviator stress and cumulative crack number as a function of axial strain, obtained from the failure of (a) intact sample and fractured samples with (b) β = 60°, (c) β = 45°, (d) β = 35° and (e) β = 27° under 20 MPa confining pressures.
equivalent force, is displayed in Fig. 7b. Two arrows of equal length pointing away from each other represent a tensile event, while two arrows in parallel and pointing in opposite directions mean a shear event (Al-Busaidi et al., 2005). The length of an arrow is proportional to the magnitude of corresponding principal value of the moment tensor matrix (Eq. (1)). The moment tensors for tensile cracks indicate that the tensile failure of rock matrix plays a dominant role in the failure process of the intact sample. The moment tensors for shear cracks are relatively small in length and randomly distributed around the induced fractures and in the rock matrix. When β decreases, the magnitudes of the moment tensors for both tensile and shear cracks decrease in the fractured samples, and the moment tensors for shear cracks accumulate along the
and tensile failure of smooth joint are negligible. When β decreases, the dominant failure mode of the fractured samples changes from the tensile failure of parallel bond to the shear failure of smooth joint. In Fig. 7, the spatial distributions of AE events and corresponding moment tensors recorded from the DEM models interpret the failure pattern and strain energy release of the intact and fractured samples. The diameter of red circle in Fig. 7a represents the magnitude of an AE event. In the intact sample, the AE events with various magnitudes randomly occur in the rock matrix. For the fractured samples, with decreasing β , both the magnitude and quantity of the AE events in the rock matrix decrease, and the large magnitude AE events concentrate along the pre-existing fractures. The moment tensor, depicted as 5
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Fig. 6. Failure modes of parallel bond and smooth joint at the peak stress and the end of the post-peak stage, respectively, obtained from the numerical tests on (a) intact sample and fractured samples with (b) β = 60°, (c) β = 45°, (d) β = 35° and (e) β = 27° under 20 MPa confining pressures.
log N = a − bM
pre-existing fractures. Fig. 8 shows the frequency and cumulative AE count as a function of magnitude. The frequency of AE events is high in the intact sample, and decreases with smaller β in the fractured samples. This result agrees with those shown in Fig. 3. Similar to previous results (e.g., Lockner, 1993; Amitrano, 2003), the relation between the cumulative AE count and magnitude follows the Gutenberg-Richter law (Gutenberg and Richter, 1954):
(2)
where N is the frequency of events with magnitudes greater than M, and a and b are constants. The b value can be used to describe the relative occurrence of large and small seismic events, and a larger b value indicates a smaller proportion of large event (Schorlemmer et al., 2005). The intact sample fails accompanied by a large proportion of small magnitude AE events, 6
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Fig. 7. Spatial distributions of (a) AE events and (b) moment tensors obtained from the numerical tests on the intact sample and fractured samples with β = 60°, 45°, 35° and 27° under 20 MPa confining pressure.
summarizes the peak stress and b value as a function of β . Comparing to the intact sample, the peak stress of the fractured samples significantly decreases (Fig. 9a). The peak stress drops with smaller β . The maximum peak stress appears when β = 60°, which agrees with the analytical solution of Jaeger (1960). The b value has been used successfully to predict seismic events occurred in intact samples (Lockner et al., 1991). However, for the fractured samples, the change of b value in the prepeak stage is independent to β (Fig. 9b). Both the experimental and numerical results reveal that the fractured samples with relatively small β release negligible AE energy (Figs. 3 and 5). In the post-peak stage, the b value significantly reduces when β is relatively small (e.g., 27°), as the shear failure along the pre-existing fractures is dominant in the failure process. When the fracture is favorable for activation, the low b value indicates a great proportion of large events occurred along the fracture (see Fig. 7a). Our experimental and numerical results also indicate that rock excavation varies both the magnitude and orientation of principal stresses acting on adjacent fractures, presumably resulting in the shear rupture of the fractures. Fig. 10 presents the possible mechanism of the shear rupture. The Mohr circle lies below the failure envelope under the insitu stress condition (see the solid purple circle). After the excavation, the minimum principal stress (i.e., the radial stress at the tunnel perimeter) reduces to zero, whereas the maximum principal stress increases in the vertical direction. This change thus enlarges the radius of the Mohr circle, and leads the circle to exceed partially the failure envelope (see the red circle). Meanwhile, the shear rupture is also dependent on the change of the maximum principal stress orientation. When the preexisting fracture orientation, 2β away from the maximum principal stress orientation, falls in the range marked as damage zone (see the red
while large magnitude AE events are dominant during the failure of fractured samples. This speculation can be verified by the spatial distributions of AE events shown in Fig. 7a. In most of the cases, the b value in the pre-peak stage is larger than that in the post-peak stage, indicating that large magnitude AE events mainly occur when the peak stress is reached. Previous studies also show that smaller cracks are induced in the pre-peak stage and results in a larger b value, and larger cracks with higher strain energy release occurred in the post-peak stage lead to a smaller b value (Wang et al., 2000). Several studies show that the b value obtained in the experimental studies is larger than that recorded in the field measurements (Lockner et al., 1991; Schorlemmer et al., 2005; Thompson et al., 2006). The experimental studies overestimate the portion of small seismic events, as the effect of pre-existing fractures cannot be fully considered in laboratory-scale samples. Moreover, the b value calculated in the DEM model is even larger than that obtained in the experimental and field investigations. This model particularly records the force changes at particle contacts to calculate the moment tensors, which amplifies the portion of small seismic events and finally leads to a large b value (Hazzard and Young, 2002, 2004; Zhang and Zhang, 2017). 4.3. Discussion Although the experimental and numerical configurations are simple in this study, it is easy to control desired parameters and to interpret complex engineering problems. Both the experimental and numerical results indicate that the angle between the maximum principal stress orientation and pre-existing fracture orientation significantly influences the failure pattern and strain energy release of fractured samples. Fig. 9 7
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Fig. 8. Frequency and cumulative AE count as a function of magnitude obtained from the numerical tests on (a) intact sample and fractured samples with (b) β = 60°, (c) β = 45°, (d) β = 35° and (e) β = 27° under 20 MPa confining pressures.
studies (e.g., Cai, 2008), the unloading process is associated not only with the confining pressure decrease but also with the axial stress increase. Hence, instantaneously controlling the changes of confining pressure and axial stress is a necessary improvement to reasonably simulate excavation-induced seismicity.
zone above the failure envelope), the fracture fails along a favorable orientation. Additionally, the magnitude of seismic events is associated with stress evolution. The failure of favorably oriented fractures is mostly along pre-existing planes and likely release less strain energy from rock matrix, as shown in Fig. 7. Fig. 10 also shows the limitation of the triaxial test setup in the study of excavation-induced seismicity. In the triaxial loading test, the confining pressure is fixed, and the diameter of the Mohr circle increases with larger axial stress (see the dashed purple circle). The triaxial unloading test uses the same setup, but applies the fixed axial stress and decreasing confining pressure (Duan et al., 2019), which also leads to the increase of the Mohr circle diameter (see the dotted purple circle). However, as illustrated by the red circle in Fig. 10 and other
5. Conclusions We carried out the experimental and numerical investigations to consider the change of the angle between the maximum principal stress orientation and pre-existing fracture orientation and to interpret the possible mechanism of fault rupture adjacent to rock excavation. Our study shows that the change of the angle is a possible cause of fracture 8
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Fig. 9. (a) Peak stress and (b) b value as a function the angle between the maximum principal stress orientation and fracture orientation (β) at the pre-peak and postpeak stages, respectively.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.tust.2019.103041. References Al-Busaidi, A., Hazzard, J., Young, R., 2005. Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J. Geophys. Res.: Solid Earth 110 (B6). Amitrano, D., 2003. Brittle-ductile transition and associated seismicity: experimental and numerical studies and relationship with the b value. J. Geophys. Res.: SolidEarth 108 (B1). Cai, M., 2008. Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—insight from numerical modeling. Int. J. Rock Mech. Min. Sci. 45 (5), 763–772. Cundall, P.A., Strack, O.D.L., 1979. A discrete numerical model for granular assemblies. Géotechnique 29 (1), 47–65. Duan, K., Wu, W., Kwok, C.Y., 2018. Discrete element modelling of stress-induced instability of directional drilling boreholes in anisotropic rock. Tunnel Undergr. Space Tech. 81, 55–67. Duan, K., Ji, Y.L., Wu, W., Kwok, C.Y., 2019. Unloading-induced failure of brittle rocks and implications for excavation-induced strain burst. Tunnel Undergr. Space Tech. 84, 495–506. Gutenberg, B., Richter, C.F., 1954. Frequency and energy of earthquakes. Seismicity Earth Assoc. Phenomena 17–19. Hazzard, J., Young, R., 2004. Dynamic modelling of induced seismicity. Int. J. Rock Mech. Min. Sci. 41 (8), 1365–1376. Hazzard, J., Young, R., 2002. Moment tensors and micromechanical models. Tectonophysics 356 (1–3), 181–197. He, M.C., Miao, J.L., Feng, J.L., 2010. Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions. Int. J. Rock Mech. Min. Sci. 47 (2), 286–298. International Society for Rock Mechanics, 2007. The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974-2006. International Society for Rock Mechanics, Commission on Testing Methods. Itasca. PFC2D: particle flow code in 2 dimensions. 4.0 ed. Minneapolis: Itasca; 2010. Ivars DM, Potyondy D, Pierce M, Cundall P. The smooth-joint contact model. In: Proceedings of WCCM8-ECCOMAS. 2008; 8th. Jaeger, J., 1960. Shear failure of anistropic rocks. Geol. Mag. 97 (1), 65–72. Jiang, Q., Zhong, S., Cui, J., Feng, X.T., Song, L., 2016. Statistical characterization of the mechanical parameters of intact rock under triaxial compression: an experimental proof of the Jinping marble. Rock Mech. Rock Eng. 49 (12), 4631–4646. Jouinaux, L., Masuda, K., Lei, X., et al., 2001. Comparison of the microfracture localization in granite between fracturation and slip of a preexisting macroscopic healed joint by acoustic emission measurements. J. Geophys. Res.: Solid Earth 106 (B5), 8687–8698. Lockner, D.A., 1993. The role of acoustic emission in the study of rock fracture. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30 (7), 883–899. Lockner, D.A., Byerlee, J.D., Kuksenko, V., Ponomarev, A., Sidorin, A., 1991. Quasi-static fault growth and shear fracture energy in granite. Nature 350 (6313), 39–42. Manouchehrian, A., Cai, M., 2018. Numerical modeling of rockburst near fault zones in deep tunnels. Tunnel Undergr. Space Tech. 80, 164–180. Potyondy, D.O., Cundall, P.A., 2004. A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 41 (8), 1329–1364.
Fig. 10. Change of principal stresses on a pre-existing fracture before (solid purple circle) and after (solid red circle) rock excavation, and comparison the limitation of stress paths in the triaxial loading (dashed purple circle) and unloading (dotted purple circle) tests. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
instability and significantly influences rock failure pattern and strain energy release during the failure process. When the angle β decreases from 60° to 27°, the failure pattern of fractured samples changes from the tensile failure of rock matrix to the shear failure along pre-existing fractures. If the tensile failure of rock matrix is less involved in the failure process, small magnitude AE events diminish in rock matrix and large magnitude AE events concentrate along pre-existing fractures, resulting in relatively small b value. For favorably oriented fractures, the AE energy released in the pre-peak stage is negligible, indicating that b value may not be reliable as a seismic precursor for the fracture failure. Our data also implicate that the excavation-induced fault rupture highly depends on the magnitude and orientation of principle stresses, and the intensity of seismic events is associated with the portions of rock matrix and fractures involved in the failure process.
Acknowledgements This work was mainly supported by the Start-Up Grant from Nanyang Technological University, Singapore. Zhijun Wan acknowledges the Fundamental Research Funds for the Central Universities (Grant No. 2017CXNL01). 9
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Schorlemmer, D., Wiemer, S., Wyss, M., 2005. Variations in earthquake-size distribution across different stress regimes. Nature 437 (7058), 539–542. Snelling, P.E., Godin, L., McKinnon, S.D., 2013. The role of geologic structure and stress in triggering remote seismicity in Creighton Mine, Sudbury, Canada. Int. J. Rock Mech. Min. Sci. 58, 166–179. Scholz, C.H., 1968. Microfractures, aftershocks, and seismicity. Bull. Seismol. Soc. Am. 58 (3), 1117–1130. Thompson, B.D., Young, R.P., Lockner, D.A., 2006. Fracture in Westerly granite under AE feedback and constant strain rate loading: nucleation, quasi-static propagation, and the transition to unstable fracture propagation. Pure Appl. Geophys. 163 (5–6), 995–1019. Wang, Y.C., Yin, X.C., Ke, F.J., Xia, M.F., Peng, K.Y., 2000. Numerical simulation of rock failure and earthquake process on mesoscopic scale. Pure Appl. Geophys. 157, 1905–1928. Wu, W., Zhao, Z., Duan, K., 2017. Unloading-induced instability of a simulated granular fault and implications for excavation-induced seismicity. Tunnel Undergr. Space Tech. 63, 154–161.
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Excavation-induced fault instability: Possible causes and implications for seismicity Kang Duana, Yinlin Jib, Nuwen Xuc, Zhijun Wand, Wei Wub,
T
⁎
a
School of Civil Engineering, Shandong University, Jinan, China School of Civil and Environmental Engineering, Nanyang Technological University, Singapore c State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, China d Key Laboratory of Deep Coal Resource Mining, School of Mines, China University of Mining and Technology, Xuzhou, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Underground excavation Stress evolution Fault instability Discrete element method
Fault rupture and associated seismicity have been reported frequently in underground excavation. The mechanism that drives the human-induced geohazards still eludes explanation, and uncovering this mechanism relies heavily on our understanding of the failure characteristics of fractured rock. We carried out the triaxial compression testing and discrete element modelling on intact and fractured granite samples to consider the controllable change of the angle β between the maximum principal stress orientation and pre-existing fracture orientation and to interpret the complicated mechanism of fault rupture adjacent to rock excavation. Our results show that the reduction of the angle β leads to the failure pattern of fractured samples changing from the tensile failure of rock matrix to the shear failure along pre-existing fractures. This transition results in relatively small b value, as small magnitude AE events decrease in the rock matrix and large magnitude AE events concentrate along pre-existing fractures. The change of b value in the pre-peak stage is independent to the angle β, implying the challenge in rock failure prediction. Our study also indicates that fault rupture adjacent to rock excavation is due to the changes of magnitude and orientation of principal stresses, and the associated seismicity is likely dependent on the portions of rock matrix and fractures involved in the failure process.
1. Introduction Multiple lines of evidence indicate that excavation activities perturb the stress equilibrium of rock masses, presumably resulting in the shear rupture of nearby faults (Snelling et al., 2013; Wu et al., 2017; Yang et al., 2018). Although fault instability is primarily induced by the unloading activities, it is also controlled by geological conditions (e.g., in-situ stress, rock type, fault geometry and distribution). One notable example was the Jinping II hydropower station project in China, in which fault reactivation was frequently reported due to the excavationinduced disturbance on pre-existing faults in highly stressed rock masses (Zhang et al., 2013; Xu et al., 2016; Manouchehrian and Cai, 2018). Fig. 1 illustrates an activated fault recognized at the periphery of an excavated tunnel after a seismic event with a Richter magnitude of 2.0 occurred on November 28th, 2009 (Xu et al., 2016). The in-situ stress is obtained from Zhang et al. (2013). After the tunnel excavation, the in-situ stress was not subjected to any change in the far-field region. However, the radial stress at the tunnel perimeter approached zero, and the maximum principal stress became vertical (Cai, 2008). The changes
⁎
of principal stress magnitude and orientation from the far-field region to the tunnel boundary indicated stress evolution along the fault. Consequently, one portion of the fault close to the tunnel was collapsed, but the other portions remained stable. Understanding the mechanism of excavation-induced fault instability is critical for optimizing excavation strategies in underground projects. The complicated process of rock collapse and associated seismicity is dependent not only on the change of principal stress orientation with respect to unvaried fault orientation, but also on the portions of rock matrix and faults involved in this process. Because the excavation activities can modify stress distribution near the tunnel boundary, the principal stresses may rotate to accommodate the change in stress state (Yin and Rogers, 1995). The stress rotation also influences the magnitude and orientation of the stresses acting on nearby faults. Meanwhile, the change of the angle between the maximum principal stress orientation and pre-existing fault orientation may lead to fault reactivation from unfavorable orientation with damage in rock matrix to favorable orientation slipping along discontinuous planes. Our capability of acquiring the tempo-spatial characteristics of rock
Corresponding author. E-mail address: [email protected] (W. Wu).
https://doi.org/10.1016/j.tust.2019.103041 Received 29 January 2019; Received in revised form 6 April 2019; Accepted 12 July 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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method can simulate realistic rock with pre-existing fractures and mimic AE events during rock failure (Cundall and Strack, 1979; Ivars et al., 2008). The objective of this study is to investigate the possible causes and associated seismicity of excavation-induced fault instability. Because stress rotation is difficult to simulate in laboratory experiments, we maintain the maximum principal stress orientation in triaxial compression tests and change the inclination angles of single fractures in granite samples. The intact and fractured granite samples are collected from the same geological area, but may exhibit different matrix and fracture behaviours. The DEM model is thus used to simulate the effect of inclination angle change on the failure process of a fractured sample with fixed matrix and fracture properties. The evolutions of AE event, moment tensor and b value are also studied to interpret the seismic events during the failure process. 2. Experimental study We carried out a suite of triaxial compression tests to investigate the effect of the angle between the maximum principal stress orientation and pre-existing fracture orientation on the failure process of fractured samples. We used the Bukit Timah granite sourced from the central region of Singapore Island. The typical mineralogy of this light-grey and medium-grained granite includes 60–65% feldspar, 30% quartz, as well as 5–10% biotite and hornblende (Zhao, 1996). The bulk density, water content, porosity and P-wave velocity of the granite were 2660 kg/m3, 0.07%, 0.26% and 5900 m/s, respectively, which were measured based on the suggested methods proposed by the International Society for Rock Mechanics (ISRM, 2007). We collected two fractured samples and an intact sample from 51.4 mm diameter granite cores at similar depths. The lengths of the two fractured samples were 100 mm and 120 mm, respectively. The intact sample was 100 mm long without visible surface cracks and used as a comparison. Because the orientation of the maximum principal stress was not variable in the experimental setup, we selected one granite sample containing single pre-existing unopened fracture with 45° inclination angle and the other containing similar fracture configuration with 63° inclination angle. The angle between the maximum principal stress orientation and pre-existing fracture orientation was defined as β. Thus, the corresponding β for the two fractured samples were 45° and 27°, respectively. We used the MTS rock mechanics test system to conduct the triaxial compression tests and the SAMOS AE monitoring system to record AE events. The MTS test system is able to supply an axial load up to 2600 kN accurate to ± 0.3% and a confining pressure up to 140 MPa accurate to ± 0.3%. The axial and circumferential extensometers attached on the central part of a granite sample measure the axial and radial deformation, respectively, with an accuracy of ± 0.2%. The acoustic emission system enables data transfer at speeds up to 132 Mb/ s, and covers frequencies ranging from 1 kHz to 400 kHz. We used three piezoelectric sensors to detect AE events at a sampling rate of 1 MHz, and maintained both pre-amplitude gain and amplitude threshold values at 40 dB to compensate for ambient noise. For each triaxial compression test on a granite sample, we increased
Fig. 1. Evolution of principal stresses along a pre-existing fault from the farfield region to the periphery of an excavated tunnel in the Jinping Ⅱ hydropower station project. σ30 is the maximum principal stress. (modified from Zhang et al. 2013).
failure can improve our understanding of excavation-induced rock collapse and associated seismicity. The instantaneous failure rate and invisible cracking process of rock are the major barriers to the direct observation of rock failure characteristics. Acoustic emission (AE) is an effective approach to monitor the brittle failure of rock due to its high sensitivity, real-time measurement, and source localization capability (Lockner, 1993). The rapid release of strain energy stored in rock produces elastic waves, known as AE events, which directly reflect crack development. The AE events monitored from laboratory-scale rock failure are similar to the seismic waves generated from natural earthquakes (Amitrano, 2003) and explain the occurrence of earthquake aftershock sequences (Scholz, 1968). The AE events can also be used to illustrate crack nucleation and propagation (Lockner, 1993; He et al., 2010). However, the AE events recorded from laboratory experiments cannot distinguish different types of cracks, which are important to identify the portions of rock matrix and fractures involved in the failure process. Shear cracks likely concentrate along favorably oriented fractures, whereas tensile cracks mainly distribute in rock matrix (Jouinaux et al., 2001). Therefore, we employ the discrete element method (DEM) to identify shear and tensile cracks. The numerical
Table 1 Micro-parameters used to represent the intact and fractured granite samples. The micro-parameters of particle, parallel bond and smooth joint are calibrated based on the triaxial compression tests on the intact sample and fractured sample with β = 27°. Particle property
Value
Parallel bond property
Value
Smooth joint property
Value
Contact modulus (GPa) Ratio between normal and shear stiffness of particle Coefficient of friction Particle radius ratio Minimum particle radius (mm)
46.5 1.86 0.50 1.66 0.2
Parallel bond modulus (GPa) Ratio between normal and shear stiffness of parallel bond Tensile strength of parallel bond (MPa) Shear strength of parallel bond (MPa) Parallel bond radius ratio
46.5 1.86 239 ± 23.9 239 ± 23.9 1.0
Normal stiffness (GPa/s) Shear stiffness (GPa/s) Friction coefficient Dilation angle (°) Tensile strength (MPa) Cohesion (MPa) Friction angle (°)
800 800 0.82 0 32 32 40
2
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Fig. 2. (a) Intact sample and two fractured samples with (b) β = 45° and (c) β = 27° after the triaxial compression tests under 20 MPa confining pressure. The diameter of all the samples is 51.4 mm, and the heights of the intact sample and fractured samples with β = 45° and 27° are 100 mm, 100 mm and 120 mm, respectively.
stiffness was equal to the shear stiffness, and subsequently varied the tensile strength, cohesion and friction angle to fit the magnitude of the peak stress. Finally, we adjusted the friction coefficient to match the residual strength in the post-peak stage. For the fractured sample with β = 45°, we simply altered the dip angle to obtain the DEM model. Additionally, we considered two fractured samples with β = 60° and 35°, which were not available in the experimental study, to assess the overall changes of deviator stress and crack number as a function of β . In the DEM model, strain energy is released when the bonds break, and seismic source information can be simultaneously tracked. We adopted a validated technique proposed by Hazzard and Young (2002, 2004) to calculate moment tensor in the bonded particle model. This technique sums the components of force changes at neighboring particle contacts to obtain the elements of moment tensor matrix:
the confining pressure to 20 MPa and the deviator stress at an axial displacement rate of 0.001 mm/s. After the failure of the sample, the confining pressure and axial displacement rate were maintained until the residual stress became stable. We simultaneously monitored AE events during the test. The confining pressure was used to simulate the stress level at potential excavation sites in Bukit Timah formation and also considered as an intermediate stress level to study the mechanical properties of rock from the Jinping II hydropower station project (Jiang et al., 2016). The axial displacement rate was applied to perform a quasi-static compression test and to avoid the rate-dependent effect on rock behaviors. 3. Numerical model As selecting rock samples containing pre-existing fractures with similar configurations and desired inclination angles was very challenging, we used the two-dimensional particle flow code (PFC 2D) based on DEM to further study the effect of the angle between the maximum principal stress orientation and pre-existing fracture orientation on the failure process of fractured samples. Rock samples were represented by bonded particle models, which were assemblies of rigid particles bonded at their contacts (Potyondy and Cundall, 2004). Each contact was bonded through a set of elastic springs with constant normal and shear stiffness. The movement of particles followed Newton’s second law, and the interaction between adjacent particles was based on forcedisplacement law. The geometrical and mechanical properties of the DEM models were the same as those used in the experimental study. The intact sample consisted of 20,694 particles following the uniform size distribution with Rmin = 0.2 mm and Rmax/Rmin = 1.66, where R is the radius of particles. The micro-parameters used to represent the sample are listed in Table 1. The micro-parameters of particles and parallel bonds were calibrated based on the triaxial compression test on the intact sample under 20 MPa confining pressure, following the calibration process recommended by Itasca (2010). In the fractured samples, to represent pre-existing fractures, we used a series of continuous smooth joint contacts dipping at desired angles to the sample axis in the bonded particle models (Ivars et al., 2008; Duan et al., 2018). The micro-parameters of smooth joint contacts were calibrated to reproduce the mechanical properties of the fractured sample with β = 27°. We first chose the stiffness of smooth joint contacts by assuming high tensile strength and cohesion (e.g., 100 MPa) to fit the slope of the stress-strain curve. We then assumed that the normal
Mij =
∑ ΔFi Rj S
(1)
where ΔFi is the ith component of force change, Rj is the jth component of the distance from event centroid to contact point, and S is the surface involved in the event. The moment magnitude is then calculated based on the eigenvalues of moment tensors. 4. Results and discussion 4.1. Experimental results Fig. 3 shows the triaxial compression test results of the intact and fractured samples under 20 MPa confining pressure, in terms of deviator stress, cumulative AE count and AE energy rate. The three samples experience similar pre-peak behaviors. The deviator stresses increase linearly until the peak stresses are reached. For the intact sample, the high deviator stress increases slowly before the peak value appears likely owing to the generation and interaction of induced cracks. The intact sample breaks accompanied by both the tensile and shear failure occurred in the rock matrix (Fig. 2a). The residual strength of the intact sample is relatively high due to the mechanical interaction of randomly formed cracks. However, pre-existing fractures significantly degrade the stiffness and strength of fractured samples and affect the post-peak behaviors. The fractured sample with β = 45° exhibits both the shear failure along the pre-existing fracture and the tensile failure in the rock matrix (Fig. 2b). The residual strength is relatively low as the pre-existing fracture partially dominates the postpeak behavior. The failure of the fractured sample with β = 27° is 3
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Fig. 4. Deviator stress as a function of axial strain obtained from the experimental and numerical tests on the intact and fractured samples with β = 27°, respectively, under 20 MPa confining pressure.
cracks. For the fractured sample with β = 45° (Fig. 3b), the cumulative AE count also jumps at the peak stress and slightly increases in the postpeak stage due to the mechanical interaction of limited tensile failure in the rock matrix. The fractured sample with β = 27° exhibits the lowest AE energy rate at the peak stress and nearly constant cumulative AE count in the post-peak stage, indicating that the shear failure along the favorably oriented fracture releases negligible strain energy. 4.2. Numerical results The DEM model evaluates the tensile and shear failure modes of parallel bonds and smooth joints, respectively, to identify the portions of rock matrix and fractures involved in the failure process. Fig. 4 shows that the DEM model can replicate the strength and stiffness of both the intact sample and fractured sample with β = 27°. The DEM model can also reproduce the general trend of deviator stress, in terms of sudden drop and residual strength. All the cases shown in Fig. 5 indicate that the deviator stress in the pre-peak stage gradually increases from zero to the peak value, implying that both the intact and fractured samples experience elastic deformation. Very few cracks appear in this stage. When the deviator stress approaches the peak value, a slight increase of crack number emerges in the intact sample and fractured samples with β = 60° and 45°. Most of the cracks are formed by the tensile failure of parallel bonds in the model, suggesting the cracks likely initiate in the rock matrix. After that, the deviator stress drops, and the number of cracks jumps simultaneously. In the fractured samples with β = 35° and 27°, a little number of cracks appear in the pre-peak stage. The shear failure of smooth joints in the model dominates the post-peak stage, indicating limited damage in the rock matrix. The failure modes of parallel bonds and smooth joints in the five cases are further analyzed in Fig. 6. The crack numbers obtained from different failure modes at the peak stress and the end of the post-peak stage exhibit that the majority of induced cracks appears when the peak stress is reached, which align with the results of AE energy rate monitored in the experimental study (Fig. 3). For the intact sample, approximately 90% of the parallel bonds fail in tension (Fig. 6a). In the fractured sample with β = 60°, the tensile failure of parallel bond also dominates the failure process, and the shear failure of smooth joint is relatively insignificant. However, for the fractured sample with β = 45° (Fig. 6c), a considerable amount of the shear failure of smooth joint occurs at the post-peak stage. With further decrease of β , the shear failure of smooth joint becomes the dominant failure mode (Fig. 6d and e). For all the fractured samples, both the shear failure of parallel bond
Fig. 3. Results obtained from the triaxial compression tests on (a) the intact sample and fractured samples with (b) β = 45° and (c) β = 27° under 20 MPa confining pressure.
induced along the pre-existing fracture (Fig. 2c). The favorably oriented fracture shows the lowest residual strength and no obvious damage in the rock matrix. The result of AE events aligns with the measurement of deviator stresses and the observation of failure patterns. The vertical axis scale of cumulative AE count shown in Fig. 3a is much greater than those given in Fig. 3b and c. Fig. 3a shows that the cumulative AE count of the intact sample slowly increases in the pre-peak stage, and suddenly jumps when the peak stress appears. This observation confirms our above explanation that the pre-peak non-linear deformation is mainly associated with the generation and interaction of induced cracks. After that, the cumulative AE count still increases with occasional jumps of AE energy rate, due to the mechanical interaction of randomly formed 4
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Fig. 5. Numerical results of deviator stress and cumulative crack number as a function of axial strain, obtained from the failure of (a) intact sample and fractured samples with (b) β = 60°, (c) β = 45°, (d) β = 35° and (e) β = 27° under 20 MPa confining pressures.
equivalent force, is displayed in Fig. 7b. Two arrows of equal length pointing away from each other represent a tensile event, while two arrows in parallel and pointing in opposite directions mean a shear event (Al-Busaidi et al., 2005). The length of an arrow is proportional to the magnitude of corresponding principal value of the moment tensor matrix (Eq. (1)). The moment tensors for tensile cracks indicate that the tensile failure of rock matrix plays a dominant role in the failure process of the intact sample. The moment tensors for shear cracks are relatively small in length and randomly distributed around the induced fractures and in the rock matrix. When β decreases, the magnitudes of the moment tensors for both tensile and shear cracks decrease in the fractured samples, and the moment tensors for shear cracks accumulate along the
and tensile failure of smooth joint are negligible. When β decreases, the dominant failure mode of the fractured samples changes from the tensile failure of parallel bond to the shear failure of smooth joint. In Fig. 7, the spatial distributions of AE events and corresponding moment tensors recorded from the DEM models interpret the failure pattern and strain energy release of the intact and fractured samples. The diameter of red circle in Fig. 7a represents the magnitude of an AE event. In the intact sample, the AE events with various magnitudes randomly occur in the rock matrix. For the fractured samples, with decreasing β , both the magnitude and quantity of the AE events in the rock matrix decrease, and the large magnitude AE events concentrate along the pre-existing fractures. The moment tensor, depicted as 5
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Fig. 6. Failure modes of parallel bond and smooth joint at the peak stress and the end of the post-peak stage, respectively, obtained from the numerical tests on (a) intact sample and fractured samples with (b) β = 60°, (c) β = 45°, (d) β = 35° and (e) β = 27° under 20 MPa confining pressures.
log N = a − bM
pre-existing fractures. Fig. 8 shows the frequency and cumulative AE count as a function of magnitude. The frequency of AE events is high in the intact sample, and decreases with smaller β in the fractured samples. This result agrees with those shown in Fig. 3. Similar to previous results (e.g., Lockner, 1993; Amitrano, 2003), the relation between the cumulative AE count and magnitude follows the Gutenberg-Richter law (Gutenberg and Richter, 1954):
(2)
where N is the frequency of events with magnitudes greater than M, and a and b are constants. The b value can be used to describe the relative occurrence of large and small seismic events, and a larger b value indicates a smaller proportion of large event (Schorlemmer et al., 2005). The intact sample fails accompanied by a large proportion of small magnitude AE events, 6
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Fig. 7. Spatial distributions of (a) AE events and (b) moment tensors obtained from the numerical tests on the intact sample and fractured samples with β = 60°, 45°, 35° and 27° under 20 MPa confining pressure.
summarizes the peak stress and b value as a function of β . Comparing to the intact sample, the peak stress of the fractured samples significantly decreases (Fig. 9a). The peak stress drops with smaller β . The maximum peak stress appears when β = 60°, which agrees with the analytical solution of Jaeger (1960). The b value has been used successfully to predict seismic events occurred in intact samples (Lockner et al., 1991). However, for the fractured samples, the change of b value in the prepeak stage is independent to β (Fig. 9b). Both the experimental and numerical results reveal that the fractured samples with relatively small β release negligible AE energy (Figs. 3 and 5). In the post-peak stage, the b value significantly reduces when β is relatively small (e.g., 27°), as the shear failure along the pre-existing fractures is dominant in the failure process. When the fracture is favorable for activation, the low b value indicates a great proportion of large events occurred along the fracture (see Fig. 7a). Our experimental and numerical results also indicate that rock excavation varies both the magnitude and orientation of principal stresses acting on adjacent fractures, presumably resulting in the shear rupture of the fractures. Fig. 10 presents the possible mechanism of the shear rupture. The Mohr circle lies below the failure envelope under the insitu stress condition (see the solid purple circle). After the excavation, the minimum principal stress (i.e., the radial stress at the tunnel perimeter) reduces to zero, whereas the maximum principal stress increases in the vertical direction. This change thus enlarges the radius of the Mohr circle, and leads the circle to exceed partially the failure envelope (see the red circle). Meanwhile, the shear rupture is also dependent on the change of the maximum principal stress orientation. When the preexisting fracture orientation, 2β away from the maximum principal stress orientation, falls in the range marked as damage zone (see the red
while large magnitude AE events are dominant during the failure of fractured samples. This speculation can be verified by the spatial distributions of AE events shown in Fig. 7a. In most of the cases, the b value in the pre-peak stage is larger than that in the post-peak stage, indicating that large magnitude AE events mainly occur when the peak stress is reached. Previous studies also show that smaller cracks are induced in the pre-peak stage and results in a larger b value, and larger cracks with higher strain energy release occurred in the post-peak stage lead to a smaller b value (Wang et al., 2000). Several studies show that the b value obtained in the experimental studies is larger than that recorded in the field measurements (Lockner et al., 1991; Schorlemmer et al., 2005; Thompson et al., 2006). The experimental studies overestimate the portion of small seismic events, as the effect of pre-existing fractures cannot be fully considered in laboratory-scale samples. Moreover, the b value calculated in the DEM model is even larger than that obtained in the experimental and field investigations. This model particularly records the force changes at particle contacts to calculate the moment tensors, which amplifies the portion of small seismic events and finally leads to a large b value (Hazzard and Young, 2002, 2004; Zhang and Zhang, 2017). 4.3. Discussion Although the experimental and numerical configurations are simple in this study, it is easy to control desired parameters and to interpret complex engineering problems. Both the experimental and numerical results indicate that the angle between the maximum principal stress orientation and pre-existing fracture orientation significantly influences the failure pattern and strain energy release of fractured samples. Fig. 9 7
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Fig. 8. Frequency and cumulative AE count as a function of magnitude obtained from the numerical tests on (a) intact sample and fractured samples with (b) β = 60°, (c) β = 45°, (d) β = 35° and (e) β = 27° under 20 MPa confining pressures.
studies (e.g., Cai, 2008), the unloading process is associated not only with the confining pressure decrease but also with the axial stress increase. Hence, instantaneously controlling the changes of confining pressure and axial stress is a necessary improvement to reasonably simulate excavation-induced seismicity.
zone above the failure envelope), the fracture fails along a favorable orientation. Additionally, the magnitude of seismic events is associated with stress evolution. The failure of favorably oriented fractures is mostly along pre-existing planes and likely release less strain energy from rock matrix, as shown in Fig. 7. Fig. 10 also shows the limitation of the triaxial test setup in the study of excavation-induced seismicity. In the triaxial loading test, the confining pressure is fixed, and the diameter of the Mohr circle increases with larger axial stress (see the dashed purple circle). The triaxial unloading test uses the same setup, but applies the fixed axial stress and decreasing confining pressure (Duan et al., 2019), which also leads to the increase of the Mohr circle diameter (see the dotted purple circle). However, as illustrated by the red circle in Fig. 10 and other
5. Conclusions We carried out the experimental and numerical investigations to consider the change of the angle between the maximum principal stress orientation and pre-existing fracture orientation and to interpret the possible mechanism of fault rupture adjacent to rock excavation. Our study shows that the change of the angle is a possible cause of fracture 8
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Fig. 9. (a) Peak stress and (b) b value as a function the angle between the maximum principal stress orientation and fracture orientation (β) at the pre-peak and postpeak stages, respectively.
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Fig. 10. Change of principal stresses on a pre-existing fracture before (solid purple circle) and after (solid red circle) rock excavation, and comparison the limitation of stress paths in the triaxial loading (dashed purple circle) and unloading (dotted purple circle) tests. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
instability and significantly influences rock failure pattern and strain energy release during the failure process. When the angle β decreases from 60° to 27°, the failure pattern of fractured samples changes from the tensile failure of rock matrix to the shear failure along pre-existing fractures. If the tensile failure of rock matrix is less involved in the failure process, small magnitude AE events diminish in rock matrix and large magnitude AE events concentrate along pre-existing fractures, resulting in relatively small b value. For favorably oriented fractures, the AE energy released in the pre-peak stage is negligible, indicating that b value may not be reliable as a seismic precursor for the fracture failure. Our data also implicate that the excavation-induced fault rupture highly depends on the magnitude and orientation of principle stresses, and the intensity of seismic events is associated with the portions of rock matrix and fractures involved in the failure process.
Acknowledgements This work was mainly supported by the Start-Up Grant from Nanyang Technological University, Singapore. Zhijun Wan acknowledges the Fundamental Research Funds for the Central Universities (Grant No. 2017CXNL01). 9
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