挡墙水平变位诱发地表沉降的显式解析解

将基坑看作平面应变边值问题，借助挡墙刚性平移诱发地表沉降的基本解析解，利用微积分思想，推导得到挡墙刚性变位和柔性变位下的地表沉降显式解析解。其中，在挡墙刚性平移影响范围无穷大时，显示解析解与基本解析解形式一致。通过与挡墙刚性平移解析解和绕墙趾转动、绕墙顶转动、三角形变位、抛物线柔性变位模式等几种已有的积分形式解析解作对比，验证了显式解析解的正确性。将显式解析解应用于实际工程，通过与实测数据对比分析，对解析解的适用范围进行了探讨。当围护结构水平位移较小时，显式解析解可较好地预测墙后地表沉降；当围护结构水平位移较大时，由显式解析解计算得到的墙后地表沉降归一化曲线可偏安全地估计墙后地表沉降，说明了该显式解析解的工程实用性。

Analytical formula for ground settlement induced by horizontal movement of retaining wall

The excavation-induced settlement of soil behind retaining wall is analytically deduced based on displacement boundary problem under plain strain condition. The analytical formula of ground settlement caused by the rigid movement or parabolic flexible movement of retaining wall is derived by the fundamental solution for ground settlement caused by rigid horizontal movement of retaining wall. If the retaining wall influences infinity, the analytical formula and the fundamental solution are in the same. The fundamental solution induced by rigid horizontal movement of retaining wall is used to verify the analytical equation. The solutions of integrated form under deformation conditions of rotation with respect to bottom, rotation with respect to top, triangle-bugling movement and parabolic flexible movement are also used to verify the analytical equation, respectively. The results are in good agreement. Finally, the analytical formula is applied to prediction of measured data in the field. The extent of application is illustrated by the comparison between the analytical equation and in-situ measured data. When the wall deflection is small, the proposed analytical equation can predict settlement well. When the wall deflection is large, the normalized settlement curves derived from the analytical equation can predict settlement anywhere behind retaining wall safely. The results prove that the proposed analytical equation is practicable.