深部隧道力学分析的离散元与理论解分区耦合方法初探

离散单元法适合室内试验和局部小尺度问题的模拟，但在分析隧道开挖等大尺度问题时计算复杂且耗时.为拓展离散元在大尺度问题分析中的适用性，尝试将离散元与理论解分区耦合.针对深埋圆形隧道围岩开挖过程，采用离散元模拟内部近孔口处围岩，外部采用理论解，耦合边界上使用迭代算法，控制收敛以保证力与位移连续条件，在弹性阶段范围内对两区域进行耦合以分析解法的适用性和误差.针对隧洞有、无内压两类算例，采用该分区耦合方法经15步左右迭代收敛，所得边界位移与理论解分别相差1.86%、3.2%；所得离散元结果与理论解对比良好：位移误差随角度有关、最大处在13.5%以内，应力误差除在少量部位为15%左右外，其余各处在8.6%以内.据此表明，该方法具有相当的精度及可行性.

Preliminary study of coupled DEM-analytical method in analyses of deeply buried tunnel excavation

Distinct element method (DEM)is suitable in simulations of laboratory test and local small-scale problem.As for large scale problems including tunnel excavation,DEM simulation could be complex and time consuming.In order to expand the applicability of DEM in large scale analyses,acoupled DEM-analytical solu-tion methodis proposed.So as to study the feasibility and error of the coupled method,the excavation of a deeply buried circular tunnel is analyzed during the elastic stage.The surrounding rock which nears the tunnel is ana-lyzed by DEM,and the displacement and stresses of far field area are obtained by analytical solutions.Iteration procedure is used to ensure the continuity of stress and displacement along coupled boundary.Tunnels with and without inner-pressure are both analyzed as two cases.Generally,after 15 iterations,the difference between the resulting boundary displacement and the theoretical solution were 1.86% and 3.2% for two cases,respectively. Results of the DEM model comparing with the theoretical solution arefine:the errors of the displacement are related with the angle and the largest one is less than 13.5%;the errors of stress in some points are about 15%and the rest are within around 8.6%.It is shown that the coupled method has considerable accuracy and feasibility in mechanical analysis of tunneling.