基于DDM的杂交边界点法及岩体多裂隙演化的快速模拟

When the present various numerical methods are used to study the fractured rock mass, the research focuses on damage evolution based on equivalent theory. In this project, we will develop the mechanical model and computation method which can be used to easily and quickly simulate the multi-cracks propagation evolution path, and study the micro-failure mechanism of fractured rock mass . The displacement discontinuity method (DDM) can characterize the discontinuity of complex multicracks problem, and the adavantages of the hybrid boundary node method are dimensional reduction and meshfree. The displacement discontinuity method is combined with the hybrid boundary node method, and the new boundary integral equation is constructed, and the dual reciprocity method is employed to deal with the nonlinear problem, then the hybrid boundary node method based on DDM is proposed, which can track the propagation evolution path of crack. In order to speed up the convergence and improve calculation efficiency, the fast multipole method is introduced. The expansion coefficients and tranlation formulations of fundamental solutions are deduced, the preconditioned approach is improved, and a new tree structure is constructed. Then a sufficient fast computing technology is proposed, which can reduce the computational cost and memory requirements in simulating propagation evolution of multi-cracks. The code of the fast hybrid boundary node method based on DDM will be developed. Verification and validation will be done by means of classic benchmarking problems and the physical model tests. Because the distribution of cracks of the rock mass is random in actual project, the probability statistics method is introducted, the code will be employed to analyze the failure mode of fractured rock mass and the interaction among multi-cracks influenced by crack dip angle and distribution, which will serve as an important guidance for the stability evaluation of rock engineering.

鉴于目前裂隙岩体的数值分析大多采用基于损伤力学的宏观等效方法,为了研究多裂隙岩体的细观破坏机理,本项目发展一种能快速模拟岩体多裂隙扩展演化轨迹的力学模型和计算方法.位移不连续法(DDM)能直接表征复杂多裂隙的不连续特性,通过将其与具有降维和无网格特性的杂交边界点法结合,构造新的边界积分方程,采用双互易法处理非线性问题,提出基于DDM的杂交边界点法,实现对裂纹演化过程的跟踪模拟;通过引入快速多极算法,推导各基本解的级数展开和传递公式,改进预处理方法,建立新型树结构,提出一种高效快速的计算技术,实现多裂纹演化模拟时计算和存储量级的降低;开发基于DDM的快速杂交边界点法程序,采用典型算例和物理模型试验对程序进行调试和验证;针对实际岩体中裂隙的随机性,结合概率统计的方法,利用该程序探索不同裂隙倾角和分布形式对多裂隙岩体破坏模式的影响规律及多裂纹间的相互作用,为岩体工程的稳定性评价提供重要的指导.

发展一种能方便快速的模拟节理岩体中多裂纹的扩展、相互作用和贯通形式等破裂过程和规律的新型数值计算方法，具有十分重要的理论和实际意义。位移不连续法（DDM）作为一种间接边界元方法，其直接以裂隙面上的相对位移为未知量，在处理不连续体问题时非常简单方便，因此特别适合于求解多裂纹的扩展问题。本项目将位移不连续方法引入杂交边界点法中，提出了可模拟节理岩体裂纹扩展演化过程的基于DDM的杂交边界点方法，在此基础上编制了相应的计算分析程序，利用一些经典算例对该方法和程序进行了验证。对各种裂纹扩展判据进行分析比较，并根据实际的载荷条件和裂纹面接触关系，对这些判据进行修正，结合压缩荷载作用下的裂纹尖端应力强度因子，并且考虑裂纹面之间的摩擦作用推出了针对压缩荷载作用下的岩石裂纹扩展的应变能密度因子理论。利用高性能并行计算技术，并结合快速多极算法（FMM）来加速问题的求解，提高计算效率、增大计算规模。改进初始快速多极算法，增加指数展开，将原有的计算量级较大的多极展开系数向局部展开系数的传递过程替换成多极展开系数向指数展开系数传递、指数展开系数之间的传递和指数展开系数向局部展开系数的传递这三个较小计算量级的新过程。从软件和硬件两个方面，提出了前处理、并行计算方法、程序算法、后处理实现等核心问题的解决方案。采用室内试验方法，利用岩石破裂过程细观力学试验系统和声发射试验系统等室内试验对裂隙岩体的破裂过程进行细观观测，通过对比分析对数值算法的正确性和效率进行验证。