1 Introduction

During the underground coal mining process, there are various hazards, among which water inrush accidents rank as the second most significant disaster, following closely behind gas-related incidents (Ma and Bai 2015; Dash et al. 2016; Sun et al. 2016; Wang et al. 2022a). According to statistics from 2001 to 2022, there have been 1105 water inrush accidents in Chinese coal mines, resulting in a total of 4491 fatalities (Fangpeng et al. 2018; Yin et al. 2023) (Fig. 1).

Fig. 1
figure 1

Statistics of water inrush accidents in Chinese coal mines during 2001–2022

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The presence of water inrush accidents poses a tremendous threat to the safety of coal mining operations (Maiti et al. 2009; Bukowski 2015; Ma et al. 2019; Wang et al. 2022b; Liu et al. 2023a). During the excavation of roadways, various water inrush problems are frequently encountered (Gui and Lin 2016; Polak et al. 2016). When a water inrush occurs, groundwater rapidly flows into roadway through fractures in rock mass under the influence of water pressure (Ma et al. 2022; Liu et al. 2023b). Failure to promptly discharge the inflowing water can lead to the flooding of roadway, resulting in the scrapping of mining equipment at best and causing severe injuries or fatalities to personnel at worst (Singh 2015; Zhao et al. 2020). The influx of large amounts of groundwater into roadway also weakens the surrounding rock properties, significantly reducing the overall stability of roadway and leading to disasters such as roof collapse and floor heave (Cui et al. 2018; Ma et al. 2018). Furthermore, the ingress of groundwater can cause irreversible damage to roadway, making repairs extremely difficult and costly, and sometimes even rendering roadway irreparable (Zhang et al. 2019b).

To prevent water inrush disasters, it is common practice in mine development to leave a certain width of coal pillars between adjacent working faces, as shown in Fig. 2, to block the accumulation of water in the gob (Wang et al. 2021; Chen et al. 2022a; Galav et al. 2022; He and Huang 2022; Fang et al. 2023). The stability of these waterproof coal pillars has long been one of the critical research topics in coal mine development (Wang 2006; Hu et al. 2019; Li et al. 2021; He et al. 2023).

Fig. 2
figure 2

Illustration of the water immersion failure process of waterproof coal pillar: a seepage of water from the gob into the plastic zone of waterproof coal pillar; b weakening and collapse of coal pillar’s plastic zone due to water immersion; c seepage of water from the gob into the deeper region of waterproof coal pillar

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Experimental research is an important method for studying waterproof coal pillars (Chen et al. 2022b). Currently, experimental investigations on waterproof coal pillars primarily focus on the weakening effects of water content on the mechanical parameters of coal samples (Yao et al. 2021b). Yao et al. (2020) conducted tests involving variable-angle shear on coal samples with different water contents, while (Lu et al. 2016; Wang et al. 2018; Zhang and Nie 2020) performed uniaxial and triaxial tests on coal samples with varying water contents. The findings from these studies consistently demonstrate that the mechanical properties of coal pillars, such as compressive strength, shear strength, friction angle, and cohesion, decrease with an increase in water content.

Furthermore, numerical simulations play a crucial role in studying waterproof coal pillars. Liu et al. (2020) analyzed the effects of coal pillar width, dip angle, and water pressure on the stability of waterproof coal pillars. Their findings suggest that water pressure has a more significant influence than coal seam dip angle, which, in turn, has a more significant impact than coal pillar width when the coal pillar width ranges from 12 to 18 m, water pressure varies from 0 to 0.3 MPa, and coal seam dip angle ranges from 2° to 10°. Shao et al. (2022) simulated waterproof coal pillars under fault conditions, examining damage and water inrush situations. Additionally, Chen et al. (2017) simulated the evolution of internal fractures within waterproof coal pillars.

Scholars have made substantial contributions in experimental and simulation research regarding waterproof coal pillars (Zhang et al. 2023). However, in existing studies, experimental research has been unable to fully reveal the actual situation of waterproof coal pillars, and simulation studies have not highlighted the complete cycle of failure mechanisms for waterproof coal pillars. The Dongzhuang Coal Mine has decided to advance the 30,204 tailgate along the water-containing gob side in order to improve the coal recovery rate. During this process, the coal pillar in the section will undergo the mining effects of the 30,203 panel, water infiltration in the gob, and disturbances caused by the excavation of the 30,204 tailgate. In light of this, this study employs FLAC3D to establish a fluid–structure interaction model for waterproof coal pillars, developing a system to assess the weakening of coal pillars due to water inflow during roadway excavation. By employing real-time monitoring of zone’s elastic–plastic state, stress, strain, and water saturation, the dynamic updating of mechanical parameters within coal pillar is achieved. This approach has uncovered the instability mechanism of waterproof coal pillars during “mining—water immersion softening—roadway excavation” coupling effect while driving roadway along gob. The result of this research is of significant importance for determining the width and stability analysis of waterproof coal pillars.

2 Development of fluid–structure interaction system

2.1 Calculation of coal pillar permeability

After the mining of working face, segmented coal pillar undergo prolonged stress variation and damage, leading to varying degrees of internal structural changes and alterations in physical properties. Consequently, it is necessary to separate internal zones of coal pillar into elastic and plastic zones for individual calculations. In this study, the permeability of waterproof coal pillar is calculated using the permeability formula proposed by (Zhang et al. 2019a):

$${k}_{E}=7.9549{e}^{-4.8879\left(1-{e}^{-0.3888{\sigma }_{1}}\right)}$$
(1)
$${k}_{P}=142.2316{e}^{-2.6349\left(1-{e}^{-0.3415{\sigma }_{1}}\right)}$$
(2)

where, \({k}_{E}\) is the permeability of coal samples in elastic state, md; \({k}_{P}\) is the permeability of coal samples in plastic state, md; \({\sigma }_{1}\) is effective stress, MPa.

The relationship between the permeability of coal samples and effective stress is illustrated in Fig. 3. The permeability of coal samples is significantly higher in plastic state than in elastic state. Distinguishing between elastic and plastic states is crucial for fluid–structure interaction calculation of coal, as it can significantly improve the accuracy of the prediction results.

Fig. 3
figure 3

The relationship between the permeability of coal samples and effective stress

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2.2 Coal pillar weakening criterion

Existing research suggests that water gradually infiltrates into coal pillars, and when water pressure gradient exceeds initiation pressure gradient of coal pillars, permeation occurs (Yao et al. 2022). The relationship between initiation pressure gradient of coal pillars and permeability follows a power-law function, as shown below:

$$G=0.03252{k}^{-1.4155}$$
(3)

where \(G\) is initiation pressure gradient of coal pillars, MPa/cm; \(k\) is permeability, m2.

When coal pillars are subjected to water infiltration, their mechanical properties are weakened. Based on numerous laboratory experiments, Xue (2017), Yao et al. (2021a) have identified that elastic modulus, cohesion, and friction angle of coal exhibit negative exponential relationships with water saturation. The softening coefficients due to water infiltration are given by:

$$\left\{\begin{array}{c}{l}_{E}=0.8947{e}^{\left(-{S}_{w}/68.36\right)}+0.1053\\ {l}_{C}=0.31496{e}^{\left(-{S}_{w}/37.36\right)}+0.685\\ {l}_{\varphi }=0.0638{e}^{\left(-{S}_{w}/2.08\right)}+0.9362\end{array}\right.$$
(4)

where \({l}_{E}\) is the weakening coefficient of elastic modulus; \({l}_{C}\) is the weakening coefficient of cohesion; \({l}_{\varphi }\) is the weakening coefficient of friction angle; \({S}_{w}\) is water saturation, % (Fig. 4).

Fig. 4
figure 4

The relationship between the weakening coefficient and water saturation

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2.3 Calculation of coal pillar damage

In the process of mining, coal pillars are influenced by mining, water immersion and excavation, leading to plastic deformation of coal pillars (Zhang et al. 2021). Previous studies mostly focused on monitoring a single cross-section to observe the characteristics of plastic zone. However, in reality, coal pillars are three-dimensional structures, and observing only one cross-section is insufficient to describe the overall plastic behavior of pillars (Han et al. 2022). Therefore, this study introduces the concept of “coal pillar damage degree,” defined as the ratio of the total volume of plastic zones in monitoring area to the volume of the entire monitoring area, as shown in Fig. 5.

$$D=\frac{\sum_{i=1}^{n}{V}_{i}}{V}\times 100\text{\%}$$
(5)

where, \(D\) is coal pillar damage degree; \({V}_{i}\) is the volume of a plastic zone; \(V\) is the volume of monitoring area.

$$V=LWH$$
(6)

where \(L\) is the length of monitoring area, m; \(W\) is the width of coal pillar, m; \(H\) is the height of coal pillar, m.

Fig. 5
figure 5

Calculation model for coal pillar damage degree

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2.4 Overview of deviatoric stress indicators

Based on the theory of elastoplastic mechanics (Wang et al. 2022c), the stress tensor can be divided into deviatoric stress tensor (the first term on the right of Eq. 7) and spherical stress tensor (the second term on the right of Eq. 7). The deformation of an object is primarily caused by changes in volume and shape, where the deviatoric stress tensor induces changes in the shape of the object, and the spherical stress tensor induces changes in the volume of the object (Shan et al. 2021).

$$\left[\begin{array}{ccc}{\sigma }_{1}& 0& 0\\ 0& {\sigma }_{2}& 0\\ 0& 0& {\sigma }_{3}\end{array}\right]=\left[\begin{array}{ccc}{\sigma }_{1}-{\sigma }_{m}& 0& 0\\ 0& {\sigma }_{2}-{\sigma }_{m}& 0\\ 0& 0& {\sigma }_{3-{\sigma }_{m}}\end{array}\right]+\left[\begin{array}{ccc}{\sigma }_{m}& 0& 0\\ 0& {\sigma }_{m}& 0\\ 0& 0& {\sigma }_{m}\end{array}\right]$$
(7)

where, \({\sigma }_{1}\), \({\sigma }_{2}\) and \({\sigma }_{3}\) are the principal stresses in three mutually perpendicular directions, MPa; \({\sigma }_{m}\) is the spherical stress tensor, and its expression is as follows:

$${\sigma }_{m}=\frac{{\sigma }_{1}+{\sigma }_{2}+{\sigma }_{3}}{3}$$
(8)

where, \({\sigma }_{i}-{\sigma }_{m}\) (\(i\)=1,2,3) is the deviatoric stress. In this study, the deformation and failure characteristics of waterproof coal pillar are analyzed based on the maximum deviatoric stress, which can be expressed as follows:

$${\sigma }{\prime}={\sigma }_{1}-{\sigma }_{m}={\sigma }_{1}-\frac{{\sigma }_{1}+{\sigma }_{2}+{\sigma }_{3}}{3}$$
(9)

2.5 Operation process of fluid–structure interaction system

Combining Eqs. (1) and (2), the permeability tensor components \({k}_{E1}\), \({k}_{E2}\) and \({k}_{E3}\) in elastic zone, as well as the permeability tensor components \({k}_{P1}\), \({k}_{P2}\) and \({k}_{E}\) in plastic zone can be obtained, as illustrated in Fig. 6. Among these, \({k}_{P1}\) and \({k}_{P2}\) lie on the fracture surface and are perpendicular to each other, while \({k}_{E}\) is perpendicular to the fracture surface (Li et al. 2023).

Fig. 6
figure 6

Permeability tensor of internal zones in coal pillar

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Building upon the aforementioned foundation, this study developed a Fish-language program for water-inrush weakening of waterproof coal pillars using FLAC3D. Through iterative calculations, a dynamic coupling between seepage parameters and coal pillar mechanical properties is achieved. The specific workflow is illustrated in Fig. 7.

Fig. 7
figure 7

Operation process of fluid–structure interaction system

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3 Reconstruction of mechanical environment for waterproof coal pillars

3.1 Project overview

The 3# coal at Dongzhuang Coal Mine in Shanxi has a burial depth of approximately 350 m and a thickness of 2.5 m. It is a nearly horizontal coal seam. The 30,203 panel has been fully mininged, resulting in a significant accumulation of water in the gob. The elevation of the 30,204 panel ranges from + 720 to + 750 m, with a strike length of 150 m. The 30,204 tailgate is planned to adopt a method of mining small coal pillars along the gob, as illustrated in Fig. 8. The waterproof coal pillar between 30,203 gob and 30,204 panel is influenced by factors such as mining-induced stress, water infiltration weakening, and excavation disturbances. It is necessary to conduct stability studies to ensure safe mining production in the mine.

Fig. 8
figure 8

Layout of working face: a mine location; b plan view; c section A–A

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Based on the geological information provided by Dongzhuang Coal Mine, a borehole profile for 30,204 panel is constructed, as shown in Fig. 9. The strata above 3# coal include a 1.0 m thick mudstone, a 1.8 m thick siltstone, a 5.6 m thick mudstone, and a 2.6 m thick medium sandstone, which are characterized as weak to semi-hard rock layers. Below 3# coal, there is a 4.0 m thick mudstone, also categorized as weak to semi-hard rock layer.

Fig. 9
figure 9

Borehole profile of 30,204 panel

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3.2 The establishment of numerical model

Based on the on-site engineering survey, a FLAC3D fluid–structure interaction numerical simulation model is established with dimensions of 180 m × 300 m × 52 m. The roadway size is set as 5.2 m × 3.5 m, with a total of 547,200 elements and 569,618 nodes, as shown in Fig. 10. The simulation progresses through three sequential stages based on the actual mining sequence: “mining of 30,203 panel to form the gob (Stage 1) → water erosion in 30,203 gob, causing infiltration into coal pillar (Stage 2) → excavation of 30,204 tailgate, leading to deformation and failure of coal pillar”. The model is constrained at the bottom, simply supported on four sides, and subjected to an 8.0 MPa load on top to simulate the load from overlying strata. In the second stage, a water pressure of 0.1 MPa is applied along the gob side of the coal pillars, considering the water accumulation in the adjacent gob. Material mechanical parameters used in the model are presented in Table 1.

Fig. 10
figure 10

Numerical calculation model: a overall diagram; b cross section view; c legend; d area A; e area B

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Table 1 Mechanical parameters of the model
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3.3 Mechanical characteristics of gob

The formula for calculating the height of caving zone is as follows (Chen et al. 2023):

$${h}_{c}=\frac{100{h}_{m}}{{c}_{1}{h}_{m}+{c}_{2}}$$
(10)

where, \({h}_{c}\) is the height of caving zone; \({h}_{m}\) is the height of mining; \({c}_{1}\) and \({c}_{2}\) are correction factors, and their values can be found in Table 2.

Table 2 Calculation coefficients for average caving zone height (Chen et al. 2024b)
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For the mine with a mining height of 2.5 m and average roof rock strength greater than 20 MPa and less than 40 MPa, the appropriate parameters from Table 2 are chosen and plugged into the formula to calculate the caving zone height, which results in 8.1 m.

The Salamon theoretical model is used to describe the stress–strain relationship of the gob rock mass (Salamon and Munro 1967, Salamon and Ozbay 1998). The formula is given as:

$$\sigma =\frac{{E}_{0}{\varepsilon }_{g}}{1-{\varepsilon }_{g}/{\varepsilon }_{g max}}$$
(11)

where, \(\sigma\) is the vertical stress acting on the gob rock mass; \({\varepsilon }_{g}\) is the strain that occurs in the gob rock mass under the influence of vertical stress; \({E}_{0}\) is the initial modulus of the gob material, which can be calculated using the following formula:

$${\varepsilon }_{g max}=\frac{{b}_{g}-1}{{b}_{g}}$$
(12)

where, \({b}_{g}\) is the crushing expansion coefficient of the gob material; \({\varepsilon }_{g max}\) maximum strain of rock mass in gob.

$${b}_{g}=\frac{{h}_{c}+{h}_{m}}{{h}_{c}}$$
(13)
$${E}_{0}=\frac{10.39{\sigma }_{c}^{1.042}}{{b}_{g}^{7.7}}$$
(14)

where \({\sigma }_{c}\) is the strength of rock mass in the caving zone.

Based on laboratory tests, the average uniaxial compressive strength of the roof rock layer is 35 MPa. Plugging this value into the above formula, the dilation coefficient of the gob material is calculated as 1.3086, the maximum strain is 0.2358, and the initial modulus is 53.2257 GPa. The stress–strain relationship of the gob rock mass is shown in Table 3.

Table 3 Stress–strain relationship of the gob rock mass
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After the mining of the coal, the rock mass in the gob undergoes a process of collapse followed by gradual compaction, experiencing continuous changes in stress and deformation. The double-yield model can more accurately describe the nonlinear behavior of rock mass and the stress recovery process (Chen et al. 2024a). In this study, a single element block with a side length of 1m is used to conduct uniaxial compression tests in FLAC3D. The model was constrained at the bottom and around its perimeter to prevent displacement, while a vertical load of 10–5 m/step was applied at the top to mimic the actual loading conditions. The simulated results are compared with the data from Table 3, and the comparative analysis is presented in Fig. 11. Based on this comparison, the material parameters for the gob are determined and listed in Table 4.

Fig. 11
figure 11

stress–strain relationship of gob material

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Table 4 Materials parameters of gob
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3.4 Verification of stress environment

To ensure the accuracy of the numerical simulation results, double-yield model is applied to 30,203 gob and overlying collapsed zone rock mass, followed by an equilibrium run. To validate the stress environment, a measurement line was arranged along the strike of working face. As depicted in Fig. 12, at a distance of 80 m from the edge of 30,203 gob, vertical stress has recovered to 99% of virgin stress, reaching 7.62 MPa. On the solid coal side, the stress reaches its peak value of 24.0 MPa at a distance of 8 m from the roadway surface.

Fig. 12
figure 12

Stress distribution in numerical simulation

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3.5 Verification of coal pillar immersion environment

After the stable mining of 30,203 panel, 30,203 gob starts accumulating water. A water pressure of 0.1 MPa was applied to the side edge of the coal pillar near the gob to simulate the erosive effect of accumulated water in the gob on the coal pillar. Following the fluid–structure interaction system described in Chapter 2, perform 50 cycles of calculation, with each cycle consisting of 1000 steps. Five monitoring points are strategically placed inside the coal pillar to observe the variation of pore pressure at different locations, as illustrated in Fig. 13.

Fig. 13
figure 13

Layout of measuring points

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The results of water pressure monitoring at points A-E are shown in Fig. 14. After 50 cycles of operation, the water pressure at each measuring point tended to stabilize, indicating that the water seepage inside the coal pillar had stabilized. At Point A, the water pressure reaches 0.09 MPa, which is close to the 0.1 MPa applied at the surface of roadway. Moving from the waterproof coal pillar surface towards its interior, the water pressure gradually decreases, and at Point E, the water pressure remains at 0 MPa. This indicates that during this period, no water infiltration occurs at Point E.

Fig. 14
figure 14

Pore pressure of coal pillar under different iteration times

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4 Stability of waterproof coal pillar under fluid–structure interaction

4.1 Development of vertical stress in waterproof coal pillar

The left side of waterproof coal pillar is adjacent to 30,203 gob, while the right side is adjacent to 30,204 tailgate. Based on the three stages defined according to the actual mining conditions, vertical stress distribution within waterproof coal pillar at each stage is depicted in Fig. 15.

  1. (1)

    Stage 1 Under the influence of the mining of 30,203 panel, waterproof coal pillar reaches its peak stress of 25.6 MPa at a distance of 2.25 m from the surface of 30,203 tailgate.

  2. (2)

    Stage 2 The left side of waterproof coal pillar is affected by the softening effect of water intrusion, leading to a reduction in its load-carrying capacity. As a result, the stress peak diminishes to 22.1 MPa, representing a decrease of 13.7%. Due to the degradation of mechanical properties in the water-inundated area on the left side, stress is transferred predominantly towards the right side.

  3. (3)

    Stage 3 Waterproof coal pillar is affected by the excavation of 30,204 tailgate. The stress peak experiences a slight increase to 26.2 MPa and shifts towards the right side by 0.75 m.

Fig. 15
figure 15

Vertical stress distribution at different stages of waterproof coal pillar: a stage 1; b stage 2; c stage 3

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4.2 Water-barrier performance of waterproof coal pillar

Using the FLAC3D fluid–structure interaction system developed in Fig. 7, permeability and water-softening coefficient are dynamically updated, and the combination of deviatoric stress, plastic zone, and seepage zone for three stages is obtained, as illustrated in Fig. 16.

  1. (1)

    Stage 1 During this stage, waterproof coal pillar is only influenced by the mining activities of 30,203 panel, and the width of plastic zones reaches 2.25 m. Points a–d are all in elastic state.

  2. (2)

    Stage 2 The left side of waterproof coal pillar is affected by water infiltration, causing plastic zones to expand into deeper parts of coal pillar. Point a is located in seepage zone, and although plastic failure has not occurred yet, its load-carrying capacity has been reduced, with the deviatoric stress at point a decreasing from 7.0 to 6.5 MPa.

  3. (3)

    Stage 3 The waterproof coal pillar is affected by the excavation of 30,204 tailgate, resulting in the extension of both plastic zone and seepage zone towards the interior of coal pillar. At this stage: point a transition from elastic state to plastic state; point b enters seepage zone; point c remains water-free and in elastic state; point d is water-free but in plastic state, indicating a relatively poor water-barrier effect.

Fig. 16
figure 16

Water blocking performance of waterproof coal pillar under fluid–structure interaction: a stage 1; b stage 2; c stage 3

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In the middle section of waterproof coal pillar, there is a complete region with a width of at least 0.85 m, which remains in elastic state, and the coal remains water-free, with the deviatoric stress ranging from approximately 4–5 MPa. This region exhibits good water-barrier and load-carrying capabilities (Fig. 17).

Fig. 17
figure 17

Damage degree of coal pillar

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The waterproof coal pillar undergoes three stages: “mining of 30,203 panel—water infiltration and softening—excavation of 30,204 tailgate”. The damage degree of waterproof coal pillar in each stage is as follows:

  • Stage 1: The damage degree is 25.3%.

  • Stage 2 The damage degree is 31.4%.

  • Stage 3 The damage degree is 64.6%.

These damage values represent the extent to which the waterproof coal pillar has been affected and weakened during each stage of the mining process. As the mining progresses and water infiltration occurs, the damage to the coal pillar increases, indicating a gradual reduction in its load-carrying capacity and stability.

4.3 Stability analysis of different width waterproof coal pillars

The comparative stability analysis of five different width waterproof coal pillars (3 m, 5 m, 7 m, 9 m, 11 m) is presented in Fig. 18.

Fig. 18
figure 18

Stability of waterproof coal pillars with different widths

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For the 3 m width pillar, plastic zones of coal pillar are completely connected, and there is no concentration of vertical stress within it. The overall induced stress is relatively low, resulting in a loss of load-bearing capacity for coal pillar.

For the 5 m width pillar, noticeable stress concentration occurs at the center of coal pillar, indicating that it possesses some load-bearing capacity. However, plastic zones inside coal pillar are interconnected, rendering it ineffective in providing adequate water isolation.

For the 7 m width pillar, the induced deviatoric stress peak zone exhibits a crescent-shaped distribution near the gob side of coal pillar. Plastic zones inside coal pillar is not fully interconnected, with a 1.75 m undamaged section.

For the 9 m width pillar, the vertical stress shifts towards the right side, leading to a larger range of deviatoric stress peak zone near 30,204 tailgate side of coal pillar. Plastic zones on the right side is significantly deeper than that on the left side. Compared to the 7 m width pillar, the undamaged zone width increases by only 0.25 m, indicating that the 9 m width pillar poses greater challenges to the surrounding roadway support.

For the 11 m width pillar, plastic zones on both sides of coal pillar exhibit an approximately symmetric distribution. The depth of plastic zones on the right side decreases significantly, and the width of undamaged zone in the middle reaches 6.0 m. The deviatoric stress peak zone on the left side of coal pillar changes from a wide crescent shape to a narrow one, while the deviatoric stress peak zone on the right side shifts upwards and is predominantly located within the overlying mudstone.

The internal stress-damage conditions of the different width waterproof coal pillars are depicted in Fig. 19.

Fig. 19
figure 19

Internal stress-damage situation of waterproof coal pillar: a vertical stress; b damage degree

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For the 3 m width pillar, the stress peak is only 7.7 MPa, indicating poor load-bearing capacity, and the damage level reaches 100%. As the width of coal pillar increases from 5 to 11 m, the stress curve gradually transforms from a single-peak shape to a double-peak shape, and the stress peak shifts towards the right side. Consequently, the damage level of coal pillar decreases from 94.5% at 5 m width to 40.5% at 11 m width.

5 Conclusion

This study utilized numerical simulations to investigate the failure characteristics and optimal width of waterproof coal pillars along the gob-side roadway under the influence of mining, excavation and seepage coupling. The main conclusions are as follows:

  1. (1)

    A numerical model for fluid–structure interaction of waterproof coal pillar was established, and a Fish language program was developed to account for the weakening of coal due to water immersion. This method enables the dynamic coupling of permeability parameters and coal pillar mechanical properties by calculating the weakening coefficient of elastic modulus, cohesion, and friction angle based on its water saturation.

  2. (2)

    The coupling characteristics of stress distribution, plastic zone, and seepage zone of waterproof coal pillars were revealed during the “mining—water immersion softening—roadway excavation” stages. The region where both seepage and plasticity coexist is the primary area responsible for water drainage in waterproof coal pillar. The area where seepage occurs but remains elastic represents the maximum diffusion boundary of water drainage, while the area without seepage but with elasticity plays a vital role in determining the water resistance of coal pillar.

  3. (3)

    The water resistance capacity of waterproof coal pillars depends on the extent of the seepage area on the gob side and the plastic zones on both sides. Under the conditions of 30,204 panel, when the width of waterproof coal pillar is 3 m and 5 m, plastic zones are interconnected, forming water drainage channels. Conversely, for widths of 7 m, 9 m, and 11 m, seepage zones and plastic zones are not connected, indicating that coal pillar possesses load-bearing and water-isolating characteristics.

Future research endeavors could leverage advanced sensing devices and techniques for field investigations to validate the results obtained from numerical simulations. Conducting on-site studies will provide real data to corroborate the accuracy of our model and further enhance its predictive capabilities.