Analytical solutions for nonlinear consolidation of soft soil around a shield tunnel with idealized sealing linings

This paper presents the analytical solutions for nonlinear consolidation of soft soil around a shield tunnel with idealized sealing linings. By introducing the empirical relation between permeability and compressibility, along with the conformal transformation, the governing equations of nonlinear consolidation are established, and the corresponding analytical solutions are derived. Then, the Terzaghi consolidation solutions are derived from the degenerate governing equation of nonlinear consolidation. Through the predictions of different consolidation theories in both completely permeable and impermeable lining conditions, the influences of a tunnel acting as a drain and impacting the dissipation of pore pressure, degree of consolidation, long-term ground settlements and ground settlement rates are investigated. During the early stages of consolidation, the case studies reveal that the predictions made by this study strongly agree with the field data when a completely permeable lining is applied. This study confirms that a tunnel acting as a drain can accelerate the consolidation of soil and enlarge soil deformation due to consolidation. During long term consolidation, a notable nonlinearity of the soil consolidation is exhibited by a small and gradually decreasing settlement rate, showing agreement with the tendency of field data from the impermeable conditions.