土体在一维传热方程解析解及热扩散系数测定.pdfVIP

第30 卷第5 期 岩土工程学报 Vo l. 30 No.5 2008 年 5 月 Chinese ]ournal of Geotechnícal Engíneeríng May , 2008 土体一维传热方程解析解及热扩散系数测定 涂新斌，戴福初 (中国科学院地质与地球物理研究所，北京 1∞029) 摘 要:传热方程是一类常见的基本数学物理方程，热导率是士体重要的热物理参数。从基本传热方程出发，详细地 推导了利用傅立叶级数求解…维传热方程的方法，以地面植股随时间变化的波动方程得到地下不间深度处土体温度分 布的解析解。在此慕础上，讨论了利用热导率进行土体含水擦，恻攘的藕本原理，详细地推导了根据地下不间深度的掘 度计算土体热扩散系数的振幅法、相位法及其应用，介绍了利用传热方程进行数值模拟的计算原理。最后结合实例介 绍了该方法的应用效果。 羔键词:热导率:热扩散系数:传热万程;地温梯度 中圈分类号: TU441 文献标识码:A 文章编号: 1∞o 4548 (2∞8) 05-0652-06 作者简介t 涂新斌(1971 翩)，湖北孝感人，博士，烹姿从摹工程地质、岩土工程研究。巳mail: 阳且inbin@mail.igc脱ac.cn. Analytical solution for one-dimensional heat transfer equation of soil and evaluation for thermal diffusivity TU Xin-bin , DAI Fu-chu (1nstituωof Geology and Geopbysics. CAS. Beijing 1α)()29. Cbina) Abstract: Heat transfer equ础。n is a lrind of basic mathematical-physical 叫uation. The thermal d讶fusivity is an important th缸mal physical parameter for soil. The derivation was presented for the one-dimensional heat tr础úer equation by me咀ns of Fourier series. With the assumption of wave 叫uati.on for ground temperaωr哩，也e analyticaJ solution for the distribution of ground temperature at di仔erent depths was 伊-esen切d. Based on 伽.e analytical solution of heat transfer equation. 伽e principle of measured soil moisture by means of thermal diffusivity was discuss时， and two kinds of methods were forw缸d put to evaluate the soil thermal diffusivity. i.e. , the amplitude method and the ph制method. The principle of numerical me仙也ωsimulate heat 阳lsfer in soil wωalso discussed. Finally, these m础。ds were verified by examples. Key words: thermaI conducti. vity; 也ermaI d