Numerical Simulation Study of Variable-Mass Permeation of the Broken Rock Mass under Different Cementation Degrees

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 themass 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. (e study approach and results not only help enhance coal mining operations safety by better understanding KCPwater inrush risks. It can also be extended to other engineering applications such as backfill paste piping and tailing dam erosion.


Introduction
e 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].
e cave gradually collapses under the gravity and penetrates the coal seam, eventually forming a plug-shaped geological structure (Figure 1).e 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.erefore, an experimental study of seepage characteristics for broken rock mass is an important precondition to correctly reveal the water inrush mechanism of the KCP.e 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][5][6][7].Li et al. [8] established unsteady seepage dynamics models of non-Darcy seepage, gas seepage, and temperatureseepage 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][15][16].
e aforementioned research results have important reference significance and value for understanding permeability characteristics of broken rock mass [17][18][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 variablemass 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.

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 ρ is the fluid density, t is the time, u is the fluid velocity, and ε is the volume fraction.e momentum conservation equation of the fluid phase is expressed as follows: where g is the gravitational acceleration, μ is the viscosity, S is the momentum sink which is the resultant resistance F acting in grid cells.e resistance is generated by relative movement between the fluid and solid phases, and its computational formula is as follows: where V is the volume of CFD grid cells and F D i is the drag force of the particle i. e Ergun and Wen and Yu resistance model is adopted, and the computational formula of its resistance F D is as follows: where V s is the particle volume, v is the relative velocity between particles and the fluid, α is the free volume of CFD grid cells, computational formula of β is as follows: where d is the diameter of solid particles and C D is the resistance coefficient and its computational formula is as follows: where Re is the Reynolds number.In the computational process of the EDEM-FLUENT coupling model, the 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 llings.
e 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.e ow monitor is set as model outlet to monitor the change of outlet ow quantity.e model is initialized, the time step is set to be 2e − 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.

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 lling 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 llings, the less the mass loss.When the lling cohesive force is 15 J/m 2 and the total mass loss is 260.92 g which occupies about 20.91% of the total lling mass; when the lling 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 lling mass, respectively; when the lling cohesive force is 30 J/m 2 , the total mass loss is 125.16 g, which occupies about 10.43% of the total lling mass.3 and Figure 6 give data and curves related to the time-dependent change of model mass loss rates under di erent cementation degrees.It can be seen that the model mass loss rate presents rstly increasing and then decreasing change trends on the whole, and the greater the cohesive force, the smaller the maximum mass loss rate.

Mass Loss Rate. Table
e 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.e maximum mass loss rate is about 1,450 g/s when the cohesive force is 30 J/m 2 .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 lling particles, initially porosity and permeability increase slowly, and then they rapidly increase and nally tend to be steady.e greater the cohesive force, the smaller the increase of amplitudes of model porosity and permeability.After the cohesive force increases from 15 J/m 2 to 30 J/m 2 , nal model porosity reduces from 0.3663 to 0.3292; permeability reduces from 32.33 µm 2 to 20.99 µm 2 .

Particles Erosion
Process. Figure 9 gives the cloud chart of the internal lling particle loss process of the model with the cohesive force being 25 J/m 2 under the erosion e ect.It can be clearly seen that particle loss is a dynamic process.
ere is no particle transport at t 0 s, and few particles run o between t 0 and t 0.2 s, while more particles port out between t 0.2 s and t 0.4 s, and the particle erosion e ect 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 nally becomes steady.In addition, a run-through channel is gradually formed with particle loss.

Discussion
According to change curves of model permeability characteristics under the erosion e ect, the seepage can be     Advances in Civil Engineering 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; llings abruptly run o 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; lling 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 e ect is similar to dynamic change laws of water inrush of the KCP (Figure 10), indicating that the particle migration e ect is a key factor causing water inrush of broken geologic structures like KCP in the coal mine.Its water inrush mechanism can be simpli ed 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 llings), liquid ( uid) media in holes and fractures, and ne lling particles in liquid media; under the water erosion e ect, ne lling particles inside the KCP migrate and run o ; and porosity of the KCP increases, so does its permeability; increasing permeability accelerates water ow and enhances water carrying capacity in turn, and consequently, more particles migrate and run o 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 in uence on variable-mass permeability characteristics of KCPs.

Conclusions
e 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 di erent cementation degrees, and the following conclusions were mainly drawn: (1) Permeability change of the broken rock mass under the erosion e ect 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 in uence 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 e ect is an important cause for its water inrush.When the KCP is exposed in coal mining, lling particles continuously run o under water erosion, accompanied by continuously enhanced permeability; the rising permeability accelerates water ow and reinforce water carrying capacity in turn, and as    is interaction process continuously enlarges permeability and water in ow of the KCP, and nally it will cause the water inrush accident of the KCP.e study of variable-mass permeation of the broken rock mass under di erent 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 back ll paste piping and tailing dam erosion.

Data Availability
e complete (curve) data used to support the ndings of this study are included within the supplementary information le (curve data).

Figure 5 :
Figure 5: Time-dependent change curves of mass losses under di erent cohesive forces.

Figure 6 :
Figure 6: Time-dependent change curves of mass loss rates under di erent cohesive forces.

Figure 11 :
Figure 11: Schematic diagram of the seepage change process of broken rock mass seepage under the erosion e ect.

Figure 10 :
Figure 10: Curve of the water ow volume for a KCP.

Table 3 :
Mass loss rates under di erent cohesive forces (g/s).