A Simplified Viscoelastic Solution of the Frost Heaving Force of Cavity Water behind Tunnel Linings

Abstract

With the high demand for construction of tunnels in China’s severe cold regions, the problem of frost heaving has become an important factor that endangers tunnel safety. This paper attempts to investigate the effect of frost heave of cavity water that widely exists in the tunneling engineering on the tunnel stability. According to the actual deformation of the surrounding rock of the tunnel, the viscoelastic behavior is considered to the surrounding rock. On the premise of the elastic solution of stagnant water frost heave, the viscoelastic solution of frost heaving pressure is deduced by Laplace transform using the generalized Kelvin model based on the elastic-viscoelastic correspondence principle. The frost heaving force is analyzed through a case study with variations in the size of the cavity defect as well as the constitutive model parameters. It is concluded that the frost heaving force increases with the cavity defect size; over time, the frost heaving force gradually increases, but it will eventually stabilize. It is found that when the frost heaving force reaches a certain level, the surrounding rock with low strength or the lining with insufficient strength will crack, and the frost heaving force will not continue to increase.