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The mechanical responses of tunnels with stiff and yielding linings were predicted using an analytical method. A theoretical model of a stiff lining-supported tunnel was established, which considered the effects of tunnel face advancement and lining installation delay. The deformation process in the yielding lining can be divided into three stages based on the elastic–plastic–stiff deformation characteristics of the yielding elements. The circumferential shortening of the yielding lining during Stage 1 was caused by the elastic deformations in the segmental linings and yielding elements. The theoretical stiffness of the yielding lining at this stage was determined, and analytical solutions were derived from the theoretical stiffness in the mechanical model of the stiff lining. The yielding lining deformation during Stage 2 was induced by plastic compression of the yielding elements, and the lining resistance pressure remained unchanged. The yielding lining was reduced to a stiff lining during Stage 3, and analytical solutions for the tunnel displacement and lining resistance pressure during Stages 2 and 3 were provided. The analytical solutions for a stiff lining-supported tunnel were compared with those provided in previous studies, and an analytical model of a tunnel that used a yielding lining was applied to an actual tunnel. The effectiveness and reliability of the solutions were verified by comparing them with the application results. Theoretical analysis showed that tunnel deformation could be controlled using a stiff lining, because the increasing rate of pressure is considerably less than that of the lining bearing capacity. However, a 1.4 m lining thickness was required to prevent lining damage. The yielding lining resistance pressure decreased from 3.46 to 0.68 MPa when the lining was 0.2 m thick, and the yielding displacement increased from 50 to 150 mm. The maximum stress in the lining decreased by 56.95 MPa when the yielding lining was displaced by 50 mm, and the thickness increased from 0.2 to 0.5 m. The application of a stiff lining could be considered for rocks that exhibit weak or average deformability; however, attention should be paid to the yielding lining in rocks that exhibit strong rheology. [ABSTRACT FROM AUTHOR]

• A plastic Stillinger-Weber potential for soft rocks is proposed. • The plastic fracture behavior of soft rocks is effectively simulated. • The dependence of simulation results on mesh size is effectively mitigated. • Influence factors on the failure behaviors of soft rock tunnels are investigated. Soft rocks present some undesirable behaviors, such as low strength, high plasticity and softening. These traits pose challenges in the design and construction of soft rock tunnels. To address these issues and model plastic fracture behaviors of soft rocks, we proposed a plastic Stillinger-Weber (PSW) potential and integrated it into the discretized virtual internal bond (DVIB) model. The PSW-DVIB model combines the strengths of the plastic DVIB and the SW-DVIB models. It not only effectively reproduces the plastic fracture behavior but also accurately reflects the Poisson's ratio. Moreover, due to the inclusion of fracture energy in the PSW potential, the simulation results are basically mesh size independent. The PSW-DVIB model is then utilized to investigate the failure behaviors of soft rock tunnels. The effects of the coefficient of lateral pressure, in-situ stress, Poisson's ratio and tunnel shape on tunnel failure are investigated. The simulated results indicate that the coefficient of lateral pressure has significant influence on the failure zone distribution of the surrounding rock. With the coefficient of lateral pressure increasing, the failure degree of surrounding rock decreases firstly and then increases. The optimum coefficients of lateral pressure for the stability of circular, arched and square tunnels are about 1.00, 0.75 and 0.75, respectively. When the in-situ stress or Poisson's ratio is larger, the influence of the coefficient of lateral pressure on tunnel failure is more obvious. The influence of the coefficient of lateral pressure on square tunnels are more significant than the arched tunnels, and then the circular tunnels. These findings provide valuable insights for the design and construction of soft rock tunnels. [ABSTRACT FROM AUTHOR]