Analytical Solution for Temperature Field of Artificial Ground Freezing Induced by Adiabatic Boundary

Abstract:

The construction of underground tunnel engineering using the AGF method often encounters the problem of diaphragm walls affecting the frozen curtain development， which brings difficulties to the design of the freezing scheme and the evaluation of the sealing water effect， and endangers the safety of subsequent excavation operations. In order to find out the freezing temperature distribution under the action of adiabatic boundary such as diaphragm wall， and to grasp the development law under the local restriction of freezing curtain， a mathematical model of temperature field containing adiabatic boundary in semi-infinite plane was established. The analytical solution of single， double and triple freezing pipes were derived based on the thermal potential function and mirror method， and their accuracy and applicability were verified by numerical simulation. The results show that the analytical solution agrees well with the steady-state numerical results， the error with the transient results decreases gradually with freezing time， and the errors of three models on the 50th day are 0.39℃， 0.17℃， and 0.06℃， which can be controlled within 0.5℃. The isotherm is perpendicular to the boundary， and there is only heat flux parallel to the boundary but no normal heat flux. The adiabatic boundary is beneficial to the temperature reduction between the freezing pipes and adiabatic boundary. As the distance d increases， the effect of adiabatic boundary gradually decreases， and the freezing model transforms into an infinite model. Therefore， the pipe spacing l and boundary distance d should be reasonably matched according to the designed thickness of the frozen curtain in practical projects.