Discrete Element Method Based On Coulomb Friction Damping

Soil is discontinuous medium which is composed of granules with different sizes and varied shape. As a numerical method for discontinuous medium, Discrete Element Method is perfectly suitable to solve the problems related to the granular media. Usually, viscous damping is used by DEM to dissipate the energy in the movement of granular system so as to force the calculation to be converged quickly. As a matter of fact, tangential contact force between granules accords with Coulomb friction force. In this paper, a contact model based on Coulomb damping was applied in Discrete Element Method instead of viscous damping, and relevant computational methods with Coulomb damping was developed.Firstly, the characteristics of one-dimensional vibration with Coulomb damping were analyzed. The numerical method to solve vibration with Coulomb damping was illustrated with the vibration of a block and a group of blocks on a frictional surface. As for the two-dimentioal problems, the contact model on basis of Coulomb damping was established and the corresponding computational formula of Discrete Element Method was derived. The calculational methods of the tangential friction between granules were one of difficult problems in this method. The program was compiled with c++ language. A simple example was computed to illustrate the the rationality of calculation models and feasibility of calculational methods in this paper.Compared with the traditional DEM, Discrete Element Method based on Coulomb damping has the following advantages. Firstly, Coulomb damping is able to more truely describe the tangential effects between granules. Secondly, the material coefficients in the Coulomb damping model is easier to be determined than those in conventional DEM. Moreover, there is only coefficient of normal stiffness rather than coefficient of tangential stiffness between granules in the model, which is rather convenient for determination of computational parameters.