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模型范围是影响数值分析计算精度与效率的重要因素,针对深埋隧洞开挖数值模拟分析问题,采用有限差分软件FLAC~(3D)和复合失稳准则,对计算模型的纵向范围取值问题展开研究。首先分析了深埋隧洞开挖过程中围岩纵向变形以及未开挖岩塞对围岩变形的约束作用,然后研究了近端边界和远端边界对监测断面位置处围岩变形的影响,最后采用最小二乘法对多组计算结果进行了位移误差分析,并给出了纵向模型范围的取值建议。研究结果表明,当监测断面距掌子面大于10倍洞径时,未开挖岩塞的约束作用基本消失;远端边界以及近端边界与监测断面的最大位移误差值之间均基本满足幂函数关系,且远端边界对监测点位移误差的影响要大于近端边界;深埋隧洞开挖数值模拟中,纵向模型范围取7.5倍洞径即可满足一般数值分析的精度要求。
The range of the model is an important factor that affects the accuracy and efficiency of numerical analysis. According to the numerical simulation analysis of deep tunnel excavation, the finite-difference software FLAC (3D) and composite instability criterion are used to solve the problem of calculating the longitudinal range of the model the study. Firstly, the longitudinal deformation of surrounding rock during excavation of deep tunnel and the restraint effect of the un-excavated rock plug on the surrounding rock deformation are analyzed. Then, the influence of proximal boundary and distal boundary on the deformation of surrounding rock at monitoring section is studied. Finally, The least square method was used to analyze the displacement error of multiple sets of calculation results, and the suggestions of the value of the longitudinal model range were given. The results show that when the monitoring section is greater than 10 times the diameter of the tunnel face, the constraint of the un-excavated rock plug basically disappears. The maximum displacement error between the far boundary and the near boundary and the monitoring section basically satisfy the power Function, and the influence of the remote boundary on the displacement error of the monitoring point is greater than that of the near boundary. In the numerical simulation of deep-hole tunnel excavation, the range of the longitudinal model is 7.5 times the diameter to meet the accuracy requirements of general numerical analysis.