基于相似变换法的半无限空间饱和土一维热固结解析解  

Analytical solutions for 1-D thermo-consolidation process of semi-infinite saturated soil using similarity transformation method

作　　者：韩涛 周扬[1,3] 卢萌盟 HAN Tao;ZHOU Yang;LU Mengmeng(School of Mechanics&Civil Engineering,China University of Mining&Technology,Xuzhou 221116,China;State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering,China University of Mining&Technology,Xuzhou 221116,China;YunLong Lake Laboratory of Deep Underground Science and Engineering,Xuzhou 221116,China)

机构地区：[1]中国矿业大学力学与土木工程学院,江苏徐州221116 [2]中国矿业大学深地工程智能建造与健康运维全国重点实验室,江苏徐州221116 [3]深地科学与工程云龙湖实验室,江苏徐州221116

出　　处：《岩土工程学报》2025年第5期1055-1063,共9页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(52178373)。

摘　　要：针对半无限空间饱和土在表面外荷载及变温作用影响下的一维热固结过程,考虑两类传热及渗流边界条件,给出了温度及超静孔压耦合演化过程的基本方程。引入组合变量对耦合方程进行了解耦,应用相似变换法获得了组合变量在半整数次幂函数边界条件下的通解,并基于该通解构建了任意幂级数形式荷载及边界条件下温度与超静孔压的解析解答。通过文献进行了对比验证,随后应用本解答计算分析了半无限空间饱和土在表面正弦温度及热流边界作用下土中温度及超静孔压的耦合响应特性,结果表明:土体变形功项对传热方程贡献很小,对温度及超静孔压演化的影响基本可以忽略;固结方程中温度化率项系数为正值时,温度变化会引起相反趋势的超静孔压变化,而该系数为负值时,温度变化则会引起相同趋势的超静孔压变化。For a 1-D thermo-consolidation process of semi-infinite saturated soil induced by external loads and changing temperature at the surface,basic equations are proposed to describe the coupled evolvement of temperature and excessive porewater pressure,and two types of heat transfer and seepage boundary conditions are considered.The combination variables are introduced to decouple the governing equations,and their general solutions under the boundary conditions in the form of half-integer power functions are developed by applying the similarity transformation method.After expanding the external loads and the boundary conditions into power series,the analytical solutions for the temperature and the excessive porewater pressure can be obtained using these general solutions directly.After their verification by certain solution in the literature,our solutions are then employed to calculate and analyze the coupled response characteristics of soil temperature and excessive porewater pressure for semi-infinite saturated soil under the effects of sinusoidal temperature and heat flux at the soil surface.The results show that,the term of soil deformation work contributes very little to the heat transfer equation,and its impact on the evolution of temperature and excessive porewater pressure can basically be ignored.When the coefficient for the term of temperature changing rate in the consolidation equation is positive,temperature changes will cause changes in the excessive porewater pressure with the opposite trend,and when the coefficient is negative,temperature changes will cause changes in the excessive porewater pressure with the same trend.

关 键 词：热固结 半无限空间 饱和土 解析解 相似变换 

分 类 号：TU431[建筑科学—岩土工程]