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对于浅埋隧道施工引起土层位移的解析解,其边界条件的数学处理上比较困难,因此实际工程的应用中受到限制。为解决这一缺陷,基于弹性力学的Airy应力函数,将半无限平面内土体的应力及位移分布转化为解析函数。然后,采用边界配点的方法,控制地表处的应力边界条件(σy=0,τxy=0)及隧道周边土体的位移边界条件(ur=-u0,uθ=0)。最后,采用最小二乘法,确定土体应力及位移函数的各项系数,求得浅埋隧道在周边土体产生径向位移的作用下,地表及深层土体位移的半数值半解析解。算例分析表明,该方法可以考虑任意荷载及位移作用的边界条件,能够充分发挥解析法和数值法两者的优点,且计算结果与实测结果较吻合,在预测地表及深层土层位移中具有一定的实用价值,可为进一步采取工程措施控制地层变形提供理论依据。
For the analytic solution of soil displacement caused by the construction of shallow tunnel, the mathematical treatment of the boundary conditions is more difficult, so the practical engineering application is limited. In order to solve this problem, based on the Airy stress function of elastic mechanics, the stress and displacement distribution of soil in semi-infinite plane are transformed into analytic functions. Then, the boundary conditions are used to control the stress boundary conditions (σy = 0, τxy = 0) and the displacement boundary conditions (ur = -u0, uθ = 0) of the soil surrounding the tunnel. Finally, using the least square method, the coefficients of soil stress and displacement function are determined, and the semi-numerical solution of the displacement of the soil surface and deep soil under semi-analytical solution of the radial displacement of the surrounding soil is obtained. The case study shows that this method can consider the boundary conditions of arbitrary load and displacement, and can give full play to the advantages of both analytic method and numerical method. The calculated results are in good agreement with the measured ones, A certain practical value, can provide theoretical basis for further engineering measures to control formation deformation.