# Settlement Foundations by Exploring the Collapse of Unsaturated Soils
###### Abstract
It was confirmed that the BBM elastoplastic model adequately predicts volume change under precipitation [36; 37; 38; 39; 40]. \begin{table}
\begin{tabular}{l} \hline [PERSON] and [PERSON] (1992) [3] \\ \(CP=48.496+0.102\ C_{u}-0.457\ w_{i}-3.533\ \gamma_{d}+2.80\ln(p)\) \\ \(CP=47.506-0.072\ (S-C)-0.439\ w_{i}-3.123\ \gamma_{d}+2.851\ln(p)\) \\ [PERSON] and [PERSON] (2004) [15] \\ \(\mathrm{I_{c}}=9.805+0.102\ C_{u}-0.261\ w_{i}-0.424\ \gamma_{d}+0.0580\ PI+0.0697\ C\) \\ [PERSON] and [PERSON] (2008) [18] \\ \(\varepsilon_{u}=a(\gamma_{d}-15.27)+bw_{i}+17\) \\ \(a=(-0.036\ C_{u})-1.379\) \\ \(b=0.0006\ C_{u}{}^{2}-0.089\ C_{u}+1.3\) \\ \(c=0.55\ C_{u}+38\) \\ [PERSON] and [PERSON] (2009) [17] \\ \(\mathrm{I_{c}}=0.9081\left[\left(1.3891\ e^{0.0116\ (f)}\right)\right)\times\left(2.3136\ln( \epsilon_{0})+4.3635\right)^{0.5522}\) \\ [PERSON] et al. (2015) [16] \\ \(CP=3.501\times(1-R_{d})^{0.6687}\times\left(1-\frac{S}{100}\right)^{2.121} \times\left[C^{0.528}\times ln\left\{\frac{p^{1.33}}{P_{u}}\right\}+5.719\right]\) \\ [PERSON] et al. (2020) [19] \\ \(CP=-17.373+1.355\ln(p)+16.156\epsilon_{0}+21.366\ e^{-5.55},+0.00088\ C_{u}{}^{2}\) \\ [PERSON] et al. (2023) [20] \\ \(CP=0.206\ p+0.0016\ (u_{a}-u_{w})_{i}-0.0007(p)^{2}-2.7\times(10)^{-8}\times(u_{a}-u_{w})^{2}+X\) \\ \((X=-15.15\) for \(Dr\approx 35\%\), \(w_{i}=5\%\), fines content = 40\%). \\ \hline \end{tabular} \(CP\): the collapse potential (\(\%\)); \(\mathrm{I_{c}}\): the collapse index; \(\mathrm{C_{a}}\): the coefficient of uniformity of the soil; \(p\): the soaking pressure (\(\mathrm{PA}\)); \(w_{i}\): the initial water content (\(\%\)); \(\gamma_{d}\): the compaction dry unit weight (\(\mathrm{kN}/\mathrm{m}3\)); \(C\): the clay-size fraction (\(\%\)): \(S\): the sand-size fraction (\(\%\)); \(S\): the degree of saturation (\(\%\)). \(Pl\): the plasticity index (\(\%\)); \(p_{a}\): the atmospheric pressure (\(\mathrm{kPa}\)); \(\epsilon_{0}\): the initial void ratio (\(-\)); \(f\): the fines content (\(\%\)); \(RD\): the dry density ratio (\(-\)): \((u_{a}-u_{w})_{i}\); the matric suction before wetting (\(\mathrm{kPa}\)); \(Dr\): the relative density (\(\%\)).  
\end{table} 
Table 1: Equations predicting the collapse potential of the soil. In recent years, efforts have been made to develop hydromechanical frameworks that can accurately simulate the wetting-induced soil deformations under various foundation types and different wetting conditions. [PERSON] (2018) [PERSON] (2018) presented a hydromechanical model that incorporates stress equilibrium equations and water mass balance, including the BBM and the Soil Water Retention Curve (SWRC), to explain the settlement caused by an elevated groundwater level in loess soils. Achieving favorable consistency between in situ results and numerical simulations, the hydromechanical model is suggested to be efficiently applicable to other loess soils, provided knowledge of SWRC. Investigations reported by [PERSON] et al. (2013) [PERSON] (2018) demonstrated that hydromechanical frameworks utilizing the Barcelona Expansive Model (BExM) [PERSON] (2018) effectively describe the swelling pressure and microstructural volume changes occurring as suction decreases in bentonite/sand mixtures. [PERSON] (2012) [PERSON] and [PERSON] et al. (2017) [PERSON] et al. (2017) successfully implemented the hydro-mechanical models to predict settlements of shallow foundations due to rainfall infiltrations. [PERSON] et al. (2023) [PERSON] et al. (2023) investigated the impact of saturated hydraulic conductivity and the duration of rainfall on collapse using the EBBM model. The study concluded that the simulated results generally align with the field results, verifying the hydro-mechanical model's accuracy. [PERSON] et al. (2024) [PERSON] et al. (2024) presented a hydro-mechanical model to analyze strip foundation behavior on loess soil. The calibration involved experimental data and retrofit analysis from full-scale prototypes, proving that the model's prediction of settlements caused by wetting is accurate.