加锚岩体的阶谱复合单元法研究

加锚岩体有着复杂的非线性的变形模式，常规的线性基函数不能满足成模拟这种非线性的要求，若进一步细分网格，又会增加前处理的工作。引入阶谱技术，建立阶谱复合单元法，其基本思想是在复合单元中增加虚节点，扩大容许函数容量，通过使用阶谱基函数，提高计算精度。在广义节点下分析复合单元，使用阶谱复合单元法模拟加锚岩体，随着升阶，能够从物理本质上更好的拟合加锚岩体复杂的力学性质；在粗糙单元网格下逼近真实值，减轻网格的束缚。对阶谱复合单元法进行理论推导和实例研究，通过与有限单元法和复合单元法计算结果的比较，发现在较粗糙计算网格情况下随着升阶，阶谱复合单元法计算结果有明显的改善。

STUDY ON BOLTED ROCK MASS BY HIERARCHICAL COMPOSITE ELEMENT METHOD

The conventional basic function can not completely simulate the deformation pattern of bolted rock, which is complex and highly nonlinear. Subdivision of the mesh can solve the problem,but it makes the preprocess more difficult. Using hierarchical technique,hierarchical composite element method(CEM) is adopted for the rock mass reinforced by bolt. The basic idea is to extend the tolerant function by adding virtual nodes,to improve the numerical precision by using hierarchical basic function,and to analyze the composite elements under the generalized nodes. With basic function upgrading,the hierarchical composite element method can better simulate the complex characters of bolted rock in physical hypostasis,which makes calculation results be closer to the true ones with coarse mesh. The analytic process of hierarchical composite element method is explained;and the way to realize this method in bolted rock is introduced. The comparison of the calculation results with finite element method(FEM) and conventional CEM shows the robustness of the proposed method. It is proven that upgrading composite element method can improve the calculation results evidently with fewer meshes.