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

Authors: Chong Li; Banghua Yao; Qingqing Ma
Journal: Advances in Civil Engineering
 (2018)

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## 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.


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## Body

## 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].Figure 1
Schematic diagram of KCPs in the strata.As shown in Figure1, 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:(1)∂ερ∂t+∇⋅ρεu=0,where ρ is the fluid density, t is the time, u is the fluid velocity, and ε is the volume fraction.The momentum conservation equation of the fluid phase is expressed as follows:(2)∂ερu∂t+∇⋅ρεμu=−∇ρ+∇με∇u+ρεg−S,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. The resistance is generated by relative movement between the fluid and solid phases, and its computational formula is as follows:(3)S=∑i=1nFDiV,where V is the volume of CFD grid cells and FDi is the drag force of the particle i.The Ergun and Wen and Yu resistance model is adopted, and the computational formula of its resistanceFD is as follows:(4)FD=βVsvv1−α,where Vs 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:(5)β=1501−e2ned2+1.751−eρsvd,ϕ<0.8,34CDρse−1.651−ev,ϕ≥0.8,where d is the diameter of solid particles and CD is the resistance coefficient and its computational formula is as follows:(6)CD=24Re,Re≤0.5,0.44,Re>1000,241+0.25Re0.687Re,0.5<Re≤1000,where Re is the Reynolds number. In the computational process of the EDEM-FLUENT coupling model, the buoyancy force Fa of solid particles should be taken into consideration besides resistance, and its computational formula is as follows:(7)Fa=ρgVs.


## 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 Figure2. 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.Figure 2
EDEM-FLUENT coupling numerical calculation model.Figure 3
Model grid generation.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 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.Figure 4
Particle model generated through EDEM.Table 1
Numerical simulation parameters.
Simulation parameter
Value
Water density
1,000 kg/m3
Dynamic viscosity
1.01 × 103 Pa·s
Particle material density
2,400 kg/m3
Circular pipe material density
7,850 kg/m3
Large particle size
10∼20 mm
Small particle size
0∼10 mm
Total mass of generated particles
2,400 g
Filling height
180 mm
Inlet water pressure
0.05 MPa
Mass proportion of skeleton to filling substance
1 : 1


## 4. Numerical Simulation Results and Analysis

### 4.1. Mass Loss

Table2 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/m2 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/m2 and 25 J/m2, 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/m2, the total mass loss is 125.16 g, which occupies about 10.43% of the total filling mass.Table 2
Mass losses under different cohesive forces (g).
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
0
0
0
0
0.02
2.915673
2.345672
1.0806894
0.5644316
0.04
10.03126
7.102347
4.5906528
2.6465132
0.06
23.63215
16.21364
11.857165
8.1136458
0.08
49.31643
33.43365
29.824248
23.6453347
0.1
89.12305
65.81369
59.029935
49.8764224
0.12
135.9103
108.4919
94.535887
79.1346576
0.14
165.3503
129.4325
120.68845
98.1346571
0.16
186.5103
140.3165
128.45919
102.346158
0.18
199.9216
148.347
133.89105
105.045673
0.2
208.3682
155.9135
140.9066
107.136543
0.22
215.1744
161.7844
145.09607
110.316414
0.24
221.9103
168.6543
149.53669
112.513643
0.26
225.1029
174.698
153.94155
114.143547
0.28
229.521
180.3546
158.06276
115.231615
0.3
235.1205
185.8135
161.2561
116.543167
0.32
238.5642
189.1365
162.56408
117.314658
0.34
240.3615
193.2136
164.73661
118.346577
0.36
242.1361
198.0781
165.18808
119.453146
0.38
244.0135
201.6021
167.02905
120.046579
0.4
245.2035
205.3025
167.973
120.864533
0.42
245.9123
208.6102
169.37403
121.765455
0.44
246.5232
210.1315
170.4286
122.611325
0.46
247.1935
212.4614
171.26218
123.013278
0.48
248.0123
213.3462
171.6217
123.546133
0.5
249.3025
214.0132
172.37396
123.846521
0.52
250.921
214.6806
173.35134
124.431645
0.54
250.921
214.6806
173.35134
124.846254
0.56
250.921
214.6806
173.35134
125.161336
0.58
250.921
214.6806
173.35134
125.161336
0.6
250.921
214.6806
173.35134
125.161336Figure 5
Time-dependent change curves of mass losses under different cohesive forces.


### 4.2. Mass Loss Rate

Table3 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/m2; when the cohesive force is 20 J/m2 and 25 J/m2, 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/m2.Table 3
Mass loss rates under different cohesive forces (g/s).
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
0
0
0
0
0.02
145.7837
117.2836
54.03447
28.22158
0.04
355.7792
237.8337
175.4982
104.1041
0.06
680.0447
455.5648
363.3256
273.3566
0.08
1284.214
861.0002
898.3541
776.5844
0.1
1990.331
1619.002
1460.284
1311.554
0.12
2339.36
2133.91
1775.298
1462.912
0.14
1472.001
1047.031
1307.628
950
0.16
1058.003
544.1986
388.5371
210.575
0.18
670.565
401.5245
271.593
134.9758
0.2
422.3284
378.3245
350.7773
104.5435
0.22
340.3102
293.5446
209.4738
158.9935
0.24
336.7964
343.4966
222.031
109.8615
0.26
159.6263
302.1867
220.2428
81.49519
0.28
220.908
282.8294
206.0608
54.40341
0.3
279.9756
272.9424
159.6668
65.57761
0.32
172.1822
166.1544
65.39905
38.57454
0.34
89.86789
203.853
108.6264
51.59596
0.36
88.72557
243.2259
22.57376
55.32845
0.38
93.8745
176.2005
92.04816
29.67164
0.4
59.49542
185.0206
47.19755
40.89772
0.42
35.44457
165.3844
70.05147
45.0461
0.44
30.54103
76.06155
52.72885
42.29347
0.46
33.51493
116.4955
41.67863
20.09766
0.48
40.94394
44.242
17.9763
26.64279
0.5
64.50564
33.35155
37.61299
15.0194
0.52
80.92889
33.36984
48.86872
29.25619
0.54
0
0
0
20.73045
0.56
0
0
0
15.75408
0.58
0
0
0
0
0.6
0
0
0
0Figure 6
Time-dependent change curves of mass loss rates under different cohesive forces.


### 4.3. Porosity and Permeability

Table4 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/m2 to 30 J/m2, final model porosity reduces from 0.3663 to 0.3292; permeability reduces from 32.33 µm2 to 20.99 µm2.Table 4
Porosity coefficients under different cohesive forces.
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
0.292286
0.292286
0.292286
0.292286
0.02
0.293146
0.292978
0.292605
0.292452
0.04
0.295244
0.29438
0.29364
0.293066
0.06
0.299255
0.297067
0.295782
0.294678
0.08
0.306828
0.302145
0.301081
0.299258
0.1
0.318567
0.311693
0.309693
0.306994
0.12
0.332363
0.324278
0.320163
0.315621
0.14
0.341045
0.330453
0.327875
0.321224
0.16
0.347284
0.333663
0.330166
0.322466
0.18
0.351239
0.336031
0.331768
0.323262
0.2
0.35373
0.338262
0.333837
0.323878
0.22
0.355737
0.339993
0.335072
0.324816
0.24
0.357723
0.342019
0.336381
0.325464
0.26
0.358664
0.343801
0.33768
0.325945
0.28
0.359967
0.345469
0.338896
0.326266
0.3
0.361618
0.347079
0.339837
0.326652
0.32
0.362634
0.348059
0.340223
0.32688
0.34
0.363164
0.349261
0.340864
0.327184
0.36
0.363687
0.350695
0.340997
0.32751
0.38
0.364241
0.351735
0.34154
0.327685
0.4
0.364592
0.352826
0.341818
0.327927
0.42
0.364801
0.353801
0.342231
0.328192
0.44
0.364981
0.35425
0.342542
0.328442
0.46
0.365179
0.354937
0.342788
0.32856
0.48
0.36542
0.355198
0.342894
0.328717
0.5
0.3658
0.355394
0.343116
0.328806
0.52
0.366278
0.355591
0.343404
0.328978
0.54
0.366278
0.355591
0.343404
0.329101
0.56
0.366278
0.355591
0.343404
0.329194
0.58
0.366278
0.355591
0.343404
0.329194
0.6
0.366278
0.355591
0.343404
0.329194Figure 7
Porosity coefficients under different cohesive forces.Table 5
Permeability coefficients under different cohesive forces (μm2).
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
12.7343
12.7343
12.7343
12.7343
0.02
12.87826
12.85001
12.7875
12.76205
0.04
13.23524
13.08734
12.96158
12.86492
0.06
13.94018
13.55196
13.32814
13.13825
0.08
15.35577
14.46711
14.27119
13.94088
0.1
17.78363
16.32616
15.92116
15.38791
0.12
21.039
19.07583
18.13715
17.14637
0.14
23.33393
20.56052
19.92918
18.37542
0.16
25.11156
21.36981
20.48942
18.65758
0.18
26.29694
21.98401
20.88886
18.84034
0.2
27.06779
22.57632
21.41444
18.98292
0.22
27.70295
23.04515
21.7336
19.2015
0.24
28.3441
23.60423
22.07626
19.35376
0.26
28.6524
24.10555
22.42067
19.46736
0.28
29.08381
24.58293
22.74701
19.54351
0.3
29.63861
25.05123
23.00263
19.63563
0.32
29.98431
25.34002
23.10804
19.68999
0.34
30.16612
25.6982
23.28401
19.76289
0.36
30.34655
26.13122
23.32073
19.84132
0.38
30.53847
26.44879
23.47094
19.88349
0.4
30.66065
26.78581
23.54827
19.94173
0.42
30.73363
27.09016
23.66346
20.00605
0.44
30.79664
27.23113
23.75048
20.0666
0.46
30.86592
27.44825
23.81945
20.09543
0.48
30.95073
27.5311
23.84925
20.13369
0.5
31.08475
27.59369
23.91171
20.15529
0.52
31.25361
27.65644
23.99306
20.19742
0.54
31.25361
27.65644
23.99306
20.22732
0.56
31.25361
27.65644
23.99306
20.25006
0.58
31.25361
27.65644
23.99306
20.25006
0.6
31.25361
27.65644
23.99306
20.25006Figure 8
Permeability coefficients under different cohesive forces.


### 4.4. Particles Erosion Process

Figure9 gives the cloud chart of the internal filling particle loss process of the model with the cohesive force being 25 J/m2 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.Figure 9
Particles loss under water erosion. (a)t = 0 s. (b) t = 0.2 s. (c) t = 0.4 s. (d) t = 0.6 s.
(a)
(b)
(c)
(d)


## 4.1. Mass Loss

Table2 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/m2 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/m2 and 25 J/m2, 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/m2, the total mass loss is 125.16 g, which occupies about 10.43% of the total filling mass.Table 2
Mass losses under different cohesive forces (g).
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
0
0
0
0
0.02
2.915673
2.345672
1.0806894
0.5644316
0.04
10.03126
7.102347
4.5906528
2.6465132
0.06
23.63215
16.21364
11.857165
8.1136458
0.08
49.31643
33.43365
29.824248
23.6453347
0.1
89.12305
65.81369
59.029935
49.8764224
0.12
135.9103
108.4919
94.535887
79.1346576
0.14
165.3503
129.4325
120.68845
98.1346571
0.16
186.5103
140.3165
128.45919
102.346158
0.18
199.9216
148.347
133.89105
105.045673
0.2
208.3682
155.9135
140.9066
107.136543
0.22
215.1744
161.7844
145.09607
110.316414
0.24
221.9103
168.6543
149.53669
112.513643
0.26
225.1029
174.698
153.94155
114.143547
0.28
229.521
180.3546
158.06276
115.231615
0.3
235.1205
185.8135
161.2561
116.543167
0.32
238.5642
189.1365
162.56408
117.314658
0.34
240.3615
193.2136
164.73661
118.346577
0.36
242.1361
198.0781
165.18808
119.453146
0.38
244.0135
201.6021
167.02905
120.046579
0.4
245.2035
205.3025
167.973
120.864533
0.42
245.9123
208.6102
169.37403
121.765455
0.44
246.5232
210.1315
170.4286
122.611325
0.46
247.1935
212.4614
171.26218
123.013278
0.48
248.0123
213.3462
171.6217
123.546133
0.5
249.3025
214.0132
172.37396
123.846521
0.52
250.921
214.6806
173.35134
124.431645
0.54
250.921
214.6806
173.35134
124.846254
0.56
250.921
214.6806
173.35134
125.161336
0.58
250.921
214.6806
173.35134
125.161336
0.6
250.921
214.6806
173.35134
125.161336Figure 5
Time-dependent change curves of mass losses under different cohesive forces.


## 4.2. Mass Loss Rate

Table3 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/m2; when the cohesive force is 20 J/m2 and 25 J/m2, 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/m2.Table 3
Mass loss rates under different cohesive forces (g/s).
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
0
0
0
0
0.02
145.7837
117.2836
54.03447
28.22158
0.04
355.7792
237.8337
175.4982
104.1041
0.06
680.0447
455.5648
363.3256
273.3566
0.08
1284.214
861.0002
898.3541
776.5844
0.1
1990.331
1619.002
1460.284
1311.554
0.12
2339.36
2133.91
1775.298
1462.912
0.14
1472.001
1047.031
1307.628
950
0.16
1058.003
544.1986
388.5371
210.575
0.18
670.565
401.5245
271.593
134.9758
0.2
422.3284
378.3245
350.7773
104.5435
0.22
340.3102
293.5446
209.4738
158.9935
0.24
336.7964
343.4966
222.031
109.8615
0.26
159.6263
302.1867
220.2428
81.49519
0.28
220.908
282.8294
206.0608
54.40341
0.3
279.9756
272.9424
159.6668
65.57761
0.32
172.1822
166.1544
65.39905
38.57454
0.34
89.86789
203.853
108.6264
51.59596
0.36
88.72557
243.2259
22.57376
55.32845
0.38
93.8745
176.2005
92.04816
29.67164
0.4
59.49542
185.0206
47.19755
40.89772
0.42
35.44457
165.3844
70.05147
45.0461
0.44
30.54103
76.06155
52.72885
42.29347
0.46
33.51493
116.4955
41.67863
20.09766
0.48
40.94394
44.242
17.9763
26.64279
0.5
64.50564
33.35155
37.61299
15.0194
0.52
80.92889
33.36984
48.86872
29.25619
0.54
0
0
0
20.73045
0.56
0
0
0
15.75408
0.58
0
0
0
0
0.6
0
0
0
0Figure 6
Time-dependent change curves of mass loss rates under different cohesive forces.


## 4.3. Porosity and Permeability

Table4 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/m2 to 30 J/m2, final model porosity reduces from 0.3663 to 0.3292; permeability reduces from 32.33 µm2 to 20.99 µm2.Table 4
Porosity coefficients under different cohesive forces.
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
0.292286
0.292286
0.292286
0.292286
0.02
0.293146
0.292978
0.292605
0.292452
0.04
0.295244
0.29438
0.29364
0.293066
0.06
0.299255
0.297067
0.295782
0.294678
0.08
0.306828
0.302145
0.301081
0.299258
0.1
0.318567
0.311693
0.309693
0.306994
0.12
0.332363
0.324278
0.320163
0.315621
0.14
0.341045
0.330453
0.327875
0.321224
0.16
0.347284
0.333663
0.330166
0.322466
0.18
0.351239
0.336031
0.331768
0.323262
0.2
0.35373
0.338262
0.333837
0.323878
0.22
0.355737
0.339993
0.335072
0.324816
0.24
0.357723
0.342019
0.336381
0.325464
0.26
0.358664
0.343801
0.33768
0.325945
0.28
0.359967
0.345469
0.338896
0.326266
0.3
0.361618
0.347079
0.339837
0.326652
0.32
0.362634
0.348059
0.340223
0.32688
0.34
0.363164
0.349261
0.340864
0.327184
0.36
0.363687
0.350695
0.340997
0.32751
0.38
0.364241
0.351735
0.34154
0.327685
0.4
0.364592
0.352826
0.341818
0.327927
0.42
0.364801
0.353801
0.342231
0.328192
0.44
0.364981
0.35425
0.342542
0.328442
0.46
0.365179
0.354937
0.342788
0.32856
0.48
0.36542
0.355198
0.342894
0.328717
0.5
0.3658
0.355394
0.343116
0.328806
0.52
0.366278
0.355591
0.343404
0.328978
0.54
0.366278
0.355591
0.343404
0.329101
0.56
0.366278
0.355591
0.343404
0.329194
0.58
0.366278
0.355591
0.343404
0.329194
0.6
0.366278
0.355591
0.343404
0.329194Figure 7
Porosity coefficients under different cohesive forces.Table 5
Permeability coefficients under different cohesive forces (μm2).
Time (s)
Cohesive force
15 J/m2
20 J/m2
25 J/m2
30 J/m2
0
12.7343
12.7343
12.7343
12.7343
0.02
12.87826
12.85001
12.7875
12.76205
0.04
13.23524
13.08734
12.96158
12.86492
0.06
13.94018
13.55196
13.32814
13.13825
0.08
15.35577
14.46711
14.27119
13.94088
0.1
17.78363
16.32616
15.92116
15.38791
0.12
21.039
19.07583
18.13715
17.14637
0.14
23.33393
20.56052
19.92918
18.37542
0.16
25.11156
21.36981
20.48942
18.65758
0.18
26.29694
21.98401
20.88886
18.84034
0.2
27.06779
22.57632
21.41444
18.98292
0.22
27.70295
23.04515
21.7336
19.2015
0.24
28.3441
23.60423
22.07626
19.35376
0.26
28.6524
24.10555
22.42067
19.46736
0.28
29.08381
24.58293
22.74701
19.54351
0.3
29.63861
25.05123
23.00263
19.63563
0.32
29.98431
25.34002
23.10804
19.68999
0.34
30.16612
25.6982
23.28401
19.76289
0.36
30.34655
26.13122
23.32073
19.84132
0.38
30.53847
26.44879
23.47094
19.88349
0.4
30.66065
26.78581
23.54827
19.94173
0.42
30.73363
27.09016
23.66346
20.00605
0.44
30.79664
27.23113
23.75048
20.0666
0.46
30.86592
27.44825
23.81945
20.09543
0.48
30.95073
27.5311
23.84925
20.13369
0.5
31.08475
27.59369
23.91171
20.15529
0.52
31.25361
27.65644
23.99306
20.19742
0.54
31.25361
27.65644
23.99306
20.22732
0.56
31.25361
27.65644
23.99306
20.25006
0.58
31.25361
27.65644
23.99306
20.25006
0.6
31.25361
27.65644
23.99306
20.25006Figure 8
Permeability coefficients under different cohesive forces.


## 4.4. Particles Erosion Process

Figure9 gives the cloud chart of the internal filling particle loss process of the model with the cohesive force being 25 J/m2 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.Figure 9
Particles loss under water erosion. (a)t = 0 s. (b) t = 0.2 s. (c) t = 0.4 s. (d) t = 0.6 s.
(a)
(b)
(c)
(d)


## 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 (Figure10), 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.Figure 10
Curve of the water flow volume for a KCP.Figure 11
Schematic diagram of the seepage change process of broken rock mass seepage under the erosion effect.


## 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.



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*Source: 3592851-2018-09-30.xml*