Analytical study on multiple-mode deformation behaviors of tunnels subjected to asymmetric loading in composite strata

Underground tunnels subjected to asymmetric load or ground conditions are susceptible to experiencing uneven longitudinal bending, shearing, and torsional deformations, which further induce cross sectional flattening and warping. The intrinsic damages caused by multiple deformation modes are critical for tunnel health and safety but have long been neglected in practice. In the paper, a three-dimensional analytical model for soil–tunnel interactions was proposed with multiple-mode deformations incorporated, where the tunnel is assumed as a thin-walled pipe resting on an elastic foundation with five deformation modes: bending, shearing, torsion, warping, and flattening. Besides, a three-dimensional variable soil spring model was adopted, accounting for the strata discontinuities in longitudinal and transverse directions. A finite element solution for the proposed model was derived under arbitrary external loads using the principle of minimum potential energy. The validity of the proposed model was substantiated through three case studies. Based on the model, the coupling relationship of tunnel structure in transverse and longitudinal directions was revealed. Furthermore, parametric analysis was conducted to reveal the impact of tunnel width-to-thickness ratio, soil resistance coefficient, and composite strata on tunnel behaviors. These results significantly contribute to a deeper understanding of the intricate behaviors of tunnels, offering potential advancements for improved tunnel design methodologies.