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Limited mathematical analytical studies for tunnel leakage-induced surface and subsurface soil movements and tunnel responses incorporated the distribution of excess pore water pressure, in which the concrete lining was often assumed perfectly permeable or impermeable. This mechanical closed-form model will bring calculation errors and inconsistencies in engineering practice. This article introduces a new set of mathematical model for analyzing tunnelling-induced dissipation of excess pore water pressure and ground consolidation settlement considering long-term leakage influence through a semi-permeable lining, in which the soil-lining permeability ratio is used as the relative parameter to measure the influence of lining permeability on consolidation settlement. The interesting point is that the theoretical model conducts coupling with the Terzaghi-Rendulic consolidation theory through solving of the conformal mapping technique in complex variable theory and the separation variable method in classical mathematical physics equation. The accuracy of presented solutions is verified by comparisons with numerical simulation and  in-situ  measurements of engineering profiles and reasonable agreements are obtained. Furthermore, a sensitivity analysis is implemented on the subsurface consolidation settlement and the distribution of excess pore water pressure, and the results indicate that the soil-lining permeability and the soil Young’s modulus notably affect the tunnel leakage-induced ground responses.

Effects of long-term leakage of shield lining on tunnelling-induced ground consolidation movements