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。 Since the permeability coefficient of unsaturated soil is a function of the suction force of the matrix, the governing equation has a strong non-linear characteristic, which makes it difficult to solve the governing equations analytically. The homotopy analysis method has more freedom and flexibility for the choice of series basis functions and auxiliary linear operators, and the control and adjustment of convergence are easier to implement. When choosing a linear operator for solving strong nonlinear differential equations and Auxiliary parameters have obvious advantages. Therefore, for the nonlinear characteristics of unsaturated soil consolidation equation, assuming that the pore pressure is atmospheric pressure in the unsaturated soil layer in the shallow surface, based on Richard’s empirical formula and one-dimensional consolidation theory of unsaturated soil, The governing equations for unsaturated one-dimensional consolidation are deduced. By using the homotopy analysis method, by choosing the appropriate initial guess and auxiliary parameters, the nonlinear equations are converted into linear differential equations and solved to obtain the level of the consolidation problem Number solution. In addition, based on the compaction of kaolin, based on the collection of relevant test parameters, the approximate analytic solution of the consolidation problem obtained by the homotopy analysis is compared with the numerical results of the finite difference method. The analytical results verify that Correctness