关键词: 连续损伤模型, 随机分析, 概率配点法, 随机场, Karhunen-Loeve展开

Abstract: 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.

Key words: continuum damage model, stochastic analysis, probabilistic collocation method, random field, Karhunen-Loeve expansion