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本文把开挖引起的地表移动看成是层间既满足力学平衡条件又满足几何接触条件的多层层状弹性介质的弹性力学平面问题。其四周边界条件为:上部为自由的地层表面,下部为开挖造成的附加位移,而左右两侧在无限远处开挖所造成的影响为零。文章通过富氏积分变换和反演公式,求得了这一边值问题在滑动接触和弹性接触状态下的解析解,并给出了数值计算的计算机程序。数值计算结果与现场实测数据的对比表明,滑动接触模型是令人满意的。从而为计算开挖造成的地表移动提供了一种新的既简便又经济的方法。
In this paper, the surface movement caused by excavation is regarded as the elastic mechanics plane problem of multilayered elastic media which meets the mechanical equilibrium conditions and meets the geometric contact conditions. The surrounding conditions are: the upper part is a free surface of the strata, the lower part is additional displacement caused by excavation, and the effect of excavation on the left and right sides at infinity is zero. In this paper, the analytic solution of this boundary value problem under sliding contact and elastic contact condition is obtained by Fourier’s integral transform and inversion formula, and the computer program of numerical calculation is given. Comparing the numerical results with the field data shows that the sliding contact model is satisfactory. Thus providing a new simple and economical method of calculating surface movement caused by excavation.