A fully coupled numerical model within two-dimensional disk DDA framework for simulating the interaction between negative Poisson's ratio material bolts and rock masses

This paper established a fully coupled bolt numerical model within the framework of two-dimensional disk DDA (DDDA) to simulate the mechanical interaction between negative Poisson’s ratio (NPR) material bolts and rock masses. Initially, the fundamental theory and algorithm of the bolt numerical model are described, including a bolt segmentation algorithm proposed to divide a bolt into sub-bolts, derivation of the sub-matrix for a sub-bolt that is superimposed into the DDDA simultaneous equilibrium equations, and establishment of the bolt mechanical constitutive model and failure criterion based on the elongation-tension relationship obtained from NPR bolt pullout physical tests. Subsequently, a series of verification numerical simulations are carried out. The simulation results are in excellent agreement with theoretical values or physical tests, demonstrating that the proposed bolt numerical model can accurately simulate the constant-resistance large-deformation energy absorption process of NPR bolts under tension and shear, as well as their strengthening effect on fractured rock masses. Lastly, an engineering application case is presented, showing that the proposed bolt numerical model can be used to reveal complex bolt-rock mass mechanical interactions and has broad practical application prospects in rock bolting for rock engineering.