中文摘要：

由于非饱和土的渗透系数是基质吸力的函数，使得控制方程带有强非线性的特征，进而使得控制方程的解析求解变得十分困难。同伦分析法对级数基函数和辅助线性算子的选择具有更大的自由性、灵活性，且收敛性的控制和调节更加容易实现，求解强非线性微分方程时在选择线性算子以及辅助参数上具有明显的优势。因此，针对非饱和土固结方程的非线性特征，对于处于地表浅层的非饱和土层，假设孔隙气压力为大气压力，在Richard经验公式与非饱和土一维固结理论的基础上，推导了非饱和一维固结无量纲控制方程；应用同伦分析法，通过选取适当的初始猜测解与辅助参数，将该非线性方程转换为线性的微分方程组并求解得到固结问题的级数解。此外，以压实高岭土为研究对象，在收集相关试验参数基础之上，将由同伦分析法求得的固结问题的近似解析解与有限差分法数值结果相对比，分析结果验证了解析解的正确性。

英文摘要：

In a one-dimensional consolidation equation, the permeability coefficient is the function of matric suction in an unsaturatedsoil. The consolidation equation in one dimension is strongly nonlinear due to the presence of the permeability coefficient. As ananalytic solution to nonlinear problems, a homolopy analysis method （HAM） is efficient in the selection of series basis functions andauxiliary linear operators, and easily make the solution convergence. In order to analytically solve the equation, the HAM wasintroduced in the present study. During the solution, the pore air pressure was assumed as the atmospheric pressure. The equationswith two unknown variables were then reduced to dimensionless pore water pressure as only one basic unknown variable subjected toconstant pore air pressure. Firstly, a governing equation in a dimensionless form was derived from the basic one-dimensionalconsolidation theory after the integration with the Richard empirical formula. The method was then used for a mapping technique totransfer the original nonlinear differential equations to a number of linear differential equations. These differential equations are notdependent on any small parameters, which is convenient to control the convergence region. After this transferring, a series solution tothe equations was then obtained by the HAM after selection of auxiliary linear operator parameters. Finally, comparisons were carriedout between the analytical solutions and the finite difference method in case of compacted kaolin. It can be found that the seriessolutions indicate that the pore water pressure increases firstly, and then decreases with the depth after the consolidation of thecompacted kaolin. The results indicate that the analytical solution in the present study is reasonable.