大尺度基岩抗剪强度的有限元随机模拟与理论公式研究

Finite Element Random Simulation Analysis and Theoretical Formulas Research on the Shear Strength of Large-scale Rock Mass

从能反映小尺度力学性质空间变异性的随机场出发,并借助现代物理学逾渗临界理论,通过结合弹塑性有限元与随机模拟两种方法,研究了同一地质单元内的大尺度基岩整体屈服时的临界屈服条件及屈服概率,并以此为基础推导了用有限个小尺度岩体试块抗剪试验结果确定大尺度基岩宏观抗剪强度的理论公式。然后对岩体宏观抗剪强度的理论公式值与有限元随机模拟值进行了对比分析。最后探讨了小尺度摩擦系数和黏聚力的不同概率分布类型,以及弹性模量和泊松比的随机性对大尺度基岩宏观抗剪强度的影响。研究结果表明:岩体宏观抗剪强度的理论公式值与有限元随机模拟值基本一致,且大尺度基岩发生整体屈服时的小尺度岩体的屈服比例为2/3。通过对比计算分析,在小尺度材料参数实际可能变异的范围内,小尺度摩擦系数和黏聚力服从的概率分布类型,以及弹性模量和泊松比的随机性对宏观抗剪强度的影响都不大。

Based on the random fields of small-scale rock mechanical parameters and the critical theory of percolation of modern physics,this paper studies the critical yield condition and probability of large-scale rock mass in the same geological unit by finite element random simulation method. Then the theoretical formulas of the macroscopic shear strength of large-scale rock mass are deduced,which just need a finite group of shear strength test results gained by small specimens. And results of such theoretical formulas are compared with the finite element random simulation. Finally,the different probability distribution types of small-scale friction coefficient and cohesion,and the influence of randomness of elastic modulus and Poisson’s ratio on macroscopic shear strength of large-scale rock mass are discussed. The results show that the theoretical formulas of the macroscopic shear strength of the rock mass agrees with the value of finite element random simulation,and the yield ratio of small-scale rock mass is 2/3 when the large-scale rock mass start to yield as a whole. Through comparative calculation and analysis,the probability distribution types of small-scale friction coefficient and cohesion,and the randomness of the elastic modulus and Poisson’s ratio have little influence on macroscopic shear strength in the range of the actual variation of the parameters of the small-scale materials.