Damage mechanism modelling of shield tunnel with longitudinal differential deformation based on elastoplastic damage model

Shield tunnels with great longitudinal differential deformations will adversely affect the service performance and optional safety of the metro system. Previous studies on the longitudinal mechanical behavior of shield tunnel are mostly carried out within the framework of elastic or elastic-plastic theory. However, assuming the concrete as elastoplastic body cannot properly reflect its nonlinear mechanical characteristics such as strain softening, stiffness degradation, etc., while damage or crack inevitably occurs when shield tunnel suffers large deformations. Therefore, the nonlinear damage characteristics of concrete material are considered in this paper, a novel positive/negative decomposition of stress tensor in energy norm is introduced herein to consider the asymmetric tensile/compressive material behavior of concrete, and a bi-scalar damage constitutive model of concrete is developed in turn. Then, to investigate the damage and degradation mechanisms of shield tunnel with differential deformation, the 3D discontinuous contact model is employed to develop the elaborate tunnel-soil numerical model. Results show that when shield tunnel suffers differential deformation, tensile damage dominates while compressive damage is minor, additional shear force and bending moment are induced, the ovality of tunnel cross section and serviceability also vary along the longitudinal direction. The damage and degradation of concrete material will reduce the tunnel integral stiffness and attenuate its ability to resist longitudinal and circumferential deformation. Besides, the segmental rebar is hard to yield, while the longitudinal coupling bolts on the lower half of tunnel segments with large deformation are inclined to yield. It should be noted that, the segmental rings near the inflection point of longitudinal deformation profile are most severely damaged, and exhibit the largest convergence deformation and lowest serviceability, where special attentions should be paid.