Nonlinear elasto-plastic formulation for tunneling effects on superstructures

The paper presents a formulation for evaluating the effect of tunneling on existing buildings. The formulation involves the matrix condensation method to represent the response of a linear elastic building and macro-elements to represent the nonlinear elasto-plastic soil behavior. The formulation includes new features that allow interaction between macro-elements, both through the soil continuum and the structure, to result in the final displacements of the foundations due to tunneling. One of the advantages of the formulation is its ability to incorporate a general input of a greenfield field displacement for the interaction analysis, allowing consideration of various tunneling scenarios. The formulation is evaluated by a comparison to a continuum based solution obtained using the finite difference method. The formulation is then used to conduct a parametric analysis of tunneling-soil-superstructure interaction, considering three different approaches: (1) the suggested elasto-plastic formulation, (2) purely elastic analysis, and (3) simplified analysis in which the foundations are forced to displace as the greenfield. It is shown that the vertical settlements of the foundations, due to tunneling, are the greatest when the first approach is considered. This is an outcome of the combined vertical and horizontal yielding, depicted in the formulation by the coupled yield function and plastic flow potential. Yet damage, which relates to differential settlement, appears to be smaller in the elasto-plastic formulation.