A generalized joint pyramid method for removability analysis of rock blocks: Theoretical formulation and numerical implementation

Abstract The traditional Block Theory divides a concave block into a finite number of convex sub-blocks before the removability analysis, and deals with the removability and kinematics independently, which are computationally inefficient. This paper proposes a new concept of removable domain, based on which a generalized joint pyramid (GJP) method is established to overcome the aforementioned limitations. The translational removability analysis of convex and concave blocks can be unified through GJP based on the fact that concave regions have no contribution to the removability and can thus be omitted accordingly, avoiding partition of concave blocks into convex sub-blocks. To achieve this, joints are classified as essential joints and redundant joints. Only essential joints are considered in kinematics analysis as the block will not penetrate the rock mass when sliding along the essential joints, and its motion changes once the essential joints are altered. Thereby, the number of joint planes in the removability analysis and the number of possible motion modes that need to be assessed in the kinematics analysis can be significantly reduced. The GJP method was implemented in the stereo-analytical method and its efficiency and effectiveness in the removability and kinematics analysis of translational motion were demonstrated through some generic scenarios.