Nonlinear Analysis of Tunneling Effects on Buildings Using Macro-Elements

The paper presents a formulation for evaluating the effects of tunneling induced displacement on existing buildings. Using the matrix condensation method, the building behavior is represented by a relatively small matrix, associated with the foundations of the superstructure. In the formulation, each foundation (with up to 6 degrees of freedom) is represented by a macro-element that captures the elasto-plastic behavior of the soil, using a yield function, a plastic flow potential, and a hardening law. The formulation includes new features that allow interaction between macro-elements, and the effects of the tunneling induced displacements. Since the solution depends on the foundations force level before tunneling (due to the soil nonlinear behavior), the construction process of the building is taken into account in the solution scheme. The formulation is used for the solution of an example problem of a tunnel excavation underneath a six story 3D frame structure. It is shown that vertical plastic displacement may increase even when there is vertical unloading of the foundation, as an outcome of the coupling between the degrees of freedom in the plastic flow potential.