Numerical Simulation of the Stress Field in Repeated Mining of Coal Seams Based on In Situ Stress Measurement

We established an evaluation index of the rock mass stress state for underground coal mines using the strength-stress ratio based on the measured in situ stress and the generalized Hoek–Brown strength criterion. )ree in situ stress states, σcm/σ1m< 1.4 (high), 1.4< σcm/σ1m< 3.6 (medium), and σcm/σ1m> 3.6 (low), were established based on the value of the unconfined compressive strength (σcm) and the maximum principal stress of the rock mass (σ1m).)is index classifies the Burtai mine as a medium-high in situ stress field, which is in agreement with the on-site situation, establishing the reliability of the index. )e working face was a three-dimensional geological model based on the log sheets. )e initial conditions for the model were determined using the combined measurements of the in situ stress regression model. We performed numerical simulations of the roof stress field distribution under repeated mining. Mining the overlying coal seam leads to significant variation in the value and direction of the main roof, σ1, within the range of the front abutment pressure under the pillar and gob. Along the main roof strike direction, σ1 under the pillar is 1.5 times that under the gob, and the σ1 direction under the pillar is deflected by 5°, which is 30° smaller than that under the gob. )is provides a reference for optimized underground coal mining.


Introduction
e combination of in situ stress and mining stress in underground coal mines forms a mining stress field. is stress field is directly related to the stress state of the overlying strata of the coal seam and the structural movement characteristics, and it affects the safe mining of the working face. e cause of in situ stress is complex, and it has an irregular distribution. It is affected by several factors, including depth, topography, structure, lithology, and residual stress. Hast [1] studied the distribution of in situ stress in different regions of western European countries, such as Norway and Sweden, based on which Stephansson et al. [2] established a regional in situ stress database in 1969. Brown and Hoek [3] analyzed the results of in situ stress in the shallow crust at a depth of 3 km in 1978. Haimson [4] summarized the in situ stress distribution in the United States at a depth of 0-5 km in 1980. Sheorey [5] proposed a crustal stress calculation model suitable for 138.87 m∼33.73 km. e World Stress Map (WSM) project [6] compiles the direction of the maximum horizontal principal stress (σ H ). WSM 2016 has 42,870 data records, which is double that of WSM 2008. Statistical studies on the distribution of crustal stress fields have been conducted in mainland China [7][8][9][10][11][12]. Kang et al. [13] compiled 1,357 in situ stress data in the "Database of in situ stress in underground coal mines in China," and observed three stress field distributions: (150-1000 m), and σ v > σ H > σ h (>1000 m). Yang [14] investigated the in situ stress in 26 groups of the northern Ordos Basin, China, and analyzed the principal stress distribution with depth, σ H � 5.3367 ± 0.023 H, correlation coefficient R 2 � 0.94, and σ h � 0.6559 ± 0.017 H, R 2 � 0.55; the dominant orientation of σ H is the NEE. However, it cannot be used for establishing mine-scale engineering practice guidelines due to the variation in survey locations, and therefore, area-specific studies on in situ stress measurement and application are required. e in situ stress state and the strength of the intact rock mass are essential for the stability of underground coal mines.
At present, the empirical method, the strength-stress ratio method, the stress ratio method, and the geological marker method are used for evaluating the in situ stress state. Although 20 MPa is the typical high-stress standard, Yu et al. [15] proposed a standard of 0-10 MPa (low stress), 10-18 MPa (medium stress), 18-30 MPa (high stress), and greater than 30 MPa (superhigh stress). e strength-stress ratio method is the most widely used method [16,17], but it lacks a unified standard. e Sheorey model [5] has been widely recognized in engineering design since it can predict horizontal stress and address the discrete stress values. e evaluation parameters include weathered rock mass or shallow surface engineering areas, which do not conform to the actual condition of coal mines [18][19][20][21][22]; therefore, the stress state evaluation indicators based on in situ stress data are required. e strength-stress ratio method was used to establish the evaluation index for the stress state of the mine rock mass based on the in situ stress measurement through Kaiser effect and the generalized Hoek-Brown rock mass strength criterion, and a preliminary engineering verification was carried out. A refined geological model for the stratum occurrence conditions in the Burtai mine was established with 42# coal seam mining combined with the measured in situ stress regression model. e roof stress field of the working face under repeated mining conditions provided a reference for optimizing the mining plan in the Burtai mine and provided the guidelines for mines under similar conditions.

In Situ Stress Measurement in the Study Area
e Burtai mine is an extra-large mine in the Shendong mining area in China with a designed production capacity of 20 Mt/a and a service life of 71.9 a. Currently, 22# coal seam, having a thickness between 0.82 and 5.80 m and an average thickness of 2.52 m, and 42# coal seam, with thickness between 0.90 and 7.68 m and 6.50 m average thickness of the coal seam, are mined in the entire area. e coal seam has a simple structure with a stable layer, and it is a low-gas mine. e upper and lower coal seams of 22# and 42# are mined at the same time. With the increase in mine depth beyond 400 m, in situ stress becomes prominent due to increased mining intensity. Repeated mining causes severe disturbance with complex breaking characteristics of the overlying rock. For example, roof sinks and the bottom heaves were observed in the return roadway along the 22103 working face, resulting in the roadway being re-dug twice. e slab was damaged in the 0.2-1.5 m depth along the 42105 working face because of mechanized mining and poor caving technology, and roof weighting over a large area was observed. e above phenomena are inseparable from the in situ stress field.
Yang [14,23,24] established an in situ stress test based on the Kaiser effect of a borehole core and analyzed the in situ stress distribution in and around the boreholes of the Burtai mine, as shown in Figure 1.
e principal stress values are discrete but increase with an increase in depth (Figure 1(a)) and the fitting equations are as follows (equation (1)). ree stress field distributions (1) In Figure 1(b), the variation of k ((σ H + σ h )/2σ v ) with depth is shown in equation (2) and compared with the k envelope (equation (3)) obtained by Brown and Hoek. e variation is similar to the progressive value of the inner envelope, and the k range reduces with an increase in depth (at 350 m, k � 0.98).

Evaluation Index of the Stress State.
e rock mass stress state affects the rock mass stability and includes in situ stress, rock mass strength, and rock mass structural quality. Several classification systems have been developed for rock mass. e rock quality designation (RQD), proposed by Deere in 1964 [25], is one of the simplest systems of rock mass classification. e rock mass rating system (RMR) [26] and tunneling quality index (Q system) [27] are the most widely utilized rock mass classification schemes, and they have been widely adopted in the mining industry. e Hoek-Brown strength criterion, developed in 1980 [28][29][30][31], can account for the nonlinear behavior of the ultimate principal stresses when a rock mass fails and describes the influence of the rock mass structure and stress state on its strength. e parameters can be obtained qualitatively or quantitatively using conventional mechanical tests and field structure descriptions. e associated geological strength index (GSI) is widely used for estimating the strength and deformation of heavily jointed rock masses. e stress-based failure criteria developed by Coulomb, Mohr, and Hoek and Brown are extensively applied in rock mechanics. e Hoek-Brown strength criterion has undergone several modifications, and the final version (2018) is given by the following equation and described by Hoek and Brown in 2019: where m b , s, and α are the rock mass material constants, given by 2 Mathematical Problems in Engineering where σ 1 and σ 3 are the maximum and minimum principal stresses at failure, respectively; σ ci is the unconfined compressive strength; m b is a rock property, modified by the GSI and degree of disturbance of the rock mass, respectively; s is a constant determined by the GSI and degree of disturbance of the rock mass; α is a constant determined by the GSI; m i , s � 1, and α � 0.5 are the material constants for intact rock; and D is a factor that depends upon the degree of disturbance to which the rock mass has been subjected to blast damage and stress relaxation. When σ tm < σ 3 < σ ci /4, the expression is given by the following equation: Incorporating equation (6) into the Hoek-Brown strength criterion, let η � [ ������� (1 + μ 2 ) + μ] 2 , σ ci � k m σ cm . en, e relationship between the σ cm /σ 1 ratio and GSI for different friction coefficients is shown in Figure 2. With an increase in the friction coefficient, the σ cm /σ 1 ratio changes significantly. When 0.2 < μ < 0.6, σ cm /σ 1 ratio is between 0.01 and 0.3, when 0.6 < μ < 1.0, σ cm /σ 1 ratio lies between 0.05 and 0.7, and the σ cm /σ 1 ratio generally varies between 0.05 and 0.5. e relationship between the σ cm /σ 1 ratio and GSI for different disturbance coefficients is shown in Figure 3. With a decrease in GSI, the variation of the disturbance coefficient (D) increases, indicating that the deteriorating geological conditions increase the degree of disturbance in the in situ rock masses because of blasting, rock mass excavation, and rock mass unloading. e in situ deformation tests of 50 groups of rock masses indicate that D around the prospecting drift is 0.25 [32], while D caused by the excavation of the mining roadway is less than 0.4. When μ � 0.3 and m i � 24, the ratio of roadway excavation to σ cm /σ 1 does not exceed 0.02; when μ � 0.6 and m i � 24, the ratio of roadway excavation to σ cm /σ 1 exceeds 0.1. erefore, the mining roadway is less sensitive to D compared to GSI. e coal-measure strata are clastic sedimentary rocks, mainly sandstone. e values of m i for various rocks are as follows: siltstone 7 ± 2, hard sandstone 18 ± 3, sandstone 17 ± 4, conglomerate 21 ± 3, and breccia 19 ± 5 [30,31]. Most mined sandstones have a core length greater than 10 cm, and the joints are weakly weathered or non-weathered. e GSI of the surrounding rock of the coal seam is above 30-40. e friction coefficient of sandstones ranges between 0.1 and 0.6, with an average of 0.3. e σ cm /σ 1 ratio of sandstone in most coal-measure strata lies between 0.1 and 0.4 for different friction coefficients. e higher boundary value of the σ cm /σ 1 ratio is suitable for most rock mass stress state evaluation of Principal stresses (MPa)     Mathematical Problems in Engineering coal-measure strata. e rock mass stress will significantly impact its stability for σ cm /σ 1 < 0.4 and may cause rock mass instability, which is defined as a state of rock mass with high stress. Stress concentrations occur in the rock mass around the roadway during underground mining. erefore, the stress concentration factor should be considered for calculating the maximum principal stress in the rock mass; hence, σ 1 can be expressed as where η is the maximum stress concentration factor of the rock mass around the roadway and σ 1m is the measured maximum principal stress. e rock surrounding the roadway is a nonhomogeneous, discontinuous, and nonlinear material with complicated loading and boundary conditions. For a circular roadway, the maximum stress concentration factor is 2.0 and 3.0 under uniform and nonuniform stress field conditions, respectively. e maximum stress concentration factor for a rectangular roadway stays below 4.0 and is generally less than 3.5. Under most coal seam and mining conditions, the front abutment pressure of the working face is in the range of 2.5-3.5 [33]. At η � 3.5, the rock mass starts to fail for σ cm /σ 1m < 1.4, which corresponds to a high in situ stress state. e corners where the two working faces meet experience stress concentration seven times the vertical stress of the original rock, or even higher. e rock mass failure occurs locally in the roadway section for η � 9.0 and 1.4 < σ cm /σ 1m < 3.6, and the stress state corresponds to the middle in situ stress state. When σ cm / σ 1m > 3.6, local rock mass collapses, or the structural plane becomes unstable because it is difficult to achieve a ninefold stress concentration factor in coal-measure strata, and this corresponds to a low in situ stress state. Based on the strengthstress ratio, the evaluation index for the rock mass stress state of coal mines is presented in Table 1.
σ cm is the unconfined compressive strength of the original rock mass of the surrounding rock of the roadway and can be estimated using the Hoek-Brown strength criterion (equation (4)) or using RocData software; σ 1m is the maximum principal stress in the in situ stress field of the surrounding rock of the roadway, which can be calculated using the theoretical model of in situ stress, or obtained using in situ stress testing.

Engineering Verification.
e relationship between σ cm / σ 1m and the depth of all rock formations in the Burtai mine is used to verify the in situ stress evaluation index of the rock mass strength-stress ratio (Table 1) as shown in Figure 4(a). e roof and floor data around the 22#, 42#, and 52# down coal seams are shown in Figure 4(b), where σ ci is the average uniaxial compressive strength of the rock, σ cm is the average rock mass strength, and σ 1m is the measured maximum principal stress. GSI is determined using a combination of the rock quality designation (RQD), the rock block index (RBI), and the core recovery percentage (CRP), with the disturbance coefficient D set to 0. e parameters are listed in Tables 2 and 3. Figure 4(a) shows 89 measuring points in the Burtai mine, of which 59, with σ cm /σ 1m < 1.4, account for 66.3% of the total; 27, with 1.4 < σ cm /σ 1m < 3.6, account for 30.3%; and 3, with σ cm /σ 1m > 3.6, account for 3.4%. In Figure 4(b), among the 24 measuring points in Burtai mine, 11, with σ cm / σ 1m < 1.4, account for 45.8% of the total; 12, with 1.4 < σ cm / σ 1m < 3.6, account for 50.0%; and 1, with σ cm /σ 1m > 3.6, accounts for 4.2%. e average values of σ cm /σ 1m of the roof and floor around 22#, 42#, and 52# down coal seams were 1.59, 1.25, and 2.00, respectively. e groups with σ cm / σ 1m < 1.4 are divided according to the depth into 350-450 m, 450-550 m, and 550-650 m, which account for 37.5%, 50.0%, and 42.9% of the total, respectively. e ratio of σ cm / σ 1m < 1.4 increases with an increase in the depth, indicating the Burtai mine to be a medium-high in situ stress field.
According to the empirical method, 39 groups with σ h < 10 MPa account for 43.8% of the total; 42 with 10 < σ H < 18 MPa account for 47.2%; and 8 with σ H > 18 MPa account for 9%. Among them, 34 groups were above 350 m, of which 29 groups with σ h < 10 MPa, account for 85.3%; 55 groups were below 350 m, of which 11 groups with σ h < 10 MPa account for 20%; and 65.5% groups have 10 < σ h < 18 MPa. erefore, the in situ stress field in the Burtai mine is low in situ stress field above 350 m and medium in situ stress field below 350 m. According to the stress ratio method, there are 86 groups with (σ 1 + σ 2 + σ 3 )/ σ V > 2, accounting for 96.6% of the total, indicating the majority of the Burtai mine as high in situ stress field, which does not conform to the actual condition of the Burtai mine. e current mining depth of 42# coal seam in the Burtai mine is greater than 400 m, resulting in nonlinear dynamic phenomena such as bottom heave, slab, and large-area roof weighting. With a further increase in mining depth, the roof and floor will be under high in situ stress along with an increase in the accumulated elastic energy. is justifies the medium-high in situ stress field of the Burtai mine and necessitates the active adoption of the mine pressure prevention technology, and establishes the reliability and applicability of the strength-stress ratio index.

Model Construction.
We analyzed six log sheets (E014, E019, E026, E030, E051, and E060) around the 42107 working face in the Burtai mine corresponding to the SJ-3 log sheet on the 42105 working face [34]. e representative marker layer, which roughly divides the Burtai mine into 15 strata from top to bottom, was selected as the strata interface. A refined three-dimensional geological model of the working face was constructed using Rhinoceros software and imported into Flac3D using griddle software ( Figure 5). e spatial position of the working face is illustrated in Figure 6. e numerical model of the working face was length × width × height � 800 m × 900 m × 600 m, and it was divided into 1,605,551 units and 283,006 nodes. e initial conditions of the model are determined in combination with the measured in situ stress regression model (equation (1)).      Mathematical Problems in Engineering e physical and mechanical parameters of the model strata were determined using laboratory tests of the coal and rock in the SJ-3 borehole at 42105 working face in the Burtai mine [34]. e tensile strength of rock mass (σ tm ) is calculated by RocLab 1.0 software (Table 4). e rock follows the Mohr-Coulomb elastoplastic model, while the broken rock mass in the caving zone follows the double-yield-surface elastoplastic model. Based on the compaction characteristics of the broken rock mass, the stress-strain relationship of the caving zone rock mass aligns well with the actual conditions of the coal mine and is given by the following equation:

Mathematical Problems in Engineering
where σ v is the vertical stress of the caving zone in the gob (MPa); ε is the vertical strain, ε m is the maximum vertical strain, taken as ε m � (b -1)/b; b is the comprehensive crushing expansion coefficient of the rock mass in the caving zone, calculated using the caving zone H c � h/(b -1); E 0 is the initial elasticity modulus of the rock mass, MPa, calculated using E 0 � 10.39σ c 1.042 /b 7.7 [35]; and σ c is the uniaxial compressive strength (UCS) of the rock mass in the caving zone, MPa. e UCS of the roof above 22# and 42# coal seams are greater than 40 MPa, indicating them to be hard rock strata. According to the coal mining conditions, the average thickness of coal seam 22# is 3.6 m, and the average thickness of the 42# coal seam, which uses mechanized mining with sublevel caving technology, is 6.5 m. e machine mining height is 3.6 m, the coal caving height is 2.9 m, and the top coal caving rate is 80%, indicating the actual mining height of the 42# coal seam to be 5.92 m. e heights of the caving zone (H c ) and the fissure zone (H f ) can be calculated using equations (10) and (11) and Table 5 [35][36][37]. e heights of the two zones formed after the 22# and 42# coal seam working faces with longwall mining are 15.3 m, 57.0 m, and 20.8 m; and 65.0 m, 1.236 and 1.284, respectively; and ε m is 0.19 and 0.22, respectively. e mechanical parameters of the caving zone rock mass in the gob are tabulated in Table 6.  (Figures 7(a) and 7(c)). e principal stress increases by different degrees with the increase in the width of the pillar from 300 m. e larger the pillar width, the faster the increase in stress. e increase rate increases from 60 m advances and reaches the maximum for 4-9 m advances. e rate decreases rapidly above and behind the working face and reduces to 6 MPa and 30 m behind the gob. Original rock stress zones, stress increase zones, and stress reduction zones are present on the strike of the working face under the pillar, and the size of the stress increase zone is different under different pillars. Although σ 1 increases with an increase in pillar width, the rate of increase reduces, while the principal stress influence ranges remain unchanged. e peak value distance from the rib is approximately 3 m, and the stress peak coefficients are 1.95, 2.19, 2.31, 2.35, and 2.45, respectively, under different pillar widths. e distribution of σ 1 on strike under the gob is similar to that under the pillar, and the peak coefficients are reduced to 1.32, 1.41, 1.47, 1.56, and 1.66, respectively. e roof σ 1 direction of the working face under the pillar is first deflected towards the z-axis in the advanced range and then deflected in the reverse direction (Figures 7(b) and 7(d)). e angle between the σ 1 direction and the z-axis is 6°f or advancing 350 m, and it is biased towards the gob. e angle increases to 13°from advancing 300 m and gradually decreases to 3°for 50 m. e angle remains constant with the increase in pillar width, and the reverse deflection occurs within advancing 50 m, reaching 30°above the working face, and 55°at 30 m behind the gob. e deviation of the σ 1 direction below the pillar remains constant beyond 350 m and is subsequently affected by the overlying coal mining. e angle between the σ 1 direction and the z-axis increases sharply to 68°within advancing 350 m to 250 m. Subsequently, reverse deflection occurs, and the angle decreases. e deflection angle ranges between 50°and 80°and decreases with an increase in pillar width, with a sharp decrease to 35°within advancing 16 m. After the working face, the σ 1 direction continues to deflect to the gob, and the deflection reaches 60°for 25 m behind the gob. e main roof σ 1 deflection angle within 25 m in front of the rib under the gob is 35°because of the overlying coal mining and is 10°larger than solid coal. e friction coefficient of rock is distributed between 0.1°and 0.8°, and the predominant fracture angle is 25-45°, as seen from the Griffith physical model of closed microcrack propagation under pressure [38]. e shear-type (II) and tension-shear mixed-type (I-II) expansion of the coal and rock mass cracks are observed along the vertical plane within the severely affected range of mining. e principal stress of the roof remains unchanged, and the principal stress direction is rotated according to the conditions of the tensile type (I) expansion of the roof cracks [38]. When σ 1 rotates to the dominant angle, the maximum Table 4: Physical and mechanical parameters of the model strata.   Table 6: Mechanical parameters of the rock mass in the caving zone.

Results and
Lithology tensile stress reaches the tensile strength of the roof, and the microcracks in the top coal expand. e expansion of the roof (top coal) cracks can be attributed to the principal stress rotation, the increase in σ 1 , and the decrease in σ 3 .

Maximum Principal Stress and Deviator Stress in the Inclined Direction.
e principal stress distribution of the main roof has a "single-peak" shape ( σ 1 distribution, the deviator stress on inclined direction also presents a "single-peak" shape, with peak values of 15. e deviator stress is the largest within the severe influence range of the pillar and fluctuates significantly. e main roof in the front of the rib breaks under tensile stress because of considerable accumulated strain energy, which transforms into the fracture surface energy and the initial velocity of the fractured rock block, resulting in an impact load. Roof fracture and instability can cause a dynamic catastrophe of the working face due to the combined dynamic and static load.

Conclusion
e strength-stress ratio method was used to establish the evaluation index for the stress state of the mine rock mass based on the in situ stress measurement through Kaiser effect and the generalized Hoek-Brown rock mass strength criterion, and a preliminary engineering verification was carried out. A refined geological model for the stratum occurrence conditions in the Burtai mine was established with 42# coal seam mining combined with the measured in situ stress regression model. e roof stress field of the working face under repeated mining conditions is studied, and the main conclusions are as follows: (1) An evaluation index of the rock mass stress state for an underground coal mine was established using the strength-stress ratio. It corresponds to high in situ stress state for σ cm /σ 1m < 1.4, medium in situ stress state for 1.4 < σ cm /σ 1m < 3.6, and low in situ stress state for σ cm /σ 1m > 3.6. (2) e index is applied in the Burtai mine and classifies it as a medium-high in situ stress field, which is in agreement with the on-site situation, establishing the reliability of the index. (3) e value and direction of the main roof σ 1 within the range of the front abutment pressure under the pillar and gob vary significantly because of the mining of the overlying coal seam. e value of σ 1 under the pillar along the main roof strike direction is 1.5 times that under the gob, and the σ 1 direction under the pillar is deflected by 5°, which is 30°smaller than that under the gob. e rotation of principal stress direction, the increase in σ 1 , and the decrease in σ 3 can cause the expansion of the roof (top coal) cracks.

Data Availability
e datasets used during the study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare no conflicts of interest.