QQ群聊

• CN 62-1112/TF
• ISSN 1005-2518
• 创刊于1988年

## Numerical Simulation of Collapse Disaster Before and After Weakening of Thick and Hard Roof

LV Nao,, WANG Haibo,

School of Civil Engineering and Architecture，Anhui University of Science and Technology，Huainan 232001，Anhui，China

 基金资助: 国家自然科学基金项目“无限岩体深孔超前破裂爆破岩体破碎机理及应用基础研究”（编号：51404010）、安徽省高校自然科学研究重大项目“高应力场岩体爆破破岩机理研究”（编号：KJ2017ZD11）和安徽省科技攻关计划项目“矿山爆破安全与灾害控制技术”.  编号：1501041123

Received: 2018-04-14   Revised: 2018-07-10   Online: 2019-04-29

Abstract

In view of the impact disaster caused by large area roof caving on mechanical equipment and workers in mining area，the related research was conducted relying on 210108 working face of Xinji No.2 Mine.According to the difference of block volume before and after roof weakening.A a three-dimensional calculation model of two kinds of caving bodies with the same height and width，coal seam，goaf and floor is established by using ANSYS/LS-DYNA finite element software.The calculation adopts Euler-Lagrange fluid-solid coupling algorithm.Rock and coal are described by Lagrange mesh and Lagrange element，air is described by ALE mesh and Euler element.The cloud map of hurricane velocity in goaf and roadway ，and the cloud map of effective stress in the bottom of coal seam in typical moment behind roof collapse are obtained by simulation under two kinds of calculation conditions.The variation rule of hurricane wind speed in roadway caused by collapse of different volume before and after roof weakening and the influence of impact load on coal seam in working face are analyzed.The results show that: For two kinds of condition，the attenuation law of hurricane velocity in goaf and roadway is basically the same，but the distribution characteristics of effective stress at the bottom of coal seam are different.From goaf to roadway entrance，hurricane speed tends to increase，and the wind speed increases sharply at roadway entrance，but the wind speed decreases with the increase of the distance between the location and the roadway entrance.With the increase of roof falling time，the wind speed in the roadway rises as a whole，but the attenuation and deceleration decay rate of the wind speed in the roadway decreases gradually，and the peak wind speed decreases logarithmically with the increase of the distance between the location and the roadway entrance.After roof weakening，the length of collapse body decreases，and hurricane wind speed decreases at different times.The maximum wind speed value ofin roadway entrance decreases from 298.62 m/s to 224.89 m/s，which decreases by 25$%$，and the reduction increases gradually with the increase of the distance to roadway entrance，which is 42$%$ at 90 m.According to the fitting formula of the relationship between peak wind speed and distance，when the maximum allowable wind speed is 6 m/s，the influence range of Hhurricane after roof weakening decreases from 247 m to 158 m，which reduces by 36$%$.Large area of roof collapse causes stress concentration in coal seam of working face.After roof weakening，the stress distribution in coal seam of working face is more uniform，and the peak value of maximum effective stress decreases from 10 MPa before weakening to 4.3 MPa，which decreases by 57$%$.Controlling the cyclic step distance of roof weakening caving below 30 m can significantly reduce the impact range of hurricane and the impact load on the stability of coal seam in working face.

Keywords： roof collapse ; hurricane ; impact load ; wind velocity ; distance ; numerical simulation thick-hard strata ; mine goaf

LV Nao, WANG Haibo. Numerical Simulation of Collapse Disaster Before and After Weakening of Thick and Hard Roof[J]. Gold Science and Technology, 2019, 27(2): 257-264 doi:10.11872/j.issn.1005-2518.2019.02.257

### 图1

Fig.1   Side diagram of calculation model

（1）未进行顶板弱化，顶板垮落体尺寸（长×宽×高）为83 m×73 m×20 m；

（2）采用顶板弱化后，顶板垮落体尺寸（长×宽×高）为30 m×73 m×20 m。

### 图2

Fig.2   Calculation model of roof before and after weakening

### 1.3 算法选择

LS-DYNA软件为单元提供了3种基本算法，即Lagrange算法、Euler算法和ALE算法。Lagrange算法是通过Lagrange坐标系描述物体的变形，坐标网格随着物体的变形而变形，方程计算简单但单元易发生畸变。Euler算法是指用Euler坐标系描述物体的运动，坐标系不随物体运动而变化，只研究一定时刻坐标系中介质的运动，适用于大变形但不方便描述材料的复杂本构关系。ALE算法综合了Lagrange算法与Euler算法的特征，开始时采用Lagrange算法，当材料单元即将发生畸变时采用Euler算法。

LS-DYNA软件为流固耦合的研究提供了相关的材料模型和状态方程，2种工况计算模型均采用Euler-Lagrange流固耦合算法：岩石和煤体均采用Lagrange网格，用Lagrange单元描述；空气采用ALE网格，用Euler单元描述，使用单点Euler积分。在有限元网格划分时，岩石的Lagrange网格与空气的ALE网格可以重叠在一起，计算中通过关键字*CONSTRAINED_LAGRANGE_IN_SOLID定义罚函数约束法将岩石等固体与空气流体耦合在一起，实现力学参数的传递。

### 1.4 参数选择

Table 1  Physical and mechanical parameters of rock

Table 2  Calculation parameters of coal and air

### 图3

Fig.3   Wind velocity cloud map of goaf and roadway at different times before roof weakening

### 图4

Fig.4   Wind velocity cloud map of goaf and roadway at different times after roof weakening

（1）由采空区到巷道口处，飓风速度呈增大趋势，且在巷道口处风速急剧增大。分析认为采空区顶板垮落时，在顶板的重力作用下，采空区内的空气由于受到压缩而储存了相当高的气压能，为了能够与周围环境的能量平衡分布，受压缩的空气携带强大的压力能向周边低气压区迅速流动，即流向巷道口。由于巷道口的断面面积远小于采空区的断面面积，所以空气在流入巷道口时流动速度会迅速增大。

（2）随着与巷道口距离的增加，飓风的速度呈衰减趋势。分析认为采空区内的压缩空气经巷道口冲出并沿巷道流动时，空气内部的流动粘滞性及惯性会引起沿程的能量损失，使风速出现逐渐衰减的现象。

### 图5

Fig.5   Variation of wind velocity at different positions in roadway at different times before roof weakening

### 图6

Fig.6   Variation of wind velocity at different positions in roadway at different times after roof weakening

### 图7

Fig.7   Attenuation law of peak wind velocity in roadway before and after roof weakening

Table 2  Peak velocity of wind at different distance from roadway entrance before and after roof weakening

0298.62224.89
10216.98157.82
20169.92131.90
30147.89114.44
40133.0998.93
50117.9883.24
60100.8670.01
7092.6964.76
8082.7340.30
9061.3835.81

v=372.81-66.6 ln（L） （R2=0.9835）

v=368.67-70.97 ln（L+7.78） （R2=0.9925）

《煤矿安全规程》[23]规定，机巷和回风巷的容许最高风速为6 m/s，代入式（1）和式（2）可得顶板弱化前后飓风的影响范围分别为距巷道口247 m和 158 m。经过顶板弱化，在巷道口处的风速峰值由298.62 m/s降至224.89 m/s，降低了24.7%，飓风的影响范围由247 m降至158 m，降低了36%，表明顶板弱化可有效降低垮落体形成的飓风风速。

### 图8

Fig.8   Von mises stress cloud map of coal seam bottom before and after roof weakening

## 3 结论

（1）在顶板下落过程中，由采空区到巷道口处，飓风速度呈增大趋势，且在巷道口处风速急剧增大，随着所处位置与巷道口距离的增加，飓风的速度呈衰减趋势。

（2）随着顶板下落时间的增加，巷道内飓风的速度整体呈上升趋势，但巷道内风速的衰减速率降低，且巷道内的风速峰值呈负对数衰减；相比弱化前垮落体，长度为30 m垮落体形成的飓风在巷道内的影响距离缩短了36%。

（3）大面积顶板垮落使工作面煤层产生应力集中现象，顶板弱化后，垮落块度的减小极大地降低了工作面煤层的应力峰值，且应力在工作面长度范围内分布更均匀，通过顶板弱化可以有效防治工作面前方煤层扰动失稳现象的发生。

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