Analytical Solution for Frost Heave Force of Cold Region Tunnel Caused by Non-uniform Frost Heave of Surrounding Rock Considering Freezing Temperature Gradient

Abstract:

To account for the non-uniform frost heave deformation at different directions and freezing depths caused by the unidirectional freezing and the radial freezing temperature gradient of tunnel surrounding rock in cold regions， this study introduces the radial freezing temperature Tr and the non-uniform frost heave coefficient k in parallel and vertical freezing directions to characterize the non-uniform frost heave of the rock mass. Theoretical derivations establish an analytical solution for frost heave force in cold region tunnels， followed by a case study and analysis of influencing factors. The research reveals that neglecting the impact of freezing temperature gradient leads to a significantly overestimated frost heave force. Considering the influence of freezing temperature gradient effectively enhances the reliability of frost heave force calculations. The frost heave force， when influenced by freezing temperature gradient， increases logarithmically with the growth of the non-uniform frost heave coefficient k. Additionally， it decreases linearly with the increase in the elastic modulus ratio E_Ⅱ/E_Ⅲ of frozen and unfrozen surrounding rock， with larger EⅡ/EⅢ requiring a higher critical value of k to generate frost heave force. Furthermore， tunnel frost heave force increases with the enlargement of the frozen surrounding rock's outer radius， the elastic modulus of the unfrozen surrounding rock， and field stress. Conversely， it gradually decreases with the increase in the inner radius of the lining and the frost heave coefficient per unit temperature of the frozen surrounding rock.