Study on the development height of “two zones” under repeated mining of medium-thick coal seams at close range

Introduction: The coal faces I0104105 and I0104204 of coal seams 4-1 and 4-2 in the I01 mining area of Shuangma No.1 Mine are taken as the engineering background.

Methods: In this manuscript, UDEC numerical simulation, similar material simulation, downhole drilling imaging method measurement, and empirical formula calculation methods are employed to address the high development of the “two zones” in close-range medium-thick coal seams during repeated mining. An analysis is conducted on the movement and collapse laws of overlying rocks under the separate mining of 4-1 coal and the repeated mining of 4-1 coal and 4-2 coal. The development height of the “two zones” under repeated mining is determined, compared, and verified against the empirical formulas. Linear analysis is conducted through on-site measurements and empirical formula differences.

Results: The existing calculation formula coefficients are corrected to propose an empirical formula for the development height of the “two zones” applicable to the Shuangma Mine. The results show that the “two zones” development height presents three significant stages under the repeated mining of medium-thick coal seams at close range: rapid growth, slow growth, and final stability. The height of the “two zones” is not simply added; however, a superposition effect is observed, which is closely related to the physical and mechanical parameters of the rock layers between coal seams, coal seam spacing, and coal seam thickness.

Discussion: The research results have theoretical significance and guiding value for determining the “two zones” height of the overlying rock under repeated mining of medium-thick coal seams at close range.

1 Introduction

Coal is the cornerstone for ensuring energy security and independence, which provids strategic support for the industrialization process, the stable operation of the power grid, and people’s energy consumption. The coal is projected to constitute no less than 50% of the energy mix by 2050 (Wang et al., 2023; Liu et al., 2024). The formation of the “two zones” (the caving zone and the water-conducting fracture zone) originates from the instability and failure of the overlying strata structure following coal seam extraction. Mining-induced disturbance triggers the collapse of the immediate roof, forming the caving zone. Concurrently, the coupled interaction between mining-induced stress and the self-weight stress of the overlying strata propagates fracture networks within the upper strata, forming the water-conducting fracture zone. Furthermore, repeated mining operations exacerbate the cumulative damage in the overlying strata and stress redistribution, which leads to the height expansion of the “two zones” and a superposition effect. In the context of the westward shift of coal mining strategy, ecologically sensitive western mining areas exhibit typical characteristics such as thicker coal seams, closer interlayer distances, dense occurrence of multiple coal seam groups, and large reserves compared to the east. As a critical technical parameter for green mining, the development height of the “two zones” following coal extraction directly governs the degree of damage to overlying aquifers/aquitards and goaf (Li et al., 2020; H et al., 2023; Ning et al., 2020). Consequently, it is clear that developmental patterns of the “two zones” height under repeated mining in close-distance medium-thick seams becomes particularly critical for preventing roof water disasters in western mining areas.

Regarding the development height of the “two zones” under the single coal seam mining, numerous scholars have conducted a series of studies. They concluded that the development height of the “two zones” is related to parameters such as geological conditions and mining techniques. The main factors affecting the development height of the “two zones” include burial depth, mining thickness, mining width, overburden lithology, and mining speed. For a long time, scholars have summarized various methods for predicting and calculating the development height of the “two zones” by combining various disciplines, including theoretical analysis (Ren et al., 2021; Lu et al., 2024; Peng et al., 2025), empirical formula calculation (Lu et al., 2022; Miao et al., 2011), downhole observation method (Chang et al., 2025; Li et al., 2025), drilling flushing fluid leakage method (Xiong et al., 2015; Cao et al., 2024), numerical simulation (Zhou and Yu, 2022; Zhao et al., 2024; Wang et al., 2021), and similar material simulation (Wang et al., 2022; Yang et al., 2025; Shi and Zhang, 2022), laying various theoretical and methodological foundations for the study of the development law of the “two zones”.

Coal mining has gradually shifted from one layer to two or even multiple layers due to the increasing intensity of coal mining in China. Moreover, the development height of the “two zones” will further increase under the repeated mining of close-range coal seams (Cheng et al., 2025; Hou et al., 2022; Ran and Yu, 2020; Zhang et al., 2021). Many scholars have conducted relevant researches on the aforementioned phenomenon. Cui et al. (2020) investigated the fracture distribution characteristics of overlying strata and the developmental patterns of the “two zones” through similar material simulation, borehole television imaging, micro-seismic monitoring, and discrete element modeling. Huang et al. (2020) employed numerical simulation to examine the displacement behavior of surrounding rock and stress distribution patterns during multi-seam extraction in gently inclined close-distance coal seam groups. They also revealed the complex stress field distribution within the affected area of gently inclined close-packed multi-coal seams, the deformation and failure forms of overlying strata, and the interaction patterns among coal seams. Ge et al. (2023) utilized FLAC^3D modeling to analyze the caving behavior of overlying strata above an ultra-close-distance goaf. They demonstrated that continuous extraction in such seam groups induces more intense stress redistribution disturbances than single-seam mining, accelerating the breakdown of the critical layer.

The above research results on the failure characteristics of overlying strata under repeated mining of coal seams have significant practical guiding significance for the prevention and control of roof water disasters in mines. However, studies on the developmental patterns of the “two zones” under repeated mining in close-distance medium-thick coal seams remain relatively scarce. Therefore, the I0104₁05 and I0104₂04 coalfaces of the medium-thick coal seams 4-1 and 4-2 at close range in Shuangma No.1 Mine are taken as the engineering background. In this study, multi-dimensional research methods such as UDEC numerical simulation, similar material simulation, underground borehole imaging measurement, and empirical formulas are combined to explore the height variation law of the “two zones” during the repeated mining process of medium-thick coal seams at close range. An empirical correction formula for the development height of “two zones” under repeated mining of medium-thick coal seams at close range is proposed based on on-site measurement, empirical formulas, and the combination of adjacent mining areas. The main goal is to provide a theoretical basis and practical guidance for the safe mining of coal seams under repeated mining conditions.

2 Engineering context

The 4-1 and 4-2 coal seams at the Shuangma No. 1 Coal Mine are within the Yan’an Formation of the Middle Jurassic System. The 4-1 and 4-2 coal seams have average recoverable thicknesses of 3.80 m and 1.58 m respectively, with an average inter-burden spacing of 6.6 m between them. According to the current mining and excavation production conditions, the I0104₁05 and I0104₂04 fully mechanized mining faces are selected as research objects for the height detection of the water-conducting fracture zone of the overbearing rock in the stope. The average inclined length of the I0104₁05 coalface is 257.5 m, with an area of 761,015.5 m². A single-direction long-wall comprehensive mechanized coal mining method is adopted, and the management of the goaf is handled by the complete collapse method. The inclination length of the I0104₂04 coalface is 236 m, and its area is 319,734.6 m². This coalface also adopts a single-direction long-wall comprehensive mechanized mining method. Based on the comprehensive columnar chart of the mine, the ventilation measures tunnel 6# of the I01 mining area, the columnar chart of the 3# drilling site in the 6# transfer chamber of the tunnel, and the geological conditions of the I0104₁05 coalface and the I0104₂04 coalface, the Comprehensive histogram of overburden and floor strata in coal seams 4-1 and 4-2 have been determined (Figure 1).

Figure 1

Figure 1. Comprehensive histogram of overburden and floor strata in coal seams 4-1 and 4-2.

3 Numerical simulation of “two zone” height development under repeated mining in close-distance medium-thick coal seams

3.1 Establishment of numerical model and layout of monitoring lines

By using the UDEC numerical simulation software, based on the I01 mining area of Shuangmao No.1 mine (with coalfaces I0104₁05 and I0104₂04 as the prototypes), a model with a length of 470 m and a height of 195 m was established. The length of the coalface was 250 m, with 30 m coal pillars on both sides and an 80 m boundary. The mining height of the 4-1 and 4-2 coal seams is 3.8 m and 1.58 m, respectively, with all strata inclined at 9°. The height of the overlying rock layer is 175 m, with an additional stress of 0.5 MPa. The left and right boundaries restrict horizontal movement, and the bottom boundary restricts vertical movement, and the top boundary applies an equivalent load of 0.5 MPa. In order to better reflect the in situ stress characteristics of shallow mining, the influence of stress factors is considered in the simulation, and the initial stress is the maximum horizontal stress, and the Mohr-Coulomb constitutive model is selected. A finer quadrilateral mesh is used within 50–100 m above the coal seam roof and 25 ∼ 50 m below the coal seam floor. A gradually thickened quadrilateral mesh is used beyond this range. The numerical model is shown in Figure 2; the corresponding lithomechanical parameters are detailed in Table 1. By adopting a step-by-step excavation method for the model, the initial roof surcharge interval and the periodic surcharge interval during the actual mining process can be simulated. In order to better study the development height of the “two zones” during the mining process of the coalface, and considering the convergence and stability of the calculation process in the UDEC numerical simulation software, the calculation is conducted every time after 5 m of excavation.

Figure 2

Figure 2. Numerical model of the development height of the “two zones” under mining in the I0104₁05 and I0104₂04 coalfaces of the I01 mining area of Shuangma No.1 Mine.

Table 1

Table 1. Physical and mechanical parameters of the roof and floor layers of coal seams 4-1 and 4-2.

3.2 Selection of physical and mechanical parameters of rock strata

The rock material failure criterion of UDEC is the Mohr-Coulomb criterion (Equation 1), which corresponds to the linear failure plane of shear failure:

$f_s=\left({\sigma }_1-{\sigma }_3\right)N_{\varphi }+2c\sqrt{N_{\varphi }}(1)$

where $N_{\varphi }=\frac{1+\sin \varphi }{1-\sin \varphi }$, σ₁ is the maximum principal stress, σ₃ is the minimum principal stress, $\varphi$ is the internal friction angle, and c is the cohesion.

If f_s < 0, shear yielding occurs. The two strength constants $\varphi$ and c can be easily derived from triaxial tests in the laboratory. However, the yield surface is extended to σ₃ for simplicity, which is the area equal to its tensile strength σ^t. The minimum principal stress cannot exceed the tensile strength (Equation 2):

$f_t={\sigma }_3-{\sigma }^t(2)$

If f_t > 0, tensile yielding occurs. It should be noted that the tensile strength cannot exceed the value of σ₃, which corresponds to the upper limit of the Mohr-Coulomb relationship. The maximum value is determined by the following Equation 3:

${\sigma }_{\mathit{max}}^t=\frac{c}{\tan \varphi }(3)$

The rock mechanics parameters that UDEC software requires include bulk modulus K, shear modulus G, normal stiffness k_n, and tangential stiffness k_s of rock layers or rock joints. Joint properties are usually obtained from indoor experiments (i.e., triaxial or direct shear tests). The specific calculation method is shown in the following equations by consulting materials and referring to previous achievements (Equations 4–7):

$K=\frac{E}{3\left(1-2\mu \right)}(4)$

$G=\frac{E}{2\left(1+2\mu \right)}(5)$

$k_s=0.4k_n(6)$

$k_n=\max \left[\frac{K+\frac{4}{3}G}{△Z_{\min }}\right](7)$

In Equations 4, 5, E is the elastic modulus, GPa, and μ is poisson’s ratio. In Equation 7, ΔZ_min represents the minimum width between adjacent block elements in the normal direction of the contact surface, m; max[] represents the maximum value of each element adjacent to the joint (the materials of each block adjacent to the same joint may not be the same).

Five simulation schemes were established with coalface lengths of 50 m, 100 m, 150 m, 200 m, and 250 m. The monitoring lines were deployed along the seam dip direction above each coalface, with the vertical interval of the lines being equal to the thickness of each stratum (detailed configurations in Tables 2, 3). In all schemes, these lines captured displacement and stress variations at identical horizontal coordinates but varying elevations within the overlying strata as face length increased. After extracting the I0104₁05 and I0104₂04 coalfaces, the development heights of the “two zones” were determined by comprehensively analyzing monitoring data and visualization outputs.

Table 2

Table 2. Distribution of monitoring locations for overlying rock mass on coal seam 4-1.

Table 3

Table 3. Distribution of monitoring locations for overlying rock mass on coal seam 4-2.

3.3 Analysis of numerical simulation results

3.3.1 Overlying strata movement law during mining of the 4-1 coal seam

After the excavation of the I0104₁05 coalface, the overlying rock layer structure of the mining area underwent a process of “balance → failure → re-balance,” forming a stable caving structure and the distribution of the “three overlying zones”. The stress and displacement laws of the overlying strata for different coalface lengths are shown in Figure 3. Subsidence data for the overlying strata were obtained from various monitoring lines. And then the data were processed. The critical height positions of the “three overlying zones” in I0104₁05 were determined based on the differences between different monitoring lines and the graphical patterns displayed. The measured subsidence values of the overlying strata at different elevations (monitoring lines) after mining completion are presented in Figure 4.

Figure 3

Figure 3. The evolution process of overlying rock failure under different pushing distances. (a) 50 m advance (b) 100 m advance (c) 150 m advance (d) 200 m advance (e) 250 m advance.

Figure 4

Figure 4. The subsidence curves of the overlying strata for the 4-1 coal seam at different survey line positions after mining.

As shown in Figure 3, the overlying strata of the entire mining area form various forms of parabolic arch-like balanced mechanical support structures. At the upper end of the coalface, the arch foot end was the first to experience slab failure due to the influence of overlying rock stress and the lack of effective constraints on its own. Concurrently, the lower end of the coalface is in a metastable state due to the constraints of strength. Overlying strata deform predominantly toward the tailgate side due to the gravitational forces and the 9° seam dip, generating a significantly asymmetric deformation zone. This deformation progressively transfers deeper into the surrounding rock mass at the tailgate, forming an inclined deformation arch distinctly oriented toward the lower section of the panel.

At 50 m of face advance, the unsuspended overburden strata undergo sequential fracturing, loosening, and collapse under gravitational loading, triggering caving of the immediate roof where limited rock fragmentation fails to compact the goaf fully. As a result, a void is formed within the caving zone. Even though uniform roof subsidence occurs across the coal face, no significant bed separation develops.

At 100 m advance, bed separation failure initiates in the mid-upper bedrock strata. As a result, overburden movement stabilizes with decelerated fracture propagation, establishing structural equilibrium with clearly differentiated the caving zone and the water-conducting fracture zone exhibiting distinct characteristics.

The failure height plateaus despite intense structural reorganization as the advance extends to 150 m and 250 m. Stress redistribution propagates upward through beam transfer mechanisms. Moreover, near-seam strata contact the goaf floor with maximized vertical displacement, while overlying strata continue experiencing displacement growth until post-mining self-equilibration eliminates further vertical movement.

As evidenced in Figure 4, overlying strata exhibit dip-induced migration toward the tailgate side due to immediate roof caving once 250 m coal face advance is completed. Monitoring line 1 records maximum subsidence, while subsidence variation rates demonstrate asymptotic convergence above 9 m elevation–indicating 9 m above the seam 4-1 roof as the critical height boundary of the caving zone (monitoring line 2 position). Further elevation increase to 30.9 m reveals negligible subsidence variation beyond this threshold, denoting the definitive interface between the water-conducting fracture zone and bending zone.

3.3.2 Overlying strata movement patterns under repeated mining of seams 4-1 and 4-2

Following the extraction of the vertically underlying I0104₂04 coalface beneath the I0104₁05 goaf, the overburden structure undergoes another cycle of “equilibrium → failure → re-equilibration”, forming a stable caving structure with a distinct upper “three zones” distribution (caving zone, water-conducting fracture zone, and bending zone). Stress-displacement patterns across varying face lengths are illustrated in Figure 5. The composite critical heights of the upper “three zones” were definitively determined after sequential extraction of I0104₁05 and I0104₂04 by analyzing differential subsidence data from monitoring lines and profile morphology. Figure 6 quantifies post-mining subsidence magnitudes at discrete elevations.

Figure 5

Figure 5. Evolution process of overlying rock failure under repeated mining with different pushing distances. (a) 50 m advance (b) 100 m advance (c) 150 m advance (d) 200 m advance (e) 250 m advance.

Figure 6

Figure 6. The subsidence curves of the overlying strata for the 4-1 coal seam at different survey line positions after the mining of I0104₁05 and I0104₂04.

As illustrated in Figure 5, the overlying strata start to move with the advancement of the I0104₂04 coal face—the entire stope overburden forms parabolic arch-shaped balanced mechanical support structures of varying configurations.

At a face 50 m advance, the suspended mudstone layer collapses under its own gravity and pressure, undergoing fracturing, loosening, and subsequent caving. This process triggers the collapse of the immediate roof. The caved roof immediately fills the goaf due to the high fragmentation coefficient of the mudstone. Since the goaf in the upper seam struggles to form a stable structure, it exerts a uniformly distributed load on the fractured rock mass in the lower goaf, further compacting it. Consequently, the voids within the caving zone of the I0104₁05 goaf expand, inducing bed separation failure in the overlying strata.

At a face advance distance of 100 m, the overlying strata sequentially experience the initial and periodic caving of the immediate and main roofs. As the strata gradually subside, the bed separation spaces and fragmentation-induced voids progressively diminish, while fracture propagation stabilizes. The overburden structure reaches equilibrium, exhibiting distinct characteristics in the caving zone and the water-conducting fracture zone. Ultimately, the extraction of coal seams 4-1 and 4-2 results in a stratified overburden structure comprising the caving zone, water-conducting fracture zone, and bending zone.

As shown in Figure 6, once the I0104₂04 coalface advanced to 250 m, the overlying strata exhibited a downward movement toward the lower end of the coalface due to the influence of the seam dip angle. The immediate roof comprising mudstone completely collapsed and filled the goaf. In contrast, the overlying 4-1 coal seam goaf and its caving zone directly subsided, further compacting the underlying goaf. Consequently, measuring lines 2 and 3 recorded the maximum subsidence magnitude at their respective heights.

At a measuring height of 19.6 m (line 4), the subsidence magnitude of all measuring lines gradually stabilized as the height increased. This height (19.6 m above the roof of the 4-2 coal seam) is identified as the critical height of the caving zone. At a measuring height of 41.5 m, the subsidence magnitude remained constant with further height increases. The area at 41.5 m can be considered as a bending zone.

4 Development under repeated mining in close-distance medium-thick coal seams

4.1 Principles for selecting similarity ratios in similar material simulation experiments

The principle of similarity in model testing refers to the fact that the phenomena reproduced on the model should be similar to the physical model. According to the principle of similarity, the model is required to follow the rules of similar geometric conditions, boundary conditions (displacement and stress state), mechanical properties, rock mass structure, and deformation characteristics (Table 4).

Table 4

Table 4. Main similarity ratios between experimental models and prototypes.

4.2 Design of similar material simulation model

A steel-framed test rig (3000 mm × 200 mm × 1700 mm) was employed based on experimental requirements and similarity theory (Table 4) to simulate stratigraphy along the strike direction. The mixture comprised sand aggregates blended with lime, gypsum, cement, and borax in specific proportions to replicate the mechanical properties of roof/floor strata and coal seams. Mica powder (6–10 mesh) was an interlayer material, while lime and gypsum acted as binding agents. The scaling ratios were defined as follows: Geometric similarity ratio C_l = 1 : 100, Density similarity ratio C_γ = 1 : 1.67, Poisson’s ratio similarity ratio C_μ = 1 : 1, Time similarity ratio C_t = 1 : 10, and stress/strength similarity ratio C_σ = 1 : 166.67. The bottom boundary is a fixed hinge support to restrict vertical and horizontal movement. The boundaries on both sides are set as laterally movable constraints. The constraints allow the model to move freely in the vertical direction but restrict its lateral expansion to simulate the boundary effect of an infinitely large rock mass. Consequently, the boundary effect is prevented from interfering with observing the mining movement’s influence area. The upper boundary is subjected to a vertical load according to the burial depth of the rock layer.

4.3 Fabrication and excavation of a similar material model

The model strata were constructed using standard, similar simulation materials applied according to predetermined material ratios. Thicker roof and floor strata were subdivided through stratified layering based on the established experimental protocols. The specific material formulations and quantities for each simulated rock layer are detailed in Table 5.

Table 5

Table 5. Test rock material ratio and dosage.

The face advance rate scaling ratio was 10 to satisfy kinematic similarity requirements. Given an actual mining rate of 10 m/d, the model advance rate was set at 1 cm/h—the excavation protocol implemented three operational shifts daily, advancing the model face by 1 cm/h. Total excavation durations were 7.5 days per coalface, culminating in 15 days for both faces.

4.4 Analysis of similar material simulation results

4.4.1 Caving behavior of overburden strata during seam 4-1 extraction

Initial excavation commenced 60 m from the model’s left end, forming a 10 m starter cut. When the coalface advanced 0–30 m, the immediate roof remained cantilevered without fracture or caving due to its intrinsic strength. At 39 m advance, the overburden reached its critical caving span, triggering large-scale collapse of the immediate roof and initiating the initial caving event (Figure 7).

Figure 7

Figure 7. Simulation for the caving process of the immediate roof in coal seam mining 4-1. (a) 10 m advance (b) 30 m advance (c) 39 m advance.

During coalface advance in a similar material model, the instability-induced collapse of overlying strata progressively forms the caving zone, the water-conducting fracture zone, and bending zone. The evolutionary process and strata-specific caving characteristics at distinct stratigraphic levels under varying advance distances are illustrated in Figure 8.

Figure 8

Figure 8. The collapse characteristics of overlying strata and the formation process of the “two zones” of overlying strata at different pushing distances of coal seam 4-1. (a) 58 m advance (b) 98 m advance (c) 120 m advance (d) 129 m advance (e) 166 m advance (f) 180 m advance.

At 58 m of coalface advance, mining-induced disturbances propagated to the overlying strata, triggering renewed instability and collapse. The breakage angle measured 60° behind the goaf and 50° ahead of the active face, with opposing rotation directions of fractured rock blocks across these zones. The caving height reached 10.4 m, corresponding to an initial caving span of 58 m. As the coalface advanced to 98 m, the main roof above seam 4-1 collapsed completely, marking its second periodic caving event. The first periodic weighting interval measured 40 m, where micro-fractures developed in seam 4-1. The primary fracture line migrated forward with face advance, transitioning from fracture line 1 to fracture line 2. Consequently, fractures along line 1 tended to close, while slight bed separation persisted in the overlying strata.

At 120 m of coalface advance, the immediate roof of seam 4-1 collapsed with a caving interval of 22 m; moreover, subtle bed separation developed in the overlying siltstone strata that remained structurally intact. The main roof experienced renewed instability at 129 m of coal face advance, inducing a second periodic weighting event with an interval of 31 m. Fractures propagated vertically upward through the overburden, generating new bed separation horizons. In addition, pre-existing separations progressively closed due to bulking of the collapsed strata. Concurrently, the dominant fracture line migrated from Fracture Line 2 to Fracture Line 3, with fractures along Line 2 exhibiting progressive closure.

Once the coalface of seam 4-1 advanced to 166 m, the main roof underwent renewed fracture and collapse, triggering a third periodic weighting event with an interval of 37 m. Mining ceased at 180 m advance, where the caving angle measured 60° near the starter cut and 47° adjacent to the stopping line, with the maximum water-conducting fracture zone height reaching 40.15 m.

Integrated analysis of experimental results and observations of unstable rock block collapse demonstrates that the maximum caving zone height reaches 10.4 m. In comparison, the maximum water-conducting fracture zone height attains 40.15 m during the solitary extraction of seam 4-1.

4.4.2 Overburden caving behavior under repeated mining of seams 4-1 and 4-2

The failure patterns of overlying strata under repeated extraction of seams 4-1 and 4-2 are illustrated in Figure 9. The patterns are analyzed using representative cross-sections at 10 m, 60 m, 110 m, and 180 m from the starter cut.

Figure 9

Figure 9. Characteristics of overlying rock collapse and development process of “two zones” at different pushing distances under repeated mining of coal 4-1 and 4-2. (a) 10 m advance (b) 60 m advance (c) 110 m advance (d) 180 m advance.

When the coal face advanced to a distance of 0 ∼ 30 m, the immediate roof remained suspended without fracturing or collapsing due to its inherent strength. As the coal face advanced to 60 m, the overlying strata reached their critical span limit, resulting in the integral collapse of the roof above the 4-2 coal seam. Consequently, the caving zone within the roof of the 4-1 coal seam experienced further subsidence. The initial caving span of the 4-2 coal seam was measured at 60 m, slightly greater than that of the 4-1 coal seam. This difference is attributed to the increased caving span in the lower seam induced by pressure relief from mining the overlying coal seam and the formation of the overlying goaf.

Once the coalface advanced to 110 m, a second integral collapse occurred in the roof of the 4-2 coal seam. The periodic weighting interval was 50 m, accompanied by intense strata pressure. This process manifested as the fracture line propagating upward rapidly, leading to the interconnection between the fracture lines in the 4-2 and 4-1 coal seams. As a result, significant deformation occurred in the overlying strata along the lower end of the coalface due to the coal seam dip angle. This deformation progressively propagated deeper into the surrounding rock at the lower end. Subsequently, when the coalface advanced to 180 m, a third integral collapse occurred in the roof of the 4-2 coal seam, with a weighting interval of 70 m.

According to the aforementioned experiments and the observed instability of collapsing rock blocks, it is determined that the “two zones” coincide with those of the underlying 4-1 coal seam when mining the overlying goaf in the 4-2 coal seam. The maximum height of the caving zone above the 4-2 coal seam reaches 18.0 m, while the maximum height of the water-conducting fracture zone extends to 50.5 m.

5 Field measurements of “two zones” development heights under repeated mining in close-distance medium-thick coal seams

5.1 Drilling location and layout design

Drilling site 1 was positioned within the #1 ventilation roadway of the I0104₂04 coal face based on site-specific geological conditions, mining progress around the observation area, and field construction constraints.

Drilling site 2 was located at the #1 track-changing chamber of the intake airway in the I0104₃02 coalface. Site 1 investigated “two zone” development heights in the 4-1 coal seam, while site 2 examined “two zone” development under repeated mining in 4-1 and 4-2 coal seams. Two observation wells were initially designed for each site according to the estimated ranges of the caving zone and the water-conducting fracture zone. The borehole distribution and design are illustrated in Figures 10–13.

Figure 10

Figure 10. Observation of drilling construction location at the height of coal “two zones” development in 4-1.

Figure 11

Figure 11. Observation of drilling construction location at the height of “two zones” development under repeated mining of 4-1 coal and 4-2 coal.

Figure 12

Figure 12. 4-1 coal “two zones” development height observation drilling design schematic diagram.

Figure 13

Figure 13. Schematic diagram of borehole design for observing the development height of the “two zones” under repeated mining of 4-1 coal and 4-2 coal. (a) Design schematic of drill 3# (b) Design schematic of drill 4#.

5.2 Analysis of field measurement results

Field measurements were conducted according to the aforementioned borehole design. Partial screenshots from the drill camera surveys for drills#1 and #2 at drilling site 1 are shown in Figure 14. Coal seams were encountered when the inspection probe advanced to depths of 6.08 m and 6.5 m, indicating entry into the goaf of the I0104₁05 coalface. As the probe extended to 19.1 m and 19.2 m, the drill hole walls exhibited densely distributed vertical and horizontal fractures with fragmented surrounding rock structures. Significant caving zones were observed, characterized by fragmented rock blocks accumulated within the borehole, confirming this section as the caving zone formed by the I0104₁05 goaf. The drill hole walls displayed sparse concentric fractures that progressively diminished within the depth intervals of 19.1 m–39.39 m and 19.2 m–39.97 m. The walls remained structurally intact, allowing this section to be identified as the water-conducting fracture zone.

Figure 14

Figure 14. Observation results of drills #1 and #2 in drilling site 1. (a) Drill 1# advanced to 6.08 m (b) Drill 1# advanced to 19.1 m (c) Drill 1# advanced to 39.39 m (d) Drill 2# advanced to 6.5 m (e) Drill 2# advanced to 19.2 m (f) Drill 2# advanced to 39.97 m.

Drill hole trajectories, maximum azimuth angles, designed inclination angles, and actual depths of drills #1 and #2 at drilling site 1 were employed to perform calculations after applying the mean dip angle correction, which yielded caving zone heights of 8.8 m and 8.6 m. Moreover, the water-conducting fracture zone heights of 28.48 m and 28.66 m were used, respectively.

Similarly, according to the partial screenshots from the drill camera surveys for drills #3 and #4 at drilling site 2 (Figure 15), when the inspection probe advanced beyond depths of 24.97 m and 24.15 m, the drill hole walls exhibited densely distributed vertical and horizontal fractures with fragmented surrounding rock structures. Significant caving zones were observed, characterized by fragmented rock blocks accumulated within the drill, confirming entry into the goaf of the I0104₂02 coalface and its overlying caving zone. The fragmentation of surrounding rock significantly decreased beyond depths of 47.65 m and 45.51 m, transitioning to predominantly vertical and horizontal fractures with structurally intact drill hole walls. This phenomenon confirms the entry into the water-conducting fracture zone. However, further camera surveys were impeded due to construction constraints, preventing complete delineation of the water-conducting fracture zone extent.

Figure 15

Figure 15. Observation results of drills # 3 and #4 in drilling site 2. (a) Drill #3 advanced to 24.97 m (b) Drill #3 advanced to 47.65 m (c) Drill #4 advanced to 24.15 m (d) Drill #4 advanced to 45.51 m.

The heights of both the caving zone and water-conducting fracture zone in the 4-2 seam were superimposed onto those of the 4-1 seam based on the drill’s trajectories, maximum azimuth angles, designed inclination angles, and actual depths of drills #3 and #4 at drilling site 2. Furthermore, the penetration of the caving zone of the 4-2 coal seam into that of the 4-1 coal seam was also considered. Consequently, the composite caving zone height under repeated mining of the 4-1 and 4-2 coal seams was determined to be 17.26 m.

Theoretical formula predictions were made to verify the accuracy of the measured results. An equation for a single coal seam with an inclination angle of no more than 55° is selected according to the empirical formula in the “Regulations on the reservation of coal pillars under buildings, water bodies, railways and major shafts and the mining of pressed coal”. The overlying rock types are hard, medium hard, weak, and extremely soft, with a mining height of 3 m as the dividing line. The height prediction formula for the “two zones” of thick coal seam layered mining in Appendix 4-1 of the “Code for three under coal mining” is selected for coal seams with no more than 3 m mining height. On the other hand, a height formula for the “two zones” of fully mechanized top coal caving mining in Table 2-2 of Section 2.1.1 of the “Guidelines for three under coal mining” is selected for coal seams with a mining height greater than 3 m but not more than 12 m. The specific calculation formula is shown in Table 6.

Table 6

Table 6. Calculated formulas for the heights of the “two zones” induced by single coal seam mining within a 55° angle.

According to the drilling column chart shown in Figure 1, the top of coal seam 4-1 in this mining area mainly comprises siltstone with a uniaxial compressive strength of 18.55 MPa, followed by fine-grained sandstone and medium to coarse-grained sandstone with a uniaxial compressive strength of 83.54 MPa. Based on the lithology of the roof in mining area 4-1, the roof belongs to a medium-hard rock layer. Hence, the following formula is used to calculate the development height of the “two zones” under the mining of 4-1 coal in Shuangma No.1 Mine:

$H_k=\frac{100M}{4.7M+19}\pm 2.2(8)$

$H_{li}=\frac{100M}{1.6M+3.6}\pm 5.6(9)$

where H_K refers to the caving zone height (m); H_li represents the water-conducting fracture zone height (m); M refers to the cumulative mining thickness (m).

According to Equations 8, 9, the maximum predicted heights for the 4-1 coal seam at the Shuangma No.1 Mine are 12.51 m for the caving zone and 44.86 m for the water-conducting fracture zone.

Since 4-1 and 4-2 coal seams at the Shuangma No.1 Mine constitute close-distance coal seams, the development heights of the caving zone and water-conducting fracture zone for this coal seam group must be calculated according to the Regulations’ methodology for closely spaced coal seam clusters.

1. When the distance h between adjacent coal seams in a close range coal seam group (the vertical distance between the upper and lower coal seams) is greater than the height pressure of the caving zone of the lower coal seam, the maximum height of the water-conducting fracture zone between the upper and lower coal seams can be calculated respectively using the formulas in Table 6 based on the thickness of the upper and lower coal seams. The highest elevation can be taken as the maximum height of the water-conducting fracture zone of the two coal seams, as shown in Figure 16.

2. When the caving zone of the lower coal seam contacts or completely enters the range of the upper coal seam, the maximum height of the water-conducting fracture zone of the upper coal seam is calculated based on the mining thickness of this coal seam. The maximum height of the water-conducting fracture zone of the lower coal seam should be calculated based on the comprehensive mining thickness of the upper and lower coal seams. Moreover, the highest elevation should be taken as the maximum height of the water-conducting fracture zone of the two coal seams (Figure 17).

Figure 16

Figure 16. Calculating the height of the water-conducting fracture zone in a close-range coal seam (h > Hxm).

The comprehensive mining thickness of the upper and lower coal seams can be calculated as follows:

$M_{Z1-2}=M_2+\left(M_1-\frac{h_{1-2}}{y_2}\right)(10)$

where M₁ represents the thickness of the upper coal mining; M₂ is the thickness of the lower coal mining layer; H_1-2 is the normal distance between the upper and lower coal layers; y is the ratio of the height of the lower coal layer to the mining thickness.

Figure 17

Figure 17. Calculating the height of the water-conducting fracture zone in a close-range coal seam (h < Hxm).

The average spacing h_1-2 between coal seams 4-1 and 4-2 is 6.6 m. Therefore, the maximum caving zone after 4-2 coal mining is calculated separately according to Table 6. The value of H_k4-2max = 8.18 m can be obtained by substituting M_4-2 = 1.58, greater than the spacing between coal seams 4-1 and 4-2. Therefore, coal seams 4-1 and 4-2 belong to the closer distance coal seams in the close distance coal seam group. The maximum height of the caving zone and water-conducting fracture zone after mining coal seams 4-1 and 4-2 should be calculated based on the comprehensive mining thickness of the upper and lower coal seams. According to Equation 10; Table 6, M_Z1-2 = 4.06 m, H_k4-2max = 12.86 m, and H_li4-2max = 45.81 m. Therefore, the height of the caving zone H’_k4-2max = max (H_k4-2max-M_4-2-h_1-2, H_k4-1) = 12.51 m, and the height of the water-conducting fracture zone H’_li4-2max = max (H_li4-2max-M_4-2-h_1-2, H_li4-1) = 44.86 m can be calculated under repeated mining of coal 4-1 and 4-2.

6 Comprehensive evaluation and empirical formula correction of the development height of the “two zones” under repeated mining of medium-thick coal seams at close range

6.1 Statistical analysis of the “two zones” height in adjacent mines of medium-thick coal seams at close range

The research results of the caving zone and water-conducting fracture zone of Jinfeng Coal Mine, Shicaocun Coal Mine, Meihuajing Coal Mine, Maidoushan Coal Mine, Hongliu Coal Mine, and Yangchangwan Coal Mine in the surrounding mining areas of Shuangma No.1 Mine were statistically analyzed to accurately predict the development height of the “two zones” in Shuangma No.1 Mine (Table 7).

Table 7

Table 7. Development height of “two zones” in the surrounding mines of Shuangma No.1 Mine.

The research results show that the maximum development height of the water-conducting fracture zone varies significantly due to the different thicknesses of the main coal seams in the four coal mines. However, the maximum fracture mining ratio of the four mines is relatively similar due to similar coal seam occurrence conditions, with the lowest being 11.28 in Shicaocun coal mine and the highest being 19.93 in Maidoushan coal mine. The collapse mining ratio of the four mines varies greatly, with the lowest being 2.2 in the Yangchangwan coal mine and the highest being 8.8 in the Meihuajing coal mine. Based on the roof characteristics of the No. 4 coal seam in Shuangma No. 1 Mine, its occurrence conditions are similar to those of the No. 2 coal seam in Yangchangwan Coal Mine. Therefore, it can be inferred that the maximum fracture mining ratio of the water-conducting fracture zone developed in Shuangma No.1 Mine is approximately 18, and the maximum caving mining ratio is roughly 3.

6.2 Comprehensive evaluation of the “two zones” development height under repeated mining of medium-thick coal seams at close range

The maximum development heights of the “two zones” across all methodologies are statistically summarized in Table 8 based on the findings from numerical simulations, similar material simulations, field measurements, and empirical formula predictions.

Table 8

Table 8. Summary of the maximum height of “two zones” development in coal face under various methods.

Results demonstrate that the maximum development heights of the “two zones” under single-seam mining of the 4-1 coal seam follow a consistent descending order: empirical formulas > similar material simulations > numerical simulations > field measurements. The reason for the relatively small height of the “two zones” under separate mining of coal 4-1 using drilling observation may be due to the difficulty in accurately interpreting the top boundary of the caving zone caused by drilling collapse, as well as a slightly subjective understanding of the fracture development degree by humans. However, this result is within the error range compared to numerical simulations, empirical formulas, and similar material simulations.

Conversely, under the repeated mining of 4-1 coal and 4-2 coal, the magnitudes of the maximum development heights of the “two zones” are ranked as follows:

a. Development height of caving zone: numerical simulations > similar material simulations > field measurements > empirical formulas;

b. Development height of water-conducting fracture zone: similar material simulations > empirical formulas > numerical simulations.

Furthermore, the development height values of the water-conducting fracture zone at the same step distance were compared between the separate mining of 4-1 coal and the repeated mining of 4-1 coal and 4-2 coal, the result shows that numerical simulation < similar material simulation. This discrepancy stems from limitations inherent to each methodology. In other words, numerical simulations are constrained by mesh discretization errors and non-representative parameter selection. In contrast, similar material simulations are affected by scale effects and operator-induced experimental errors. Nevertheless, the differences observed remain minor and fall within allowable error margins. Given the average inter-burden spacing of 8.37 m between the 4-1 and 4-2 seams and considering the maximum two zones’ heights across all methodologies, repeated mining of both seams induces a slight increase in the two zones’ heights compared to single-seam mining of the No. 4-1 coal seam. The potential mechanism is that the overlying rock layer is no longer an original, intact, high-strength geological body, but a medium that has been pre-damaged and weakened by initial mining. On this basis, repeated mining causes “secondary damage” to the rock strata through mechanisms such as stress field superposition, secondary fracturing of key layers, and reactivation and expansion of fractures, significantly increasing the development height of the “two zones” compared to single coal seam mining. Although empirical formulas produce conservative estimates of the water-conducting fracture zone height, they effectively validated the accuracy of field measurements.

6.3 Revision of empirical formula for the “two zones” development height under repeated mining of medium-thick coal seams at close range

The precise calculation of the “two zones” height after the single mining of 4-1 coal and the combined mining of 4-1 and 4-2 is analyzed in this paper based on the actual situation of Shuangma No.1 Mine, and in combination with the research understanding of predecessors. A linear analysis was conducted on the difference between the measured and theoretical values based on the original calculation formula. The coefficients of the existing calculation formula were corrected. Moreover, a calculation formula for the height of the “two zones” applicable to the study area was proposed to prevent and control mine water disasters, while increasing the upper limit of the coal pillar for mining.

According to the empirical formula form given in the “Regulations on the reservation of coal pillars under buildings, water bodies, railways and major shafts and the mining of pressed coal” (hereinafter referred to as the “Three-down” coal mining standards), the height prediction formulas for the caving zone and the water-conducting fracture zone can be set as follows Equation 11:

$H_{k/li}=\frac{100M}{aM+b}\pm m(11)$

where H_k represents the height of the caving zone, m; H_li represents the height of the water-conducting fracture zone, m; M represents the thickness of the sample, m; m represents the mean error (standard deviation of the sample).

The least square method is used for fitting, and the formula is modified as follows: $H_{k/li}=\frac{100M}{aM+b}$. Let $y=\frac{100x}{ax+b}$, let $y=H_{k/li}$, x = M.

$\text{Then},y=\frac{100x}{ax+b},\frac{1}{y}=\frac{ax+b}{100x}$

$y^{\prime }=\frac{1}{y},x^{\prime }=\frac{1}{x},a^{\prime }=\frac{a}{100},b^{\prime }=\frac{b}{100},$

$y^{\prime }=a^{\prime }+b^{\prime }{x}^{\prime }$

The values of a' and b' can be obtained by using simple linear regression. Then, the values of a and b can be derived. In Equation 11, m represents the mean error, which is calculated by reversing the first half of the formula and comparing it with the measured value to obtain the difference value—the normalized standard deviation of the m-sample for the second half of the term.

The relationship between the caving zone, water-conducting fracture zone, and coal thickness was fitted based on data from surrounding mines with similar values of cross mining ratio, split mining ratio, and Shuangma No.1 mine (Table 6). The fitting results are shown in Figure 18.

Figure 18

Figure 18. Relationship between the caving zone, water-conducting fracture zone, and coal seam thickness in Shuangma No.1 Mine.

According to Figure 18, the equation for the caving zone is Equation 12

$y^{\prime }=0.0334+0.1884x^{\prime }(12)$

Therefore, it can be concluded that b = 18.44, a = 3.34. The normalized standard deviation is equal to m = 3.29.

The fitting equation for the caving zone is Equation 13

$H_k=\frac{100M}{3.34M+18.44}\pm 3.29(13)$

Similarly, as shown in Figure 18, the equation for the water-conducting fracture zone is

$y^{\prime }=0.1664x^{\prime }-0.0126(14)$

According to Equation 14, b = 16.64, a = 1.26. The corresponding normalized standard deviation is m = 7.37.

The fitting equation for the water-conducting fracture zone can be expressed as Equation 15

$H_{li}=\frac{100M}{-1.26M+16.64}\pm 7.37(15)$

The close range coal seam group in close water coal mining specifically refers to two or more coal seams with a distance h (vertical distance between upper and lower coal seams) between adjacent coal seams less than or equal to the height H_k of the caving zone of the lower coal seam. The calculation method for the height of the “two zones” adopts the conversion height method M_zs. The calculation method is described below.

The converted mining height M_zsi (i > 1) of the target coal seam (ith layer) for the closer coal seam group in the close range coal seam group can be calculated as follows Equation 16:

$M_{zs,i}=M_{zs,i-1}+M_i-\frac{M_{zs,i-1}{h}_{i-1}}{M_i{y}_i}(16)$

After consulting relevant materials and conducting reverse calculation verification based on a large amount of measured data, and for safety reasons and calculation convenience, the value of y is taken as 7.

The height of the “two zones” is calculated by converting the mining height M_zs from the bottom of the target coal seam as the starting point. In contrast, the final height of the “two zones” (Equation 17) for the mining of the target coal seam in the close-range coal seam group is the highest elevation among all the calculated “two zones” heights of the mined coal seams:

$\begin{array}{ll}\hfill & \hfill {\left(H_{k/li}\right)}_{imax}=\max \left[{\left(H_{k/li}\right)}_1,{\left(H_{k/li}\right)}_2-M_1-h_1,...,{\left(H_{k/li}\right)}_i\right.\\ \hfill & \left.-\sum \left(M_{i-1}+h_{i-1}\right)\right]\hfill \end{array}(17)$

7 Conclusion

This manuscrip takes the coalfaces I0104₁05 and I0104₂04 of coal seams 4-1 and 4-2 in the I01 mining area of Shuangma No.1 Mine as the engineering background. In this study, UDEC numerical simulation, similar material simulation, downhole drilling imaging method measurement, and empirical formula calculation methods are employed to address the high development of the “two zones” in close-range medium-thick coal seams under repeated mining. An analysis is conducted on the movement and collapse laws of overlying rocks under the separate mining of 4-1 coal and the repeated mining of 4-1 coal and 4-2 coal. The development height of the “two zones” under repeated mining is determined, compared, and verified against the empirical formulas. Linear analysis is conducted through field measurements and empirical formula differences. The existing calculation formula coefficients are corrected to propose an empirical formula for the development height of the “two zones” applicable to the Shuangma Mine. The main conclusions are as follows:

1. Numerical simulations were employed to determine the development heights of the two zones at varying excavation advancement distances under both single-seam mining of the 4-1 coal seam and repeated mining of the 4-1 and 4-2 coal seams. The results exhibit three distinct phases: rapid growth, gradual growth, and stabilization. The caving zone height reached 9.0 m after mining the 4-1 seam alone, while the water-conducting fracture zone height attained 30.9 m. Under repeated mining of both seams, these values increased to 19.6 m and 41.5 m, respectively. These results confirm that repeated extraction significantly increases the two zones’ heights compared to single-seam mining.

2. The results of similar material simulation experiments indicate that: the caving zone height reached 10.4 m under 4-1 coal seam mining conditions, while the water-conducting fracture zone height reached 40.15 m. The corresponding caving height ratio and fractured height ratio were calculated as 2.54 and 9.79, respectively. The two zones’ heights are spatially superposed with those formed by 4-1 seam extraction alone under repeated mining of the 4-1 and 4-2 coal seams. The development heights of the “two zones” in the 4-2 seam increased significantly due to the weight of the overlying goaf strata, reaching 18.0 m for the caving zone and 50.5 m for the water-conducting fracture zone.

3. Based on downhole drill imaging measurement, the height of overlying rock caving zone in the I0104105 and I0104204 coalface of Shuangma No.1 Mine was 8.7 m and 17.35 m respectively, with corresponding caving height ratios of 2.25 and 4.28, respectively. The caving zone height under repeated mining of the 4-1 and 4-2 seams increased by approximately 8.65 m compared to single-seam extraction of the overlying 4-1 seam. The accuracy of the measured results was estimated using empirical formulas. Further linear analysis was conducted based on field measurements and the differences between empirical formulas, refining the coefficients of existing calculation formulas. A new empirical formula for the development height of the “two zones” was proposed, which is suitable for Shuangma Mine.

4. The methodology demonstrates strong predictive efficacy for the development heights of “two zones” under repeated mining in close-distance medium-thick coal seams. The proposed method can be extended to analogous geological settings, including small-interval and moderate-interval repeated mining scenarios.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, upon request and without undue reservation.

Author contributions

DZ: Formal Analysis, Methodology, Software, Writing – original draft. YW: Formal Analysis, Methodology, Writing – original draft. LK: Software, Supervision, Validation, Writing – review and editing. ZL: Supervision, Validation, Writing – review and editing. HY: Supervision, Validation, Writing – review and editing. MY: Supervision, Validation, Writing – review and editing.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Conflict of interest

Authors DZ, YW, LK, ZL, HY, and MY were employed by China Energy Group Ningxia Coal Industry Co., LTD. Shuangma No.1 Coal Mine.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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