复杂动荷载作用下岩体破裂的显式无网格数值流形法研究

One of the major problems in rock engineering is that rock mass suffers from damage and failure induced by complex dynamic loads such as blasting and seismic ground motion, which can be harmful to the practical usage of rock mass. It is, therefore, of great significance to give a research on the failure mode of rock mass subjected to complex dynamic load, which helps to evaluate the deformation and stability involving in rock engineering. The meshfree-numerical manifold method (M-NMM), which integrates meshfree method and numerical manifold method in one framework, can be favourable to solve such fracture problems, and has successfully been applied in studying rock mass failure mode under static loads. However, it faces challenges with how to solve the cracked rock mass under dynamic loads efficiently and accurately. For this project, based on my former foundation in M-NMM, I plan to first adopt a new boundary treatment, introduce a rigorous mass lumping technique, a scheme of inheritance of extended degrees of freedom with energy consistency, a high-effect explicit time integration scheme, failure criteria and so on, which further contributes to establish a simulation platform with explicit M-NMM under complex dynamic loads and models the whole deformation and destruction process of rock mass. Besides, the numerical results are validated by some typical rock experiments. Eventually, the platform is used to investigate the dynamic fracture mechanism of rock mass, providing technical support for resolving the relevant practical problems in rock engineering.

在岩石工程中，岩体经常会遭受爆破或地震等复杂动荷载作用而导致失稳破坏，影响其正常使用。因此，研究复杂动荷载作用下岩体破坏规律对于评价岩石工程的变形及稳定性具有十分重要的意义。兼具有无网格法和数值流形法优势的无网格数值流形法非常适合求解破裂问题，已被成功应用到静载下岩体破坏规律的研究。但如何高效率高精度地求解岩体在动载下的破坏问题还未解决。本项研究拟以无网格数值流形法为基础，采用新的边界条件施加方法，引入具有严格数学基础的集中质量矩阵生成方法、保能量守恒的扩展自由度继承策略、高效稳定的显式时间积分方案和破坏准则等，建立适用于复杂动荷载作用下岩体破裂的显式无网格数值流形法仿真平台，实现岩体变形破坏全程模拟，并与相应的实验结果比对。最后，利用此平台，进行岩体动破裂机理探究，为实际岩石工程问题提供技术支持。

动载下岩体破裂规律对正确评价岩石工程的安全性具有重要意义。本项研究基于无网格数值流形法，发展了适合动荷载作用下岩体破裂的数值分析方法。引入保能量守恒的扩展自由度继承策略、具有严格数学基础的集中质量矩阵生成方法、复杂边界条件施加方法，及岩石破坏准则等，开发了模拟岩石破裂过程的无网格数值流形法程序，主要研究成果如下：.(1) 提出了以含裂纹尖端的复合片和四叉树加密后的规则变尺寸数学片为特征的高精度无网格数值流形法。该方法能改善岩体中多裂纹接近交汇或靠近边界时的模拟精度。.(2) 发展了岩石破坏强度准则，该准则可实现裂纹扩展长度的自动计算。同时结合积分网格施加接触约束，以及“先时间后空间”离散的保能量守恒扩展自由度继承策略，建立了岩体破坏过程的动力隐式无网格数值流形法。.(3) 提出了一种基于物理覆盖信息的与物理片重合的积分网格和区域内任意积分点具有相同数目物理片影响的规则一致的数学节点布置方法。该方法从数值积分和节点插值角度，提高了无网格数值流形法的求解精度。.(4) 建立了通过在物理片上构造满足渗流奇异点或本质边界跳跃点的局部近似函数来反映渗流局部特性的全局解，并采用规则一致的新数学节点布置和积分方案，实现了无网格数值流形法对复杂边界渗流问题的高精度便捷模拟。.(5) 发展了复杂动荷载作用下动态裂纹扩展的显式无网格数值流形法。即：基于具有严格数学基础的集中质量矩阵生成方法和保能量守恒的扩展自由度继承策略等，建立了适合显式时间积分的动力无网格数值流形法。.本项目显著改善了无网格数值流形法的模拟精度，提升了对复杂工程问题的求解能力，丰富了岩体破坏问题的数值分析方法。