## 5 Discussion
While our system uses a rigid material rather than laminated rubber, the design intent remains similar: to isolate the structure from soil-induced tension strains and accommodate differential displacements. An important aspect of this study involves quantifying the effect of horizontal tensile deformation of soils on foundation settlement, which is particularly relevant in conditions such as undermining, seismic loading, or lateral ground movement. The relationship between settlement under tensile soil strains (Su) and the baseline settlement without horizontal displacement (S\({}_{0}\)) is described by the following empirical expression [9]:  
\[S_{u}=S_{0}\cdot(1+D\cdot c), \tag{10}\]  
where \(D\) is an empirical coefficient that characterizes the sensitivity of foundation settlement to horizontal tensile strain in the surrounding soil;  
\(\varepsilon\)--horizontal tensile strains of the surface soils (tensile deformation), \(0\leq\varepsilon\leq 9\cdot 10^{-3}\) m;  
\(S_{u}\)--settlement with horizontal displacement of soils;  
\(S_{0}\)--settlement without horizontal displacement of soils. The coefficient \(D\) in Equation (7) is an empirical, site-specific parameter that reflects the sensitivity of foundation settlement to horizontal tensile deformation of the surrounding soil. Its value depends on factors such as soil type, stress-strain characteristics, foundation geometry, and loading conditions. In this study, \(D\) was determined through curve fitting of laboratory and field test results for different types of conical foundations. For practical applications, \(D\) can be estimated by calibrating finite element simulations with site-specific soil parameters, or by conducting reduced-scale physical model tests under controlled horizontal displacement conditions. In cases where testing is not feasible, practitioners may refer to published values of \(D\) from similar geotechnical conditions; however, such use should be approached with caution, due to the variability in soil behavior. The \(S_{u}/S_{0}\) relationship is illustrated in Figure 15, which shows settlement trends for different foundation types under increasing horizontal tensile strain \(\varepsilon\). Based on experimental and numerical results, the empirical coefficient \(D\)--which represents the increase in settlement per unit of horizontal tensile strain--was found to be approximately 55 for standard conical foundation models and 41 for cone-top pile foundations under laboratory and simulated conditions. In contrast, field testing revealed \(D\) = 44 for conical foundations and \(D\) = 90 for cone-top pile foundations, indicating greater sensitivity to tensile soil deformation in real ground conditions for the latter. These findings indicate that while cone-top pile foundations demonstrate lower baseline settlement, their response to horizontal tensile deformation may be more pronounced in certain field conditions, as reflected in the higher \(D\) value. However, this also suggests that cone-top pile systems are more sensitive to strain, but retain structural integrity and bearing capacity, without reaching failure. Importantly, if the value of \(D\) is known for a given soil-foundation system, this equation allows practitioners to estimate the expected increase in settlement due to horizontal soil strain, aiding in risk assessment and deformation control for critical infrastructure. To support and complement these empirical findings, numerical simulations in this study were conducted using the Mohr-Coulomb model in PLAXIS 2D. This approach was selected for its simplicity and effectiveness in representing axisymmetric behavior under vertical loading. The model captured key deformation trends and stress concentration zones observed in the experimental tests. However, we acknowledge that more advanced constitutive models, such as the Hardening Soil or HS-Small models, could more accurately represent nonlinear stress-strain behavior, stiffness degradation, and small-strain effects in soft or structured soils.