A closed form shape function describing 3D settlement field around a deep excavation in sand

Soil movements produced around deep excavations are one of the main issues to be addressed during design and construction of underground structures in urban environment. Several methods to predict ground movements are currently available. Semi-empirical methods correlate displacements and simple geometrical features of the excavation; these methods predict separately transversal and longitudinal settlement troughs or at least provide a conservative envelope of them and they are mainly based on empirical data of excavations in clay. Numerical methods based on the solutions of FEM or DFM models usually provide prediction of the green field subsidence. In this paper existing 2D semi-empirical methods are first shortly reviewed. Some of these methods are then modified and combined into a new 3D analytical description of the subsidence trough around a deep excavation. The proposed two variable subsidence function depends on several parameters: four independent parameters defining the overall shape and the maximum settlement acting as a scale parameter. Settlement fields reproduced by a 3D FEM nonlinear parametric study of deep excavations inspired by real case studies are thus presented and discussed. The newly proposed 3D analytical description is applied to fit the FEM results and some fundamental relationships among geometrical features of the excavation pit and the 3D shape function parameters are identified. These relationships are validated via the application to three case studies of deep excavations in sand where the subsidence was controlled by the deformation of the retaining structures finding a satisfactory and encouraging agreement.