## 5 Discussion and Conclusions  
The results of laboratory tests presented in this paper have confirmed that the liquefaction phenomenon may also occur in partially saturated non-cohesive soils in a contractive state subjected to monotonic loading and that the potential for liquefaction decreases as saturation decreases. Furthermore, our investigations have shown that, under conditions of partial saturation characterized by positive values of Skempton's parameter \(B\) corresponding to the degree of saturation over 80% or higher, the behaviour of non-cohesive soil changes smoothly from that typical of a dry medium (or a medium under drained conditions) to that characteristic of a fully saturated medium.  
Both experimental data and model predictions (Figure 25) show the decrease of undrained shear strength with the increasing saturation level expressed by Skempton's parameter \(B\). For the analyzed saturation range, the maximum stress deviator normalized by initial mean effective stress varies from 0.38 to 1.67 for \(B\) values between 0.93 and 0.29, respectively. Furthermore, linear dependency can be observed across the whole spectrum of partially saturated states.  
In order to reproduce the test results obtained, a modified theoretical model describing the process of excess pore pressure generation in partially saturated soils has been developed. The modification of the original model consisted in extending the formula for calculating the compressibility of pore fluid using soil skeleton compressibility functions based on dedicated laboratory tests and incorporating soil response under isotropic unloading to reflect the behaviour of soil during mean effective stress reduction due to an increase of pore water pressure. The proposed model reproduces the results of triaxial tests much better than the original one.  
The model has been verified for two non-cohesive soils with different granulation characteristics, showing acceptable qualitative and quantitative agreement between predicted values and experimental results.  
The research reported here offers a semi-empirical incremental approach to modelling the phenomenon of liquefaction or a significant weakening of partially saturated non-cohesive soils under undrained conditions.  
Figure 25: Linear changes of normalized maximum stress deviator with [PERSON]’s parameter \(B\).  
**Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app12042076/s1](https://www.mdpi.com/article/10.3390/app12042076/s1)]([https://www.mdpi.com/article/10.3390/app12042076/s1](https://www.mdpi.com/article/10.3390/app12042076/s1)), Repository S1: Experimental data.
* [2]**Author Contributions:** Conceptualization, W.S.; methodology, W.S. and M.S.; software, M.S.; validation, M.S. and W.S.; formal analysis, W.S. and M.S.; investigation, M.S.; resources, W.S. and M.S.; data curation, M.S.; writing--original draft preparation, W.S. and M.S.; writing--review and editing, W.S. and M.S.; visualization, M.S.; supervision, W.S.; project administration, W.S.; funding acquisition, W.S. All authors have read and agreed to the published version of the manuscript.
* [3]**Funding:** This research received no external funding.
* [4]**Institutional Review Board Statement:** Not applicable.
* [5]**Informed Consent Statement:** Not applicable.
* [6]**Data Availability Statement:** The data presented in this study are available in Supplementary Materials: \"Repository S1: Experimental data\" and in external repository at [[https://doi.org/10.5281/zenodo.5774184](https://doi.org/10.5281/zenodo.5774184)]([https://doi.org/10.5281/zenodo.5774184](https://doi.org/10.5281/zenodo.5774184)).
* [7]**Conflicts of Interest:** The authors declare no conflict of interest.