# Deformation Behavior of Mining beneath Flat and Sloping Terrains in Mountainous Areas

Authors: Zhao Jianjun; Wan Xun; Shi Yanbing; Wei Jiangbo; Min Lee Lee
Journal: Geofluids
 (2021)

---

## Abstract

Slope structures and surface terrains are two significant factors affecting the deformation behavior of mining slopes in mountainous areas. This research is aimed at investigating the deformation characteristics of a mining slope wielding Particle Flow Code (PFC), with 9 different mining configurations (i.e., horizontal distance from extracted panel center to slope shoulder,D = −200 m, −150 m, −100 m, −50 m, 0 m, 50 m, 100 m, 150 m, and 200 m). A representative slope in Faer Town, Liupanshui City, Guizhou Province, China, was selected, which was characterized by soft and hard interbedded rock strata. The results indicated that the overlying rock mass tended to move towards the sloping surface with mining beneath sloping terrain, which brought an asymmetrical subsidence funnel, and formed a wider relative disturbance range on the slope surface. With the vertical subsidence increasing additionally, the stability of the overall slope deteriorated. A safe mining range should be proposed based on evaluating the time-dependent deformation behavior at the slope shoulder and the overall slope stability.


---

## Body

## 1. Introduction

Longwall mining is one of the most generally adopted underground mining methods, particularly in mining areas with relatively uniform and thick coal beds [1]. Surface subsidence is the leading form of mining-induced geological hazards which has caused various adverse effects to the environment [2, 3].Analyzing the mechanism of ground movement and estimating their magnitudes and geometries have long been the main concerns in risk management of mining operations. A reliable prediction of ground subsidence caused by the mining operations remains a great challenge [4]. An extracted panel formed, the deformation of the overlying rock mass depends on many factors, i.e., bedding structure, thickness, strength, discontinuous geometric, mechanical characteristics of the panel, thickness of the mined coal seam, and width and length of the extracted panel [5–8]. In addition to the properties of the coal seams and the overlying rock masses, in situ stress conditions, groundwater conditions, terrain gradient, mining method, process of extraction, and distribution of pillars may all add complexity to the ground subsidence estimation [4, 9, 10]. The ground deformation induced by the mining operation is thus a multifactor coupling problem in temporal and spatial scales.The prediction of ground subsidence can be performed by various methods, such as numerical simulation, physical modelling, influence function method, empirical approach, and analytical technique [10–14]. In addition, with the advancement in geographic information system (GIS) and remote sensing (RS) technologies, the spatial database can be constructed to analyze the shape and magnitude of the subsidence [15, 16]. The capability of GPS network application in measuring ground horizontal displacement has made great contributions to monitoring and early warning systems for mining-induced geological hazards [17]. Application of geophysical methods enables geologists to develop a comprehensive understanding of fracture evolution in the overburden rock masses induced by shallow mining activities [18, 19].Many researchers performed numerical and physical modelling to estimate the subsidence of complex ground profiles. The physical modelling normally has difficulties dealing with an in situ stress state of rock mass (i.e., effect of gravitational force), which can be only simulated by geotechnical centrifuge [20, 21]. Performing a large geotechnical centrifuge test, however, can be extremely costly. The numerical simulation has been widely used to analyze mining slopes with complex geometries and simulate discontinuous and nonlinear mechanical behavior of rock masses [4, 9, 22–27]. The Discrete Element Method (DEM) is an efficient tool for analyzing instability of jointed rock slope, as proven by numerous successful cases [28–30].There were in total 356 incidents of geological hazards (refer to Table1) reported in the mountainous area in Liupanshui City, Guizhou Province, southwest of China. By the end of 2016, most of the hazards occurred on the P3l and T1f strata. A typical mining slope named Jianshanying slope in Faer Town, Liupanshui City, was selected. Wielding Particle Flow Code (PFC) to analyze deformation behavior with underground mining operations.Table 1
Distributions of mining-induced geological hazards in Liupanshui City on different strata (data compiled by end of 2016).
Types of geological hazardsMain distribution strataTotalC2hnC3mpP2lP2m+qP3lP3βT1fT1yT1ynT2gELandslide1140862731310181Collapse00029119260139Surface subsidence0021692374800122Ground fissure0001304310012Debris flow000020000002Total11641698133101811356


## 2. Mechanisms of Mining-Induced Slope Instability

Numerous previous studies reported that slopes subjected to underground mining are prone to caving and landslides [31–34]. There were 2 main models of mining-induced slope failures: (1) progressive rock falls and caving failures, which cause nearly vertical cliffs [25, 35], and (2) rock masses extruded from the slope toe causing holistic instability [36]. With underground extraction performed beyond the slope shoulder, most instabilities are initiated [37, 38].According to Salmi et al. [4], the surface topography has a considerable impact on the mechanisms of mining-induced slope instability. Mining in hilly and mountainous terrains usually increases the risk of slope failure. In addition, mining beneath sloping terrains imposes an additional threat on ground subsidence, which usually occurs near a valley [35]. The coal seam extracted beneath flat terrains, the rock masses above the extracted panel were fragmented and caved into the panel immediately, and the fragmented rocks tend to fill the void forming a goaf. As a result of ascending step-loading imposed by the upper caving block, the stiffness of rock mass increases gradually [39]. The overburden strata remain intact and bend towards the extracted panel [40]. Owing to the expansibility of rock, the rock masses falling into the panel are subjected to lateral forces from the virgin strata, which rise gradually with the increase of depth and reach the maximum value at the coal pillar [41]. The boundary conditions on both sides of the extracted panel are identical, and hence, the magnitude and direction of lateral forces are completely symmetrical. Under the circumstances, there are different horizontal deformations in the rock masses, and it causes a symmetrical subsidence funnel on the surface [42]. In an extraction performed near or beneath a cliff, the lateral forces induced above the goaf (directed from the plateau towards the valley) are not counterbalanced by an identical force in the opposite direction. The rock mass near the valley has a greater horizontal displacement, and hence, an asymmetric subsidence funnel occurs on the slope surface.The magnitude and shape of the surface subsidence, which is induced by mining operations under the condition of flat terrains, have been studied extensively. The localized deformation and overall instability constitute much more uncertainties attributed to the complex combination of terrains and structures in the sloping terrains. Studies on ground subsidence induced by mining activities in sloping terrains are still very limited. Several previous case studies of large-scale slope failures induced by mining include the Zhangjiawan collapse and Madaling landslide in Guizhou, China [36], and one of the largest contemporary landslides and mass movements reported at Nattai North, Australia [43], have drawn the global attention on the mass movement caused by mining activities and provoke the present study to be carried out.This research is rooted in the exploration of mining-induced subsidence rules inP3l and T1f with Liupanshui City, Guizhou Province, China, as the typical. To be detailed, this research innovatively proposed 9 mining configurations for expounding the deformation behavior of mining beneath flat and sloping terrains by wielding Particle Flow Code, which is applied to the soft and hard interbedded and jointed slopes in the mountainous area. Furthermore, the time-dependent deformation was measured at the slope shoulder, as the transition part of the flat and sloping terrains, to propose a safe mining range, which was meaningful in the risk management of mining operations.


## 3. Case Study

### 3.1. Model Development

Liupanshui City in Guizhou Province, China, is known for its proven coal resources and reserves. The city which is known as the “Southwest Coal Sea” has developed multistage coal seams on theP3l stratum. In 2015, there were more than 800 mines in the city, while more than 400 landslide and ground subsidence incidents have been reported, which were mainly caused by improperly planned mining activities. In the present study, a mining slope named Jianshanying slope in Faer Town, Liupanshui City, was selected as the case study. The specific geographical coordinates of the study area are E104°44′11″ and N26°18′20″ (Figures 1 and 2).Figure 1
Location of study area.Figure 2
3D terrains of Jianshanying mining slope.In the western part of the Guizhou plateau, a low mountainous terrain was formed because of the tectonic erosion. Typically, both steep and gentle structures were formed in the mining slope. Most of the coal-bearing strata are located in the flat terrains, while the interbedded sandstone and mudstone are mainly located in the sloping terrains. The surface terrain of the Jianshanying slope was reasonably generalized to simplify the subsequent numerical modelling processes. Three sets of dominant joints were considered in each strata, and one set has the same tendency as the strata. The general stratifications of the slope are presented in Figure3. Coal and mudstone formed the relatively weak strata in the slope, however, the effect of the stratified structure was not considered in them.Figure 3
Generalized profile of mining slope model (“T1f” is Feixianguan group and “P3l” is Longtan group).Mining slopes are typically prone to time-dependent failures in the form of ground subsidence and slope sliding [44]. After going through a long process of mining, 6 coal layers had been mined out beneath the Jianshanying mining slope forming a total of 13 mining panels. These mining activities had caused severe impact on the stability of the slope. To simplify the analysis, the present study only focused on the impact of mining with the first coal layer on the slope instability. Nine mining configurations with different horizontal distances (D) from the extracted panel center to slope shoulder (where the flat terrain intersected with the sloping terrain) were set, namely, D = −200 m, −150 m, −100 m, −50 m, 0 m, 50 m, 100 m, 150 m, and 200 m (see Figure 4 and Table 2). The width of each extracted panel along the strata dip direction was within the range of 150~250 m, while the thickness of the coal seam was ranging from 2 to 4 m in statistics. The width of the extracted panel and the thickness of the mined-out coal seam were fixed at 200 m and 6 m in practice. The above configurations were set to systematically study the influences of extracted panel depth, horizontal distance between the center of extracted panel and slope shoulder, and surface terrain condition on the instability of the mining slope. The extracted panel was located beneath a flat terrain with D ≤ −100 m, while the extracted panel was beneath a sloping terrain with D ≥ 100 m (Figure 4). A total of 29 monitoring points with a horizontal interval of 50 m were set in the numerical model, for revealing the deformation characteristics of the slope surface with various configurations.Figure 4
Mining configurations considered for numerical simulation.Table 2
Details of mining configurations.
D (m)-200-150-100-50050100150200Extracted panelsA+B+C+DB+C+D+EC+D+E+FD+E+F+GE+F+G+HF+G+H+IG+H+I+JH+I+J+KI+J+K+LPanel depth (m)345.5336.6328319.2310.1261.5217.1170.9112.1


### 3.2. Particle Flow Code

Rock masses are discontinuous medium, and hence, the use of the DEM is justifiable [4]. PFC (Particle Flow Code), a popular program based on the DEM, is widely used to simulate the macroscopic characteristics of rock-soil masses. The soil/rock aggregates are modelled as either rigid disks (2D) or spheres (3D), and they are connected by specific contact models as an equivalent model of rock-soil mass [45]. The PFC adopts the time step iterative calculation method (Figure 5). Newton’s second law and the law of force and displacement are repeatedly applied in the calculation for updating the motion state of units in real-time, and the contact force and torque between the updated units are further determined by the force-displacement relationship [46].Figure 5
Workflow of PFC analysis.The law of force-displacement reflects the contact relationship between particles, also the relationship between the contact force and relative motion. In the PFC model, the contact force ball-ball and ball-wall can be divided into normal force and transverse force (Equation (1)). The particles move and rotate under the action of unbalanced forces and unbalanced torques (Equations (2) and (3)). The motion equation of PFC is solved using the centered finite difference method in relation to time step (Δt). The translational and rotational acceleration (x¨it and ω̇it) of particles at any time can be obtained from Equations (4) and (5). The translational velocity (ẋit), angular velocity (ωit), and displacement (xit) of particle motion can be obtained from equation transformation (Equations (6), (7), and (8)). The definitions of the model parameters are summarized in Table 3:
(1)Fi→=Fin→+Fis→,(2)Fi→=mx¨i→−gi→,(3)Mi→=H¨i→,(4)x¨it=1Δtẋit+Δt/2−ẋit−Δt/2,(5)ω̇it=1Δtωit+Δt/2−ωit−Δt/2,(6)ẋit+Δt/2=ẋit−Δt/2+Fitm+giΔt,(7)ωit+Δt/2=ωit−Δt/2+MitIΔt,(8)xit+Δt=xit+xit+Δt/2Δt.Table 3
Definitions of symbols.
SymbolDefinitionSymbolDefinitionFiContact forceẋiTranslational velocityFinNormal contact forcexiDisplacementFisShear contact forceω̇iSlew accelerationgiGravitational accelerationωiAngular velocityMiUnbalance momentIInertia momentH¨iAngular momentumΔtTime stepx¨iTranslational accelerationmParticle quality


### 3.3. Rock Mass Parameters

In particle flow simulation, the macroscopic mechanical behaviors of the rock and soil masses are governed by the microscopic mechanical properties of particles, nevertheless, there is a highly nonlinear relationship between them. Typically, the transformations of the macroscopic and microscopic parameters are carried out by means of biaxial compression tests [47]. The most common set of siltstone and pelitic siltstone was selected for parameter calibration to avoid the discreteness of rock samples. The stress-strain curve obtained from the PFC simulation under the condition of no confining pressure was reasonably consistent with that of the laboratory (Figure 6). Both siltstone and pelitic siltstone showed significant brittle failure characteristics. The initial balance was carried out after gravity loading in the process of engineering scale simulation, and the increment of displacement and velocity during the process was cleared, and hence, the consistency of the stress-strain curve in the compaction stage was superfluous. The elastic modulus (E) and unconfined compressive strength (UCS) of siltstone and pelitic siltstone obtained from the laboratory and PFC are shown in Table 4; moreover, the fitting degree of their magnitude values is a measure index of calibration. Both mudstone and coal retrieved in the field had great discreteness with mechanical properties, which obstructed calibration by the PFC test. This research attempted to bring empirical values to the parameters of coal and mudstone, and the full mining model simulation was used in comparison with the actual situation. The parameter inversion method was used to adjust the rock block parameters as empirical.Figure 6
Stress-strain curves obtained from uniaxial compression tests (red lines: (a, b) represent siltstone; black lines: (c, d) represent pelitic siltstone. Solid lines are results obtained from laboratory tests, while dashed lines are results obtained from PFC calibration test).Table 4
Uniaxial compression test results.
ParameterSiltstonePelitic siltstoneLaboratory testPFC testLaboratory testPFC testE (GPa)15.7511.4413.69.35UCS (MPa)111.49105.2696.8783.76The mechanical parameters of rock masses are generally smaller than those of intact rock with laboratory scale because of the size effect and discontinuity of rock masses [48]. Practically, the effects of bedding plane and dominant joints are often considered in simulation, and the equivalent jointed rock masses technology is applied. The smooth-joint model was chosen over the flat-joint model, which is poor in simulating the plane dilation mechanics, to reflect the constitutive relation. Furthermore, the smooth-joint model enabled the joint properties to a limited range on both sides of them, and a random joint model was formed to verify and correspond to the characteristics of the slope on-site. For this purpose, based on the laboratory mechanical experimental results, numerical simulation calibration testing, and the equivalent rock masses technique, the full mining model (the six-coal-seam mining model) simulation was used in comparison with the actual situation, which ensured that the simulation outputs were reasonably consistent with the actual field deformation (i.e., occurrence of deposition at the slope toe, presence of tensile cracks in the middle of the slope, and subsidence at the edge of slope), which was acquired through the UAV survey (Figure 7). In this paper, parameters related to rock and soil masses materials were obtained and adjusted by parameter inversion. The calibrated microscopic mechanical parameters of the rock masses, which were adopted for the PFC simulation of the Jianshanying mining slope, are summarized in Table 5.Figure 7
Comparisons of a typical PFC simulated deformation and the actual field observation.Table 5
Microstrength parameters used for PFC simulations.
ParameterDefinitionSiltstonePelitic siltstoneMudstoneCoalRminMinimum particle radius (m)1.61.61.20.8Rmax/RminParticle radius ratio, uniform distribution1.251.251.331.5ρParticle density (kg/m3)2850265030501850EcInterparticle contact modulus (GPa)7622KNormal-to-shear stiffness ratio1.822.22.4μMicrofriction coefficient0.30.380.750.58Ec′Bond effective modulus (GPa)7622K′Bond normal-to-shear stiffness ratio1.822.22.4σcParallel bond normal strength (MPa)3530109τcParallel bond shear strength (MPa)3530109KjJoint stiffness ratio1μjJoint microfriction coefficient0.35


## 3.1. Model Development

Liupanshui City in Guizhou Province, China, is known for its proven coal resources and reserves. The city which is known as the “Southwest Coal Sea” has developed multistage coal seams on theP3l stratum. In 2015, there were more than 800 mines in the city, while more than 400 landslide and ground subsidence incidents have been reported, which were mainly caused by improperly planned mining activities. In the present study, a mining slope named Jianshanying slope in Faer Town, Liupanshui City, was selected as the case study. The specific geographical coordinates of the study area are E104°44′11″ and N26°18′20″ (Figures 1 and 2).Figure 1
Location of study area.Figure 2
3D terrains of Jianshanying mining slope.In the western part of the Guizhou plateau, a low mountainous terrain was formed because of the tectonic erosion. Typically, both steep and gentle structures were formed in the mining slope. Most of the coal-bearing strata are located in the flat terrains, while the interbedded sandstone and mudstone are mainly located in the sloping terrains. The surface terrain of the Jianshanying slope was reasonably generalized to simplify the subsequent numerical modelling processes. Three sets of dominant joints were considered in each strata, and one set has the same tendency as the strata. The general stratifications of the slope are presented in Figure3. Coal and mudstone formed the relatively weak strata in the slope, however, the effect of the stratified structure was not considered in them.Figure 3
Generalized profile of mining slope model (“T1f” is Feixianguan group and “P3l” is Longtan group).Mining slopes are typically prone to time-dependent failures in the form of ground subsidence and slope sliding [44]. After going through a long process of mining, 6 coal layers had been mined out beneath the Jianshanying mining slope forming a total of 13 mining panels. These mining activities had caused severe impact on the stability of the slope. To simplify the analysis, the present study only focused on the impact of mining with the first coal layer on the slope instability. Nine mining configurations with different horizontal distances (D) from the extracted panel center to slope shoulder (where the flat terrain intersected with the sloping terrain) were set, namely, D = −200 m, −150 m, −100 m, −50 m, 0 m, 50 m, 100 m, 150 m, and 200 m (see Figure 4 and Table 2). The width of each extracted panel along the strata dip direction was within the range of 150~250 m, while the thickness of the coal seam was ranging from 2 to 4 m in statistics. The width of the extracted panel and the thickness of the mined-out coal seam were fixed at 200 m and 6 m in practice. The above configurations were set to systematically study the influences of extracted panel depth, horizontal distance between the center of extracted panel and slope shoulder, and surface terrain condition on the instability of the mining slope. The extracted panel was located beneath a flat terrain with D ≤ −100 m, while the extracted panel was beneath a sloping terrain with D ≥ 100 m (Figure 4). A total of 29 monitoring points with a horizontal interval of 50 m were set in the numerical model, for revealing the deformation characteristics of the slope surface with various configurations.Figure 4
Mining configurations considered for numerical simulation.Table 2
Details of mining configurations.
D (m)-200-150-100-50050100150200Extracted panelsA+B+C+DB+C+D+EC+D+E+FD+E+F+GE+F+G+HF+G+H+IG+H+I+JH+I+J+KI+J+K+LPanel depth (m)345.5336.6328319.2310.1261.5217.1170.9112.1


## 3.2. Particle Flow Code

Rock masses are discontinuous medium, and hence, the use of the DEM is justifiable [4]. PFC (Particle Flow Code), a popular program based on the DEM, is widely used to simulate the macroscopic characteristics of rock-soil masses. The soil/rock aggregates are modelled as either rigid disks (2D) or spheres (3D), and they are connected by specific contact models as an equivalent model of rock-soil mass [45]. The PFC adopts the time step iterative calculation method (Figure 5). Newton’s second law and the law of force and displacement are repeatedly applied in the calculation for updating the motion state of units in real-time, and the contact force and torque between the updated units are further determined by the force-displacement relationship [46].Figure 5
Workflow of PFC analysis.The law of force-displacement reflects the contact relationship between particles, also the relationship between the contact force and relative motion. In the PFC model, the contact force ball-ball and ball-wall can be divided into normal force and transverse force (Equation (1)). The particles move and rotate under the action of unbalanced forces and unbalanced torques (Equations (2) and (3)). The motion equation of PFC is solved using the centered finite difference method in relation to time step (Δt). The translational and rotational acceleration (x¨it and ω̇it) of particles at any time can be obtained from Equations (4) and (5). The translational velocity (ẋit), angular velocity (ωit), and displacement (xit) of particle motion can be obtained from equation transformation (Equations (6), (7), and (8)). The definitions of the model parameters are summarized in Table 3:
(1)Fi→=Fin→+Fis→,(2)Fi→=mx¨i→−gi→,(3)Mi→=H¨i→,(4)x¨it=1Δtẋit+Δt/2−ẋit−Δt/2,(5)ω̇it=1Δtωit+Δt/2−ωit−Δt/2,(6)ẋit+Δt/2=ẋit−Δt/2+Fitm+giΔt,(7)ωit+Δt/2=ωit−Δt/2+MitIΔt,(8)xit+Δt=xit+xit+Δt/2Δt.Table 3
Definitions of symbols.
SymbolDefinitionSymbolDefinitionFiContact forceẋiTranslational velocityFinNormal contact forcexiDisplacementFisShear contact forceω̇iSlew accelerationgiGravitational accelerationωiAngular velocityMiUnbalance momentIInertia momentH¨iAngular momentumΔtTime stepx¨iTranslational accelerationmParticle quality


## 3.3. Rock Mass Parameters

In particle flow simulation, the macroscopic mechanical behaviors of the rock and soil masses are governed by the microscopic mechanical properties of particles, nevertheless, there is a highly nonlinear relationship between them. Typically, the transformations of the macroscopic and microscopic parameters are carried out by means of biaxial compression tests [47]. The most common set of siltstone and pelitic siltstone was selected for parameter calibration to avoid the discreteness of rock samples. The stress-strain curve obtained from the PFC simulation under the condition of no confining pressure was reasonably consistent with that of the laboratory (Figure 6). Both siltstone and pelitic siltstone showed significant brittle failure characteristics. The initial balance was carried out after gravity loading in the process of engineering scale simulation, and the increment of displacement and velocity during the process was cleared, and hence, the consistency of the stress-strain curve in the compaction stage was superfluous. The elastic modulus (E) and unconfined compressive strength (UCS) of siltstone and pelitic siltstone obtained from the laboratory and PFC are shown in Table 4; moreover, the fitting degree of their magnitude values is a measure index of calibration. Both mudstone and coal retrieved in the field had great discreteness with mechanical properties, which obstructed calibration by the PFC test. This research attempted to bring empirical values to the parameters of coal and mudstone, and the full mining model simulation was used in comparison with the actual situation. The parameter inversion method was used to adjust the rock block parameters as empirical.Figure 6
Stress-strain curves obtained from uniaxial compression tests (red lines: (a, b) represent siltstone; black lines: (c, d) represent pelitic siltstone. Solid lines are results obtained from laboratory tests, while dashed lines are results obtained from PFC calibration test).Table 4
Uniaxial compression test results.
ParameterSiltstonePelitic siltstoneLaboratory testPFC testLaboratory testPFC testE (GPa)15.7511.4413.69.35UCS (MPa)111.49105.2696.8783.76The mechanical parameters of rock masses are generally smaller than those of intact rock with laboratory scale because of the size effect and discontinuity of rock masses [48]. Practically, the effects of bedding plane and dominant joints are often considered in simulation, and the equivalent jointed rock masses technology is applied. The smooth-joint model was chosen over the flat-joint model, which is poor in simulating the plane dilation mechanics, to reflect the constitutive relation. Furthermore, the smooth-joint model enabled the joint properties to a limited range on both sides of them, and a random joint model was formed to verify and correspond to the characteristics of the slope on-site. For this purpose, based on the laboratory mechanical experimental results, numerical simulation calibration testing, and the equivalent rock masses technique, the full mining model (the six-coal-seam mining model) simulation was used in comparison with the actual situation, which ensured that the simulation outputs were reasonably consistent with the actual field deformation (i.e., occurrence of deposition at the slope toe, presence of tensile cracks in the middle of the slope, and subsidence at the edge of slope), which was acquired through the UAV survey (Figure 7). In this paper, parameters related to rock and soil masses materials were obtained and adjusted by parameter inversion. The calibrated microscopic mechanical parameters of the rock masses, which were adopted for the PFC simulation of the Jianshanying mining slope, are summarized in Table 5.Figure 7
Comparisons of a typical PFC simulated deformation and the actual field observation.Table 5
Microstrength parameters used for PFC simulations.
ParameterDefinitionSiltstonePelitic siltstoneMudstoneCoalRminMinimum particle radius (m)1.61.61.20.8Rmax/RminParticle radius ratio, uniform distribution1.251.251.331.5ρParticle density (kg/m3)2850265030501850EcInterparticle contact modulus (GPa)7622KNormal-to-shear stiffness ratio1.822.22.4μMicrofriction coefficient0.30.380.750.58Ec′Bond effective modulus (GPa)7622K′Bond normal-to-shear stiffness ratio1.822.22.4σcParallel bond normal strength (MPa)3530109τcParallel bond shear strength (MPa)3530109KjJoint stiffness ratio1μjJoint microfriction coefficient0.35


## 4. Results of Numerical Analysis

### 4.1. Evaluation of Crack Propagation

In the panel extracted, tensile cracks initiated to propagate in the overburden materials. The cracks mainly aggregated at the boundary of the extracted panel and extended up to the surface [49]. Obviously, tensile cracks were observed beneath the slope shoulder with D=−100 m. The panel was extracted directly below the slope shoulder (D=0 m); the tensile cracks had developed in front of the slope shoulder and extended to the sloping terrain (Figure 8(e)). These results implied that there was an “aggregation” on the extension of tensile cracks beneath the slope shoulder.Figure 8
Crack propagations after coal seam extractions with different mining configurations.According to Salmi et al. [50], neglecting the effect of stratum bedding in simulating mining-induced subsidence in flat terrains would yield a wider but shallower subsidence trough as compared with the field conditions. Therefore, the strata bedding surface and joints should be carefully modelled to improve the simulation outputs (Figure 3).The sum of upside and downside crack angles (γ+β) was wielded to characterize the relative disturbance range of overburden rock masses. The term “relative” was used to indicate that the thickness of rock strata, which is above the extracted panel, was not taken into consideration. A low value of “γ+β” indicated a large relative disturbance range, and vice versa (refer to Figure 9). The extracted panel is partially or completely located beneath the sloping terrains; the relative disturbance ranges for the cases were greater than those beneath the flat terrains. With the upside crack angle decreasing, the subsidence trough of the latter was wider than that of the former (see in Figure 8). Moreover, the propagations of tensile cracks at the extracted panel boundary were almost parallel with all mining configurations. The crushing of the coal pillar resulted in an increment in the distance between the position of boundary tensile cracks and the center of the extracted panel and hence altered the crack angle (Figure 10). The center of the extracted panel positioned in front of the slope shoulder; the otherness between upside and downside crack angles increased. The upside crack angle reached the minimum value of 64°, and the summation angle of “γ+β” reached the minimum value of 151° withD=0m; moreover, the rock masses above the extracted panel were disturbed to the greatest.Figure 9
Changes in crack angle for different mining configurations.Figure 10
Mechanical mechanisms of mining-induced subsidence in (a) flat terrains and (b) sloping terrains (adapted from [41]).


### 4.2. Evaluation of Horizontal Displacement

Coal mining causes significant vertical deformations. For materials which are characterized by low compactness and high expansibility in the subsidence area, the lateral compression of the strata surrounding the extracted panel would increase and cause an expansion to the sloping terrains. Subsidence immediately causes lateral deformation with the constraining forces of surrounding rock mass. A lower confining pressure makes the effect of lateral deformation more prominent [41]. Therefore, symmetrical and high constraining forces make the lateral deformation inappreciable [51]. In sloping terrains, the overburden rock masses produce relatively low lateral constraining forces, which are insufficient to offset the dilatational forces of rock masses caving into the panel. As a result, the disturbed rock mass would displace towards the sloping terrains (Figure 10). The extraction panels are located at different positions; Figure 11 shows the lateral deformations of rock masses. The lateral deformation of overburden rock mass above the extracted panel was not symmetrical, with flat-sloping terrains as simulated. The lateral deformation beneath the flat terrain side was lower than that of the sloping side. The extraction panel was located close to the sloping terrain; the lateral deformation was intensified and caused an outcrop towards the sloping surface.Figure 11
Contours of horizontal displacements after coal seam extractions with different mining configurations.Bedding planes provided a suitable path for lateral movement of strata in both flat and sloping terrains. A bedding plane, with a low bonding strength, provided less resistance in the direction of the overburden material movement and hence caused the sliding between the layers. The “zigzag” horizontal displacement change zone can be seen in Figures11 and 12.Figure 12
Horizontal displacement at the ground surface for different mining configurations.Interestingly, lateral deformations towards the slope inner part were observed in the mudstone layer withD<100, with the maximum value reaching 0.98 m (Figure 12(b)). However, there was no similar phenomenon in the mudstone directly above the extracted panel (Figure 11). With the in situ stress releasing, the materials at the slope shoulder poorly cemented were further loosed. Holding a more complete and dense layered structure, the siltstone and pelitic siltstone were subjected to stick-slip resistances along the bedding plane in the lateral motion. Conversely, the resultant force, including the gravitational force, redistributed stress, and the cementing force between the materials, leading to the deformation of mudstone.A potential through slip plane appeared on the slope withD=−100 m (Figure 11(c)), which was initiated from the inner boundary of the extracted panel, extended upward to the goaf and the thin mudstone layer, and subsequently spread from the outer boundary of the extracted panel to the toe of the slope, causing the overall instability of slope. A horizontal displacement was observed of 0.4 m at the toe.


### 4.3. Evaluation of Surface Subsidence

The maximum surface subsidence is consistently located above the inner part of the extracted panel under various mining configurations in the countertilt slope. Furthermore, the sloping surface with thinner overburden materials has a larger maximum subsidence area, as indicated by the cases ofD≥0 m (Figure 13(a)). These results proved that the slope has reached the “sufficient mining conditions” with D≥0 m. For obtaining the increment in surface subsidence beneath the sloping terrains, the maximum subsidence (W0) of flat terrains was brought to the present research, which was referred to Equation (9) proposed by Zou [52] under the “sufficient mining conditions”:
(9)W0=qmcosα,where q is the subsidence coefficient under the “sufficient mining conditions,” m is the thickness of the mining coal seam, and α is the dip angle of the coal seam.Figure 13
Vertical displacement at the ground surface for different mining configurations.Wielding the lithology comprehensive evaluation indexp to characterize the degree of influence of lithology on surface subsidence [52]:
(10)p=∑1nhiQi∑1nhi,where hi is the thickness of overburden rock strata and Qi is the lithologic classification index of overburden rock mass. The value of Qi ranges from 0 to 1 for the first mining slope according to the hardness of the lithology. The Qi values for the coal seam, mudstone, pelitic siltstone, and siltstone in this research were set at 0.9, 0.8, 0.4, and 0.05, respectively.Based on the comprehensive evaluation index of lithologyp, the subsidence coefficient q of flat terrains under the “sufficient mining conditions” can be acquired by the following:
(11)q=0.45+0.5p.From the above computations,W0 for the 5 mining configurations with D≥0 m were 3.761 m (D=0 m), 3.702 m (D=50 m), 3.436 m (D=100 m), 3.126 m (D=150 m), and 3.294 m (D=200 m). Accordingly, the increment in subsidence of sloping terrains as compared with the flat terrains was 2.761 m, 2.822 m, 3.101 m, 2.836 m, and 2.424 m, respectively.Khanal et al. [53] suggested that the ratio of subsidence to thickness of overburden rock mass (S/T) could be positively correlated with the width to depth ratio of the mine (W/D1). In this research, the thickness (T) and width (W) were fixed at 6 m and 200 m, respectively. The findings from the mining configurations of D<100 m showed consistency with that of Khanal et al. [53], but an opposite trend was observed with D>100 m (Figure 13).


### 4.4. Evolution of Deformation at Slope Shoulder

The deformation behavior of the slope shoulder, a transition from flat terrains to sloping terrains, has been focused on in this research. The monitoring data of M13 was selected to characterize the deformation of rock mass at the slope shoulder. Figures14–17 present the vertical and horizontal deformation characteristics of the rock mass over time under short-term and long-term conditions, respectively. The following findings are reported from the analyses:
(a)
Short term(i)
Initiating the horizontal displacement and subsidence concurrently at the time step of 3000 with various mining configurations, which indicated that both the horizontal displacement and subsidence occurred right after the formation of the extracted panel(ii)
The extracted panel is located below the slope shoulder (−100m≤D≤100m); the subsidence rate and value at the slope shoulder were higher than that in flat terrains(b)
Long term(i)
The rock mass at the slope shoulder showed prominent horizontal displacement (1.23 m) and subsidence (6.52 m) withD=0 m and 50 m(ii)
The time required to stabilize the deformation at the slope shoulder was longer in flat terrain mining(iii)
The rock mass at the slope shoulder initially displaced horizontally towards the inner part and, subsequently, displaced outwards to the slope facing withD<0 m. The horizontal displacement behavior depended on the location of the inner boundary of the extracted panel with D≥0 m. The rock mass at the slope shoulder displaced horizontally towards the direction of the slope facing with D=0, 50, and 100 m. Observing a lower or negligible value with D≥100m, which was identical to the cases of D<0 m in the pattern of rock mass displacementFigure 14
Variations in vertical displacement over time at slope shoulder for different mining configurations (short-term condition).Figure 15
Variations in horizontal displacement over time at slope shoulder for different mining configurations (short-term condition).Figure 16
Variations in vertical displacement over time at slope shoulder for different mining configurations (long-term condition).Figure 17
Variations in horizontal displacement over time at slope shoulder for different mining configurations (long-term condition).


## 4.1. Evaluation of Crack Propagation

In the panel extracted, tensile cracks initiated to propagate in the overburden materials. The cracks mainly aggregated at the boundary of the extracted panel and extended up to the surface [49]. Obviously, tensile cracks were observed beneath the slope shoulder with D=−100 m. The panel was extracted directly below the slope shoulder (D=0 m); the tensile cracks had developed in front of the slope shoulder and extended to the sloping terrain (Figure 8(e)). These results implied that there was an “aggregation” on the extension of tensile cracks beneath the slope shoulder.Figure 8
Crack propagations after coal seam extractions with different mining configurations.According to Salmi et al. [50], neglecting the effect of stratum bedding in simulating mining-induced subsidence in flat terrains would yield a wider but shallower subsidence trough as compared with the field conditions. Therefore, the strata bedding surface and joints should be carefully modelled to improve the simulation outputs (Figure 3).The sum of upside and downside crack angles (γ+β) was wielded to characterize the relative disturbance range of overburden rock masses. The term “relative” was used to indicate that the thickness of rock strata, which is above the extracted panel, was not taken into consideration. A low value of “γ+β” indicated a large relative disturbance range, and vice versa (refer to Figure 9). The extracted panel is partially or completely located beneath the sloping terrains; the relative disturbance ranges for the cases were greater than those beneath the flat terrains. With the upside crack angle decreasing, the subsidence trough of the latter was wider than that of the former (see in Figure 8). Moreover, the propagations of tensile cracks at the extracted panel boundary were almost parallel with all mining configurations. The crushing of the coal pillar resulted in an increment in the distance between the position of boundary tensile cracks and the center of the extracted panel and hence altered the crack angle (Figure 10). The center of the extracted panel positioned in front of the slope shoulder; the otherness between upside and downside crack angles increased. The upside crack angle reached the minimum value of 64°, and the summation angle of “γ+β” reached the minimum value of 151° withD=0m; moreover, the rock masses above the extracted panel were disturbed to the greatest.Figure 9
Changes in crack angle for different mining configurations.Figure 10
Mechanical mechanisms of mining-induced subsidence in (a) flat terrains and (b) sloping terrains (adapted from [41]).


## 4.2. Evaluation of Horizontal Displacement

Coal mining causes significant vertical deformations. For materials which are characterized by low compactness and high expansibility in the subsidence area, the lateral compression of the strata surrounding the extracted panel would increase and cause an expansion to the sloping terrains. Subsidence immediately causes lateral deformation with the constraining forces of surrounding rock mass. A lower confining pressure makes the effect of lateral deformation more prominent [41]. Therefore, symmetrical and high constraining forces make the lateral deformation inappreciable [51]. In sloping terrains, the overburden rock masses produce relatively low lateral constraining forces, which are insufficient to offset the dilatational forces of rock masses caving into the panel. As a result, the disturbed rock mass would displace towards the sloping terrains (Figure 10). The extraction panels are located at different positions; Figure 11 shows the lateral deformations of rock masses. The lateral deformation of overburden rock mass above the extracted panel was not symmetrical, with flat-sloping terrains as simulated. The lateral deformation beneath the flat terrain side was lower than that of the sloping side. The extraction panel was located close to the sloping terrain; the lateral deformation was intensified and caused an outcrop towards the sloping surface.Figure 11
Contours of horizontal displacements after coal seam extractions with different mining configurations.Bedding planes provided a suitable path for lateral movement of strata in both flat and sloping terrains. A bedding plane, with a low bonding strength, provided less resistance in the direction of the overburden material movement and hence caused the sliding between the layers. The “zigzag” horizontal displacement change zone can be seen in Figures11 and 12.Figure 12
Horizontal displacement at the ground surface for different mining configurations.Interestingly, lateral deformations towards the slope inner part were observed in the mudstone layer withD<100, with the maximum value reaching 0.98 m (Figure 12(b)). However, there was no similar phenomenon in the mudstone directly above the extracted panel (Figure 11). With the in situ stress releasing, the materials at the slope shoulder poorly cemented were further loosed. Holding a more complete and dense layered structure, the siltstone and pelitic siltstone were subjected to stick-slip resistances along the bedding plane in the lateral motion. Conversely, the resultant force, including the gravitational force, redistributed stress, and the cementing force between the materials, leading to the deformation of mudstone.A potential through slip plane appeared on the slope withD=−100 m (Figure 11(c)), which was initiated from the inner boundary of the extracted panel, extended upward to the goaf and the thin mudstone layer, and subsequently spread from the outer boundary of the extracted panel to the toe of the slope, causing the overall instability of slope. A horizontal displacement was observed of 0.4 m at the toe.


## 4.3. Evaluation of Surface Subsidence

The maximum surface subsidence is consistently located above the inner part of the extracted panel under various mining configurations in the countertilt slope. Furthermore, the sloping surface with thinner overburden materials has a larger maximum subsidence area, as indicated by the cases ofD≥0 m (Figure 13(a)). These results proved that the slope has reached the “sufficient mining conditions” with D≥0 m. For obtaining the increment in surface subsidence beneath the sloping terrains, the maximum subsidence (W0) of flat terrains was brought to the present research, which was referred to Equation (9) proposed by Zou [52] under the “sufficient mining conditions”:
(9)W0=qmcosα,where q is the subsidence coefficient under the “sufficient mining conditions,” m is the thickness of the mining coal seam, and α is the dip angle of the coal seam.Figure 13
Vertical displacement at the ground surface for different mining configurations.Wielding the lithology comprehensive evaluation indexp to characterize the degree of influence of lithology on surface subsidence [52]:
(10)p=∑1nhiQi∑1nhi,where hi is the thickness of overburden rock strata and Qi is the lithologic classification index of overburden rock mass. The value of Qi ranges from 0 to 1 for the first mining slope according to the hardness of the lithology. The Qi values for the coal seam, mudstone, pelitic siltstone, and siltstone in this research were set at 0.9, 0.8, 0.4, and 0.05, respectively.Based on the comprehensive evaluation index of lithologyp, the subsidence coefficient q of flat terrains under the “sufficient mining conditions” can be acquired by the following:
(11)q=0.45+0.5p.From the above computations,W0 for the 5 mining configurations with D≥0 m were 3.761 m (D=0 m), 3.702 m (D=50 m), 3.436 m (D=100 m), 3.126 m (D=150 m), and 3.294 m (D=200 m). Accordingly, the increment in subsidence of sloping terrains as compared with the flat terrains was 2.761 m, 2.822 m, 3.101 m, 2.836 m, and 2.424 m, respectively.Khanal et al. [53] suggested that the ratio of subsidence to thickness of overburden rock mass (S/T) could be positively correlated with the width to depth ratio of the mine (W/D1). In this research, the thickness (T) and width (W) were fixed at 6 m and 200 m, respectively. The findings from the mining configurations of D<100 m showed consistency with that of Khanal et al. [53], but an opposite trend was observed with D>100 m (Figure 13).


## 4.4. Evolution of Deformation at Slope Shoulder

The deformation behavior of the slope shoulder, a transition from flat terrains to sloping terrains, has been focused on in this research. The monitoring data of M13 was selected to characterize the deformation of rock mass at the slope shoulder. Figures14–17 present the vertical and horizontal deformation characteristics of the rock mass over time under short-term and long-term conditions, respectively. The following findings are reported from the analyses:
(a)
Short term(i)
Initiating the horizontal displacement and subsidence concurrently at the time step of 3000 with various mining configurations, which indicated that both the horizontal displacement and subsidence occurred right after the formation of the extracted panel(ii)
The extracted panel is located below the slope shoulder (−100m≤D≤100m); the subsidence rate and value at the slope shoulder were higher than that in flat terrains(b)
Long term(i)
The rock mass at the slope shoulder showed prominent horizontal displacement (1.23 m) and subsidence (6.52 m) withD=0 m and 50 m(ii)
The time required to stabilize the deformation at the slope shoulder was longer in flat terrain mining(iii)
The rock mass at the slope shoulder initially displaced horizontally towards the inner part and, subsequently, displaced outwards to the slope facing withD<0 m. The horizontal displacement behavior depended on the location of the inner boundary of the extracted panel with D≥0 m. The rock mass at the slope shoulder displaced horizontally towards the direction of the slope facing with D=0, 50, and 100 m. Observing a lower or negligible value with D≥100m, which was identical to the cases of D<0 m in the pattern of rock mass displacementFigure 14
Variations in vertical displacement over time at slope shoulder for different mining configurations (short-term condition).Figure 15
Variations in horizontal displacement over time at slope shoulder for different mining configurations (short-term condition).Figure 16
Variations in vertical displacement over time at slope shoulder for different mining configurations (long-term condition).Figure 17
Variations in horizontal displacement over time at slope shoulder for different mining configurations (long-term condition).


## 5. Discussion

This research investigated the mechanical mechanisms of mining activities in flat and sloping terrains, with the considerations of deformation of overburden rock masses and propagation of tensile cracks. A model was established based on the typical mining-induced slope structure of a case study in southwest China. To the authors’ knowledge, this is the first research reported on the use of PFC for analyzing the mining slope deformation behavior, with the extracted panel located beneath various complex terrains (i.e., flat terrain, slope shoulder, and sloping terrain). The time-dependent deformation characteristics of the rock mass at the slope shoulder were studied in detail. The sum of upside and downside crack angles was proposed to characterize the relative disturbance range of overburden rock mass, and reasonable and safe configurations of single-layered mining operations in mountainous areas were put forward.It should be noted that the findings from the present research were handicapped by several limitations, such as the width of the extracted panel along the inclined strata was remained constant at 200 m, and the interval of two adjacent extracted panels in all mining configurations was kept at 50 m. In addition, the microstrength parameters of coal and pelitic siltstone were not derived from the uniaxial compression simulation by the PFC. Owing to these limitations, the functional relationship between surface subsidence and geological and geotechnical factors cannot be fully revealed in this research. These issues can be solved if the following future improvements are taken: (i) setting the extracted panel width as an independent variable and shortening the interval, (ii) increasing the number of samples for coal and pelitic siltstone and acquiring the mechanical parameters by wielding the support vector machine (SVM) coupled with the microstrength parameters by PFC, and (iii) setting the number of configurations of mining in sloping terrains to be 5 to 10 times of independent variables, for finding the regression relationship between the maximum subsidence and geological and geotechnical factors.


## 6. Conclusion

The present research investigated the deformation behavior of slopes under different mining configurations (i.e., horizontal distance from extracted panel center to slope shoulder,D=−200 m, −150 m, −100 m, −50 m, 0 m, 50 m, 100 m, 150 m, and 200 m) by wielding PFC. The Jianshanying mining slope, which was generalized based on the actual field investigation and laboratory experiment data, in Faer Town, Shuicheng county, Guizhou Province, was selected. Based on the laboratory mechanical experimental results, numerical simulation calibration testing, and the equivalent rock mass technique, the full mining model (the six-coal-seam mining model) simulation was used in comparison with the actual situation, which ensured the rationality of microstrength parameters of rock masses and joints. The following conclusions can be drawn for the study of deformation behavior of mining slopes in mountainous areas with gentle anti-incline overburden rock strata:
(i)
Mining in mountainous areas usually meets with the risk of slope instability. The overlying rock masses tended to move towards the sloping surface with mining beneath sloping terrain, which brought an asymmetrical subsidence funnel, and formed a wider relative disturbance range on the slope surface. In particular, the rock masses above the extracted panel were disturbed to the greatest withD=0 m(ii)
The constraining forces of overburden rock masses towards the valley decrease; mining beneath sloping terrains usually acquire larger subsidence (up to 3 m) and additional horizontal displacement (up to 1.4 m) than flat terrains. The “zigzag” horizontal displacement change zone formed with the control of bedding planes(iii)
It is important to remain the center position of the extracted panel behind the slope shoulder, beyond which the deformation rate and ultimate value of the rock mass at the slope shoulder would increase drastically. In addition, the boundary of the extracted panel should also be avoided to cross over the slope shoulder (i.e.,D≤−100m) to prevent an overall slope instability



---

*Source: 6689966-2021-02-19.xml*