Numerical Simulation of Mechanical Characteristics and Safety Performance for Pre-Cracked Tunnel Lining with the Extended Finite Element Method

The service performance of tunnel lining is affected by crack properties and development states. In this paper, numerical simulation models were established to investigate the mechanics characteristics and safety performance for lining structures under different cracks based on the extended finite element method (XFEM). Analyze multiple quantitative factors in simulation, including changes in crack location, crack length, and crack distribution range in the lining structure. The axial force and bending moment of the preset cracks in the lining structures were first studied. The maximum safety factor attenuation rate (Dkmax) was proposed to analyze the impact of longitudinal and annular cracks on the safety performance. The axial force at the vault of the lining arch is the most significantly affected by the combined longitudinal cracks at multiple locations. When the length of a longitudinal crack increases from 1 m to 6 m, the axial force value at the crack point decreases by 33.77%, 36.15%, and 11.32%. However, the bending moment value increases by 4.47 times, 2.50 times, and 1.69 times. Under the influence of longitudinal cracks in an “arch crown + arch shoulder”, “arch crown + arch waist”, and “arch crown + arch shoulder + arch waist”, the axial force in the arch vault increased by 21.55%, decreased by 17.52%, and decreased by 13.45%. The distribution pattern of the bending moment under the influence of circumferential cracks shows convexity at the arch shoulder and arch foot, and concavity at the arch waist and side walls. The safety factor scatter curve with longitudinal cracks shows a gradual transition from a “W” shape to a “U” shape. The safety factor curve with circumferential cracks presents an approximately symmetrical wave-shaped distribution.