Formulation of a thick beam-column element with embedded discontinues for modelling hinges in simple and double-lined tunnels

Abstract

In this paper, damage in simple and double-lined tunnels is modelled as the occurrence of hinges. Primary and secondary linings are modelled with a beam-column element with embedded discontinuities, which was derived from a variational formulation. In this element, damage is modelled as the development of hinges under flexural forces, transverse dislocations under shear forces and axial discontinuities under axial forces. This element uses constitutive models of reinforced concrete prismatic sections to include independently the capacities of the moment, shear force and axial force, based on damage mechanics. The formulated beam-column element with embedded discontinuities was calibrated with an experimental test of a simple tunnel lined reported in the literature, the numerically computed load-displacement curve was in agreement with that of the experimental test. To show the ability of the formulated element for modelling damage, numerical examples of simple and double-lined tunnels were carried out. In these numerical examples, ovalisation load vs ovalisation curves were computed, showing that maximum ovalisation load-carrying capacity in the double-lined tunnel is approximately the double than the maximum ovalisation load-carrying capacity in the single-lined tunnel, but the latter is more flexible.