Polyurethane foam, when used as a compressible layer in deep soft rock tunnels, offers a feasible solution to reduce the support pressure on the secondary lining. The foam spraying method using sprayed polyurethane material is convenient for engineering applications; however, the compressive behaviour and feasibility of sprayed polyurethane material as a compressible layer remain unclear. To address this gap, this study conducts uniaxial compression tests and scanning electron microscope (SEM) tests to investigate the compressive behaviour of the rigid foams fabricated from a self-developed polyurethane spray material. A peridynamics model for the composite lining with a polyurethane compressible layer is then established. After validating the proposed method by comparison with two tests, a parametric study is carried out to investigate the damage evolution of the composite lining with a polyurethane compressible layer under various combinations of large deformations and compressible layer parameters. The results indicate that the polyurethane compressible layer effectively reduces the radial deformation and damage index of the secondary lining while increasing the damage susceptibility of the primary lining. The thickness of the polyurethane compressible layer significantly influences the prevention effect of large deformation-induced damage to the secondary lining within the density range of 50-100 kg/m3. In accordance with the experimental and simulation results, a simple, yet reasonable and convenient approach for determining the key parameters of the polyurethane compressible layer is proposed, along with a classification scheme for the parameters of the polyurethane compressible layer. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

The polyurethane foam (PU) compressible layer is a viable solution to the problem of damage to the secondary lining in squeezing tunnels. Nevertheless, the mechanical behaviour of the multi-layer yielding supports has not been thoroughly investigated. To fill this gap, large-scale model tests were conducted in this study. The synergistic load-bearing mechanics were analyzed using the convergenceconfinement method. Two types of multi-layer yielding supports with different thicknesses (2.5 cm, 3.75 cm and 5 cm) of PU compressible layers were investigated respectively. Digital image correlation (DIC) analysis and acoustic emission (AE) techniques were used for detecting the deformation fields and damage evolution of the multi-layer yielding supports in real-time. Results indicated that the loaddisplacement relationship of the multi-layer yielding supports could be divided into the crack initiation, crack propagation, strain-hardening, and failure stages. Compared with those of the stiff support, the toughness, deformability and ultimate load of the yielding supports were increased by an average of 225%, 61% and 32%, respectively. Additionally, the PU compressible layer is positioned between two primary linings to allow the yielding support to have greater mechanical properties. The analysis of the synergistic bearing effect suggested that the thickness of PU compressible layer and its location significantly affect the mechanical properties of the yielding supports. The use of yielding supports with a compressible layer positioned between the primary and secondary linings is recommended to mitigate the effects of high geo-stress in squeezing tunnels. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/).