1 INTRODUCTION

The development of new mining technologies and an unprecedented increase in the volume of work have led to a noticeable rise in the number and energy of large earthquakes associated with man-made activities.

Large induced earthquakes in mining industries are prevalently associated with underground mining operations conducted at substantial depths in massifs with a significant tectonic stress component. Focal areas of major seismic events are associated with either the collapse of large areas as a result of pillar disintegration and rock failure in the vicinity of mining operations (such seismic events are not considered in this study) or slips along faults or tectonic fractures (Heesakkers et al., 2011a; Kocharyan, 2016; Sainoki & Mitri, 2014). In total, the literature describes several hundred earthquakes with M > 2.8 associated with the extraction of solid minerals in mines and pits in Australia, China, Russia, South Africa, and other regions (Foulger et al., 2018 и ссылки там), but this does not include all such events.

The foci of strongly induced events can be located not only near the work area but also at a substantial distance from it, specifically, at a depth of 5–10 km. The largest earthquake observed there to date is the 1981 M = 5.7 earthquake, which is thought to have nucleated in the deeper zone (Foulger et al., 2018). Here, and below, the type of magnitude is given according to the original publications. Earthquakes with deep sources (depth down to 7 km) were observed in coal mining in China (Taiji coalmine) (Li et al., 2007); well-known earthquakes attributed to oil extraction (1983, M_w = 6.2 Coalinga, California; 1985, M_w = 6.1 Kettleman, North Dome; and 1987, M_L = 5.9 Montebello Fields) nucleated at depths of about 10 km (McGarr, 1991); injection of gas in storage at a depth of 1.75 km in Spain provoked earthquakes at depths down to 10 km (Gaite et al., 2016); the strongest earthquake (with a magnitude of M_w = 4.2) took place 2 weeks after the gas injection had stopped. Hereafter, M_L denotes the local magnitude, M_w is the moment magnitude, and m_b refers to the short-period body wave magnitude. The magnitudes are listed as they appear in the sources. For some events, especially old ones, the magnitude types are not always indicated.

Powerful seismic events (with magnitudes up to M_L ~ 5.5–5.6), triggered by mine-induced seismicity, have occurred in many regions of intensive mining (Gibowicz & Kijko, 1994), specifically in the United States (Knoll, 1990; Kubacki et al., 2014), South Africa (Durrheim et al., 2006; Heesakkers et al., 2011a, 2011b; Riemer & Durrheim, 2012), China (Li et al., 2007), and Europe (Bischoff et al., 2010; Lizurek et al., 2015). Strong seismic events also occur regularly at mining enterprises in Russia, but the man-induced earthquakes that took place in Russia are poorly covered in relevant world literature. The oldest Russian mines are located in the Urals. The industrial production of iron ore and coal was launched in the Urals in the mid-19th century, but salt mining began much earlier. The first seismic events were registered here when mining depths had reached approximately 300 m. Events with a magnitude of M = 4.0 occurred on April 19, 1955, on June 10, 1980, and June 10, 1987, in the Middle Ural. In the Northern Ural, substantial induced seismicity was recorded after the mining depths reached 300–340 m in the 1970s. Events that caused severe consequences occurred at the Solikamsk salt mine on October 19, 1985, with M = 4.0. Ten years later, on January 5, 1995, an earthquake of magnitude m_b = 4.7 occurred at the salt mine. The mine destruction covered an area of 300 000 m² (Malovichko et al., 2001). On February 26, 1987, a large earthquake with a magnitude of M = 4.3 occurred in the North Ural bauxite mine. Three events with magnitudes of M = 4.2–4.7 occurred on May 28, 1990, in the South Ural bauxite deposit (Adushkin & Turuntaev, 2015). Strong induced earthquakes are not uncommon in the mines of the Kola Peninsula, to name just a few examples of induced earthquakes: on April 16, 1989, with a magnitude of M = 4.8–5 in the Khibiny massif (Tryapitsin & Syrnikov, 1992); on October 26, 1995, with a magnitude of M = 4.5 in the Rosvumchorsky mine; and on August 17, 1999, with a magnitude of M = 4.4 in the Lovozero mine (Melnikov, 2002). Weaker seismic events have been recorded in the mining area of the Pechora coal basin. An earthquake of magnitude M = 4.0 occurred on December 24, 2012, in Vorkuta, where mines and open pits are located. Earthquakes that are caused by excavation in quarries (open pits) are rare manifestations of anthropogenic seismicity. Nevertheless, open-pit coal mining is associated with the most powerful seismic event that has been initiated by mining operations. This earthquake, namely, the Bachat earthquake, which had a magnitude of M = 5.5 (M_L = 6.1), occurred on June 18, 2013, in Kuzbass, Siberia, near the Bachatsky coal mine (Emanov et al., 2017; Yakovlev et al., 2013).

The study on the nature of the Bachat earthquake M_L = 6.1 is initiated on the score of the following reasons. First, it is a rare case when a major earthquake with a strong probability is triggered by mining in an open pit. Second, man-caused earthquakes that took place in Russia are poorly covered in the previous relevant world literature. Third, numerous investigations have been performed on weak seismicity, whereas strong earthquakes triggered by anthropogenic activities are less studied.

This study explored the Bachat earthquake in detail in the following aspects: the possibility of triggering a strong earthquake by the overall anthropogenic impact on the area, the effect of seismic waves generated by explosions, the excavation and displacement of rock in mining operations, and the changes in the hydrodynamic regime.

A dense network of seismic stations promptly installed made it possible to locate the foci of a significant number of the Bachat earthquake aftershocks. Accordingly, the data on the volume changes in extracted and displaced rock in time and explosion yields could also be known. Such data, most often, are not available in deep underground mining. In addition, the change in the stress field is significantly more complex in the vicinity of an extensive network of underground workings than under an open pit, which complicates the analysis and generalization. In the case of the Bachat quarry, it is possible to study in detail the contribution of each potentially dangerous factor to triggering a major seismic event produced by a movement on an active fault. The results of the seismic measurements obtained by the local seismic network (Emanov et al., 2017) were used to analyze the extent to which near-surface mining operations can cause a large earthquake. On this basis, this study identified the processes that would be the most likely to trigger the dynamic release of a portion of the strain energy that has accumulated in the rock massif. With reference to the example of Kuzbass, the main factors that could trigger such a strong earthquake were considered and the impact of the excavation on the enclosing massif was calculated. As the results show, a pit that occupies 20 km² on the surface can serve as the trigger for sliding a fault, which is located at a depth of approximately 4 km. Until now, no such analysis has been conducted for the Bachat earthquake or large open pits in general.

The analysis performed will be relevant and useful for the investigation of potential triggers of major earthquakes for both open-pit mines and deep underground excavations.

2 INDUCED SEISMICITY AND OPEN PITS

Knowledge regarding induced seismicity has significantly advanced in recent decades as digital methods of seismic data recording and processing have developed rapidly. The number of installed seismic stations and sensors has substantially increased, and the sensitivity of the equipment now enables the recording of weak and minor seismic events (Foulger et al., 2018; Gibowicz & Kijko, 1994; Li et al., 2007).

An analysis of a large amount of data on induced seismicity sources identified different types of earthquakes. These may be weak microevents for which the spatial and temporal coordinates of their sources match the areas of mining activities and virtually mark the stress zones (Arabasz et al., 2005; Boltz et al., 2014; Gibowicz & Kijko, 1994; Li et al., 2007; Richardson & Jordan, 2002). More powerful man-caused earthquakes with energies Es > 10⁹ J (M > 2.5) may be localized near existing fault zones, both in the vicinity of ongoing mining operations and at some distance from them, and can occur with appreciable delays relative to the operations (Foulger et al., 2018; Yabe et al., 2015). Such events are likely triggered by preexisting and prestressed faults in the region. Previous studies have obtained evidence for links between induced earthquakes and established faults in focal areas of earthquake consequences (Heesakkers et al., 2011a, 2011b; Kremenetskaya & Trjapitsin, 1995). For example, an earthquake at a depth of approximately 1 km with M = 4.8–5.0 and E = 10¹² J occurred in the Apatit ore mine in the Khibiny mountains (Russia) immediately after an ordinary industrial ripple-fired explosion (total yield of approximately 200 tons of TNT) on April 16, 1989. During this earthquake, a fracture of approximately 1 km developed in an existing fault. The fault is primarily an aegirite vein 15–25 cm thick that was indistinguishable in the surrounding massif in terms of strength. Fresh slickensides were detected on the fracture edges, and a distinct area of clay gouge was clearly observed (Tryapitsin & Syrnikov, 1992).

It should be noted that spatial correlations between seismic events and the mining sites or faults can be identified only if the events' locations are marked accurately enough (Arabasz et al., 2005; Boltz et al., 2014; Gibowicz & Kijko, 1994).

In this study, possible triggers were considered for earthquakes of appreciable magnitudes (Es > 10⁹ J; M > 2.5), whose sources are dynamic slips along preexisting and prestressed tectonic faults.

Although open-pit mining is the most “ancient” way to recover minerals, it remains in high demand. Currently, the largest open pits reach areas of tens of square kilometers and depths of several hundred meters. For example, one of the world's largest open pits, the Garzweiler strip mine in Germany, is located in the densely populated Ruhr region, occupies an area of approximately 50 km², and reaches a depth of 200 m. In Russia, there are also enormous open pits. For example, the Neryungrinsky open-pit coal mine in Yakutia has a vast mining area of more than 37 km² and a mining depth of 320 m, and the Bachatsky open-pit coal mine (Kuznetsk coal basin in Siberia) occupies an area of 22 km² with a mining depth of 320 m.

The open-pit method is also used for the mining of other minerals. For example, the Hull Rust open-pit mine (an iron mine in Minnesota, USA) is approximately 25 km² and 180 m deep; the Lebedinsky open-pit mine (an iron mine in the Kursk magnetic anomaly, Russia, which is the most powerful iron ore pool in the world) occupies an area of approximately 25 km² and has a depth of 500 m; and the Asbestovskiy open-pit mine in the Urals, Russia, occupies an area of approximately 22 km² and is 350 m deep.

For a long time, it was thought that open-pit mining does not provoke earthquakes. However, a sequence of earthquakes with the main shock of a magnitude of M = 3.3 occurred in 1974 near Wappingers Falls (New York, USA). The earthquakes were associated with surface quarrying. The events' focal depth was between 0.5 and 1.5 km. The earthquake sources were located directly under the open pit, and the focal mechanism was thrust (McGarr et al., 2002). The open pit was not excessively large—its length was approximately 1 km, and its depth was 50 m—but the pit location had a high horizontal compression. In one more case, earthquakes with magnitudes up to 4.6 occurred in Belchatow, Poland. These were provoked by open-pit coal recovery (Gibowicz et al., 1981).

Seismic activity in the area of open-pit mining is also registered in Russia. For example, in Khibiny (Kola Peninsula), earthquakes with magnitudes of up to M = 4 occurred in the Central mine open pit in October 1995 (Melnikov, 2002). Other large events presumably provoked by mining took place in Siberia (June 18, 2013, M_L = 6.1: Emanov et al., 2017; and a series of earthquakes with M > 3.7 in Novosibirsk district: Emanov et al., 2020).

3 SEISMICITY AND ANTHROPOGENIC IMPACT ON THE TERRITORY OF KUZBASS

The Kuznetsk Basin, which is often abbreviated as Kuzbass, is located in Russia in the south of Western Siberia in the northwestern part of the Altai-Sayan region (Figure 1). It can be outlined by boundaries with coordinates 53–56.5° N and 85–89° E. The coal reserves of the Kuznetsk Basin are among the largest in the world. Coal, iron, and gold ores have been actively extracted in the basin for approximately 100 years.

In the 1960s, about 100 million tons of coal per year were extracted in Kuzbass. In 2018, this amount increased to 258.3 million tons. In total, more than 10 billion tons of coal have been extracted, and overburdened rocks with mass several times larger were displaced. Blasting operations are also intensive. The explosive weight in one ripple-fired explosion reaches hundreds and sometimes exceeds a thousand tons. The total consumption of explosives has exceeded 600 000 tons per year.

Mining operations are conducted within a limited area of approximately 27 000 km² on which hundreds of mines and pits are located. The maximum depth of the coal mines does not exceed 900 m, with an average depth of approximately 300 m. The Bachatsky open pit, which is one of the largest mines in Kuzbass, had, according to the site drawing, dimensions of 10 km × 2.2 km and a depth of 320 m at the time of the earthquake in 2013. The geology and tectonics of the region have been briefly reviewed by Kocharyan et al. (2019).

This is a vast and often inaccessible territory, which is why seismic stations began to be installed here only in the middle of the 20th century and at large distances from each other. For Kuzbass, it is reliably known that only two strong earthquakes with М ~ 6 occurred (Ashurkov, 2006; Tolmachev, 1898) in the same area. A description of the first earthquake, which occurred on June 7, 1898, was published by a member of the Academy of Sciences of the Russian Empire. The event on March 12, 1903, occurred in the same area of southern Kuzbass and was recorded in an area of approximately 200 000 km². This earthquake was recorded by seismographs. This study collected data on all earthquakes that were related to the territory of Kuzbass in the International Seismological Centre (ISC; http://www.isc.ac.uk) and Geophysical Service of the Russian Academy of Sciences (OBN; http://www.ceme.gsras.ru/new/ssd_news.htm) catalogs. The data from January 1, 1950 to October 31, 2019 were reviewed. During this time, eight events with magnitudes from M = 4.5 to 5.5 and 43 events with M = 4.0 were recorded in the territory of Kuzbass. In addition, for the period from 2013, a catalog of the regional Altai-Sayan seismic network was used, which was more detailed.

The substantial seismic activity started in the area of the Bachatsky mine more than a year before the strong earthquake. After February 09, 2012, at 13:24 (20:24 local time), when the earthquake of M_L = 4.3 occurred, temporary local monitoring was organized within the area of ongoing mining operations. In parallel, the network of regional stations was expanded, and permanent stations of the local network were installed. In 2014, the regional network already had 13 stations that were located within a distance of approximately 100 km from the largest open pits. From that moment on, the monitoring system became capable of recording seismic events M_L = 1–2 and higher (Emanov et al., 2017).

On June 18, 2013, at 23:02 (on June 19 at 06:02 local time), an event with m_b = 5.5 (M_L = 6.1) occurred; its hypocenter (54.29° N, 86.17° E) was at a depth of several kilometers in the Bachatsky open-pit mine. The earthquake caused severe damage to homes in nearby villages. The shaking was felt at distances of more than 200 km. For example, vibrations that were felt in Novosibirsk (approximately 220 km away from the source) correspond to an earthquake intensity of M_L = 4 on the modified Mercalli scale. Unfortunately, by the time of the Bachat earthquake, the regional seismic network had just begun to be installed. A temporary seismic network was installed immediately after the main shock in the vicinity of the mine, which enabled the registration of thousands of aftershocks (0 ≤ M_L ≤ 4.2) during the period until October 2013. This study used the data from the local seismic network that had been presented in the article (Emanov et al., 2017). According to these materials, approximately 70 earthquakes per day occurred immediately after the main event. A month and a half later, the activity of the seismic process decreased to several events per day. Six months later, only several events with M_L > 2 per month were recorded. In total, 1698 aftershocks were recorded within the magnitude range of 0.1 < M_L < 4.2 from June 18, 2013 to August 31, 2015 (Emanov et al., 2017). The locations of aftershock hypocentres are illustrated in Figure 1 (Emanov et al., 2017). The cloud of aftershocks roughly coincides with the contour of the open-pit mine on the map.

Locations of the source of the Bachat earthquake and its aftershocks show that they belong to the zone of the thrust fault (Kocharyan et al., 2019 and references therein). There are no precise data on the parameters of the fault plane in the area of the Bachat open pit. The local team of seismologists (Emanov et al., 2017) estimated the depth of the source as 4 km. Based on the geophysical data and the distribution of aftershock sources (which were determined accurately, since they were recorded by the temporal seismic network), it seemed that this depth was closer to the truth (Kocharyan et al., 2019). However, an assessment of the depth of an earthquake source with incomplete seismic measurements always implies uncertainty. Different seismic stations obtained different estimates of the depth of the Bachat earthquake source. In the catalog of the Geophysical Survey of the Russian Academy of Sciences (http://www.gsras.ru/new/ssd_news.htm), the depth of this event appears to be 10 km. There is no exact mapping of the fault, so the dip of the fault is also unknown. In this study, it was assumed that the plane of this large fault in the vicinity of the Bachat open-pit mine was of south-west dip and spreading from north-west to south-east. Although near the surface the slope of the principal slip zone (PSZ) is 30°–50°, according to geophysical data (Kocharyan et al., 2019 and references therein), the fault flattens out very fast and, at a depth of about 4 km, becomes nearly horizontal with a dip angle of 10° or less.

So the estimates were obtained for different depths (from 1 up to 14 km) and dips (from 10° to 60°) to consider all possible options.

The top panel of Figure 2 is a plot of the coal production and the total consumption of explosives versus time. As is expected, the curve demonstrates clear proportionality of the production output to the total consumption of explosives (energy of explosions). It is obvious that by analyzing only statistical information of seismic events, it is impossible to discriminate between the actions of quasistatic initiating factors (massif destruction and rock excavation) and the actions of dynamic initiating factors (seismic waves from explosions and vibrations that are due to machine and mechanism operations).

The symbols in Figure 2a show the magnitudes of the strongest earthquakes in the region (Table 1). As can be easily seen, the largest seismic events occur irrespective of the amount of coal recovery and total consumption of explosives.

It is almost impossible to determine the reason for the frequency of occurrence of seismic events with M > 4, which seems to be increasing since 1990–2000 years (see Figure 2a). It is probably closely related to the development of seismic observations in the Kuzbass region, which has long remained inaccessible for the installation of equipment. Until 1990, only a few analog stations were installed on an area of about 250 000 km². After 1990, the number of stations increased to 10–13. After 2000, the measurements began to be converted to digital operation, so there were more chances to register seismic events.

To study the relationship between mining and seismic events in Kuzbass during this period, various data sets from catalogs were used. The attempt to determine that the explosion should be included in the seismic catalogs is based on two facts. The first is that blasting is not carried out at night. The second is that the magnitude of the signals from the explosions does not exceed M = 4. Accordingly, the data chosen were as follows: all seismic events with a magnitude M > 4 (1); or “night” seismic events with M > 4 registered from 6 p.m. to 9 a.m. local time (2); or a set of “night” events and large magnitude events (M > 4.4) that occurred in the daytime (3); or events with nonzero source depth (h > 0.5 km) from the catalog of the local seismic service (Altai-Sayan Branch of the Geophysical Survey of the Russian Academy of Sciences) (4). The result can be seen in Figure 2b. For convenience, the radiated energy values are scaled by the average annual Es value for each data set. As can be seen, none of the data series with seismic energies radiated during earthquakes shows correlations with the amount of consumed explosives. Furthermore, since the magnitude error of is equivalent to scatter in the estimated energy of about an order of magnitude, the annual variations in energy radiated by earthquakes in 1990–2018 (excluding 2013) fall within the limits of the magnitude error.

So the total anthropogenic load on the upper part of the crust does not necessarily affect the process of triggering large earthquakes. This demonstrates the tectonic nature of powerful earthquakes in Kuzbass, while all the anthropogenic factors can only be triggers. To estimate the possibility of the anthropogenic triggering of earthquakes with sources at a depth of several kilometers (as it is for the Bachat earthquake), the direct influence of anthropogenic factors on the source area should be considered.

4 MINING OPERATIONS AND THEIR POTENTIAL TRIGGERING OF SEISMICITY

4.1 Stress redistribution due to excavation and displacement of rock

The approach that is common in seismology for estimating the configuration of the aftershock zones is used to estimate a possible effect of stress redistribution caused by mining on triggering powerful earthquakes whose sources are at a depth of several kilometers (King et al., 1994; Stein & Lisowski, 1983; etc.).

Dynamic failure occurs when the shear stresses are large enough to overcome the friction that prevents a locked fault from slipping. This balance can be characterized by the Coulomb's failure criterion (Jaeger et al., 2007), for which the Coulomb's failure function , is given by

(1)

where and denote the normal and shear stresses acting on the fault, respectively; is the pore fluid pressure; represents the static coefficient of friction; and C is cohesive strength. The case σ _c = 0 corresponds to Byerlee's law for frictional failure (Byerlee, 1980), and a positive change in σ _c indicates that the stress state has moved incrementally toward failure.

Although the absolute value of stress on a fault may not be known, the change in Coulomb's failure function can be calculated using the expression

(2)

where denotes the increment.

From this equation, it can be estimated whether a fault has been brought closer to () or further away from () failure. Note that calculations are independent of regional stress fields.

Based on the available data on the geometry of the fault zone in the vicinity of the Bachatsky open coal pit, the modified variation can be estimated in Coulomb's function at the expected plane of rupture that is caused by the induced earthquake.

It is convenient to use the solution of the Love problem (Love, 1892), in which the stress field is considered when a load is applied to a rectangular area at the surface of an elastic half-space. Later, Florin (1959) showed that if the excavation depth d is significantly less than the linear dimensions of the open pit, the deformation of the massif can be simulated by removing the load that is uniform across the excavation area (Figure 3, incut). The difference between the applied rectangular calculation scheme and the actual shape of the quarry does not significantly affect the calculated values of stress components, since the dimensions of the pit are large compared to the irregularity of the shape (Florin, 1959). Consequently, the scheme in Figure 3 (incut) can be used to calculate the stress components underneath the open-pit bottom. The difference between the applied calculation scheme and the real structure does not significantly affect the calculated values of the stress components because the pit dimensions are large (Florin, 1959).

The solution presented in the original paper (Love, 1892) contains analytical formulas only for the vertical component of the stress . The paper (Korotkin, 1938) presents the formulas for all components of the tensor. The formula for defining the vertical stress at the points on the vertical line that passes through the area center ( x = 0, y = 0, see Figure 3 (incut)) is

(3)

Figure 3 shows how the vertical stress component varies with the depth of excavation for a pit with parameters that are close to those of the Bachatsky open pit. The rock density is ρ = 2.7 × 10³ kg/m³. At a depth of several kilometers, the change in the vertical stress component that is caused by excavation is less than 1% of the lithostatic pressure. The increments of all components of the stress field are calculated in the coordinate system that is shown in Figure 3 (incut) for a half-space that contains a pit of 10 km × 2 km × 0.3 km in size. On this basis, the changes in Coulomb's function (1) at a fault plane with a specified orientation are estimated by using the incremental Equation (2). For the calculations, it is assumed that the pore pressure does not change: . There are no precise data on the parameters of the fault interface in the area of the Bachat open pit. According to the estimates, the most probable value at the depth of the Bachat earthquake source (4 km) is a 10° dip (Kocharyan et al., 2019), but the estimates were obtained for different depths (from 1 up to 14 km) and dips (from 10° up to 60°). Examples of the results of calculations are given in Figure 4.

As mentioned above, according to the data (Figure 1) obtained by the local team of seismologists (Emanov et al., 2017), the hypocenter of the main event is located beneath the south-eastern part of the quarry at a depth of ~4 km. The focal mechanism of the Bachat earthquake is an upthrust, one of the nodal planes being oriented along the long axis of the cut (Emanov et al., 2017). According to the above analysis, this upthrust belongs to a thrust fault, which becomes subhorizontal at a depth of 4 km with a dip angle of about 10° (Kocharyan et al., 2019). Thus, the calculations show (Figure 4) that Coulomb's function increment is positive at the expected depth of the earthquake hypocentre; hence, the fault state is close to the critical one. The value of Coulomb's stress change is approximately 1 MPa.

There is another factor that can be of critical significance in underground mining operations: an extensive network of tunnels can noticeably affect the effective stiffness of rock massif, which, in turn, can influence the stability of the tectonic fault in the vicinity of the mining field. Accordingly, a two-dimensional (2D) elastic numerical modeling method was used to estimate this influence.

The inset of Figure 5 illustrates the model that was used to simulate the influence. With the right side of the block fixed, a linearly increasing shear stress was applied to the left side of the block. The applied shear stress was increased at a rate that ensured nearly quasistatic deformation of the block. For the calculation, a 2D solution that was developed based on the Lagrangian numerical method “Tensor” was used (Mainchen & Sack, 1967).

Equations that describe the motion and stress state of solid deformable material in the Cartesian coordinate system are as follows:

(4)

where t denotes time; x, y, and z are coordinates; ρ is density; v _x and v _y refer to components of the velocity vector ; g is gravity; Р is pressure; s _ij is deviator of the tensor of stresses; is deviator of the tensor of deformation rates; ε is specific internal energy; d/d t is Lagrange derivative for time: The axes of the Cartesian coordinate system x (horizontal) and y (vertical) lie in the plane of symmetry of the problem and the z-axis is perpendicular to this plane.

The relationship for ideal elasticity was used to describe the process of deformation of the medium because the problem of estimating the effect of underground tunnels on the effective shear modulus of a structural block requires no accounting for the strength properties of rock. Specifically, an elastic block of 600 m × 780 m in size was used (density  = 2.7 × 10³ kg/m³, bulk modulus K = 28 GPa, and shear modulus G = 11.435 GPa, P-wave velocity a₀ = 4000 m/s). In this case, gravity was neglected. Shear stress that increased linearly with the rate of 0.1 MPa/s was specified at the upper side of the block. Special calculations showed that such a rate of shear stress increase ensured a regime of block deformation close to the quasistatic one.

The calculation results for an H-wide monolithic block show that the effective shear modulus that was evaluated by using a linear approximation of the ratio of the shear stress to the relative shear value is GPa (linear regression with a determination coefficient of ), which is approximately 20% less than the block material shear modulus, where W_r is the shear displacement of the block's top-left corner. This difference is due to the inapplicability of the assumption of a uniform stress distribution across the block for a block with finite dimensions. Here, only an effective shear modulus of block is considered, which is the proportionality factor between stresses and deformations (Besedina et al., 2021).

To estimate the impact of worked-out mining openings on G_eff, calculations were conducted for the elastic block with empty and filled-in cavities. The opening length and height were 100 and 60 m, respectively, and the distance between openings was 100 m. The calculations were for one, two, and up to six worked-out horizons. The distance between the horizons was 80 m. As is expected, the effective shear modulus decreased as the massif damage increased. For one horizon, the G_eff value decreased by approximately 20%, and for two—by a factor of 1.5. For three horizons, the effective modulus of the massif became nearly twice as low.

Interestingly, the results that were obtained for a specified range of parameters yield a good fit to estimates of the effective modulus of the medium with respect to the Nur critical porosity model (Nur et al., 1998), according to which the shear modulus of dry porous media G _eff can be estimated as

(5)

where G _s is the shear modulus of the solid material; is the effective porosity of the medium; is the critical porosity value, which is the pore volume at which the material loses its adhesive capacity; and is an empirical parameter. The dashed line in Figure 5 represents relation ( 5) for and . The values of the effective shear modulus for each case are scaled by the relevant value for the intact rock mass. The solid line deviates from the ratio (5) for large percentages of worked-out areas.

If worked-out openings are filled with broken rock with an elastic modulus of  GPa and Poisson's ratio of (curve 2 in Figure 5), the modulus decreases more slowly (only by 34% for a massif that contains three horizons); hence, the occurrence of instability is significantly less probable than for a massif with empty openings.

4.2 Fault slip triggered by seismic vibrations from explosions

The physical prerequisites for the direct initiation of an earthquake by an explosion impact were explored in more detail.

Triggering seismic events by waves from distant earthquakes (located hundreds and thousands of kilometers from the site) is a not common but recognizable phenomenon (Freed, 2005; Gomberg et al., 2004; Hill et al., 1993; Velasco et al., 2008, and references in these articles).

According to data from numerous studies on dynamic triggering, in most cases, a level of the dynamic strain of ~5 × 10⁻⁷–10⁻⁶ is marginally required for triggering, although some researchers specified much lower values (Van der Elst & Brodsky, 2010; Sobolev et al., 2016). In most cases, the occurrence of dynamically triggered seismicity is associated with the impact of low-frequency surface waves with periods of 20–40 s. Additionally, it is emphasized that triggering by high-frequency body waves is less probable. A detailed overview of this topic is presented in several studies (Freed, 2005; Kocharyan, 2016).

To estimate the probability of initiating a large earthquake by an industrial explosion, the amplitude of seismic vibrations in the vicinity of the earthquake source must be evaluated. This study relied on the results of instrumental observations of seismic waves that are radiated by large short-time delay explosions with a total yield of up to 3000 tons of TNT. The key parameter that affects the maximum amplitude of the vibrations is the explosive weight in the simultaneous blasting series of the delay stage.

An example of a waveform that was recorded at a distance of 1.1–3.6 km from the array of blast holes with a total yield of 2411 tons is illustrated in Figure 6. The main periods of vibrations lie in the range from 2 to 30 s.

Figure 7 plots the measured values of the peak ground velocity vector modulus versus the scaled hypocentre distance for several open pits and mines that are located in various regions of Russia. For each data set, the best fit via linear regression is specified. Here, Q is the explosive weight at a time delay interval (in kg), and R is the distance to the blasting block (in m).

For example, for the Lebedinsky open-pit mine (Kursk magnetic anomaly [KMA]), which is comparable in terms of area with the Bachatsky open-pit mine, the best fit is

(6)

with a determination coefficient of R = 0.63. The total mass of the explosions is 500–2500 tons of TNT. The charge per delay stage is from 0.5 to 10 tons of explosives, and the total duration of vibrations is tens of seconds.

For the Chernogorsky coal mine (Siberia, Khakassia), whose geological conditions are most similar to those of the Bachatsky open-pit mine, the best fit is

(7)

with a determination coefficient of R = 0.77. The total mass of the explosions is 1–250 tons of explosives. The charge per delay stage is from 0.3 to 15 tons of explosives.

Explosions in underground mines trigger vibrations with higher frequency and much smaller amplitude, which should be considered when estimating the blasting impact on fault zones. For the Gubkin mine (KMA), where block caving is used, the best fit takes the form

(8)

with a determination coefficient of R = 0.91, the mining chambers are located at depths of 245–285 m from the daylight surface. The explosive weights in the chambers are 10–20 tons. The charge per delay stage is usually 0.5–1.5 tons of explosives. The total duration of vibrations does not exceed 5–6 s. The vibration spectrum is of higher frequency than that in open-pit blasting.

The parameters of seismic vibrations depend on both the characteristics of blasting rocks and the mining technology. For example, according to Figure 7, the seismic amplitude was recorded after explosions at Sheregeshsky mine (Kuzbass, porphyritic textures, granites and syenites; the uniaxial strength σ_p is ~170–230 MPa) corresponded to the upper limit of the data variation for KMA deposits. For soft limestone of the Novogurovsky open-pit (Central Russia, limestone, σ_p is ~40–60 MPa), the amplitude that was recorded in the same range of the scaled distances is much lower.

With the obtained generalized dependence, the range of possible parameters of seismic waves from explosions at the Bachatsky open-pit mine can be estimated.

It can be assumed that the described data cover the main range of amplitudes of seismic vibrations for ripple-fired explosions. Based on these results, it is possible to estimate the dynamic impact of ripple-fired explosions on faults at the expected depths of foci of large induced earthquakes in Kuzbass.

According to the hypocenter location data (Figure 1), the potential earthquake source's depth can be assumed to be 2–5 km.

For open-pit blasting, the explosive weight of one delay stage can be approximately Q ~1–15 t, but, as a rule, it does not exceed ~1–3 t. Accordingly, the scaled distance to the focus is R/Q^1/3 ~100–500 m/kg^1/3. For open-pit blasting, there are typically many delay stages; hence, the exposure time is long, namely, tens of seconds. The explosive weight of one delay stage in most underground mines in Russia does not exceed 1–2 t. Namely, the scaled distance to the hypocentre is not less than 150 m/kg^1/3. In this respect, the duration of seismic vibrations after explosions in mines is substantially less than after open-pit blasting and rarely exceeds a few seconds. Thus, in most cases, while conducting industrial explosions in quarries and mines, the peak particle velocity at depths of greater than 2 km does not exceed 1–2 mm/s, and the expected value of V_m is substantially lower. It has been established that the impact of seismic waves on a stressed fault can lead to the occurrence of residual displacements, which have been repeatedly observed during deformation measurements (Adushkin et al., 2009; Glowacka et al., 2002). Precise measurements of fault side displacements were conducted, and the faults were exposed to seismic waves from explosions at various test sites. The measurement technique has been described in the study conducted by Adushkin et al. (2018). Relative residual displacement of fault sides produced by seismic waves from the explosion was measured by the laser sensor of displacement ILD2300-100 (Micro-Epsilon) accurate to 1 mcm or by the linear variable differential transformer (LVDT) sensor M-022A (Micromech) accurate to 0.2 mcm. Sensors (2–4 in Figure 8) were mounted on the vertical wall of the tunnel so that the measuring basis intersected the PSZ of the fault (1 in Figure 8). Both normal and shear components of displacement were measured. The sensor was mounted on one of the fault sides with anchor bolts or with an epoxy agent. A bar was mounted on the other side of the fault. The bar held either a target (8 in Figure 8) that reflected the laser beam or a quartz rod that supported the LVDT sensor (7 in Figure 8). Reference sensors were mounted at sections without any macroscopic discontinuities (5 in Figure 8). No significant residual deformations were registered.

Figure 9a presents an example of the relative displacement of the sides of tectonic fractures under the action of an industrial explosion. The residual displacements are clearly observed after the propagation of seismic waves from the last explosion (closest to the fault).

The measurements of the residual displacements in various fault zones after the passage of seismic waves from explosions are summarized in Figure 9b. Circles are the result of our measurements at different natural and engineering objects (Kocharyan, 2016). The line in the figure represents the regression dependence that was formulated via the least-square method as

(9)

The trend of the function demonstrates that the residual displacements are proportional to the PGV (peak ground velocity) value. Seismic vibrations with amplitudes that vary by 1–2 orders of magnitude sometimes have similar residual effects, which can be explained by the various stress states of the fault zones.

The largest values of the residual displacements, which are labeled in Figure 9 as 1, 2, and 3, were registered at the stressed faults in California after the Hector Mine earthquake in 1999, which had a magnitude of M = 7.1 (Rymer, 2002). These data were not considered when estimating regression (9). In earthquakes, the effective trigger is low-frequency surface waves (0.025–0.050 Hz). In contrast, explosions produce much more high-frequency vibrations. Thus, according to the available data, the expected value of a residual displacement along a fault after an explosion, when PGV varies in the range of 0.1 mm/s < PGV < ~4 mm/s, cannot exceed some tens of microns.

5 DISCUSSION

The Kuzbass earthquake of М_L = 6.1 on June 18, 2013, was the strongest seismic event that occurred close to the Bachatsky open coal pit. This seismic event is suitable for investigating the triggering of seismic events due to its size, its readily identifiable connection of the source to the mining area, extensive previous exploration of the region in which it occurred, and the well-known history of the anthropogenic impact.

Based on the assumption that powerful earthquakes with sources at depths of several kilometers and even more are the results of dynamic movements along existing faults, the possible causes of its initiation were analyzed. The following factors could be considered as possible triggers: redistribution of stresses resulting from excavation and displacement of great amounts of rock, effects of seismic vibrations from explosions, and alteration of the fluid dynamic regime.

Specifically, the increment of Coulomb's function (1) at fault planes with different dip angles was analyzed (Figure 4b). As mentioned above, the estimated depth of the hypocenter of the Bachat earthquake is about 4 km. The thrust fault, to which the source apparently belongs, has a dip angle of 10° at those depths. According to the results of calculations (Figure 5), a positive increment of the Coulomb's function (1) reaches the value of about 1 MPa at that depth. It is important that such a change takes place at a lengthy section of the fault plane, which is comparable to the size of the quarry (~10 km × 2 km). This noticeably exceeds the anticipated size of the nucleation zone for an earthquake of M_L = 6.1. Through the comparison between the calculation results and the observational data of aftershock locations in the vicinity of earthquake sources (Freed, 2005; King et al., 1994), it can be concluded that this value (which makes a negligible share of the lithostatic stresses) may turn out to be enough to trigger seismogenic slip along stressed faults.

When considering the deformation processes occurring in the vicinity of a mining enterprise, the actual dimensions of the quarry—length, width, and depth—act as the first characteristic size of the problem. It is clear that changes in the natural stress field within the elastic solution are determined by these parameters, and the effect of variations in the physical and mechanical characteristics of the rock is not so significant.

Direct triggering of such a powerful earthquake by seismic vibrations of ripple-fired explosions seems hardly probable because of very low amplitudes of such vibrations at the depth of the source occurrence. With the measurements of seismic vibrations performed at different mines and quarries in Russia, the characteristics of dynamic effect at a depth of the hypocenter occurrence are reliably estimated. It is shown that PGV from explosions in quarries turns out to be knowingly less than 1 mm/s at such depths. So, the ultimate level of dynamic deformations is: . These values are noticeably lower than the dynamic deformations in seismic waves from distant earthquakes in cases when the effects of dynamic triggering were observed () (Freed, 2005; Kocharyan, 2016). In most cases, it should be emphasized that the occurrence of dynamically triggered seismicity is thought to result from the action of low-frequency surface waves with periods of 20–40 s. It is noted that triggering by high-frequency bulk waves is less likely.

It can be assumed that the action of ripple-fired explosions may hypothetically affect the effective strength of a fault zone through the effect of cumulating small deformations. According to the results of a detailed laboratory investigation, if the amplitudes of seismic vibrations are low, the process of cumulating residual displacements along the fault damps would be represented as repeated cycles of action (Amadei & Saeb, 1990; Bandis et al., 1983; Kocharyan et al., 2018). Judging by the results of the performed deformation measurements (Figures 8 and 9), the anticipated residual displacement, produced by a ripple-fired explosion on a fault located at a depth of several kilometers, does not exceed the value of about 10 mcm. Thus, it seems highly unlikely that this effect can be noticed.

Hypothetically explosions may affect watering of the sliding surface at the expense of crossflows resulting from local redistribution of pressure. Such crossflows may be provoked by the destruction by the seismic wave of plugs of weak colloidal films that essentially decrease the fracture permeability of the rock. Such a mechanism was described previously (Brodsky et al., 2003; Kocharyan et al., 2011). However, estimations performed in the cited works show that this mechanism turns to be effective for PGVs noticeably higher than several millimeters per second, which are anticipated at a depth of the Bachat earthquake source occurrence.

It is well known that one of the conditions for a dynamic instability to occur is compliance with the following relation (Scholz, 1998):

(10)

where τ denotes shear stress, D is the displacement of fault sides, G is the shear modulus of intact rock, η is the coefficient of shape ( η–1), and represents the length of the rupture.

That is, the rate of frictional resistance weakening during slip (the stiffness of the fault) should be higher than that of the decrease of elastic stresses in host rock (the stiffness of the rock massif), resulting from the slip along the fault. This condition is analogous to the energetic criterion for Griffith's crack propagation: the dynamic energy release rate should not be less than the specific energy of crushing.

In this way, the change of the stiffness ratio of the host rock to the tectonic fault resulting from mining operations may provoke a dynamic movement even at a segment that is previously thought to be aseismic. In the case of underground mining, the specific size of the segment of stiffness decrease is not so big if compared to the area of redistribution of stresses in open-pit mining; it is unlikely that the magnitude of such events could exceed M ~3–4. In this case, provided that there is no anthropogenic interference, the stresses cumulated in the rock massif could most likely relax through creep or slow slip events.

Analysis of existing concepts suggests that the Coulomb stresses on many faults that have experienced displacements in recent times are quite close to the ultimate frictional strength, regardless of whether these slips are seismogenic or aseismic.

6 CONCLUSIONS

With the Bachat earthquake of June 18, 2013 (M_L = 6.1), which occurred in Kuzbass, as an example, this study investigated a possible mechanism for the initiation of large tectonic earthquakes by mining operations. The general man-induced load on the region, the impact of seismic vibrations from explosions, the excavation and movement of large volumes of rock, and a change in the fluid-dynamic regime were considered probable triggers.

No noticeable correlation was revealed by the comparison between the periodicity of powerful earthquake occurrence and data on the amount of recovered coal and the consumption of explosives by enterprises in Kuzbass. This leads to the conclusion that the main factor determining the nucleation of large seismic events is the regional stress field, while anthropogenic triggering occurs only during direct actions on the fault zone.

Based on the data of instrumental observations, it has been established that the direct triggering of a large earthquake by seismic vibrations from quarry explosions is extremely unlikely.

As is revealed by the results, the redistribution of stresses is most likely the main trigger of the Bachat earthquake. Calculations show that rock excavation in a large mining open pit leads to a change of ~1 MPa in Coulomb stresses on the fault plane in areas that exceed the size of the nucleation zone for earthquakes with a magnitude . This may be sufficient to initiate seismogenic movements along stressed faults. One of the most important conditions for initiation is the fact that a change in slip conditions should occur over a sufficiently large area, obviously larger than the size of the earthquake nucleation zone—the area where the rupture rate increases to a dynamic value. The typical size of this area for an earthquake with a magnitude of M ~ 6 can be in the order of 1000 m.

Thus, the long-term excavation and displacement of vast amounts of the rock bring forward the moment of the earthquake, which is prepared by the natural evolution of the crust.

The importance ranking of the various triggers is obviously applicable to underground mining. Underground development of mineral deposits changes the effective elastic properties of the rock massif in the vicinity of a tectonic fault. At the same time, the calculation of Coulomb stress variations on the fault plane turns out to be, as a rule, more complicated than in the open-pit case and requires numerical modeling. In addition, for underground mining, the size of the zone in which the conditions for dynamic instability are met turns out to be smaller than for large quarries. Because of this, triggering such major events as the Bachat one by underground operations seems unlikely. On the other hand, underground mining operations can induce a moderate earthquake even in seismically inactive regions due to the modification of elastic properties of the enclosing rock in the vicinity of a tectonic fault.

Judging by the results of the performed numerical simulations, a branching network of tunnels located at several horizons can decrease the effective shear modulus of the host rock by 1.5–2.0 times and can serve as a trigger for an earthquake with a magnitude of up to M = 3–4.

The results obtained can be of practical importance in optimizing the technology of safe open-pit mining. It is important to take into account the possibility of triggering an earthquake with a significant increase in the area of the quarry.

AUTHOR CONTRIBUTIONS

Conceptualization of the research has been performed by Gevorg Kocharyan and Chengzhi Qi. Methodology and formal analysis have been performed by Gevorg Kocharyan and Svetlana Kishkina. Preprocessing data of quarry explosions were done by Vladimir Kulikov. All authors analyzed and interpreted the results and wrote the manuscript.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

ETHICS STATEMENT

We follow all responsibilities and ethics of authors. All authors consented to the publication.