An iterative algorithm for analyzing the mechanical behavior of cracked tunnel linings considering crack-state evolution

Accurately assessing the mechanical behavior of cracked linings is essential for selecting effective rehabilitation strategies. The opening and closing states of existing cracks are highly sensitive to the lining’s stress condition, yet most existing analytical models simply treat the cracked‑section stiffness as a fixed function of initial crack depth, ignoring this stress‑dependent behavior. To address this limitation, this study proposes an iterative algorithm that dynamically couples the crack state with the evolving internal forces. The research first introduces a simplified mechanical model to quantify the nonlinear variation of flexural stiffness with respect to internal forces and initial crack depth. The model is validated through simulations of the crack opening process in four-point bending beams using the eXtended Finite Element Method (XFEM). Results confirm that flexural stiffness and bending moment exhibit a strongly nonlinear relationship, governed by both the initial crack geometry and the prevailing stress state. Subsequently, the mechanical behavior of cracked linings is investigated numerically using a beam-spring model, which integrates the proposed iterative algorithm to continuously update flexural stiffness based on the real-time crack opening state and internal force distribution. The accuracy and feasibility of the approach are verified through comparisons with model tests in terms of internal forces and deformations. This study provides a practical and mechanically consistent reference for the performance evaluation of cracked tunnel linings and demonstrates strong potential for application in structural safety assessment and maintenance decision-making.