Rainfall-induced landslides are widely distributed in many countries. Rainfall impacts the hydraulic dynamics of groundwater and, therefore, slope stability. We derive an analytical solution of slope stability considering effective rainfall based on the Richards equation. We define effective rainfall as the total volume of rainfall stored within a given range of the unsaturated zone during rainfall events. The slope stability at the depth of interest is provided as a function of effective rainfall. The validity of analytical solutions of system states related to effective rainfall, for infinite slopes of a granite residual soil, is verified by comparing them with the corresponding numerical solutions. Additionally, three approaches to global sensitivity analysis are used to compute the sensitivity of the slope stability to a variety of factors of interest. These factors are the reciprocal of the air-entry value of the soil alpha, the thickness of the unsaturated zone L, the cohesion of soil c, the internal friction angle phi related to the effective normal stress, the slope angle beta, the unit weights of soil particles gamma(s), and the saturated hydraulic conductivity K-s. The results show the following: (1) The analytical solutions are accurate in terms of the relative differences between the analytical and the numerical solutions, which are within 5.00% when considering the latter as references. (2) The temporal evolutions of the shear strength of soil can be sequentially characterized as four periods: (i) strength improvement due to the increasing weight of soil caused by rainfall infiltration, (ii) strength reduction controlled by the increasing pore water pressure, (iii) strength reduction due to the effect of hydrostatic pressure in the transient saturation zone, and (iv) stable strength when all the soil is saturated. (3) The large alpha corresponds to high effective rainfall. (4) The factors ranked in descending order of sensitivity are as follows: alpha > L > c > beta > gamma(s) > K-s > phi.

In recent years, with the increasing difficulty of foundation pit projects, the frequency of leakage accidents has also increased. In order to ensure that the excavation of foundation pits is carried out smoothly, water-stop curtains are generally used to protect the foundation pit. Once leakage occurs in the water-stop curtain, it will inevitably delay the schedule, cause significant harm, and even jeopardize life. Therefore, this paper analyses and investigates the two-steady-state seepage field of the foundation pit when the permeable anisotropic soil layer suspends the leakage of the water curtain. To calculate head distribution solutions, the soil layer surrounding the curtain was divided into five regular regions, and the superposition method and method of separating variables were used. These results were then combined with the continuity conditions between the regions to obtain the explicit analytical solutions of the seepage flow field around the pit. Calculations were compared using finite element software and other references, and the results were in good agreement, verifying the correctness of the analytical solution. Parameter analysis showed that the location and width of vertical leakage cracks have limited influence on the head distribution of the foundation pit and water pressure around the water curtain, but significant influence on the seepage flow at the leakage location.

To consider the influence of the interaction of each clayey layer in the interbedded soils of a foundation on the soil consolidation, a two-dimensional calculation model based on the overall analysis is proposed and the controlling equations of each layer are established. A semianalytic solution for the excess pore-water pressure in the frequency domain is derived by combining the Laplace transform with the Fourier cosine transform and introducing the boundary transformation method. The theoretical solution is compared with numerical simulations for verification, and the relevant parameters are also analyzed to further explore the consolidation characteristics of the foundation. The results show that the proposed theoretical solution can effectively reflect the distribution of excess pore-water pressure in each soil layer under the given foundation conditions; the deviation of the average degree of consolidation from the numerical results is less than 2.0%. When only one sandy layer is laid out in the foundation, it is most conducive to the consolidation to arrange the sandy layer in the middle-lower part of the soil layer. When the total thickness of the sandy layer is the same, the maximum consolidation rate that can be achieved by arranging two sandy layers in the lower part of the foundation is slightly faster than that achieved by arranging a single sandy layer. When the ratio of the horizontal permeability coefficient of the sand to the permeability coefficient of the adjacent clay is greater than or equal to 20, the excess pore-water pressure in the sandy layer can be considered to be evenly distributed along the vertical direction.

Laboratory one-dimensional consolidation tests were conducted to measure the variation trend of the soil pore pressure at the drainage boundary with time under different magnitudes of loads. Based on the test data, continuous drainage boundary interface parameters under arbitrary loads were inversely derived, the reasonableness of which was verified by comparing the theoretical values of the boundary pore pressure with the experimental results. Moreover, the one-dimensional consolidation model of the layered foundation was established with a continuous drainage boundary. The semianalytical solution of the corresponding model under an arbitrary load was given by using the boundary transformation method. A comparison with degraded results and the finite-element calculation results verified the correctness of the present solutions. Finally, the influences of the interface parameters and loading rate on the soil consolidation behavior were studied, where three different types of loads (i.e., linear, exponential, and simple harmonic) were considered. The results revealed that the consolidation rate reaches the peak value for the linear loading pattern when the loading is completed. Moreover, the exponential load used to describe the surcharge preloading method also positively influenced the theoretical analysis due to its concise expression form. When the simple harmonic load was applied, the excess pore-water pressure in the soil element presented stable periodic vibration after the first cyclic load. In addition, the loading rate and interface parameters exhibited different influences on the consolidation behaviors. The research results of this paper can provide a theoretical reference for the settlement calculation of subgrades during the construction and operation phases.