Deep rock is characterised by high stress and large deformation in underground engineering. It is of great significance to investigate its mechanical properties by conducting the triaxial tests under high confining pressure and considering a residual strength. The distinct element method (DEM) is an essential numerical method for analysing the mechanical properties of rock. However

there have been many challenges in quantitatively simulating the rock by DEM in the triaxial tests. The reason is that it is challenging to quantitatively reproduce the complete stress-strain curves of rock using DEM. By considering the residual strength of rock

the triaxial compression tests on deep sandstone were quantitatively simulated by DEM using the improved three-dimensional (3D) bond model incorporating rolling and twisting resistance. The results show that this study successfully achieves the quantitative reproducing of the complete stress-strain curves. The large peak/residual internal friction angle and nonlinear strength envelope of rock are obtained as well. Meanwhile

this study overcomes three prominent challenges of the classic bonded-particle model (BPM). The relationships among the peak/residual internal friction angle

cohesion and microscopic parameters of DEM are discussed through a large number of simulations. At the same time

the high computational efficiency is proved using the improved model

which can satisfactorily meet the requirements of the 3D simulation for conventional laboratory tests.