摘要
将隧道非齐次的瞬态传热分解为周期函数边界下的瞬态传热和恒温边界下的稳态传热,利用分离变量与Laplace变换相结合的方法,求解有保温隔热层的寒区隧道瞬态温度场的显式解析解。根据能量守恒,建立隧道洞内气体的气–固耦合传热模型,并获得洞内气体年平均温度和温度振幅的显式解析解。衬砌温度影响因素分析表明,随着隧道埋深和年平均气温的增加,二衬内、外两侧的温度呈线性增加,当年平均气温低于0℃,季冻区隧道埋深小于80m时,5cm厚隔热层很难单独满足防寒需求,应与主动供暖措施联合;随着隔热层厚度的增加,二衬的温度呈增长趋势,但增长速率却逐渐减小;当隔热层厚度超过5cm时,通过增加隔热层厚度来提高衬砌温度要考虑其经济性。依据隧址区的气候及地形条件,采用工程类比和解析解相结合的方法分段计算隔热层厚度。与实测值对比结果表明,理论解满足工程精度要求。
The problem of time-dependent heat conduction for tunnel in cold region with nonhomogeneous outer boundary conduction is transformed into both transient heat conduction with convection boundary condition of air temperature changed with sinusoid and steady heat conduction.Using the separation of variables and Laplace transform technique can obtain analytical solution to temperature fields of tunnel with insulation layer in cold region.The analytical solutions of the annual mean temperature and temperature amplitude can be obtained by energy conservation and experiential method considering heat conduction/convection between the tunnel ground and the air flow in the tunnel.Temperature of lining varies with both tunnel depth and annual mean temperature linearly.When the annual mean temperature is below 0 ℃ and the tunnel depth is less than 80 m,5 cm thick insulation layer alone can not satisfy the anti-freezing requirements.As the increase in thickness of insulation layer,lining temperature presents an upward trend,but the growth rate has gradually decreased;when the thickness of insulation layer is more than 5 cm,the increase in the thickness of insulation to improve the lining temperature is not economical.The insulation thickness can be calculated by engineering analogy and analytical solution based on climate and terrain conditions with piecewise calculation.Accuracy of the analytical solution is examined by comparing the calculated results with measured results.It is found that the calculated values agree well with those measured in the field.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2010年第9期1767-1773,共7页
Chinese Journal of Rock Mechanics and Engineering
基金
国家自然科学基金资助项目(50878150)
交通部西部交通建设科技项目资助(2009318822047)
内蒙古自治区交通科技项目(NJ-2008-25)
关键词
隧道工程
寒区隧道
温度场
解析解
隔热层厚度
分段计算
tunnelling engineering
tunnel in cold region
temperature field
analytical solution
insulation layer thickness
piecewise calculation
