Timoshenko beam models for the coupled analysis of building response to tunnelling

Abstract

Timoshenko beam theory and the limiting tensile strain method are implemented into the computer program ASRE for the coupled analysis of building response to tunnelling using an elastic two-stage analysis method. A framework to characterise an equivalent Timoshenko beam is proposed that is consistent with previous works. More specifically, buildings are represented through equivalent anisotropic beam models in terms of axial, shear and bending cross-sectional stiffnesses, as well as the offset between the axis and the ground surface. Firstly, model predictions are compared with centrifuge results of tunnelling-induced distortions of building models with façade openings. Then, simple beams with varying Young’s modulus to shear modulus ratios are analysed. Results detail tunnelling-induced displacements, internal forces, and deformations, as well as bending and diagonal strains of the Timoshenko beams; the way in which both axis-ground offset and shear flexibility level alter the tunnel-structure interaction mechanism was quantified. For damage assessments, an improved approach is proposed to estimate bending and diagonal strains. Finally, to enable practical implementation, design charts that relate both the relative soil-structure stiffness parameters (that account for both bending and shear contributions) and the foundation plan size ratio to the deflection ratio modification factors are given.