## 4 Conclusions  
* The settlement and bearing capacity of rectangular footings are regarded as the main calculation parameters when designing foundations used in construction.
* These calculations show that geo-mechanical models for foundation, including geometric parameters of the footing (length, width, depth, initial and boundary conditions) and computational soil models, such as linear and non-linear models with different systems of physical equations (Hooke and Hencky), have a significant influence on the evaluation of settlement and bearing capacity.
* The computational soil model used in this article, with the possibility of lateral expansion (\(\epsilon_{x}\
eq 0\), and \(\epsilon_{y}\
eq 0\)), along with the elastic-plastic model for shear strain-stress dependency and the non-linear model for volumetric strain-stress dependency as parts of Hencky's system of physical equations, allows us to present the total deformation as the sum of the volumetric and shear components (\(\epsilon_{x}=\epsilon_{y}+\epsilon_{y}\)). Only in this case do the strain-stress curve and the settlement-load curve both have decaying and persistent (double curvature) characteristics.
* The computational soil model proposed here indicates that, thanks to the choice of different combinations of stiffness (\(G^{\varepsilon}\), \(\
u\), \(\varepsilon^{\ast}\), \(\alpha\)) and strength parameters (\(\phi\) and c), the curve of dependency between settlement and load can be observed as decaying or persistent with various bending degrees of the curvature.
* This article presents a substantial dependency of total deformation on stress as well as total settlement on load, depending on the various values of pre-overburden pressure  
Figure 10: The dependency curve between total settlement \(S(q)\), calculated by Equation (35), and load \(q\) with various values of pre-overburden pressure \(\sigma_{\rm p}\) and foundation depth \(z\).  
Figure 9: The dependency curve between \(S_{\gamma}(q)-1\), \(S_{\rm p}(q)-1\), and \(S(q)-3\), calculated using Equation (35), and load \(q\).  
\(\sigma_{\rm P}\). The growth of pre-overburden pressure \(\sigma_{\rm P}\) leads to an increase in the bearing capacity of the foundation soil, and a decrease of total settlement compared to the case with lower values of \(\sigma_{\rm P}\).  
Conceptualization, methodology, investigation, software, Z.G.T.-M. and A.Z.T.-M.; formal analysis, H.H.D. and A.Z.T.-M.; writing--original draft preparation, Z.G.T.-M. and A.Z.T.-M.; writing--review and editing, all authors; visualization, H.H.D.; supervision, Z.G.T.-M. and A.Z.T.-M. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by the Ministry of Science and Higher Education (grant # 075-15-2021-686). All tests were carried out using research equipment of The Head Regional Shared Research Facilities of the Moscow State University of Civil Engineering.  
Not applicable.  
The data used to support the findings of this study are included within the article. The original details of the data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.