# Stability and Force Chain Characteristics of \"Inclined Step Cutting Body\" in Stope
## 2 Materials and Methods
### Numerical Simulation of Mining Working Face in the Study Area  
#### 2.3.1 Characteristics and Principle of Particle Flow Code Method  
The overlying strata movement and deformation caused by coal mining is a large deformation problem. The main popular methods to solve this problem are SPH [18], DEM [19], MPM [20; 21; 22], FEM [23], PFC [28; 29; 30] and so on. SPH (Smoothed Particle Hydrodynamics) is a meshless method developed over the past 20 years. This method describes the continuous fluid (or solid) with an interacting particle group. By solving the dynamic equation of the particle group and tracking the trajectory of each particle, the mechanical behavior of the whole system is obtained, which is suitable for solving the dynamic large deformation problem. DEM (Discrete Element Method) is another powerful numerical method which is used to analyze the dynamic problems of a material system after finite element method and computational fluid dynamics (CFD). The method regards the jointed rock mass as being composed of discrete rock blocks and joint surfaces between rock blocks, which can simulate the nonlinear large deformation characteristics of jointed rock mass more realistically. MPM (material point method) is a new calculation method which combines the Euler method and the Lagrange method. By mapping the information onto the material point to the node of the background grid using the shape function, the large deformation problem is simulated. FEM (Finite Element Method), also known as the finite element method, is used to solve the mechanical problems of a continuum by dispersing the continuum into a set of finite-size elements. PFC (Particle Flow Code) is a discrete element method to simulate the interaction and motion between particles. Different from the method based on continuum mechanics, particle flow theory connects the microscopic mechanical properties and macroscopic mechanical properties of particles, and can reflect the macroscopic state of particles through interaction, which makes the process and results of numerical simulation closer to the real mechanical behavior. Initially, this method is a tool for studying the properties of granular media. It uses the numerical method to divide the object into hundreds of representative particle elements, and expects to use the local simulation results to study the constitutive model of the continuous calculation of boundary value problems. With the development of computer technology, it is possible to simulate practical problems with the particle model. Therefore, particle flow becomes an effective way to solve practical problems [28; 29; 30]. This paper uses PFC2D 5.0, a computing software developed by Itasca, USA, to study the analysis of granular particles or systems that can be simplified into granular particles. At present, the software consists of two modules: 2D (PFC2D) and 3D (PFC3D). This study adopts the two-dimensional version. The numerical calculation model established by PFC is a bonded particle model, which is composed of multiple particles. Under the action of stress, the interaction between particles makes the relative position change, so that this method can simulate the dynamic evolution process of cracks. The main steps of numerical simulation with the particle flow method are: defining simulation object--establishing the simplified model--supplementing the data of the simulation problem--running the calculation model [28; 29; 30]. Different from the traditional numerical simulation method, the model established by PFC is dominated by the microscopic properties of particles, which have the characteristics of high efficiency and the blocks formed by particles will not be separated from each other due to failure. The numerical calculation model established by PFC does not need to be meshed as with the finite element method. Therefore, in the simulation calculation, the following assumptions need to be made:  
1. The basic elements of the particle flow numerical model are spherical or disc-shaped and are rigid bodies;
2.