## 5 Conclusions  
In this paper, we established a comprehensive computational model that takes multiple factors into account. Subsequently, we conducted validation and analysis, leading to the following conclusions:  
1. When the permeability of the lower soil is higher than that of the upper soil, or the compressibility of the lower soil is lower than that of the upper soil, it is beneficial to the consolidation of the foundation.
2. Exchanging interface parameters between the upper and lower soil layers yields limited impact when their compressibility and permeability exhibit similarity. Nevertheless, notable effects emerge when the compression index to penetration index ratio deviates across these layers, leading to substantial variations in soil consolidation rates. Given that layered soil typically displays heterogeneous properties, the interface pa  
Figure 16: Comparison curve between theory and experiment of consolidation degree [23].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\sigma_{\mathbf{0}}^{i}\)-\(\sigma_{\mathbf{f}}^{i}\) (kPa) & \(e_{\  
rameters, i.e., the interface permeability on consolidation and settlement calculations, are of considerable significance and cannot be disregarded in most instances.
3. For \(c_{ci}/c_{ki}<1\), both the average degree of consolidation defined by settlement (\(U_{\rm s}\)) and pore water pressure (\(U_{\rm p}\)) increase with rising \(N_{\sigma}\) values. Furthermore, the effect of \(N_{\sigma}\) on (\(U_{\rm s}\)) is more pronounced than on (\(U_{\rm p}\)) under continuous boundary conditions.
4. In cases where \(c_{ci}/c_{ki}=1\), the \(U_{\rm s}\) increases with increasing \(N_{\sigma}\) values under continuous boundary conditions. This contradicts the existing outcome based on the traditional Terzaghi drainage boundary, where changes in \(N_{\sigma}\) had no effect on the \(U_{\rm s}\) consolidation curve. In cases where \(c_{ci}/c_{ki}>1\), \(U_{\rm p}\) decreases with increasing \(N_{\sigma}\) values. The influence of \(N_{\sigma}\) on \(U_{\rm s}\) is multifaceted: during early consolidation, \(U_{\rm s}\) increases with rising \(N_{\sigma}\), but in the middle and later stages of consolidation, \(U_{\rm s}\) decreases with increasing \(N_{\sigma}\).
5. Unlike the consolidation characteristics under traditional boundary conditions, in the case of continuous drainage boundary conditions, the pore pressure at the boundary interface is no longer consistently maintained at zero. As the interface parameters decrease, the pore pressure at the interface gradually increases, and the rate of pore pressure dissipation progressively decreases. Furthermore, the pore pressure diminishes as both \(a\) and \(b\) values decrease proportionally, indicating that in foundations where the upper layer exhibits better permeability and the lower layer experiences less compression, the dissipation rate of pore pressure is faster.  
Conceptualization, W.W., M.Z. and G.M.; methodology, Y.Z. and Y.Y.; validation, Y.Z. and Z.Z.; formal analysis, Y.Y., M.Z. and W.W.; investigation, Y.Z. and M.Z.; writing--original draft preparation, Y.Z. and M.Z.; writing--review and editing, Y.Z. and Y.Y.; project administration, Z.Z.; funding acquisition, Y.Z. and W.W. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the National Natural Science Foundation of China (grant no. 52108322) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (grant no. 23 KJB560004).  
Not appliable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.