复杂岩体工程无网格分析的若干关键问题研究

Because of its maturity and popularity, the Finite Element Method(FEM) is taking an increasingly important role in the analysis of the large scale rock engineering. The element topology or mesh constitutes the theoretical basis of the FEM. However, it also brings entanglement in dealing complex boundary problems, such as the difficulties associated with mesh distortion, meshing of special elements and mesh updating, which practically limits the application of FEM to rock engineering. Investigations will be carried out on the numerical stability of the meshless interpolation based on finite cover theory, the algorithms for auto-arrangement of the discrete meshless nodes for rock engineering analysis, the meshless model for material discontinuities and rock joints, the theory of numerical integration in meshless analysis of rock engineering, and the meshless coupling methods of solid elements of rock mass with support structural elements such as beam and plate elements. The project aims to develop a simple and convenient meshless theory for the numerical analysis of complex rock problem, to realize the implementation of highly automated rock engineering analysis, and to reduce the knowledge requirement on computational mechanics for practical geotechnical engineers. The proposed research topic will have profound significance both to theoretical development and substantial engineering.

作为一种成熟、通用的计算方法，有限元法目前已在越来越多的大型岩体工程分析中发挥了十分重要的作用。单元网格是有限元法构造和理论发展的基础，但也带来了网格畸形、特殊单元网格划分、网格变动等方面的困难，给有限元法的岩土工程应用带来了很大的限制。本项目拟对基于覆盖理论的无网格插值函数及其稳定性、岩体工程无网格布点技术、材料不连续及岩体节理断层的无网格处理方法、岩体工程无网格分析的数值积分理论与方法、梁板支护结构与岩体耦合分析的无网格实施技术等关键问题开展系统地研究，力图为复杂岩体工程分析提供一种简单、方便的无网格计算新理论，实现岩体工程分析过程的高度自动化，大幅度降低对岩土工程师计算力学知识的要求，让无网格理论与计算方法真正走向实际工程应用。项目研究具有重要的学术意义和工程应用价值。

结合流形覆盖和无网格插值思想，提出和发展了一类新的、适合复杂岩体工程分析的混合覆盖无网格MCMM（Mixed Cover Meshless Method）方法。该MCMM方法基于离散点插值，在不同的分析区域内可根据需要灵活地使用重叠的或独立的结点覆盖，避免了几何边界相适应的网格剖分，具有十分简洁的计算公式和简单的数值实施过程，其计算时间略高于相同自由度的有限元方法，但远低于传统的无网格方法，为岩土工程分析过程自动化并真正走向实际工程应用奠定了良好的基础。完成了基于MCMM的虚拟裂纹闭合法、裂纹扩展、无网格结点布置、高效数值积分、节理断层、材料不连续面、开挖支护模拟等关键算法和实施技术，提出和发展了基于独立覆盖的适合岩体工程支护结构模拟的简单高效的厚壁通用板单元。利用标准算例、磷矿边坡稳定性分析实例及模型实验研究等对项目理论及方法的正确性进行了测试和验证。