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韩涛, 周扬, 卢萌盟. 基于相似变换法的半无限空间饱和土一维热固结解析解[J]. 岩土工程学报. DOI: 10.11779/CJGE20240206
引用本文: 韩涛, 周扬, 卢萌盟. 基于相似变换法的半无限空间饱和土一维热固结解析解[J]. 岩土工程学报. DOI: 10.11779/CJGE20240206
Analytical solution for 1-D thermo-consolidation process of semi-infinite saturated soil using similarity transformation method[J]. Chinese Journal of Geotechnical Engineering. DOI: 10.11779/CJGE20240206
Citation: Analytical solution for 1-D thermo-consolidation process of semi-infinite saturated soil using similarity transformation method[J]. Chinese Journal of Geotechnical Engineering. DOI: 10.11779/CJGE20240206

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

  • 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。通过文献中解答对本文解答进行了对比验证,随后应用本文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,它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。

     

    Abstract: For a 1-D thermo-consolidation process of semi-infinite saturated soil induced by external load and changing temperature at the surface, basic equations are presented to describe the coupled evolvement of temperature and excessive porewater pressure, and two types of heat transfer and seepage boundary conditions are considered. Combination variables are introduced to decouple the governing equations, and general solutions of combination variables under the boundary conditions in the form of half-integer power functions are developed by applying the similarity transformation method. After expanding the external load and the boundary conditions into power series, the analytical solution for the temperature and the excessive porewater pressure can be obtained using these general solutions directly. After verification of our solution by certain solution in the literature, our solution is then applied 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 excessive porewater pressure with the opposite trend, and when the coefficient is negative, temperature changes will cause changes in excessive porewater pressure with the same trend.

     

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