In the context of long-term and large-scale underground mining in Chinese coal mines, the goaf represents one of the critical factors influencing the safety of mine production. Coal pillars are the main structural units contributing to the stability of a goaf, and therefore, it is crucial to evaluate the stability of coal pillars to enable efficient and safe mining in underground mines.

In recent decades, scholars have adopted various methods to understand and predict the stability of coal mine pillars. Empirical methods are usually based on an empirical formula that is used to estimate the strength of each coal pillar (Hustrulid, 1976; Jawed et al., 2013; Lai et al., 2020). Because it is difficult to determine the actual stress on an underground mine, the safety factor (FS) of the coal pillar (i.e., the ratio of its average strength to average stress) is computed to evaluate its stability (Deng et al., 2003). In general, FS > 1.0 is stable, whereas FS < 1.0 is unstable (Zhou et al., 2011; Wattimena, 2014; Zhou et al., 2022).

Numerical simulation technology has gradually been applied for coal pillar stability analysis. Deng et al. combined Monte Carlo and FLAC (Fast Lagrangian Analysis of Continua) methods to analyze the stability of coal pillars. Mortazavi et al. (2009) used UDEC (Universal Distinct Element Code) software to evaluate the influence of a pillar’s geometry and mechanical parameters on its deformation and failure. These studies have significantly improved our understanding regarding the stability of coal pillars; however, because of the numerous influencing factors, these two methods have difficulty considering the impact of uncertainty, and the limit of the safety factor is not clear.

With recent advances in data mining technology, intelligent evaluation models have been successfully applied in the field of mining engineering, which constitutes a key development direction for the future of coal mining. For example, Deng et al. (2002) used an improved finite element Monte Carlo method to analyze the reliability of point pillars in metal mines. Zhao et al. (2003) and Luo et al. (2007) evaluated the stability of coal pillars based on dynamic fuzzy reliability. Cauvin et al. (2009) combined the Monte Carlo and safety factor methods to analyze the stability of coal pillars Monjezi et al. (2011). used a neural network algorithm to predict coal pillar stress to guide coal pillar design strategies Idris et al. (2015). combined the Monte Carlo method, neural networks, and FLAC3D (Universal Distinct Element Code 3D) to analyze the stability of coal pillars during excavation. Wattimena et al. (2013) used multiple logistic regression model to predict the stability of 89 hard rock coal pillars. Zhou et al. (2015) compared the performance of six supervised learning algorithms [i.e., linear discriminant analysis (LDA), polynomial logic regression (MLR), random forest (RF), artificial neural network (ANN), support vector machine (SVM), and gradient hoist (GBM)] for coal pillar stability identification based on 251 examples of hard rock coal pillars; they determined that the SVM and RF algorithms showed superior performance. Ghasemi et al. (2010) used Monte Carlo simulations to study the influence of various parameters (e.g., uniaxial compressive strength of coal sample, width of coal pillar, height of coal pillar, width of entrance, and depth of covering) on the FS of coal pillars. Zhou et al. (2011) proposed two models for predicting the stability of coal pillars by employing support vector machine and Fisher discriminant analysis. However, the evaluation indicators of each of the described models are different, and anomaly detection is particularly important in high-dimensional data analysis. Thus, it is necessary to develop a reasonable and effective input parameter database and an intelligent model to evaluate the stability of coal pillars in Chinese mines.

Considering the limitations of the aforementioned models, the main contributions of the present study can be summarized as follows: 1) an energy conservation model of the longwall stope is introduced to identify the factors influencing coal pillar stability; 2) 125 historical cases of coal pillars in China are collected, and a large dataset comprising Chinese coal pillar information is compiled following anomaly detection and treatment; 3) the mean impact value (MIV) is used to evaluate the sensitivity of variables, and a genetic algorithm (GA) and back-propagation (BP) neural network fusion model is established to verify the prediction performance; 4) two field cases are discussed to evaluate the model’s prediction performance for coal pillar stability analysis.

Longwall mining induces the fracture of coal and rock mass. The phenomena of energy storage, energy consumption, and energy distribution co-exist during this process, which can be regarded as a gradual failure caused by energy transfer. As shown in Supplementary Figure S1, as the coal seam is mined out, the energy inside the system reaches an equilibrium state, resulting in the generation of an excavation disturbed zone (EDZ) (Lai et al., 2006), and the coal pillar is the main structural unit affecting the stability of the EDZ.

As shown in Supplementary Figure S2, the longwall stope and surrounding rock are regarded as a system wherein the balance between their energy components should be maintained. During the mining process of the working face, the back rock layer is allowed to collapse at a certain distance; the released energy increases the strain of the roof rock stratum, which causes the roof rock to fracture and cave, thus relieving the pressure and producing an area with a certain height above the stope, namely, the EDZ. The energy conservation model of the longwall stope was established by Rezaei et al. (2015). The total stress is determined according to the difference between the weight of overburden rock and the weight of the failure area. Then, the vertical component of the mining stress is determined by calculating the reciprocal angle of the strata collapse. Finally, the stress concentration coefficient of the coal pillar can be calculated according to the vertical component of the mining stress, which can guide the flow of the coal pillar stability analysis, as shown in Supplementary Figure S3.

The total strain energy consumption is stored in the mined coal body during roof rock fracture, caving, and pressure relief. Therefore, the strain energy in the mined coal body should be equal to that in the collapsed material in the failure area, as expressed in Eq. 1, U m = U d (1) where U _m is the strain energy in the EDZ, and U _d is the strain energy in the EDZ.

Rezaei et al. (2015) derived the formulas for calculating the stored strain energy in the coal seam, and the final equations for calculating the total energy storage of the coal seam are shown in Eqs 2, 3, U m = ( 1 + v ) ( 1 − 2 v ) γ A m δ v 2 ( 1 − v ) E ( h s 2 3 + H 2 + H h s ) (2) U d = U E + U v = E e − a t A d H d δ c 2 2 ( E + b δ c b − 1 ) + ( ξ 2 2 K − λ ξ 2 2 ) A d H d = A d H d δ c 2 2 ( E + b δ c b − 1 ) 2 ( 2 E e − a t + δ s u 1 B t 2 − λ ) (3) where v is the Poisson ratio of the rock mass; γ is the volume density of the overlying strata (N/m³); h _s is the height of the coal seam; L _w is the height of the working face; A _m is the cross-sectional area of the coal seam (such that A _m = L _w × h _s); σ _v is the vertical stress; H is the buried depth of the coal seam; and E is the elastic modulus of the coal seam. In general, in the failure zone (U _d), the storage strain energy of the material consists of elastic strain energy (U _E) and viscoplastic strain energy (U _v ). Here, A _d is the unit surface of the goaf (such that A _d = L _w × 1 m); σ _c is the uniaxial compressive strength of the goaf material; b is the expansion coefficient; σ _s is the stress threshold; B is the material constant related to viscosity and temperature; t is the pressure time of the goaf material; λ is the slope of the material hardening stage; and ω, a, and μ ₁ are material constants.

By substituting Eqs 2, 3 into Eq. 1, the EDZ height (H _d) under long-term conditions can be obtained using: H d = ( 1 + v ) ( 1 − 2 v ) γ A m δ v ( 1 − v ) E ( h s 2 3 + H 2 + H h s ) ( E + b σ c b − 1 ) 2 A d δ c 2 ( 2 E e − a t + δ s u 1 B t ∂ − λ ) (4)

The vertical component of the mining stress (σ _a(v)) and the stress concentration coefficient (K) of the load transferred to the roadway and coal pillar can then be obtained, as shown in Eqs 5, 6, respectively: σ a ( v ) = σ a ⁡ cos ⁡ β = γ ( H − H d ) cos ( tan − 1 ( X H d ) ) = [ γ H − ( 1 + v ) ( 1 − 2 v ) γ A m δ v ( 1 − v ) E ( h s 2 3 + H 2 + H h s ) ( E + b σ c b − 1 ) 2 A d δ c 2 ( 2 E e − a t + δ s u 1 B t ∂ − λ ) ] H d 2 H d 2 + X 2 (5) K = σ s σ v = σ v + σ a ( v ) σ v = [ σ v + ( σ v − γ H d ) H d 2 H d 2 + X 2 ] σ v (6)

These values enable the design of roadway supports and coal pillar stability analysis. The load of the overlying strata is transferred to the coal pillar through the suspended roof, which reveals different levels of integrity in different sections of the coal pillar (i.e., a crushing zone, a plastic zone, and an elastic zone).

Hou and Ma (1989) proposed a method for calculating the width of the stress limit equilibrium zone, as expressed in Eq. 7, x = m A 2 ⁡ tan ⁡ ψ ln [ K γ H + c tan ⁡ ψ c tan ⁡ ψ + P x A ] (7) where φ and c represent the internal friction angle and cohesion of the coal seam, respectively.

Therefore, the coal pillar stability analysis in longwall mining involves a multi-factor nonlinear coupling problem, and the following factors affecting the stability of the coal pillar must be considered as thoroughly as possible.

1) Static parameters (the static physical and mechanical parameters of the coal and rock mass): elastic modulus, Poisson’s ratio, internal friction angle, cohesion, bulk density, etc.

In conclusion, the influencing factors of coal pillar stability were determined, thereby providing a theoretical basis for establishing a coal pillar database. Additionally, the analysis offers reasonable model input factors for predicting coal pillar multi-factor nonlinear coupling disasters under engineering disturbance. Moreover, coal pillar stability control measures can be designed based on stope stress transfer to reduce mining stress transfer (e.g., via roof cutting and pressure relief), strengthen the support strength (i.e., roadway support), and optimize the coal pillar size.

In mining and geotechnical engineering, it is difficult to determine reliable input parameters and find effective methods for accurately describing this nonlinear relationship, and as a result, it is often challenging to assess reliability. This report aims to establish a coal pillar database and develop reliable datasets through data mining technology to improve the calculation performance of the described prediction model. The coal pillar data transfer pathway is illustrated in Supplementary Figure S4.

The Yujing coal mine (YCM) and the Xiaobaodang coal mine (XCM) were used to validate the engineering applicability of the developed model for real mines. The location and development plan of these mines are presented in Supplementary Figure S14.

The results presented herein lead to the following conclusions:

1) Coal pillar instability induced by mining stress transfer was analyzed, and the main influencing factors are static parameters (e.g., E, μ, φ, c, γ, σ) and engineering design parameters (L, h, H, θ, M).