An analytical model is derived for predicting the flow field and stability of an unsaturated infinite slope subjected to steady infiltration. The proposed model is novel because it accounts for the hydraulic anisotropy of unsaturated soil. The governing equation for steady-state seepage in an infinite slope is established in terms of matric suction under a constant surface flux boundary condition. On the basis of the available experimental findings on the hydraulic anisotropy behavior of unsaturated soils, the relative hydraulic conductivity for a soil under unsaturated conditions with respect to the soil at saturation is postulated to be a direction-independent scalar. This postulation simplifies the governing equation to a form that is directly solvable via the relative hydraulic conductivity and the saturated hydraulic conductivity tensor. To enable sophisticated applications, an exponential law and a power law that are well established in the unsaturated soil literature are used to relate the relative hydraulic conductivity to the matric suction and the effective degree of saturation, respectively. Closed-form solutions are derived for the matric suction, the flow net (potential function and stream function), and the effective degree of saturation. Analytical solutions are also derived for the soil unit weight and overburden stress. These solutions are incorporated into the unsaturated infinite slope stability formula constructed on a suction stress-based effective stress failure criterion. Hydraulic anisotropy has been shown to directly affect the flow field and the change in matric suction, which, in turn, drastically affects the slope safety factor against shallow landslides. This finding demonstrates that neglecting hydraulic anisotropy can cause a considerable overestimation of the safety factor, resulting in an unsafe slope stability prediction. The proposed model is useful for preliminary evaluation of the long-term stability of unsaturated slopes during wet periods and the antecedent slope conditions for shallow landslide initiation under transient infiltration.

中文翻译：

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稳态入渗下水力各向异性非饱和无限边坡的渗流稳定性分析


推导了一个解析模型，用于预测稳态渗透作用下非饱和无限边坡的流场和稳定性。所提出的模型是新颖的，因为它考虑了非饱和土壤的水力各向异性。无限斜率中稳态渗流的控制方程是根据恒定表面磁通量边界条件下的矩阵吸力建立的。根据关于非饱和土壤水力各向异性行为的现有实验结果，假设非饱和条件下土壤相对于饱和土壤的相对水力传导率为与方向无关的标量。这个假设将控制方程简化为一种可以通过相对水力传导率和饱和水力传导率张量直接求解的形式。为了实现复杂的应用，使用非饱和土壤文献中公认的指数定律和幂定律分别将相对水力传导率与基质吸力和有效饱和度联系起来。矩阵吸力、流网（势函数和流函数）和有效饱和度得出了闭式解。此外，还得出了土壤单位重量和覆盖层应力的解析解。这些解被纳入基于吸力应力的有效应力失效准则构建的非饱和无限边坡稳定性公式中。水力各向异性已被证明直接影响流场和矩阵吸力的变化，这反过来又极大地影响了针对浅层滑坡的边坡安全系数。 这一发现表明，忽视水力各向异性会导致对安全系数的严重高估，从而导致不安全的边坡稳定性预测。所提出的模型可用于初步评估非饱和边坡在潮湿期的长期稳定性以及瞬态渗透下浅层滑坡起始的前因边坡条件。