Temperature Field Analytical Solution and Optimization Scheme after Excavation in Large-scale Ground Freezing Projects

Large-scale freezing projects, especially horizontal freezing projects, suffer from the problem of long exposure times, and weakening of the frozen curtain often occurs in the excavation stage. An analytical solution for the temperature between the freezing pipe and excavation surface was deduced in this study to evaluate the freezing effect at this stage. The solution is verified by in-situ measurements of a large-scale freezing project. The analytical solution shows that the temperature is related to the thermal conductivity of the frozen curtain, the shotcrete, the refrigerant temperature, the excavation surface temperature, and the design scheme of the frozen curtain. Moreover, the excavation surface temperature (T_s) is the critical factor. Then, the equations for the thickness and average temperature of the frozen curtain on the side close to the excavation area are derived. Numerical calculations of the frozen curtain base on analytical solution were carried out to analytical frozen curtain. The results show that when the heat dissipation of the exposed excavation surface is considered, the tensile stresses of the vault and bottom plate increase by up to 135%, the compressive stress of the sidewall increases by 29%, and the shear stress of the shoulder increases by 144%. While three solutions were proposed, and their application scenarios and effects are discussed. This study can provide a reference for the design of large-scale freezing projects to protect the frozen curtain after excavation.