绝热边界作用下人工冻结温度场解析解

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

摘要:

隧道地下工程采用冻结法施工时经常遇到地连墙等构筑物影响冻土帷幕发展的问题，给冻结方案设计和封水效果评估带来困难，危及后续开挖作业安全。为探明地连墙等绝热边界作用下冻结温度场的分布状态，掌握冻结壁局部受限时的发展规律，建立了半无限平面内包含直线绝热边界的温度场数学模型。通过热势函数叠加结合镜像法求解了单根、2根以及3根冻结管的温度场解析解，并采用数值模拟验证了其准确性和适用性。结果表明：解析解与稳态数值解吻合较好，与瞬态数值解的误差随冻结时间延长而减小，冻结第50天3种模型的误差分别为0.39℃、0.17℃和0.06℃，均能控制在0.5℃以内；等温线在绝热边界处与边界垂直，只存在平行于边界的热流而没有法向热流，绝热边界对于其与冻结管之间区域的温度降低更加有利；随着绝热边界与冻结管距离d的增加，对冷量传递的阻断作用降低，冻结模型逐渐向无限大平面模型转化，实际工程应根据冻结壁设计厚度，合理匹配管间距l和边界距离d的取值。

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.