Aiming at the continuous-discontinuous failure process of rock and soil materials in slope engineering

a novel deformable block discrete element method which combined spring element method(SEM) and discrete element method(DEM) together is presented. Compared with the accustomed element in traditional finite element method(FEM)

the element in SEM is described as a spring system that contained some orthogonal generalized springs. This generalized springs are defined in 3D space

which means that each spring can has two or three spring stiffness. How to determine the generalized spring stiffness for continuous material is the difficult and most important in SEM. With the triangle element as an example

the basic theory of SEM is introduced in detail. Assuming the relationship between the generalized spring deformation and the element strain

the generalized spring stiffness can be obtained directly by comparing the elastic strain energy of the element and the elastic potential energy of the spring system. The Poisson and shear stiffness coefficients were defined as system parameters to describe the relationship between different generalized springs. The SEM can consider the Poisson effect accurately for any Poisson’s ratio material; and the result using SEM are the same with using traditional FEM. This method does not need to know the expression of the element-stiffness-matrix. It can be used in 4-node element; and the stiffness expressions of springs are given clearly. With the SEM used to compute the block deformation and the contact-spring used to calculate the interaction between blocks

the combined SEM/DEM program can be used to simulate the failure process of rock and soil material from continuous to discontinuous. The SEM and DEM are combined in the motion equation of each node in each element. The contact-spring in DEM satisfied specific strength criterion. When the contact-spring force exceeded its limit

the material became discontinuous from continuous. The combined SEM/DEM program is implemented easily in the continuum-based discrete element method(CDEM) program. The simulation of a homogeneous soil slope under gravity shows that the SEM is performed as good as FEM when using line elastic constitutive and reasonable when using Mohr-Coulomb strength criterion. The simulation of a bedrock and overburden layer slope shows that the combined program is suitable to simulate the slope failure process.