考虑寒区隧道围岩冻结温度渐变的冻胀力解析解

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

摘要:

为考虑寒区隧道围岩单向冻结和径向冻结温度渐变会引起的不同方向和不同冻结深度处的非均匀冻胀变形，通过引入冻胀围岩径向冻结温度Tr和平行与垂直冻结方向的非均匀冻胀系数k反映围岩的非均匀冻胀性，理论推演建立了寒区隧道冻胀力解析解，并进行了案例和影响因素分析。研究表明：忽略冻结温度渐变影响时冻胀力明显偏大，考虑冻结温度渐变可有效提高冻胀力计算的可靠性；考虑冻结温度渐变影响的冻胀力随着非均匀冻胀系数k的增大呈对数函数增大，随冻结与未冻围岩的弹性模量比E_Ⅱ/E_Ⅲ的增大而线性减小，且E_Ⅱ/E_Ⅲ越大时冻胀力产生所需围岩达到的临界k值也越大；隧道冻胀力随围岩冻结圈外径、未冻围岩弹性模量和原岩应力的增大而增大，但随衬砌内径、冻结围岩单位温度冻胀系数的增大而逐渐降低。

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.