To rationalize the setting of joint parameters, model size, and initial value of vertical stress in simulation of mining of steeply inclined coal seams, a fault tree analysis method of discrete element numerical simulation was used and a mathematical model was proposed. A method of eliminating the influences of size-effect errors on the parameters of coal and rock samples was obtained based on previous work. Furthermore, the constitutive equation and eigenvalue determination formula of a joint discontinuity surface were established, and a method of determination of the joint parameters was proposed, forming the complete “coupling chain” between parameters for numerical simulation. In addition, a formula for the initial value of vertical stress was constructed by way of the compression and shear model of the element body. Also, the minimum dimension was determined by means of strength factor analysis of fracture mechanics. Taking the research literature as an example, the model size and initial value of vertical stress were calculated. On this basis, the physical parameters of coal samples, the physical parameters of coal rocks considering the influence of the size effect and the calculated coal rock joint parameters considering the influence of size effect were directly used to comparatively analyze the displacement and stress fields, thus verifying the reasonability and correctness of the mathematical model.

为了合理设置急倾斜煤层开采模拟中的节点参数、模型尺寸和竖向应力初始值，采用离散元数值模拟的故障树分析方法，建立了数学模型。在前人工作的基础上，提出了一种消除尺寸效应误差对煤岩样品参数影响的方法。进一步建立了关节间断面的本构方程和特征值确定公式，提出了关节参数的确定方法，形成了数值模拟参数之间完整的“耦合链”。另外，根据单元体的压缩和剪切模型，建立了竖向应力初始值的计算公式。此外，最小尺寸是通过断裂力学强度因子分析确定的。以研究文献为例，计算了模型尺寸和竖向应力初始值。在此基础上，直接利用煤样物性参数、考虑尺寸效应影响的煤岩物性参数以及计算得到的考虑尺寸效应影响的煤岩节理参数，对位移场和应力场进行对比分析，从而验证数学模型的合理性和正确性。