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Ground surface settlement (GSS) is one of the major concerns in design and construction of a deep excavation. This paper proposes an analytical approach for the prediction of GSS induced by a braced deep excavation. Considering wall deformation and stress release, the problem investigated is formulated as a system of two second-order partial differential equations (Lame equations) with mixed boundary conditions based on the elastic theory. Taking advantage of the superposition principle, the mixed boundary conditions are decomposed into displacement and stress boundary. The separation of variables method is applied to solve the governing equations with displacement boundary, while the Fourier Transform Method is employed to derive the solution for the governing equations with stress boundary. A novel least-squares based method is proposed to transform the scatter data of wall deflection into a continuous function, which is used to determine the unknown coefficients in the solution. The validity of the proposed solution is checked by predicting the GSS of two well-documented cases and by comparing with some empirical approaches. Parametric studies are conducted to demonstrate the impact of the modulus ratio on the excavation responses.
Chen et al. (Wed,) studied this question.