隧道围岩变形及支护刚度三维分析模型研究
Three-Dimensional Analysis Model of Surrounding Rock Deformation and Support Stiffness for Tunnel Construction

鉴于既有力学模型在分析三维隧道施工力学问题时存在精度不高、计算资源要求高和计算时效不能满足工程要求等诸多困难，将隧道围岩视为半无限大或无限大弹性体，以作用于洞壁和掌子面处的等效作用力模拟隧道开挖效应，建立了一种深埋圆形隧道的三维分析模型.基于Mindlin解和Kelvin解分别推导了掌子面在洞口附近和掌子面远离洞口两种工况下围岩位移的积分计算公式，并编制了相应的计算程序，然后将待开挖介质视为"支护体"，通过刚度分析将支护反力引入力学模型，推导了围岩变形的求解方程，可以快速计算隧道围岩变形场和围岩对支护结构刚度需求的量化值.研究结果表明：两种工况下围岩位移的分布规律基本一致，掌子面距离洞口较近时，隧道纵剖面围岩轴向位移最大值的解析和数值结果分别为6.1 mm和 5.5 mm，隧道横截面掌子面处径向位移最大值分别为2.4 mm和 2.6 mm，误差分别为9.8%和8.3%；在掌子面距离洞口较远的工况下，隧道纵剖面围岩轴向位移最大值分别为6.0 mm和5.7 mm，误差为 5.0%；对于任选的一组隧道围岩和支护结构参数，考虑支护反力后计算得到的围岩纵向变形与数值分析结果吻合较好，超前位移分别为3.6 mm和3.0 mm，最终位移分别为9.1 mm和8.5 mm，误差分别为16.7%和6.6%；大岗山隧道2#压力管道的超期变形的计算结果和监测结果分别为0.4 mm和0.4 mm，最终变形分别为1.0 mm和1.1 mm，误差分别为0和10%.基于变形控制标准和新建力学模型可对围岩的刚度需求进行量化计算并指导支护结构设计参数的确定.
： In the field of analyzing 3D tunnel construction mechanics, the current mechanical models have many difficulties, including low computing accuracy, high computing resource requirements, and low computing efficiency, which can't meet the practical requirements; thus, a new analysis model of a deep-buried circular tunnel was proposed with considering the equivalent force acting on the wall and the face to simulate the excavation effect. To evaluate two cases of a tunnel face near the entrance and far from it, the integral formulae of the deformation field of the surrounding rock were derived based on the Mindlin and Kelvin solutions, respectively. The paper treated the excavation medium as "support mass" and developed the formulae of surrounding rock deformation through introducing the support force into the analysis model. According to the above formulae, the deformation field of surrounding rock and the quantitative values of its demand for the support structures might be calculated. The results show that under the two cases, the deformation distribution of the surrounding rock is basically consistent; while the face is near to the entrance, the maximum calculation and numerical results of the axial displacement of the lengthwise section are 6.1 mm and 5.5 mm, and the radial displacements at the face are 2.4 mm and 2.6 mm, and the errors are 9.8% and 8.3%, respectively. When the face is far from the entrance, the maximum calculation and numerical results of the axial displacement of the lengthwise section are 6.0 mm and 5.7 mm, respectively and the error is 5.0%; for an arbitrary set of calculation parameters of surrounding rock and supporting structures, the results of advanced displacement at the face are 3.6 mm and 3.0 mm and the results of final displacement are 9.1 mm and 8.5 mm, and the errors are 16.7% and 6.6%, respectively, showing that the calculation results of