## 1 Introduction  
A rock mass not only contains intact rock but also discontinuous structural planes. The rock mass mechanical properties are controlled by both the rock and the structural planes, often showing the characteristics of non-uniformity, discontinuity, anisotropy and multiple phases [1, 2, 3, 4]. The existence of structural planes greatly weakens the mechanical properties and stability of a rock mass. The deformation and strength properties of discontinuity often play a controlling role in the deformation and stability of a rock mass [5, 6, 7]. A large number of facts show that the instability of geotechnical engineering takes the crack expansion inside a rock mass as the breakthrough point, causing large deformation and displacement of the rock mass and leading to the occurrence of disasters and accidents (p. 1, [8]). Consequently, it is very significant to research the initiation, propagation and connection of fissuring in rock mass to reveal the failure mechanism of rock masses and to evaluate the safety and reliability of geotechnical engineering (pp. 1-2, [8]), [9, 10, 11, 12]. In practical engineering, it is difficult to obtain an analytical solution owing to the heterogeneity of rock mass, the nonlinear constitutive relationship of rock mass, the discontinuity caused by discontinuities of rock mass and the complexity of boundary conditions, and the approximate solution can only be obtained by numerical analysis (pp. 206-208, [13]), therefore, numerical simulation and digital rock technology are playing increasingly important rolesin the study of rock properties, and many scholars have obtained important conclusions by using these methods [14; 15; 16; 17]. The deformation and failure of rock masses occur through discontinuous deformation. A discontinuous numerical method--discontinuous deformation analysis (DDA)--which can fully consider the discontinuity of a rock mass has been proposed and can be used to simulate the discontinuous deformation and large displacement motion of massive rock masses [18; 19]. Based on the DDA method, an analysis method for the failure process of discontinuous jointed rock masses--discontinuous deformation analysis for rock failure (DDARF)--has been constructed and can be used to simulate the entire process of crack initiation, expansion, convergence and connection in jointed rock masses, opening up a new way to simulate the entire failure process of rock masses (p. 132, [8]), [11; 20]. In numerical simulation, as the number of grids in the model increases, the accuracy of calculation increases, but the efficiency of calculation decreases [9; 21; 22; 23; 24]. However, the DDARF program can only generate uniform grids in the process of establishing the model. In order to achieve the calculation accuracy requirements, DDARF needs to generate a large number of grids, which not only increases the amount of calculation required but also reduces computational efficiency and can even sometimes lead to the failure of the calculations. These characteristics of DDARF limit its use in large-scale geotechnical engineering [25; 26]. In order to balance the accuracy and efficiency of calculation, the authors optimized the grid generation of DDARF so that it could generate heterogeneous grids; dense grids were generated at the preset joints, and sparse grids were generated far away from the preset joints, which not only ensured the accuracy of calculation but also improved the efficiency of calculation. The DDARF method is based on the improved DDA method, which is used to solve the failure problem of the discontinuous jointed rock mass. In this method, the computational region is automatically divided into triangular block elements by the traveling wave method, and the block boundary is divided into the real joint boundary and virtual joint boundary. For all joints in the model, they are defined as virtual joints when they fail to reach the fracture failure criterion.