充填节理岩体中应力波传播特性的颗粒流离散元数值模拟研究.pdf

专业硕士学位论文 充填节理岩体中应力波传播特性的颗粒流离散 元数值模拟研究 汤云坤 导师姓名职称田威教授柴少波副教授 申请学位类别工程硕士 专业学位类别 及领域名称 建筑与土木工程 论文提交日期2021年3月20日 论文答辩日期2021 年 5 月 27 日 学位授予单位长安大学 分类号 TU459 10710-2018228012 Numerical simulation of stress wave propagation characteristics in filled jointed rock masses by particle flow discrete element A Thesis ted for the Degree of Master CandidateTang Yunkun SupervisorTian WeiChai Shaobo Chang’an University,Xi’an,China i 摘摘要要 在岩土工程领域，譬如工程爆破、大规模断面开挖、山体滑坡失稳治理和地震超 前预报等实际工程均涉及到动载应力波对岩体的扰动影响。节理是岩体断裂现象中极 为普遍的一种存在形式，其对应力波的传播特性会产生重要影响。自然界中的岩体含 有大量节理，而这些天然节理往往由诸如泥砂、岩土和碎石等异于岩体材料的充填物 质组成，无论是强度还是变形特性，充填介质与岩体材料均存在较大差异。国内外学 者利用块体元程序 UDEC 和 3DEC 进行了大量的应力波传播特性模拟研究，但将颗粒 流离散元程序 PFC 用于充填节理中应力波传播特性模拟研究的实践相对较少。鉴于数 值模拟方法简便、快捷等优势，本文使用 PFC2D 颗粒流软件开展了充填节理岩体中应 力波传播特性的数值模拟研究，主要研究工作有 （1）基于 PFC 数值理论、PFC 命令流、FISH 编程语言和接触模型本构关系，使 用 FISH 编程语言实现了对岩体模型的创建和 “颗粒串边界” 类似无反射粘弹性边界的 设定，使用 PFC 模拟了应力波在岩体介质中的传播过程，并对颗粒间接触力链和颗粒 速度-时间关系进行分析， 从细观和宏观两个方面验证了 PFC 用于应力波传播特性的模 拟研究的可行性。 （2）基于 PFC 程序，对单个充填节理岩体中应力波传播特性进行了模拟研究， 得到了透射系数 PFC 数值解， 并与薄层理论与等效波阻抗理论的理论解进行对比验证， 对比结果表明 PFC 数值解与上述两种理论解误差较小、吻合较好，这说明使用 PFC 程 序对充填节理岩体中应力波传播特性进行模拟研究是合理的。 （3）基于单个充填节理岩体 PFC 模型，研究了入射波频率、入射波振幅、入射 波形、充填厚度对应力波传播特性的影响规律。当充填厚度不断增加时，透射系数逐 渐减小，“滤波效应”更强；透射系数随入射波频率的增加而减小，随着入射波频率 持续增大，透射系数将逐步趋近于 0，也即具有“通低频、阻高频”的特点；当充填 厚度越大时，入射波频率对应力波的衰减影响越强。当充填节理厚度一定时，透射系 数会随入射波幅值的增大而增大；充填厚度越大，入射波幅值对透射系数的影响也就 越强。矩形波在充填节理岩体中的传播效果最好，正弦波在充填节理岩体中的传播效 果比三角波略好。 （4）建立了含两个充填节理岩体的 PFC 模型，研究了充填节理间距比率对应力 波传播特性的影响规律。结果表明，在充填节理间距比率ξ取值较小时ξ2，两个充 ii 填节理岩体中的透射系数并不等于单节理岩体透射系数的简单相乘；充填节理间距比 率ξ较小时ξ2，透射系数与应力波在两个充填节理处的“厚薄”传递顺序有关。充 填节理间距比率ξ存在两个界限值ξ1 和ξ2，当ξ ξ1 时，透射系数会随着充填节理间距 比的增大而增大；当ξ1 ξ ξ2 时，透射系数趋于一个稳定值。 （5）建立了含多个充填节理岩体的 PFC 模型，研究了充填节理分布形式对应力 波传播特性的影响规律。结果表明，对于间距相同、充填厚度相同的多个充填节理来 说，当充填节理间距比率较小时ξ2，充填节理的数量对透射系数影响很小。同时， 当ξ5时，对于间距不同、充填厚度相同的多个充填节理来说，透射系数与充填节理 的疏密程度有关，当充填节理呈“疏密”分布时，透射系数最大；充填节理呈“密 疏”分布时，透射系数次之；充填节理呈“疏密疏”分布时，透射系数最小。 （6）在充填节理岩体的 PFC 模型的基础上，研究了充填节理分布状态对爆炸应 力波在岩体中的破坏机理，具体分析了爆炸应力波作用下充填节理岩体的的破坏方式 和裂纹演化过程，研究发现当充填节理与最小抵抗线相交且通向自由面时，充填节 理薄弱层产生剪切、拉伸破坏，充填节理的存在使得应力波的传力路径发生改变，爆 炸能量沿充填节理方向“逃逸”，爆炸波有效作用时间极短，爆炸能量衰减幅度最大、 爆破效果最差。 关键词PFC，传播特性，充填节理岩体，应力波，破坏机理 本文得到深部岩土力学与地下工程国家重点实验室开放基金（SKLGDUEK1811）的资助 iii Abstract In the field of geotechnical engineering, practical engineering such as engineering blasting, large-scale section excavation, landslide instability treatment, and advanced earthquake prediction all involve the disturbing influence of dynamic stress waves on rock masses. Joints are a very common of rock fractures, which have an important impact on the propagation characteristics of stress waves. The rock mass in nature contains a large number of joints, and these natural joints are often composed of filling materials that are different from rock materials such as mud, sand, rock soil, and gravel. No matter the strength or deation characteristics, the filling medium and the rock material are relatively different. In view of the advantages of simple and fast numerical simulation s, this paper uses PFC2D particle flow software to carry out a numerical simulation study on the propagation characteristics of stress waves in filled jointed rock masses. The main research work of this paper includes （1）Based on the PFC numerical theory, PFC command flow, FISH programming language and contact model constitutive relationship, the rock model is created and the “particle string boundary“ that similar to the non-reflective viscoelastic boundary is set. Using PFC to simulate the propagation process of stress waves in rock mass media and analyzing the contact force chain between particles and the particle velocity-time relationship. The result presents that it is feasible to simulate the propagation characteristics of stress wave by PFC . （2）Based on PFC program, the propagation characteristics of stress wave in single filled jointed rock mass are simulated, and the numerical solution of transmission coefficient PFC is obtained, which is compared with the theoretical solution of thin layer theory and equivalent wave impedance theory. The comparison results indicate that the error between PFC numerical solution and the above two theoretical solutions is small and the coincidence is good, which indicate that it is reasonable to use PFC program to simulate the propagation characteristics of stress wave in jointed rock mass. （3）Based on PFC model of single filled joint rock, the influence law of incident wave frequency, amplitude, wave shape and filling thickness on the propagation characteristics of iv stress wave is studied. Results show that when the filling thickness increases continuously, the transmission coefficient gradually decreases, and the “filtering effect”becomes stronger; The transmission coefficient decreases as the frequency of the incident wave increases. As the frequency of the incident wave continues to increase, the transmission coefficient will gradually approach 0, that is, it has the characteristics of “passing low frequencies and blocking high frequencies”. When the filling thickness is larger, the frequency of the incident wave has a stronger influence on the attenuation of the stress wave. When the thickness of the filling joint is constant, the transmission coefficient will increase with the increase of the incident wave amplitude. The greater the filling thickness, the stronger the influence of the incident wave amplitude on the transmission coefficient. Rectangular waves have the best propagation effect in filled jointed rock masses, followed by sine waves, and triangular waves are lower. （4）PFC model of rock with two filled joints is established, and the influence of the ratio of filling joint spacing on the propagation characteristics of stress wave is studied. Results illustrate that when the ratio ξ of the filling joint spacing is small ξ2, the transmission coefficient of the two filled jointed rock masses is not equal to the simple multiplication of the transmission coefficient of the single jointed rock mass; when the filling joint spacing ratio ξ is small ξ2, the transmission coefficient is related to the “thickness“ transmission sequence of the stress wave at the two filling joints. There are two limit values ξ1 and ξ2 for the filling joint spacing ratio ξ. When ξξ1, the transmission coefficient will increase with the increase of the filling joint spacing ratio; when ξ1 ξ ξ2, the transmission coefficient tends to a stable value. （5）The PFC model of rock with multiple filling joints is established, and the influence of the distribution of filling joints on the propagation characteristics of stress wave is studied. Results present that for multiple filling joints with the same spacing and the same filling thickness, when the filling joint spacing ratio is small ξ2, the number of filling joints has little effect on the transmission coefficient. At the same time, when ξ5, for multiple filling joints with different spacing and the same filling thickness, the transmission v coefficient is related to the density of the filling joints. When the filling joints are in a “sparse-dense“ distribution, the transmission coefficient is the largest, when the filling joints are in a “dense-sparse“ distribution, the transmission coefficient is second, and when the filling joints are in a “sparse-dense-sparse“ distribution, the transmission coefficient is the smallest. （6）On the basis of the PFC model of filling jointed rock mass, the damage mechanism of the filling joint distribution state on the explosive stress wave in the rock mass is studied, and the damage mode and crack evolution of the rock mass under the action of the explosive stress wave by the filling joint are analyzed in detail. During the process, the study found that when the filling joint intersects the minimum resistance line and leads to a free surface, the weak layer of the filling joint produces shear and tensile failure. The existence of the filling joint changes the force path of the stress wave, and the explosion energy follows the filling. The joint direction “escapes“, the effective action time of the explosion wave is extremely short, the explosion energy attenuation amplitude is the largest, and the blasting effect is the worst. Keywords PFC, propagation characteristics, rock mass with filling joints, Stress wave, destruction mechanism This research was supported by the Open Fund of the State Key Laboratory of Deep Geomechanics and Underground Engineering SKLGDUEK1811 vi vii 目录 第一章 绪论...............................................................................................................................1 1.1 选题背景.......................................................................................................................1 1.2 国内外研究现状...........................................................................................................2 1.2.1 节理岩体中应力波传播特性理论分析研究现状.............................................3 1.2.2 节理岩体中应力波传播特性物理试验研究现状.............................................4 1.2.3 节理岩体中应力波传播特性数值仿真研究现状.............................................4 1.3 本文研究主要内容.......................................................................................................9 1.4 本文研究技术路线.....................................................................................................10 第二章 颗粒流离散元数值方法.............................................................................................10 2.1 颗粒流离散元方法简介.............................................................................................11 2.2 颗粒流离散元法基本假设.........................................................................................12 2.3 颗粒流离散元法计算原理.........................................................................................12 2.3.1 计算方法...........................................................................................................12 2.3.2 力位移方程...................................................................................................13 2.3.3 运动方程...........................................................................................................16 2.4 颗粒流离散元法接触本构模型.................................................................................17 2.4.1 接触刚度模型...................................................................................................18 2.4.2 黏结模型...........................................................................................................19 2.4.3 接触滑动模型...................................................................................................23 2.5 颗粒流离散元程序 PFC.............................................................................................24 2.6 本章小结.....................................................................................................................25 第三章 PFC 模拟应力波传播可行性研究.............................................................................27 3.1 PFC 数值模型建立方法..............................................................................................27 3.1.1 动荷载设定方法...............................................................................................27 3.1.2 数值模型创建过程...........................................................................................27 3.1.3 边界条件设定...................................................................................................28 3.1.4 阻尼设定...........................................................................................................28 3.2 PFC 模拟无节理岩体中应力波传播算例分析..........................................................30 3.2.1 模型创建过程...................................................................................................30 3.2.2 监测点选取.......................................................................................................36 3.2.3 波传播过程模拟...............................................................................................36 3.2.4 结果分析...........................................................................................................38 viii 3.3 本章小结.....................................................................................................................40 第四章 PFC 模拟应力波在充填节理处传播规律的合理性验证及参数研究.....................41 4.1 PFC 模拟应力波在充填节理处传播规律的验证......................................................41 4.1.1 理论计算方法...................................................................................................41 4.1.2 数值模型建立...................................................................................................42 4.1.3 结果对比验证...................................................................................................45 4.2 入射波频率对应力波传播特性的影响.....................................................................48 4.2.1 计算工况...........................................................................................................48 4.2.2 结果分析...........................................................................................................48 4.3 入射波频率与充填节理厚度对应力波传播特性的耦合影响.................................49 4.3.1 计算工况...........................................................................................................49 4.3.2 结果分析...........................................................................................................49 4.4 入射波幅值对应力波传播特性的影响.....................................................................50 4.4.1 计算工况...........................................................................................................50 4.4.2 结果分析...........................................................................................................51 4.5 入射波形对应力波传播特性的影响.........................................................................51 4.5.1 计算工况...........................................................................................................51 4.5.2 结果分析...........................................................................................................52 4.6 充填节理间距比率对应力波传播特性的影响.........................................................53 4.6.1 试算模型...........................................................................................................53 4.6.2 试算模型结果分析...........................................................................................56 4.6.3 计算模型...........................................................................................................57 4.6.4 计算模型结果分析...........................................................................................57 4.7 充填节理分布形式对应力波传播特性的影响.........................................................58 4.7.1 计算工况...........................................................................................................58 4.7.2 结果分析...........................................................................................................59 4.8 本章小结.....................................................................................................................60 第五章 爆炸应力波作用下充填节理岩体破坏机理研究...................................................