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.