#### Abstract

In order to analyze variable-mass permeation characteristics of broken rock mass under different cementation conditions and reveal the water inrush mechanism of geological structures containing broken rock masses like karst collapse pillars (KCPs) in the coal mine, the EDEM-FLUENT coupling simulation system was used to implement a numerical simulation study of variable-mass permeation of broken rock mass under different cementation conditions and time-dependent change laws of parameters like porosity, permeability, and mass loss rate of broken rock specimens under the erosion effect were obtained. Study results show that (1) permeability change of broken rock specimens under the particle migration effect can be divided into three phases, namely, the slow-changing seepage phase, sudden-changing seepage phase, and steady seepage phase. (2) Specimen fillings continuously migrate and run off under the water erosion effect, porosity and permeability rapidly increase and then tend to be stable, and the mass loss rate firstly rapidly increases and then gradually decreases. (3) Cementation degree has an important effect on permeability of broken rock mass. As cementing force of the specimen is enhanced, its maximum mass loss rate, mass loss, porosity, and permeability all continuously decrease. The study approach and results not only help enhance coal mining operations safety by better understanding KCP water inrush risks. It can also be extended to other engineering applications such as backfill paste piping and tailing dam erosion.

#### 1. Introduction

The karst collapse pillar (KCP) is a concealed vertical geological phenomenon widespread in Carboniferous Permian coalfields in north China, which is caused by the karst subsidence that occurs in Ordovician limestone aquifers [1]. The cave gradually collapses under the gravity and penetrates the coal seam, eventually forming a plug-shaped geological structure (Figure 1). The existence of the geological phenomenon reduces the recoverable coal reserves by damaging coal seams and influences full-mechanized coal mining. More importantly, the Ordovician limestone KCP usually functions as a channel for groundwater inrush, thus posing a great threat to safe production in the coal mines [2].

As shown in Figure 1, the KCP is a broken rock mass in essence [3]. Moreover, it consists of a solid skeleton and filling particles. Therefore, an experimental study of seepage characteristics for broken rock mass is an important precondition to correctly reveal the water inrush mechanism of the KCP. The research team led by Xiexing Miao firstly used the MTS815 mechanical testing machine to conduct a systematic study of permeability of the rock mass and obtained permeability change laws of the broken rock mass under different lithological characteristics and different stress states [4–7]. Li et al. [8] established unsteady seepage dynamics models of non-Darcy seepage, gas seepage, and temperature-seepage coupling of the broken rock mass. Chen et al. [9] used the truncated spectral method to study the dynamic response of the broken rock mass seepage system under time-dependent change of permeability characteristics and boundary conditions.

Based on the experimental and theoretical study on broken rock mass, a number of investigations have been performed to explore the water inrush mechanism of KCPs using single or combined methods of theoretical analysis, numerical simulation, and experimental studies. For instance, Bai et al. [10] established a mechanical model-plug model, which was used to describe the behavior of water seepage flow in the coal-seam floor containing KCPs. Furthermore, the variable-mass dynamics and nonlinear dynamics were introduced, and the seepage properties of KCPs associated with particles migration were investigated using numerical simulation [11]. Ma et al. [2] numerically studied the impacts of mining-induced damage on KCPs and the surrounding rocks and on the formation of the fracture zone and analyzed mining-induced KCP groundwater inrush risk. Wang and Kong [12] explored the time-varying and nonlinear characteristics of the dynamic seepage system of broken rocks and examined the varying behavior of the mass loss rate. Yao [13] experimentally studied the evolution of the crushed rock mass seepage properties under different particle sizes and stresses and analyzed the particle migration feature and the KCPs’ water inrush mechanism. Moreover, there are also some studies focused on the permeability change of the KCPs to investigate the water inrush mechanisms [14–16].

The aforementioned research results have important reference significance and value for understanding permeability characteristics of broken rock mass [17–19] and revealing the water inrush mechanism of geological structures like KCPs. However, the present research results have scarcely considered influence of erosion on broken rock mass permeability characteristics. Even though some scholars have recognized that water inrush of KCPs is actually a sudden change process of permeability of a broken geologic structure due to internal filling particle loss under the erosion effect [20, 21], there is still a lack of effective experimental means of observing dynamic loss of variable-mass permeable filling particles in the broken rock mass under the erosion effect, and there is no systematic study of variable-mass permeability change characteristics under different cementation conditions of broken rock mass. Based on the above research results, the EDEM-FLUNENT coupling system considering the particle migration effect was used in this paper to simulate the dynamic development process of particle migration of broken rock mass under the erosion effect. Chang laws of parameters like mass loss rate, porosity, and permeability of broken rock mass under different cementation conditions were studied, expecting to provide an experimental basis for guiding water inrush prevention and control of KCPs in the coal mine.

#### 2. EDEM-FLUENT Coupling Theory

In the Eulerian model of EDEM, solid particles will generate an influence on fluid flow, so the volume fraction is added in the conservation equation to correct the continuity equation of the fluid phase:where is the fluid density, is the time, is the fluid velocity, and is the volume fraction.

The momentum conservation equation of the fluid phase is expressed as follows:where is the gravitational acceleration, is the viscosity, is the momentum sink which is the resultant resistance *F* acting in grid cells. The resistance is generated by relative movement between the fluid and solid phases, and its computational formula is as follows:where is the volume of CFD grid cells and is the drag force of the particle .

The Ergun and Wen and Yu resistance model is adopted, and the computational formula of its resistance is as follows:where is the particle volume, is the relative velocity between particles and the fluid, is the free volume of CFD grid cells, computational formula of is as follows:where is the diameter of solid particles and *C*_{D} is the resistance coefficient and its computational formula is as follows:where is the Reynolds number. In the computational process of the EDEM-FLUENT coupling model, the buoyancy force *F*_{a} of solid particles should be taken into consideration besides resistance, and its computational formula is as follows:

#### 3. Establishment of EDEM-FLUENT Coupling Numerical Simulation Model

The established circular straight-pipe model with diameter being 100 mm and height being 200 mm is shown in Figure 2. Face 1 is the pressure inlet boundary, and face 2 is the pressure outlet boundary. The established model is imported into grid generation software to obtain the model grid generation diagram as shown in Figure 3.

As shown in Fig. 4, after grid creation, two particle models with sizes of 0∼10mm and 10∼20mm are generated inside the circular pipe, in which the particles with larger particles become the skeleton of the broken rock mass, while particles with small size are used as fillings. The particle material is rock, and the circular pipe material is steel. Inlet pressure is set as water pressure 0.05 MPa, and the boundary condition of pressure outlet is the standard atmospheric pressure. The flow monitor is set as model outlet to monitor the change of outlet flow quantity. The model is initialized, the time step is set to be 2*e* − 05 s, and the number of iterative time steps is 40,000. Data are saved every other 0.02 s during the calculation process, and the model parameter setting is shown in Table 1.

#### 4. Numerical Simulation Results and Analysis

##### 4.1. Mass Loss

Table 2 and Figure 5 give data and curves related to the time-dependent change of model filling particle mass loss. It can be seen from Figure 5 that overall model mass loss presents a continuously increasing trend, and the greater the cohesive force of fillings, the less the mass loss. When the filling cohesive force is 15 J/m^{2} and the total mass loss is 260.92 g which occupies about 20.91% of the total filling mass; when the filling cohesive force is 20 J/m^{2} and 25 J/m^{2}, respectively, the total mass loss will be 214.68 g and 173.351 g, respectively, occupying 17.89% and 14.45% of the total filling mass, respectively; when the filling cohesive force is 30 J/m^{2}, the total mass loss is 125.16 g, which occupies about 10.43% of the total filling mass.

##### 4.2. Mass Loss Rate

Table 3 and Figure 6 give data and curves related to the time-dependent change of model mass loss rates under different cementation degrees. It can be seen that the model mass loss rate presents firstly increasing and then decreasing change trends on the whole, and the greater the cohesive force, the smaller the maximum mass loss rate. The maximum mass loss rate is about 2,350 g/s when the cohesive force is 15 J/m^{2}; when the cohesive force is 20 J/m^{2} and 25 J/m^{2}, the maximum mass loss rate is 2,150 g/s and 1,750 g/s, respectively. The maximum mass loss rate is about 1,450 g/s when the cohesive force is 30 J/m^{2}.

##### 4.3. Porosity and Permeability

Table 4 and Figure 7 give data and curves related to the time-dependent change of model porosity and Table 5 and Figure 8 give data and curves related to the time-dependent change of model permeability. It can be seen that their variation tendencies are similar to change laws of mass loss; namely, with migration and loss of model filling particles, initially porosity and permeability increase slowly, and then they rapidly increase and finally tend to be steady. The greater the cohesive force, the smaller the increase of amplitudes of model porosity and permeability. After the cohesive force increases from 15 J/ to 30 J/, final model porosity reduces from 0.3663 to 0.3292; permeability reduces from 32.33 *µ*m^{2} to 20.99 *µ*m^{2}.

##### 4.4. Particles Erosion Process

Figure 9 gives the cloud chart of the internal filling particle loss process of the model with the cohesive force being 25 J/m^{2} under the erosion effect. It can be clearly seen that particle loss is a dynamic process. There is no particle transport at *t* = 0 s, and few particles run off between *t* = 0 and *t* = 0.2 s, while more particles transport out between *t* = 0.2 s and *t* = 0.4 s, and the particle erosion effect decreases from *t* = 0.4 s to *t* = 0.6 s, which indicate that particle transport is very slow at the beginning, and then it sharply increases and finally becomes steady. In addition, a run-through channel is gradually formed with particle loss.

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#### 5. Discussion

According to change curves of model permeability characteristics under the erosion effect, the seepage can be divided into three phases: slow-changing seepage phase, sudden-changing seepage phase, and steady seepage phase. Filling loss is very slow in the slow-changing seepage phase, and porosity and permeability also increase slowly; fillings abruptly run off and porosity and permeability sharply increase in the sudden-changing seepage phase, and porosity and permeability change of the particle model system mainly happens in this phase; filling loss phenomenon disappears and porosity and permeability remain steady in the steady seepage phase.

It can also be seen that a change trend of permeability characteristics of broken rock mass under the erosion effect is similar to dynamic change laws of water inrush of the KCP (Figure 10), indicating that the particle migration effect is a key factor causing water inrush of broken geologic structures like KCP in the coal mine. Its water inrush mechanism can be simplified as follows (Figure 11): broken geologic structures like water-inrush KCP in the coal mine can be regarded as consisting of three-type media—broken solid media (skeleton and fillings), liquid (fluid) media in holes and fractures, and fine filling particles in liquid media; under the water erosion effect, fine filling particles inside the KCP migrate and run off; and porosity of the KCP increases, so does its permeability; increasing permeability accelerates water flow and enhances water carrying capacity in turn, and consequently, more particles migrate and run off and permeability of the KCPs is further strengthened. In the meantime, the cementation degree of the KCPs decides mass of erodible particles, so it also has an important influence on variable-mass permeability characteristics of KCPs.

#### 6. Conclusions

The EDEM-FLUENT coupling simulation system was utilized in this paper to study change laws of parameters like mass loss rate, porosity, and permeability of broken rock specimens under different cementation degrees, and the following conclusions were mainly drawn:(1)Permeability change of the broken rock mass under the erosion effect can be divided into three phases, namely, the slow-changing seepage phase, sudden-changing seepage phase, and steady seepage phase. Permeability of the broken rock mass slowly increases in the slow-changing seepage phase; it suddenly increases by several and even dozens of times in the sudden-changing seepage phase; after sudden seepage change, permeability basically remains unchanged in the steady seepage phase.(2)Cementation degree has an important influence on permeability characteristics of the broken rock mass. As the cohesive force of the specimen increases, the maximum mass loss rate, mass loss, porosity, and permeability all continuously decrease.(3)Filling particle loss in the KCP under the erosion effect is an important cause for its water inrush. When the KCP is exposed in coal mining, filling particles continuously run off under water erosion, accompanied by continuously enhanced permeability; the rising permeability accelerates water flow and reinforce water carrying capacity in turn, and as a result more particles are brought out. This interaction process continuously enlarges permeability and water inflow of the KCP, and finally it will cause the water inrush accident of the KCP.

The study of variable-mass permeation of the broken rock mass under different cementation degrees not only helps enhance the safety of coal mining operations by better understanding KCP water inrush risks. It can also be extended to other engineering applications such as backfill paste piping and tailing dam erosion.

#### Data Availability

The complete (curve) data used to support the findings of this study are included within the supplementary information file (curve data).

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This project was supported by the National Natural Science Foundation of China (nos. 51874277, 51304072, and 51774110), Program for Innovative Research Team in University of Ministry of Education of China (no. IRT_16R22), and the Postdoctoral Science Foundation of China (no. 2017M612398).