## 5 Geotechnical Interpretations
### Measuring the Unified Plasticity Potential of Soils
Considering, the relationship of PI and sand content with plasticity potential was individually defined by logarithmic and linear functions, respectively. The nonlinear regression model should also be assigned in that way. Also, the parameter's estimate and a constant were included in the regression. Therefore, the below expression was run to predict the best-suited equation of plasticity potential (Equation (8)). \[y=a\ln(x)\pm b(z)\pm c \tag{8}\]  
Here, \(y\) is the plasticity potential, \(x\) is the plasticity index, \(z\) is the sand content, \(a\) and \(b\) are the parameter's estimates, and \(c\) is the constant of the function. Considering the above equation, the nonlinear regression model was tested and found to be best suited as the following expression (Equation (9)). This relationship of PI and sand content to plasticity potential yielded a very high coefficient of correlation of 0.944. This high value of the coefficient proves that Equation (9) has an undeniable statistical significancy to represent the plasticity potential of soils in a unified form. \[\text{Unified Plasticity Potential }(\%)=31.9\ln(PI)-0.44(SC)-69.9 \tag{9}\]  
Considering Equation (9), which includes two different soil properties, Equations (5) and (6) should not be used to determine the exact value of the plasticity potential. Rather, the interested user should only utilize Equation (9) to define the unified plasticity potential of soils. Equation (9) works with a minimum plasticity index of 9%, thus the user should assign the plasticity potential as zero for lesser values of PI. In this sense, if any outcome is negative or greater than 100, then the plasticity potential should be assigned as 0 and 100, respectively. Also, the authors proposed to the interested user to use the following figures for quick assessment. In this case, Figure 8 is best suited for greater values of the plasticity index and Figure 9 for lesser values. Additionally, the extent of this study includes sand content between 0 and 50 percent. Therefore, Figures 8 and 9 have been created by extrapolating the sand content up to 80%. The 60 and 80% lines are theoretical and should be used cautiously. Especially, where sand content exceeds 50% with very high plasticity index, above 150%, this model should be a rough guidance concerning the soil plasticity potential rather than assigning a definitive value. The factor analysis was carried out after transforming the soil properties to normal distribution. Based on this fact, the plasticity potential between 0 and 100 was also assigned to the soils as normally distributed. This distribution can be used to categorize the plasticity potential statistically. For this purpose, the three-sigma rule also as known as the 68-95-99.7 rule was applied to the data [73]. This rule allows the researcher to categorize the data in percentages based on certain intervals, if the data are normally distributed. These certain percentages are 2.35, 15.85, 49.85, 83.85, and 97.85 and correspond to the plasticity potential of 5.4, 27.5, 48.7, 70.0, and 85.6, respectively. To avoid any confusion, the percent of 15.85 corresponds to a plasticity potential from 0 to 27.5. Based on this approach, the plasticity potential is divided into six categories starting from negligible to severe plasticity, as shown in Table 7. A generalized indication of these categories is also represented in terms of effective angle of internal friction \(\phi^{\prime}\)  
Figure 8: Visual representation of plasticity potential best suited for greater plasticity index values. Figure 7.0 The plasticity potential of soils that are best suited for lesser plasticity index values. undrained shear strength (\(s_{u}\)), compressibility while compacted and saturated and volume change potential upon wetting and drying. These positive and negative relationships of plasticity potential between material properties are a generalized derivation from the literature [74; 75; 76; 77; 78; 79].