Study on Surrounding Rock Failure Law of Gob-Side Entry Based on the Second Invariant of Deviatoric Stress

Abstract

The second invariant of deviatoric stress of the coal and rock mass is closely related to the distortion energy driving the deformation and failure of the surrounding rock. Based on the second invariant of deviatoric stress, this study built a global model of gob-side entry with different widths of the coal pillar through numerical analysis, and compared and analyzed the evolution law of the surrounding rock distortion energy, plastic location state, and roadway deformation with the width of the coal pillar. This study concluded that the peak distortion energy in the virgin coal rib and the roof and floor of the gob-side entry gradually increases with the reduction in the coal pillar width. When the coal pillar width is 5 m, the second invariant peak value of deviatoric stress in the virgin coal rib reaches the maximum of 294.8 MPa². When the width of the coal pillar is reduced from 30 m to 5 m, the second invariant of the deviatoric stress in the side of the coal pillar and the roof and floor of the side presents the law of first increasing and then decreasing. The greater the damage degree of the coal pillar, the smaller the distortion energy it contains. The distortion energy is the key factor in driving the deformation and failure of the surrounding rock. The greater the distortion energy, the greater the deformation degree of the surrounding rock, the more vulnerable it is to external mining stress disturbance, and the greater the difficulty in controlling the stability of the roadway-surrounding rock.

1. Introduction

At present, China’s coal-mining technology is dominated by strike longwall mining. A gob-side entry is a mining roadway along the edge of the goaf after the previous section of the working face is mined. Generally, a certain width of coal pillar is reserved along the goaf roadway and goaf; on the one hand, it separates the goaf from the roadway environment, and, on the other hand, it provides a supporting structure for the goaf side of the roadway. However, when the width of the coal pillar is large, it will cause a waste of coal resources. When the width of the coal pillar is too small, the bearing capacity of the surrounding rock of the roadway will be greatly reduced [1,2]. Therefore, it is urgent that we conduct a comprehensive and effective evaluation method to study the deformation and failure characteristics of the surrounding rock in the goaf-side entry with different pillar widths.

In view of the research on the deformation and failure characteristics of the surrounding rock of the gob-side entry under the width of the coal pillar, many scholars at home and abroad have made a series of research results combining theoretical analysis with practice, including a numerical calculation and test. The numerical analysis method can comprehensively consider the geological conditions of the surrounding rock of the roadway, the stress characteristics of the original rock, the strength of coal and rock, and other factors. It is an effective method to analyze the displacement, stress, and deformation of the surrounding rock of the roadway. Shen [3] studied the failure mechanism of the roadway through the case of the stability of a coal mine roadway in Shanxi Province. Through a numerical simulation, the stability and deformation of the roadway under different roof support conditions are evaluated. Based on the modeling results, a new roadway support design is proposed, which can significantly improve the roadway stability under soft rock conditions. Li et al. [4], through a numerical analysis of the influence of high horizontal original rock stress in different directions on roadway stability, concluded that with the increase in the excavation angle relative to the maximum horizontal stress, the stress concentration, roadway deformation, failure degree, and range are all increasing. In addition, the interface stress of coal and rock changes rapidly in space, and coal is more prone to deformation and failure than rock over time. The research results provide a theoretical basis for the layout of coal seam roadways. Xiong et al. [5] aimed to address the problem of the asymmetric deformation and failure characteristics of the surrounding rock of the right-angle trapezoidal roadway in Shitan No. 2 mining area causing great difficulties to the stability control and support of the roadway. The distribution law of vertical stress, horizontal stress, and failure characteristics of the roadway is analyzed by a numerical simulation system, which is further verified by a laboratory model test and practical engineering application. Wu et al. [6] studied the deformation and failure characteristics of the roadway-surrounding rock under static dynamic coupling stress through a numerical simulation. The results show that the horizontal stress, vertical stress, and dynamic disturbance are positively correlated with the plastic failure of the surrounding rock, of which the dynamic disturbance has the most significant influence, while the horizontal stress has a more significant influence on the roadway than the vertical stress, and the roof deformation and plastic failure are greater than the floor under the same stress conditions. Wang et al. [7], based on the theory of a butterfly-shaped plastic zone in a non-uniform stress field, studied the influence of the principal stress ratio and direction on the plastic zone of the roadway using FLAC3D, and concluded that, when the two-way stress ratio is large, the plastic zone of the roadway-surrounding rock is butterfly-shaped and the failure direction is related to the principal stress direction. The asymmetric damage mode of the roadway under the nearby residual coal pillar area is affected by the presence of the roadway in the non-uniform stress field where the principal stress direction is deflected. Wang et al. [8] studied the serious problem of the surrounding rock deformation and failure of the deep soft rock roadway via FLAC3D and MATLAB numerical analysis software, and made it clear that the vertical stress of the surrounding rock was concentrated on the direct roof, the horizontal stress was concentrated on both sides and the bottom of the roadway, and the plastic deformation and failure first appeared on one side of the roadway, and then extended to other parts, and mastered the time and space evolution characteristics of soft rock deformation and failure. The bending deformation, elastic–plastic transformation, and unloading failure mechanism of the surrounding rock in the deep soft rock roadway are revealed. Xia, Z. et al. [9] and others used Maple mathematical drawing software and a FLAC three-dimensional numerical simulation to combine the influence of the principal stress ratio and direction on the plastic zone of the roadway. A meticulously validated numerical model was developed to investigate the dynamic evolution characteristics of the 6.0-m coal pillar vertical stress and plastic state. In the analysis of failure mechanism of roadway-surrounding rock under special geological conditions such as water bearing and soft surrounding rock, Lis C. et al. [10] and others carried out large-scale geomechanically model tests against the engineering background of thick coal seams in Zhao Lou Coal Mine in Juye Mining Area, explored the deformation and failure mechanism of deep roadway-surrounding rock in thick coal seams, and studied the displacement and stress evolution law of surrounding rock under the yielding type anchor cable box girder support system. Through comparison between the test results and field tests, the main failure characteristics and mechanism of surrounding rock are verified and analyzed. Ma et al. [11] explored the damage and failure characteristics and fracture development law of roadway-surrounding rock by constructing a new ultimate stress intensity model of water-bearing surrounding rock, and carried out prefabricated fracture uniaxial compression test on water-bearing surrounding rock. The failure process of prefabricated fracture water-bearing surrounding rock is clarified, and the theoretical model can be used for stability evaluation and dynamic risk monitoring of water-bearing surrounding rock in coal mine.

Under the combined action of dynamic load and static load, the stress environment of roadway-surrounding rock becomes more and more complex. Zhao et al. [12] put forward the static and dynamic stress superposition (SDSO) method to explain the influence of static stress concentration and mine earthquake caused by coal mining according to the impact failure mechanism of coal pillar, and evaluated the failure degree of coal pillar in different mining stages of Zhaolou Coal Mine, which set up a systematic framework for the risk assessment of coal pillar impact failure. He H. et al. [13] By using dynamic and static numerical calculation FLAC3D to simulate the deformation field of roadway-surrounding rock, the site stress field under different SDCS conditions and the dynamic influence of roadway deformation and failure load, the characteristics were revealed. He et al. [14,15,16,17,18] combined the classical theory of mechanics and engineering geology to carry out the systematic characteristics of deformation and failure of deep soft rock roadway to analyze the causes, classify the evolution of disasters and study the control methods, pointing out the direction for the design of soft rock support such as coal pillar. CHEN et al. [19] found through experiments that the deformation and stress changes caused by the characteristics of surrounding rock are the root causes of major change disasters in mines. Yuan et al. [20] reflected and analyzed the influence of mining parameters on coal pillar displacement and stress through the establishment of structural model. Ma et al. [21,22,23,24] put forward a failure theory for evaluating the plastic zone of roadway coal pillar, which can be used to predict the potentially hazardous area when the coal pillar is damaged during mining, and analyzed the accumulation and release of energy of coal pillar and rock mass when it is damaged. as Along with other scholars [25,26,27,28,29,30], they carried out a series of complex loads to test the strength of different lithology problems of coal pillars during coal seam mining.

In view of the problems that the failure mechanism of surrounding rock of gob-side entry in previous studies usually takes one-way bearing stress as the evaluation index and changes with the change of coordinates, this study explores the stress field, deformation field and plastic zone state of surrounding rock of gob-side entry under different pillar widths based on the second invariant of deviatoric stress, which comprehensively considers the first, second and third principal strains and has the advantage of being independent of coordinates. Therefore, the second deviator stress invariants can be used as an evaluation index to more comprehensively and accurately analyze the deformation and failure law of surrounding rock in goaf side entry.

2. Simulation Model and Parameters

2.1. Theory of Second Deviator Stress Invariant

Based on the elastic–plastic theory, the stress at a point in the coal and rock mass can be expressed by three principal stresses, which are composed of hydrostatic stress and deviatoric stress, as shown in Formula (1), where deviatoric stress is the main driving force leading to the failure and deformation of the coal [1].

$$\underset{\mathrm{Deviatoric} \mathrm{stress} \mathrm{tensor}}{\underbrace{\left[\begin{array}{ccc}{\sigma }_1-{\sigma }_m& 0& 0\\ 0& {\sigma }_2-{\sigma }_m& 0\\ 0& 0& {\sigma }_3-{\sigma }_m\end{array}\right]}}+\underset{\mathrm{spherical} \mathrm{stress} \mathrm{tensor}}{\underbrace{\left[\begin{array}{ccc}{\sigma }_m& 0& 0\\ 0& {\sigma }_m& 0\\ 0& 0& {\sigma }_m\end{array}\right]}}=\underset{\mathrm{Principal} \mathrm{stress} \mathrm{tensor}}{\underbrace{\left[\begin{array}{ccc}{\sigma }_1& 0& 0\\ 0& {\sigma }_2& 0\\ 0& 0& {\sigma }_3\end{array}\right]}}$$

(1)

Among them,

$${\sigma }_m=\frac{{\sigma }_1+{\sigma }_2+{\sigma }_3}{3}$$

where σ₁, σ₂, σ₃ is the main stress component; σ_m is the average value of the main stress component.

Furthermore, the invariant expression of the deviatoric stress tensor can be deduced as:

$$J_2=\frac{1}{6}\left[({\sigma }_1-{\sigma }_2{)}^2+({\sigma }_2-{\sigma }_3{)}^2+({\sigma }_3-{\sigma }_1{)}^2\right]$$

(2)

where J₂ and others are the first, second and third invariants of deviating stress, the unit is MPa².

The expression of distortion energy given by study [2] is:

$$W=\frac{({\sigma }_1-{\sigma }_2{)}^2+({\sigma }_2-{\sigma }_3{)}^2+({\sigma }_3-{\sigma }_1{)}^2}{12G}$$

(3)

where G is the shear modulus.

Its expression can be described by the second invariant of deviatoric stress:

$$W=\frac{J_2}{3G}$$

(4)

Therefore, the second invariant of deviatoric stress can characterize the distortion energy in coal and rock mass. At the same time, the second invariant of deviatoric stress is used to evaluate the reasonable width of coal pillar, which has the advantage of independent of coordinate selection and comprehensive consideration of the three principal stresses in coal and rock mass.

2.2. Global Model for Pillar Width

Build a numerical analysis global model as shown in Figure 1. A pressure of 7.5 MPa is applied to its top to simulate the load on the upper rock layer. The bottom and other sides of the model are fixed condition. The model adopts rectangular grid division, and the grid near the gob-side entry is refined considering computational efficiency and accuracy. The width of the model is 500 m, and the height is 92 m. The model is composed of 18 m thick fine sandstone, 15 m thick siltstone, 4 m thick coal seam 2#, 5 m thick mudstone, 5 m thick coarse sandstone 2#, 6 m thick coal seam 1#, 20 m thick medium fine sandstone, 10 m thick coarse sandstone 1# and 9 m thick kaolinite rock from the bottom plate.

In coal seam 2#, a working face with a mining height of 6 m and a length of 200 m and a roadway with a width of 4 m and a height of 3 m are arranged; six groups of schemes are set for the width of interval coal pillar between roadway and goaf, which are40 m, 35 m, 30 m, 25 m, 20 m, 15 m, 10 m and 5 m.

Figure 2 shows the layout plan of stress acquisition data. Three data lines are arranged below the roadway floor: data line 1 (4 m from floor), data line 2 (2 m from floor), data line 3 (0 from floor), data line 4 (2 m from floor), and data line 5 (2 m from floor) are arranged for the roadway coal pillar and virgin coal rib, and data line 6 (3 m from floor), data line 7 (5 m from floor) and data line 8 (7 m from floor) are arranged for the roadway roof.

2.3. Simulation Parameters and Constitutive Relation of the Rock and Coal Seam

Table 1. Mechanical parameters in simulation model.

Lithology	Density D (kg/m3)	Bulk K (GPa)	Shear G (GPa)	Friction Angle φ (°)	Cohesive c (MPa)
Kaolinite rock	2550	3.5	2.7	32	1.7
Coarse sandstone 1#	2500	6.0	5.1	34	1.8
Medium fine sandstone	2800	7.2	6.1	36	2.5
Coal seam 1#	1450	1.5	0.8	25	1.0
Coarse sandstone 2#	2500	6.0	5.1	34	1.8
Mudstone	1900	3.3	2.5	31	1.2
Coal seam 2#	1450	1.8	1.0	28.0	1.2
Siltstone	2540	5.5	3.5	32.0	1.6
Fine sandstone	2850	7.4	6.3	37.0	2.0

shows the mechanical parameters of each coal bed in the numerical analysis. Among them, rock strata and coal seam 1# use the Morh Coulomb constructive relationship; coal seam 2# applies the straight soft constructive relationship. Double-yield constructive relation is used for filling materials in goaf. Mechanical parameters are given in

Table 2. Double-yield parameters in double-yield constitution.

Lithology	Density D (kg/m3)	Bulk K (GPa)	Shear G (GPa)	Friction Angle φ (°)	Cohesive C (MPa)	Tensile T (MPa)	Dilation d (°)
Gob rock	1000	3.2	1.0	10	5.0	0.03	2

, and cap pressure is given in

Table 3. Cap pressure of gob rock in double-yield constitution.

Strain	Pressure (KPa)	Strain	Pressure (KPa)
0.01	150	0.10	3500
0.02	350	0.15	12,000
0.05	1250	0.18	18,000

. The mechanical parameters are obtained based on the basic properties of each rock [31].

3. Results Analyses

It can be seen from Figure 3 that the width of the coal pillar is reduced from 30 m to 15 m, the second invariant of the deviatoric stress of the surrounding rock (coal pillar, virgin coal rib and roof and floor) of the gob-side entry gradually increases, and the peak values of the second invariant of the deviatoric stress of the coal pillar and virgin coal rib are 310 MPa² and 77.1 MPa², respectively. The width of the coal pillar is reduced from 15 m to 5 m, and the second invariant of the deviatoric stress in the coal pillar and the side roof and floor of the coal pillar is continuously reduced, with a decrease of 522.8 MPa². The second invariant of deviatoric stress in the virgin coal rib is still increasing, with an increase of 89.5 MPa². At the same time, when the coal pillar width is 15 m–30 m, the second invariant peak value of deviatoric stress in the coal pillar and the side roof and floor of the coal pillar is greater than the solid coal slope and the side roof and floor of the solid coal slope, while the opposite is true when the coal pillar width is 5 m–10 m. When the coal pillar width is 35 m and 45 m, the distribution law and value of deviatoric stress in the surrounding rock of the two roadways are close. In the roadway with a coal pillar width of 5 m–30 m, there is only one peak value of the second invariant deviatoric stress in the roof and floor. Different from the deviatoric stress invariant of roadway with coal pillar width of 5 m–35 m, it in roof and floor presents a shape likes the hump when the coal pillar width is 35 m and 45 m. There are two peaks at a distance of about 5 m from the edges of both sides of the coal pillar, and the peak value is significantly higher on the side near the goaf than on the side near the roadway. Under different pillar widths, the second invariants of the floor bias stress of gob-side entry are greater than those of the roof.

The above rule shows that when the coal pillar is relatively wide, such as 40 m–15 m, there is a lot of distortion energy in the surrounding rock, especially when the coal pillar is 15 m wide. The distortion can be the main driving force for the destruction of the surrounding rock, which will have a great impact on the stability of the surrounding rock of the roadway. Therefore, setting wide coal pillars to protect the roadway is not conducive to the maintenance of the roadway. When the width of the coal pillar is narrow, such as 10 m and 5 m, the distortion energy contained in the coal pillar and the roof and floor at the side of the coal pillar decreases sharply, and the distortion can be transferred to the virgin coal rib and the roof and floor at this side. At this time, the solid coal side of the roadway is prone to deformation and damage under the influence of external mining stress.

Figure 4 shows the evolution law of surrounding rock plastic zone along goaf roadway with coal pillar width. When the width of coal pillar is 40 m, 35 m, 30 m, 25 m and 20 m, the plastic area of surrounding rock is not connected with the damaged area of the goaf. Among them, the depth of the surrounding rock failure of roadway with 40 m coal pillars is close to 35 m, and it is smaller than the coal pillar width of 30 m–5 m. When the coal pillar is 35 m, the failure depth of the roadway roof and coal pillar side is reduced by 2 m and 1.6 m, respectively, compared to when the coal pillar is 15 m; when the coal pillar is 25 m, the destruction depth of the coal pillar wall and the floor is unchanged compared with when the coal pillar is 30 m, and the destruction depth of the roof and the virgin coal rib increases by 1.2 m and 0.8 m, respectively. The failure depth of 20 m coal pillar is not increased compared with the 25 m coal pillar, while the virgin coal rib and coal pillar wall are increased by 0.4 m and 0.6 m, respectively. When the width of the coal pillar is reduced to 15 m, the plastic zone of surrounding rock is connected with the damaged area of the goaf. When the coal pillar is continuously reduced to 10 m and 5 m, the damaged depth of the virgin coal rib is no longer increased, the connecting range between the side of the coal pillar and the plastic zone of the roof is expanded, and the plastic zone of the wall rock floor is continuously reduced.

Based on the above analysis and in combination with the quantitative relationship between the second deviatoric stress invariant of surrounding rock and the width of coal pillar, it can be seen that the potential distortion energy of surrounding rock in the damaged area is lower than that of the undamaged surrounding rock, indicating that elastic coal and rock mass will produce large distortion and accumulate deformation energy under the external stress drive, while plastic damaged coal and rock mass will release the distortion energy after undergoing large deformation and high distortion energy failure. Therefore, when the width of the coal pillar is narrow (5 m and 10 m), due to the influence of the mining of the previous working face, the coal pillar and the roof and floor at the side of the coal pillar are damaged, and the distortion energy and bearing capacity are reduced. Therefore, the stress migrates to the solid coal and the roof and floor at the side, causing the distortion energy in the surrounding rock at the solid coal side to rise significantly. At the same time, when the width of coal pillar is 15 m, the plastic zone and distortion energy of surrounding rock are maximum, which is extremely unfavourable to the maintenance of roadway stability.

Figure 5 shows the deformation law of surrounding rock of gob-side entry with different pillar widths (5 m, 10 m, 15 m, 20 m, 25 m, 30 m, 35 m and 45 m). In the process of roof deformation (Figure 5a), the roof subsidence of 5 m and 10 m coal pillars is close, and the deformation is larger than that of other width coal pillars. When the width of coal pillar is 40 m, the minimum roof subsidence is 14.6 cm, and the roof subsidence increases with the reduction in coal pillar width. In floor deformation, except that the floor heave of 5 m coal pillar roadway (1.42 cm) is the largest, the floor heave of other width coal pillars is similar. In the deformation of coal pillar wall, the deformation of 10 m wide coal pillar is the largest, reaching 35.9 cm, while the deformation of 5 m coal pillar is less than 15 m coal pillar. In the deformation of virgin coal rib, the deformation increases with the decrease in coal pillar width; the deformation of 40 m coal pillar virgin coal rib is the minimum, 10.3 cm, and the maximum is the 5 m coal pillar, 27.4 cm.

The stability of surrounding rock of roadway is not only related to the deformation amount of surrounding rock, the scope and extent of damage, but also closely related to the distortion energy contained in the surrounding rock. When the width of the coal pillar is 5 m, although the coal pillar is damaged as a whole, the distortion energy contained in it is small, so the deformation of the coal pillar wall is smaller than 10 m and 15 m. However, because the distortion energy in the virgin coal rib is much higher than the side of the coal pillar, the deformation of the virgin coal rib is greater than the side of the coal pillar. When the width of the coal pillar is large, such as a 15 m coal pillar, although the deformation of the roof and floor and the virgin coal rib is smaller than that of the 5 m coal pillar, the surrounding rock contains a large distortion energy to drive the deformation and destruction; therefore, the plastic zone of the surrounding rock is large, and it is very easy to be affected by external disturbance to produce large deformation and then destroy the instability.

4. Conclusions

(1) The width of the coal pillar is reduced from 30 m to 5 m, and the second invariant peak value of the deviatoric stress in the solid coal and the side roof and floor continuously increases. When the width of the coal pillar is 5 m, the second invariant peak value of the deviatoric stress in the virgin coal rib reaches the maximum of 294.8 MPa²; however, the second invariant peak value of the partial stress in the coal pillar and the roof and floor at the side of the coal pillar of the gob driving roadway decreases gradually with the decrease in the coal pillar width. When the coal pillar width is 15 m, the second invariant peak value of the partial stress in the coal pillar is the largest (540 MPa²), and when the coal pillar width is 5 m, the minimum peak value is 17.7 MPa².

(2) The second invariant numerical evolution law of deviatoric stress in surrounding rock is closely related to the regional distribution characteristics of surrounding rock failure. The greater the damage degree of roadway-surrounding rock, the smaller the value of the second deviatoric stress invariant, that is, the smaller the distortion energy contained therein. When the width of coal pillar is 5 m, the whole coal pillar wall is destroyed, and the peak value of the second invariant of deviatoric stress is only 17.7 MPa² while the peak value of the second invariant of deviatoric stress in the elastic area of virgin coal rib is 234.6 MPa² more than that of other width coal pillars.

(3) The failure and instability of surrounding rock is not only related to the deformation of roadway and the position and shape of its plastic zone, but also controlled by the distortion energy. The greater the distortion energy of surrounding rock, the greater the failure energy contained in coal and rock mass, and the impact failure is very easy to occur under the mining disturbance to release the energy. Although the damage degree of surrounding rock in narrow coal pillar gob-side entry is large and wide, the deformation and damage distortion energy of driving surrounding rock is small, and its control difficulty is to support the broken coal and rock with poor bearing capacity.

This study clarifies the decisive role of coal pillar size on accident risk during mining operations, and provides specific risk prevention size values. At the same time, the second invariant numerical evolution law of surrounding rock deviatoric stress and the regional distribution characteristics of surrounding rock failure are given. Specifically, the greater the distortion energy of surrounding rock, the greater the failure energy contained in coal and rock mass, and the impact failure is very easy to occur under the mining disturbance to release the energy. Although the damage degree of surrounding rock in narrow coal pillar gob-side entry is large and wide, the deformation and damage distortion energy of driving surrounding rock is small, and its control difficulty is to support the broken coal and rock with poor bearing capacity.

Although this article has conducted extensive numerical calculations and analysis, there is still a lack of experimental data and engineering examples, which will be the main focus of further research in the future.

Compared with previous research results, this research achievement is the first to consider the relationship between coal and rock deviatoric stress and surrounding rock distortion energy. Through numerical models under different coal pillar widths, the evolution laws of distortion energy, plastic location state, and roadway deformation with coal pillar width were revealed. The greater the distortion energy, the greater the deformation degree of the surrounding rock, and the more vulnerable it is to external mining stress disturbance, and the greater the difficulty in controlling the stability of roadway-surrounding rock. This enriches new methods for numerical calculation and analysis of such engineering problems, and provides new ideas for risk prediction in coal mining.