A pragmatic modelling framework for long-term deformation analyses of urban tunnel under multi-source cyclic loads

Current numerical modelling frameworks face challenges in producing long-term deformations of urban tunnel, mainly due to unaffordable time cost in capturing cycling process of high-frequency load using constitutive models purely based on elastoplastic theory. To resolve this problem, a pragmatic framework was proposed by integrating the thermo-hydro-mechanical governing equations and empirical constitutive equations, which can accommodate the influences of multi-source cyclic loads. The framework relies on the assumptions of separability between yielding-induced and cycle-induced plastic strain and the decoupling of different cyclic loads. Moreover, representative static load is used to substitute the high-frequency load, in order to reconcile the frequency disparity among different loads, and state variables are updated iteratively under such a hybrid loading condition to calculate the cycle-induced plastic strain. The framework was validated against the 8-year monitoring data of an urban tunnel in soft soil from Nanjing Metro Line 2. Numerical results under combined thermo-mechanical loads from seasonal temperature variation and train operation closely matched with the field results, with minor discrepancies attributed to hydraulic cyclic load omitted. With this framework, long-term deformation characteristics of urban tunnel were further examined under such combined loads, and sensitivity analyses were performed by varying the parameters associated with cyclic loads and thermo-hydraulic properties of soil and lining. Numerical results reveal the importance of thermal cyclic load in transforming the morphologies of ground settlement and lining deformation and offer quantitative insights into mitigate the long-term deformation of urban tunnel from the relative importance comparison among the parameters.