# Settlement Foundations by Exploring the Collapse of Unsaturated Soils
## 3 Validation of the Theoretical Framework  
For accurate prediction results and the successful application of the EBBM model in COMSOL, it is necessary to validate the model. To achieve this, an oedometer test was conducted, applying the wetting path on a compacted soil [57]. The soil is characterized as a low-plasticity, poorly graded type, and the proportion of the clay was 17%, while that of the fine sand was greater than 50%. The specific gravity of the soil was 2.69. The Afterberg limits were 25% for the plastic limit and 12% for the liquid limit. The initial void ratio and initial dry density were 0.67 and 1.61 Mg/m\({}^{3}\), respectively. In the conducted oedometer test, the samples were initially subjected to an increase in vertical stress up to 0.4 MPa under constant water content (suction = 0.2 MPa). Subsequently, wetting occurred under constant vertical stress, and the specific stress path performed for the samples is illustrated in Figure 2. To ensure the accurate replication of the experimental conditions, the bottom border was set in both vertical and horizontal directions, and the vertical boundaries were only constrained horizontally. The same stress path as in the experimental condition was applied. The model's input parameters of EBBM were sourced from the literature [25] (see Table 2). Notably, the smoothing parameter, a new addition for EBBM, was set to b = 100. The comparison between the experimental and predicted results, as depicted in Figure 3, revealed a commendable agreement with only a maximum deviation of approximately 4%. This validates the accuracy of the EBBM model. Table 3 presents the hydraulic parameters of the studied soil, derived from the estimated wetting curve. The values of Van Genuchten parameters (\(\alpha\), n, \(\theta_{s}\), and \(\theta_{r}\)) along the drying path and K\({}_{\text{s}}\) are derived from the UNSODA (UNsaturated SOil hydraulic DAtabase) database. The data are easily accessible through the UNSODA [58]. Soil reference \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Description** & **Value** \\ \hline G & Shear modulus & 7 [MPa] \\ K & Swelling index & 0.0077 \\ Ks & Swelling index for variation in suction & 0.001 \\ \(\lambda(0)\) & Compression index at zero suction & 0.066 \\ \(\lambda\)s & Compression index for variation in suction & 0.025 \\ P\({}_{\text{ref}}\) & Reference pressure & 0.012 [MPa] \\ \(P_{0}^{\alpha}\) & Initial preconsolidation pressure & 0.02 [MPa] \\ w & Weight parameter & 0.25 \\ m(1/\(\beta\)) & Soil stiffness parameter & 0.05 [MPa] \\ b & Plastic potential parameter & 100 \\ Sy0 & Initial yield value for suction & 0.3 [MPa] \\ k\({}_{\text{s}}\) & Tension-to-suction ratio & 0.8 \\ M & Slope of critical state line & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: EBBM parameters related to the studied soil. Figure 2: Stress path applied in the oedometer test. 2642 corresponds closely to the selected soil in terms of both texture and porosity. Then, the wetting parameters are determined using the methods of [PERSON], 2018 [55] and [PERSON] et al., 2005 [56] (see Figure 4). The parameters, \(\chi_{\text{p}}\) and \(\chi_{\text{f}}\) signify the soil matrix's compressibility and the compressibility of water, respectively. Development of a Deterministic Framework Affected by Rainfall Infiltration on the Collapsibility of the Foundation  
Infiltration is an extremely complex unsaturated seepage process which can be effectively described by [PERSON] equation [49; 59; 60]. Here, the infiltration process was modelled in the hydromechanical framework using [PERSON] equation and the Van Genuchten retention curve [50]. A 2D model was constructed using Comsol Multiphysics version 6.1. It features a shallow foundation with a length of 1.5 m and a thickness of 0.3 m, which is based on a homogeneous layer of compacted soil (lower Cromer till). The soil is assumed to exhibit elastoplastic behavior and characterized by the EBBM, with parameters determined in the  
Figure 4: Evaluation of the wetting path of SWRC.