节理岩体力学性能不确定性分析方法研究

基于连续介质损伤力学框架，通过损伤张量和有效应力来描述节理岩体的力学性能，自主研发了基于损伤力学模型的有限元程序（CD-FEM），用于节理岩体等效力学性能研究。同时，采用Karhunen-Loeve（K-L）展开来分解随机输入场，用混沌多项式来表示随机输出场，采用概率配点法生成配点，再由连续损伤有限元分析系统CD-FEM求解确定性方程组，最终得到输出域的统计数据，从而提出了一种将随机分析与基于连续损伤力学模型的数值分析方法解耦进行节理岩体不确定性力学行为分析的方法。利用该方法，对一典型节理岩体在加载条件下的力学行为进行不确定性分析，并与蒙特卡罗方法进行对比，结果表明，所提方法的计算量大大减少，极大地提高了节理岩体力学性能不确定性分析的效率，可应用于对节理岩体在不同载荷条件下的不确定性进行分析。

Uncertainty analysis of mechanical behavior of jointed rock mass

Based on the framework of continuum damage mechanics (CDM), mechanical properties of jointed rock mass are characterized by using damage tensor and the effective stress. A numerical code named CD-FEM is developed to study the equivalent mechanical behaviour of rock mass. To investigate the uncertainty mechanical behavior of jointed rock mass, random input fields are represented using the Karhunen-Loeve expansion, and random output fields are expressed by polynomial chaos expansions. Probabilistic collocation method is used to generate collocations, and then the numerical code CD-FEM is adopted to solve the deterministic equations. Finally the output domain statistical results are obtained, from which a method for uncertainty analysis of jointed rock mass is proposed by the coupling of random analysis and CDM-based finite element method. The uncertainty analysis of mechanical behaviour of a typical jointed rock mass under external loading is conducted by this method. The computational efficiency of the proposed method is improved to a greater extent than that of the Monte-Carlo method. The developed method can be used to analyze efficiently the uncertainty of mechanical behavior of jointed rock mass under different loading conditions.