The High-Precision Monitoring of Mining-Induced Overburden Fractures Based on the Full-Space Inversion of the Borehole Resistivity Method: A Case Study

Abstract

The evolution of mining-induced overburden fractures (MIOFs) and their dynamic monitoring are critical for preventing roof water hazards and gas disasters in coal mines. Conventional methods often fail to provide sufficient accuracy under the thin soft–hard interbedded roof strata, necessitating advanced alternatives. Here, we address this challenge by proposing a borehole resistivity method (BRM) based on Back-Propagation Neural Network full-space inversion (BPNN-FSI). Based on the Carboniferous Taiyuan Formation in the North China Coalfield, geoelectric models of MIOFs were established for different mining stages. Finite element simulations generated apparent resistivity responses to train and validate the BPNN-FSI model. At the 9-204 working face of Dianping Coal Mine (Shanxi Province), we compared the proposed BRM based on BPNN-FSI with an empirical formula, numerical simulation, similarity physical simulation, and underground inclined drilling water-loss observations (UIDWLOs). Results demonstrate that the BRM based on BPNN-FSI achieves sub-1% error in height of MIOF (HMIOF) monitoring, with a maximum detected fracture height of 52 m—significantly outperforming conventional methods. This study validates the accuracy and robustness of BRM based on BPNN-FSI for MIOF monitoring in thin soft–hard interbedded roof strata, offering a reliable tool for roof hazard prevention and sustainable mining practices.

1. Introduction

Coal serves as a critical pillar for China’s energy security [1,2]. The development patterns of mining-induced overburden fractures (MIOFs) are significantly influenced by the complex interplay between soft rock plasticity and hard rock brittleness, particularly under the challenging conditions of deep high ground stress and the dynamic evolution of fracture networks [3,4,5]. Under the coupled effects of high-intensity mining and deep high ground stress, the dynamic evolution mechanisms of MIOFs remain poorly understood [6,7]. Given that MIOFs serve as primary pathways for water inrush and gas migration, they pose direct threats to mine safety. Although monitoring methods for MIOFs have advanced in recent years, existing methods still lack high-precision dynamic monitoring capabilities under the thin soft–hard interbedded roof strata of central and western China, especially for fracture evolution in soft–hard interbedded roofs. High-precision dynamic monitoring of MIOFs can effectively elucidate these mechanisms, providing a scientific foundation for the proactive prevention of roof water hazards and gas disasters.

Current research methodologies for MIOF evolution can be classified into four primary categories. Empirical formula methods, based on statistical analysis of extensive field measurements, provide rapid predictive models for engineering applications. Mechanical analysis methods employ theoretical frameworks to develop analytical models, elucidating the mechanisms of MIOF evolution under varying geological conditions. Numerical simulations and similarity physical simulations visually reconstruct the dynamic development of MIOF through computational modeling and scaled physical testing. In situ monitoring techniques, integrating borehole television, distributed optical fiber sensing, hydrogeological testing, and geophysical prospecting, enable real-time monitoring of MIOF evolution. These approaches, each with distinct advantages, collectively form a comprehensive methodological framework for MIOF research. Liu Tianquan [8] pioneered empirical models for predicting MIOF height by systematically analyzing mining data from eastern China, establishing a quantitative foundation for MIOF studies. From a mechanical perspective, Zhang et al. [9] derived a plastic zone boundary equation using elastoplastic theory and the Mohr–Coulomb criterion, clarifying fracture initiation and propagation in thick–hard roofs. Meanwhile, Xiao et al. [10] applied key stratum theory to reveal how dominant strata control fracture orientation and extent. Numerical studies by Guo et al. [11] uncovered the dynamic evolution of annular fracture zones in longwall panels and their correlation with gas migration. In contrast, Han et al. [12] identified saddle-shaped plastic zones in gobs, linking their height to shear stress distribution through orthogonal numerical experiments. Sun et al. [13] combined physical and numerical simulations to demonstrate the inverse relationship between coal pillar width and overburden damage in twin-seam mining. For in situ monitoring advancement, Yang et al. [14] observed the development of MIOFs in a fully mechanized mining face using underground borehole television, obtaining the height of MIOF development. Meanwhile, Zhang et al. [15,16,17] monitored the evolution of MIOFs during coal mining using distributed optical fiber sensing and combined this with lithological analysis to determine the height of MIOF development. Further advancing the field, Zhang et al. [18] used theoretical analysis, numerical simulation, and underground inclined drilling water-loss observations (UIDWLOs) to clarify the failure mode of weak overburden under thick loose strata and the evolution of MIOFs. Wang et al. [19] studied the temporal effect of MIOF development under shallow loose strata by applying borehole flushing fluid consumption, borehole television, and rock core RQD indicators to investigate the post-mining closure effect of MIOFs. Beyond fracture characterization, Cheng et al. [20] proposed an algorithm for optimizing the layout of microseismic monitoring points, achieving high-precision source location in underground confined-space microseismic monitoring. Additionally, the borehole resistivity method (BRM) has emerged as a dynamic, full-space monitoring tool. For instance, Hou et al. [21] applied this technique to delineate fracture zones, guiding optimal gas drainage borehole placement.

Current methodologies for investigating MIOF evolution exhibit significant limitations in addressing the thin soft–hard interbedded roof strata prevalent in central and western China. Traditional approaches—including empirical formulas, mechanical analyses, numerical simulation, similarity physical simulation, and static monitoring techniques—are constrained by theoretical simplifications and static observation paradigms, resulting in inadequate accuracy for dynamic fracture characterization. While the UIDWLO method demonstrates high precision in HMIOF monitoring in overlying strata during coal seam roof failure and has been widely adopted in field applications, its effectiveness is constrained by its limited detection range (restricted to borehole vicinity), construction complexity, and susceptibility to borehole collapse [22]. While BRM offers dynamic monitoring capabilities, its dependence on conventional half-space inversion theory compromises inversion precision, failing to meet practical engineering requirements for accurate fracture identification. This coexistence of multiple methods with their respective limitations severely restricts the accurate revelation of the evolution of MIOFs under thin soft–hard interbedded roof strata. In this study, we address the technical challenge of high-precision dynamic monitoring of MIOFs under thin soft–hard interbedded roof strata in the central and western regions of China. Taking the typical strata of the Taiyuan Formation in the Carboniferous System of the North China Coalfield as the research object, we constructed geoelectric models of the MIOFs of overburden at different mining stages. The apparent resistivity responses of these models were calculated using the finite element method to build the training and testing sets for the Back-Propagation Neural Network full-space inversion (BPNN-FSI) model. We then established the BPNN-FSI model and proposed a BRM based on BPNN-FSI. Using the 9-204 working face of Dianping Coal Mine in Shanxi Province as an engineering case, we comprehensively applied the empirical formula, numerical simulation, similarity physical simulation, UIDWLO, and the BRM based on BPNN-FSI to investigate the evolution of MIOFs. By comparing and analyzing the results obtained from these four methods, we validated the reliability of the BRM based on BPNN-FSI, which achieved high-precision dynamic monitoring of MIOFs. This method can effectively monitor the evolution of MIOFs and provides a new technical means for safe coal mining under thin soft–hard interbedded roof strata in the central and western regions.

2. Case Study Area and Methods

2.1. Geological Setting of the Case Study

The Dianping Coal Mine is located in Dianping Village, Dawu Town, Fangshan County, Lüliang City, Shanxi Province. The coal-bearing strata in the mining area primarily consist of the Upper Carboniferous Taiyuan Formation (C₃t) and the Lower Permian Shanxi Formation (P₁s). The recoverable coal seams include the No. 3, No. 5, and No. 9 seams, with burial depths of 248.9 m, 268.45 m, and 322.03 m, respectively. The interlayer spacing between the No. 5 and No. 9 seams ranges from 63 m to 67.1 m. According to the adjusted mining sequence plan, priority is given to extracting the deeper No. 9 seam. However, MIOFs due to the extraction of the No. 9 seam may compromise the structural integrity of the overlying No. 5 seam. To ensure the safe subsequent mining of the No. 5 seam, it is of theoretical significance to investigate the development height and evolution patterns of MIOFs. This study focuses on the 9-204 working face, with Figure 1 illustrating its roof structure and Figure 2 presenting the layout schematic. Based on the stratigraphic occurrence characteristics illustrated in Figure 1 and the comprehensive rock physical–mechanical parameters presented in

Table 1. Mechanical parameters of rock strata.

Lithology	Average Tensile Strength/MPa	Young’s Modulus /GPa	Cohesion /MPa	Friction Angle/(°)	Poisson Ratio	Density/(kg/m3)	Compressive Strength/MPa
Limestone	2.70	8.69	11.4	38	0.18	2800	34.18
Mudstone	2.48	0.81	2.8	30	0.29	2699	17.8
Sandy mudstone	3.65	1.99	7.8	32	0.28	2600	18.15
Coarse sandstone	4.34	7.92	3.0	40	0.15	2700	49.35
Coal seam	0.20	1.12	0.2	31	0.30	1410	4.7
Fine sandstone	8.50	3.58	9.2	33	0.26	2570	59.96
Medium sandstone	3.50	3.92	5.0	34	0.22	2560	39.4

for the roof and floor strata of the No. 9 coal seam, this study conducted a systematic investigation of the mechanical properties of surrounding rocks. To ensure parameter accuracy, the research team performed rigorous rock mechanics tests on samples collected from the vicinity of the working face. The resultant mechanical properties of both roof and floor strata are systematically summarized in Table 1. The evolution patterns and development height of MIOFs are analyzed, providing a scientific basis for safe coal seam extraction.

2.2. Numerical Simulation

Numerical simulation is an effective method for studying the evolution laws of mining-induced fractures in coal seam roofs during coal mining processes. This study employs the COMSOL Multiphysics 6.1 finite element analysis software to conduct numerical simulations investigating the evolution patterns and development height of MIOFs at the 9-204 working face. In this study, COMSOL Multiphysics 6.1 finite element analysis software was employed, utilizing the steady-state study in the Solid Mechanics module of the Structural Mechanics branch. The modeling procedure essentially follows the same workflow as conventional finite difference software (FLAC3D). The software utilizes an automatic remeshing technology for large-deformation geometries, effectively addressing the mesh adaptation challenges encountered by conventional numerical methods when simulating large roof deformations. Through its advanced visualization capabilities, the spatial distribution characteristics of MIOFs are quantitatively characterized, while the dynamic evolution of fracture development height is visually demonstrated.

2.2.1. Numerical Simulation Model

Based on the geological conditions of the 9-204 working face in the No. 9 coal seam, this study established a three-dimensional numerical model to simulate the evolution characteristics of MIOFs. The model dimensions are 349 m × 349 m × 100 m, incorporating two roadways and one working face (Figure 3). The simulated coal seam has a burial depth of 322 m, with a working face length of 246 m and an average dip angle of 2°. To accurately represent the mining process, a progressive excavation method was adopted to simulate the complete 246 m face advance. For boundary effect mitigation, 50 m wide boundary coal pillars were set on both sides along the x and y directions. This configuration ensures computational reliability by reducing interference from boundary constraints on the analysis of MIOF evolution, thereby enhancing the accuracy of numerical simulations.

2.2.2. Numerical Simulation Scheme

This study employs numerical simulation methods to analyze the in situ stress environment in 250 m deep underground rock strata. The initial in situ stress field (Figure 4) was established by applying 6 MPa vertical stress (Z-axis) and equivalent horizontal stresses (X and Y axes), consistent with the regional in situ stress characteristic of a horizontal-to-vertical stress ratio of 1. The model boundary conditions were configured with fixed constraints at the bottom and normal constraints in horizontal directions. Based on the borehole columnar diagram of the 9-204 working face in Shanxi Dianping Coal Mine, the rock strata were appropriately consolidated and simplified to establish the computational model. The numerical simulation was performed using the Mohr–Coulomb failure criterion [23,24].

2.3. Similarity Physical Simulation

Similar physical simulation of coal mining can visually demonstrate the development process of MIOFs in the coal seam roof. Based on similarity theory, a physical simulation experiment was designed to replicate the mining process of the No. 9 coal seam in Dianping Coal Mine, considering the geological conditions and mining parameters. The model utilized artificially proportioned materials to simulate the mechanical properties of coal and rock strata, with scaling ratios applied to geometry, time, and strength (including density, elastic modulus, uniaxial compressive strength, and Poisson’s ratio). Displacement sensors and stress sensors were employed to monitor real-time fracture development and evolution in the overburden strata during simulated mining. The experimental data were then converted into full-scale strata movement parameters using similarity principles for practical mining applications.

The experiment employed a similarity material model with dimensions of 2.0 m (length) × 0.2 m (width) × 1.15 m (height). The scaling ratios were set as follows: geometric similarity ratio (1:150), time similarity ratio (1:12), density similarity ratio (1:1.5), stress similarity ratio (1:225), and Poisson’s ratio (1:1). The material composition of the model was determined based on the actual physico-mechanical parameters and layer thicknesses of the coal seam roof and floor in the 9-204 working face. These parameters were converted using the aforementioned similarity ratios to ensure that the experimental conditions strictly adhered to the in situ geological conditions.

In the similarity physical simulation, the completed model was first subjected to 72 h of shade drying before removing the channel steels and formworks. Based on the geometric similarity ratio, horizontal and vertical displacement measurement lines were arranged on the No. 9 coal seam roof surface at 10 cm intervals, with densified monitoring points in critical areas (roof strata of both No. 9 and No. 5 coal seams). Reflective targets (2 cm × 2 cm crosses) were fixed using thumbtacks and monitored via total station to track overburden movement (Figure 5). During the mining simulation, a 10 cm protective coal pillar (equivalent to 15 m in situ) was maintained outside the starter cut. The No. 9 coal seam was excavated for 180 cm, with each 10 cm advance followed by a 30 min interval to ensure complete strata movement. The experiment was conducted by two operators working cooperatively to promptly remove excavated materials. High-resolution cameras were employed after each mining increment to document overburden deformation characteristics.

2.4. UIDWLO Monitoring Method

The UIDWLO monitoring method is an effective approach for determining the development height of MIOFs during coal seam roof failure. The UIDWLO monitoring method (Figure 6) represents a high-precision technique for assessing MIOFs in overburden strata. This approach involves establishing an observation chamber at the longwall panel’s stopping line and drilling upward-inclined boreholes to enable accurate monitoring of fracture height development in the overlying strata. The implementation procedure was conducted as follows: A monitoring station was positioned 17 m west of the stopping line in Gateway 9-2042, where a 5 m long drilling chamber was excavated to install the No. 2 hole (detailed drilling parameters are presented in

Table 2. The parameter of the observation borehole.

No.	Diameter (mm)	Orientation Angle (°)	Elevation Angle (°)	Drilling Depth (m)	Measured Height (m)
No. 2 hole	73~89	56	45	94	66

). The borehole was specifically designed with the following technical specifications, ensuring comprehensive coverage of the fracture development zone within the roof strata: a diameter ranging from 73 to 89 mm, an azimuth angle of 56°, an inclination angle of 45°, and a total depth of 94 m (controlling a vertical height of 66 m), the arrangement diagram of UIDWLO is presented in Figure 7. The monitoring system employed a “Double-Packer Leakage Detection Device” to conduct segmented water injection tests, which precisely measured leakage flow rates in each borehole segment (with positioning errors maintained below 5%). This methodology provides reliable quantitative data for characterizing fracture development patterns and determining fracture heights in the overburden strata, offering crucial technical support for stability assessment in mining operations.

2.5. BRM Based on BPNN-FSI Monitoring Method

2.5.1. Working Principle and Advantages of BRM

The BRM is a full-space resistivity method based on the electrical property differences in rock masses. This technique integrates electrical sounding, electrical profiling systems, and drilling monitoring technology to achieve dynamic monitoring of MIOF development in overlying strata during coal seam extraction [25,26,27]. The fundamental principle lies in the fact that stress redistribution in the roof strata caused by coal mining alters the pore structure, mechanical state, and water-bearing characteristics of rock masses, consequently inducing significant changes in their electrical parameters [28,29,30,31]. In practical implementation, electrode arrays identical to those used in conventional high-density resistivity methods are installed in underground boreholes (Figure 8). Current is injected into surrounding rocks through current electrodes while simultaneously measuring potential differences between monitoring electrodes. The apparent resistivity (${\rho }_S$) at each measurement point is then calculated using the apparent resistivity formula [32] (Equation (1)). Through programmed control of electrode combinations and spacings, potential data at different depths can be automatically acquired, enabling real-time monitoring of electrical property evolution from initial strata deformation to the complete process of MIOF development. This approach provides critical data for investigating the evolution patterns of MIOFs and serves as an important foundation for hazard monitoring.

$${\rho }_S=K{\displaystyle \frac{\nabla U}{I}}$$

(1)

In the formula, $K$ represents the full-space array coefficient, $\nabla U$ denotes the potential difference between measuring electrodes M and N, and $I$ stands for the current intensity.

2.5.2. Engineering Design of BRM

This study established a dynamic monitoring method for MIOFs at the 9-204 working face using the BRM. The implementation procedure comprised (1) installation of a monitoring station 17 m west of the stopping line in the 9-2042 Roadway, where a 5 m drilling chamber was excavated to deploy the No. 1 hole (parameters detailed in

Table 3. Parameters of BRM observation borehole.

No.	Diameter (mm)	Orientation Angle (°)	Elevation Angle (°)	Drilling Depth (m)	Measured Height (m)
No. 1 hole	73~89	56	50	105	72

); (2) configuration of the borehole with a 73–89 mm diameter, 56° azimuth angle, 50° inclination angle, and 105 m depth (controlling a vertical height of 72 m) to cover the roof fracture development zone; (3) deployment of a Wenner tripole array featuring 50 electrodes at 2 m intervals through integrated push-in installation technology. The system incorporated borehole cleaning for fractured strata and cement grouting to achieve optimal electrode–wall coupling, forming a complete technical protocol encompassing “borehole design–electrode arrangement–device installation–data acquisition” (layout schematic shown in Figure 9). This solution enabled real-time monitoring of MIOFs within 72 m of the roof strata, providing reliable technical support for safe mining operations. The methodology demonstrated three key innovations: (a) enhanced spatial resolution through optimized electrode spacing, (b) improved data quality via advanced coupling techniques, (c) operational efficiency gains through automated measurement sequences.

2.5.3. BRM Based on BPNN-FSI

(1)

BPNN-FSI model structure

This study conducts research into a full-space inversion borehole resistivity method based on a BPNN algorithm, with particular focus on solving the full-space inversion problem of the geoelectric model for overburden in “two zones”. The BPNN-FSI process essentially represents an iterative optimization of network weights and thresholds, where the training terminates when the mean square error between the network output (inverted resistivity) and desired output (true resistivity of geoelectric model) reaches the preset accuracy. Figure 10 illustrates the network structure of the BPNN-FSI model. In this structure, the input layer consists of apparent resistivity observation data from the geoelectric model, while the output layer produces corresponding inverted resistivity values.

The BPNN-FSI model employs a dual-hidden-layer structure, mathematically expressed as follows: The input layer $X=\left(x_1,x_2,\dots ,x_n\right)$ is mapped to the first hidden layer $H_1$ through weight matrix $W$ and bias vector $b_1$, with its output computed by activation function $f_1$:

$$H_1=f_1\left(WX+b_1\right)$$

(2)

where the $i$ node of $H_1$ is denoted as $h_{1i}$.

The second hidden layer $H_2$ is computed via weight matrix $V$ and bias vector $b_2$, using activation function $f_2$:

$$H_2=f_2\left(VX+b_2\right)$$

(3)

where the $j$ node of $H_2$ is denoted as $h_{2j}$.

The final output layer $C=\left(c_1,c_2,\dots ,c_{2n}\right)$ is determined by weight matrix $D$, bias vector $b_3$, and activation function $f_3$:

$$H_3=f_3\left(DX+b_3\right)$$

(4)

This model achieves the mapping from apparent resistivity data to inverted resistivity values through layer-wise nonlinear transformations.

(2)

Model Training and Testing

Taking the typical stratigraphy of the Carboniferous Taiyuan Formation in North China coalfield as a case study, this research established geoelectric models of MIOFs for different mining stages, based on the developmental patterns of MIOFs during longwall retreating [33,34]. The COMSOL Multiphysics 6.1 finite element method was employed to calculate the apparent resistivity responses of these models, generating the training and testing datasets for BPNN inversion [35]. Field data collection utilized a tripole electrode configuration with 51 measuring electrodes deployed at 2 m intervals. The study systematically constructed 810 representative geoelectric models [35], producing 442,260 sample data points through models. The dataset was partitioned into 730 models (398,580 data points) for training and 80 models (43,680 data points) for independent testing, with the test set rigorously excluded from all training phases to ensure unbiased model evaluation.

To ensure high prediction accuracy while maintaining reasonable training duration, a 4-layer BPNN-FSI network structure was selected [36], as illustrated in Figure 10. The number of neurons in the hidden layers critically determines model performance: insufficient neurons compromise prediction accuracy, whereas excessive neurons not only prolong training time but also degrade the model’s generalization capability. To optimize this parameter, the study first constrained the neuron count range using empirical formulas [36], then systematically evaluated different configurations under fixed hyperparameters (learning rate = 0.01, maximum iterations = 3000, convergence error = 10⁻⁶). The final neuron count was determined through this rigorous trial process, balancing computational efficiency with inversion accuracy.

$$m=\sqrt{n+l}+\alpha$$

(5)

In the formula, m represents the number of neurons in the hidden layer, n denotes the number of neurons in the input layer, and l indicates the number of neurons in the output layer. The constant α ∈ [1, 10]. For the BPNN-FSI prediction, the number of input features is 3, that is, n = 3, and the number of outputs is 2, that is, l = 2. Based on the empirical Formula (5), substituting the feature numbers into the formula yields the range of the hidden layer neurons m as 3–12.

Figure 11 presents comparative results after 3000 training iterations, demonstrating that both prediction accuracy and training duration exhibit positive correlations with neuron quantity. While increasing the number of neurons prolongs training time, the correlation coefficient peaks at 12 neurons. Although this configuration requires marginally longer training, the selected 12-neuron structure optimally balances computational efficiency with predictive precision.

To validate the generalization capability of the BPNN-FSI model, an independent test set (80 model samples excluded from training) was employed for evaluation. The results indicate that inversion accuracy ranges between 0.81 and 0.96 across test samples, with all cases exceeding the 0.8 threshold. This confirms the model’s robust training effectiveness and reliable predictive performance for geophysical inversion tasks.

3. Results

3.1. Numerical Simulation Results

Numerical simulation can effectively reproduce the evolution of MIOFs during coal seam extraction. Under the combined action of tensile and shear stresses, the MIOFs exhibit a stage-wise development characteristic. These fractures include vertical tensile fractures and horizontal shear fractures, which interconnect with each other, ultimately forming a complex three-dimensional spatial network of MIOFs. The failure modes of the rock strata are primarily manifested as follows: tensile failure occurs when the tensile stress exceeds the tensile strength of the rock mass, while shear failure occurs when the shear stress surpasses the peak strength of the rock mass [37,38].

The study analyzed four typical stages of working face advancement at 50 m, 100 m, 150 m, and 246 m (Figure 12). The results demonstrate that the development of MIOFs exhibits distinct stage-wise characteristics. When the 9-204 working face advanced to 50 m, the maximum fracture height reached 8.3 m; this increased to 12.7 m at 100 m and rose significantly to 24.7 m at 150 m. Upon reaching 246 m, the fracture height peaked at 50 m. Notably, when the working face advanced beyond 246 m, fracture development was primarily characterized by horizontal propagation, with the height stabilizing, indicating that the MIOFs entered a stable phase. Further analysis revealed that the fully developed fracture zones were predominantly concentrated directly above the surrounding rock of the stope. Based on these findings, pre-reinforcement measures can be implemented in the coal mining face and roadways to ensure safe extraction.

3.2. Similarity Physical Simulation Results

The interburden strata, serving as the key rock layers between the No. 9 coal seam and No. 5 coal seam, function both as the roof of the No. 9 coal seam and the floor of the No. 5 coal seam. Their structural stability and fracture development characteristics directly influence the minability of the No. 5 coal seam. Similarity physical simulation tests reveal that MIOFs exhibit two dominant patterns: alternating development of bed-separation fractures and newly generated fractures, with fractures primarily inclined from the starter cut toward the goaf direction. These rock layers not only act as potential pathways connecting the goafs of the upper and lower coal seams but also critically affect mine safety through their fracture and movement behavior. Research indicates that as mining depth increases, the fracture patterns of overlying strata become more regular, with damage severity decreasing progressively from the lower to upper sections. This phenomenon provides theoretical support for safe extraction from the No. 5 coal seam.

The development of MIOFs exhibits distinct stage-wise characteristics (Figure 13). The initial fracture stage demonstrates intense rock breakage, followed by periodic fracturing that results in regularly arranged rock blocks with reduced bulking factors, effectively constraining the movement of upper strata. As the goaf expands, the strata transfer fracture forces through voussoir beam articulated structures, while the suspended roof effect promotes upward propagation of bed separation. Notably, fracture development near the coal seam is significantly more pronounced than in distant strata. Interlayer deformation analysis reveals that the fracture of thick, hard strata can induce grouped movement of overlying formations, forming enclosed bed-separation structures near the No. 5 coal seam. Physical simulation tests confirm that after mining the No. 9 coal seam, the HMIOF reaches 30 cm (equivalent to 45 m in prototype scale).

3.3. UIDWLO Results

The results of UIDWLO (Figure 14) show that the mining-affected zone can be divided into two typical areas: Zone I (the zone of MIOFs) exhibits water leakage rates of 4.8–30.2 L/min, reflecting significant fracture development, while Zone II (the bending subsidence zone) shows reduced leakage rates of 1.2–3.2 L/min, notably, within the borehole interval of 79–83 m, localized increases in drilling fluid loss were observed. However, analysis of the borehole log indicates that this elevated loss is attributable to bed separation in the coal seam roof. Based on the geometric relationship of boreholes, the measured data indicate that the maximum HMIOF above the 9-204 working face reaches 51.62 m, with the fracture development apex located at a borehole depth of 73 m. These quantitative results provide important evidence for accurately evaluating the degree of overburden damage.

3.4. BRM Based on BPNN-FSI Results

The monitoring results obtained from the BRM based on BPNN-FSI reveal the dynamic evolution characteristics of MIOFs (Figure 15a–d). When the working face was 40 m from the termination line, the fracture development height reached 44 m (from the roof elevation of 848 m to 892 m in the No. 9 coal seam). The resistivity profile showed a high-resistivity fracture zone at borehole depths of 5–28 m, while micro-fracture development features appeared in surrounding rocks at 30–55 m. As the face advanced to 20.5 m, the fracture height increased to 49 m (elevation 897 m), with a significant high-resistivity response observed in the 30–54 m range. The maximum development height of 52 m (elevation 900 m) was achieved when approaching 3.5 m from the stopping line, where a distinct high-resistivity zone formed between 5 and 71 m due to moisture loss. After 67 days of stopping, the height stabilized at 51 m (elevation 899 m). This study demonstrates that the dynamic evolution process of MIOFs can be accurately characterized through resistivity anomalies, providing crucial empirical evidence for understanding fracture development patterns in overlying strata.

The BRM based on BPNN-FSI successfully revealed the evolutionary characteristics of MIOFs during the extraction of the No. 9 coal seam. Through detailed analysis of resistivity profiles at various monitoring stages, the maximum fracture development height in the overlying strata of the 9-204 working face was determined to be 52 m.

4. Discussion

Considering the geological characteristics of thin interbedded soft–hard strata in the Taiyuan Formation coal measures, this study systematically investigated fracture development patterns in MIOFs at the 9-204 working face through four complementary methodologies: (1) numerical simulation, (2) physical similarity modeling, (3) upward-inclined borehole water leakage observation (UIDWLO), (4) a BRM based on BPNN-FSI. The measured HMIOF showed strong methodological consistency, yielding 50 m (numerical simulation), 45 m (physical simulation), 51.62 m (UIDWLO), and 52 m (BRM based on BPNN-FSI), respectively. While UIDWLO demonstrated superior reliability in HMIOF accuracy monitoring compared to conventional methods, three inherent limitations were identified: (i) restricted spatial resolution limited to borehole-adjacent fractures, (ii) operational complexity due to sophisticated construction requirements, (iii) susceptibility to borehole collapse, impairing field applicability. Notably, the developed BRM based on BPNN-FSI exhibited exceptional agreement with UIDWLO results (relative error < 1%), validating its effectiveness as an alternative monitoring approach. All methods conclusively demonstrated that MIOF propagation from the No. 9 coal seam terminated below the 63–67.1 m interburden zone, preserving the structural integrity of the No. 5 coal seam’s floor. This multi-methodological verification provides robust evidence for (1) absence of hydraulic connectivity between seams, (2) maintenance of load-bearing capacity in underlying strata, (3) feasibility of safe extraction in the No. 5 coal seam under current mining conditions.

Comparative analysis reveals that traditional empirical formulas [8] exhibit significant calculation errors ranging from 18.18% to 24.26% (

Table 4. Comparison of fracture height.

	Equation	HMIOF (m)		Relative Error (%)
		${\mathit{H}}_1$	${\mathit{H}}_2$	${\mathit{H}}_1$	${\mathit{H}}_2$
Empirical formula [8]	$H_1={\displaystyle \frac{100\sum M}{1.5M+3.6}}\pm 5.6$ $H_2=20\sqrt{\sum M} + 10$	39.11	42.25	24.26	18.18
Numerical simulation		50		3.18
Similarity physical simulation		45		12.84
BRM based on BPNN-FSI		52		0.7
UIDWLO		51.62

), while the novel method proposed in this study controls the error within 1%. Regarding monitoring techniques, microseismic monitoring—which captures the microseismic signals released by rock mass fracturing and inversely deduces the location, intensity, and evolution patterns of the fractures [39,40]—while suitable for high-energy rock fracturing, still requires improvement in locating weak fracturing signals within the thin interbedded strata of the Taiyuan Formation. This study innovatively proposes a BRM based on BPNN-FSI, which not only achieves high-precision monitoring of MIOF height (relative error < 1%) but also accurately characterizes the spatial distribution of fractures. It should be noted that the method’s accuracy heavily depends on the initial geoelectric model construction, suggesting that future research should focus on optimizing neural network algorithms to enhance model adaptability. The research outcomes provide a reliable technical approach for safe mining in Shanxi’s complex coal measures, particularly demonstrating that the No. 5 coal seam maintains structural integrity after No. 9 coal seam extraction and can be safely mined without water inrush or strata instability risks.

However, the current research still faces several limitations: the BRM remains at the qualitative analysis stage and has yet to achieve quantitative characterization of fracture development intensity; additionally, the inversion algorithm’s precision requires further improvement. Addressing these challenges will constitute critical future research directions to advance methodological refinement and practical applications.

5. Conclusions

This study systematically investigated the evolution law of MIOFs under thin soft–hard interbedded roof strata in the Taiyuan Formation in Shanxi Province through integrated approaches, including numerical simulation, similarity physical modeling, UIDWLO, and a BRM based on BPNN-FSI. The main conclusions are as follows:

(1)

Comprehensive results from numerical simulation, similarity physical modeling, UIDWLO, and the BRM based on BPNN-FSI consistently demonstrate that MIOFs from the No. 9 coal seam did not propagate to the No. 5 coal seam, confirming the structural integrity of the No. 5 coal seam’s floor without rupture occurrence.

(2)

BPNN-FSI achieved high-precision dynamic monitoring of fracture development height (relative error < 1%), showing significant advantages over traditional empirical formulas, numerical simulation, and similarity physical modeling approaches.

(3)

The monitoring accuracy of the proposed BRM based on BPNN-FSI depends on initial geoelectric model construction, suggesting that future research should incorporate artificial intelligence algorithms for model optimization.

(4)

The research outcomes not only provide technical support for dynamic monitoring of MIOFs, but also offer methodological references for similar open-pit slope engineering. Under thin soft–hard interbedded roof strata, these findings significantly guide safe and efficient coal mining operations by effectively preventing roof water inrush and gas disasters, while providing a scientific basis for sustainable ecological development in mining areas.