This paper presents a deformable block modelling technique based on the Block-Spring Model (BSM) for jointed rocks. The Block-Spring Model was originally developed with an assumption that the rock blocks are rigid which is suitable for the highly jointed hard rocks under relatively low stresses. The deformable block approach presented in this paper extended the capability of the model in simulating the jointed rocks where the deformation of both the joints and the intact blocks cannot be ignored. The deformable block model is capable of simulating a wide range of weak rock structural problems. It is not only suitable for highly jointed rocks at shallow depth where the joints are major concerns, but also suitable for deep underground works where the deformation of the intact rock may also be important. The presented model is therefore a significant improvement of the original rigid block model. The new model has been verified with the closed form solutions of a circular tunnel.
The Block-Spring Model (BSM) is a numerical modelling technique for stress and deformation analysis of jointed rocks. Its theory, applications and further developments have been published since 1990 (Wang and Garga, 1990, 1993, Wang et al 1995.) In the cases where the rocks are under high stress or the intact blocks are relatively weak, the plastic behaviour and the deformation of the blocks may significantly affect the stability of the rock structure. A deformable block model based on the original rigid model has therefore been developed to account for the deformation of the rock blocks. In the deformable block model, the jointed rocks are simulated by an assemblage of blocks which can be represented by various shaped polygons. The blocks are allowed to slide or separate from each other. To simulate the deformation of the intact rock, each block is defined as a deformable element with constant strain. A first order approximation of the rock displacement is used in the construction of the stiffness matrix. The numerical solution of the rock structural deformation therefore results from the deformation of the individual blocks and that of the joints. The resulting deformable block model is capable of simulating a wide range of weak rock structural problems. It is not only suitable for loosened rocks at shallow depth where the joints are major concerns, but also for deep underground works where the deformation of the intact rock cannot be ignored. This paper presents the theory of the deformable block model and verifications of the model with the closed form solutions of a circular tunnel.
In the original Block-Spring Model, the jointed rock masses were assumed to be an assemblage of blocks discretized by the joints. The blocks were randomly shaped polygons which are in contact on the faces or corners. The blocks were assumed rigid. Hence, each block had three degrees of freedom. The displacement components of the centroid of the block were used as the degrees of freedom, i.e., the horizontal transition U.