Introduction

As the readily mineable reserves of shallow coal seams in China’s central and eastern regions approach depletion, coal mining activities have progressively shifted towards more geologically complex regions such as Shanxi, Shaanxi, Inner Mongolia, and Xinjiang1,2,3. The Binchang mining area, located in Xianyang, Shaanxi Province, primarily exploits the 4# coal seam of the Jurassic Yan’an Formation. The overburden structure in this region exhibits a distinctive upper hard and lower soft configuration, characterized by thick sandstone formations overlaying weaker mudstone or siltstone layers4,5. This structural setting significantly influences fracture evolution during coal seam extraction and poses substantial challenges for mining-induced water inrush prevention.

Overburden fracture development is critical in controlling water migration pathways in such mining environments6. When a coal seam is extracted, stress redistribution within the overlying strata induces fractures that may propagate upward and establish hydraulic connections between confined aquifers and the mined-out voids7,8,9. In the Binchang mining area, the water-conductive fractures formed in the overburden have been observed to extend over 120 m above the coal seam, reaching the Cretaceous Luohe Formation’s massive sandstone aquifers10. This process leads to substantial aquifer depletion11, increased roof instability12, and elevated risks of water inrush events13. Therefore, an accurate understanding of fracture evolution mechanisms in an upper hard-lower soft overburden is essential for improving water hazard predictions and guiding effective mine water control strategies.

Existing studies on mining-induced overburden fractures have primarily focused on single lithology conditions, analyzing either hard or soft overburden in isolation14,15,16,17,18,19,20,21,22,23,24. Due to its low tensile strength and weak structural integrity, soft overburden tends to fracture progressively, with fractures propagating gradually from the coal seam roof into the upper strata14. Unloading effects15 mainly govern the evolution of such fractures, rotational movements of overlying rock masses16, and abutment pressures at the advancing face17. In contrast, hard overburden, with its high compressive and tensile strength, exhibits distinct fracture characteristics18. Large break distances and abrupt failure events lead to widely spaced fractures, with caving occurring in discrete blocks rather than continuous zones19,20,21. However, the fracture evolution process becomes more complex when an upper hard-lower soft configuration is present, as the mechanical interaction between the two lithological layers influences fracture initiation, propagation trajectory, and connectivity22,23,24. The combined effect of brittle fracture in the hard stratum and ductile deformation in the soft stratum introduces unique stress redistribution patterns that have not been adequately addressed in previous studies.

A significant challenge in fracture prediction lies in the limitations of conventional empirical formulas, which primarily rely on key stratum theory to estimate water-conducting fracture heights25,26. These formulas assume a simplified overburden response and do not account for variations in mechanical stratigraphy, particularly the influence of lithological discontinuities and stress transfer mechanisms across stratified rock masses. In regions with upper hard-lower soft overburden, measured fracture heights often exceed empirical predictions by a factor of 20 or more, highlighting the inadequacy of existing models. Furthermore, theoretical analysis of overburden failure often employs elastic-plastic constitutive models without explicitly incorporating fracture mechanics principles, resulting in inaccuracies in predicting fracture initiation and propagation behavior27,28.

This study systematically investigates the fracture evolution mechanisms in an upper hard-lower soft overburden structure to address these gaps using a multi-method approach. A physical similarity model with a geometric ratio of 1:250 is developed to replicate mining-induced fracture propagation under controlled conditions. Complementary numerical simulations using FLAC3D quantitatively reveal the evolution of the overburden stress field. Based on fracture mechanics principles and Griffith’s energy release rate criterion, a theoretical framework for predicting fracture height is also established. By integrating experimental, numerical, and theoretical analyses, this study aims to enhance the predictive accuracy of water-conducting fracture evolution and contribute to improved mine water hazard assessment and mitigation strategies.

Methods

Geological and hydrogeological overview of the study area

The Tingnan coal mine is located within the boundaries of Xianyang City, Shaanxi Province, as shown in Fig. 1. This mine operates on a large scale with comprehensive mechanized mining techniques, primarily targeting the 4# coal seam of the Jurassic period. The 4# coal seam has a depth ranging from 401.32 to 788.60 m, with an average mining thickness of 9.00 m. The seam has a dip angle of less than 5°, classifying it as a nearly horizontal coal seam.

Fig. 1
Fig. 1
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Location map of Tingnan coal mine.

The 304 working face is located in the southern part of the mine. Above the coal seam, there is a massive Luohe Formation sandstone aquifer approximately 127.81 m thick. The aquifer has a water inflow rate ranging from 1.30 to 2.00 L s− 1 m− 1. Geological drilling was conducted to retrieve rock cores from the aquifer and aquicludes at various depths. These cores were then subjected to tests for porosity, permeability, and mineral composition. The results of these tests are displayed in Table 1; Fig. 2.

Table 1 Test results for porosity, permeability, and mineral composition of the roof rock core in the 304 working face.
Full size table

Figure 2 indicates that the Luohe Formation aquifer has a porosity ranging from 16.94 to 28.21% and a permeability between 60.10 and 151.45 mD, characterizing it as a strongly water-rich and saturated aquifer. The Yijun and Anding formations contain silicate minerals (quartz + feldspar) in proportions ranging from 53.30 to 85.80%, while the Zhiluo Formation’s silicate mineral content (quartz + feldspar) ranges from 40.30 to 49.30%, typifying upper hard and lower soft overburden structural configuration29.

Fig. 2
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Test results for porosity, permeability, and mineral composition of the roof rock core in the 304 working face.

Physical similarity simulation experiment

For the physical similarity simulation experiment, rock cores collected from geological drilling with a diameter of 108.00 mm were processed into cylindrical standard specimens with a diameter of 50.00 mm and a height-to-diameter ratio of 2:1. The parallelism of the two end faces of each specimen was maintained to be less than or equal to 0.05 mm. These specimens underwent quality testing, uniaxial compression tests, and tensile tests to determine the physicomechanical parameters of the coal-rock mass at the 304 working face30. The tensile strength was determined using the Brazilian splitting test, an indirect tensile test recommended by ISRM (1978) and widely applied in rock mechanics research31,32,33. The results of these tests are presented in Table 2.

Table 2 Physical and mechanical parameters of the coal-rock mass at the 304 working face.
Full size table

The experiment utilized a two-dimensional physical similarity simulation apparatus, with dimensions of 2.00 m in length, 0.20 m in width, and 1.40 m in height. Given the total thickness of the geological strata under investigation is 300.00 m, and considering the height constraints of the experimental apparatus, the model’s designed height was set at 1.20 m, resulting in a geometric similarity ratio (Cj) of 1:250. Based on the theory of similarity34, the similarity ratios for other parameters of the model were derived accordingly.

$$\left\{ \begin{gathered} {C_r}=\frac{1}{{1.5}} \hfill \\ {C_e}={C_r} \cdot {C_j}=\frac{1}{{375}} \hfill \\ \end{gathered} \right.$$
(1)

In the Formula (1), Cr represents the bulk density similarity ratio, and Ce denotes the strength similarity ratio.

For the experiment, eight sets of displacement observation lines were arranged along the coal seam direction, labeled from Line 1 to Line 8 as shown in Fig. 3a. Line 1 was positioned 5.00 cm vertically from the top interface of the coal seam, with each subsequent line spaced 10.00 cm apart vertically. Each line featured 16 evenly distributed observation points, with the first point situated above the coal seam’s open cut and the last point located above the coal seam’s stopping line. To simulate the load on the model, the overburden pressure from 176.88 cm (equivalent to the actual 442.19 m) of the topsoil layer and the water pressure from the sandstone aquifer were applied uniformly at the top of the model as equivalent loads.

The model was constructed using river sand, calcium carbonate, and gypsum, employing a tamping and layering method during the laying process, as depicted in Fig. 3b. The initial setup of the physical similarity model is provided in Supplementary Figure S1. The specific material composition and modeled layer thickness for each lithology are detailed in Supplementary Table S1. Layers of different rock types were separated using mica powder to simulate geological stratification accurately. For enhanced detection and analysis of fracture patterns by Image-Pro Plus 6.0 software, the fracture observation surfaces of the model were uniformly coated with white talcum powder. To mitigate boundary effects, coal pillars measuring 0.25 m were left on both sides of the coal seam before mining began. The model was advanced in steps of 0.03 m to simulate the excavation process. After each step, cubic wooden blocks were inserted to represent the mined section and then gradually extracted. This approach ensured precise control over the excavation distance and time intervals between stages, which is crucial for maintaining consistency and accurately simulating the mining-induced changes in the overburden.

Additionally, after each advance, the rock layers were allowed to stabilize before measurements were taken using a theodolite to track displacements at the observation points. Photographs were also captured to document the fracture patterns of the overburden. The total advance distance was 1.50 m.

Fig. 3
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Design and initial state diagram of the physical model. (a) Physical model design diagram. (b) Initial state diagram of the physical model.

Mica powder was applied at interlayer boundaries in the physical similarity experiments to simulate weak bedding planes in sedimentary formations. The choice of mica powder was based on its fine particle structure and low shear strength, which allow it to mimic weakly bonded sedimentary interfaces and facilitate relative slip under stress conditions. In natural geological settings, bedding planes often consist of clay-rich layers or fine-grained interbeds that are potential slip surfaces when subjected to differential stress. Mica powder in the experiments replicated this behavior by reducing interlayer bonding strength, enabling controlled slip along the interfaces, and capturing the mechanical characteristics of weakly bonded stratification in overburdened layers. Experimental observations confirmed that the presence of mica powder allowed for interlayer displacement under stress, aligning with geological conditions where weak bedding planes act as preferential zones for deformation.

Furthermore, stress redistribution patterns observed in the experiment indicate that including mica powder influenced interfacial shear response, leading to localized stress concentration along bedding planes, similar to natural sedimentary sequences. This mechanical behavior ensured consistency between the physical experiments and the studied geological conditions, supporting the validity of using mica powder as an analog material. Without mica powder, interlayer slip would be notably restricted, altering the failure mode and stress transfer mechanisms observed in the overburden fracture process.

Numerical simulation experiment

To analyze the stress state at the fracture tips of the overburden following the mining of the 304 working face, and to reveal the fracture evolution mechanisms in thick coal seams under upper hard and lower soft overburden, a numerical simulation model was constructed using FLAC3D 6.0 software, as shown in Fig. 4. The numerical simulation model had a strike length of 500 m, a dip width of 280 m, and a height of 300 m. The initial rock stress for this simulation was a static stress field, with the rock layers treated as a continuous medium. The stress field was numerically simulated using a three-dimensional strain model. The Mohr-Coulomb yield criterion assessed rock failure initiation, assuming a linear elastic response without post-failure plastic flow. The physical and mechanical parameters required for the solid module are detailed in Table 2. Additional parameters for numerical simulation, such as shear modulus and internal friction angle, are listed in Supplementary Table S2.

Fig. 4
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Numerical simulation model diagram.

The boundary conditions for the simulation model were defined as follows: The lateral (left and right) and front and back faces of the model were set with displacement constraints, where the displacement along the X-axis and Y-axis directions was 0, allowing only movement along the Z-axis. The bottom face of the model was a fixed boundary, meaning that displacements in the X-axis, Y-axis, and Z-axis directions were all set to 0. The top surface of the model was subjected to a load that combined the gravitational force of the topsoil layer and the water pressure from the aquifer, totaling 12.30 MPa (11.05 MPa from the topsoil layer and 1.25 MPa from the water pressure). Once the initial equilibrium state calculations were complete, excavation of the 4# coal seam began. To balance computational efficiency and accuracy, a uniform mesh with an average element size of 1 m provided sufficient resolution to capture stress redistribution and fracture development without excessive computational cost. Numerical convergence was evaluated based on stress residual norms and displacement criteria, with a tolerance set at 1 × 10− 3 for relative stress changes and 5 × 10− 5 m for displacement changes per iteration step. The maximum number of iterations per step was set at 5000, ensuring equilibrium was reached before proceeding to the next excavation step.

The numerical model incorporated weak discontinuities at interlayer boundaries to accurately represent interlayer interactions using the Mohr-Coulomb slip criterion for weak interlayer slip. The interface cohesion was set at 0.5 MPa, and the friction angle ranged from 25° to 30°, consistent with the mechanical behavior observed in sedimentary formations. These values were selected to align with the physical similarity experiments, where mica powder facilitated interlayer slip. Including these interface properties ensured that the model captures interlayer slip effects while maintaining overall mechanical stability.

The numerical simulations adopted a quasi-static approach, where fracture evolution was modeled as a progressive stress redistribution process rather than a dynamic event governed by inertial effects. This assumption is justified by the observed fracture propagation speed, which remains within a range of negligible inertial effects. Specifically, the characteristic time scale of stress redistribution in the overburden is significantly larger than that of dynamic fracture propagation, ensuring the validity of the quasi-static assumption. Furthermore, the FLAC3D modeling framework does not incorporate explicit dynamic fracture propagation mechanisms. Instead, it computes stress redistribution and fracture development under mechanical equilibrium conditions at each simulation step. This approach captures stress-driven fracture evolution, aligning with experimental and field observations. The applicability of the Griffith energy release rate criterion in this study remains valid, as fracture propagation occurs within a quasi-static regime, where stress redistribution reaches equilibrium before significant propagation occurs.

Results

Evolution law of overlying strata fractures due to mining activities

Physical similarity experiment results

When the working face had advanced to 180.00 m, the observed caving angles were 56° on the side of the open cut and 67° on the working face side. The development height of the water-conductive fractures reached 39.60 m, extending to the boundary between the Zhiluo Formation and the Anding Formation—this was the interface between the soft and hard rock layers, where an abscission layer space became evident. The curvature of the wing fractures changed minimally, and the inclination angle of these fractures was 70°. The distribution pattern of the fractures is illustrated in Fig. 5.

Fig. 5
Fig. 5
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Fracture distribution in overlying strata at a working face advance of 180.00 m. (a) Experiment photograph. (b) Fracture morphology.

When the mining face had advanced to 375.00 m, the caving angles were observed at 66° on the open cut side and 64° on the working face side. The development height of the water-conductive fractures reached 266.40 m, extending to the top interface of the Luohe Formation aquifer, where the abscission layer space at the interface was not pronounced. The curvature of the wing fractures underwent significant changes, and the inclination angle of these fractures was 80°. The distribution pattern of the fractures is illustrated in Fig. 6.

Fig. 6
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Fracture distribution in overlying strata at a working face advance of 375.00 m. (a) Experiment photograph. (b) Fracture morphology.

Field data validation results

To verify the accuracy of the physical similarity experiment, an underground upward borehole water injection test was conducted to measure the height of fracture development in the roof, as shown in Fig. 7a, b. This method involved drilling small-diameter inclined boreholes from the transportation roadway into the roof fracture zone and sequentially sealing the borehole sections using double-packers. After sealing, water was injected into the isolated sections, and the leakage rate was monitored to determine the height of fracture development.

Fig. 7
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Borehole layout and fracture profile in the 204 working face. (a) Borehole layout and fracture profile along the coal seam strike. (b) Borehole layout and fracture profile along the coal seam dip.

Given that the shortest distance between the 4# coal seam in the 304 working face and the bottom boundary of the Luohe Formation aquifer had been determined to be 142.00 m—considerably lower than the predicted fracture height of 266.40 m from the physical similarity experiment—the test was conducted in the transportation roadway of the 204 working face, where geological conditions were more favorable. Two inclined boreholes (D01 and D02) were drilled, with their final depths positioned 20.00 m above the predicted upper boundary of the water-conducting fracture zone. The test results are presented in Fig. 7b. Field measurements indicated that the actual height of the water-conducting fracture zone in the 4# coal seam of the 204 working face was 159.30 m, corresponding to a fracture-to-mining ratio of 26.6. Based on this, the height of the water-conducting fracture zone in the 304 working face was inferred to be 239.4 m.

Although the field-measured height (239.4 m) was slightly lower than the physical experiment’s prediction (266.40 m), this deviation is acceptable, given the significant influence of scale effects in physical similarity experiments. This indicates that physical similarity experiments are reasonably reliable in predicting the height of the water-conducting fracture zone. Although the borehole water injection test is the most reliable method, its accuracy diminishes when the fracture zone is close to the roof aquifer. In such cases, the test method struggles to provide complete measurement data. Therefore, while physical similarity experiments are a valuable supplementary tool for fracture height prediction, further refinements and calibrations based on numerical modeling accuracy are needed to enhance predictive precision.

Stress distribution in overlying strata due to mining activities

In the numerical simulation model, the advance length of the working face was set at 375.00 m, with a coal pillar of 62.50 m left at both ends along the strike, and the width of the working face was 280.00 m. After the advancement of the working face was completed, the stress slices along the xz interface of the model at the stages of 180.00 m and 375.00 m advancement were processed using Tecplot 360 software. Additionally, the tip positions of the fractures observed in the physical similarity simulation experiment were marked on the stress slice images.

When the working face had advanced to 180.00 m, within the xz interface, the tip of the left-wing fracture was designated as point A, and the tip of the right-wing fracture as point B. At fracture tip A, the vertical stress was measured at −17.95 MPa, the horizontal stress at −14.00 MPa, and the shear stress at −1.30 MPa, as shown in Figs. 8a and 9a, and 10a. Consequently, there existed a compressive shear stress field at the tip of fracture A.

When the working face had advanced to 375.00 m, within the xz interface, the tip of the left-wing fracture was denoted as point A’, and the tip of the right-wing fracture as point B’. At fracture tip A’, the vertical stress was − 11.05 MPa, the horizontal stress was − 8.85 MPa, and the shear stress was − 0.40 MPa, as illustrated in Figs. 8b and 9b, and 10b. Therefore, a compressive shear stress field was present at the tip of fracture A’.

Fig. 8
Fig. 8
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Vertical stress slice diagram at the xz interface of the numerical simulation model. (a) Working face advanced to 180.00 m. (b) Working face advanced to 375.00 m.

Fig. 9
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Horizontal stress slice diagram at the xz interface of the numerical simulation model. (a) Working face advanced to 180.00 m. (b) Working face advanced to 375.00 m.

Fig. 10
Fig. 10
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Shear stress slice diagram at the xz interface of the numerical simulation model. (a) Working face advanced to 180.00 m. (b) Working face advanced to 375.00 m.

Discussion

The physical similarity experiments and FLAC3D numerical simulations in this study both adopt the continuum mechanics assumption, representing the geological formation as an equivalent homogeneous medium. Under this assumption, fracture propagation follows the principles of classical linear elastic fracture mechanics (LEFM), a framework extensively validated in similar engineering applications35. While anisotropic fracture mechanics (AFM) offers a means to account for directional material properties, it requires explicitly modeling the anisotropy, which is beyond the scope of this study. Since experimental and numerical approaches use a homogeneous representation, LEFM remains an appropriate theoretical foundation for analyzing stress redistribution and fracture evolution in this study. The following sections further discuss the implications of this assumption in the context of stress conditions and crack propagation mechanisms.

Stress model at fracture tip under compressive-shear conditions

In the stress analysis of the fracture tip A and the surrounding rock, if we defined the direction of tensile stress as positive, and shear stress as positive in the clockwise direction, we could conceptualize a far-field stress model at the fracture tip A as shown in Fig. 11. The major axis of the fracture tip A had a length of 2r, and the angle between the major axis direction and the horizontal direction was denoted as θ. The surrounding rock mass at the fracture tip A was subjected to vertical stress, σ, and horizontal stress, λσ, where λ was the lateral pressure coefficient.

Fig. 11
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Stress model at the far field of fracture tip A.

Based on the theory of linear elasticity36,37, the expressions for the far-field normal stress σm, axial stress σn, and shear stress τmn at the tip of a fracture (point A) were derived as follows:

$$\left\{ \begin{gathered} {\sigma _m}=\frac{1}{2}[(\sigma +\lambda \sigma )+(\sigma - \lambda \sigma )\cos 2\theta ] \\ {\sigma _n}=\frac{1}{2}[(\sigma +\lambda \sigma ) - (\sigma - \lambda \sigma )\cos 2\theta ] \\ {\tau _{mn}}=\frac{1}{2}(\sigma - \lambda \sigma )\sin 2\theta \\ \end{gathered} \right.$$
(2)

Simplification of Eq. (2) yielded Eq. (3):

$$\left\{ \begin{gathered} {\sigma _m}=\sigma ({\cos ^2}\theta +\lambda {\sin ^2}\theta ) \\ {\sigma _n}=\sigma ({\sin ^2}\theta +\lambda {\cos ^2}\theta ) \\ {\tau _{mn}}=\sigma (1 - \lambda )\sin \theta \cos \theta \\ \end{gathered} \right.$$
(3)

Based on the results of numerical simulations in Sect. 3.2, the vertical stress at fracture tip A was σ = −17.95 MPa, horizontal stress λσ = −14.00 MPa, and shear stress τ = −1.30 MPa. Substituting vertical stress σ = −17.95 MPa, θ = 70°, and λ = 0.78 into Eq. (3) resulted in σm = −14.49 MPa, σn = −17.50 MPa, and τmn = −1.27 MPa. These calculated results were in good agreement with the numerical simulation outcomes. Therefore, Eq. (3) could be used to characterize the stress state at fracture tip A under a combined compression-shear condition, indicating that fracture tip A was a type of mixed-mode fracture.

Initiation criteria and extension direction for composite fracture

A polar coordinate system was established to elucidate the criteria for fracture initiation and its propagation direction, with the singular point at fracture tip A, denoted as point o, serving as the origin. This setup led to the stress model at the singular point of fracture tip A, as illustrated in Fig. 12.

Fig. 12
Fig. 12
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Stress model at the singular point of fracture tip A.

Based on Figs. 11 and 12, as well as the findings of Horii et al., the stress intensity factor at crack tip A under compression-shear conditions was determined using Eq. (4)38.

$$\left\{ \begin{gathered} K{\text{I=}}{\sigma _n}\sin \varphi /{\left[ {\pi (a+0.27r)} \right]^{1/2}}+{(\pi a)^{1/2}}\frac{1}{2}\left[ {\sigma +\lambda \sigma - (\sigma - \lambda \sigma )\cos 2(\varphi - \beta )} \right] \\ K{\text{II=}} - {\sigma _n}\cos \varphi /{\left[ {\pi (a+0.27r)} \right]^{1/2}} - {(\pi a)^{1/2}}\frac{1}{2}(\sigma - \lambda \sigma )\sin 2(\varphi - \beta ) \\ \end{gathered} \right.$$
(4)

In Eq. (4), KI represents the stress intensity factor for Type I and KII for Type II fractures. φ represents the polar angle of the infinitesimal element near point o, while a denotes the radial distance of the infinitesimal element from point o. β is the angle between the major axis of the crack and the vertical direction.

When a approached 0, meaning the infinitesimal element infinitely approached the singular point o, Eq. (4) could be simplified as follows.

$$\left\{ \begin{gathered} K{\text{I=}}{\sigma _n}\sin \varphi /{(0.27\pi r)^{1/2}} \\ K{\text{II=}} - {\sigma _n}\cos \varphi /{(0.27\pi r)^{1/2}} \\ \end{gathered} \right.$$
(5)

From Eq. (5), the following expression could be further derived.

$$K{\text{I=}} - K{\text{IItan}}\varphi$$
(6)

When a was a constant value, according to fracture mechanics theory39, the expressions for the circumferential stress (σφ), radial stress (σa), and radial shear stress (τaφ) could be derived for a microelement located at coordinates (a,φ) near the singular point o:

$$\left\{ \begin{gathered} {\sigma _\varphi }=\frac{1}{{2{{(2\pi a)}^{1/2}}}}\cos \frac{{_{\varphi }}}{2}[K{\text{I}}(1+\cos \varphi ) - 3K{\text{II}}\sin \varphi ] \\ {\sigma _a}=\frac{1}{{2{{(2\pi a)}^{1/2}}}}[K{\text{I}}(3 - \cos \varphi \cos \frac{\varphi }{2})+K{\text{II}}(3\cos \varphi - 1)\sin \frac{\varphi }{2}] \\ {\tau _{a\varphi }}=\frac{1}{{2{{(2\pi a)}^{1/2}}}}\cos \frac{\varphi }{2}[K{\text{I}}\sin \varphi +K{\text{II}}(3\cos \varphi - 1)] \\ \end{gathered} \right.$$
(7)

From Eq. (7), it was evident that fracture initiation at the tip A occurred under the combined effects of circumferential stress (σφ) and radial shear stress (τaφ), leading to a compression-shear type of fracture initiation.

If the fracture initiation conformed to the maximum circumferential stress criterion39, it had to satisfy the fracture criterion specified in Eq. (8).

$$\left\{ \begin{gathered} {\left( {\frac{{\partial {\sigma _\varphi }}}{{\partial \varphi }}} \right)_{\varphi {\text{=}}{\varphi _0}}}{\text{=}}0 \\ {\left( {\frac{{{\partial ^2}{\sigma _\varphi }}}{{\partial {\varphi ^2}}}} \right)_{\varphi {\text{=}}{\varphi _0}}}<0 \\ \end{gathered} \right.$$
(8)

In Eq. (8), φ0 represents the fracture initiation angle at the tip A.

By substituting Eq. (7) into Eq. (8) and simplifying, we could derive the following result:

$$\left\{ \begin{gathered} \cos \frac{{{\varphi _0}}}{2}\left[ {K{\text{I}}\sin {\varphi _0}+K{\text{II}}(3\cos {\varphi _0} - 1)} \right]{\text{=}}0 \\ K{\text{I}}\cos \frac{{{\varphi _0}}}{2}(3\cos {\varphi _0} - 1) - K{\text{II}}\sin \frac{{{\varphi _0}}}{2}(9\cos {\varphi _0}+5)<0 \\ \end{gathered} \right.$$
(9)

Substituting Eq. (6) into Eq. (9) yielded a crack initiation angle of 50° at crack tip A, consistent with the results of the physical similarity simulation experiments.

If the fracture initiation conformed to the maximum radial shear stress criterion40, it had to satisfy the fracture criterion specified in Eq. (10).

$$\left\{ \begin{gathered} {\left( {\frac{{\partial {\tau _{a\varphi }}}}{{\partial \varphi }}} \right)_{\varphi {\text{=}}{\varphi _0}}}=0 \\ {\left( {\frac{{{\partial ^2}{\tau _{a\varphi }}}}{{\partial {\varphi ^2}}}} \right)_{\varphi {\text{=}}{\varphi _0}}}<0 \\ \end{gathered} \right.$$
(10)

By substituting Eq. (7) into Eq. (10) and simplifying, we could derive the following result:

$$\left\{ \begin{gathered} K{\text{I}}\cos \frac{{{\varphi _0}}}{2}(3\cos {\varphi _0} - 1) - K{\text{II}}\sin \frac{{{\varphi _0}}}{2}(9\cos {\varphi _0}+5)=0 \\ K{\text{I}}\sin \frac{{{\varphi _0}}}{2}( - 5 - 9\cos {\varphi _0}) - K{\text{II}}\cos \frac{{{\varphi _0}}}{2}(27\cos {\varphi _0} - 13)<0 \\ \end{gathered} \right.$$
(11)

Similarly, by substituting Eq. (6) into Eq. (11), φ0 = 226° was obtained. This result did not align with the outcomes of physical similarity modeling experiments.

Therefore, under the influence of compression-shear stresses, the fracture initiation at tip A conformed to the maximum circumferential stress criterion.

Extension height of composite fracture

Since the crack initiation at tip A in the physical similarity model conformed to the maximum circumferential stress criterion, the Mode I stress intensity factor primarily influenced the crack propagation. Therefore, according to the Griffith energy release rate criterion41, the findings of Zhang et al. and Lakirouhani et al.42,43, it was concluded that:

$$\left\{ \begin{gathered} G=\frac{{K{\text{I}}{{\text{C}}^2}}}{E} \\ {\sigma _t}=8.88K_{{{\text{IC}}}}^{{0.62}} \\ \end{gathered} \right.$$
(12)

In Formula (12), G represents the energy release rate, KӀC is the fracture toughness, E is the elastic modulus, and σt denotes the tensile strength.

Substituting E = 360.00/375 MPa = 0.96 Mpa and σt = 0.80/375 MPa = 0.002 MPa into Eq. (12), KӀC was calculated as 5.7 × 10− 3 MPa m1/2, and G was determined as 3.4 × 10− 5 MPa m.

If crack tip A propagated to position A’ after time t, then according to the Griffith energy release rate criterion41 and the preceding discussion, it could be concluded that:

$$\left\{ \begin{gathered} S^{\prime}=\frac{{K{\text{I}}{{\text{C}}^2}}}{{GE^{\prime}}} \hfill \\ H={\text{250}}\frac{{K{\text{I}}{{\text{C}}^2}}}{{GE^{\prime}}}\sin \left( {\frac{7}{{18}}\pi } \right) \hfill \\ \end{gathered} \right.$$
(13)

In Eq. (13), S′ represents the crack propagation distance in the physical similarity model, E′ is the equivalent elastic modulus, and H is the crack propagation height.

Substituting KӀC = 5.7 × 10− 3 MPa m1/2, G = 3.4 × 10− 5 MPa m and E′ = 1.00 MPa into Eq. (13) yielded H = 225.53 m. This outcome was generally consistent with the results of physical similarity modeling experiments, which showed 266.40 m.

Comparison with previous studies

Previous studies of mining-induced fracturing have predominantly focused on simplified single-lithology scenarios, analyzing either hard or soft overburden conditions in isolation. These studies can be broadly categorized into two groups: (1) research on soft strata, such as Zhang et al.14, which demonstrated that weak overburden collapses in sync with face advance due to the absence of a strong key bed, and (2) research on hard strata, as reported by Gao et al.23, showing that competent roofs develop constrained fractures with lower permeability. Additionally, laboratory studies on high-strength rocks like granite further illustrate the distinct fracture behaviors in strong lithology under confined conditions27. However, these single-material approaches fail to capture the interactive dynamics between hard and soft layers in a composite overburden system.

Many earlier approaches also exhibit notable limitations in treating fracture mechanics and stratigraphic structure. Traditional predictive models for the water-conducting fractured zone (WCFZ) often neglect key fracture mechanics aspects and structural influences. For instance, the classic key-stratum-based methods fail to account for the impact of strata beyond the model’s range and the evolving fracture geometry as mining progresses25. This can lead to oversimplified assumptions. Han et al.29 highlight that stress transfer modeling in the overburden under a rigid key stratum remains a fundamental challenge, revealing gaps in layered structural considerations. An upper-hard/lower-soft configuration adds complexity that such models did not originally incorporate. Notably, the mere presence of a hard-over-soft layering does not automatically produce a separation fracture along the interface, as observed in field studies by Fan et al.24. Moreover, previous numerical simulations often lacked rigorous fracture mechanics integration, leading to non-conservative predictions. For example, using a continuum Mohr-Coulomb model without dynamic fracture damage drastically underestimated the WCFZ height in one study (35.6 m vs. an observed ~ 70 m)15. In contrast, incorporating a dynamic damage mechanism aligned the predicted fracture height (68.6 m) with field measurements15. Such findings underscore that without explicit fracture propagation and structural considerations, earlier models could fail to capture the true extent and behavior of mining-induced fractures in mixed lithology settings.

This study addresses these gaps by integrating physical experiments, numerical modeling, and theoretical analysis to examine an upper-hard/lower-soft overburden scenario. This comprehensive approach contrasts with most prior works that relied on a single method or assumed homogeneous material properties. Using similar material experiments and FLAC3D simulations calibrated with site-specific parameters, we explicitly capture the interaction between a stiff upper stratum and a weak lower stratum—an interaction that previous single-lithology models could not represent.

A key novel finding is the differential fracture propagation angles observed in the two lithologies: fractures in the soft rock layer propagate at roughly 70°, whereas in the overlying hard rock, they propagate at about 80° (measured from the horizontal). Earlier studies have documented overall fracture zone geometry in mining, such as general caving or fissure angles under various settings, but they did not distinguish how different rock types within the overburden might exhibit distinct fracture inclinations30. Our experiments and simulations reveal that the hard roof tends to fracture in a steeper, more vertical manner, forming a concentrated and narrow fracture zone, while the softer layer produces relatively shallower-angled cracks that contribute to a more laterally extensive fractured zone. This nuanced insight into fracture geometry is a direct outcome of the multi-faceted methodology and was absent from previous analyses that lacked either the material contrast or a detailed fracture mechanics focus.

Importantly, the differentiated fracture angles suggest that water-conducting fractures will propagate through the soft and hard strata along distinct paths. The soft layer promotes a wider lateral influence due to its gentler ~ 70° fractures, whereas the hard layer contributes to the vertical reach of the fracture zone via ~ 80° steep fractures. This interplay has not been explicitly characterized before and represents a significant contribution of the present work to understanding mining fracture behavior under layered conditions.

These findings bear practical significance for mine safety and engineering. Understanding the distinct fracture propagation mechanisms in an upper-hard/lower-soft roof enables more accurate assessments of water inrush risk. In particular, our findings allow for improved prediction of the spatial extent of the water-conducting fractured zone, which is crucial for the prevention and control of water hazards in mines30. For instance, recognizing that a weak immediate roof will likely generate broader-angled fractures can inform hydrological modeling and help identify a larger zone of potential aquifer connectivity, prompting more vigilant water monitoring or pre-grouting in those areas. Likewise, understanding that the hard caprock fails along steeper planes can help engineers anticipate the ultimate height of fracture penetration toward overlying aquifers or water-bearing strata.

Incorporating these insights into existing prediction models can refine their accuracy. Improved key-stratum theories and related models can be updated to account for different fracture trajectories in composite strata25, leading to more reliable estimates of fracture evolution above longwall panels14. Additionally, by integrating fracture mechanics considerations and stratified overburden effects, the present study provides a stronger scientific basis for hazard mitigation strategies. Mine planners can better tailor support systems and water-control measures (such as optimizing pillar dimensions or roof reinforcement) in upper-hard/lower-soft conditions, and regulators can update guidelines for safe mining under aquifers.

This study has certain limitations concerning the scope of data and modeling assumptions. First, the field data were obtained from a single mining site, which ensures strong relevance to the specific geological conditions but limits the broader representativeness of the findings. Second, the physical experiments and numerical simulations are subject to scale-related constraints. The physical similarity model, restricted by the dimensions of the experimental apparatus, necessarily simplified actual mining conditions, potentially introducing scale effects and deviations arising from idealized boundary settings. Similarly, the numerical simulations involved assumptions such as treating the rock mass as a relatively homogeneous continuous medium, without explicitly accounting for factors like complex joint networks or groundwater effects. As a result, the findings are most applicable to geological environments similar to those tested, and caution should be exercised when extending them to significantly different conditions without further validation. It is important to note, however, that these limitations do not undermine the overall conclusions of the study. The key patterns and fracture mechanisms identified are theoretically well-founded and align with qualitative results reported in related research. Recognizing these limitations highlights areas for future improvement, including incorporating data from multiple mining sites to assess applicability under diverse geological settings, conducting larger-scale or in situ experiments to mitigate scale effects, and refining numerical models by integrating rock mass heterogeneity and other critical factors. These efforts would enhance the applicability of the research outcomes and further improve their reliability under varied field conditions.

Conclusions

(1) This study systematically investigated the fracture evolution mechanisms during thick coal seam mining under an upper hard–lower soft overburden structure using physical similarity experiments, numerical simulations, and theoretical analysis. The results reveal that the fracture inclination angles differ significantly between the two lithological types: fractures propagate at approximately 70° in soft rock layers and steepen to 80° in hard rock formations. The maximum height of the water-conducting fracture zone was measured at 266.4 m in physical experiments and estimated at 225.53 m using theoretical analysis, with a relative deviation of 15.3%. These findings confirm that fracture initiation follows the maximum circumferential stress criterion, leading to compressive-shear failure.

(2) Field validation using borehole water injection tests demonstrated that the actual water-conducting fracture height (239.4 m) aligns well with experimental predictions, supporting the reliability of the proposed approach. Integrating fracture mechanics principles into overburden failure analysis enhances the predictive accuracy compared to conventional empirical models.

(3) Despite these advancements, certain limitations remain. The assumption of homogeneous mechanical properties within numerical simulations may not fully capture the complexity of real-world geological conditions, and the scale effects in physical similarity experiments introduce uncertainties in absolute fracture height predictions. Future research should focus on refining multi-scale modeling approaches and incorporating dynamic fracture propagation effects to improve predictive accuracy further.