Abstract: For rock or loess shallow tunnel, the entire area and time effect solutions of tunnel construction under slope boundary are formulated considering viscoelastic rheological properties of rock and supporting effect. According to the solving method of general viscoelastic problem, the solutions of stress and displacement are derived by using the function of complex variable method, Laplace transformation and the superposition principle of viscoelastic problem. These solutions consider the supporting effect by applying the varying supporting force with time and space and are applicable to arbitrary viscoelastic model of rock, initial stress state and supporting time. And the solutions are consistent with finite element results of the same model. According to the solutions, the excavation of shallow tunnel is analyzed basing on the generalized Kelvin viscoelastic model of rock. The influences of lateral pressure coefficient, angle of slope and depth of tunnel on the stable subsidence value and range of surface, the stress and displacement of tunnel border are given; and the depth of tunnel is recommended to regard the shallow problem as the deep buried problem. Solutions can be used in the preliminary design of the rock and loess tunnel and provide free displacement field to the analysis method of two stages in the interaction between tunnel and underground structure.

Key words: shallow tunnel, supporting effect, viscoelasticity, analytical solution