# Simulation of the Compaction Behavior and the Water Permeability Evolution of Broken Rock Masses of Different Shapes in a Goaf

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Method

#### 2.1. Generation Method of the Rock Mass Model with Different Morphologies

_{k}is the angle corresponding to the K-edge of the polygon, b

_{k}is a random number in [0, 1], δ is a constant less than 1, and n is the number of edges of a polygon. After determining the number of polygon edges, to ensure n, the sum of θ

_{k}was set to 2π, which involved a pair of θ

_{k}to perform the correction.

_{0}and y

_{0}are vertex coordinates of the inner circle of a polygon, representing the horizontal coordinates and vertical coordinates, respectively, of the position of the caving rock mass.

#### 2.2. Establishment of the Compaction Characteristics and the Water Permeability Test Model of Broken Rock Masses

_{min}= 320, R

_{max}/R

_{min}= 1.66, and R

_{max}= 0.83 mm.

_{t}), compressive strength (σ

_{c}), deformation modulus (E

_{T}), Poisson ratio’s (ν), bond strength (c) and friction angle (φ). The physical and mechanical parameters of this rock are shown in Table 1 [10].

## 3. Test Results of Numerical Simulation

#### 3.1. Compaction and Deformation Characteristics of Caving Rock Masses with Different Shapes

#### 3.2. Stress–Strain Relationship and Deformation Modulus of Caving Rock Mass with Different Shapes

#### 3.3. Influence of Different Caving Rock Mass Shapes on the Porosity and the Coefficient of Fragmentation

- (1)
- Fragmentation expansion coefficient

_{0}[5].

_{1}is the volume after the collapse of the caving rock masses and v

_{0}is the original volume [5].

- (2)
- Porosity

_{1}is the volume after the collapse of the caving rock masses and v

_{0}is the original volume.

#### 3.4. Influence of Different Shapes of Caving Rock Mass on the Water Permeability Characteristics

#### 3.5. Differential Degree of Compacted and Fractured Rocks with Different Shapes

#### 3.6. Characteristics of Energy Evolution during Compaction and Fracture of Caving Rock Masses with Different Shapes

## 4. Discussion

#### 4.1. Change in Particle Movement State in the Caving Rock Mass

_{1}is the maximum inscribed radius of the caving rock masses and r

_{2}is the minimum circumscribed radius.

_{1}to r

_{2}. The larger the number of broken rock edges, the smaller the difference between r

_{1}and r

_{2}, and the closer the ratio is to 1.0, and the more circular the shape of the broken rock mass. Therefore, caving rock masses with more edges tend to be rounder and more regular in shape. The porosity between broken rock masses is relatively small, the degree of looseness is poor, and there are many contact points. Therefore, caving rock masses have less rotation and translation movement during the compaction process. Caving rock masses have a lower fragmentation rate, and their bearing capacity is better than that of caving rock masses with fewer edges. However, the smaller the number of edges, the more irregular the shape of the caving rock masses, with many gaps between the caving rock masses. During the compaction process, the caving rock masses easily rotate, break, and grind, resulting in an increase in their breaking rate [18].

#### 4.2. Mechanism of the Influence of the Shape of the Caving Rock Mass on its Force Chain Evolution

#### 4.3. Mechanism of Influence of Caving Rock Mass Shape on the Water Permeability during Compaction

#### 4.4. Mechanism of Influence of Caving Rock Mass Shape on Energy Dissipation during Compaction

## 5. Conclusions

- The number of edges on a caving broken rock mass is negatively correlated with the limit strain of compaction, the initial void ratio and the final breaking ratio. It is positively correlated with the deformation modulus and the residual dilatancy coefficient.
- When the shape of caving rock masses is quadrilateral, pentagonal or hexagonal, the initial compaction state of the caving rock masses occurs in a rotary motion, and the later motion state is vertical compression. When the shape of caving rock masses is octagonal or decagonal, the compaction motion of the caving rock masses is mainly vertical compression.
- The water permeability ratio of broken rock masses of different shapes decreases rapidly at the initial stage, and then gradually reaches a stable stage. The less edges there are on broken rock masses, the faster the rate of decline is in the water permeability ratio, and the lower the final water permeability is.
- With an increasing number of edges, the total strain energy and the dissipative strain energy of caving rock masses show a decreasing trend, while the elastic strain energy shows a growing trend.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Comparison of simulation results [10].

**Figure 9.**Relation curves of tangent modulus, stress and strain of caving rock mass in different shapes.

**Figure 10.**Relation curve of secant modulus, stress and strain of caving rock mass in different shapes.

**Figure 12.**Relationship curve of porosity, the crushing expansion coefficient and the stress of caving rock masses of different shapes.

**Figure 13.**Variation curve of residual dilatancy coefficient of caving rock masses of different shapes.

**Figure 14.**Numerical simulation results of porosity at initial compaction stage and compaction displacement nephogram.

**Figure 15.**Numerical simulation results of porosity and compaction displacement nephogram after compaction.

**Figure 18.**Relation curve of crack quantity, fracture rate and strain of caving rock mass with different shapes.

**Figure 19.**Compaction stress–strain curve and strain energy evolution curve of caving rock masses with different shapes.

**Figure 25.**Relationship between the water permeability, the porosity and the stress of broken rock masses of different shapes.

**Figure 26.**Relationship curve of caving rock mass shapes with total strain energy, elastic strain energy and dissipative strain energy.

**Table 1.**Physical and mechanical parameters of rock [10].

Lithology | $\mathit{\rho}$ (kg/m^{3}) | σ_{t} (MPa) | σ_{c} (MPa) | E_{T} (GPa) | ν | c (MPa) | φ (°) |
---|---|---|---|---|---|---|---|

Sandy mudstone | 2690 | 6.5 | 71.8 | 25.3 | 0.25 | 28.3 | 33.8 |

Mesoscopic Parameters | Parameter Meaning | Parameter Value |
---|---|---|

${\rho}_{s}$ | Density (kg/m^{3}) | 2690 |

${\mathrm{\mu}}_{s}$ | Friction coefficient | 0.50 |

L/R_{min} | Size ratio | 320.00 |

R_{max}/R_{min} | Maximum and minimum particle ratio | 1.66 |

deform_emod | Linear contact modulus (GPa) | 4.37 |

pb_deform_emod | Effective modulus of parallel bond (GPa) | 25.56 |

pb_ten | Tangential strength (MPa) | 43.00 |

pb_coh | Normal strength (MPa) | 52.00 |

kratio | Stiffness ratio | 1.80 |

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**MDPI and ACS Style**

Guo, Y.; Qin, Y.; Chen, P.; Xu, N.
Simulation of the Compaction Behavior and the Water Permeability Evolution of Broken Rock Masses of Different Shapes in a Goaf. *Water* **2023**, *15*, 1190.
https://doi.org/10.3390/w15061190

**AMA Style**

Guo Y, Qin Y, Chen P, Xu N.
Simulation of the Compaction Behavior and the Water Permeability Evolution of Broken Rock Masses of Different Shapes in a Goaf. *Water*. 2023; 15(6):1190.
https://doi.org/10.3390/w15061190

**Chicago/Turabian Style**

Guo, Yuxi, Yan Qin, Ping Chen, and Nengxiong Xu.
2023. "Simulation of the Compaction Behavior and the Water Permeability Evolution of Broken Rock Masses of Different Shapes in a Goaf" *Water* 15, no. 6: 1190.
https://doi.org/10.3390/w15061190