Abstract: The application of buffer layer provides an effective solution to the problem of secondary lining failure. Different buffer layer materials exhibit significant variations in mechanical properties, making it essential to establish a widely applicable theoretical model. For this purpose, this study firstly divides the nonlinear compressive stress-strain curve of buffer layer materials into n deformation stages, and the deformation characteristic of each stage is described by replacing with a straight line. Secondly, an interaction mechanical model between rheological surrounding rock and support considering the effect of the buffer layer is established. By using the deformation coordination in both the surrounding rock-buffer layer interface and the buffer layer-secondary lining interface during the whole interaction process, analytical solutions for tunnel displacement and contact pressures at different interfaces during various deformation stages of buffer layer materials are presented. Furthermore, the effectiveness of the proposed theoretical model is validated by comparison with previous studies and numerical results. Finally, a parametric analysis of the mechanical responses of tunnels with polyurethane and polyethylene foam buffer layers (with differing deformation characteristics) is carried out based on the theoretical model. The results show that the proposed model is applicable to different buffer layer materials. The division of deformation stages in buffer layer materials significantly impacts prediction outcomes. For polyurethane foam buffer layer, the prediction result of the secondary lining pressure without considering the deformation stage division is 35.2% higher than that under consideration, while for polyethylene foam buffer layer, the predicted value is even 96% higher than that considering the deformation stage division. For a given tunnel, the thickness of buffer layer has a reasonable range, with an optimal thickness of 25 cm for both polyurethane and polyethylene foam buffer layers under these conditions. Installing a buffer layer is more beneficial for tunnels subject to significant long-term deformation, as it effectively reduces secondary lining pressure and ensures long-term safety.

Key words: soft rock tunnel, time-dependent deformation, buffer layer, deformation coordination, theoretical model