## 4 Results
### Soil Type--Plasticity Index (PI)  
Plasticity index (_PI_) is the fundamental physical property of cohesive soil and, by many researchers, is considered one of the most important factors affecting the dynamic properties of cohesive soil [14; 16]. Therefore, in Figure 9, minimal damping ratios depending on the plasticity index are shown. Every tested soil (except _K5_) has a few different \(D_{MINs}\). It is connected with the next steps of the consolidation process at which damping tests were conducted (see Figure 7). Based on this figure, the following can be observed: the \(D_{MIN}\) decreases with the rise of the _PI_ from 0% to about 20%, and then the trend changes and an increase in the plasticity index causes an increase in the minimal damping ratio. This phenomenon is related to the soil structure. Namely, below _PI_ = 20% soil has a lot of sandy fraction, and these grains dominate in soil structure. Thus, when the _PI_ is small, the friction between the grains is significant, and much of the motion energy is dissipated and changes into thermal energy, so the minimal damping ratio is high. When the plasticity index increases, water and clay friction act as a lubricant and reduces friction, and, therefore, the \(D_{MIN}\) decreases. However, above _PI_ = 20%, the situation changes. Clayey and silty fractions start to dominant in soil structure, and connections between these grains are the most important. The contact area is very small compared to sandy grains, so a lot of motion energy is lost on those connections; as a result, energy dissipation increases,  
Figure 8: Damping ratio (\(D\)) dependant on shear strain (\(\gamma\)) for sample _K8_. Figure 7: Minimal damping ratio (\(D_{MIN}\)) dependant on effective stress (\(p\)’) for tested soils. and therefore the minimal damping ratio also rises. Similar conclusions can be found in [42], however, in that work, \(PI\) value, above which the minimal damping ratio characteristic was changed, was equal to 50%. Soil cohesion also has influence over the shape of the damping ratio curve. Figure 10a shows examples of damping ratio curves for soils with a different plasticity index, namely, \(K4\), \(K7\), \(K13\), and \(K15\), compared to [PERSON] and [PERSON] curves [16]. The presented damping ratio curves are obtained at similar effective stress levels from 110 to 160 kPa, and the \(PI\) range is from 6.6% for the \(K4\) sample to 36.68% for the \(K13\) sample. The curves provided by [PERSON] and [PERSON] are correct for soils with a plasticity index from 0% to 50% and an OCR from 1 to 8. However, it can be seen that Warsaw cohesive soils have a completely different shape and do not fit with the range proposed by [PERSON] and [PERSON] [16]. Figure 10a is evidence that we cannot compare soils from Europe to soils from the US, because of differences in origins and genesis, which influence not only the values of the damping ratio but also the shape of the damping ratio curves. The real influence of the plasticity index on the damping ratio curves is presented in Figure 10b. On the \(y\) axis, the normalized damping ratio (\(D/D_{MIN}\) (-)) is shown. In this configuration, elastic range of soil response is denoted as \(D/D_{MIN}=1\). The \(x\) axis shows the standard shear strain (\(\gamma\)) (%) of a soil sample. The curve for the \(K4\) sample increases the fastest and crosses the nonlinearity threshold strain as the first soil. This is due to a very small \(PI\) value, namely, 6.6%. Every curve is located beneath  
Figure 10: Examples of damping ratio curves compared to [PERSON] and [PERSON] curves [16] (**a**) and examples of normalized damping ratio curves (**b**) for soils (\(K4\), \(K7\), \(K13\), and \(K15\)) with a different plasticity index (\(PI\)). Figure 9: Minimal damping ratio (\(D_{MIN}\)) depending on plasticity index (\(PI\)) for tested soils. another in line with the increase of the plasticity index, so the first is for _K4_, the second is for _K15_, the third is for _K7_, and the fourth is for _K13_.