岩体次级结构模拟的材料力方法及有限元实现与应用

MATERIAL FORCE METHOD FOR SIMULATING SECONDARY STRUCTURES IN ROCK MASSES AND ITS FINITE ELEMENT IMPLEMENTATION AND APPLICATION

针对现有岩体次级结构模拟的等效方法和直接离散方法存在的缺点,从复合材料力学的角度出发,提出次级结构模拟的材料力方法。该方法中,岩石被看成基质,次级结构被看成夹杂。次级结构的力学效果以由本征应变产生的材料力得以体现。在分析计算弹塑性力学实质的基础上,以有限元方法为数值平台,通过提出双重网格法将材料力方法融合于弹塑性有限元分析中。与等效连续介质力学方法相比,材料力方法不仅可以考虑次级结构与岩石变形性质的差异,同时还可以考虑次级结构与岩石强度性质的差异;与直接离散的数值模拟方法相比,材料力方法的子域积分网格完全独立于有限元网格,因此它可降低分析域前处理离散的困难。另外,弹塑性有限元与材料力方法具有相同的实质——逐步求取本征应变引起的材料力。因此,材料力方法在保证原有有限元方程规模不变的前提下尽可能将额外计算开销极小化。2个算例表明材料力方法的有效性和可行性。

Material force method for simulating secondary structures in rock mass is innovated based on composite material mechanics considering the disadvantages of existing equivalent methods and discrete methods. In this method, rock is regarded as matrix, and secondary structures are regarded as inclusions. The mechanical effects of secondary structures are embodied in material forces induced by eigen strain. Based on the essence of analysis and calculation of elastoplastic mechanics, material force method is planted into elastoplastic finite element method with the adoption of a dual-mesh system for quadrature. Compared with equivalent methods, material force method takes both the difference of deformation properties and the difference of strength properties between rock and secondary structures into consideration. Compared with discrete methods, the complication of pre-processor is reduced at great scale because its sub-meshes for quadrature are completely independent of the finite element meshes. In addition, calculating the material force induced by eigen strain step by step is the same essence of material force method and elastoplastic FEM. Therefore, the extra cost caused by material force method is minimized while keeping total degrees of freedom unaltered. The validity and effectiveness of material force method are shown by two examples.