Strength Reduction Method for Stability Analysis of Local Discontinuous Rock Mass with Iterative Method of Partitioned Finite Element and Interface Boundary Element

Abstract

SRM (strength reduction method) with iterative method of PFE (partitioned fnite element) and IBE (interface boundary element) is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.

A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis

“…The stability analysis of a rock slope containing a symmetrical wedge is a classic three-dimensional limit equilibrium problem, which is often used to verify the correctness and rationality of a new numerical method. Hoek [37] and Li [27] have solved this problem using different methods. The overall model is a homogeneous rock slope composed of bedrock and a symmetric wedge, as shown in Figure 10.…”

“…The PFE-IE method absorbs the advantages of FEM, DEM, and DDA and partitions the large-scale model with structural discontinuity and nonlinear mechanical properties so that each region can be solved independently and the solution speed can be improved. Moreover, the PFE-IE method can conveniently calculate the stability safety factor of rock slopes with the SRM [27].…”

A fast local nonlinear solution technique based on the partitioned finite element and interface element method

“…If the contact surface material is not considered, the contact can be regarded as an ideal spring, and the force‐displacement relation between the node pair across the contact surface is ensured within a reasonable range by adding two spring stiffnesses in the normal and tangential directions. If the contact surface material strength is considered, 27 when the structural surface is in a continuous state, the appropriate normal contact stiffness and tangential stiffness can be selected. The stiffness matrix is expressed as: where is taken as 500–1000 in the case of a discontinuous medium and can be chosen as in accordance with the equivalent uniaxial compressive deformation when the measured elastic modulus and thickness are known for the structural surface.…”

“…If the contact surface material is not considered, the contact can be regarded as an ideal spring, and the force-displacement relation between the node pair across the contact surface is ensured within a reasonable range by adding two spring stiffnesses in the normal and tangential directions. If the contact surface material strength is considered, 27 when the structural surface is in a continuous state, the appropriate normal contact stiffness k 𝜉 and tangential stiffness k 𝜂 can be selected. The stiffness matrix is expressed as:…”

A PFE/IE – SPH joint approach to model landslides from initiation to propagation

“…An interactive method, called partitioned finite elements and interface elements (PFE/IE), has been developed by Li et al [29] specifically for the analysis of stability in local discontinuous problems. The applicability of PFE/IE in the analysis of slope stability in both static and dynamic problems was subsequently proven in references [30,31].…”