Arab J Geosci (2016) 9: 69 DOI 10.1007/s12517-015-2027-9

ORIGINAL PAPER

Effect of fault-slip source mechanism on seismic source parameters Atsushi Sainoki 1 & Hani S. Mitri 1

Received: 6 February 2015 / Accepted: 10 September 2015 / Published online: 17 December 2015 # Saudi Society for Geosciences 2015

Abstract Fault-slip bursts in underground mines could cause devastating damage to mine openings. In the present study, three types of underlying mechanisms that could trigger faultslip are examined, namely asperity shear, stope extraction, and a combination thereof, with numerical analysis. First, a numerical model is constructed, in which a fault running parallel to a steeply dipping, tabular orebody is modeled. Static analysis is then performed, whereby stopes in the orebody are extracted. Based on the stress state obtained from the analysis, dynamic analyses are carried out to simulate fault-slip, using different simulation techniques representing the mechanisms of fault-slip. The results show that when fault-slip is induced by asperity shear, slips could spread over an extensive area of the fault. In contrast, the fault-slip area is limited to the vicinity of an extracted stope when fault-slip is caused by stope extraction. The results further indicate that asperity shear could induce strike-slip faulting. It is revealed that when fault-slip is caused by the combination, the magnitude of fault-slip significantly increases. Investigation of the slip rate shows that fault-slip induced by stope extraction induces slightly higher slip rates than that caused by asperity shear. It is also found that fault-slip induced by stope extraction ruptures faster along the fault than that induced by asperity shear. Lastly, the effect of the mining rate on the magnitude of fault-slip is examined. The result indicates that stope extraction with a low mining rate can considerably decrease the cumulative seismic moment of fault-slip that takes place during the mining sequence.

* Atsushi Sainoki [email protected] 1

Department of Mining and Materials Engineering, McGill University, 3450 University Street, Montreal, QC H3A 0E8, Canada

Keywords Fault-slip . Asperity shear . Seismic source parameters . Slip rate . Numerical analysis

Introduction Fault-slip burst is one of the most hazardous phenomena that could occur in underground mines. Seismic waves arising from fault-slip as well as slip movements along a fault could seriously damage underground openings and important facilities. A number of fault-slip-related seismic events that left behind damage in underground mines have been reported over the past several decades (Blake and Hedley 2003; Ortlepp 2000; White and Whyatt 1999). Presumably, those hazardous events would impose an enormous economic burden on a mining company. In the future, mining depths are expected to be even greater to satisfy a great demand for mineral resources, thereby increasing the likelihood of burst-prone conditions in mining areas. Thus, enhancing knowledge about fault-slip taking place in underground mines is of paramount importance. It is widely recognized that fault-slip is a dynamic phenomenon entailing the generation of seismic waves that propagate through rockmass from its source location (McGarr 1991; McGarr 2002). In addition, in underground mines where faults are present, fault-slip potential intermittently varies according to the progression of mining sequences. Therefore, comprehensive understanding of the dynamic behavior of a fault as well as the stress state of rockmass that fluctuates in response to mining activities is indispensable in order to gain insight into evaluating fault-slip potential and damage that could be inflicted by fault-slip. In order to address those problems, numerical analyses with mine-wide models encompassing orebodies and geological structures have been performed by many researchers with a variety of numerical methods, such as

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the finite element method and the finite difference method (Alber and Fritschen 2011; Alber et al. 2009; Hofmann and Scheepers 2011; Potvin et al. 2010; Sainoki and Mitri 2014a; Sjöberg et al. 2012). In those studies, fault-slip taking place in underground mines is simulated basically with either extraction of an orebody (Sainoki and Mitri 2014a; Sjöberg et al. 2012) or an instantaneous drop in the mechanical properties of a causative fault (Hofmann and Scheepers 2011; Sainoki and Mitri 2014b). Importantly, both of the simulation techniques are capable of reproducing conceivable processes and mechanisms of mining-induced fault-slip. For instance, stress redistribution resulting from a large amount of extraction of orebodies exerts an influence on the stress state of rockmass locally and regionally, which could cause the normal stress acting on a nearby fault to decrease, i.e., unclamping of the fault. Fault-slip is then induced by a decrease in the maximum shear strength of the fault resulting from the unclamping. The former simulation technique attempts to replicate the abovementioned process. On the other hand, the latter simulation technique aims at simulating fault-slip induced by an instantaneous drop in resistance force to a slip resulting from either the breakage of fault surface asperities or the formation of a fault plane propagating within intact rock. As suggested by many shear strength models, changes in fault surface properties, such as surface roughness, lead to a sudden decrease in the maximum shear strength of a fault, which could give rise to a slip on the fault (Ryder 1988; Sainoki and Mitri 2014b). Through those studies aimed at enhancing knowledge about mining-induced fault-slip, both simulation techniques have proved useful in that the seismic moment of fault-slip can be evaluated while calibrating the mechanical properties of causative faults through a comparison of seismic moment estimated from microseismic monitoring systems installed in underground mines with that obtained from numerical analyses. However, as mentioned above, fault-slip is considered a dynamic phenomenon, which thus implies that other seismic source parameters, such as the slip rate and rupture speed, would play an important role in determining the characteristics of mining-induced fault-slip. More importantly, it is presumed that the dynamic behavior of a fault during fault-slip would differ depending on the process for fault-slip to take place. In other words, it is conceivable that fault-slip caused by asperity shear exhibits different characteristics in terms of its dynamic behavior from that induced by extraction of an orebody. Although a few studies have been carried out for ascertaining the dynamic behavior of mining-induced faultslip with the two simulation techniques, adequate knowledge has not yet been gained with respect to the difference in fault dynamic behavior during fault-slip between different underlying fault-slip mechanisms. For better understanding of mining-induced fault-slip, it is indispensable to elucidate discrepancies in seismic source parameters between those two types of fault-slip.

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In this paper, a comparative study is carried out with respect to two types of fault-slip: fault-slip caused by ore extraction and fault-slip triggered by breakage of fault surface asperities. Through the comparison, the influence that each fault-slip mechanism exerts on its seismic source parameters is examined, considering its dynamic behavior. The present study helps in gaining useful insight into the dynamic behavior of mining-induced fault-slip and enhancing knowledge about numerical simulation of fault-slip taking place in underground mines.

Methodology In the present study, a comparison of numerical simulation techniques for mining-induced fault-slip is carried out with a numerical model exemplifying typical geological configurations and stress states in the Canadian Precambrian shield (Arjang and Herget 1997; Diederichs 1999; Sainoki and Mitri 2014c; Zhang and Mitri 2008). A numerical model encompassing a steeply dipping, tabular orebody and a fault running parallel to the orebody is constructed with FLAC3D code (Itasca 2009), which employs an explicit finite difference method. In this section, detailed descriptions of the numerical model and analysis procedures as well as analysis conditions are provided. Numerical model Figure 1 shows the numerical model constructed with FLAC3D code. The model is basically identical to those used

Fig. 1 Numerical model representing a steeply dipping, tabular orebody with a fault in the hanging wall running parallel to the orebody

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for investigating the dynamic behavior of mining-induced fault-slip (Sainoki and Mitri 2014a; Sainoki and Mitri 2014b; Sainoki and Mitri 2014e). As can be seen in the figure, the numerical model consists of three types of rockmass, namely hanging wall, orebody, and footwall. The orebody steeply dips at 80°, strikes in the y-direction, and is 22 m in width. In the hanging wall, a fault running parallel to the orebody is modeled. The distance between the fault and the orebody is 30 m. After carrying out preliminary analyses, the width, length, and height of the model were determined to be 332, 300, and 300 m, respectively. Within the orebody, stopes are modeled, which are extracted in accordance with bottom-up sublevel stoping method with delayed backfill. The detailed explanation on the mining sequence is given in the latter part of this section. The numerical model is densely discretized in the vicinity of the orebody in order to simulate stress re-distribution due to extraction of the stopes as accurately as possible. Zones in the numerical model become coarser towards the model boundaries. More specifically, the smallest and largest widths of zones in the model are 3 and 12 m, respectively. The number of grid points and zones in the model is 230,643 and 215,040, respectively. Modeled stopes in the orebody are depicted on the plan and sectional views of the model in Fig. 2. It is found from Fig. 2b that stopes are located on nine levels from the bottom to the top of the model. The distance between each level is 30 m, which corresponds with the height of the stope. As can be seen from Fig. 2a, b, two stopes, of which the strike length is 200 m, are extracted from the orebody on each level. In the present study, a comparison of fault-slips simulated with different methods is made when Stope7H is extracted, i.e., after proceeding with stope extractions according to the mining

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sequence from level 1 to level 6. This is because a small amount of ore extraction does not induce fault-slip potential that is high enough for a large slip to take place on the fault. Fault-slip taking place at an early stage of the mining sequence has relatively small magnitudes. Thus, there is a possibility that the difference between fault-slips simulated with the different simulation techniques becomes unclear. As a result of preliminary analysis, when stopes are extracted until that stage (extraction of Stope7H), it was confirmed that fault-slip with a large magnitude occurs, which will emphasize the difference in seismic source parameters between fault-slips simulated with the two simulation methods. Although the stope strike length of 200 m seems to be significantly long when compared to ordinary stope dimensions designed in real underground mines (Zhang and Mitri 2008), extracting a number of stopes from the orebody until the stage at which the comparison is made is time-consuming. Hence, the stope design shown in Fig. 2 has been adopted. It is however to be noted that the effect of the mining rate (stope strike length) on the seismic source parameters of fault-slip is examined as well in the present study when Stope7H is extracted. The detailed analysis procedures for simulating fault-slip with different methods are given in the following section. Analysis procedures for fault-slip simulation methods In the present study, two types of simulation methods for mining-induced fault-slip are employed, whereby four different numerical analyses are performed while considering the source mechanism of fault-slip and mining rates. Fault-slip simulated in each analysis is compared in terms of its seismic source parameters, taking into consideration the dynamic

Fig. 2 Plan and sectional views showing stopes extracted in accordance with a sublevel stoping method: a plan view at z=150 m, b sectional view at y= 150 m

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behavior of the fault. In this section, procedures to simulate fault-slip with those methods are provided. Procedure to simulate fault-slip caused by stope extraction The procedure to simulate fault-slip induced by sudden unclamping of the fault is as follows. First, a pre-mining stress state is applied to the numerical model, and then static analysis is performed with FLAC3D code until stress states in the model reach equilibrium. Afterwards, stopes from levels 1 to 6 are extracted and backfilled in static conditions in accordance with the mining sequence as per the bottom-up sublevel stoping method. During the static analysis, the mining sequence proceeds after unbalanced force resulting from extraction of each stope converges to a negligible value. The stress states of rockmass in the model are saved after extracting Stope6F. Based on the stress state obtained from the static analysis, dynamic analysis is carried out. At the beginning of the dynamic analysis, Stope7H, which is 200 m in strike length, is extracted in one shot. Fault-slip induced by the extraction of Stope7H is examined. The stope strike length of 200 m can be considered an extreme case representing a high mining rate. As mentioned in the previous section, the effect of the mining rate on the seismic source parameters of mining-induced fault-slip is additionally investigated in this study. In order to examine the effect, Stope7H is divided into eight stopes that are 25 m in strike length. Figure 3 depicts a plan view showing those stopes. While, in this case, the stress state of rockmass immediately before dynamic analysis is performed is exactly the same as in the case where Stope7H is extracted in one shot, stopes are extracted sequentially from Stope7H1 to Stope7H8

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during the dynamic analysis. This represents a case where stopes are extracted at a low mining rate. During the dynamic analysis, a subsequent stope is extracted after the shear displacement increments on the fault induced by extraction of a previous stope decrease to negligible values. It is to be noted that the same volume of orebody is eventually extracted for both cases with low and high mining rates. The comparison of the seismic source parameters of fault-slip between these two conditions gives a clue to the influence of mining rate on the severity of mining-induced fault-slip.

Procedure to simulate fault-slip induced by asperity shear In the same way as the analysis to simulate fault-slip caused by stope extraction, the pre-mining stress state is applied to the model. Subsequently, stopes are extracted in static conditions according to the mining sequence. Importantly, in this case, the static analysis is carried out until Stope7H is extracted according to the mining sequence. After extracting Stope7H, the stress state is saved and used as an initial stress state for dynamic analysis to simulate fault-slip induced by asperity shear. Sainoki and Mitri (2014b) simulate fault-slip triggered by asperity shear with a newly developed ubiquitous joint model into which Barton’s shear strength model (Barton 1973) is implemented. The present paper adopts the same methodology. The detailed procedure is as follows. At the beginning of the dynamic analysis, the stress state on the fault is investigated, and for areas where the shear stress acting on the fault exceeds its maximum shear strength determined by Barton’s shear strength model (Barton 1973), the joint surface roughness (JRC) and the friction angle of the fault are decreased to certain values. The reduction in those parameters denotes the breakage of fault surface asperities, and gives rise to slips along the fault resulting from the sudden decrease in resisting force.

Fault-slip simulated with the combination of the two methods

Fig. 3 Plan view showing stopes with a shorter strike length at z=210 m in a model to investigate the effect of a low mining rate

The last analysis conducted in this study is intended to simulate fault-slip with a combination of the abovementioned two simulation methods. In this case, an initial stress state for dynamic analysis is the same as that for simulating fault-slip induced by stope extraction. Based on the stress state, dynamic analysis is performed, in which both of the simulation methods are applied. Thus, at the beginning of the dynamic analysis, Stope7H with 200 m strike length is extracted in one shot. Afterwards, the surface roughness and the friction angle of the fault are decreased for areas where the shear stress on the fault exceeds its maximum shear strength.

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Mechanical properties of rockmass and fault A constitutive model that represents perfect elasto-plastic behavior is applied to the discretized zones in the hanging wall, the footwall, and the orebody of the numerical model. Corresponding rockmass mechanical properties to simulate the perfect elasto-plastic behavior as well as the mechanical properties of backfill are derived from literature (Henning 1998; Zhang and Mitri 2008). Table 1 lists the elastic modulus, E; cohesion, C; internal friction angle, ϕ; the unit weight, γ; Poisson’s ratio, ν; tensile strength, σT; and dilatancy angle, ψ; of those rockmasses as well as backfill. The rockmass properties are based on the case study conducted for Bousquet 2 mine, Canada. This is a deep hard rock mine with a steeply dipping orebody extracted with sublevel stoping methods, which is considered as a typical geological condition encountered in the Canadian Shield (Malek et al. 2009; Sainoki and Mitri 2014c; Zhang and Mitri 2008). As explained in the previous section, the numerical model used in the present study aims at representing typical geological conditions in the Canadian Shield. For this reason, the case study was selected as a base for the numerical model to be analyzed. As mentioned above, the fault in the numerical model is modeled with ubiquitous joint models into which Barton’s shear strength (Barton 1973) is implemented (Sainoki and Mitri 2014b). The implemented Barton’s shear strength is expressed as follows: 
  JCS τ ¼ σn tan JRClog10 þ φb ð1Þ σn where JRC and JCS is a joint roughness coefficient and joint wall compressive strength, respectively, and σn and ϕb are the effective normal stress acting on the joint and the basic friction angle of the joint, respectively. According to Barton and Choubey (1977). JRC varies from 0 to 20, depending on the roughness of a rock joint. In light of the study, a JRC of 10, which is the median value of the range, is adopted. As for the basic friction angle, Barton and Choubey (1977) showed that

Table 1 Mechanical properties of rockmass derived from a case study (Henning 1998)

HWa Ore FWb BFc a

E (GPa) C (MPa) ϕ (°) ν

γ (kN/m3) σT (MPa) ψ (°)

31 115 49 2.5

25.5 25.5 25.5 23.0

Hanging wall

b

Footwall

c

Backfill

2.6 11.5 4.3 0.1

38 48 39 35

0.21 0.1 0.15 0.35

1.1 5.9 1.8 0.3

9.3 12.0 9.5 0.0

the basic friction angle of typical rock joints falls between 21° and 38°. Considering the range, 30° is adopted as the basic friction angle of the fault in the present study. Regarding JCS, it should be noted that Barton’s shear strength model (Barton 1973) is valid only when JCS is greater than σn. The normal stress acting on the fault derived from preliminary analyses varies from 30 to 90 MPa due to stress re-distribution induced by stope extraction during the mining sequence. Considering the result, JCS is set to 120 MPa. During the static and dynamic analyses to simulate faultslip caused by stope extraction, all of the constants in Eq. 1 are kept constant, while, during the dynamic analysis to simulate fault-slip triggered by asperity shear, JRC and ϕb are decreased to zero and 15°, respectively, for areas where the shear stress of the fault reaches the failure envelope derived from Barton’s shear strength model (Barton 1973). As for fault-slip simulated with the combination of the two simulation methods, stope extraction as well as the reduction in those parameters is executed. Pre-mining stress state The pre-mining stress state applied to the model is computed as follows. The vertical in situ stress, σov, is calculated based on the overburden pressure (Zhang and Mitri 2008) as σov ¼ γH

ð2Þ

where γ and H are the unit weight of the rockmass and the depth below the ground surface, respectively. In the present study, the depth at the top boundary of the model is set to 1500 m, and the unit weight of overlying rockmass is assumed to be 25.5 kN/m3. The magnitude of maximum and minimum horizontal stresses is calculated based on the vertical in situ stress, using the following equations proposed by Diederichs (1999). 25 k max ¼ 1 þ pffiffiffiffi H

ð3Þ

8 k min ¼ 1 þ pffiffiffiffi H

ð4Þ

σoHmax ¼ k max σov

ð5Þ

σoHmin

ð6Þ

¼

k min σov

where k is a horizontal to vertical in situ stress ratio. By employing Eqs. 2 to 6, the maximum and minimum horizontal stresses, which vary with the depth below the ground surface, can be calculated and applied to the numerical model as the pre-mining stress state. The maximum horizontal in situ stress is oriented perpendicular to the orebody strike. This setting of initial stress states is based on the research by Zhang and Mitri (2008).

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Analysis conditions During the static analysis, the model boundaries are fixed in the direction perpendicular to the boundaries. When the dynamic analyses to simulate fault-slip are performed, the boundary condition is transformed to viscous to prevent seismic waves arising from simulated fault-slip as well as stress waves resulting from the instantaneous stope extraction from reflecting on the model boundaries. It is widely recognized that rockmass significantly attenuates seismic waves arising from seismic events. In order to reproduce the attenuation, local damping, which is implemented in FLAC3D code, is executed during the dynamic analysis, assuming 5 % of critical damping as a local damping coefficient. Detailed description of the local damping system is described in the literature (Sainoki and Mitri 2014d). Although the local damping system cannot capture energy loss accurately when wave forms are complex, the damping system is deemed sufficient in the present study because this study is focused on the behavior of the fault within the source regions of fault-slip rather than the propagation of seismic waves arising from fault-slip through the rockmass. A timestep used in the dynamic analysis is automatically optimized on the basis of the volume of each zone of the model, P-wave velocity derived from the rockmass mechanical properties, and the face area of each zone (Itasca 2009). The dynamic analysis is continued until the shear displacement increments on the fault become negligible. Seismic source parameters In order to evaluate discrepancies between fault-slips simulated with the different methods, seismic source parameters, such as seismic moment (Aki and Richards 1980), seismically radiated energy, slip rates, and rupture time, are utilized. Seismic moment, Mo, and seismically radiated energy, Es, are widely used indices that represent the magnitude and severity of a seismic event, and computed as follows: M o ¼ GDA

ð7Þ

E s ¼ 0:5ΔσDA Z 1 Δσ ¼ ½σðt 2 Þ−σðt 1 Þ dA A

ð8Þ ð9Þ

A

where G, D, and A denote the shear modulus of rockmass involved in fault-slip, an average shear displacement, and area where a slip takes place, respectively; Δσ is a stress drop calculated with the average difference between the stress on the fault before a seismic event, σ(t2) and the stress after the event, σ(t1). Seismic moment and moment magnitude computed from seismic moment are widely used to evaluate the intensity of seismic events taking place in underground mines

(Domański and Gibowicz 2008; McGarr 1994). Regarding the calculation of energy radiated during a seismic event, a couple of formulae have been proposed (Kanamori 2001; McGarr and Fletcher 2001). In this study, the formulae shown by Kanamori (2001) are adopted, which are expressed as Eqs. 8 and 9. Importantly, most of seismically radiated energy is dissipated to generate permanent deformation and fractures in the vicinity of the hypocenter of a seismic event in reality. Neither the methodology used in this study nor the formulation to calculate seismically radiated energy takes into consideration the energy dissipation. Thus, seismically radiated energy computed with Eqs. 8 and 9 based on the result of numerical analysis could significantly overestimate the energy, but it does not have a negative influence on the comparison of fault-slip simulated with the two entirely distinct methods as long as the energy is evaluated with the same equation for the fault-slips. In this way, it is possible to evaluate the difference in the intensity of fault-slip between the two types of fault-slip, using seismically radiated energy computed from the equations. The slip rate is computed by dividing relative shear displacement on the fault by time, and examined in the present study. Since a half of the slip rate is equivalent to near-field peak ground motion (McGarr 1991), better understanding of the difference in slip rate between the two types of fault-slip is crucial in gaining an insight into assessing damage induced by fault-slip. In addition, rupture time is investigated on the fault in the present study. Rupture time denotes time at which a fault surface starts slipping. Fault-slip starts from its hypocenter and then propagates along the fault. Thus, rupture time is almost zero in the vicinity of the hypocenter and increases with an increasing distance from the hypocenter. Rupture speed can be estimated from the rupture time. Since the rupture speed is directly related to seismic energy that propagates into far-field (McGarr and Fletcher 2001), investigating rupture time and understanding its difference between the different types of fault-slip would give a clue to important characteristics of mining-induced fault-slip. In the present study, rupture time is defined as time at which a relative shear displacement increment during dynamic analysis has reached 0.005 m.

Results and discussion First, the difference in the distribution of relative shear displacement increments on the fault between the two types of fault-slip mechanisms is examined. Figure 4 depicts the relative shear displacement increments on the fault; y and z in the figure correspond with the coordinate system shown in Fig. 1. It is to be noted that the shear displacement increments took place only during the dynamic analyses explained in the previous sections. It is found from Fig. 4 that there are significant

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Fig. 4 Distribution of relative shear displacement increments on the fault: a fault-slip induced by a sudden decrease in JRC and a friction angle (asperity shear), b fault-slip induced by stope extraction

differences in the propagation of a slip along the fault as well as its magnitude between the two types of fault-slip. Shear displacement increments in Fig. 4a show that there are three regions with particularly large shear displacement increments on the fault: both sides of the fault along y=50 and 250 m and an area around z=200 m, which are colored in red. The redcolored regions indicate that the stress state of the regions reached critical state immediately before the dynamic analysis, and during the dynamic analysis, fault-slip was triggered in the regions due to asperity shear and propagated along the fault. It is assumed that generation of those regions with high slip potential is attributed to the geological configurations and the mining sequence adopted in the present study. It is intriguing that fault-slip could occur below the level on which a stope is extracted immediately before the dynamic analysis. Relative shear displacement increments shown in Fig. 4b are induced by the extraction of Stope7H. In contrast to fault-slip induced by asperity shear, slips concentrate more on the level where the stope is extracted just before the dynamic analysis, and the maximum relative shear displacement increment induced by the stope extraction appears to be greater than that due to asperity shear. It should be noted that the shear displacement increments induced by stope extraction are considered an extreme case with a high mining rate. Figure 5 depicts the vectors of displacement increments during fault-slip induced by asperity shear. As can be seen in Fig. 5a, displacements take place in the z-direction around the level where stope extraction is carried out immediately before the dynamic analysis, whereas it is found that displacements increase in the y-direction (horizontal direction) below the level, suggesting the occurrence of strike-slip. The slips in the horizontal direction shown in Fig. 5a can be explained by considering the stress state of the fault before the dynamic

analysis. The areas where slips take place in the horizontal direction are located around extremities of stopes extracted during the static analysis. It is thus envisaged that, as a result of the stope extractions, σyy is released from stope walls at the extremities, which increases the shear stress on the fault particularly in the horizontal direction, thereby contributing to the occurrence of strike-slip around the regions. Comparing Fig. 5a with Fig. 5b indicates that shear displacements take place in the direction parallel to the fault when fault-slip is induced by asperity shear. In contrast, it is found from Fig. 6a, b that displacements on the fault induced by extracting Stope7H take place mainly in the direction perpendicular to the fault rather than parallel, which implies that displacements associated with unclamping of the fault due to the stope extraction surpass those related to fault-slip. The displacements in the y-direction around the extremities of Stope7H in Fig. 6a can be explained in the same way as in Fig. 5a. Figure 7 depicts relative shear displacement increments on the fault induced by a combination of stope extraction and asperity shear. The magnitude of relative shear displacements shown in the figure significantly surpasses that shown in Fig. 4. The maximum shear displacement induced by asperity shear or stope extraction in Fig. 4 is no more than 4 cm, whereas the maximum shear displacement is more than 20 cm in the case that fault-slip is driven by both asperity shear and stope extraction. This result suggests that when both of the mechanisms contribute to the occurrence of fault-slip, fault-slip could significantly become violent. Hence, it is strongly recommended that both of the mechanisms are taken into consideration, especially in a case where local unclamping of a fault is anticipated because of nearby stope extraction as modeled in the present study.

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Fig. 5 Vector field of displacement increments during fault-slip induced by asperity shear: a displacement vectors on the fault plane, b displacement vectors on the cross section of the fault

For fault-slip with the different underlying mechanisms, slip rates are investigated at a point where the maximum relative shear displacement takes place on the fault. The increments of relative shear displacements at the locations for each fault-slip are shown in Fig. 8. Slip rates can be derived from the figure by dividing the shear displacement increments by time. Although there is no significant difference in slip rates between fault-slips simulated with the different techniques, it appears that the fault-slip induced by stope extraction results in higher slip rates than that induced by asperity shear at an early stage of fault-slip (the enlarged part in Fig. 8). For instance, slip rates calculated around 0.01 s in Fig. 8 is 2.2 m/s for fault-slip simulated with asperity shear, while a slip rate is 5.2 m/s for fault-slip induced by stope extraction. As nearfield peak ground motion is half of a slip rate (McGarr 1991), peak particle velocity (PPV) of 2.6 m/s is expected Fig. 6 Vector field of displacement increments during the fault-slip induced by stope extraction: a displacement vectors on the fault plane, b displacement vectors on the cross section of the fault

for fault-slip due to stope extraction, although this is an extreme case assuming a high mining rate. Figure 8 additionally indicates that fault-slip induced by a combination of asperity shear and stope extraction continues for a long period of time, compared to the other cases. As can be seen from the figure, the shear displacement takes the maximum value approximately 0.12 ms after the onset of the dynamic analysis when fault-slip is simulated with the combination, while, for the other cases, the shear displacements stop increasing and remain relatively constant much earlier. Specifically, the shear displacement becomes constant at 0.02 s for fault-slips induced by asperity shear; and in the case of fault-slip induced by stope extraction, the shear displacement stops increasing at 0.05 s. It seems that the shear displacement induced by asperity shear becomes almost constant at the earliest stage (0.02 s) amongst fault-slips simulated with the different methods.

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Fig. 7 Distribution of relative shear displacement increments on the fault induced by the combination of asperity shear and stope extraction

Presumably, the difference in time at which the shear displacement on the fault becomes constant is attributed to the extent of fault-slip areas around the point where the maximum shear displacement takes place. In Fig. 4, the maximum shear displacement takes place around y=150 m on level 7 where Stope7H is extracted, for both types of fault-slip. It is evident that the fault-slip area around the region where the maximum slip takes place in Fig. 4b is greater than that in Fig. 4a, which suggests that slips propagating along the fault provoke additional slips at the location. Figure 9 shows rupture time investigated on the center line (y=150 m) of the fault. The definition of rupture time is given in the previous section. It is found from the figure that when fault-slip is induced by asperity shear, a slip is initiated at the

Fig. 8 Relative shear displacement increments with time during faultslip in dynamic analyses at a point where the maximum shear displacement takes place on the fault

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Fig. 9 Rupture time (time at which the fault surface starts slipping during dynamic analyses) observed on the center line (y=150 m) of the fault

hypocenter in the least time after the onset of the dynamic analysis. This is because when fault-slip is induced by stope extraction, it takes some time for stress waves arising from the stope extraction to reach the fault and trigger fault-slip. Dividing the difference in rupture time between adjacent zones by its distance provides an approximation of the rupture speed. In other words, the smaller the difference in rupture time between adjacent zones is, the larger the rupture speed is. A comparison of red and black bullets in Fig. 9 gives an insight into the difference in rupture speed between the two types of fault-slip mechanisms. The comparison indicates that the rupture speed of fault-slip induced by stope extraction is greater than that of fault-slip induced by asperity shear around the hypocenter. It is conjectured that this is because stress waves arising from the stope extraction reaches the fault at almost the same time. In contrast, when fault-slip is triggered by asperity shear, fault-slip needs to propagate from its hypocenter, thereby resulting in relatively low rupture speeds. Figure 9 further suggests that rupture takes place with high speeds in the vicinity of the hypocenter, while the rupture speed becomes lower with an increasing distance from the hypocenter. The difference in rupture area amongst the simulation methods is also found from Fig. 9. It is clear from the figure that rupture takes place in larger areas in the case of fault-slip caused by the combination of asperity shear and stope extraction. In particular, rupture takes place at 50 m, where no fault-slip takes place for the other two cases. The difference agrees well with the shear displacement increments shown in Figs. 4 and 7. As can be seen in the figures, fault-slip is induced at z=50 m and y=150 m only when it is caused by the combination. It is assumed that the much larger shear displacements during fault-slip caused by the combination enable rupture to propagate to the regions. Interestingly, there is an obvious time lag between ruptures at 50 m and at other locations as shown in Fig. 9, i.e., rupture does not occur

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continuously on the center line of the fault (y=150 m). The discontinuity can be explained with Fig. 7. It is found from the figure that the fault-slip taking place at z=50 m is associated with rupture that propagates through the sides of the fault, i.e., rupture does not directly propagate to the region along the center line from the hypocenter. Consequently, it causes the time lag. Table 2 shows seismic source parameters of fault-slip simulated with the different techniques. In the table, the seismic source parameters are computed from Eqs. 7 to 9, and the maximum slip rate denotes the maximum instantaneous slip rate calculated in a time interval of 0.1 ms during fault-slip. As can be seen in the table, there are great discrepancies in the seismic source parameters amongst fault-slips simulated with the different techniques. Although the maximum shear displacement of fault-slip induced by stope extraction is larger than that of fault-slip induced by asperity shear as shown in Figs. 4 and 8, the seismic source parameters indicate that faultslip induced by asperity shear could become more violent. This is because a sudden reduction in the resisting force of the fault due to asperity shear could trigger fault-slip in regions where the shear stress of the fault is critical on the entire fault. On the other hand, stope extraction is able to induce fault-slip only in areas where stress waves arising from the fault-slip are intense enough to trigger fault-slip. As expected from Fig. 7, the seismic moment and seismically radiated energy of faultslip induced by the combination of stope extraction and asperity shear significantly surpass those of the other fault-slip, suggesting fault-slip could considerably become violent if those two mechanisms are involved in the occurrence of fault-slip. Regarding the maximum slip rates shown in Table 2, although significantly high slip rates are obtained when fault-slip is induced by stope extraction, it was found out that the high slip rate is due to stress waves arising from the stope extraction rather than due to the slip of the fault. Hence, slip rates estimated from Fig. 8 are more representative as the slip rate for fault-slip induced by stope extraction. For fault-slip induced by asperity shear, the slip rate could reach 4.0 m/s under the adopted stress state and geological configurations, as shown in the table. Lastly, the effect of mining rate on seismic source parameters of fault-slip induced by stope extraction is examined. Stope extraction with a low mining rate is simulated

in accordance with the mining sequence shown in Fig. 3. In this case, stopes with a strike length of 25 m are extracted on level 7 with dynamic analysis as explained in the previous section. Seismic moment and seismically radiated energy are computed after extracting each stope. The results are shown in Fig. 10. As can be seen in the figure, cumulative seismic moment and seismically radiated energy constantly increase as the mining sequence proceeds. Each stope extraction causes fault-slip with seismic moment of 2.0×1011 N·m and seismically radiated energy of 7.0×107 J at a rough estimate. Eventually, the cumulative seismic moment and energy reach 1.46 × 1012 N·m and 4.6×108 J, respectively. It is remarkable that the cumulative seismic source parameters after extracting all the stopes shown in Fig. 3 are evidently less than those of fault-slip induced by extracting Stope7H in one shot. According to Table 2, the seismic moment of fault-slip induced by stope extraction is 2.6× 1012 N · m, which is almost twice that of fault-slip induced by stope extraction carried out with the low mining rate. It is postulated that the difference in seismic source parameters between the different mining rates is associated with the amount of seismic energy released by the stope extraction at each stage during the mining sequences. As discussed by Mitri et al. (1999), the energy release rate during mining activity is strongly related to the occurrence of seismic events (rockbursts). Note that the seismic energy discussed here is energy released due to stope extraction. Even though the amount of cumulative energy released by stope extraction might not be significantly different between the high and low mining rates, there would be a great difference in energy release rate between high and low mining rates. Thus, these results indicate that mining rate could significantly affect the severity of fault-slip directly caused by stope extraction, and highlight the importance of proposing an appropriate mining rate when faults are located in the vicinity of stopes to be extracted.

Table 2 Summary of seismic parameters calculated from fault-slip simulated with different simulation techniques Mo (N·m)

Es (J)

Maximum slip rate (m/s)

5.6×1012 1.4×109 3.9 Stope extraction 2.6×1012 1.1×109 9.1 Asperity shear+stope extraction 20.5×1012 6.7×109 9.1 Asperity shear

Fig. 10 Cumulative seismic source parameters for fault-slip induced by stope extraction with a low mining rate shown in Fig. 3

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Conclusion

References

Enhancing knowledge about fault-slip taking place in underground mines is of paramount importance, considering the severe damage inflicted by fault-slip bursts. In the present study, a numerical model exemplifying the stress state and geological configurations in the Canadian Precambrian shield is constructed, and static and dynamic analyses are performed to simulate mining-induced fault-slip. Specifically, fault-slip induced by stope extraction, asperity shear, and a combination thereof is simulated in the present study, and a comparison of fault-slips caused by the different underlying mechanisms is made. First, this study reveals that the distribution of relative shear displacements induced by fault-slip considerably differs depending on underlying mechanisms of fault-slip. When fault-slip is triggered by the breakage of fault surface asperities, fault-slip could occur in extensive areas of the fault; on the other hand, fault-slip areas are limited in the vicinity of a stope for fault-slip induced by stope extraction. It is additionally shown that strike-slip could take place in certain areas when fault-slip is triggered by asperity shear. Regarding the magnitude of fault-slip, it is found out that seismic source parameters of fault-slip induced by asperity shear surpass those of fault-slip induced by stope extraction. More importantly, numerical analysis shows that when fault-slip is caused by a combination of the two mechanisms, fault-slip could become significantly violent. In addition to the magnitude of fault-slip, the slip rate is examined, and it is then found that stope extraction causes a more intense slip than asperity shear at an early stage of fault-slip, although the difference in slip rate between those types of fault-slip is not significant. Investigation of rupture time on the fault implies a high rupture speed when fault-slip is induced by stope extraction. It is presumed that this is because stress waves arising from the stope extraction reach the fault at almost the same time, thereby inducing slips along the fault simultaneously. Lastly, it is shown that extracting stopes with a low mining rate yields considerably small cumulative seismic moment and seismically radiated energy at the final stage of the mining sequence, compared with a case in which a high mining rate is simulated. The result implies that the mining rate could exert a large influence on the severity of faultslip directly induced by unclamping of a fault resulting from stope extraction. This study gives an insight into characteristics of mining-induced fault-slip triggered by different underlying mechanisms.

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Acknowledgments This work is financially supported by a grant from the Natural Science and Engineering Research Council of Canada (NSERC)—Discovery Grant Program and McGill University (MEDA Fellowship Program); the authors are grateful for their support.

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