冻结管引起的周围土体温度场演变规律及参数化分析

针对稳定线性冷源热传导问题,为研究人工冻结法冻结管周围土体温度场的瞬态变化,基于冻结锋面将土体分为冻结区及降温区,构建相应人工冻结相变温度场模型,并采用变量替换法得到冻结温度场解析解,利用指数积分函数解析式表达了冻结区和未冻结区的温度场分布。将理论解析计算结果与冻结槽试验结果进行比对,验证了理论封闭解的有效可靠性,并进一步通过参数化分析了与土体传热介质冻结温度场演变规律有关的初始温度、冻结温度、冻结温差、结冰潜热、盐水温度和冻结管吸热系数等影响因素的敏感性。结果表明:冻结锋面半径与冻结时间存在着平方根关系,冻结温度场呈对数型函数分布,且曲线曲率随冻结时间的增加而逐渐减小;土体初始温度、冻结温度、结冰潜能和盐水温度与冻结锋面半径均呈负相关,冻结管吸热系数与冻结锋面半径呈正相关;土体冻结温差、土体结冰潜能和冻结管吸热系数与土体冻结锋面半径的发展均呈现近似线性关系,传热介质初始温度和盐水温度对冻结锋面半径随冻结时间变化的对数型曲线曲率影响最大,结冰潜热和冻结管吸热系数次之,冻结温度最小。研究成果对认识稳定线性冷源作用下冻结管周围不良地基土温度场演变规律和进一步形成规范及指导冻结法施工技术具有重要意义。

Evolution law of soil temperature field around freezing pipe and relevant parametric analysis

In order to study the transient change of the temperature field of the soil around the freezing pipe of the artificial ground freezing method，the soil mass is divided into the frozen zone and the cooling zone for the problem of stable linear cold source-heat conduction based on freezing front and then a corresponding freezing-phase change temperature field model is established，while the analytical solution of the freezing temperature field is obtained with variable substitution method and the distributions of the temperature fields of both the frozen zone and the cooling zone are expressed by the analytic formula of exponential integral function. Comparing the theoretical analytic calculation result with the result of freezing tank experiment，the effectiveness and reliability of the theoretical closed-form solution are verified，furthermore，the sensitivities of the influence factors，such as the initial temperature，freezing temperature，freezing temperature difference，freezing latent heat，brine temperature，heat absorption coefficient of the freezing pipe，etc. ，related to the evolution law of the freezing temperature field of the soil heat transfer medium are analyzed through the relevant parameterizations. The result shows that a square root relationship is there between the freezing front radius and the freezing time and the freezing temperature field exhibits a logarithmic function distribution，while the curvilinear curvature gradually decreases along with the increase of the freezing time. The soil initial temperature，freezing temperature difference，freezing latent heat and brine temperature exhibit negative correlations with the freezing front radius，while the heat absorption coefficient of the freezing pipe exhibits a positive correlation with the freezing front radius. The soil freezing temperature difference，freezing latent heat and the heat absorption coefficient of the freezing pipe exhibit approximate linear relations with the development of the soil freezing front radius，while the influences from the initial temperature of the soil heat transfer medium and the brine temperature on the logarithmic curvilinear curvature of the change of the freezing front radius that depends on time are the maximums，for which the freezing latent heat and the heat absorption coefficient of the freezing pipe are secondary and the freezing temperature is the minimum. The study has an important significance for understanding the evolution law of the temperature field of the poor foundation soil around the freezing pipe under the effect of stable linear cold source，further forming a criterion and guiding the construction technology of the ground freezing method.