基于解析解的高地温圆形隧道温度场分布研究  

Research on temperature field distribution of circular tunnel with high geo-temperature based on analytical solution

作　　者：张毅峰 刘琛尧 李国良[2] 晏启祥[1] 陆志明 ZHANG Yifeng;LIU Chenyao;LI Guoliang;YAN Qixiang;LU Zhiming(Key Laboratory of Transportation Tunnel Engineering of Ministry of Education,Southwest Jiaotong University,Chengdu 610031,China;China Railway First Survey and Design Institute Group Co.,Ltd.,Xi'an 710043,China)

机构地区：[1]西南交通大学交通隧道工程教育部重点实验室,四川成都610031 [2]中铁第一勘察设计院集团有限公司,陕西西安710043

出　　处：《武汉大学学报（工学版）》2024年第7期925-932,共8页Engineering Journal of Wuhan University

基　　金：国家自然科学基金联合基金项目(编号:U21A20152)。

摘　　要：高地温隧道相对于常规隧道在径向有着更复杂的结构,研究隧道断面温度场对解决隧道高地温相关问题有着重要意义。采用极坐标形式建立圆形高地温隧道断面温度场的数学模型,并采用Laplace公式对热传导问题进行求解,得到了衬砌-隔热层-围岩3层结构下温度场的解析公式;经过MATLAB编程求解计算,得到了温度场的时空演变规律,并建立了对应的数值模型验证其结果的可靠性。结果表明:隧道内部大气温度波动时衬砌与隔热层的温度呈周期性变化,且随着距隧道中心距离增大温度场振幅逐渐减小;温度场呈环状分布,隔热层处的温度梯度最大,衬砌和围岩的温度梯度较小;衬砌内侧温度与隔热层内部温度同步,而隔热层外侧温度波动滞后于衬砌内侧温度;数值模型解析解结果与隔热层外侧温度变化规律一致。Compared with conventional tunnels,high-geothermal tunnels have a more complex structure in the radial direction during construction,so it is of great significance to study the temperature field of tunnel section to solve the problems related to high ground temperature in the tunnel.In this paper,a mathematical model of the temperature field of a circular tunnel section with high ground temperature is established in the form of polar coordinates,and the heat conduction problem is solved by the Laplace formula,and the analytical formula of the temperature field under the three-layer structure of liningheat insulation-surrounding rock is obtained.Through MATLAB programming and calculation,the spatiotemporal evolution law of temperature field is obtained,and the corresponding numerical model is established to verify the reliability of the results.The results show that the temperatures of the lining and insulation layers change periodically when the atmospheric temperature inside the tunnel fluctuates,and the amplitude of the temperature field decreases gradually with the increase of the distance from the tunnel center.The temperature field is distributed in a ring,the temperature gradient at the insulation layer is the largest,and the temperature gradients of the lining and surrounding rock are smaller.The inner temperature of the lining is synchronized with the inner temperature of the insulation layer,while the outer temperature of the insulation layer fluctuates behind the inner temperature of the lining.The numerical model is consistent with the analytical solution of the outer temperature variation of the thermal insulation layer.

关 键 词：高地温 隧道 温度场 数值模型 解析解 

分 类 号：U45[建筑科学—桥梁与隧道工程]