Chinese Science Bulletin © 2009 SCIENCE IN CHINA PRESS CONDENSED MATTER PHYSICS Citation: Liu S H, Yao Y P, Sun Q C, et al. Microscopic study on stress-strain relation of granular materials. Chinese Sci Bull, 2009, 54: 4349―4357, doi: 10.1007/ s11434-009-0599-z SPECIAL TOPIC ARTICLES Microscopic study on stress-strain relation of granular materials LIU SiHong 1† , YAO YangPing 2 , SUN QiCheng 3 , LI TieJun 1 & LIU MinZhi 1 1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; 2 Department of Civil Engineering, Beihang University, Beijing 100191, China; 3 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China A biaxial shearing test on granular materials is numerically simulated by distinct element method (DEM). The evolution of the microstructures of granular materials during isotropic compression and shearing is investigated, on which a yield function is derived. The new yield function has a similar form as the one used in the modified Cam-clay model and explains the yield characteristics of granular materials under the isotropic compression and shear process through the change of the contact distribution N(θ) defining the contacts at particle contact angle θ. DEM, granular materials, yield surface, microstructure Granular materials, like sands, consist of particles and surrounding voids. The macro-mechanical behavior of granular materials is therefore inherently related not on- ly to the distinct particles constituted, but also to its in- ner microstructures reflecting how distinct particles are arranged in space. In the past decades, great efforts have been devoted to study the macroscopic mechanics beha- vior of granular materials in terms of its microstructures. For example, Oda [1] studied the particle contact normals of sand samples after triaxial compression tests, and found that the frequency distribution of particle contact normals concentrates on the direction of the major prin- ciple stress during shearing. Matsuoka [2] carried out di- rect shear tests on assemblies of both photoelastic and aluminum rods, on which a stress-shear dilatancy equa- tion was derived from the frequency distribution of par- ticle contacts on the mobilized plane. Wang et al. [3] stu- died the development of the stress self-organizing process during the outbreak of slope debris flows and the critical properties of the clayey debris transmission, so as to reveal the mechanism of the debris flows and forecast debris flows. On the hypothesis of the unsatu- rated soil mechanics and the theory of multiphase por- ous media, Zhao and Zhang [4] gave an expression for the total deformation work and proposed a formula of the effective stress in unsaturated soil. Zhen and Jin [5] estab- lished a material model for particulate materials to cha- racterize the cyclical distribution of the elastic modulus and the thermal expansion coefficient in space, by taking the thermal stress distribution and the particle interaction into account. Experiments and theoretical analysis have been two main approaches for studying the mechanical behaviors of granular materials in early times. As granular mate- rials consist of particles, it is more realistic to study their mechanical behaviors if we use distinct element ap- proaches in which the particle arrangement is modeled explicitly. Recent distinct element approaches started with the distinct element method (DEM) that was first developed by Cundall (1971) for rock mass problems and later applied to granular materials by Cundall and Strack [6] . DEM can provide sufficient model microme- chanical data such as the displacement of individual par- ticles, contact orientations, contact forces and mobilized Received June 16, 2009; accepted August 13, 2009 doi: 10.1007/s11434-009-0599-z † Corresponding author (email: sihongliu@hhu.edu.cn) Supported by the National Natural Science Foundation of China (Grant Nos. 10672050, 10872016)