Acquisition of normal contact stiffness and its influence on rock crack propagation for the combined finite-discrete element method (FDEM)

The combined finite-discrete element method (FDEM) has been widely used in numerical studies in the fields of rock mechanics and geotechnical engineering. The normal contact stiffness between triangular elements is an important influencing parameter, but there is currently no effective method of measuring it. First, an equation for normal contact stiffness is proposed (Pb = αPf, where Pb is the basic stiffness, α is the coefficient, and Pf is the joint penalty; the specific stiffness of each contact couple is determined by Pb and the geometric sizes of the triangular elements together); then, the compression-shear failure of a single joint element is used to study the value range and robustness of α; finally, uniaxial compression and tunnel excavation simulations are used to study the influence of different α values on rock crack propagation. The study results show that (1) an α value of 0.1448 is optimal and robust for a single joint element simulation and is therefore suitable for all simulation conditions; in other words, the value of α should not be too low to avoid decreasing the rock mass stiffness of existing natural fractures and deviating from the actual situation; in addition, the value of α should also not be too large to avoid the development of additional cracks, especially for hard rock simulation, in which the value of α is more sensitive; and (2) the crack topologies of the surrounding rock obtained by tunnel excavation simulation with a large α value deviate from the actual rock core (i.e., when α = 0.1448, the simulation results coincide well with the actual fractures). Through this study, the reliability of FDEM numerical simulation results is improved.