Study of the evolution of the frost–heaving pressure of a tunnel lining based on a constant stiffness constraint model

Abstract

To study the evolution of the frost–heaving pressure and frost–heaving deformation of the lining for a tunnel in cold regions, a frost–heaving strain model of rocks with self–constraint that considers the porosity, water content, temperature, and elastic modulus of the rock is first derived through the mechanical balance equation and geometric equation of the rock mesostructure. The laboratory test results verify that the frost–heaving strain model of the rocks with self–constraint is reliable. After analyzing the boundary conditions of the freeze–thaw ring of the surrounding rock along the radial direction of the tunnel, a constant stiffness constraint model of the freeze–thaw ring is proposed. Then the frost–heaving process of the surrounding rock is divided into three stages, and the mechanical models for the calculation of the frost–heaving pressure and the frost–heaving deformation are derived based on the constant stiffness constraint model and the frost–heaving strain model of the rocks. Finally, the evolutions of the frost–heaving pressure and the frost–heaving deformation of the tunnel lining are investigated. The results show that the frost–heaving ratio of the surrounding rock of the tunnel increases nonlinearly as the frost–heaving factor increases. The frost–heaving factor has a linearly positive correlation with the porosity and the water content of the surrounding rock, and a negative correlation with the unfrozen water mass ratio and the rock elastic modulus. The rock resistance coefficient and the lining equivalent resistance coefficient affect the frost–heaving pressure and the frost–heaving deformation significantly. With the increase in the rock resistance coefficient or in the lining equivalent resistance coefficient, the frost–heaving deformation increases or decreases, respectively, while the frost–heaving pressure increases gradually as the rock resistance coefficient or the lining equivalent resistance coefficient increases.