Stability evaluation of goaf in closed mining area: a case study of Sanhejian closed mining area in Jiangsu Province, China

Stability evaluation of goaf in closed mining area: a case study of Sanhejian closed mining area in Jiangsu Province, China | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Stability evaluation of goaf in closed mining area: a case study of Sanhejian closed mining area in Jiangsu Province, China Zhanghao Shi, Weiqiang Zhang, Fengming Zhang, Yue Luo, Shangbin Chen, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4425036/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The stability of goaf is one of the decisive conditions for the redevelopment and utilization of underground spaces after mine closure. Taking the Sanhejian closed mine area as an example, this study comprehensively evaluates the stability of the goaf using numerical simulation, Analytic Hierarchy Process (AHP), and Vulnerability Index (VI). Firstly, the numerical model of the goaf was built using FLAC 3D software to obtain the stress field, displacement field, and characteristics of plastic zone development. Based on the simulation results, stability evaluation criteria for the goaf were formulated, and stability levels were determined. Secondly, a vulnerability assessment model was established using AHP, selecting geological factors, mining factors, and hydrological factors as primary indicators and further determining eight secondary indicators, including geological structural complexity, roof lithology and thickness, geostress, stop mining time, depth-to-coal ratio, goaf width, goaf area, and water volume in goaf. The weights of each indicator were determined, and the indicators were quantified to calculate the VI value of the vulnerability assessment model. The stability zoning threshold of the goaf was obtained using a natural breakpoint classification method and verified against the numerical simulation results to enhance the accuracy of stability evaluation. By integrating the results of both methods and adhering to a conservative risk assessment principle, the stability level of the goaf was ultimately determined, providing reference for the stability evaluation of related underground spaces. Closed coal mine Goaf stability Numerical simulation Vulnerability index Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Introduction Due to decades of intensive mining, the Sanhejian coal mine has formed a large-scale group of goaf areas within the mining area, leaving behind substantial underground space resources after closure (Jing Qian et al.). The current development patterns of underground space resources mainly include the construction of underground gas storage facilities and underground energy storage stations. However, the stability of the goaf determines the prospects for the utilization of underground space resources in closed mines. If the stability of the goaf is poor, it not only restricts the utilization of space resources but also poses risks of collapse or geological changes, which may lead to damage to surrounding structures and affect their safe operation (Liu et al. 2021 ; Li et al. 2023 ; Zhang et al. 2023b ). Therefore, studying the stability of the goaf in the Sanhejian closed coal mine is crucial for its redevelopment and utilization. The stochastic, fuzzy, and uncertain nature of factors influencing goaf stability severely impedes the evaluation of goaf stability (Guo et al. 2024 ; Li et al. 2024 ). Research methods in goaf stability assessment mainly focus on numerical simulation and theoretical analysis (Ao et al. 2017 ; Yuan et al. 2023 ; Zhang et al. 2023c ). In numerical simulation research methods, Yang (Yang et al. 2019 ) utilized theoretical analysis and numerical simulation to analyze the key strata fracture mechanism, stress distribution laws, and influencing factors under mining influence, revealing that horizontal stress on roadways is more prominent than vertical stress. Luo (Luo et al. 2015 )based on precise measurements of goaf models using CMS, coupled Surpac and Midas-Gts, combined with the basic equations of stress-permeability in equivalent continuum mechanics and disturbance equivalent load theory in deep-hole blasting, conducted numerical analysis on the stability of mining area under the coupling of stress-permeability-dynamic disturbance. Wang (Wang et al. 2023 ), through PFC numerical simulation, found a close correlation between the mechanical properties of RCG (rock-like specimens containing goaf) and the fractal dimension (FD) of the goaf. Peak stress, peak strain, and elastic modulus are linearly negatively correlated with FD. In addition to numerical simulation methods, grey system theory, fuzzy comprehensive evaluation, etc., are widely applied in mining disaster prediction (Qin et al. 2019 ; Han et al. 2022 ). Guo (Guo et al. 2019 ) et al. evaluated the unstable risk of the construction site of a highway above abandoned goaf using fuzzy theory and grey theory analysis, ultimately deciding to use geogrids for the roadbed based on the analysis. Liu (Liu et al. 2022 ), combined with numerical simulation results, predicted the subsidence deformation of the mine under thick loose layers using grey relational analysis, finding that coal thickness has the greatest impact on maximum settlement, while cohesion is the smallest factor. He (He et al. 2022 ) established a goaf stability model using fuzzy comprehensive evaluation and determined the treatment method for the goaf based on the results of this model. Wu (Wu et al. 2018 ) similarly conducted a fuzzy comprehensive evaluation of the ground stability of the goaf and effectively validated it based on actual site conditions. Current research on goaf stability mostly focuses on pre-mining or during mining stages (Cai et al. 2021 ; Tao et al. 2022 ), while the closure of coal mines, due to complex and unknown underground conditions, cannot be continuously monitored, leading to limited research on goaf stability in closed coal mines, which requires further exploration. This paper evaluates the stability of goaf areas within closed coal mines through a combination of comprehensive numerical simulation and AHP-based Vulnerability Index. Ultimately, the stability levels derived from both methods are integrated based on a conservative risk principle. The aim is to provide evaluation guidance for the utilization of underground spaces within the Sanhejian closed mine area, with the objective of enhancing mine safety and environmental sustainability. Additionally, it aims to offer a more scientifically grounded evaluation method and reference for the study of goaf stability. Goaf overview The Sanhejian mining area is located in the northwest region of Xuzhou City, Jiangsu Province, situated in the inclined part extending southwest from the Tengyu anticline. Owing to the depletion of recoverable coal resources, significant challenges in ensuring safe mining operations, and economic and policy factors, the mining area ceased operations officially in 2019. The coal-bearing formations within the mining area primarily span from the Carboniferous to the Permian period, comprising four main exploitable coal seams, namely seams 7, 9, 17, and 21, arranged in ascending order of depth. Notably, seams 17 and 21, affected by aqueous gray strata and comprising high-sulfur coal respectively, remain unexploited. The goaf areas within the closed mining area are primarily concentrated in seams 7 and 9, with seam 9 experiencing fewer extraction activities due to its greater burial depth across the entirety of the mining area. Therefore, in the analysis of goaf stability, particular emphasis is placed on examining the stability of goaf areas within seam 7. Given the scattered distribution of goaf areas within seam 7, these areas are delineated into 14 distinct regions based on factors such as size and distribution patterns. These regions are labeled as depicted in Fig. 1 . Due to the irregular shapes of goaf areas within the mining area, which could introduce uncontrollable influences during numerical simulation, it is necessary to generalize the treatment of goaf areas within the mining area. Numerical model construction The numerical model of 14 goaf areas was established using FLAC 3D software. The relevant information of the numerical model of the goaf in each region is shown in Table 1 . Due to minimal geological variations and limited fault impacts within the regions, to streamline computational processes, the upper and lower strata of the goaf areas were unified during model setup. In the Sanhejian mining area, the predominant formations are sandstone and mudstone, with specific information on each stratum and rock strength test results depicted in Fig. 2 . The strata have an inclination angle of 6°. Additionally, the model was adjusted based on the scale of each goaf area and coal seam thickness. The bottom layer from 50m below the goaf to 100m above the goaf was particularly delineated in the model. Table 1 Information on the numerical model of the goaf in each region Area number Model length/m Model width/m Average mining thickness/m Roof depth/m Goaf width/m Goaf square /10 4 m² 1 660 440 5 657 342 17 2 580 300 2 647 97 4 3 1000 820 2 978 521 37 4 1280 860 3 828 569 55 5 1840 1180 3 918 880 136 6 1020 920 3 903 629 45 7 2040 1340 2 541 1048 170 8 720 700 5 705 55 9 9 1620 1240 5 400 1042 149 10 1400 760 5 590 70 11 11 1500 1000 9 546 705 79 12 1260 600 5 650 328 28 13 1440 1320 5 650 916 96 14 2220 1340 5 651 948 159 Due to the considerable distance between the bottom boundary and the surrounding boundaries of the goaf area, displacement values are negligible and can be considered immobile. Therefore, during the numerical simulation process, constraint conditions were applied to the bottom boundary and surrounding boundaries, setting the displacement to zero. The numerical simulation employed the Mohr-Coulomb elastoplastic constitutive model. $$\sigma =\rho gh$$ 1 ρ—the average density of the upper strata of the model, and unit is kg/m³. g—acceleration due to gravity, and unit is m/s² h—thickness of the upper strata of the model, and unit is m. Numerical simulation results and analysis After coal excavation, surrounding geological formations undergo stress redistribution to achieve a new equilibrium. During this process, irreversible stress concentration occurs in the surrounding geological formations. The greater the stress around the goaf area, the higher the likelihood of collapse within the goaf (Zhang et al. 2023a ). Therefore, in the numerical simulation, the evaluation of goaf stability mainly focuses on three aspects: stress field, surrounding rock deformation, and plastic zone. The final numerical simulation results are summarized in Table 2 . Table 2 Numerical simulation results of each goaf Area number Maximum compressive stress/MPa Maximum tensile stress/MPa Maximum displacement of the top plate/m Goaf roof failure height/m 1 87.11 2.96 0.31 10.5 2 54.53 2.09 0.07 12.8 3 108.3 4.34 0.53 24.1 4 111.15 5.33 0.65 24.5 5 154.56 7.86 2.12 88.7 6 106.12 4.75 0.63 22.2 7 126.84 6.50 1.89 42.7 8 37.43 2.55 0.05 5.0 9 115.77 5.53 1.42 25.3 10 46.99 2.33 0.12 9.8 11 89.49 4.67 0.78 23.5 12 63.57 2.87 0.23 11.2 13 105.29 6.62 1.22 26.5 14 131.49 6.99 2.12 67.4 In the numerical simulation results, there is a significant variation in stress within the study area's goaf regions. Based on the overall stress distribution, three thresholds of 65MPa, 100MPa, and 125MPa were selected to analyze the characteristics of goaf areas within each stress range. Regions where the maximum compressive stress is less than 65MPa include areas 2, 8, 10, and 12. These goaf areas are generally small in scale, and each of these areas is separated by coal pillars, resulting in relatively low vertical compressive stress on both sides of these goaf areas and relatively low vertical tensile stress on the roof. The area of goaf where the maximum vertical compressive stress is between 65MPa and 100MPa increases slightly, similar to the goaf areas where the vertical compressive stress is between 100MPa and 125MPa. The goaf areas where the compressive stress is between 100MPa and 125MPa generally have a greater burial depth compared to those where the stress is between 65MPa and 100MPa. Regions where the vertical compressive stress exceeds 125MPa include areas 5, 7, and 14. These three goaf areas have relatively large areas within the entire mining area and experience significant vertical compressive stress on both sides of the goaf. Among them, the goaf area 5 has a burial depth of below 900m, and due to its greater depth, it experiences greater stress influences in its surrounding goaf areas. In most of the goaf areas within the study area, the roof subsidence is less than 1m, and the corresponding maximum tensile stress on the roof is generally below 5MPa. However, areas 5, 7, and 14, where the maximum tensile stress exceeds 6.5MPa, are characterized by relatively large roof subsidence within the study area. By fitting the maximum tensile stress from numerical simulation results with the roof subsidence (as shown in Fig. 3 ), it is found that they can be well fitted with a binomial function. Additionally, the maximum roof failure height of goaf areas is also related to stress concentration. The goaf areas with a maximum failure height of less than 15m have a maximum roof pressure below 3MPa. Conversely, the goaf areas with the maximum roof failure height are also areas 5, 7, and 14, consistent with the areas of large roof subsidence. When fitting the maximum pressure with the maximum roof failure height, it is found that they can be well fitted with an exponential function (as shown in Fig. 4 ). Through the above analysis, it is found that stress concentration in the goaf area is significantly influenced by its area and burial depth. Among the 14 goaf areas, by comparing regions 1, 2, 13, and 14 with similar burial depths, it is observed that stress generally increases logarithmically with area. Additionally, the displacement of the goaf roof and the height of the plastic zone also increase with the increasing goaf area (as shown in Fig. 5 ). From this, it can be inferred that smaller mining extents and shallower burial depths result in lower concentrated stress in the goaf area, thus rendering the goaf area more stable. By selecting simulation results from four goaf areas (5, 7, 9, and 14) with approximately equal areas, it is observed that the maximum compressive stress and maximum tensile stress exhibit a good linear fit with the burial depth of the goaf area, which aligns with practical observations. Moreover, higher concentrated stress corresponds to greater deformation and failure height of the goaf roof (as shown in Fig. 6 ). Correspondingly, in these four goaf areas, higher burial depths result in greater displacement of the roof and height of the plastic zone in the goaf area. Through comparative analysis, the goaf in the Sanhejian closed mining area can be roughly divided into two categories. One is that in the mining process, due to the relatively close location of the working face, a large goaf with similar areas 3, 4, 5 and 7 will be formed after the mining is completed (hereinafter referred to as through goaf). The other type is the goaf formed by separate working face mining in areas 2, 8, 10 and 12 (hereinafter referred to as separate goaf), and there are thicker protective coal pillars between each working face. In the following introduction of numerical simulation results, the simulation results of two types of goaf are compared and analyzed in areas 3 and 8 (Figs. 7 to 12 ). Due to the large hanging length of the roof and side wall of the goaf through the goaf, the rock fracture and subsidence may be more significant, resulting in the redistribution and increase of stress. Taking region 3 as an example, when the goaf reaches a stable state, the maximum vertical compressive stress appears on the left and right sides of the goaf, and the maximum is 108.31MPa. The tensile stress on the top and bottom of the goaf is up to 4.34MPa, and the maximum roof settlement is up to 0.53m, which is located in the center of the goaf roof. Meanwhile, the plastic zone mainly appears in the upper right corner and two wings of the goaf, and the maximum height of the plastic zone is 24.1m. The separated goaf is more stable because the single goaf is smaller and has less influence on each other. Taking the simulation results of region 8 as an example, the maximum vertical compressive stress is 37.43MPa, the maximum tensile stress is 2.55MPa, and the maximum roof settlement is 0.05m. Different from region 3, the plastic zone of region 8 is mainly distributed in the middle of the roof in the goaf, and the failure height is also small, only 5.0m. It can be seen that the stress, roof deformation and plastic zone height of region 8 are more stable than that of region 3 when the buried depth is larger, and this phenomenon also exists in other gob domains of through gob and separated gob. According to the Code for Investigation of geotechnical engineering in coal mine goaf , the goaf in the Sanhejian mine area have all been abandoned for more than 4 years and have generally reached a stable state. Based on the numerical simulation results and detailed survey data of the goaf, a grading standard was established to classify the stability level of the goaf in the Sanhejian closed mine area into four categories: strong stability, stable, moderate stability, and basic stability. Table 3 Grading standard for goaf stability grade Goaf stability level Goaf stability evaluation criteria Ⅰ. (Strong Stability) Main Criteria: The height of plastic zone is 0 ~ 15m; The maximum vertical stress is less than 65MPa; The maximum displacement of the roof is 0 ~ 1m; Secondary criteria: The mining thickness of goaf is 0 ~ 5m; The mining width ranges from 0 to 300m. The buried depth of the gob is in the range of 0 ~ 650m. The gob area is less than 20 hectares. (Under the condition of meeting the main criteria, two of the secondary criteria are sufficient; the same below) Ⅱ. (Stable) Main Criteria: State ①: The height of the plastic zone ranges from 0m to 15m. The maximum vertical stress range is 65MPa ~ 100MPa; The maximum deformation range of the roof is 0 ~ 1m; State ② : the height range of the plastic zone is 15m ~ 30m; The maximum vertical stress range is 100MPa ~ 125MPa; The maximum deformation range of the roof is 0 ~ 1m; Secondary criteria: The mining thickness of goaf ranges from 0 to 5m. The width of the gob is within 300 ~ 700m; The buried depth of the gob is greater than 650m; The goaf area is within 20 ~ 60 hectares. Ⅲ. (Moderately Stable) Main Criteria: State ① : the height range of the plastic zone is between 15m and 30m; The maximum vertical stress is in the range of 65MPa ~ 100MPa; And the maximum settlement of the roof is less than 1m; State ②: the height of the plastic zone is between 15m and 30m; The maximum vertical stress is in the range of 100MPa ~ 125MPa; And the maximum settlement of the roof is between 1 ~ 2m; Secondary criteria: The mining thickness of the goaf is greater than 5m; Mining width greater than 700m; The buried depth of the goaf is more than 650m; The mining area is in the range of 60 to 100 hectares. Ⅳ. (Basically stable) Main Criteria: the height of plastic zone is greater than 30m; The maximum vertical stress is greater than 125MPa; Roof settlement exceeds 2m; Secondary criteria: The mining thickness of the goaf is greater than 5m; Mining width greater than 700m; The buried depth of the goaf is more than 650m; More than 100 hectares were mined. In Table 3 , the parameters such as plastic zone height, vertical stress magnitude, and roof subsidence obtained through numerical simulation are comprehensively calculated based on factors such as burial depth, mining width, and area. These objective factors serve as supplements to the evaluation criteria, mainly corresponding to the respective grades. The evaluation results are shown in Table 4 . Through overall analysis combined with these objective factors, it is found that when the burial depth is greater and the mining scale is larger, the stability of the void areas is relatively poorer. For example, areas 5, 7, and 14 all represent interconnected void areas with large scales. However, unlike these three void areas, area 9, although it also belongs to a relatively large interconnected void area, experiences less stress and deformation due to its shallower burial depth. All void areas classified under the strong stability category are formed by single working faces with effective coal pillars between them, effectively preventing excessive stress concentration in the void areas. Through comprehensive analysis, it is concluded that void stability is mainly related to factors such as void width and void area. Table 4 Classification of goaf stability grades Goaf stability rating Goaf number Ⅰ. (Strong Stability) 2、8、10、12 Ⅱ. (Stable) 1、3、4、6 Ⅲ. (Moderately Stable) 9、11、13 Ⅳ. (Basically stable) 5、7、14 Theoretical study on site stability of goaf based on AHP vulnerability index method Considering the main influencing factors of goaf site stability, three first-level indexes, including geological factors, mining factors, hydrological conditions and other influencing factors, and eight corresponding second-level indexes were selected, and a comprehensive evaluation index system for goaf site stability was established. According to Fig. 13 , there are eight quantifiable indicators. Firstly, the complexity of geological structures is quantified by calculating the fault range index, which effectively reflects the scale and development of faults in the study area. Secondly, based on previously collected information on the void areas, the void areas are quantified, including characteristics such as roof and floor lithology and thickness, void width, area, stop mining time, and water accumulation in goaf. Additionally, geological stress and mining depth are calculated based on the burial depth and mining thickness of the void areas. Finally, Surfer software is utilized to generate contour maps through data interpolation, establishing thematic maps of the major influencing factors to display their distribution and characteristics, as shown in Figs. 14 to 21 . Complexity of geological structures The quantification of fault range index can be calculated using the following formula: $$F=\frac{{\sum\limits_{{i=1}}^{n} {{L_i}{H_i}} }}{S}$$ 2 F represents the fault range index. i represents a certain fault in a certain partition of the study area. H i represents the vertical displacement of fault 𝑖, in meters. L i represents the length of fault 𝑖, in meters. n represents the number of faults in the study area partition. S represents the area of the study area partition, in square meters. According to the meaning of Eq. 2 , The size of the fault range index directly reflects the complexity of geological structures. This is clearly demonstrated in the zoning results in Fig. 14 . According to the natural breakpoint method, regions are categorized as follows: F<0.03 for simple type, 0.03 < F ≤ 0.07 for moderate type, 0.07 < F ≤ 0.11 for relatively complex type, and 0.11 < F ≤ 0.13 for complex type. Specifically, in the geological conditions of the Sanhejian mine area, the northern and eastern regions exhibit relatively complex geological structures due to the presence of long and high-displacement faults or fault intersections. This complexity is mainly attributed to the interactions between faults and the diversity of their mechanical behavior within the crust. In contrast, the geological structures in the western and southern parts of the mining area are relatively simple, with some areas even showing extremely low geological development, indicating higher geological stability and less fault activity in these areas. 2. Lithology and thickness of the roof Xu (Xu et al. 2023 ) discovered through natural equilibrium analysis that the greater the thickness of the overlying strata of a goaf, the higher its stability. Based on the geological exploration data of the Sanhejian mining area, including detailed analyses of borehole information column charts and exploration line profiles, it has been determined that both the roof and floor of the goafs in this mining area are composed of siltstone layers. During coal mining, siltstone layers play a crucial role in controlling mine pressure and roof displacement damage. The thickness of the roof is a key factor influencing the stability of goafs, with thicker roofs being more favorable for enhancing overall goaf stability. This study further assesses the geological stability of the mining area by quantifying the influence of roof thickness as a factor. According to the zoning results in Fig. 15 , the roof thickness in the northern and southeastern parts of the Sanhejian mining area is relatively large, especially in the eastern region, where the maximum roof thickness can reach 8 meters. In contrast, the roof thickness in most other areas of the mining area is less than 5.5 meters, with relatively small variations in roof thickness within these areas. 3. Geostress In the Sanhejian mining area, after coal seam mining is completed, due to the significant burial depth of the goafs, the overlying strata exert considerable self-weight stress on the goaf roof, which can easily cause damage to the surrounding geological bodies. In order to systematically analyze and evaluate the influence of self-weight stress on the stability of goafs, this study quantifies the effect of self-weight stress on the geostress indicators within the mining area. This allows for a more accurate assessment of the geostress state and surrounding rock stability within the mining area. According to the zoning results in Fig. 16 , the geostress in the eastern part of the study area is relatively low, with the lowest geostress occurring in the southeastern region at 8.5 MPa. In contrast, the geostress in the southwestern and northwestern parts of the mining area is significantly higher, exceeding 17.5 MPa. 4. Stop mining time The mining sequence in the Sanhejian mining area follows a shallow-to-deep approach. Goafs mined earlier have undergone long-term evolution, leading to a redistribution of stress and achieving a balanced state. According to the final mining information of the Sanhejian mining area, goafs 7, 9, and 11, which have shallow burial depths, were mined before 2007 and are essentially stable, with no further deformation or damage expected. Goafs 2, 3, 4, etc., however, were mined later due to their greater burial depths, and thus there is a possibility of further damage. The specific zoning of stop mining time is shown in Fig. 17 . 5. Mining depth ratio In mining engineering, the mining depth-to-thickness ratio is an important technical parameter that represents the ratio of coal seam burial depth to coal thickness. A higher ratio generally indicates better mining safety. Therefore, goafs with a larger depth-to-thickness ratio are expected to be safer and more stable. Based on this ratio, the mining area is divided into zones, as shown in Fig. 18 . Due to the shallow burial depth and greater coal thickness in the eastern part of the Sanhejian mining area, the depth-to-thickness ratio in this area is relatively small. Conversely, influenced by faults, the southwestern and northwestern parts have greater coal seam burial depths and thinner coal seams, resulting in a relatively larger depth-to-thickness ratio in the western areas. 6. Goaf width Goaf width is a key factor controlling the stability of goafs and has a significant influence on the deformation of the goaf roof. After coal seam extraction, pressure arches form above the goaf, where the weight of the overlying rock mass transfers towards the sides of the working face (at the foot of the pressure arch). Previous numerical simulation studies have shown that as the goaf width increases, the outer width of the pressure arch above the goaf also increases, resulting in greater stress concentration on the sides of the working face and thus reduced stability of the goaf. Goaf widths, as indicated by statistics, are annotated in Fig. 19 . Goafs 7, 9, 14, and 5 have larger areas, with goaf widths all exceeding 800 meters. 7. Goaf area Hu(Hu and Li 2012 ) using Bayesian discriminant analysis to identify risks in complex mining goafs, argues that larger goaf areas correspond to poorer goaf stability. Combining this with the Sanhejian closed mining area, Fig. 20 divides the goafs into four rough levels. Goafs such as 5, 7, 9, and 14 have larger mining ranges, indicating relatively poorer stability. Conversely, areas such as 1, 2, 8, and 10 have smaller goaf areas, resulting in relatively less deformation and stress, thus indicating greater stability. 8. Water accumulation in goaf When there is significant water accumulation in goafs, the hydrostatic pressure can be considerable and highly destructive. Additionally, water flow gradually erodes the rocks and coal seams within the goaf, reducing the structural strength of the rocks and increasing the risk of collapse. This poses safety hazards for the development and utilization of underground spaces. Through organization and statistical analysis of water accumulation in goafs, it is evident that there is a certain amount of water accumulation in low-lying areas of goafs. Currently, eight main locations of water accumulation are known, primarily distributed in goafs 6, 7, 8, 11, 12, and 13. According to the constructed comprehensive evaluation index system of goaf site stability, A hierarchical structure model is established, aiming at goaf site stability evaluation A. The hierarchical structure model is as follows: $$A=\left\{ {{B_1},{\text{ }}{B_2},{\text{ }}{B_3}} \right\},{\text{ }}{B_1}=\left\{ {{C_1},{\text{ }}{C_2},{\text{ }}{C_3}} \right\},{\text{ }}{B_2}=\left\{ {{C_4},{\text{ }}{C_5},{\text{ }}{C_6},{\text{ }}{C_7}} \right\},{\text{ }}{B_3}=\left\{ {{C_8}} \right\}$$ 3 According to the constructed hierarchical structure model, the 1–9 scale method is adopted to construct a judgment matrix to determine the importance of each evaluation index. The values of 1–9 scale method are shown in Table 5 . Table 5 Values of the 1 ~ 9 scale method Scale Meaning 1 Both factors are equally important 3 Slightly more important 5 Obviously important 7 Strongly important 9 Extremely important 2、4、6、8 The median value of the above judgment is expressed Number of Collapses i is more important than j is m, then j is more important than i is 1/m Each evaluation index is compared pair by pair, and combined with Table 1 , each judgment matrix is obtained, as shown in Table 6 to 9 . Table 6 A-B judgment matrix Goaf site stability evaluation A Geological factors B 1 Mining factors B 2 Hydrogeological conditions B 3 Geological factors B 1 1 1/2 5 Mining factors B 2 2 1 8 Hydrogeological conditions B 3 1/5 1/8 1 Table 7 B 1 -C judgment matrix Geological factors B 1 Geological structural complexity C 1 Roof lithology and thickness C 2 Geostress C 3 Geological structural complexity C 1 1 2 1/2 Roof lithology and thickness C 2 1/2 1 1/4 Geostress C 3 2 4 1 Table 8 B 2 -C judgment matrix Mining factors B 2 Stop mining time C 4 Depth-to-coal ratio C 5 Goaf width C 6 Goaf area C 7 Stop mining time C 4 1 1/2 1/3 1/5 Depth-to-coal ratio C 5 2 1 2 1/2 Goaf width C 6 3 1/2 1 1/4 Goaf area C 7 5 1/3 4 1 Table 9 B 3 -C judgment matrix Hydrogeological conditions B 3 Water volume in goaf C 8 Water volume in goaf C 8 1 The weights of each evaluation index are calculated according to the eigenvector method. Table 10 shows the statistics of the weights of evaluation indexes. Table 10 Statistics on the weights of evaluation indicators at all levels Target layer Criterion layer W(B/A) Assessment layer W(C/B) W(C/A) Goaf site stability evaluation A Geological factors B 1 0.3258 Geological structural complexity C 1 0.2857 0.0931 Roof lithology and thickness C 2 0.1429 0.0466 Geostress C 3 0.5714 0.1862 Mining factors B 2 Geological 0.6039 Stop mining time C 4 0.0909 0.0549 Depth-to-coal ratio C 5 0.2403 0.1451 Goaf width C 6 0.1656 0.1000 Goaf area C 7 0.5032 0.3039 Hydrogeological conditions B3 0.0703 Water volume in goaf C 8 1.0000 0.0703 The consistency test of the constructed judgment matrix is performed: $${C_R}=\frac{{{C_I}}}{{{R_I}}}$$ 4 Where, C R is the consistency ratio; C I is a general consistency index; R I is the average random consistency index. It can be obtained by calculation that the CR value of each judgment matrix is less than 0.1, which meets the requirements of consistency test. The consistency tests of judgment matrices at all levels are shown in Table 11 . Table 11 Consistency test of judgment matrix at all levels Judgment matrix λ max C R A-B 3.0055 0.0000 B 1 -C 3.0538 0.0517 B 2 -C 4.1312 0.0492 B 3 -C 1.0000 0.0000 According to the weight calculation of the evaluation index, it is found that the mining factors of the goaf are the key factors affecting the stability of the goaf, which is consistent with the conclusion obtained in the previous numerical simulation research, while the hydrogeological conditions have little influence on the stability of the goaf. Since the unit dimensions of each major influencing factor are different, it is necessary to standardize each major influencing factor in order to ensure the consistency of the evaluation factors. It can be normalized with the following formula: $${A_i}=\left\{ {_{{a+\frac{{(b - a) \times (\hbox{max} ({x_i}) - {x_i})}}{{\hbox{max} ({x_i}) - \hbox{min} ({x_i})}}{\text{, where }}x{\text{ is a negative factor}}}}^{{a+\frac{{(b - a) \times ({x_i} - \hbox{min} ({x_i}))}}{{\hbox{max} ({x_i}) - \hbox{min} ({x_i})}},{\text{ where }}x{\text{ is a positive factor}}}}} \right.$$ 5 Where Ai is the data after standardization of each major influence factor, and the lower limit and upper limit of the standardization range of a and b, as shown in this paper (a = 0, b = 1); x i is the original data before standardization, min( x i ) is the quantified minimum value of each major influence factor, and max( x i ) is the maximum value of each major influence factor. $$VI=\sum\limits_{{k=1}}^{n} {{W_k}{f_k}(x,y)}$$ 6 Where, W k represents the weight value of each major influencing factor; n is the number of influencing factors; (x, y) are geographical coordinates; \({f}_{k}\left(x,y\right)\) is a single factor influence function. The weight values of the main influencing factors obtained in the analytic hierarchy process are substituted into formula 7 o obtain the final stability evaluation model of the goaf in the Sanhejian closed mining area: $$\begin{gathered} VI=0.1087{f_1}(x,y)+0.0461{f_2}(x,y)+0.1710{f_3}(x,y)+0.0549{f_4}(x,y)+0.1451{f_5}(x,y) \hfill \\ +0.1000{f_6}(x,y)+0.3039{f_7}(x,y)+0.0703{f_8}(x,y) \hfill \\ \end{gathered}$$ 7 Since the main influencing factors C 2 , C 4 and C 5 are roof lithology and thickness, final mining time and depth ratio of coal seam respectively, they are negatively correlated with VI value, and are quantified as negative values. The smaller the absolute values of C 2 , C 4 and C 5 are, the greater the VI value is, and the worse the stability of goaf. The other five main influencing factors are positively correlated with the target layer, and the higher the VI value, the worse the stability of the gob. The VI value was obtained based on the vulnerability index model, and then the isoline map of VI was drawn using the grid value module of surfer software. The natural breakpoint classification method was used to obtain the vulnerability assessment zone thresholds of 0.09, 0.20 and 0.31 As shown in Table 12 . respectively, and the vulnerability areas of goaf stability in the study area were divided according to the vulnerability assessment thresholds. Figure 4 – 11 and Table 4 – 8 show the evaluation results. Table 12 Sanhejian closed the goaf stability and vulnerability zoning in the mining area VI Stability level VI ≤ 0.13 Ⅰ. (Strong Stability) 0.13 < VI ≤ 0.23 Ⅱ. (Stable) 0.23 < VI ≤ 0.32 Ⅲ. (Moderately Stable) 0.32 < VI Ⅳ. (Basically stable) The stability of the goaf in the Sanhejian mining area is still divided into strong stability, stability, medium stability and basic stability. The stability of goaf in the east, middle and south of Sanhejian mining area is relatively poor, and the stability of goaf 1, 2, 8, 10 and 12 is better than that of other goaf areas. Except for some areas, the classification of the stability of the goaf is basically consistent with the results of the numerical simulation, and the coincidence rate is close to 80%, which is effectively verified. Table 13 show the classification results. Table 13 Goaf stability grade grading results Goaf stability level Goaf number Ⅰ. (Strong Stability) 1、2、8、10、12 Ⅱ. (Stable) 3、4 Ⅲ. (Moderately Stable) 6、11、13 Ⅳ. (Basically stable) 5、7、9、14 Comprehensive evaluation of goaf stability Due to the different focus of the two methods, although numerical simulation provides quantitative analysis based on physical models, it ignores some key factors that may affect the evaluation results, such as faults and water deposits. The AHP method of vulnerability index improves the comprehensiveness and accuracy of assessment by supplementing the quantitative assessment of these factors. This also leads to some differences in the evaluation results of some goaf in the mine area. Specifically, compared with goaf 2, goafs 1 has a relatively large mining width, and its stress is relatively concentrated in the numerical simulation, and its stability is less stable than that of goafs 2 and 8. Due to shallow burial depth, the maximum numerical stress in goaf 9 is smaller in the simulation results, which is more stable than the goaf with large area and deep burial in goafs 5 and 14. However, the reason for the difference in goaf 6 is more complex. In goaf 6, it is mainly due to the surrounding faults and the water volume in goaf, resulting in a higher vulnerability index. However, for other areas of the goaf, the two evaluation methods obtained the same stability rating results. goafs 2, 8, 10 and 12 were rated as having strong stability in both assessment methods. On the contrary, the stability evaluation results of the goaf in areas 5, 7 and 14 are poor in both methods. In view of the differences in the evaluation results of the two methods in some areas, it is necessary to use the two methods comprehensively to effectively improve the reliability and accuracy of the stability assessment of the goaf. Conservative Risk Assessment was used to make a comprehensive analysis of the two evaluation results. The results of goaf stability evaluation are shown in Table 14 . Table 14 Comprehensive evaluation results of goaf stability Goaf stability level Goaf number Ⅰ. (Strong Stability) 2、8、10、12 Ⅱ. (Stable) 1、3、4 Ⅲ. (Moderately Stable) 6、11、13 Ⅳ. (Basically stable) 5、7、9、14 In the final evaluation results, in the goaf areas with large areas such as areas 5, 7 and 14, the existing coal pillars are small, and the roof support is almost negligible., so that the center of the goaf needs to bear a large tensile stress, due to the superposition of other factors such as faults, roof thickness, etc., it is easier to form a negative impact on the goaf; secondly, the goaf in the stable and medium stability grades, the mining scale is relatively smaller, in which the mining depth ratio of areas 3 and 4 is larger than that of areas 11 and 13, and it is relatively more stable; and the areas 2, 8, 10 and 12 generally have the characteristics of small mining scale and scattered mining, and the stability is relatively better. The evaluation results provide a basis for subsequent development and utilization. Conclusions (1) In the numerical simulation results, the maximum vertical stress, roof settlement and plastic zone height of the gob are positively correlated with the objective conditions such as the width, area, mining thickness and burial depth of the gob. These objective conditions directly lead to the stability of the through gob being significantly weaker than that of the separated gob. According to the maximum vertical stress, roof settlement and plastic zone height obtained by numerical simulation, the stability of the goaf is divided into four grades: strong stability, stable stability, medium stability and basic stability. The stress and damage degree of goafs 2, 8, 10 and 12 are small and relatively stable, while the stress and damage degree of goafs 5, 7 and 14 are large. The relative stability is poor. (2) AHP method was used to analyze the weights of 8 factors, among which mining factors accounted for the highest weight, which was consistent with the results of numerical simulation analysis; The VI model of Sanhejian closed mining area was established according to the weights of various influencing factors and goaf information, and the vulnerability assessment zone threshold was determined. The goaf was also classified into grades. The stability evaluation results of goafs 1, 6 and 9 were different from the numerical simulation evaluation results, which were mainly caused by other factors such as faults, water volume and buried depth. (3) In view of the different concerns of numerical simulation and vulnerability index for goaf, the conservative risk assessment principle is used to combine the evaluation results of numerical simulation and vulnerability index to obtain comprehensive evaluation results. The results show that goafs 2, 8, 10 and 12 are more stable, while goafs 5, 7, 9 and 14 are relatively poor in stability. Declarations Conflict of interest No potential conflict of interest was reported by the author. Funding Not applicable. Author Contribution S.Z. wrote the original manuscript; Z. W. conducted the review; Z.S. provided methodological guidance; F. Z.andY. L. conducted survey and data collection; C. S. and W. Y. provide photo guidance; All authors have read and agreed to the submitted version of the manuscript. Acknowledgements This work was supported by the Jiangsu Provincial Geological Exploration Fund (Comprehensive Evaluation and Collaborative Development and Utilization of special Space Resources in Sanhejian Coal Mine, NO. Su Caizi Ring [2021] No. 45) References Ao X, Wang X, Zhu X, Zhou Z, Zhang X (2017) Grouting Simulation and Stability Analysis of Coal Mine Goaf Considering Hydromechanical Coupling. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4425036","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":305342192,"identity":"47c0421f-311c-4789-84db-879cda00cff7","order_by":0,"name":"Zhanghao Shi","email":"","orcid":"","institution":"China University of Mining and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhanghao","middleName":"","lastName":"Shi","suffix":""},{"id":305342194,"identity":"b2e08222-31b0-497c-b9b3-479550485282","order_by":1,"name":"Weiqiang 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1","display":"","copyAsset":false,"role":"figure","size":330514,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of the study area and goaf zoning map\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/40b3b8e3e788102a5f2681f1.png"},{"id":57518553,"identity":"1c325f1e-d993-4a3d-a94f-e90b1b8a601e","added_by":"auto","created_at":"2024-05-31 20:35:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":42682,"visible":true,"origin":"","legend":"\u003cp\u003eStratigraphic histogram of the Sanhejian mining area\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/d96246db6937636d1aba6f23.png"},{"id":57519475,"identity":"6755d7d4-2bca-4e2e-8910-c40f391c61d1","added_by":"auto","created_at":"2024-05-31 20:43:59","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":14635,"visible":true,"origin":"","legend":"\u003cp\u003eStudy on the fitting results of the maximum tensile stress and Maximum displacement of roof\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/796c073663bd4ff69fe664b7.png"},{"id":57518555,"identity":"085ac9e5-580f-4e46-9a18-1734c5282419","added_by":"auto","created_at":"2024-05-31 20:35:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":13408,"visible":true,"origin":"","legend":"\u003cp\u003eFitting results of maximum compressive stress and roof failure height\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/693f930643bff08f6c851d0a.png"},{"id":57518557,"identity":"d21dd34a-1562-445b-ac3d-3d19b0ab8763","added_by":"auto","created_at":"2024-05-31 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8\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/97afbb1c5f1f240a920239fd.png"},{"id":57518564,"identity":"c1a1f98a-63e9-48d9-8e13-30c6df717bf0","added_by":"auto","created_at":"2024-05-31 20:35:59","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":48568,"visible":true,"origin":"","legend":"\u003cp\u003eEvaluation index system for site stability in goaf\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/b2c573fd53ca33810a61f1c0.png"},{"id":57518558,"identity":"76a7070a-792c-453e-963c-52974ac368a5","added_by":"auto","created_at":"2024-05-31 20:35:59","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":36592,"visible":true,"origin":"","legend":"\u003cp\u003eExponential zoning map of fault range\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/1e72a6e5794a180793397c3f.png"},{"id":57519476,"identity":"9f11b4f2-7a99-40d9-9c55-f10fce5b97f3","added_by":"auto","created_at":"2024-05-31 20:44:00","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":48867,"visible":true,"origin":"","legend":"\u003cp\u003eRoof thickness zoning map\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/c8f76f158f30838dfaceda82.png"},{"id":57518560,"identity":"dcd061ba-1716-471b-95a3-93ea689ba580","added_by":"auto","created_at":"2024-05-31 20:35:59","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":46514,"visible":true,"origin":"","legend":"\u003cp\u003eGeostress distribution zoning map\u003c/p\u003e","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/03414c76bc3ce04453055d8c.png"},{"id":57518571,"identity":"562b51ac-da30-4a64-b761-6f5e517a351a","added_by":"auto","created_at":"2024-05-31 20:36:00","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":55482,"visible":true,"origin":"","legend":"\u003cp\u003eZoning map of the final mining time of the goaf\u003c/p\u003e","description":"","filename":"floatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/d1c0baa1a1c19bdde1cabb47.png"},{"id":57518562,"identity":"de6c3630-d23b-4333-a318-e6dd44e6c659","added_by":"auto","created_at":"2024-05-31 20:35:59","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":53727,"visible":true,"origin":"","legend":"\u003cp\u003eMining deep score area map\u003c/p\u003e","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/0a077e68332c88cc150b9641.png"},{"id":57518568,"identity":"20bc31ce-e7e3-4300-89f2-0f9a640e3751","added_by":"auto","created_at":"2024-05-31 20:36:00","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":46228,"visible":true,"origin":"","legend":"\u003cp\u003eWidth zoning degree of goaf\u003c/p\u003e","description":"","filename":"floatimage19.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/a774a685202c9d1844de5c3a.png"},{"id":57518565,"identity":"3a5a5b41-8585-4116-a095-45227c3a559a","added_by":"auto","created_at":"2024-05-31 20:36:00","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":49349,"visible":true,"origin":"","legend":"\u003cp\u003eArea zoning degree of goaf\u003c/p\u003e","description":"","filename":"floatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/5fb2840299e203e481096cf2.png"},{"id":57518573,"identity":"d7dd3ca8-15aa-4f65-8bd8-15640adfcd79","added_by":"auto","created_at":"2024-05-31 20:36:00","extension":"png","order_by":21,"title":"Figure 21","display":"","copyAsset":false,"role":"figure","size":33694,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of water accumulation in goaf area\u003c/p\u003e","description":"","filename":"floatimage21.png","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/fef6845999e82439da5b9de6.png"},{"id":58537062,"identity":"de11ac37-daf5-4bd2-b6dd-0ee36112fa72","added_by":"auto","created_at":"2024-06-18 03:03:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4261739,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4425036/v1/16419de3-64bb-4a34-a0df-89286e035458.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eStability evaluation of goaf in closed mining area: a case study of Sanhejian closed mining area in Jiangsu Province, China \u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eDue to decades of intensive mining, the Sanhejian coal mine has formed a large-scale group of goaf areas within the mining area, leaving behind substantial underground space resources after closure (Jing Qian et al.). The current development patterns of underground space resources mainly include the construction of underground gas storage facilities and underground energy storage stations. However, the stability of the goaf determines the prospects for the utilization of underground space resources in closed mines. If the stability of the goaf is poor, it not only restricts the utilization of space resources but also poses risks of collapse or geological changes, which may lead to damage to surrounding structures and affect their safe operation (Liu et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023b\u003c/span\u003e). Therefore, studying the stability of the goaf in the Sanhejian closed coal mine is crucial for its redevelopment and utilization.\u003c/p\u003e \u003cp\u003eThe stochastic, fuzzy, and uncertain nature of factors influencing goaf stability severely impedes the evaluation of goaf stability (Guo et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Research methods in goaf stability assessment mainly focus on numerical simulation and theoretical analysis (Ao et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Yuan et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2023c\u003c/span\u003e). In numerical simulation research methods, Yang (Yang et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) utilized theoretical analysis and numerical simulation to analyze the key strata fracture mechanism, stress distribution laws, and influencing factors under mining influence, revealing that horizontal stress on roadways is more prominent than vertical stress. Luo (Luo et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2015\u003c/span\u003e)based on precise measurements of goaf models using CMS, coupled Surpac and Midas-Gts, combined with the basic equations of stress-permeability in equivalent continuum mechanics and disturbance equivalent load theory in deep-hole blasting, conducted numerical analysis on the stability of mining area under the coupling of stress-permeability-dynamic disturbance. Wang (Wang et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), through PFC numerical simulation, found a close correlation between the mechanical properties of RCG (rock-like specimens containing goaf) and the fractal dimension (FD) of the goaf. Peak stress, peak strain, and elastic modulus are linearly negatively correlated with FD. In addition to numerical simulation methods, grey system theory, fuzzy comprehensive evaluation, etc., are widely applied in mining disaster prediction (Qin et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Han et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Guo (Guo et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) et al. evaluated the unstable risk of the construction site of a highway above abandoned goaf using fuzzy theory and grey theory analysis, ultimately deciding to use geogrids for the roadbed based on the analysis. Liu (Liu et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), combined with numerical simulation results, predicted the subsidence deformation of the mine under thick loose layers using grey relational analysis, finding that coal thickness has the greatest impact on maximum settlement, while cohesion is the smallest factor. He (He et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) established a goaf stability model using fuzzy comprehensive evaluation and determined the treatment method for the goaf based on the results of this model. Wu (Wu et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) similarly conducted a fuzzy comprehensive evaluation of the ground stability of the goaf and effectively validated it based on actual site conditions. Current research on goaf stability mostly focuses on pre-mining or during mining stages (Cai et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Tao et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), while the closure of coal mines, due to complex and unknown underground conditions, cannot be continuously monitored, leading to limited research on goaf stability in closed coal mines, which requires further exploration.\u003c/p\u003e \u003cp\u003eThis paper evaluates the stability of goaf areas within closed coal mines through a combination of comprehensive numerical simulation and AHP-based Vulnerability Index. Ultimately, the stability levels derived from both methods are integrated based on a conservative risk principle. The aim is to provide evaluation guidance for the utilization of underground spaces within the Sanhejian closed mine area, with the objective of enhancing mine safety and environmental sustainability. Additionally, it aims to offer a more scientifically grounded evaluation method and reference for the study of goaf stability.\u003c/p\u003e"},{"header":"Goaf overview","content":"\u003cp\u003eThe Sanhejian mining area is located in the northwest region of Xuzhou City, Jiangsu Province, situated in the inclined part extending southwest from the Tengyu anticline. Owing to the depletion of recoverable coal resources, significant challenges in ensuring safe mining operations, and economic and policy factors, the mining area ceased operations officially in 2019. The coal-bearing formations within the mining area primarily span from the Carboniferous to the Permian period, comprising four main exploitable coal seams, namely seams 7, 9, 17, and 21, arranged in ascending order of depth. Notably, seams 17 and 21, affected by aqueous gray strata and comprising high-sulfur coal respectively, remain unexploited. The goaf areas within the closed mining area are primarily concentrated in seams 7 and 9, with seam 9 experiencing fewer extraction activities due to its greater burial depth across the entirety of the mining area. Therefore, in the analysis of goaf stability, particular emphasis is placed on examining the stability of goaf areas within seam 7.\u003c/p\u003e \u003cp\u003eGiven the scattered distribution of goaf areas within seam 7, these areas are delineated into 14 distinct regions based on factors such as size and distribution patterns. These regions are labeled as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Due to the irregular shapes of goaf areas within the mining area, which could introduce uncontrollable influences during numerical simulation, it is necessary to generalize the treatment of goaf areas within the mining area.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eNumerical model construction\u003c/h2\u003e \u003cp\u003eThe numerical model of 14 goaf areas was established using FLAC\u003csup\u003e3D\u003c/sup\u003e software. The relevant information of the numerical model of the goaf in each region is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Due to minimal geological variations and limited fault impacts within the regions, to streamline computational processes, the upper and lower strata of the goaf areas were unified during model setup. In the Sanhejian mining area, the predominant formations are sandstone and mudstone, with specific information on each stratum and rock strength test results depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The strata have an inclination angle of 6\u0026deg;. Additionally, the model was adjusted based on the scale of each goaf area and coal seam thickness. The bottom layer from 50m below the goaf to 100m above the goaf was particularly delineated in the model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eInformation on the numerical model of the goaf in each region\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArea number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel length/m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModel width/m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAverage mining thickness/m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRoof depth/m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGoaf width/m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGoaf square /10\u003csup\u003e4\u003c/sup\u003em\u0026sup2;\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e660\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e440\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e647\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e820\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e 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colname=\"c2\"\u003e \u003cp\u003e1020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e903\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e629\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1048\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e170\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e720\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e705\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1620\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e149\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e760\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e590\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e546\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e705\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e650\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1440\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e650\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2220\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e651\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e159\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDue to the considerable distance between the bottom boundary and the surrounding boundaries of the goaf area, displacement values are negligible and can be considered immobile. Therefore, during the numerical simulation process, constraint conditions were applied to the bottom boundary and surrounding boundaries, setting the displacement to zero. The numerical simulation employed the Mohr-Coulomb elastoplastic constitutive model.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\sigma =\\rho gh$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eρ\u0026mdash;the average density of the upper strata of the model, and unit is kg/m\u0026sup3;.\u003c/p\u003e \u003cp\u003eg\u0026mdash;acceleration due to gravity, and unit is m/s\u0026sup2;\u003c/p\u003e \u003cp\u003eh\u0026mdash;thickness of the upper strata of the model, and unit is m.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eNumerical simulation results and analysis\u003c/h2\u003e \u003cp\u003eAfter coal excavation, surrounding geological formations undergo stress redistribution to achieve a new equilibrium. During this process, irreversible stress concentration occurs in the surrounding geological formations. The greater the stress around the goaf area, the higher the likelihood of collapse within the goaf (Zhang et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2023a\u003c/span\u003e). Therefore, in the numerical simulation, the evaluation of goaf stability mainly focuses on three aspects: stress field, surrounding rock deformation, and plastic zone. The final numerical simulation results are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNumerical simulation results of each goaf\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArea number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaximum compressive stress/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMaximum tensile stress/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMaximum displacement of the top plate/m\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGoaf roof failure height/m\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e87.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e54.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e108.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e24.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e111.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e24.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e154.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e88.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e106.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e22.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e126.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e42.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e37.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e115.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e46.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e89.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e63.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e105.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e26.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e131.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e67.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the numerical simulation results, there is a significant variation in stress within the study area's goaf regions. Based on the overall stress distribution, three thresholds of 65MPa, 100MPa, and 125MPa were selected to analyze the characteristics of goaf areas within each stress range. Regions where the maximum compressive stress is less than 65MPa include areas 2, 8, 10, and 12. These goaf areas are generally small in scale, and each of these areas is separated by coal pillars, resulting in relatively low vertical compressive stress on both sides of these goaf areas and relatively low vertical tensile stress on the roof. The area of goaf where the maximum vertical compressive stress is between 65MPa and 100MPa increases slightly, similar to the goaf areas where the vertical compressive stress is between 100MPa and 125MPa. The goaf areas where the compressive stress is between 100MPa and 125MPa generally have a greater burial depth compared to those where the stress is between 65MPa and 100MPa. Regions where the vertical compressive stress exceeds 125MPa include areas 5, 7, and 14. These three goaf areas have relatively large areas within the entire mining area and experience significant vertical compressive stress on both sides of the goaf. Among them, the goaf area 5 has a burial depth of below 900m, and due to its greater depth, it experiences greater stress influences in its surrounding goaf areas.\u003c/p\u003e \u003cp\u003eIn most of the goaf areas within the study area, the roof subsidence is less than 1m, and the corresponding maximum tensile stress on the roof is generally below 5MPa. However, areas 5, 7, and 14, where the maximum tensile stress exceeds 6.5MPa, are characterized by relatively large roof subsidence within the study area. By fitting the maximum tensile stress from numerical simulation results with the roof subsidence (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), it is found that they can be well fitted with a binomial function. Additionally, the maximum roof failure height of goaf areas is also related to stress concentration. The goaf areas with a maximum failure height of less than 15m have a maximum roof pressure below 3MPa. Conversely, the goaf areas with the maximum roof failure height are also areas 5, 7, and 14, consistent with the areas of large roof subsidence. When fitting the maximum pressure with the maximum roof failure height, it is found that they can be well fitted with an exponential function (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThrough the above analysis, it is found that stress concentration in the goaf area is significantly influenced by its area and burial depth. Among the 14 goaf areas, by comparing regions 1, 2, 13, and 14 with similar burial depths, it is observed that stress generally increases logarithmically with area. Additionally, the displacement of the goaf roof and the height of the plastic zone also increase with the increasing goaf area (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). From this, it can be inferred that smaller mining extents and shallower burial depths result in lower concentrated stress in the goaf area, thus rendering the goaf area more stable. By selecting simulation results from four goaf areas (5, 7, 9, and 14) with approximately equal areas, it is observed that the maximum compressive stress and maximum tensile stress exhibit a good linear fit with the burial depth of the goaf area, which aligns with practical observations. Moreover, higher concentrated stress corresponds to greater deformation and failure height of the goaf roof (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Correspondingly, in these four goaf areas, higher burial depths result in greater displacement of the roof and height of the plastic zone in the goaf area.\u003c/p\u003e \u003cp\u003eThrough comparative analysis, the goaf in the Sanhejian closed mining area can be roughly divided into two categories. One is that in the mining process, due to the relatively close location of the working face, a large goaf with similar areas 3, 4, 5 and 7 will be formed after the mining is completed (hereinafter referred to as through goaf). The other type is the goaf formed by separate working face mining in areas 2, 8, 10 and 12 (hereinafter referred to as separate goaf), and there are thicker protective coal pillars between each working face. In the following introduction of numerical simulation results, the simulation results of two types of goaf are compared and analyzed in areas 3 and 8 (Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e to \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDue to the large hanging length of the roof and side wall of the goaf through the goaf, the rock fracture and subsidence may be more significant, resulting in the redistribution and increase of stress. Taking region 3 as an example, when the goaf reaches a stable state, the maximum vertical compressive stress appears on the left and right sides of the goaf, and the maximum is 108.31MPa. The tensile stress on the top and bottom of the goaf is up to 4.34MPa, and the maximum roof settlement is up to 0.53m, which is located in the center of the goaf roof. Meanwhile, the plastic zone mainly appears in the upper right corner and two wings of the goaf, and the maximum height of the plastic zone is 24.1m. The separated goaf is more stable because the single goaf is smaller and has less influence on each other. Taking the simulation results of region 8 as an example, the maximum vertical compressive stress is 37.43MPa, the maximum tensile stress is 2.55MPa, and the maximum roof settlement is 0.05m. Different from region 3, the plastic zone of region 8 is mainly distributed in the middle of the roof in the goaf, and the failure height is also small, only 5.0m. It can be seen that the stress, roof deformation and plastic zone height of region 8 are more stable than that of region 3 when the buried depth is larger, and this phenomenon also exists in other gob domains of through gob and separated gob.\u003c/p\u003e \u003cp\u003eAccording to the \u003cem\u003eCode for Investigation of geotechnical engineering in coal mine goaf\u003c/em\u003e, the goaf in the Sanhejian mine area have all been abandoned for more than 4 years and have generally reached a stable state. Based on the numerical simulation results and detailed survey data of the goaf, a grading standard was established to classify the stability level of the goaf in the Sanhejian closed mine area into four categories: strong stability, stable, moderate stability, and basic stability.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGrading standard for goaf stability grade\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf stability level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGoaf stability evaluation criteria\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅠ. (Strong Stability)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMain Criteria: The height of plastic zone is 0\u0026thinsp;~\u0026thinsp;15m; The maximum vertical stress is less than 65MPa; The maximum displacement of the roof is 0\u0026thinsp;~\u0026thinsp;1m;\u003c/p\u003e \u003cp\u003eSecondary criteria: The mining thickness of goaf is 0\u0026thinsp;~\u0026thinsp;5m; The mining width ranges from 0 to 300m. The buried depth of the gob is in the range of 0\u0026thinsp;~\u0026thinsp;650m. The gob area is less than 20 hectares.\u003c/p\u003e \u003cp\u003e(Under the condition of meeting the main criteria, two of the secondary criteria are sufficient; the same below)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅡ. (Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMain Criteria: State ①: The height of the plastic zone ranges from 0m to 15m. The maximum vertical stress range is 65MPa\u0026thinsp;~\u0026thinsp;100MPa; The maximum deformation range of the roof is 0\u0026thinsp;~\u0026thinsp;1m;\u003c/p\u003e \u003cp\u003eState ② : the height range of the plastic zone is 15m\u0026thinsp;~\u0026thinsp;30m; The maximum vertical stress range is 100MPa\u0026thinsp;~\u0026thinsp;125MPa; The maximum deformation range of the roof is 0\u0026thinsp;~\u0026thinsp;1m;\u003c/p\u003e \u003cp\u003eSecondary criteria: The mining thickness of goaf ranges from 0 to 5m. The width of the gob is within 300\u0026thinsp;~\u0026thinsp;700m; The buried depth of the gob is greater than 650m; The goaf area is within 20\u0026thinsp;~\u0026thinsp;60 hectares.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅢ. (Moderately Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMain Criteria: State ① : the height range of the plastic zone is between 15m and 30m; The maximum vertical stress is in the range of 65MPa\u0026thinsp;~\u0026thinsp;100MPa; And the maximum settlement of the roof is less than 1m;\u003c/p\u003e \u003cp\u003eState ②: the height of the plastic zone is between 15m and 30m; The maximum vertical stress is in the range of 100MPa\u0026thinsp;~\u0026thinsp;125MPa; And the maximum settlement of the roof is between 1\u0026thinsp;~\u0026thinsp;2m;\u003c/p\u003e \u003cp\u003eSecondary criteria: The mining thickness of the goaf is greater than 5m; Mining width greater than 700m; The buried depth of the goaf is more than 650m; The mining area is in the range of 60 to 100 hectares.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅣ. (Basically stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMain Criteria: the height of plastic zone is greater than 30m; The maximum vertical stress is greater than 125MPa; Roof settlement exceeds 2m;\u003c/p\u003e \u003cp\u003eSecondary criteria: The mining thickness of the goaf is greater than 5m; Mining width greater than 700m; The buried depth of the goaf is more than 650m; More than 100 hectares were mined.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the parameters such as plastic zone height, vertical stress magnitude, and roof subsidence obtained through numerical simulation are comprehensively calculated based on factors such as burial depth, mining width, and area. These objective factors serve as supplements to the evaluation criteria, mainly corresponding to the respective grades. The evaluation results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Through overall analysis combined with these objective factors, it is found that when the burial depth is greater and the mining scale is larger, the stability of the void areas is relatively poorer. For example, areas 5, 7, and 14 all represent interconnected void areas with large scales. However, unlike these three void areas, area 9, although it also belongs to a relatively large interconnected void area, experiences less stress and deformation due to its shallower burial depth. All void areas classified under the strong stability category are formed by single working faces with effective coal pillars between them, effectively preventing excessive stress concentration in the void areas. Through comprehensive analysis, it is concluded that void stability is mainly related to factors such as void width and void area.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eClassification of goaf stability grades\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf stability rating\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGoaf number\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅠ. (Strong Stability)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2、8、10、12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅡ. (Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1、3、4、6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅢ. (Moderately Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9、11、13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅣ. (Basically stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5、7、14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eTheoretical study on site stability of goaf based on AHP vulnerability index method\u003c/h2\u003e \u003cp\u003eConsidering the main influencing factors of goaf site stability, three first-level indexes, including geological factors, mining factors, hydrological conditions and other influencing factors, and eight corresponding second-level indexes were selected, and a comprehensive evaluation index system for goaf site stability was established.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, there are eight quantifiable indicators. Firstly, the complexity of geological structures is quantified by calculating the fault range index, which effectively reflects the scale and development of faults in the study area. Secondly, based on previously collected information on the void areas, the void areas are quantified, including characteristics such as roof and floor lithology and thickness, void width, area, stop mining time, and water accumulation in goaf. Additionally, geological stress and mining depth are calculated based on the burial depth and mining thickness of the void areas.\u003c/p\u003e \u003cp\u003eFinally, Surfer software is utilized to generate contour maps through data interpolation, establishing thematic maps of the major influencing factors to display their distribution and characteristics, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e to \u003cspan refid=\"Fig21\" class=\"InternalRef\"\u003e21\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eComplexity of geological structures\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe quantification of fault range index can be calculated using the following formula:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$F=\\frac{{\\sum\\limits_{{i=1}}^{n} {{L_i}{H_i}} }}{S}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eF\u003c/em\u003e represents the fault range index.\u003c/p\u003e \u003cp\u003e \u003cem\u003ei\u003c/em\u003e represents a certain fault in a certain partition of the study area.\u003c/p\u003e \u003cp\u003e \u003cem\u003eH\u003c/em\u003e \u003csub\u003e \u003cem\u003ei\u003c/em\u003e \u003c/sub\u003e represents the vertical displacement of fault \u0026#119894;, in meters.\u003c/p\u003e \u003cp\u003eL\u003csub\u003ei\u003c/sub\u003e represents the length of fault \u0026#119894;, in meters.\u003c/p\u003e \u003cp\u003e \u003cem\u003en\u003c/em\u003e represents the number of faults in the study area partition.\u003c/p\u003e \u003cp\u003e \u003cem\u003eS\u003c/em\u003e represents the area of the study area partition, in square meters.\u003c/p\u003e \u003cp\u003eAccording to the meaning of Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, The size of the fault range index directly reflects the complexity of geological structures. This is clearly demonstrated in the zoning results in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. According to the natural breakpoint method, regions are categorized as follows: F\u0026lt;0.03 for simple type, 0.03\u0026thinsp;\u0026lt;\u0026thinsp;F\u0026thinsp;\u0026le;\u0026thinsp;0.07 for moderate type, 0.07\u0026thinsp;\u0026lt;\u0026thinsp;F\u0026thinsp;\u0026le;\u0026thinsp;0.11 for relatively complex type, and 0.11\u0026thinsp;\u0026lt;\u0026thinsp;F\u0026thinsp;\u0026le;\u0026thinsp;0.13 for complex type. Specifically, in the geological conditions of the Sanhejian mine area, the northern and eastern regions exhibit relatively complex geological structures due to the presence of long and high-displacement faults or fault intersections. This complexity is mainly attributed to the interactions between faults and the diversity of their mechanical behavior within the crust. In contrast, the geological structures in the western and southern parts of the mining area are relatively simple, with some areas even showing extremely low geological development, indicating higher geological stability and less fault activity in these areas.\u003c/p\u003e \u003cp\u003e2. Lithology and thickness of the roof\u003c/p\u003e \u003cp\u003eXu (Xu et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) discovered through natural equilibrium analysis that the greater the thickness of the overlying strata of a goaf, the higher its stability. Based on the geological exploration data of the Sanhejian mining area, including detailed analyses of borehole information column charts and exploration line profiles, it has been determined that both the roof and floor of the goafs in this mining area are composed of siltstone layers. During coal mining, siltstone layers play a crucial role in controlling mine pressure and roof displacement damage. The thickness of the roof is a key factor influencing the stability of goafs, with thicker roofs being more favorable for enhancing overall goaf stability.\u003c/p\u003e \u003cp\u003eThis study further assesses the geological stability of the mining area by quantifying the influence of roof thickness as a factor. According to the zoning results in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e, the roof thickness in the northern and southeastern parts of the Sanhejian mining area is relatively large, especially in the eastern region, where the maximum roof thickness can reach 8 meters. In contrast, the roof thickness in most other areas of the mining area is less than 5.5 meters, with relatively small variations in roof thickness within these areas.\u003c/p\u003e \u003cp\u003e3. Geostress\u003c/p\u003e \u003cp\u003eIn the Sanhejian mining area, after coal seam mining is completed, due to the significant burial depth of the goafs, the overlying strata exert considerable self-weight stress on the goaf roof, which can easily cause damage to the surrounding geological bodies. In order to systematically analyze and evaluate the influence of self-weight stress on the stability of goafs, this study quantifies the effect of self-weight stress on the geostress indicators within the mining area. This allows for a more accurate assessment of the geostress state and surrounding rock stability within the mining area. According to the zoning results in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e, the geostress in the eastern part of the study area is relatively low, with the lowest geostress occurring in the southeastern region at 8.5 MPa. In contrast, the geostress in the southwestern and northwestern parts of the mining area is significantly higher, exceeding 17.5 MPa.\u003c/p\u003e\u003cp\u003e4. Stop mining time\u003c/p\u003e \u003cp\u003eThe mining sequence in the Sanhejian mining area follows a shallow-to-deep approach. Goafs mined earlier have undergone long-term evolution, leading to a redistribution of stress and achieving a balanced state. According to the final mining information of the Sanhejian mining area, goafs 7, 9, and 11, which have shallow burial depths, were mined before 2007 and are essentially stable, with no further deformation or damage expected. Goafs 2, 3, 4, etc., however, were mined later due to their greater burial depths, and thus there is a possibility of further damage. The specific zoning of stop mining time is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e5. Mining depth ratio\u003c/p\u003e \u003cp\u003eIn mining engineering, the mining depth-to-thickness ratio is an important technical parameter that represents the ratio of coal seam burial depth to coal thickness. A higher ratio generally indicates better mining safety. Therefore, goafs with a larger depth-to-thickness ratio are expected to be safer and more stable. Based on this ratio, the mining area is divided into zones, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e18\u003c/span\u003e. Due to the shallow burial depth and greater coal thickness in the eastern part of the Sanhejian mining area, the depth-to-thickness ratio in this area is relatively small. Conversely, influenced by faults, the southwestern and northwestern parts have greater coal seam burial depths and thinner coal seams, resulting in a relatively larger depth-to-thickness ratio in the western areas.\u003c/p\u003e\u003cp\u003e6. Goaf width\u003c/p\u003e \u003cp\u003eGoaf width is a key factor controlling the stability of goafs and has a significant influence on the deformation of the goaf roof. After coal seam extraction, pressure arches form above the goaf, where the weight of the overlying rock mass transfers towards the sides of the working face (at the foot of the pressure arch). Previous numerical simulation studies have shown that as the goaf width increases, the outer width of the pressure arch above the goaf also increases, resulting in greater stress concentration on the sides of the working face and thus reduced stability of the goaf. Goaf widths, as indicated by statistics, are annotated in Fig.\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e. Goafs 7, 9, 14, and 5 have larger areas, with goaf widths all exceeding 800 meters.\u003c/p\u003e\u003cp\u003e7. Goaf area\u003c/p\u003e \u003cp\u003eHu(Hu and Li \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) using Bayesian discriminant analysis to identify risks in complex mining goafs, argues that larger goaf areas correspond to poorer goaf stability. Combining this with the Sanhejian closed mining area, Fig.\u0026nbsp;\u003cspan refid=\"Fig20\" class=\"InternalRef\"\u003e20\u003c/span\u003e divides the goafs into four rough levels. Goafs such as 5, 7, 9, and 14 have larger mining ranges, indicating relatively poorer stability. Conversely, areas such as 1, 2, 8, and 10 have smaller goaf areas, resulting in relatively less deformation and stress, thus indicating greater stability.\u003c/p\u003e \u003cp\u003e8. Water accumulation in goaf\u003c/p\u003e \u003cp\u003eWhen there is significant water accumulation in goafs, the hydrostatic pressure can be considerable and highly destructive. Additionally, water flow gradually erodes the rocks and coal seams within the goaf, reducing the structural strength of the rocks and increasing the risk of collapse. This poses safety hazards for the development and utilization of underground spaces. Through organization and statistical analysis of water accumulation in goafs, it is evident that there is a certain amount of water accumulation in low-lying areas of goafs. Currently, eight main locations of water accumulation are known, primarily distributed in goafs 6, 7, 8, 11, 12, and 13.\u003c/p\u003e \u003cp\u003eAccording to the constructed comprehensive evaluation index system of goaf site stability, A hierarchical structure model is established, aiming at goaf site stability evaluation A. The hierarchical structure model is as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$A=\\left\\{ {{B_1},{\\text{ }}{B_2},{\\text{ }}{B_3}} \\right\\},{\\text{ }}{B_1}=\\left\\{ {{C_1},{\\text{ }}{C_2},{\\text{ }}{C_3}} \\right\\},{\\text{ }}{B_2}=\\left\\{ {{C_4},{\\text{ }}{C_5},{\\text{ }}{C_6},{\\text{ }}{C_7}} \\right\\},{\\text{ }}{B_3}=\\left\\{ {{C_8}} \\right\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAccording to the constructed hierarchical structure model, the 1\u0026ndash;9 scale method is adopted to construct a judgment matrix to determine the importance of each evaluation index. The values of 1\u0026ndash;9 scale method are shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues of the 1\u0026thinsp;~\u0026thinsp;9 scale method\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScale\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeaning\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoth factors are equally important\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSlightly more important\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eObviously important\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStrongly important\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExtremely important\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2、4、6、8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThe median value of the above judgment is expressed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of Collapses\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ei is more important than j is m, then j is more important than i is 1/m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eEach evaluation index is compared pair by pair, and combined with Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, each judgment matrix is obtained, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e to \u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eA-B judgment matrix\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf site stability evaluation A\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGeological factors B\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMining factors B\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHydrogeological conditions B\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeological factors B\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1/2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMining factors B\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHydrogeological conditions B\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1/5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1/8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eB\u003csub\u003e1\u003c/sub\u003e-C judgment matrix\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeological factors B\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGeological structural complexity C\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRoof lithology and thickness C\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeostress C\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeological structural complexity C\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1/2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRoof lithology and thickness C\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1/2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1/4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeostress C\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eB\u003csub\u003e2\u003c/sub\u003e-C judgment matrix\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMining factors B\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStop mining time C\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDepth-to-coal ratio C\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGoaf width C\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGoaf area C\u003csub\u003e7\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStop mining time C\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1/2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1/3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDepth-to-coal ratio C\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf width C\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1/2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1/4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf area C\u003csub\u003e7\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1/3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eB\u003csub\u003e3\u003c/sub\u003e-C judgment matrix\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHydrogeological conditions B\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater volume in goaf C\u003csub\u003e8\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater volume in goaf C\u003csub\u003e8\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe weights of each evaluation index are calculated according to the eigenvector method. Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the statistics of the weights of evaluation indexes.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistics on the weights of evaluation indicators at all levels\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTarget layer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCriterion layer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eW(B/A)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAssessment layer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eW(C/B)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eW(C/A)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"7\" rowspan=\"8\"\u003e \u003cp\u003eGoaf site stability evaluation A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eGeological factors B\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.3258\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeological structural complexity C\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.2857\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0931\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRoof lithology and thickness C\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.1429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0466\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeostress C\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.5714\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.1862\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eMining factors B\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eGeological\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.6039\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStop mining time C\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0909\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0549\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDepth-to-coal ratio C\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.2403\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.1451\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGoaf width C\u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.1656\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.1000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGoaf area C\u003csub\u003e7\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.5032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.3039\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHydrogeological conditions B3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0703\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWater volume in goaf C\u003csub\u003e8\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0703\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe consistency test of the constructed judgment matrix is performed:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${C_R}=\\frac{{{C_I}}}{{{R_I}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, C\u003csub\u003eR\u003c/sub\u003e is the consistency ratio; C\u003csub\u003eI\u003c/sub\u003e is a general consistency index; R\u003csub\u003eI\u003c/sub\u003e is the average random consistency index.\u003c/p\u003e \u003cp\u003eIt can be obtained by calculation that the CR value of each judgment matrix is less than 0.1, which meets the requirements of consistency test. The consistency tests of judgment matrices at all levels are shown in Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eConsistency test of judgment matrix at all levels\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJudgment matrix\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC\u003csub\u003eR\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA-B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.0055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eB\u003csub\u003e1\u003c/sub\u003e-C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.0538\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0517\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eB\u003csub\u003e2\u003c/sub\u003e-C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.1312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0492\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eB\u003csub\u003e3\u003c/sub\u003e-C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to the weight calculation of the evaluation index, it is found that the mining factors of the goaf are the key factors affecting the stability of the goaf, which is consistent with the conclusion obtained in the previous numerical simulation research, while the hydrogeological conditions have little influence on the stability of the goaf.\u003c/p\u003e \u003cp\u003eSince the unit dimensions of each major influencing factor are different, it is necessary to standardize each major influencing factor in order to ensure the consistency of the evaluation factors. It can be normalized with the following formula:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${A_i}=\\left\\{ {_{{a+\\frac{{(b - a) \\times (\\hbox{max} ({x_i}) - {x_i})}}{{\\hbox{max} ({x_i}) - \\hbox{min} ({x_i})}}{\\text{, where }}x{\\text{ is a negative factor}}}}^{{a+\\frac{{(b - a) \\times ({x_i} - \\hbox{min} ({x_i}))}}{{\\hbox{max} ({x_i}) - \\hbox{min} ({x_i})}},{\\text{ where }}x{\\text{ is a positive factor}}}}} \\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere Ai is the data after standardization of each major influence factor, and the lower limit and upper limit of the standardization range of a and b, as shown in this paper (a\u0026thinsp;=\u0026thinsp;0, b\u0026thinsp;=\u0026thinsp;1); \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the original data before standardization, min(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) is the quantified minimum value of each major influence factor, and max(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) is the maximum value of each major influence factor.\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$VI=\\sum\\limits_{{k=1}}^{n} {{W_k}{f_k}(x,y)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, W\u003csub\u003ek\u003c/sub\u003e represents the weight value of each major influencing factor; n is the number of influencing factors; (x, y) are geographical coordinates; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{k}\\left(x,y\\right)\\)\u003c/span\u003e\u003c/span\u003eis a single factor influence function.\u003c/p\u003e \u003cp\u003eThe weight values of the main influencing factors obtained in the analytic hierarchy process are substituted into formula 7 o obtain the final stability evaluation model of the goaf in the Sanhejian closed mining area:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} VI=0.1087{f_1}(x,y)+0.0461{f_2}(x,y)+0.1710{f_3}(x,y)+0.0549{f_4}(x,y)+0.1451{f_5}(x,y) \\hfill \\\\ +0.1000{f_6}(x,y)+0.3039{f_7}(x,y)+0.0703{f_8}(x,y) \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSince the main influencing factors C\u003csub\u003e2\u003c/sub\u003e, C\u003csub\u003e4\u003c/sub\u003e and C\u003csub\u003e5\u003c/sub\u003e are roof lithology and thickness, final mining time and depth ratio of coal seam respectively, they are negatively correlated with VI value, and are quantified as negative values. The smaller the absolute values of C\u003csub\u003e2\u003c/sub\u003e, C\u003csub\u003e4\u003c/sub\u003e and C\u003csub\u003e5\u003c/sub\u003e are, the greater the VI value is, and the worse the stability of goaf. The other five main influencing factors are positively correlated with the target layer, and the higher the VI value, the worse the stability of the gob.\u003c/p\u003e \u003cp\u003eThe VI value was obtained based on the vulnerability index model, and then the isoline map of VI was drawn using the grid value module of surfer software. The natural breakpoint classification method was used to obtain the vulnerability assessment zone thresholds of 0.09, 0.20 and 0.31 As shown in Table \u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. respectively, and the vulnerability areas of goaf stability in the study area were divided according to the vulnerability assessment thresholds. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e show the evaluation results.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab12\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSanhejian closed the goaf stability and vulnerability zoning in the mining area\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStability level\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVI\u0026thinsp;\u0026le;\u0026thinsp;0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eⅠ. (Strong Stability)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.13\u0026thinsp;\u0026lt;\u0026thinsp;VI\u0026thinsp;\u0026le;\u0026thinsp;0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eⅡ. (Stable)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.23\u0026thinsp;\u0026lt;\u0026thinsp;VI\u0026thinsp;\u0026le;\u0026thinsp;0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eⅢ. (Moderately Stable)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.32\u0026thinsp;\u0026lt;\u0026thinsp;VI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eⅣ. (Basically stable)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe stability of the goaf in the Sanhejian mining area is still divided into strong stability, stability, medium stability and basic stability. The stability of goaf in the east, middle and south of Sanhejian mining area is relatively poor, and the stability of goaf 1, 2, 8, 10 and 12 is better than that of other goaf areas. Except for some areas, the classification of the stability of the goaf is basically consistent with the results of the numerical simulation, and the coincidence rate is close to 80%, which is effectively verified. Table\u0026nbsp;\u003cspan refid=\"Tab13\" class=\"InternalRef\"\u003e13\u003c/span\u003e show the classification results.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab13\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 13\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGoaf stability grade grading results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf stability level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGoaf number\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅠ. (Strong Stability)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1、2、8、10、12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅡ. (Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3、4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅢ. (Moderately Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6、11、13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅣ. (Basically stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5、7、9、14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eComprehensive evaluation of goaf stability\u003c/h2\u003e \u003cp\u003eDue to the different focus of the two methods, although numerical simulation provides quantitative analysis based on physical models, it ignores some key factors that may affect the evaluation results, such as faults and water deposits. The AHP method of vulnerability index improves the comprehensiveness and accuracy of assessment by supplementing the quantitative assessment of these factors. This also leads to some differences in the evaluation results of some goaf in the mine area.\u003c/p\u003e \u003cp\u003eSpecifically, compared with goaf 2, goafs 1 has a relatively large mining width, and its stress is relatively concentrated in the numerical simulation, and its stability is less stable than that of goafs 2 and 8. Due to shallow burial depth, the maximum numerical stress in goaf 9 is smaller in the simulation results, which is more stable than the goaf with large area and deep burial in goafs 5 and 14. However, the reason for the difference in goaf 6 is more complex. In goaf 6, it is mainly due to the surrounding faults and the water volume in goaf, resulting in a higher vulnerability index. However, for other areas of the goaf, the two evaluation methods obtained the same stability rating results. goafs 2, 8, 10 and 12 were rated as having strong stability in both assessment methods. On the contrary, the stability evaluation results of the goaf in areas 5, 7 and 14 are poor in both methods.\u003c/p\u003e \u003cp\u003eIn view of the differences in the evaluation results of the two methods in some areas, it is necessary to use the two methods comprehensively to effectively improve the reliability and accuracy of the stability assessment of the goaf. Conservative Risk Assessment was used to make a comprehensive analysis of the two evaluation results. The results of goaf stability evaluation are shown in Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab14\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 14\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComprehensive evaluation results of goaf stability\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGoaf stability level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGoaf number\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅠ. (Strong Stability)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2、8、10、12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅡ. (Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1、3、4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅢ. (Moderately Stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6、11、13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eⅣ. (Basically stable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5、7、9、14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the final evaluation results, in the goaf areas with large areas such as areas 5, 7 and 14, the existing coal pillars are small, and the roof support is almost negligible., so that the center of the goaf needs to bear a large tensile stress, due to the superposition of other factors such as faults, roof thickness, etc., it is easier to form a negative impact on the goaf; secondly, the goaf in the stable and medium stability grades, the mining scale is relatively smaller, in which the mining depth ratio of areas 3 and 4 is larger than that of areas 11 and 13, and it is relatively more stable; and the areas 2, 8, 10 and 12 generally have the characteristics of small mining scale and scattered mining, and the stability is relatively better. The evaluation results provide a basis for subsequent development and utilization.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003e(1) In the numerical simulation results, the maximum vertical stress, roof settlement and plastic zone height of the gob are positively correlated with the objective conditions such as the width, area, mining thickness and burial depth of the gob. These objective conditions directly lead to the stability of the through gob being significantly weaker than that of the separated gob. According to the maximum vertical stress, roof settlement and plastic zone height obtained by numerical simulation, the stability of the goaf is divided into four grades: strong stability, stable stability, medium stability and basic stability. The stress and damage degree of goafs 2, 8, 10 and 12 are small and relatively stable, while the stress and damage degree of goafs 5, 7 and 14 are large. The relative stability is poor.\u003c/p\u003e \u003cp\u003e(2) AHP method was used to analyze the weights of 8 factors, among which mining factors accounted for the highest weight, which was consistent with the results of numerical simulation analysis; The VI model of Sanhejian closed mining area was established according to the weights of various influencing factors and goaf information, and the vulnerability assessment zone threshold was determined. The goaf was also classified into grades. The stability evaluation results of goafs 1, 6 and 9 were different from the numerical simulation evaluation results, which were mainly caused by other factors such as faults, water volume and buried depth.\u003c/p\u003e \u003cp\u003e(3) In view of the different concerns of numerical simulation and vulnerability index for goaf, the conservative risk assessment principle is used to combine the evaluation results of numerical simulation and vulnerability index to obtain comprehensive evaluation results. The results show that goafs 2, 8, 10 and 12 are more stable, while goafs 5, 7, 9 and 14 are relatively poor in stability.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eConflict of interest\u003c/h2\u003e \u003cp\u003eNo potential conflict of interest was reported by the author.\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eS.Z. wrote the original manuscript; Z. W. conducted the review; Z.S. provided methodological guidance; F. Z.andY. L. conducted survey and data collection; C. S. and W. Y. provide photo guidance; All authors have read and agreed to the submitted version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis work was supported by the Jiangsu Provincial Geological Exploration Fund (Comprehensive Evaluation and Collaborative Development and Utilization of special Space Resources in Sanhejian Coal Mine, NO. Su Caizi Ring [2021] No. 45)\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAo X, Wang X, Zhu X, Zhou Z, Zhang X (2017) Grouting Simulation and Stability Analysis of Coal Mine Goaf Considering Hydromechanical Coupling. 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Front Earth Sci 11:1063684. https://doi.org/10.3389/feart.2023.1063684\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Closed coal mine, Goaf stability, Numerical simulation, Vulnerability index","lastPublishedDoi":"10.21203/rs.3.rs-4425036/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4425036/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe stability of goaf is one of the decisive conditions for the redevelopment and utilization of underground spaces after mine closure. Taking the Sanhejian closed mine area as an example, this study comprehensively evaluates the stability of the goaf using numerical simulation, Analytic Hierarchy Process (AHP), and Vulnerability Index (VI). Firstly, the numerical model of the goaf was built using FLAC\u003csup\u003e3D\u003c/sup\u003e software to obtain the stress field, displacement field, and characteristics of plastic zone development. Based on the simulation results, stability evaluation criteria for the goaf were formulated, and stability levels were determined. Secondly, a vulnerability assessment model was established using AHP, selecting geological factors, mining factors, and hydrological factors as primary indicators and further determining eight secondary indicators, including geological structural complexity, roof lithology and thickness, geostress, stop mining time, depth-to-coal ratio, goaf width, goaf area, and water volume in goaf. The weights of each indicator were determined, and the indicators were quantified to calculate the VI value of the vulnerability assessment model. The stability zoning threshold of the goaf was obtained using a natural breakpoint classification method and verified against the numerical simulation results to enhance the accuracy of stability evaluation. By integrating the results of both methods and adhering to a conservative risk assessment principle, the stability level of the goaf was ultimately determined, providing reference for the stability evaluation of related underground spaces.\u003c/p\u003e","manuscriptTitle":"Stability evaluation of goaf in closed mining area: a case study of Sanhejian closed mining area in Jiangsu Province, China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-31 20:35:54","doi":"10.21203/rs.3.rs-4425036/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f90b4de5-d1cb-4c96-bd61-0cdb6e381cf2","owner":[],"postedDate":"May 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-18T02:55:28+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-31 20:35:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4425036","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4425036","identity":"rs-4425036","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}