中文摘要：

提出了考虑颗粒摩擦系数空间变异性的砂土双轴剪切响应分析方法。采用随机场模型表征颗粒摩擦系数空间变异性，通过Karhunen-Loeve展开方法离散接触摩擦系数随机场，编写了基于颗粒流程序PFC^2D和MATLAB的随机模拟耦合分析程序。研究了摩擦系数空间变异性对密砂试样的双轴剪切响应影响规律。结果表明：1）提出方法可有效地考虑颗粒间接触摩擦系数变异性对土体材料双轴压缩宏观力学行为影响；2）密砂试样在剪切过程中的应力-应变关系曲线、体积-应变关系曲线的变化规律与颗粒间接触摩擦系数不确定性密切相关，在初始加载阶段随机模拟的偏应力曲线、体积应变曲线基本重合，继续加载后曲线开始发散；3）垂直相关距离对峰值偏应力均值与标准差影响明显大于水平相关距离。颗粒接触摩擦系数的均值对峰值偏应力的影响大于摩擦系数空间分布的影响。摩擦系数的空间分布会影响剪切带的形成位置。

英文摘要：

This study proposed a method for biaxial compression numerical simulation considering a spatially variable inter-particle friction coefficient. A random field model is employed to represent the spatial variability of an inter-particle friction coefficient. The Karhunen-Loeve （K-L） expansion method is used to discretize the random field of inter-particle friction. A computer program that combines the discrete element method with random simulations is developed in Matlab. The effects of a spatially variable inter-particle friction coefficient on the shear responses of dense sand specimens are investigated. The results indicate that the proposed method can effectively evaluate the influences of the spatial variability of an inter-particle friction coefficient on the macro-mechanical behaviors of particle material. The uncertainty of the inter-particle friction coefficient has a substantial effect on the evolution of deviator stress and volumetric strain during biaxial compression. The stochastic response curves are identical with each other at the initial loading and begin to vary with the constant loading for the dense sand specimen. In addition, it is shown that the correlation distance in the vertical direction has a more significant influence on the mean values and standard deviation values of peak deviator stress than that in the horizontal direction. The local average values of the inter-particle friction in the domain of the specimen has a more prominent effect than that of the space distribution of the inter-particle friction. However, the space distribution of the inter-particle friction affects the locations of the shear bands significantly.