CAJ | 학술논문

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。
수치류형법작위일충신형적수치계산방법이성공응용우제다영역，단해방법재렬극암체다장우합급기작용하렬극확전과정모의분석상응용환교소。기우선탄성열역학이론，병고필온도대재료영향，건립렬극암체온도-응력우합공제방정。재차기출상，이온도화위이복개함수위기본구해량，이가권평균화산술평균사상위구역평균온도장구해산법，이수정적 Mohr-Coulomb 이론위암석렬극확전준칙，이물리복개위암석파렬기본단원，제출모의온도-응력우합과정급기작용하암체렬극확전과정적수치류형방법。해방법채용수학화물리2투복개，재렬극확전과정중불수요진행망격조정，능구유효지모의렬극암체다장우합급기작용하적렬극확전과정。통과편제상응MATLAB계산정서，대산례진행모의，험증해방법적가행성화합이성。
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.