Mechanism and prevention of bed separation water hazards in karst coal mining areas of Northern Guizhou Province, China

Abstract

This study used the Tenglong Coal Mine in northern Guizhou as a case study to prevent or control bed separation water disasters caused by complex hydrogeological conditions in karst mining areas. A systematic research approach integrating theoretical modeling, quantitative monitoring, and on-site prevention and control was used to analyze the dynamic evolution of overburden separation in karst areas and establish a prevention system. The rock mechanics theory was used to identify the location of bed separation and establish a mechanical model of the roof containing a conical funnel-shaped karst cave. The cusp catastrophe theory was applied to derive a safety distance criterion between the karst cave and the separation zone. The box-counting fractal dimension (D) was used to quantify the dynamic evolution of the separation. It was 1.1881 after the working face reached 240 m, and the maximum separation was 2.64 m. A similarity simulation was conducted, and fiber Bragg grating (FBG) sensors and digital image correlation (DIC) were employed to measure the separation space. A site-specific system was developed to analyze bed separation water disasters, perform spatiotemporal prediction, and prevent or control them. The following was observed. (1) The higher the karst water pressure, the higher the load, and the thinner the rock layer, the more prone the area was to water inrush disasters. (2) The fractal dimension accurately described bed separation. Bed separation became critical when D exhibited a sudden step-like increase above 1.15. (3) A strong positive correlation existed between the strain and the separation ratio F. The maximum subsidence of high-level separation derived from DIC was 10.5 mm, and the highest bed separation position occurred beneath the thick Changxing Formation limestone. (4) The proposed surface and underground drainage approach improved the drainage efficiency. This research provides theoretical support and technical guidance to prevent or control bed separation water disasters in karst mining areas.

Introduction

Karst landforms cover 13% of the Earth’s land and are widespread globally. Northern Guizhou, China, has one of the world’s largest karst areas. Coal mining in these regions significantly affects the environment^1,2. The form in the karst area of northern Guizhou is complex, and the simple circular karst cave model can’t reflect the asymmetric dissolution process of rocks by flowing water. Because the water in the karst area often seeps down along vertical cracks, it is easier to form an inverted conical karst cave (such as a funnel-shaped sinkhole), and the karst cave landform is shown (Fig. 1)^3,4. This region is a major coal-producing area in southern China^5,6,7. Coal mining in karst areas often has adverse environmental impacts^8,9,10,11, frequently triggering geological hazards and ecosystem degradation¹². The overlying roof strata experience bending deformation and fracturing during coal seam extraction, resulting in numerous horizontal, vertical, and oblique fractures. The layers undergo asynchronous deformation if significant differences exist in the mechanical properties between adjacent rock layers in the deformed roof strata. These regions are referred to as bed separation zones^13,14. Water may accumulate within these voids if aquifers exist above and below the separation zones. The accumulated water resulting from bed separation water can enter the working face of the mine due to mining-induced disturbances, causing bed separation water inrush disasters^{15,16,17,18,19}. The mechanism of layer separation is complex. Accurately determining its occurrence and spatiotemporal evolution is required to implement grouting measures. The hydrogeological conditions of karst regions are complex. Thick limestone roofs are prone to karst cave development. If mining operations encounter concealed, water-filled karst cavities, the combined effects of mining-induced separations and karst voids can result in hydraulic connectivity. It can cause destabilization and failure of the aquiclude, posing a significant threat to the safety and viability of coal mine operations.

Fig. 1

Schematic diagram of coal seam mining in karst areas (a) Karst landform in northern Guizhou; (b) The shape of the sinkhole on-site survey in northern Guizhou; (c) Conical funnel-shaped karst on-site survey; (d) a conical funnel-shaped cross-section formed by dissolution of vertical cracks in water flow rock (P₃c = Changxing Formation; T₁y = Yulong Formation).

Bed separation water disasters in the roof strata pose an increasing threat to coal production and have become a major focus of mine water hazard prevention research in recent years. Significant progress has been made to understand the formation mechanisms and evolution of roof separations during coal seam mining^{20,21,22,23,24,25}. For example, Qiao et al. investigated the disaster-causing mechanisms of bed separation water in coal mines, early warning and forecasting methods, and key prevention and control measures^26,27. They proposed hydrostatic pressure inrush and hydrodynamic pressure inrush mechanisms^14,28,29. Researchers have analyzed the causes of separation and implemented targeted drainage strategies by drilling single boreholes underground to release bed separation water. These approaches have mitigated the risk of bed separation water inrush and improved mine safety. However, most studies have focused on the bed separation patterns in sandstone and conglomerate aquifers in the roof strata of coal mines in central-eastern and western China. In contrast, few studies have examined the thick Permian Changxing Formation (P₃c) limestone in the northern Guizhou region of southwestern China.

Existing measures for managing bed separation water in this area are relatively simple and unsystematic and have shown limited drainage effectiveness. In addition, most researchers have studied fracture development and evolution during coal seam mining in karst regions by simplifying the karst roof strata into idealized mechanical models, such as circular thin plates with clamped edges³⁰, elliptical thin plates³¹, or circular cavities³². However, these models may not adequately consider the unique morphology of karst caves and the hydraulic pressure diffusion caused by cave water, which significantly expands the stress-affected zones in the surrounding rock mass. Dissolution in northern Guizhou’s karst mining areas commonly results in cone-shaped cross-sections of karst caves^33,34. Therefore, a more realistic approach for this region would be to model the cave roof as a circular cross-section and simplify the system consisting of the underlying aquiclude and cave floor into a frustum-shaped structure composed of thin circular plates. Furthermore, karst water inrush has been analyzed using the cusp catastrophe theory^{35,36,37,38,39} to predict critical instability states. Researchers have conducted numerical simulations and physical similarity experiments based on stratigraphic data from the roof of the working face to understand the fracture evolution of the overlying strata during coal seam mining and apply the findings to practical production^40,41,42,43.

These studies have simulated the positions of bed separations at different mining distances. For instance, numerical simulations using RFPA2D software have been employed to investigate bed separation and analyze the evolution during various stages of overburden movement during mining^44,45. In addition, physical experiments using similarity simulation materials have been carried out to study the failure characteristics of composite roofs and the fracture evolution in fully mechanized caving faces with large mining heights^46,47. However, these methods primarily provide qualitative descriptions of the spatial distribution and development of fractures or bed separations, whereas monitoring techniques are lacking. The strain inside the model cannot be observed in real time or with high precision. In particular, there is a lack of quantitative characterizations of the degree of bed separation, such as the fractal dimension D, and dynamic evolution parameters like the separation rate F. Moreover, few studies have analyzed the interaction between karst cave development and the bed separation degree. As a result, it is difficult to obtain accurate spatiotemporal evolution patterns of separations under complex karst geological conditions. Therefore, further research is urgently needed to address these issues and overcome the challenges associated with preventing or controlling bed separation water disasters in karst regions.

In response to these challenges, this study focuses on the Tenglong Coal Mine in the karst region of northern Guizhou to reveal the dynamic evolution of overburden separation in karst cave areas and overcome the limitations of traditional models that oversimplify cave morphology. A conical funnel-shaped mechanical model of the karst cave is constructed, and the critical safety distance between the cave and the separation zone is derived using the cusp catastrophe theory. The fractal theory, a fiber Bragg Grating (FBG) sensor, and digital image correlation (DIC) are utilized to quantify bed separation in real time. A closed-loop technical system, including mechanism analysis, spatiotemporal prediction, and multi-dimensional prevention and control, is developed to prevent or control bed separation water disasters in karst regions. The outcomes guide the design of water inrush prevention measures in coal mines, support the safe exploitation of coal resources, and ensure environmental protection of karst areas of northern Guizhou and the broader southwestern region.

Engineering geological information

The Tenglong Coal Mine belongs to the Daxinan Mining Co., Ltd. and is located in Jinsha County, Bijie City, in the northwestern part of Guizhou Province, China. The mine primarily extracts the No.9 coal seam of the Permian Longtan Formation, which is characterized by well-developed joints and an average thickness of 2.5 m. The roof of the No.9 coal seam consists of a composite structure comprising thick limestone interbedded with clay rock and mudstone (Fig. 2). A water inrush occurred during the mining of the 10,903 working face, with a peak water inflow of 1,100 m³/h that rapidly declined to about 500 m³/h. The event exhibited features typical of water inrush into the bed separation zone: a sudden and large volume of water, a strong destructive impact, minimal early warning signs, a short duration, and the presence of mud and silt. An analysis of the inflow volume suggests a hydraulic connection with the unevenly distributed thick P₃c limestone aquifer above, which contains karst caves. However, the development pattern of bed separations within the thick limestone roof remains unclear, and the coupling relationship between the karst caves and the separations is not well understood, making it highly challenging to accurately determine the grouting positions for mitigation. Therefore, the Tenglong Coal Mine and other coal mines in northern Guizhou with similar geological conditions require clarification of the mechanism and evolution of bed separation during mining, the location of the separation zones, and preventive and control measures.

Fig. 2

Stratigraphic column of mining working face.

Formation of bed separation and mechanism of bed separation water inrush

Method for determining the location and Spatial extent of bed separation

Bed separation occurs when the roof deforms after coal seam mining. Due to the relatively low tensile strength along the structural planes between rock strata, deformation between the upper and lower layers is not synchronous, resulting in a deflection difference Δω (bed separation). Most scholars have used simplified beam models and the key stratum theory^48,49,50 to calculate the volume of bed separation and determine its location. In this study, the rock strata are modeled as a thin plate under a uniformly distributed load, as shown in Fig. 3a. A boundary condition of four-sided fixed supports was established. The thickness of the thin plate is denoted as h, and a and b represent the length and width of the thin plate, respectively. The applied load is q = γh, where γ is the bulk density of the rock strata. A radial force without displacement is exerted on the karst cave. The strain energy during the deformation of the rectangular thin plate is expressed as follows:

Fig. 3

Mechanical model of thin plate separation under a uniform load. (a) laminated thin plate model; (b) deflection of bed separation (the applied load is denoted as q, the deflection difference is denoted as ω, the thickness of the thin plate is denoted as h, and a and b represent the length and width of the thin plate, respectively).

$$\: \cup \:\: = \frac{E}{{2\left( {1 - v^{2} } \right)}}\int_{0}^{a} {} \int_{{ - b}}^{b} {} \int_{0}^{h} {z^{2} } \left\{ {\left( {\nabla \:^{2} \omega \:} \right)^{2} - 2\left( {1 - v} \right)\left[ {\frac{{\partial \:^{2} \omega \:}}{{\partial \:x^{2} }}\frac{{\partial \:^{2} \omega \:}}{{\partial \:y^{2} }} - \left( {\frac{{\partial \:\omega \:^{2} }}{{\partial \:x\partial \:y}}} \right)} \right]} \right\}dxdydz$$

(1)

where E is the elastic modulus, and ν is Poisson’s ratio. Since the strain energy does not change in the z direction, the flexure stiffness ${\text{D}} = \frac{{{\rm E}h}}{{12(1 - \nu ^{2} )}}$ is substituted and integrated over z. The deflection of the rock plate is described using a double trigonometric series, and the deflection is solved by the energy method⁵¹. The boundary conditions of the rock plate satisfy:

$$\:\omega\:\left|{\:}_{x=0}=0,\frac{\partial\:\omega\:}{\partial\:x}\right|{\:}_{x=0}=0$$

(2)

$$\:\omega\:\left|{\:}_{x=a}=0,\frac{\partial\:\omega\:}{\partial\:x}\right|{\:}_{x=a}=0$$

(3)

$$\:\omega\:\left|{\:}_{y=\pm\:b}=0,\frac{\partial\:\omega\:}{\partial\:y}\right|{\:}_{y=\pm\:b}=0$$

(4)

The maximum deflection difference of the bed separation zone is Δω = ω_i-ω_i+1.

$$\:\varDelta\:\omega\:=\frac{{\gamma\:}_{i}{a}^{4}{b}^{4}\left({H}_{i}-{H}_{i+1}\right)}{4{\pi\:}^{4}{D}_{i}\left(3{a}^{4}+3{b}^{4}+2{a}^{2}{b}^{2}\right)}\left(1-{cos}\frac{2m\pi\:x}{a}\right)\left(1-{cos}\frac{2n\pi\:y}{b}\right)$$

(5)

Integrating the variables x and y into Eq. (5) yields the size of the bed separation zone:

$$\begin{gathered} \:Vi = \iint \:\varDelta \omega \:dxdy = \frac{{qa4}}{{4\pi \:^{4} [3 + 3\left( {\frac{a}{b}} \right)^{4} + 2(\frac{a}{b})^{2} ]}}\left( {\frac{{q_{{down}} }}{{D_{{down}} }} - \frac{{q_{{up}} }}{{D_{{up}} }}} \right)\int \: _{0}^{a} \int \: _{0}^{b} \left( {1 - {\text{cos}}\frac{{2\pi \:x}}{a}} \right)\left( {1 - {\text{cos}}\frac{{2\pi \:y}}{b}} \right)dxdy \hfill \\ \;\quad = \frac{{q^{4} }}{{4\pi \:^{4} [3 + 3\left( {\frac{a}{b}^{4} } \right) + 2(\frac{a}{b})^{2} ]}}\left( {\frac{{q_{{down}} }}{{D_{{down}} }} - \frac{{q_{{up}} }}{{D_{{up}} }}} \right).a.b = \frac{1}{4}\varDelta \:\omega \:_{{max}} a.b \hfill \\ \end{gathered}$$

(6)

where q is the total load on the rock stratum, q_down is the load from the lower rock stratum, and q_up is the load from the upper rock stratum. The maximum volume of the bed separation zone is located at the center of the thin plate.

As shown in Fig. 3b, the deflection ω of the bed separation indicates whether separation has occurred. Based on the elastic thin plate theory, the procedure for identifying the location of bed separation is as follows. This study calculates the deflection ω of each rock layer from bottom to top sequentially. If Δω > 0, the location is where separation occurs. However, this does not necessarily indicate the development of separation water. Two additional conditions must be satisfied for separation water to develop: (1) the separation space must have a water source, and (2) the water-conducting fracture zone must not be connected to the separation space. Matlab programming was used to determine the position and size of the separation layers. Calculations were performed using Eq. (5), where h_i is the thickness of the i layer, γ_i is the bulk density of the rock of the i layer, and D_i is the flexure stiffness of the i rock layer; m and n are 1. Each rock layer is calculated from bottom to top, and separation occurs when Δω > 0. Accordingly, the separations near the 10,903 working face of the Tenglong Coal Mine occur beneath the No. 9 limestone, No. 16 marlstone, and No. 24 sandstone. According to The Code for Coal Pillar Maintenance and Coal Pressure Mining in Buildings, Water Bodies, Railways, Main Shafts, and Lanes⁴⁹, the heights of the water-conducting fracture zone (H_f) and the caving zone (H_c) in the hard rock are calculated as follows:

$$\:{H}_{f}=\frac{100\sum\:M}{1.2\sum\:M+2.0}\pm\:8.9$$

(7)

$$\:{H}_{c}=\frac{100\sum\:M}{2.1\sum\:M+16}\pm\:2.5$$

(8)

The coal seam thickness M was 2.39 m, H_c ranged from 8.8 m to 13.80 m, and H_f ranged from 40 m to 57.8 m. Therefore, Layers 16 and 24 were in the caving and water-conducting fracture zones, and no separation zones occurred. However, the No. 9 limestone was 58.64 m above the C9 coal seam, making it prone to bed separation and a favorable location for separation-induced water inrush. The largest separation space occurred beneath thick limestone layers. This study used the maximum separation space below the No. 9 thick limestone as an example. The rock plate length was a = 500 m, and the width was b = 200 m. The spatial volume was calculated using Eq. (6); the results are shown in Fig. 4. Figure 4a shows the separation space in the rock strata, with the maximum development at the center of the layer. Figure 4b displays the horizontal contour cloud map of the separation, and Fig. 4c illustrates the height contour map. The figures indicate that the settlement at both ends of the rock layer is relatively small (0.37397 m), and the maximum value occurs in the center (2.6178 m). The maximum volume of the separation water is 65,445.0 m³. The area below the No. 9 thick limestone is especially prone to bed separation water inrush.

Fig. 4

Calculation results of theoretical separation layer below the thick limestone in the cave. (a) bed separation space; (b) horizontal cloud map; (c) contour map.

Mechanism of bed separation water inrush based on the cusp catastrophe theory

Water enters the bed separation space from ambient aquifers when no karst caves exist near the bed separation space or they are relatively distant, forming bed separation water. This inrush is classified as a hydrostatic pressure inrush. Most researchers have investigated this phenomenon using the empirical water inrush coefficient for the floor. It is expressed as T = P/M, where T is the water inrush coefficient (it has a critical value of 0.06 MPa/m in structurally damaged zones and 0.1 MPa/m in normal zones), and P is the water pressure between the bed separation and the water-conducting fracture zone^26,52. However, the bed separation space and water recharge influence hydrostatic bed separation inrush in karst areas with different types of caves. This process is more complex. If a karst cave is very close to the bed separation zone, the inrush occurring beneath the cave can be regarded as water inrush from the overlying cave. This inrush can be explained using the cusp catastrophe theory model³⁴.

Construction of a hydro-mechanical model of water-rich karst above the bed separation zone

The karst caves in this region have diameters of 2.0 to 20.0 m^5,34,53. The cross-sectional shape of the cave is approximately circular, and caves with widths exceeding 15 m are generally conical. Moreover, the cave’s width is much smaller than the inclined length of the coal seam working face. As shown in Fig. 5, if the cave is connected to the bed separation zone, the water inrush is regarded as cave water inrush, and the water inrush distance between the cave and the coal seam is denoted as d. When the cave is far from the bed separation zone and has a negligible influence, the thickness of the static water pressure aquiclude d₂ is expressed using the empirical water inrush coefficient, where d₂ = P / T_o, with P representing the water pressure between the bed separation zone and the water-conducting fracture zone, and T_o is 0.1 MPa/m. Therefore, the cave roof can be simplified as a circular cross-section to determine the safe distance d for cave water inrush. The system comprising the conical funnel-shaped cave and the aquiclude is regarded as an inverted trapezoidal conical frustum, with the following assumptions:

Fig. 5

Water inrush model of coal seam roof caves in karst areas (d₁ = the safety distance between the cave and the bed separation, d₂ = the static water pressure aquiclude, d = the water inrush distance between the cave and the coal seam).

(1) The water pressure in the cave is the same from top to bottom in the thin plate, and deformation occurs only within the stressed region of the rock mass, whereas the rest remains undeformed.

(2) The aquiclude is a uniform, continuous, isotropic medium. The large cross-sections at the top and bottom of the cave are regarded as circular sections with different radii, considering only the vertical forces on the aquiclude rock mass.

The radius of the cave roof is r₀, the vertical angle is θ, and the radius of the lower stress-deformed damage zone is R, where R = dtanθ + r₀. The force applied by the overlying strata is q, the cave water pressure is p_w, and the thickness of the thin plate is t, where t is much smaller than d (Fig. 6).

Fig. 6

Mechanical model of water inrush from roof caves in coal seams (R = the radius of the lower stress-deformed damage zone, r₀ = the radius of the cave roof, R(t) = the radius of the thin circular plates, p_w = the cave water pressure, t = the thickness of the thin plate, q = the force applied by the overlying strata, θ = the vertical angle).

The radius R(t) of the thin circular plates at all positions in the conical frustum is:

$$\:R\left(t\right)=\frac{R-{r}_{0}}{d}t+{r}_{0}$$

(9)

The pressure Pw(t) exerted by the water diffusion in the karst cave at different positions of the thin circular plates satisfies the following equation:

$$\:\pi\:{R\left(t\right)}^{2}{P}_{w}\left(t\right)=\:\pi\:{{r}_{0}}^{2}{P}_{w}$$

(10)

According to the elasticity theory⁵¹, the maximum deflection of the thin plate is:

$$\:{\omega\:}_{m}=\frac{\left[{p}_{w}\left(t\right)+{p}_{w}\right]{R}^{4}}{64D}$$

(11)

$$\:{p}_{w}\left(t\right)=\frac{{{r}_{0}}^{2}{p}_{w}}{{\left(\frac{R-{r}_{0}}{d}t+{r}_{0}\right)}^{2}}$$

(12)

where p_w(t) represents the water pressure on the thin plate at different positions, R is the deformation and failure zone at the bottom of the cave, and D is the flexure stiffness of the circular plate.

Karst water inrush safety distance based on the cusp catastrophe theory

Water inrush can be regarded as a dynamic, irreversible energy mutation process, which can be assessed using the cusp catastrophe model to determine the instability state³⁸. Its potential function can be expressed using two control parameters, u and v, with the standard form given as:

$$\:\prod\:\left(x\right)=\frac{1}{4}{x}^{4}+\frac{1}{2}u{x}^{2}+vx$$

(13)

where x is the state variable, and u and v are the control variables. Taking the derivative of Eq. (13) yields:

$$\:\prod\:^\prime\left(x\right)={x}^{3}+ux+v=0$$

(14)

Equation (14) represents the equilibrium surface equation, where (x, u, v) describe the surface. The equilibrium surface consists of three leaves: upper, middle, and lower leaves (as shown in Fig. 7). As the state variable x increases, a transition occurs from the lower leaf to the middle leaf, indicating a shift of the system from a stable to a critical state. The discriminant of its roots is:

Fig. 7

Cusp catastrophe model (u and v are the control variables, and x is the state variable).

$$\:4{u}^{3}+27{v}^{2}=0$$

(15)

The system undergoes catastrophic failure when u ≤ 0.

Potential energy II consists of the bending strain energy of the rock layer (U₁), the in-plane strain energy (W₁), and the work done by external forces (axial work U₂ and radial work W₂) based on the principles of elasticity theory⁵¹.

$${\text{II }} = {\text{ }}\left( {U_{{\text{1}}} + U_{{\text{2}}} } \right) - \left( {W_{{\text{1}}} + W_{{\text{2}}} } \right)$$

(16)

The expression for the bending strain energy U₁ of the aquiclude (water-resisting layer) is:

$$\:{U}_{1}=\pi\:D\int\:\left[r{\left(\frac{{d}^{2}\omega\:}{d{r}^{2}}\right)}^{2}+\frac{1}{r}{\left(\frac{d\omega\:}{dr}\right)}^{2}\right]dr=\frac{32\pi\:D{{\omega\:}_{m}}^{2}}{3{R}^{2}}$$

(17)

where U₂ is the integral of the strain energy of the thin circular plate element in the axial direction.

$$\:{U}_{2}=\int\:dUdt$$

(18)

By disregarding higher-order terms, an expression is derived using the variational method in the elasticity theory:

$$\:{U}_{dt}={c}_{1}\frac{\pi\:Edt}{\left(1-{\mu\:}^{2}\right){R\left(t\right)}^{2}}{{\omega\:}_{m}}^{4}$$

(19)

where c₁ is the variational constant, extreme conditions used to satisfy energy functionals match boundary constraints and assumptions, and the work done by external forces is:

$$\:W={W}_{1}+{W}_{2}=\iint\:\left[{p}_{w}\left(t\right)+q\right]\omega\:rd\theta\:dr+\iint\:\left[{p}_{w}\left(t\right)+q\right]{u}_{r}rd\theta\:d\omega\:$$

(20)

According to Li and Liu (2022), the system’s potential energy II is calculated³⁴, and variable substitution is performed, yielding the following:

$$\:\prod\:={c}_{1}\frac{\pi\:Ed}{\left(1-{\mu\:}^{2}\right)R{r}_{0}}{{\omega\:}_{m}}^{4}+{c}_{2}\pi\:\left(\frac{{{r}_{0}}^{2}}{{R}^{2}}{p}_{w}+q\right){{\omega\:}_{m}}^{3}+\frac{32\pi\:D}{3{R}^{2}}{{\omega\:}_{m}}^{2}-\frac{1}{3}\pi\:\left(\frac{{{r}_{0}}^{2}}{{R}^{2}}{p}_{w}+q\right){R}^{2}{\omega\:}_{m}$$

(21)

The safety distance for water inrush in a water-rich karst cave between the conical funnel-shaped roof and the coal layer ($\:d$) can be determined by substituting X into the equilibrium surface equation when u ≤ 0:

$$\:d\le\:\sqrt[4]{\frac{27{{c}_{2}}^{2}{R}^{3}{r}_{0}{\left(1-{\mu\:}^{2}\right)}^{2}{\left(\frac{{{r}_{0}}^{2}}{{R}^{2}}{p}_{w}+q\right)}^{2}}{64{c}_{1}{E}^{2}}}$$

(22)

where E is the elastic modulus of the aquiclude rock mass; µ is the Poisson’s ratio of the aquiclude rock mass; c₁ and c₂ are variational constants. They mainly reflect the adaptability between the theoretical model and engineering practice. It is assumed that the structure is an “ideal elastic thin plate”. However, in reality, the aquifuge has microcracks and inhomogeneity, and there is a deviation between the theoretical model and the reality. Thus, c₁ and c₂ are used for adjustment to make the calculation results closer to the actual engineering situation. The size of the karst cave, the karst water pressure, and the overlying load are positively correlated. They are inversely proportional to the elastic modulus E. This finding indicates that the higher the karst water pressure and load, the thinner the plate thickness, and the larger the plate span, the more prone the area is to water inrush. The safety distance d₁ between the cave and the bed separation is defined as follows:

$$\:{d}_{1}=d-{d}_{2}=\sqrt[4]{\frac{27{{c}_{2}}^{2}{R}^{3}{r}_{0}{\left(1-{\mu\:}^{2}\right)}^{2}{\left(\frac{{{r}_{0}}^{2}}{{R}^{2}}{p}_{w}+q\right)}^{2}}{64{c}_{1}{E}^{2}}}-\frac{p}{{T}_{0}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$$

(23)

Dynamic evolution of roof bed separation during mining of Thick cavernous limestone coal seams

Numerical simulation

Selection of model parameters

It is essential to consider multiple factors, such as geological conditions and experimental data, when selecting modeling parameters. This approach can improve the accuracy and reliability of numerical simulations, providing a scientific basis for understanding the development of bed separation in karst regions and implementing grouting measures. Therefore, this study selected representative adjacent rock types at various depths from ZK101 Drilling near the 10,903 working face of Tenglong Coal Mine for uniaxial compression and density tests using the SAS-2000 rock pressure apparatus to determine their physical and mechanical parameters (see Fig. 8 for rock sample selection and testing details). The loading rate for the rock samples was 0.002 mm/s, and stress-time curves were plotted. The uniaxial compression test results reflect the mechanical conditions between the upper and lower strata (see Fig. 9). Significant differences exist in uniaxial compressive strength between the rock types. Limestone (67.7-86.04 MPa, avg. 77.34 MPa) (Fig. 9a-c) is much stronger than mudstone (2.89–7.51 MPa, avg. 4.85 MPa), shale (peak strength < 10 MPa), and sandstone (30–50 MPa) (Fig. 9d-f). Limestone has lower residual strength than mudstone. It is harder and more brittle, with significantly higher yield strength than shale and mudstone. In contrast, mudstone fractures completely within 100 s, whereas limestone exhibits elastic deformation. Mudstone also differs mechanically from sandstone. The differences between hard and soft rocks cause inconsistent deformation in adjacent layers, with rock interfaces being key bed separation zones. The mechanical parameters used in the numerical simulations are listed in Table 1.

Fig. 8

Rock samples and rock mechanical parameter testing.

Fig. 9

Uniaxial compression test results of rock samples. (a-c) limestone and other rock types; (d-f) mudstone and other rock types.

Table 1 Physical and mechanical parameters of rock blocks.

Development of bed separation zones containing cavities based on fractal dimension

The fracture development of the overlying rock strata in karst regions is complex. The Universal Distinct Element Code (UDEC) is a software application for implementing the discrete element method in discontinuous media. It is used to simulate discontinuities in joints, cavities, and fractures. This method accurately models large deformations and displacements in rock systems and is widely used in rock mechanics in mining areas. Most studies on the development of bed separation zones were qualitative and had low accuracy because the bed separation fractures change from initiation to closure, making the process complex and only suitable for qualitative analysis. Therefore, this study used the fractal dimension²³ to quantify the development of bed separation zones and reveal the fracture development in the overlying rock.

(1) Quantitative characterization using fractal dimension.

Based on the parameters listed in Table 1 and measured data from the Tenglong Coal Mine, this study analyzed the working face 10,903 with a distance of 500 m in the x-direction and 120 m in the z-direction. The upper boundary was free, and the bottom boundary was fixed. The overlying P₃c limestone was simplified with a pressure of 6.5 MPa. Protective coal pillars with heights of 100 m were at both ends. The Mohr-Coulomb constitutive model and the contact-Coulomb slip criterion of the surfaces were used. The excavation step length was 30 m. Two monitoring lines were located beneath the hard and soft rocks (limestone and claystone, mudstone and claystone). The numerical model and the monitoring lines are shown in Fig. 10.

Fig. 10

Numerical model (X = horizontal direction, Z = vertical direction).

Image processing software was used to fill the cavity areas to prevent the influence of karst cavities. A custom Matlab program was applied to binarize the images of bed separation fractures. The fractal dimension D of the fracture network grid was calculated using the box-counting method and Eq. (24). The slope of the linear fitting line represented the fractal dimension.

$$\:\text{D}=-\underset{r\to\:0}{\text{lim}}\frac{\text{lg}\left(\text{N}\text{r}\right)}{\text{lg}(1/r)}$$

(24)

(2) Fractal dimension characteristics.

Nine mining stages (30, 60, 90, 120, 150, 180, 210, 240, and 270 m) were selected to analyze the fractal dimension characteristics. The box-counting dimension (D) was calculated, and the fitting curve was obtained by linear regression. The relationship curve between the fracture network lg (Nr) and lg (1/r) is shown in Fig. 11.

Fig. 11

The relationship between the fracture network lg(Nr) and lg(1/r) in different mining stages.

The R² values of the fitted curves exceeded 0.9974, indicating a high degree of self-similarity. As the working face advanced, the box dimension D decreased and increased. The caving of the overlying strata reduced the number of new fractures. Most were small, broken fractures. The box dimension D increased stepwise to 1.1531 as the working face advanced to 150 m, indicating a significant bed separation zone. D increased stepwise to 1.1881 as the working face advanced to 240 m, at which the bed separation zone reached the maximum. D decreased slightly to 1.1753 when the working face reached 270 m, indicating that the bed separation space began to close.

(3) Development of bed separation fractures in the karst region.

The evolution of the bed separation fractures at different advance distances of the working face beneath a conical funnel-shaped karst cavity is shown in Fig. 12. The fractures in the overlying strata were saddle-shaped. Initial fracturing occurred in the overlying strata as the working face advanced to 30 m. The karst cavity was far from the mining location and did not affect the fractures. Bed separation occurred in the overlying strata when the working face reached 90 m. The vertical distance from the coal seam to the bed separation zone was 13.82 m. As the working face continued to advance, fracturing and subsidence were observed at 150 m from the top strata, and the bed separation zone expanded upward, whereas the lower bed separation zone began to close. The vertical distance from the bed separation zone to the coal seam was 35.14 m. At 240 m, the working face was beneath the karst cavity. At this point, the bed separation reached the maximum value, with a bed separation length of 71.2 m and a vertical distance from the coal seam of 57.90 m, terminating beneath the P₃c limestone karst cavity. At 270 m, the fractures were dense. Tensile fractures occurred beneath the karst cavity, and the strata above the bed separation subsided. The bed separation length decreased to 68.4 m. As the working face advanced to 300 m, the length and height of the bed separation zone decreased significantly, and the area was compacted and closed.

Fig. 12

Evolution of bed separation fractures at different advance distances in a conical funnel-shaped karst cavity.

Figure 13 shows the vertical settlement in the bed separation zone layer during the mining of working face 10,903. The monitoring results for line 1 indicate that the maximum subsidence point moved forward as the working face advanced, reaching a maximum subsidence value of -1.88 m. As the working face advanced to 150 m, the subsidence value rapidly increased from 0.2 m to 0.5 m, indicating a significant increase in the bed separation area. The subsidence for line 2 rapidly increased from 1.0 m to -2.64 m as the working face reached 240 m. The settlement was significantly larger in line 2 than in line 1, indicating the maximum bed separation area. The subsidence pattern became more barrel-shaped as the distance from the coal seam increased. The thicker the limestone roof, the larger the bed separation zone. In contrast, the subsidence pattern was funnel-shaped for a smaller bed separation zone.

Fig. 13

Vertical settlement in the bed separation zone. (a) Vertical settlement of monitoring line 1; (b) Vertical settlement of monitoring line 2.

Physical similarity simulation of bed separation

Traditional physical experiments of bed separation zones typically scale down the prototype coal mine using a similarity ratio. Despite advances in physical modeling, monitoring methods have lagged behind. The stresses and strains inside the model cannot be measured precisely, which has become a major constraint in developing model experiments. An FBG sensor consists of optical fibers that can be placed inside the rock for the real-time monitoring of strain^54,55,56,57. This method has advantages, such as a simple structure, high sensitivity, accurate monitoring, and real-time observation. Since the bed separation formation is complex in karst areas, this study used an FBG sensing system and embedded FBG sensors at the bed separation layers to quantify the bed separation.

Design of similarity simulation experiment

The experiment was based on the 10,903 working face of the Tenglong Coal Mine. This study utilized on-site drilling data and the geological conditions to establish a physical similarity model with the following ratios:

(1) Model dimensions (length × width × height): 250 × 20 × 125 mm;

(2) Geometric similarity ratio: 1:150;

(3) Time similarity ratio: 1:10;

(4) Bulk density of the rock similarity ratio: 1:1.47;

(5) Strength similarity ratio: 1:220.

The simulation materials included fine sand as the aggregate and gypsum, calcium carbonate, and borax as the cementing materials. A 10–20 mesh mica powder was used as a bedding layer for stratification. The proportions of the simulation materials are listed in Table 2 based on papers describing adjacent coal mine experiments^58,59. The materials were thoroughly mixed with water and placed into the model frame. The steps of the experiment are illustrated in Fig. 14. Based on the calculations and numerical simulation results, 14 FBG sensors were embedded vertically into the physical similarity model. The sensors monitored the spatiotemporal evolution of the roof separation during the coal seam excavation in real time. The sensors were numbered gc01 to gc14, where gc01 was embedded outside the excavation boundary of the model in an area unaffected mainly used to monitor the influence of temperature changes on fiber strain. The sensors gc02, gc03, gc04, and gc05 are monitoring sensors arranged at the top, bottom, left, and right around the karst cave, mainly used to monitor the changes of fractures in the karst cave (with a variation generally less than 1 cm); gc06–gc08 are set near the open-off cut to monitor the development of bed separation on the left side of the karst cave; gc09–gc11 are used to monitor the development of bed separation directly beneath the karst cave; and gc12–gc14 are located near the stopping-line to monitor the development of bed separation on the right side of the karst cave. In Table 2, a bed separation space develops beneath the marlstone (by lithology). This space is located within the water-conducting fractured zone, with an actual distance of 34.03 m from the coal seam and a corresponding model distance of 226.9 mm. Due to the model’s bulking coefficient and the influence of the caving zone, the sensors were positioned as far away from the coal seam as possible, and it is arranged in marlstone, at least 240 mm above the bottom plate.

Table 2 Proportions and parameters of materials used in the similarity simulation.

Fig. 14

Steps of the similarity simulation experiment. (a) Model dimensions; (b) weighing; (c) mixing; (d) embedding of fiber optic sensors; (e) compaction; (f) completed model.

Fracture layer development derived from fiber Bragg grating sensors

During model excavation, 30 cm-wide protective coal pillars were retained at both ends. The working face advanced from left to right, with each excavation step progressing 5 cm, for a total advance of 190 cm. The FBG data were recorded continuously. Since the FBG sensors were vertically embedded in the rock layers, and their locations corresponded to the fracture zones identified by theoretical calculations and numerical simulations, the strain measured by the sensors can be interpreted as the response of the fracture separation.

The strain trends were similar for all sensors. This study used the gc07 sensor as an example. It was embedded 40 cm from the working face. The strain versus the distance from the working face is shown in Fig. 15. As the working face advanced from 0 to 55 cm, the strain abruptly increased from − 9.18 µε to 138.17 µε (segment AB) because the collapse of the lower rock layers created a separation space. As the working face advanced from 55 cm to 75 cm, the strain increased to 495.00 µε (segment BC), indicating an expansion of the separation space. As the working face advanced from 75 cm to 95 cm, the overlying rock layers collapsed and compacted the rock stratum where gc07 was embedded, causing the strain to decrease to 35 µε (segment CD), suggesting closure of the separation zone. As the face continued to advance to 115 cm, further compaction of the overlying collapsed layers resulted in a decrease to -40.126 µε. When the working face reached 190 cm, the strain remained stable. The strain variation recorded by sensor gc07 reflected the evolution of the separation in this rock stratum.

Fig. 15

The strain at different distances from the working face derived from fiber bragg grating sensor gc07.

The strain recorded by sensors embedded at different rock strata was closely related to the movement of the overlying strata. The strain derived from sensors gc09 to gc11 is shown in Fig. 16. The strain differed for different strata. Sensor gc09 was embedded in a relatively shallow layer and exhibited a slower change in strain and smaller values. As the working face advanced to 95 cm, the strain rapidly increased to 445.63 µε. As the face advanced to 120 cm, the strain gradually decreased, indicating the compaction of the separation space. When the face reached 145 cm, the strain remained nearly constant, suggesting that the separation zone had been fully compacted. The strain trends were similar for sensors gc09, gc10, and gc11. As the working face advanced to 110 cm, the strain of gc10 increased to 598.44 µε, indicating that the separation location had shifted backward with the advance of the working face. Stabilization occurred when the face reached 165 cm. The uppermost sensor gc11 was located in the layer with the largest separation. The peak strain was 652.88 µε when the height of the upper separation zone reached the maximum of 1.95 cm. The overlying strata separation ended beneath the karst cave. The sensors embedded accurately recorded the formation and dynamic evolution of the separation zone, demonstrating the close relationship between the separation zone and the overlying and underlying rock strata. The separation rate F was calculated as follows:

Fig. 16

The strain at different distances from the working face derived from fiber bragg grating sensors gc09-gc11.

$$\:\varvec{F}=\frac{{\varvec{S}}_{\varvec{d}\varvec{o}\varvec{w}\varvec{n}}-{\varvec{S}}_{\varvec{u}\varvec{p}}}{\varvec{h}}$$

(25)

where F represents the separation rate (in mm/m); S_up and S_down denote the subsidence of the upper and lower rock strata (in mm), i.e., the difference in subsidence between two adjacent measurement points at the same vertical location; h is the vertical distance between the upper and lower rock strata (in meters). F > 0 indicates bed separation between the strata, and F < 0 suggests compression of the strata. The subsidence was monitored using an established photogrammetry layout. The strains obtained from sensors gc07 and gc11 are listed in Table 3. A negative strain value indicates a separation rate of less than zero, i.e., no separation or compaction. The peak strain occurred at the peak separation rate, indicating a positive correlation. Thus, the FBG sensors accurately reflected the dynamic development of the rock strata, providing an accurate method for quantifying bed separation.

Table 3 Sensor strain and separation rate.

Quantitative analysis of separation using digital image correlation

DIC was used for deformation measurements to improve the detection accuracy of overlying rock displacement and validate the separation zone derived from the physical similarity simulation. This method utilizes a coherent light source (such as a laser) to illuminate a rough surface, generating speckle patterns. When the laser irradiates the rough surface of an object, light is scattered due to microscopic surface irregularities, and the scattered light interferes, creating a speckle pattern. This technique has the advantages of full-field measurements, non-contact operation, high efficiency, and high precision. It has been widely used in mining pressure monitoring, multi-field coupling, underground engineering stability assessments, and physical similarity simulation experiments. DIC is highly suitable for the precise localization of deformation and movement and the initiation and development of separation fractures in the rock mass beneath karst cavities.

The light source and DIC system were adjusted to the appropriate angles, and the surface was painted white. Black speckles were applied using ink. The DIC counting area near the karst cavity was calibrated, as shown in Fig. 17a-b. The black speckle displacement was recorded as the working face advanced by 5 cm. Figure 17d-f present the strain measurement results at distances of 30 cm to 105 cm from the working face. Figure 17d shows the strain near the karst cavity after the working face had advanced to 30 cm. The strain had a relatively small range, with a maximum of 0.07 mm, indicating minor deformation of the overlying rock and no separation near the cavity. Figure 17e shows the strain values at 80 cm. The maximum strain in the lower right area was 2.1 mm, indicating a separation zone in the limestone layer; however, the separation was some distance from the cavity and had a negligible effect on it. The strain cloud map shows a continuous upward extension along the fracture. Figure 17f shows the strain at 105 cm. As the distance from the working space increased, the separation fractures expanded upward. The largest separation fractures occurred beneath the P₃c limestone layer. The area near the cave on the mining-disturbed side was strongly affected, with a maximum subsidence of 10.5 mm, whereas the side near the final mining boundary exhibited less impact, with subsidence of 0.5 mm. The karst cavity affected the continuity of the rock layer’s subsidence, causing tensile failure around and beneath the cavity and forming tensile fractures, as shown in Fig. 17c. The DIC system improved measurement accuracy, and the results were consistent with the numerical simulation and FBG sensor results.

Fig. 17

Digital image correlation system layout and strain measurement results at 30–105 cm. (a) light source; (b) digital image correlation analysis area; (c) tensile cracks near the karst cave; (d) contour line at 30 cm; (e) contour line at 80 cm; (f) contour line at 105 cm.

On-site prevention and control techniques for separation water hazards in karst regions

On-site prevention and control of coal mine separation water hazards are complex and variable in karst regions. Real-time detection of separation zones is challenging. The key to managing separation water is accurately detecting the locations of karst caves and sites with separation water and draining separation water. Therefore, a comprehensive prevention and control technology system based on a closed-loop mechanism-prediction-control model and precise methods to detect the separation space is required to obtain accurate information for managing separation water hazards. This study used the 10,903 working face of the Tenglong Coal Mine in the northern Guizhou karst area as an example. Based on the dynamic evolution of the separation zone in the thick, cavity-containing limestone roof strata caused by mining, this study proposes a threefold approach to preventing and controlling separation water hazards. (1) Geophysical explorations should be conducted before mining to detect karst caves and water-rich zones in the roof strata of the working face to assess the expansion of karst caves. (2) Appropriate locations and methods should be used to monitor the height of the two zones of roof rock damage to determine where separation will develop. (3) The water-rich zones and the separation water should be drained.

Detecting karst cave and water-rich zones in roof strata

Karst caves and well-developed fractures are common in limestone aquifers. The water-bearing capacity of the aquifer is typically unevenly distributed, facilitating water recharge of the bed separation zone. Therefore, detecting karst caves and the water-bearing capacity is crucial to prevent or control bed separation water hazards. The transient electromagnetic method (TEM) is an effective technique to detect karst channels above the working face^60,61. Before the 10,903 working face was mined, this study conducted field investigations of the karst roof strata. Measurement points were placed every 10 m along the return and haulage roadways of the 10,903 working face, starting from the open face and ending at the stop line. This study obtained measurements in three directions: −45° dip angle, 0°, and + 45° dip angle, totaling 48 (points) × 3 (directions) × 2 (return roadway and haulage roadway) = 288 points. The coil size was 2 × 2 m. This study performed filtering, apparent resistivity calculation, depth conversion, interference correction, and Occam inversion, and extracted apparent resistivity values at the same elevation of the working face. The layout of the TEM survey lines is shown in Fig. 18a. The detection results are shown in Fig. 18b. The blue areas indicate low-resistivity anomalies (relatively watery zones), and the orange areas indicate high-resistivity anomalies (weakly water-bearing or dry zones). The survey detected variations in apparent resistivity within 80 m above the coal seam roof. The low-resistivity anomaly zone (< 10 Ω·m) corresponds spatially to the water-rich karst aquifer in P₃c limestone (Depth: 50–80 m) before mining the working face. High apparent resistivity (> 15 Ω·m) below 50 m depth confirms no hydraulic connection to the underlying P₃l stratum.

Fig. 18

Transient electromagnetic method (TEM): layout and results. (a) TEM layout; (b) TEM results.

Measurement of the heights of the two zones of overlying roof rock damage

The current study utilized the numerical simulation results for the separation zone in the 10,903 working face, the similarity simulation results, and lithology data from the nearby ZK101 Drilling site. Two methods were employed to determine the height of the two zones of roof rock damage and identify the target area for preventing and controlling separation water disasters. The present study established a drilling site 245 m from the working face and conducted static observations during three drillings. The field drilling layout is shown in Fig. 19.

Fig. 19

Field drilling layout.

Figure 20 presents the water leakage of the #1 drill hole derived from a custom-made double-ended water-blocking device. The leakage rate was recorded every meter as the drill rod advanced. The water leakages increased rapidly in the 10–14 m depth section, with water loss rates of 25.39 L/min to 32.50 L/min, averaging 28.37 L/min, indicating severe rock damage and well-developed fractures. This area was identified as the caving zone. The maximum water loss rate at 28–52 m was 27.5 L/min, with an average of 19.84 L/min. The area was identified as the water-conducting fracture zone. The maximum loss at 58–62 m was 35.4 L/min, averaging 31.84 L/min, indicating a significant increase in water volume. This area was assumed to be the upper separation zone.

Fig. 20

Water leakage during drilling of the #1 drill hole.

Figure 21 shows the detection results and Table 4 shows the designed parameter of Drilling 2. A significant increase in water leakage indicates the presence of separation; conversely, stable water leakage suggests no obvious bed separation. At the 59 m depth of Drilling 2, the water leakage suddenly increased from 16.5 L/min to 45.6 L/min, then rapidly decreased to 17.8 L/min. This process indirectly reflects the maximum displacement-subsidence space of bed separation. Gaussian fitting curve analysis shows that the range of this stage is 1.6 m. In contrast, the maximum separation space derived from the DIC-based similar simulation is 10.5 mm. Converted by the similarity ratio, this corresponds to 1.57 m in the field, which is essentially consistent with the on-site detection results.

Fig. 21

Water leakage during drilling of the #2 drill hole.

Table 4 Drilling Parameter.

Figure 22 shows images of the #1 drill hole. They indicated intact rock with no fractures at a depth of 5 m. The rock was fragmented with through-cracks at 14 m. The fracture density increased from 32 to 42 m, with intersecting longitudinal fractures. The rough drilling walls were composed of mud and detritus, indicating a water-conducting fracture zone. Bed separation was observed at 59 m. The double-ended water plugging test and the images accurately located the bed separation zone. The measured heights of the two zones of overlying roof rock damage are consistent with the numerical simulation and similarity simulation results.

Fig. 22

Images of the #1 drill hole.

Drainage of water-rich zones and bed separation water

The most effective measure for preventing and controlling bed separation water hazards is underground drainage. The drainage drillings must penetrate the target bed separation strata where the water hazard occurs to penetrate the bed separation zone and discharge the water. However, since karst caves were located above, the water in the cave continuously flowed into the bed separation zone. A single drill hole is insufficient to drain the accumulated water in the bed separation zone and does not ensure that the water level is sufficiently low after drainage.

Therefore, a coordinated surface and underground drainage approach for bed separation water surges was proposed. Drilling occurred simultaneously on the surface and underground to ensure drainage from the surface and underground boreholes. A schematic diagram of the surface and underground drainage layout is shown in Fig. 23. Surface stepped-diameter boreholes were placed above the karst caves and water-rich zones, and casing pipes were installed (ensuring the upper diameter was larger than the lower diameter) to prevent drill hole collapse. The depth of the surface drillings was sufficient to reach the bottom of the bed separation zone at the base of the P₃c limestone. If karst water or bed separation water was detected directly above the working face, drainage was performed immediately. Underground drainage drill holes were placed every 15 m between the two haulage roadways. These drillings extend 3 m below the bottom of the P₃c limestone and were one-third of the horizontal distance of the working face to ensure that the bed separation water discharged along the drainage paths. During the working face advancement, the TEM was used in real time to detect bed separation zones ahead of the excavation. If low-resistivity anomalies were found, two drainage drill holes were placed every 15 m. Water pressure gauges and flow meters were installed at the surface and underground drainage points for real-time monitoring. If the water pressure rose, the drainage volume was increased. If rock stability decreased, the drainage volume was reduced, and grouting reinforcement was applied. This drainage method improves drilling drainage efficiency and reduces the likelihood of bed separation water zones. Economic Analysis of Prevention and Control Technology in order to optimize cost-efficiency: (1) Risk-based implementation high-risk areas: deploy integrated “TEM + Multi-borehole TV + Double-end Grouting” (Cost: ~¥300,000/km), low-risk areas: simplified verification with two boreholes (Cost reduction: 40%). (2) Cost-benefit comparison, bed-separation treatment cost: ¥500,000–800,000, risk reduction: 90% decrease in water inrush probability (average accident loss avoidance: ~¥20 million). (3) High-risk area strategy: high-precision monitoring is given priority, and the prevention cost per ton of coal is increased by 8–10 yuan, but the production life can be extended by 3–5 years.

Fig. 23

Schematic diagram of surface and underground drainage of bed separation water. (a) layout of surface and underground drainage; (b) configuration of underground drainage drillings.

In conclusion, to enhance bed separation water control, a systematic prevention approach is required. In northern Guizhou’s karst areas, we propose a “Three-Level Prevention System” (Fig. 24), comprising:

Fig. 24

The conceptual framework diagram of three-level prevention system.

(1) Theoretical Analysis systems, determines bed separation positions, dynamic development patterns, and water inrush mechanism. (2) Prediction technology systems, different methods are used to detect bed separation and karst cave (such as TEM, Fiber Bragg Grating, etc.), drilling TV and double-end water plugging are used for three-zone observation, hidden danger prevention and geological guarantee. (3) Drainage engineering systems, water exploration engineering (drilling), drainage engineering (drainage through diversion drillings), water plugging engineering (grouting in separation layer) and water inrush monitoring (installing water level monitoring system).

Conclusion

This study performed theoretical analysis, numerical simulations, a similarity simulation experiment, and on-site water hazard prevention measures to investigate the disaster-causing mechanism and development of bed separation zones in the overlying strata of karst mining areas. The main conclusions are as follows:

(1) Bed separation water inrush is not caused solely by hydrostatic pressure in the separation zone in karst regions. A catastrophic instability occurs when elastic potential energy accumulates in the aquiclude and reaches a critical level. Based on the cusp catastrophe theory, a funnel-shaped mechanical model was established to quantify the relationship between cave size (R), water pressure (P), and the safe separation distance (d₁) and obtain a critical threshold. The larger the karst cave and the higher the water pressure, the greater the likelihood of inducing water inrush. This study developed a cross-scale mechanical criterion for predicting bed separation and water inrush in karst regions, improving the understanding of bed separation water inrush in complex karst environments.

(2) The fractal box dimension D obtained from numerical simulations at various stages of the working face mining was highly correlated with the area of the bed separation zone. The fitted curves had high accuracy, with a goodness of fit above 0.9974, indicating strong similarity. As the mining distance increased, the overburden fractures exhibited a saddle shape. The bed separation zone expanded toward the karst cave and terminated beneath the thick-bedded P₃c limestone karst cave.

(3) A similarity simulation experiment using FBG sensors enabled the real-time monitoring of strain in the rock mass. The FBG strain measurements and the bed separation ratio F accurately reflected the initiation and dynamic evolution of bed separation. DIC, a high-precision and non-contact technique, integrated with FBG measurements, allowed for the quantitative assessment of the magnitude of bed separation zones.

(4) The TEM was used to locate the water-rich zones of karst caves (survey line 150–200 m, 58–80 m in the roof direction). Bed separation was identified using images from the boreholes (at 59 m), and the position of the bed separation zone was confirmed using double-ended water plugging tests to monitor water leakage (58–62 m). The proposed method enabled the precise and targeted drainage of the water-conducting channel between the karst cave and the bed separation zone for the first time. In contrast to the traditional single underground drainage method, this study established a three-level prevention and control system integrating mechanism analysis, prediction, and coordinated drainage. This approach is a replicable prevention method for bed separation water hazards in karst mining areas.

(5) Since the current study focused on the Tenglong Coal Mine, the findings only represent the stratigraphic structure near the working face. Karst areas are extensive in the northern Guizhou mining area, and the morphology of karst features is highly complex; not all have the shape of standard conical funnels. Therefore, future research should focus on the overburden of karst caves and bed separations for different karst morphologies, stratigraphic structures, and water pressures to provide more accurate guidance for drainage and grouting projects related to bed separation water in karst regions.