# Numerical Simulation of the Stress Field in Repeated Mining of Coal Seams Based onIn Situ Stress Measurement

Authors: Donghui Yang; Bohu Yang; Zhaoheng Lv; Yongming Li; Hongming Cheng; Zhangxuan Ning
Journal: Mathematical Problems in Engineering
 (2021)

---

## Abstract

We established an evaluation index of the rock mass stress state for underground coal mines using the strength-stress ratio based on the measuredin situ stress and the generalized Hoek–Brown strength criterion. Three 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). This 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. The working face was a three-dimensional geological model based on the log sheets. The 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. This provides a reference for optimized underground coal mining.


---

## Body

## 1. Introduction

The combination ofin situ stress and mining stress in underground coal mines forms a mining stress field. This 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. The 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. The World Stress Map (WSM) project [6] compiles the direction of the maximum horizontal principal stress (σH). 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 [7–12]. 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: σH > σh > σv (<150 m), σH > σv > σh (150–1000 m), and σv > σH > σh (>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, σH = 5.3367 ± 0.023 H, correlation coefficient R2 = 0.94, and σh = 0.6559 ± 0.017 H, R2 = 0.55; the dominant orientation of σH 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.Thein 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). The strength-stress ratio method is the most widely used method [16, 17], but it lacks a unified standard. The Sheorey model [5] has been widely recognized in engineering design since it can predict horizontal stress and address the discrete stress values. The evaluation parameters include weathered rock mass or shallow surface engineering areas, which do not conform to the actual condition of coal mines [18–22]; therefore, the stress state evaluation indicators based on in situ stress data are required.The strength-stress ratio method was used to establish the evaluation index for the stress state of the mine rock mass based on thein 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. The 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.


## 2.In Situ Stress Measurement in the Study Area

The 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. The coal seam has a simple structure with a stable layer, and it is a low-gas mine. The 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. The 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. The 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.Figure 1
In situ stress distribution in Burtai mine: (a) principal stress vs. depth and (b) k vs. depth [24].
(a)(b)The principal stress values are discrete but increase with an increase in depth (Figure1(a)) and the fitting equations are as follows (equation (1)). Three stress field distributions are present: σH > σh > σv (<172 m), σH > σv > σh (172–800 m), and σv > σH > σh (>800 m).(1)σH=2.0386+0.0241×Hσh=1.2091+0.0172×Hσv=−0.5257+0.0273×H.In Figure1(b), the variation of k ((σH + σh)/2σv) with depth is shown in equation (2) and compared with the k envelope (equation (3)) obtained by Brown and Hoek. The 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).(2)k=126H+0.62535H+0.285<k<350H+0.6,(3)k=800H+0.4100H+0.3<k<1500H+0.5.


## 3. Evaluation of the Stress State in Underground Coal Mining

### 3.1. Evaluation Index of the Stress State

The rock mass stress state affects the rock mass stability and includesin situ stress, rock mass strength, and rock mass structural quality. Several classification systems have been developed for rock mass. The rock quality designation (RQD), proposed by Deere in 1964 [25], is one of the simplest systems of rock mass classification. The 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. The Hoek–Brown strength criterion, developed in 1980 [28–31], 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. The parameters can be obtained qualitatively or quantitatively using conventional mechanical tests and field structure descriptions. The associated geological strength index (GSI) is widely used for estimating the strength and deformation of heavily jointed rock masses. The stress-based failure criteria developed by Coulomb, Mohr, and Hoek and Brown are extensively applied in rock mechanics. The 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:(4)σ1=σ3+σcimbσ3σci+sα,where mb, s, and α are the rock mass material constants, given by(5)mb=miexpGSI−10028−14Ds=expGSI−1009−3Dα=12+16exp−GSI15−exp−203,where σ1 and σ3 are the maximum and minimum principal stresses at failure, respectively; σci is the unconfined compressive strength; mb 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; mi, 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.Whenσtm < σ3 < σci/4, the expression is given by the following equation:(6)σcm=σcimb+4s−αmb−8smb/4+sα−121+α2+α.Incorporating equation (6) into the Hoek–Brown strength criterion, let η=1+μ2+μ2, σci = kmσcm. Then,(7)km=σciσcm=21+α2+αmb+4s−αmb−8smb/4+sα−1σcmσ1≥−mb+mb2+4sη−122ηskm.The relationship between theσcm/σ1 ratio and GSI for different friction coefficients is shown in Figure 2. With an increase in the friction coefficient, the σcm/σ1 ratio changes significantly. When 0.2 < μ < 0.6, σcm/σ1 ratio is between 0.01 and 0.3, when 0.6 < μ < 1.0, σcm/σ1 ratio lies between 0.05 and 0.7, and the σcm/σ1 ratio generally varies between 0.05 and 0.5.Figure 2
Relationship betweenσcm/σ1 and GSI under different friction coefficients. (a) μ = 0.3. (b) μ = 0.4. (c) μ = 0.5. (d) μ = 0.6. (e) μ = 0.7. (f) μ = 0.8.
(a)(b)(c)(d)(e)(f)The relationship between theσcm/σ1 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.Figure 3
Relationship betweenσcm/σ1 and GSI under different disturbance coefficients. (a) μ = 0.3, mi = 24. (b) μ = 0.6, mi = 24.
(a)(b)Thein 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 mi = 24, the ratio of roadway excavation to σcm/σ1 does not exceed 0.02; when μ = 0.6 and mi = 24, the ratio of roadway excavation to σcm/σ1 exceeds 0.1. Therefore, the mining roadway is less sensitive to D compared to GSI.The coal-measure strata are clastic sedimentary rocks, mainly sandstone. The values ofmi 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. The GSI of the surrounding rock of the coal seam is above 30–40. The friction coefficient of sandstones ranges between 0.1 and 0.6, with an average of 0.3. The σcm/σ1 ratio of sandstone in most coal-measure strata lies between 0.1 and 0.4 for different friction coefficients. The higher boundary value of the σcm/σ1 ratio is suitable for most rock mass stress state evaluation of coal-measure strata. The rock mass stress will significantly impact its stability for σcm/σ1 < 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. Therefore, the stress concentration factor should be considered for calculating the maximum principal stress in the rock mass; hence,σ1 can be expressed as(8)σ1=ησ1m,where η is the maximum stress concentration factor of the rock mass around the roadway and σ1m is the measured maximum principal stress.The 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. The 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 σcm/σ1m < 1.4, which corresponds to a high in situ stress state. The corners where the two working faces meet experience stress concentration seven times the vertical stress of the original rock, or even higher. The rock mass failure occurs locally in the roadway section for η = 9.0 and 1.4 < σcm/σ1m < 3.6, and the stress state corresponds to the middle in situ stress state. When σcm/σ1m > 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 strength-stress ratio, the evaluation index for the rock mass stress state of coal mines is presented in Table 1.Table 1
Evaluation index of the rock mass stress state by the strength-stress ratio.
Evaluation indexIndex valueHighMiddleLowσcm/σ1m<1.41.4∼3.6>3.6σcm 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; σ1m 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.


### 3.2. Engineering Verification

The relationship betweenσcm/σ1m 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). The roof and floor data around the 22#, 42#, and 52# down coal seams are shown in Figure 4(b), where σci is the average uniaxial compressive strength of the rock, σcm is the average rock mass strength, and σ1m 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. The parameters are listed in Tables 2 and 3.Figure 4
σcm/σ1m vs. depth: (a) all rock formations and (b) roof and floor.
(a)(b)Table 2
Rock mass strength estimation and measured maximum principal stress.
Drilling numberLithologyDepth (m)σci (MPa)σ1m (MPa)CRP (%)GSImiσcm (MPa)σcm/σ1mEm (GPa)BK212Coarse sandstone1029.285.174955152.180.424.06Medium sandstone2036.143.812850151.300.342.48Sandy mudstone3047.963.328270152.630.798.92Fine sandstone40621.419.642750154.530.474.63Fine sandstone51043.4414.4699802121.241.4737.06Fine sandstone59040.4513.6693902126.901.9763.60BK209Sandy mudstone22212.524.908975134.460.9114.92Fine sandstone33023.538.7788752110.101.1520.46Fine sandstone40326.2712.1090902117.471.4451.25Siltstone49736.3913.4862651811.570.8614.31BK213Fine sandstone30022.915.745960217.021.228.51Siltstone40034.2210.8689751813.801.2724.67Siltstone46933.0411.9189751813.331.1224.24Fine sandstone532128.9415.6273602139.522.5317.78BK207Coarse sandstone10048.625.5464601813.862.5012.40Coarse sandstone20112.915.848875185.210.8915.15Coarse sandstone26018.8616.644465216.000.3610.30Siltstone30133.189.9792801815.331.5432.39Medium sandstone362116.2517.9755601833.141.8417.78Siltstone40051.6418.1998802125.251.3940.41Siltstone44965.4617.9754602120.061.1214.39BK220Coarse sandstone8346.624.7244501710.492.229.11Coarse sandstone1505.674.899280212.770.5713.39Coarse sandstone28577.9210.7896701727.112.5127.91Medium sandstone37590.8512.9799701731.612.4430.14Coarse sandstone43022.4410.057560216.880.688.42Sandy mudstone56251.4019.5795952123.271.1940.32Medium sandstone60384.6417.0465602125.941.5216.36Table 3
Strength estimation and measured maximum principal stress in the roof and floor.
Rock formationLithologyDepth (m)σci (MPa)σ1m (MPa)CRP (%)GSImiσcm (MPa)σcm/σ1mEm (GPa)22# coal roofFine sandstone40228.8713.8190902114.111.0225.68Fine sandstone40622.0811.2890902110.790.9622.46Fine sandstone40624.3110.7790902111.891.1023.5722# coal floorMedium sandstone36687.0014.5255601826.661.8416.59Medium sandstone355170.5516.7955601852.273.1117.78Medium sandstone36591.1918.6155601827.951.5016.9842# coal roofSiltstone40051.2717.2798802125.071.4540.27Siltstone40049.0418.3198802123.981.3139.38Siltstone40054.6118.9998802126.701.4141.56Fine sandstone51031.8716.5499802115.580.9431.75Fine sandstone51033.5013.5199802116.381.2132.55Fine sandstone51059.5815.4099802129.131.8943.4142# coal floorSiltstone47040.9014.1589751816.501.1726.97Siltstone47135.5912.4689751814.351.1525.16Siltstone47121.5212.468975188.680.7019.5652# down coal roofFine sandstone532172.2718.8173602152.802.8117.78Fine sandstone53395.4314.1173602129.252.0717.37Fine sandstone533148.6511.0973602145.564.1117.78Fine sandstone59025.3312.4393902112.371.0024.04Fine sandstone59042.2715.6293902120.681.3231.09Fine sandstone58958.8015.6193902128.751.8436.6552# down coal floorMedium sandstone60362.7215.3565602119.221.2514.08Medium sandstone603136.1115.2265602141.712.7417.78Medium sandstone60655.0820.5565602116.880.8213.20Figure4(a) shows 89 measuring points in the Burtai mine, of which 59, with σcm/σ1m < 1.4, account for 66.3% of the total; 27, with 1.4 < σcm/σ1m < 3.6, account for 30.3%; and 3, with σcm/σ1m > 3.6, account for 3.4%. In Figure 4(b), among the 24 measuring points in Burtai mine, 11, with σcm/σ1m < 1.4, account for 45.8% of the total; 12, with 1.4 < σcm/σ1m < 3.6, account for 50.0%; and 1, with σcm/σ1m > 3.6, accounts for 4.2%. The average values of σcm/σ1m of the roof and floor around 22#, 42#, and 52# down coal seams were 1.59, 1.25, and 2.00, respectively. The groups with σcm/σ1m < 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. The ratio of σcm/σ1m < 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 withσh < 10 MPa account for 43.8% of the total; 42 with 10 < σH < 18 MPa account for 47.2%; and 8 with σH > 18 MPa account for 9%. Among them, 34 groups were above 350 m, of which 29 groups with σh < 10 MPa, account for 85.3%; 55 groups were below 350 m, of which 11 groups with σh < 10 MPa account for 20%; and 65.5% groups have 10 < σh < 18 MPa. Therefore, 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 (σ1 + σ2 + σ3)/σV > 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.The 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 highin situ stress along with an increase in the accumulated elastic energy. This 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.


## 3.1. Evaluation Index of the Stress State

The rock mass stress state affects the rock mass stability and includesin situ stress, rock mass strength, and rock mass structural quality. Several classification systems have been developed for rock mass. The rock quality designation (RQD), proposed by Deere in 1964 [25], is one of the simplest systems of rock mass classification. The 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. The Hoek–Brown strength criterion, developed in 1980 [28–31], 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. The parameters can be obtained qualitatively or quantitatively using conventional mechanical tests and field structure descriptions. The associated geological strength index (GSI) is widely used for estimating the strength and deformation of heavily jointed rock masses. The stress-based failure criteria developed by Coulomb, Mohr, and Hoek and Brown are extensively applied in rock mechanics. The 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:(4)σ1=σ3+σcimbσ3σci+sα,where mb, s, and α are the rock mass material constants, given by(5)mb=miexpGSI−10028−14Ds=expGSI−1009−3Dα=12+16exp−GSI15−exp−203,where σ1 and σ3 are the maximum and minimum principal stresses at failure, respectively; σci is the unconfined compressive strength; mb 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; mi, 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.Whenσtm < σ3 < σci/4, the expression is given by the following equation:(6)σcm=σcimb+4s−αmb−8smb/4+sα−121+α2+α.Incorporating equation (6) into the Hoek–Brown strength criterion, let η=1+μ2+μ2, σci = kmσcm. Then,(7)km=σciσcm=21+α2+αmb+4s−αmb−8smb/4+sα−1σcmσ1≥−mb+mb2+4sη−122ηskm.The relationship between theσcm/σ1 ratio and GSI for different friction coefficients is shown in Figure 2. With an increase in the friction coefficient, the σcm/σ1 ratio changes significantly. When 0.2 < μ < 0.6, σcm/σ1 ratio is between 0.01 and 0.3, when 0.6 < μ < 1.0, σcm/σ1 ratio lies between 0.05 and 0.7, and the σcm/σ1 ratio generally varies between 0.05 and 0.5.Figure 2
Relationship betweenσcm/σ1 and GSI under different friction coefficients. (a) μ = 0.3. (b) μ = 0.4. (c) μ = 0.5. (d) μ = 0.6. (e) μ = 0.7. (f) μ = 0.8.
(a)(b)(c)(d)(e)(f)The relationship between theσcm/σ1 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.Figure 3
Relationship betweenσcm/σ1 and GSI under different disturbance coefficients. (a) μ = 0.3, mi = 24. (b) μ = 0.6, mi = 24.
(a)(b)Thein 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 mi = 24, the ratio of roadway excavation to σcm/σ1 does not exceed 0.02; when μ = 0.6 and mi = 24, the ratio of roadway excavation to σcm/σ1 exceeds 0.1. Therefore, the mining roadway is less sensitive to D compared to GSI.The coal-measure strata are clastic sedimentary rocks, mainly sandstone. The values ofmi 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. The GSI of the surrounding rock of the coal seam is above 30–40. The friction coefficient of sandstones ranges between 0.1 and 0.6, with an average of 0.3. The σcm/σ1 ratio of sandstone in most coal-measure strata lies between 0.1 and 0.4 for different friction coefficients. The higher boundary value of the σcm/σ1 ratio is suitable for most rock mass stress state evaluation of coal-measure strata. The rock mass stress will significantly impact its stability for σcm/σ1 < 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. Therefore, the stress concentration factor should be considered for calculating the maximum principal stress in the rock mass; hence,σ1 can be expressed as(8)σ1=ησ1m,where η is the maximum stress concentration factor of the rock mass around the roadway and σ1m is the measured maximum principal stress.The 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. The 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 σcm/σ1m < 1.4, which corresponds to a high in situ stress state. The corners where the two working faces meet experience stress concentration seven times the vertical stress of the original rock, or even higher. The rock mass failure occurs locally in the roadway section for η = 9.0 and 1.4 < σcm/σ1m < 3.6, and the stress state corresponds to the middle in situ stress state. When σcm/σ1m > 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 strength-stress ratio, the evaluation index for the rock mass stress state of coal mines is presented in Table 1.Table 1
Evaluation index of the rock mass stress state by the strength-stress ratio.
Evaluation indexIndex valueHighMiddleLowσcm/σ1m<1.41.4∼3.6>3.6σcm 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; σ1m 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.


## 3.2. Engineering Verification

The relationship betweenσcm/σ1m 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). The roof and floor data around the 22#, 42#, and 52# down coal seams are shown in Figure 4(b), where σci is the average uniaxial compressive strength of the rock, σcm is the average rock mass strength, and σ1m 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. The parameters are listed in Tables 2 and 3.Figure 4
σcm/σ1m vs. depth: (a) all rock formations and (b) roof and floor.
(a)(b)Table 2
Rock mass strength estimation and measured maximum principal stress.
Drilling numberLithologyDepth (m)σci (MPa)σ1m (MPa)CRP (%)GSImiσcm (MPa)σcm/σ1mEm (GPa)BK212Coarse sandstone1029.285.174955152.180.424.06Medium sandstone2036.143.812850151.300.342.48Sandy mudstone3047.963.328270152.630.798.92Fine sandstone40621.419.642750154.530.474.63Fine sandstone51043.4414.4699802121.241.4737.06Fine sandstone59040.4513.6693902126.901.9763.60BK209Sandy mudstone22212.524.908975134.460.9114.92Fine sandstone33023.538.7788752110.101.1520.46Fine sandstone40326.2712.1090902117.471.4451.25Siltstone49736.3913.4862651811.570.8614.31BK213Fine sandstone30022.915.745960217.021.228.51Siltstone40034.2210.8689751813.801.2724.67Siltstone46933.0411.9189751813.331.1224.24Fine sandstone532128.9415.6273602139.522.5317.78BK207Coarse sandstone10048.625.5464601813.862.5012.40Coarse sandstone20112.915.848875185.210.8915.15Coarse sandstone26018.8616.644465216.000.3610.30Siltstone30133.189.9792801815.331.5432.39Medium sandstone362116.2517.9755601833.141.8417.78Siltstone40051.6418.1998802125.251.3940.41Siltstone44965.4617.9754602120.061.1214.39BK220Coarse sandstone8346.624.7244501710.492.229.11Coarse sandstone1505.674.899280212.770.5713.39Coarse sandstone28577.9210.7896701727.112.5127.91Medium sandstone37590.8512.9799701731.612.4430.14Coarse sandstone43022.4410.057560216.880.688.42Sandy mudstone56251.4019.5795952123.271.1940.32Medium sandstone60384.6417.0465602125.941.5216.36Table 3
Strength estimation and measured maximum principal stress in the roof and floor.
Rock formationLithologyDepth (m)σci (MPa)σ1m (MPa)CRP (%)GSImiσcm (MPa)σcm/σ1mEm (GPa)22# coal roofFine sandstone40228.8713.8190902114.111.0225.68Fine sandstone40622.0811.2890902110.790.9622.46Fine sandstone40624.3110.7790902111.891.1023.5722# coal floorMedium sandstone36687.0014.5255601826.661.8416.59Medium sandstone355170.5516.7955601852.273.1117.78Medium sandstone36591.1918.6155601827.951.5016.9842# coal roofSiltstone40051.2717.2798802125.071.4540.27Siltstone40049.0418.3198802123.981.3139.38Siltstone40054.6118.9998802126.701.4141.56Fine sandstone51031.8716.5499802115.580.9431.75Fine sandstone51033.5013.5199802116.381.2132.55Fine sandstone51059.5815.4099802129.131.8943.4142# coal floorSiltstone47040.9014.1589751816.501.1726.97Siltstone47135.5912.4689751814.351.1525.16Siltstone47121.5212.468975188.680.7019.5652# down coal roofFine sandstone532172.2718.8173602152.802.8117.78Fine sandstone53395.4314.1173602129.252.0717.37Fine sandstone533148.6511.0973602145.564.1117.78Fine sandstone59025.3312.4393902112.371.0024.04Fine sandstone59042.2715.6293902120.681.3231.09Fine sandstone58958.8015.6193902128.751.8436.6552# down coal floorMedium sandstone60362.7215.3565602119.221.2514.08Medium sandstone603136.1115.2265602141.712.7417.78Medium sandstone60655.0820.5565602116.880.8213.20Figure4(a) shows 89 measuring points in the Burtai mine, of which 59, with σcm/σ1m < 1.4, account for 66.3% of the total; 27, with 1.4 < σcm/σ1m < 3.6, account for 30.3%; and 3, with σcm/σ1m > 3.6, account for 3.4%. In Figure 4(b), among the 24 measuring points in Burtai mine, 11, with σcm/σ1m < 1.4, account for 45.8% of the total; 12, with 1.4 < σcm/σ1m < 3.6, account for 50.0%; and 1, with σcm/σ1m > 3.6, accounts for 4.2%. The average values of σcm/σ1m of the roof and floor around 22#, 42#, and 52# down coal seams were 1.59, 1.25, and 2.00, respectively. The groups with σcm/σ1m < 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. The ratio of σcm/σ1m < 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 withσh < 10 MPa account for 43.8% of the total; 42 with 10 < σH < 18 MPa account for 47.2%; and 8 with σH > 18 MPa account for 9%. Among them, 34 groups were above 350 m, of which 29 groups with σh < 10 MPa, account for 85.3%; 55 groups were below 350 m, of which 11 groups with σh < 10 MPa account for 20%; and 65.5% groups have 10 < σh < 18 MPa. Therefore, 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 (σ1 + σ2 + σ3)/σV > 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.The 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 highin situ stress along with an increase in the accumulated elastic energy. This 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.


## 4. Numerical Simulation of the Stress Field in Repeated Mining of Coal Seams

### 4.1. 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]. The 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). The spatial position of the working face is illustrated in Figure 6. The 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. The initial conditions of the model are determined in combination with the measured in situ stress regression model (equation (1)).Figure 5
Refined numerical geological model of the working face.Figure 6
Layout diagram of the spatial arrangement of the working face.The 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]. The tensile strength of rock mass (σtm) is calculated by RocLab 1.0 software (Table 4).Table 4
Physical and mechanical parameters of the model strata.
Lithologyρ (kg·m−3)E (GPa)νG (GPa)K (GPa)C (MPa)φ (°)σtm (MPa)Loess16000.300.310.260.110.0313.000.03Gravelly coarse sandstone24281.310.291.040.515.4035.100.79Siltstone 122261.430.331.400.546.5830.240.75Sandy mudstone 122281.180.311.040.456.9027.641.39Coarse sandstone22241.790.311.570.688.8325.891.81Medium sandstone23476.370.295.062.4714.8030.753.16Fine sandstone 123296.980.316.122.6614.6030.003.28Sandy mudstone 223227.060.295.602.7411.1033.271.3522# coal seam14004.080.283.091.591.1325.000.82Fine sandstone 221776.710.315.892.5610.8035.601.82Sandy mudstone 323519.440.256.293.7823.0328.075.0842# up coal seam13204.620.314.051.764.2126.100.55Fine sandstone 323187.800.316.842.9818.2032.254.24Sandy mudstone 4238310.480.226.244.3024.5026.505.07Siltstone 223348.860.307.383.4117.6531.053.45The 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:(9)σv=E0ε1−ε/εm,where σv is the vertical stress of the caving zone in the gob (MPa); ε is the vertical strain, εm is the maximum vertical strain, taken as εm = (b – 1)/b; b is the comprehensive crushing expansion coefficient of the rock mass in the caving zone, calculated using the caving zone Hc = h/(b – 1); E0 is the initial elasticity modulus of the rock mass, MPa, calculated using E0 = 10.39σc1.042/b7.7 [35]; and σc is the uniaxial compressive strength (UCS) of the rock mass in the caving zone, MPa.The 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. The 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. The heights of the caving zone (Hc) and the fissure zone (Hf) can be calculated using equations (10) and (11) and Table 5 [35–37]. The 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 εm is 0.19 and 0.22, respectively. The mechanical parameters of the caving zone rock mass in the gob are tabulated in Table 6.(10)Hc=100hc1h+c2,(11)Hf=100hc3h+c4.Table 5
Mining height and strength coefficient of the roof.
Lithologyσc (MPa)c1c2c3c4Hard rock strata>402.1161.22Medium-hard strata20–404.7191.63.6Soft strata<206.2323.15Table 6
Mechanical parameters of the rock mass in the caving zone.
LithologyK (GPa)G (GPa)γ (kg·m−3)C (MPa)φ (°)σtm (MPa)22# roof14.0810.5618000.00135042# roof9.567.1719000.001400


### 4.2. Results and Analysis

The impact of the overlying pillar on the mining face was determined using simulations of simultaneous upper and lower coal seam mining. The widths of overlying 22# coal seam pillars are 5 m, 15 m, 25 m, 35 m, and 45 m. Coal seam 42# lags the 22# coal seam by 300 m, and the excavation distance is 300 m. Two survey lines (117 m and 200 m from the return roadway) on strike and one survey line (5 m from the rib) in an inclined direction are arranged on the main roof of the 42107 working face at the height of 25 m from the working face. The principal stress distribution of the main roof under different pillars and the gob is monitored, as shown in Figure7.Figure 7
Distribution of principal stress on the main roof strike line. (a) Value of σ1 under the pillar. (b) Direction of σ1 under the pillar. (c) Value of σ1 under the gob. (d) Direction of σ1 under the gob.
(a)(b)(c)(d)


#### 4.2.1. Maximum Principal Stress Distribution on the Strike

σ1 of the main roof (380 m deep) above 42# coal seam increases by 10 MPa when advancing 350 m because of the overlying pillars of 22# coal seam (Figures 7(a) and 7(c)). The principal stress increases by different degrees with the increase in the width of the pillar from 300 m. The larger the pillar width, the faster the increase in stress. The increase rate increases from 60 m advances and reaches the maximum for 4–9 m advances. The 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 σ1 increases with an increase in pillar width, the rate of increase reduces, while the principal stress influence ranges remain unchanged. The 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. The distribution of σ1 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.The roofσ1 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)). The angle between the σ1 direction and the z-axis is 6° for advancing 350 m, and it is biased towards the gob. The angle increases to 13° from advancing 300 m and gradually decreases to 3° for 50 m. The 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. The deviation of the σ1 direction below the pillar remains constant beyond 350 m and is subsequently affected by the overlying coal mining. The angle between the σ1 direction and the z-axis increases sharply to 68° within advancing 350 m to 250 m. Subsequently, reverse deflection occurs, and the angle decreases. The 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 σ1 direction continues to deflect to the gob, and the deflection reaches 60° for 25 m behind the gob. The main roof σ1 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. The 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]. The 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. The 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 σ1 rotates to the dominant angle, the maximum tensile stress reaches the tensile strength of the roof, and the microcracks in the top coal expand. The expansion of the roof (top coal) cracks can be attributed to the principal stress rotation, the increase in σ1, and the decrease in σ3.


#### 4.2.2. Maximum Principal Stress and Deviator Stress in the Inclined Direction

The principal stress distribution of the main roof has a “single-peak” shape (Figure8) along the inclined direction and 5 m in front of the rib with high values under the pillar and low values on both sides. With an increase in the pillar width, the peak coefficients of σ1 increase, the range of increase reduces, and the severe influence range increases. The principal stress peak coefficients are 1.91, 2.11, 2.26, 2.35, and 2.43, respectively, under different pillar widths of 5 m, 15 m, 25 m, 35 m, and 45 m, and the severe influence range is between 100 and 150 m. Both sides of the working face are affected by the overlying pillar. Although the principal stress increases with an increase in the pillar width, the increase is much smaller than that under the pillar. The σ1 of the main roof on the strike survey line under the pillar is 1.5 times that under the gob. Similar to the σ1 distribution, the deviator stress on inclined direction also presents a “single-peak” shape, with peak values of 15.8, 18.1, 19.8, 20.7, and 21.4 MPa, respectively, under different pillar widths of 5 m, 15 m, 25 m, 35 m, and 45 m.Figure 8
Distribution of principal stress on the main roof trend line: (a)σ1 and (b) σ1–σ3.
(a)(b)The deviator stress is the largest within the severe influence range of the pillar and fluctuates significantly. The 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.


## 4.1. 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]. The 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). The spatial position of the working face is illustrated in Figure 6. The 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. The initial conditions of the model are determined in combination with the measured in situ stress regression model (equation (1)).Figure 5
Refined numerical geological model of the working face.Figure 6
Layout diagram of the spatial arrangement of the working face.The 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]. The tensile strength of rock mass (σtm) is calculated by RocLab 1.0 software (Table 4).Table 4
Physical and mechanical parameters of the model strata.
Lithologyρ (kg·m−3)E (GPa)νG (GPa)K (GPa)C (MPa)φ (°)σtm (MPa)Loess16000.300.310.260.110.0313.000.03Gravelly coarse sandstone24281.310.291.040.515.4035.100.79Siltstone 122261.430.331.400.546.5830.240.75Sandy mudstone 122281.180.311.040.456.9027.641.39Coarse sandstone22241.790.311.570.688.8325.891.81Medium sandstone23476.370.295.062.4714.8030.753.16Fine sandstone 123296.980.316.122.6614.6030.003.28Sandy mudstone 223227.060.295.602.7411.1033.271.3522# coal seam14004.080.283.091.591.1325.000.82Fine sandstone 221776.710.315.892.5610.8035.601.82Sandy mudstone 323519.440.256.293.7823.0328.075.0842# up coal seam13204.620.314.051.764.2126.100.55Fine sandstone 323187.800.316.842.9818.2032.254.24Sandy mudstone 4238310.480.226.244.3024.5026.505.07Siltstone 223348.860.307.383.4117.6531.053.45The 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:(9)σv=E0ε1−ε/εm,where σv is the vertical stress of the caving zone in the gob (MPa); ε is the vertical strain, εm is the maximum vertical strain, taken as εm = (b – 1)/b; b is the comprehensive crushing expansion coefficient of the rock mass in the caving zone, calculated using the caving zone Hc = h/(b – 1); E0 is the initial elasticity modulus of the rock mass, MPa, calculated using E0 = 10.39σc1.042/b7.7 [35]; and σc is the uniaxial compressive strength (UCS) of the rock mass in the caving zone, MPa.The 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. The 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. The heights of the caving zone (Hc) and the fissure zone (Hf) can be calculated using equations (10) and (11) and Table 5 [35–37]. The 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 εm is 0.19 and 0.22, respectively. The mechanical parameters of the caving zone rock mass in the gob are tabulated in Table 6.(10)Hc=100hc1h+c2,(11)Hf=100hc3h+c4.Table 5
Mining height and strength coefficient of the roof.
Lithologyσc (MPa)c1c2c3c4Hard rock strata>402.1161.22Medium-hard strata20–404.7191.63.6Soft strata<206.2323.15Table 6
Mechanical parameters of the rock mass in the caving zone.
LithologyK (GPa)G (GPa)γ (kg·m−3)C (MPa)φ (°)σtm (MPa)22# roof14.0810.5618000.00135042# roof9.567.1719000.001400


## 4.2. Results and Analysis

The impact of the overlying pillar on the mining face was determined using simulations of simultaneous upper and lower coal seam mining. The widths of overlying 22# coal seam pillars are 5 m, 15 m, 25 m, 35 m, and 45 m. Coal seam 42# lags the 22# coal seam by 300 m, and the excavation distance is 300 m. Two survey lines (117 m and 200 m from the return roadway) on strike and one survey line (5 m from the rib) in an inclined direction are arranged on the main roof of the 42107 working face at the height of 25 m from the working face. The principal stress distribution of the main roof under different pillars and the gob is monitored, as shown in Figure7.Figure 7
Distribution of principal stress on the main roof strike line. (a) Value of σ1 under the pillar. (b) Direction of σ1 under the pillar. (c) Value of σ1 under the gob. (d) Direction of σ1 under the gob.
(a)(b)(c)(d)


### 4.2.1. Maximum Principal Stress Distribution on the Strike

σ1 of the main roof (380 m deep) above 42# coal seam increases by 10 MPa when advancing 350 m because of the overlying pillars of 22# coal seam (Figures 7(a) and 7(c)). The principal stress increases by different degrees with the increase in the width of the pillar from 300 m. The larger the pillar width, the faster the increase in stress. The increase rate increases from 60 m advances and reaches the maximum for 4–9 m advances. The 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 σ1 increases with an increase in pillar width, the rate of increase reduces, while the principal stress influence ranges remain unchanged. The 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. The distribution of σ1 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.The roofσ1 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)). The angle between the σ1 direction and the z-axis is 6° for advancing 350 m, and it is biased towards the gob. The angle increases to 13° from advancing 300 m and gradually decreases to 3° for 50 m. The 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. The deviation of the σ1 direction below the pillar remains constant beyond 350 m and is subsequently affected by the overlying coal mining. The angle between the σ1 direction and the z-axis increases sharply to 68° within advancing 350 m to 250 m. Subsequently, reverse deflection occurs, and the angle decreases. The 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 σ1 direction continues to deflect to the gob, and the deflection reaches 60° for 25 m behind the gob. The main roof σ1 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. The 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]. The 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. The 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 σ1 rotates to the dominant angle, the maximum tensile stress reaches the tensile strength of the roof, and the microcracks in the top coal expand. The expansion of the roof (top coal) cracks can be attributed to the principal stress rotation, the increase in σ1, and the decrease in σ3.


### 4.2.2. Maximum Principal Stress and Deviator Stress in the Inclined Direction

The principal stress distribution of the main roof has a “single-peak” shape (Figure8) along the inclined direction and 5 m in front of the rib with high values under the pillar and low values on both sides. With an increase in the pillar width, the peak coefficients of σ1 increase, the range of increase reduces, and the severe influence range increases. The principal stress peak coefficients are 1.91, 2.11, 2.26, 2.35, and 2.43, respectively, under different pillar widths of 5 m, 15 m, 25 m, 35 m, and 45 m, and the severe influence range is between 100 and 150 m. Both sides of the working face are affected by the overlying pillar. Although the principal stress increases with an increase in the pillar width, the increase is much smaller than that under the pillar. The σ1 of the main roof on the strike survey line under the pillar is 1.5 times that under the gob. Similar to the σ1 distribution, the deviator stress on inclined direction also presents a “single-peak” shape, with peak values of 15.8, 18.1, 19.8, 20.7, and 21.4 MPa, respectively, under different pillar widths of 5 m, 15 m, 25 m, 35 m, and 45 m.Figure 8
Distribution of principal stress on the main roof trend line: (a)σ1 and (b) σ1–σ3.
(a)(b)The deviator stress is the largest within the severe influence range of the pillar and fluctuates significantly. The 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.


## 4.2.1. Maximum Principal Stress Distribution on the Strike

σ1 of the main roof (380 m deep) above 42# coal seam increases by 10 MPa when advancing 350 m because of the overlying pillars of 22# coal seam (Figures 7(a) and 7(c)). The principal stress increases by different degrees with the increase in the width of the pillar from 300 m. The larger the pillar width, the faster the increase in stress. The increase rate increases from 60 m advances and reaches the maximum for 4–9 m advances. The 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 σ1 increases with an increase in pillar width, the rate of increase reduces, while the principal stress influence ranges remain unchanged. The 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. The distribution of σ1 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.The roofσ1 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)). The angle between the σ1 direction and the z-axis is 6° for advancing 350 m, and it is biased towards the gob. The angle increases to 13° from advancing 300 m and gradually decreases to 3° for 50 m. The 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. The deviation of the σ1 direction below the pillar remains constant beyond 350 m and is subsequently affected by the overlying coal mining. The angle between the σ1 direction and the z-axis increases sharply to 68° within advancing 350 m to 250 m. Subsequently, reverse deflection occurs, and the angle decreases. The 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 σ1 direction continues to deflect to the gob, and the deflection reaches 60° for 25 m behind the gob. The main roof σ1 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. The 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]. The 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. The 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 σ1 rotates to the dominant angle, the maximum tensile stress reaches the tensile strength of the roof, and the microcracks in the top coal expand. The expansion of the roof (top coal) cracks can be attributed to the principal stress rotation, the increase in σ1, and the decrease in σ3.


## 4.2.2. Maximum Principal Stress and Deviator Stress in the Inclined Direction

The principal stress distribution of the main roof has a “single-peak” shape (Figure8) along the inclined direction and 5 m in front of the rib with high values under the pillar and low values on both sides. With an increase in the pillar width, the peak coefficients of σ1 increase, the range of increase reduces, and the severe influence range increases. The principal stress peak coefficients are 1.91, 2.11, 2.26, 2.35, and 2.43, respectively, under different pillar widths of 5 m, 15 m, 25 m, 35 m, and 45 m, and the severe influence range is between 100 and 150 m. Both sides of the working face are affected by the overlying pillar. Although the principal stress increases with an increase in the pillar width, the increase is much smaller than that under the pillar. The σ1 of the main roof on the strike survey line under the pillar is 1.5 times that under the gob. Similar to the σ1 distribution, the deviator stress on inclined direction also presents a “single-peak” shape, with peak values of 15.8, 18.1, 19.8, 20.7, and 21.4 MPa, respectively, under different pillar widths of 5 m, 15 m, 25 m, 35 m, and 45 m.Figure 8
Distribution of principal stress on the main roof trend line: (a)σ1 and (b) σ1–σ3.
(a)(b)The deviator stress is the largest within the severe influence range of the pillar and fluctuates significantly. The 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.


## 5. Conclusion

The strength-stress ratio method was used to establish the evaluation index for the stress state of the mine rock mass based on thein 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. The 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 highin situ stress state for σcm/σ1m < 1.4, medium in situ stress state for 1.4 < σcm/σ1m < 3.6, and low in situ stress state for σcm/σ1m > 3.6.(2)
The index is applied in the Burtai mine and classifies it as a medium-highin situ stress field, which is in agreement with the on-site situation, establishing the reliability of the index.(3)
The value and direction of the main roofσ1 within the range of the front abutment pressure under the pillar and gob vary significantly because of the mining of the overlying coal seam. The value of σ1 under the pillar along the main roof strike direction 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. The rotation of principal stress direction, the increase in σ1, and the decrease in σ3 can cause the expansion of the roof (top coal) cracks.



---

*Source: 3588868-2021-11-09.xml*