Viscoelastic solution of circular tunnel under asymmetric hydrostatic pressure considering stress release

Firstly, taking use of the correspondence principle, the viscoelastic solution for the circular tunnel with constant ratio of stress release is obtained, based on the elastic solution of the circular tunnel under non-hydrostatic pressure. Then, the stress is released step by step during construction, and the boundary condition at the intrados will change along with the distance x between excavating face and the studred section. The distance x could be expressed as a function of excavation speed v and time t. so the boundary condition could be expressed as a function of time t and speed v. According to the Stieltjes integrals, the items of λFi(t)(i = 1-11) in the solution for constant ratio of stress release are replaced with the integrals of Fi(t) with respect to dλ (t). The solution for the circular tunnel under non-hydrostatic pressure considering the ratio of stress release could be obtained. When the ratio of horizontal pressure coefficients k0 = 1, the solution could be transformed into the viscoelastic solution for the circular tunnel under hydrostatic pressure considering the ratio of stress release. When the ratio of stress release λ = 1, the solution will be transformed into the viscoelastic solution for the circular tunnel under non-hydrostatic pressure without considering the ratio of stress release. So the latter two solutions are special cases of the solution in the paper. The non-hydrostatic pressure assumption accords with the engineering practice, and the ratio of stress release indicates the effects of construction procedure on the stress and deformation of rock. The results could be a reference for the design and construction of tunnels.