Study on Deflection of Surrounding Rock Force Chain and Disaster Mechanism of Instability in Deep Stope

The mechanism of force chain deﬂection and instability-caused disaster in the deep surrounding rock of large-scale stopes was examined in this study using theoretical analyses, laboratory experiments, PFC3D numerical simulations, and other comprehensive research methods based on a discrete element theory that included force chain research as the main line. The results indicated that the overburden strata of the stope presented an arched force chain in both the strike and the inclined direction of the working face. In addition, a force chain shell composed of strong chains similar to “ellipsoid” in shape had been formed in the overburden strata space of the entire stope. The main mechanical characteristics of the force chain shell were as follows: the strength levels of the force chains within the shell were the largest; the strength levels of the force chains inside and outside the shell were relatively low and had evolved with the advancement of the working face; the directions of the force chains in diﬀerent areas of the surrounding rock masses of the stope were deﬂected, forming an anisotropic characteristic with a certain deﬂection angle which was distributed in the vertical direction at the shell base; the force chains at the shell shoulder were angled in the horizontal direction, and the force chain at the shell top had an obvious horizontal direction; ﬁnally, the strong chain clusters of the surrounding rock masses of the stope formed a force chain shell in the stope space, and the stress shell was the macroscopic embodiment of the force transference in the force chain shell formed by the force chain clusters, which revealed not only the mechanical mechanism of the force chain shell formed by the surrounding rock but also the relationship between the macro stress shell and the stress chain shell. The stability of the shell determines the stability of the surrounding rock, and the instability of the shell will lead to dynamic disasters such as strong dynamic pressure or rock burst.


Introduction
e stability of underground mines is always the focus of researchers [1]. Chinese and international research experts have carried out many experimental studies regarding the mechanical characteristics of the rock surrounding stopes and deep stope dynamic disaster and have achieved fruitful research results. e obtained results have assisted in the formation of a wealth of theories (mainly based on continuous medium theories) for the analysis of the distribution characteristics and dynamic disaster of surrounding rock forces in stopes from a macro perspective [2,3].
At the beginning of this century, the authors led a research group which put forward the theory of a "stress shell" on the basis of field measurements and theoretical analysis results. It was believed that a stress shell was composed of "high-stress bundles" in the rock masses surrounding stopes. It was theorized that these stress shells were the main bearing capacity systems of the overlying strata of the stopes. e goaf of a working face is located in the low-stress area under the protection of the macro stress shell of the surrounding rock of a stope. Its shape and characteristics are closely related to the specific mining conditions, as well as the engineering geological conditions. e pressure appearance of a mine's working face and its adjacent roadway is controlled by the existence and evolution of the stress shell, which has a significant impact on the dynamic phenomenon of the stope [4][5][6]. e physical and mechanical properties of rocks and their stress state are the determining factors [7,8].
With the global coal mine gradually entering the deep mining, the mining intensity and mining scale of working face are gradually increasing, the ground pressure in the stope is becoming more and more complex, and the mechanism of dynamic disasters such as rock burst is also more and more complex [9,10].
It was observed that, with the advancement of the mine's working face, the mechanical properties of the overlying strata in a stope are bound to undergo constant change. As a result, the evolution process will be that of a quasicontinuous/continuous/noncontinuous/discrete pattern. e process of rock burst, as well as other dynamic disasters in the surrounding rock of deep stope, is more complex [11].
Experts in China and elsewhere in the world have carried out extensive research on the mechanical characteristics of surrounding rock and the mechanism of dynamic disasters and have obtained rich research results. However, the mechanical nature of dynamic disaster of surrounding rock has not been clearly revealed. erefore, it is of great significance to study the force chain deflection, fracture, and instability of surrounding rock in stope to reveal the mechanism of dynamic disaster of surrounding rock and its prevention and control. erefore, based on a discrete element theory, along with the previous research results of stress chains as the main line, this study adopted a comprehensive research method of theoretical analyses, numerical simulations, and field measurements in order to conduct examinations of the distribution characteristics of stress chains. During the experimental process, the mechanism of the formation of stress chain shells and the mechanical essence of the formation of stress shells were studied in depth.

Analysis of the Formation Mechanism of Coal Rock Force Chains
During the processes of the micromechanical analyses of solid material, the macroscale is defined as the entire system of the granular material. Meanwhile, the micro scale is a stable structure composed of a large number of granular material units [12]. e force transfer paths between the granular material units are referred to as the force chains. e complex dynamic response laws of force chain networks result in the interiors of the granular material presenting unique mechanical characteristics and phenomena. Previously, through systematic analyses and research experiments on the mechanics of granular material, academician Wang Guangqian and Professor Sun Qicheng of China theorized that the basis of the path of force transfer between particles was a network structure formed by the contacts between particles. It was believed that the quasi-linear path in the aforementioned structure usually transmitted a larger force, which was referred to as the strong chain. In addition, the relatively small force transfer structure was referred to as the weak force chain [13][14][15]. Some experts also used different research methods to conduct in-depth research experiments of force chains and were able to achieve certain results [16][17][18].
In the past, the research regarding force chains had mainly focused on the force chains between small-scale loose granular material. In the current study, the main focus was placed on the force chains of granular material under the conditions of large-scale surrounding rock masses in mining stopes [19,20].
Within the dense particle distribution systems of coal and rock material, the movable spaces between the particles are small, and the strong chains in the force chain system of particles mainly transmit the majority of the external loads and gravity. e particles are mainly composed of particles with large deformations, which are connected in a straight line. In contrast, the weak force chains transmit less external force, and the deformations among particles which form the weak chains are less obvious. It has been observed that, in the same force chain, the size and direction of the contact force between the particles were basically the same. Moreover, the direction of the force chain was parallel to the direction of the external force, and the force chains could only bear a small portion of the tangential external force [21,22].
After a mine's working face has been excavated, from the original rock state of the surrounding rock of the stope, the broken and collapsed blocks and noncollapsed rock masses can be regarded as the granular material. In this study, a photoelastic experiment of the surrounding rock of the stope was carried out using the biaxial particle matter photoelasticity instrument of the Key Laboratory of Mining Response and Disaster Prevention and Control at Anhui University of Science and Technology. e adopted instrument is shown in Figure 1. e distribution form of the force chains between the particles was successfully obtained, as detailed in Figure 2. e thicker force chains in the figure indicate the larger strength of the force chains, and the thinner force chains indicate the smaller strength of the force chains. It can be seen in the figure that the strong force chains had formed a root-like structure. e force chains not only represented the size of the force between the particles but also represented the direction of the force transmission, in which the thicknesses of the force chains indicated the strength levels of the force chains.
It has been determined that, when compared with the strong force chains, the weak force chains tend to be more vulnerable to shear failures due to the small contact forces and small friction forces between the particles. erefore, the particles on the strong force chains bear most of the external force, and the contact deformations between the particles are larger. When the contact force line of the particles is within the range of the friction angle, the particles in the force chain are in a "self-locking" state. Subsequently, the particles in a strong force chain can withstand a certain amount of tangential force. However, with increases in the friction coefficient on the surfaces of the particles, as well as increases in the extrusion deformations between the particles, it has been found that the greater the amount of tangential force that the force chains can bear, the higher the stability of the force chains will be. When the surfaces of particles in a force chain are smooth, the force chain cannot bear the tangential force. It can only bear the normal force, and its stability will be weak [23].
In coal and rock masses, the stress and deformation processes of the particles mainly bear the joint actions of adhesion and friction due to the contacts and extrusions between particles. erefore, it can be considered that the stability of a force chain is mainly controlled by the friction and adhesion between particles. For example, if a force chain consists of N particles with a total length L and a total deformation ε, then the deformation α of any particle can be obtained as follows: (1) Figure 3 shows a stress relationship diagram of particles within a force chain. In the figure, the external force of the force chain is represented by F 1 , and the angle between the force chain and the external force loading direction is θ. e normal contact force F can be calculated as follows: Due to the fact that there are not only external forces between the particles but also friction between the particles, it is necessary to consider these factors when calculating the forces between particles in a force chain. erefore, by assuming that the friction coefficient between particles in the force chain is μ and the elasticity coefficient between particles is k, the maximum friction force f which will be required to be overcome in order to achieve sliding between the particles can be calculated as follows: en, formulas (4) and (5) can be obtained using formula (1): f � kαμ. (5) In addition, the fracture and instability of a force chain mainly need to overcome the joint actions of the friction and adhesion between the particles. erefore, if the contact area between particles is s, the fracture and instability criterion of the force chain can be written as follows (6):

Strong force chain
Weak force chain

Shock and Vibration
where [τ] indicates the threshold value of the shear failure of a force chain; τ represents the sum of the friction force and adhesion force in a force chain; and cindicates the adhesion between the particles.
It can be seen from formula (6) that the friction and cohesive forces between the particles should be overcome at the same time in order to ensure the fracture stability of the force chain. However, if a large number of force chains in a certain area occur within the surrounding rock of a stope, this may potentially lead to the macroscopic failure of the coal rock masses.
In conclusion, for certain force chains, if the external loads overcome the tangential and inherent cohesive forces between the particles, the force chains will break and lose stability. Since coal-series rock strata are also composed of a large number of granular material, there will potentially be a large number of force chain systems composed of both strong and weak chains. In the power chain network systems of granular material in coal and rock masses, the strong chains play major supporting roles in the force chain systems. Following the stoping of a mine's working face, the shear fracture instability of a large number of strong chains within the surrounding rock of the stope may lead to the macrodestruction of the entire coal rock system. erefore, it can be said that the mechanical essence of the macrofractures of coal and rock masses in a stope is the fracture and instability of a large number of force chains on the mesoscale.

Establishment of a Numerical Model
In the present study, for the purpose of obtaining the distribution pattern of the force chains in the surrounding rock masses of a stope and its evolution law with the stoping of a mine's working face, the engineering geology data of the 21116 working face of the Xieqiao Coal Mine of Huainan Mining Group were taken as the background. A PFC3D numerical simulation analysis method was used to directly show the distribution characteristics and evolution law of the force chains during the mining processes of the working face. e inclined length of the working face was 237.7 m; the strike advance length was 1,623 m; the thicknesses of the No. 6 coal ranged between 0.3 and 4.7 m; and the average coal thickness was 2.5 m. e coal seam was black, massive, and powdery and contained vitrinite and silk charcoal.

Micromechanical Parameters of the Coal and Rock Strata.
In this experimental study, a parallel bond model was mainly used for the numerical simulations, and the mesomechanical parameters of coal seam in the numerical calculation model were mainly based on the results of previous related research. e mechanical parameters of each seam in working face 21116 of the Xieqiao Coal Mine are shown in Table 1.

Establishment of the Numerical Model.
is study's three-dimensional numerical calculation model is shown in Figure 4. e model was composed of a large number of spherical particles. e particle radius R was distributed according to the Gaussian law from small to large: R min � 0.6 m and R max � 0.8 m. e vertical movement of the bottom of the model was limited by a wall, and the horizontal movements of the two sides were also limited by the side walls. e uniform load equivalent to the gravity of the upper strata of the model was loaded on the top of the model. e model's dimensions were as follows: length of 500 m, width of 400 m, and height of 400 m. e number of particle units was 611,665. e numerical calculation sequence was as follows: successive excavation from one side of the model for a total of 230 m.

Distribution Characteristics of the Stress
Chains within the Surrounding Rock of the Stope

Distribution Characteristics of the Original Force Chains in
the Stope. Figure 5 shows the original distribution form of the force chains prior to the excavation of the working face. It can be seen in the figure that the transmission of the force chains inside the particles was nonuniform, and the strength levels of the force chains had increased from the top to the bottom of the rock layers. However, the strength levels of the force chains at the same layer level were basically the same. Figure 6 shows the arrangement of the different measurement points from the top to the bottom in the middle of the numerical simulation and the distribution of the contact force chains between the particles within different layers, which represented the sizes of the force chains. Figure 7 shows the measured vertical stress of the stratum. It was seen from this study's comparative analysis that the numerical simulation results were basically consistent with the measured in situ stress values. It was found that, with the increases in depth, the strength levels of the force chains and the vertical stress had increased linearly. Figure 8 shows the distribution characteristics of the surrounding rock force chains in the middle of the stope along the strike direction of the coal seam when the working face had advanced to 230 m. It can be seen in the figure that the force chains at the coal walls at the back and front of the working face were relatively thick and strong, forming a strong force chain area. In addition, an arched strong force chain area had been formed at 75.6 m above the goaf. e strength had reached the maximum at the arch foot of the force chain arch (10 m in front of the coal wall), which was 3.84 × 10 7 N. e main mechanical characteristic of the force chain arch was that the strength levels of the force chains inside and outside the arch were lower than the strength of the force chains within the arch. e working face was located under the force chain arch of the surrounding rock of the stope. erefore, the force chain arch played a major bearing role for the entire overlying strata. Due to the fact that the force chains could only bear a small amount of tangential force, the strengths and directions of the force chains in the surrounding rock masses of the stope represented the magnitude and direction of the maximum principal stress.

Distribution Characteristics of the Strike Force Chains within the Rock Masses Surrounding the Stope.
is study's experimental results showed that the directions of the strong chains in the overlying strata of the stope were constantly changing, and the direction of the maximum principal stress of the surrounding rock of the stope had presented a certain angle deflection.
It was observed that when the excavation and advancement of the working face had disturbed the surrounding rock masses of the stope, the internal particles of the coal and rock masses had moved and slid, with evident deformations. In order to reach a balance once again, the force chains experienced processes of transfer, reorganization, and concentration. e directions of the strong force chains were approximately parallel to the maximum principal stress. at is to say, the maximum principal stress was mainly transmitted along the directions of the stronger force chains.
is study analyzed the sizes and azimuth of the contact force chains in a certain area when the mine's working face had advanced to 230 m. en, the sizes and azimuth of the contact force chains were fit into the key areas (A/E: front and rear arch bases; B/D: arch shoulders; C: arch crown) according to the Fourier formula. e fitting formula was as follows: where f 0 is the average normal contact force traversing all of the contact forces; A indicates the Fourier fitting coefficient, representing the degree of anisotropy of corresponding variables; and θ 0 represents the main direction of the anisotropy of normal contact forces.
Finally, the contact forces and azimuth angles of each area were obtained through fitting process, as shown in Figure 9. Figure 9 shows the fitting results of the sizes and the directions of contact forces in the five key areas (A, B, C, D, and E) detailed in Figure 8. It can be seen from the figure that after the fitting was completed, the directions of the force chains were in the shape of a "peanut" as a whole, with the distribution of the stronger chains in each direction at points A and E of the arch base. e stronger and weaker chains played combined supporting roles. However, the most dominant were the strong force chains in the vertical direction, with the weak force chains in the horizontal direction and other directions playing auxiliary supporting roles. At the arch shoulder locations B and D, the strong force chains were at 60°and 130°angles to the horizontal direction, respectively, and the vertical contact force was small (e.g., weak force chains). e sizes and directions of the strong force chains in that area comprised the main paths and directions for the gravity transfer of the overlying rock masses, which was transmitted to the front and rear of the working face through the strong chains within the arch. At the top of the shell top (C), the strong force chains showed an obvious horizontal direction, and the contact force at the top of the shell was less than that observed at A and E. e above-mentioned analysis results showed that the directions of the strong force chains of the surrounding rock masses along the strike of the working face were constantly changing. However, a force chain arch was formed by force chain paths with certain directionality, which had deflected within a certain range, where the gravity of the overburden had been transferred to the front and rear of the working face. is obvious directional force chain arch was formed in the force chain networks of the surrounding rock along the strike of the working face. e force chain arch was determined to be the main transfer path and support system of the overlying rock masses. Figure 10 shows the distribution pattern of the force chains in the inclined direction at the walls of the coal-mine's working face after stoping to 230 m. e sizes and azimuth of the force chains in the different key areas of the surrounding rock masses of the stope are shown in Figure 11. It can be seen in the figure that the areas of 6.5 m above and below the coal wall at both ends of the working face were areas of force chain strength reductions, and the force chain strength levels had reached the maximum value at 11 m inside the coal wall, which was  ere was a force chain arch located in the surrounding rock above the working face. e arch height was 31.2 m, which was 12 times the thickness of the coal seam. e mechanical characteristics of the force chain arch were that the strength levels of force chains inside the arch were greater than those outside the arch, and the working face was located in the weak force chain area under the arch. In addition, phenomena of force chain transfers were observed in the surrounding rock masses of the entire working face, with the forces in the coal body transferred to unmined coal seams.

Distribution Characteristics of the Inclined Force Chains in the Surrounding Rock Masses of the Stope.
In the present study, in accordance with the strike direction, the Fourier formula was used to fit the strength levels and azimuth of the force chains in the different key areas of the overlying strata of the stope in the dip direction, as illustrated in Figure 11. It can be seen in the figure that, similar to the strike direction, the directions of the force chains within the surrounding rock masses at the upper part of the working face along the strike direction were also constantly changing. en, after fitting at points A and E of the arch base, the force chains were distributed in a "peanut" shape in the vertical direction, which indicated that the directions of the strong chains in those locations were mainly in the vertical direction and dominate. Meanwhile, the weak force chains were mainly distributed in other directions. Furthermore, following the fitting at positions B and D of the shell shoulder, it was found that the angles between the strong chains and the horizontal direction were approximately 30°a nd 150°, respectively. e strong contact force at position C of the shell top presented a near horizontal distribution. At      Shock and Vibration the same time, it was also found that the directions of the force chains at the front and rear arch bases, front and rear arch shoulders, and the arch crown were deflected according to certain rules. It is the deflection of these force chain directions that formed the force chain arch of the overlying strata, which subsequently transferred the weight of the overlying strata to the front and rear of the work face. erefore, the force chain arch that had been formed by the strong chains was considered to be the main transmission path and support system for the weight of the overlying strata. Figure 12 shows the three-dimensional spatial distribution characteristics of the force chains within the surrounding rock masses of the stope. It can be seen in the figure that, following the stoping of the working face, the stronger force chains in the surrounding rock masses were transferred to the front, back, and top of the coal walls, and the overlying strata of the stope had formed a force chain arch along the strike and trend directions of the working face. e shape of the force chain arch in the strike and trend directions of the surrounding rock of the stope was similar to that of a "semiellipsoid" type surrounding rock force chain shell. e shell base of the chain shell was located at the back of the working face and the inner sides of the unmined walls at both ends. e shell was located in the intact overlying strata, as well as the unmined coal seams around the stope. is study observed that the most remarkable mechanical characteristics of the force chain shell were as follows: the strength levels of the force chains in the force chain shell   were the largest; the strength levels of the force chains inside and outside the shell were relatively low; and the working face was located within the force chain reduction area under the protection range of the stress shell formed by the force chains. e force chain shell was determined to be the main bearing system above the working face, and the strength levels of the force chains outside the shell had become gradually close to the strength of the force chains of the original rock masses before excavation. e load of the overlying rock masses in the stope transferred the force to the coal and rock around the working area through the strong chain paths in the force chain shell in order to form the phenomenon of a strong chain concentration. e clustering and transference abilities of the strong chains reflected the transfer paths and modes of the maximum principal stress in the surrounding rock masses of the stope. e force chains of the overlying surrounding rock masses had occurred in the rock stratum. en, with the fractures and collapsing of the rock stratum under the force chain shell, the strong and weak force chains were also broken and bifurcated. e fractured rock blocks formed an articulated structure, and the rock block contact extrusion pressure chain at the hinge was reorganized in order to transfer the force once again. In addition, within the three-dimensional space of the stope, the force chain shell composed of the strong chains was the result of the reorganization of the internal strong chains of the surrounding rock masses following the coal stoping. e deflections of the strong chain directions determined the deflections of the main stress direction. e areas where the force chains were assembled into bundles were the areas where the maximum main stress was concentrated. erefore, the stress shell of the surrounding rock masses in the three-dimensional space of the stope was the macroscopic embodiment of the force transference in the force chain shell formed by the force chain clusters.

Conclusions
In this paper, the comprehensive method of indoor experiment, theoretical analysis, and numerical simulation are used to study the mechanism of the force chain deflection and instability of the surrounding rock in deep stope. is paper reveals the mechanism of the broken movement and disaster of the surrounding rock of the stope, which has important guiding significance for the prevention and control of the dynamic disaster of the stope. e following conclusions were reached in this study: (1) e distribution characteristics of the force chains of the surrounding rock masses in the stope were examined in this study using a discrete element particle material simulation method. It was found that the spaces of the overlying strata in the stope along the  strike and trend directions of the working face presented the form of a strong chain arch. e strong chain arch in the strike and trend directions formed a force chain shell in the three-dimensional space, which realized the visualization of the force chains within the surrounding rock masses in the stope. It was revealed that the macro stress shell of the surrounding rock of the stope was a mechanical essence composed of strong chain bundles. (2) e force chain shell formed by the strong chains in the overlying strata of the stope was similar in shape to a "semiellipsoid." Its main mechanical features were that the strength levels of the force chains within the shell were the largest, and the strength levels of the force chains inside and outside the shell were relatively low. It was also found that the directions of the force chains in different key areas of the surrounding rock of the stope had been deflected, forming anisotropic characteristics with a certain deflection angle. e specific performance results were that the force chains were distributed in the vertical direction at the shell base, which indicated that the distributions of the strong contact force chains were dominant in the vertical direction at that point. In addition, the force chains at the shell shoulder were at a certain angle with the horizontal direction, and the force chains at the shell top were obviously in the horizontal direction.
(3) It was observed that, in the overlying strata of the stope, the force chain shell formed by the force chains was the result of the reorganization of the internal force chains of the surrounding rock masses following the coal mining excavations. e deflection of the directions of the force chains determined the deflections of the directions of the main stress. e areas where the force chains were most concentrated were the areas where the maximum main stress was concentrated. erefore, the stress shell of the surrounding rock masses in the three-dimensional space of the stope was the macroscopic embodiment of the force transference in the force chain shell formed by the force chain clusters.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.