﻿ 冲击作用下岩石裂纹长度预测模型及数值模拟研究

1. 中国石油大学(北京)石油工程学院, 北京 102249 ;
2. 油气资源与探测国家重点实验室(中国石油大学(北京)), 北京 102249

Prediction Model and Numerical Simulation for Rock Fissure Length under Impact Load
DENG Yong1,2, CHEN Mian1,2, JIN Yan1,2, LU Yunhu1,2, ZOU Daiwu1,2
1. College of Petroleum Engineering, China University of Petroleum(Beijing), Beijing, 102249, China ;
2. State Key Laboratory of Petroleum Resources and Prospecting(China University of Petroleum(Beijing)), Beijing, 102249, China
Abstract: In order to study the rock fracture and fissure propagation and evolution rule and to predict fissure (crack) length in the process of dynamic load intruding the rock, a mathematical model for describing relationship between the maximum impact force and the impact velocity during rock breaking was developed according to the Newton's second law and the wave theory. Based on the relationship between static load and crack length of rock, the theoretical model of fissure length under impact load was established. In addition, researchers used a discrete element numerical simulation method to investigate the characteristics of fissure formation and propagation and the influence of impact velocity on crack length. The results indicate that tensile fissures are mainly formed under the impact force,and the radial cracks extend to rock free face, lateral fissures initiate from the damaged area and then extend to the inside of rock. Radial and lateral fissure lengths have a power function relationship with the impact velocity, and the numerical simulation results are consistent with the results of theoretical model. As the impact velocity increases from 15 m/s to 35 m/s, the rock breaking range and depth increase gradually, the radial crack length increased from 3.47 mm to 9.03 mm and lateral crack length increased from 7.29 mm to 14.58 mm. The research results can provide a theoretical reference for investigating rock fractures and fissure propagation under dynamic load intrusion and dynamic crushing mechanism.
Key words: rock shatter under impact     fissure length     discrete element     rock breaking     mathematical model

1 冲击破岩的力学分析

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 图 1冲击破岩受力分析 Fig.1Force analysis of rock breaking by impact load

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2 动静载荷侵入断裂分析

 图 2压头侵入材料时产生的裂纹 Fig.2Fissures formed when the press ram intruded the material
2.1 静载侵入断裂分析

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 图 3侧向裂纹的形状 Fig.3Shape of lateral crack
2.2 动载侵入断裂分析

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3 球齿冲击破岩的离散元模拟 3.1 岩石参数的确定

 图 4单轴压缩模拟试验的应力-应变曲线 Fig.4Stress-strain curve obtained by simulating uniaxial compressive test
3.2 球齿冲击破岩模型的建立

PFC方法的基本思想是采用介质最基本单元(粒子)和最基本的力学关系(粒子间的牛顿第二定律)来描述介质的复杂力学行为，介质的力学特性和本构关系取决于介质内部粒子的结构和接触模型。在PFC中颗粒之间的黏结模型有2种，分别为接触黏结和平行黏结：在接触黏结中，只要颗粒之间有接触，模型刚度就不会发生改变，即使接触黏结键被破坏；在平行黏结中，模型的刚度由颗粒的接触刚度和平行黏结刚度共同决定，当平行黏结键发生破坏时，模型的刚度会减小。平行黏结的这种性质和真实岩石比较相似，因此数值模型中采用平行黏结模型。粒子之间的接触方式和力学特征都符合基本的牛顿运动定律，即当粒子间的静力平衡被破坏时，粒子将产生运动；粒子间的接触方式和接触强度决定了粒子集合体(即介质)的基本力学特性和本构关系，介质的各种复杂力学特性都是通过粒子间的基本状态体现出来的。由于模型介质的本构特征是由介质内部粒子之间的接触模型和状态特征的变化而自动体现出来，因此在PFC方法中不需要给介质赋予某种本构关系[18-20]

 图 5球齿冲击破岩数值模型 Fig.5Numerical model for rock breaking by spherical tooth impact
3.3 结果分析

 图 6不同冲击速度下岩石裂纹的扩展情况 Fig.6Fissure propagation of rock under different impact velocities

 图 7冲击速度对径向裂纹长度的影响 Fig.7Effect of the impact velocity on the length of radial fissure

 图 8冲击速度对侧向裂纹长度的影响 Fig.8Effect of impact velocity on the length of lateral fissure
4 结论

1) 分析岩石在冲击力作用下的力学特性，得到了最大冲击力与冲击速度的函数关系，并结合岩石在静载作用下的侵入载荷与裂纹长度间的关系，建立了岩石在冲击载荷作用下形成的径向裂纹长度和侧向裂纹长度与冲击速度间的数学模型，发现裂纹长度与冲击速度之间呈幂函数关系。

2) 球齿冲击破岩的离散元数值模拟结果表明，随着冲击速度的增大，形成的径向裂纹长度和侧向裂纹长度与冲击速度间呈良好的幂函数关系，且幂指数分别为0.945和0.732，与理论模型的吻合程度较高，验证了理论模型的正确性。

3) 对于压头以一定速度冲击岩石时岩石中的开裂范围和破碎坑体积与裂纹长度之间的对应关系，有待于进一步研究。

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#### 文章信息

DENG Yong, CHEN Mian, JIN Yan, LU Yunhu, ZOU Daiwu

Prediction Model and Numerical Simulation for Rock Fissure Length under Impact Load

Petroleum Drilling Techniques, 2016, 44(04): 41-46.
http://dx.doi.org/10.11911/syztjs.201604008