## 4 Results
### Comparison of ANN Model with Other Empirical Formulas Available in the Literature  
The obtained results were compared with the results obtained from earlier tests for cohesive soils. The authors chose five formulae for the damping ratio (D) in the wide shear strain range, summarized as follows:  
[PERSON] and [PERSON] [36]:  
\[\mathrm{D}=\left(\frac{0.333\Big{(}1+\mathrm{e}^{-0.0145\mathrm{I}_{\mathrm{P}} ^{3}}\Big{)}}{2}\right)\cdot\left[0.586\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{ \mathrm{max}}}\Big{)}^{2}-1.547\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{ max}}}\Big{)}+1\right]; \tag{2}\]  
[PERSON] and [PERSON] [37]:  
\[\mathrm{D}=17.83\Bigg{[}0.56\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{max}} }\Big{)}^{2}-1.39\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{max}}}\Big{)}+1 \Bigg{]}; \tag{3}\]  
[PERSON] et al. [38]:  
\[\mathrm{D}=2+[18-0.08(\mathrm{I}_{\mathrm{P}}-15)]\cdot\left[1-\Big{(}\frac{ \mathrm{G}}{\mathrm{G}_{\mathrm{max}}}\Big{)}\right]; \tag{4}\]  
[PERSON] et al. [39]:  
\[\mathrm{D}=10.6\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{max}}}\Big{)}^{2} -31.6\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{max}}}\Big{)}+21+\Bigg{[}( 0.008\mathrm{I}_{\mathrm{P}}+0.82)\Big{(}\frac{\sigma_{0}^{\prime}}{\mathrm{ P}_{\mathrm{a}}}\Big{)}^{-0.5k}\Bigg{]}; \tag{5}\]  
[PERSON] et al. [29]:  
\[\mathrm{D}=\Bigg{[}\mathrm{a}\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{max} }}\Big{)}^{2}-\mathrm{b}\Big{(}\frac{\mathrm{G}}{\mathrm{G}_{\mathrm{max}}} \Big{)}+\mathrm{c}\Bigg{]}+\mathrm{d}\mathrm{I}_{\mathrm{P}}+\mathrm{e}\Big{(} \frac{\mathrm{p}^{\prime}}{\mathrm{P}_{\mathrm{a}}}\Big{)}^{\mathrm{f}}; \tag{6}\]  
where \(\mathrm{a}\), \(\mathrm{b}\), \(\mathrm{c}\), \(\mathrm{d}\), \(\mathrm{e}\), and \(\mathrm{f}\) are constants, different for both analyzed soil groups, and \(\mathrm{Pa}\) is the atmospheric pressure equal to 100 kPa. For low- and medium-cohesive soils with an IP \(<20\%\): \(\mathrm{a}=14.8\), \(\mathrm{b}=34.3\), \(\mathrm{c}=26\), \(\mathrm{d}=-0.31\), \(\mathrm{e}=1.36\), and \(\mathrm{f}=-0.32\); for very cohesive soil with an IP \(>20\%\): \(\mathrm{a}=6.32\), \(\mathrm{b}=20.36\), \(\mathrm{c}=14.43\), \(\mathrm{d}=0.062\), \(\mathrm{e}=0.75\), and \(\mathrm{f}=-1.49\). Each considered model in the literature was suitable only for the tested soils. The equation presented by [PERSON] and [PERSON] [36] was calibrated for cohesive soil with an IP below 50% and an effective stress below 1000 kPa. [PERSON] and [PERSON] [37] presented an equation for the average damping ratio curve based on nine publications and considered different types of clay, e.g., offshore clayey silt, Edger plastic kaolin, San Old Bay clay, Mexico City clay, etc. [PERSON] et al. [38] created an empirical model for cohesive soil with an IP from 0% to 100%. The formula shown by [PERSON] et al. [39] was appropriated for Tertiary, Quaternary, and older soils with an IP from 0% to 132%, collected from a depth  
Figure 8: Error histogram. from 0 to 326 m. The equation proposed by [PERSON] et al. [29] was calibrated on the same soil samples as the ANN model. It should be noted, however, that the formula proposed there was different for soils with an IP < 20% and different for those with an IP > 20%. The use of the ANN model allowed to avoid this division, further increasing the accuracy of the damping ratio predictions. Table 8 presents the comparison between the mean absolute error and determination coefficient. The conducted comparisons indicate that the best model for cohesive soils taken from the analyzed site is the ANN model, which was proposed by the authors of this article. The ANN model tested in the presented research can be useful to other researchers in several ways compared to traditional equations, such as Equation (6). Firstly, ANN models have the ability to learn from data and improve their predictive performance over time, which can result in more accurate and reliable predictions.