Upper Bound Analysis of Non-Persistent Jointed Rock Slope Using Rigid Block Element Method

Abstract

The upper bound method analyzing the stability of the non-persistent jointed rock slopes is proposed by considering rock bridge mechanical effects, which combines the upper bound theorem, the discretization technique of rigid block element and the nonlinear mathematical programming. The kinematically admissible velocity fields of non-persistent jointed rock are constructed. The non-linear mathematical programming models are established for solving the rigorous upper bound solution of ultimate load or safety coefficient by using successive linear programming algorithm. two numerical examples are performed and analyzed. The proposed method is successfully validated by comparing the simulation with those produced by other classical methods. The method has the following advantages: (1) it can simultaneously simulate the discontinuous mechanism properties of the rigid rock blocks and the continuous medium mechanism properties of the rock bridge failures. Both the tensile and shear mechanism effects of the rock bridges can be considered simultaneously; (2) comparing with the exiting numerical methods such as finite element method or discrete element method, this method can not only consider the tensile and shear effects of the rock bridges simultaneously, but also avoid the complex constitutive relationship between the rock masses and the joints. The safety factor and its corresponding failure mechanism can be obtained simultaneously; (3) comparing with the traditional rigid limit equilibrium method, this method does not need to make any assumption of the failure surfaces. The final critical failure mechanism can be directly obtained through mathematically programming method; (4) this method has the characteristics of clear concept, simple in the program composition and high computational efficiency.