温度–应力耦合作用下岩体裂隙扩展的数值流形方法研究

 数值流形法作为一种新型的数值计算方法已成功应用于诸多领域，但该方法在裂隙岩体多场耦合及其作用下裂隙扩展过程模拟分析上应用还较少。基于线弹性热力学理论，并考虑温度对材料影响，建立裂隙岩体温度–应力耦合控制方程。在此基础上，以温度和位移覆盖函数为基本求解量，以加权平均和算术平均思想为区域平均温度场求解算法，以修正的Mohr-Coulomb理论为岩石裂隙扩展准则，以物理覆盖为岩石破裂基本单元，提出模拟温度–应力耦合过程及其作用下岩体裂隙扩展过程的数值流形方法。该方法采用数学和物理2套覆盖，在裂隙扩展过程中不需要进行网格调整，能够有效地模拟裂隙岩体多场耦合及其作用下的裂隙扩展过程。通过编制相应MATLAB计算程序，对算例进行模拟，验证该方法的可行性和合理性。

A NUMERICAL MANIFOLD METHOD FOR FRACTURE PROPAGATION OF ROCK MASS CONSIDERING THERMO-MECHANICAL COUPLING

A new numerical method，the numerical manifold，has been used in many fields and was seldom applied to the fracture propagation of fractured rock mass under multi-field coupling. The control equations of thermo-mechanical coupling were established considering the influence of temperature on materials and based on the linear elastic theory of thermodynamics. The method of numerical manifold with the temperature and the covering function of displacements as basic unknowns，the weighted average and the arithmetic mean as the solution algorithm of average temperature，the modified Mohr-Coulomb equation as the criterion of fracture propagation of rock mass，the physical cover as the basic element of fracture propagation，was presented for simulating coupled thermo-mechanical process and fracture propagation under coupled actions. The numerical manifold method has two kinds of covers，namely the mathematical cover and the physical cover. The mathematical cover is independent of the physical domain of the problem；and its generation will not consider the number，position and orientation of the fractures，which avoids the inconvenience of mesh generation on fractured areas during the process of fracture propagation. Therefore，the proposed method is effective for simulating the processes of coupling behavior and fracture propagation. Finally，a numerical case study was conducted with the program written with MATLAB，so as to demonstrate the feasibility and soundness of the proposed method in handling the fracture propagation and coupled problems of fractured rock mass.