裂隙岩体温度场数值流形方法初步研究  

Preliminary research on numerical manifold method for temperature field of fractured rock mass

作　　者：刘泉声[1] 刘学伟[1] 

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北武汉430071

出　　处：《岩土工程学报》2013年第4期635-642,共8页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金重点项目(41130742);中国科学院重点部署项目(KZZD-EW-05-03)

摘　　要：基于三角形有限覆盖数值流形理论,提出了裂隙岩体二维不稳定温度场求解的数值流形方法(NMM),并推导了第一类温度边界条件处理的罚方法,给出了计算格式。数值流形方法采用两套覆盖,其中数学覆盖独立于求解区域,生成数学覆盖时不用考虑裂隙数量、位置和方向,避免了常规方法处理裂隙处网格划分的不便。对于裂隙岩体,裂隙两侧对应不同流形单元,可以实现温度的不连续模拟。裂隙作为内部流形单元或外部边界条件叠加进入到温度场的总体求解矩阵中,实现了裂隙岩体温度场的数值流形求解。该方法具有较高精度,且能求解任意多条裂隙的岩体温度场问题。最后对部分文献算例进行计算,结果具有较好的一致性。A numerical manifold method （NMM） for 2-dimentional unsteady temperature field of fractured rock mass is proposed based on NMM for triangle finite covers. Furthermore, the penalty method for the first temperature boundary condition is proposed and calculating format is provided. NMM has two kinds of covers, namely mathematical cover and 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 can avoid the inconvenience of mesh generation on fractured areas. The two sides of the fracture have different manifold elements, and as a result, temperature discontinuity across the crack surface is achieved. Considering the fractures as the internal manifold elements or boundary conditions, which will affect the global governing equations lastly, the temperature field of fractured rock mass can therefore be solved by using NMM The proposed method is featured in high accuracy and has the possibility of solving the temperature problem of fractured rock mass which contains arbitrary discontinuous segments. Finally, the examples from literatures show that the results are consistent with those of the general methods.

关 键 词：岩石力学 不稳定温度场 裂隙岩体 数值流形 

分 类 号：O342[理学—固体力学]