Analytical model for tunnel stability and support pressure prediction of viscoelastic-plastic rock masses under the influence of seepage

With the advancement of traffic infrastructure development in China, an increasing number of tunnels and underground projects are being built through soft rock strata characterized by notable rheological properties in high-water-pressure environments. However, the comprehensive consideration of the stress path and unsteady seepage field during the excavation and support process has not been incorporated in predicting tunnel stability and support pressure in rheological rock masses. To solve the aforementioned problem, an analytical method is proposed to rapidly and accurately predict the time-dependent variation of the surrounding rock stability and support pressure.

The viscoelastic-plastic constitutive model is employed to simulate the rheological behavior of the surrounding rock. Based on the Mohr-Coulomb yield criterion, an exact analytical solution for stress and displacement is derived for the entire construction process of a deep-buried circular tunnel with lining. This solution incorporates the influence of the stress path and unsteady seepage field, utilizing the principles of elasticity-viscoelasticity correspondence and Laplace transformation. The construction process is categorized into two distinct stages. During the excavation stage (0-t₁), the tunnel is rapidly excavated at the onset. This stage is characterized by the absence of any water flow; hence, no additional stress is generated. During this stage, the mechanical field under the release load from the excavation needs to be considered. In the support stage (t₁-t_∞), the lining is applied when t=t₁. After the support is subjected to stress, the stress of the surrounding rock reaches a safe state, leading to the complete unloading of the original plastic zone. Long-term mechanical action may cause cracks or damage in the supporting or waterproof layer, eventually leading to water leakage and gushing. In the support stage, the influence of the seepage field needs to be considered when analyzing the mechanical field. The unsteady pore pressure distribution in the entire domain and throughout the entire period can be obtained using the separation of variables method, which enables establishing an analytical model that considers the influence of seepage on the mechanical field of the surrounding rock and lining. Furthermore, the analytical solution for the aging process of the mechanical field in the surrounding rock and the supporting force of the lining is derived, with the effect of the stress path considered correctly.

Given the influence of seepage flow and the loading and unloading processes, the precise analytical solution for stress and displacement in the excavation and support stages of a tunnel was derived. This solution considered the entire construction and operation process of a deep-buried circular tunnel with lining in viscoelastic-plastic surrounding rock. The displacements at r=3.0 m and r=3.5 m over time were obtained in both the loading and unloading regions, as well as solely under the loading conditions.

The comparison of the results of these two cases shows that the displacement values obtained without considering unloading are considerably smaller. This observation highlights the potential for misjudging the stability of the surrounding rock, as the displacement values may be overestimated. Furthermore, this finding highlights the importance of considering the unrecoverable plastic strain in predicting time-dependent displacement and stress in the unloading zone. The derived analytical solution can serve as a valuable reference for designing support systems and construction processes in practical applications.