## 5 Geotechnical Interpretations
### Measuring the Unified Plasticity Potential of Soils  
In the previous sections, factor analysis was performed on the data for various purposes. One of the first aims was to reduce the soil properties from five to two and finding the hidden interrelations between them, such as uncovering the negative effect of calcium carbonate on soil plasticity. Lastly, two different factor scores were assigned to each soil based on the regression approach. These factor scores were then analysed to distinguish the plasticity characteristics, and possibly the behaviour, of CL, CH, and MH soils. The next part of this study is to create an empirical approach to quantitively measure the plasticity characteristics of clayey soils. Considering each factor score is a measurement of the soil plasticity, they can be used in a way to accomplish this purpose. One of the most convenient ways is to simply sum the first and second scores to have a final value that represents each soil. Considering each factor score has a different contribution to soil plasticity, this kind of direct approach would not be representative. In this study, the  
Figure 5: Grouping of different soil types indicate the plasticity characteristics. contribution of each factor score has been taken into account and a final resultant factor score was calculated by using a weighted summation approach. Creating a resultant factor score is the initial step to measure the plasticity potential of each soil. The equation below shows the calculation of the resultant value (Equation (3)). \[R_{f_{score}}=\frac{\left[\left(\frac{69.61}{84.14}\times F_{1_{score}}\right)+ \left(\frac{14.53}{84.14}\times F_{2_{score}}\right)\right]}{84.14} \tag{3}\]  
Here, \(R_{f_{score}}\) is the resultant factor score, \(F_{1_{score}}\) represents the first factor score and \(F_{2_{score}}\) is the second factor score. Although the above expression yields a weighted score for each soil, it is still a non-standardized way to represent each soil. Also, the value of \(R_{f_{score}}\) can vary between negative and positive numbers, which is eventually difficult to interpret. Therefore, a standardized approach was chosen in this study. The standardization of the resultant factor score should be conducted in a range that any soil assigned with a value can be easily distinguished. Therefore, the \(R_{f_{score}}\) is standardized between 0 and 100 by considering the minimum and maximum values of the resultant factor score assigned to the soils (Equation (4)). \[\text{Standardized }R_{f_{score}}=\frac{R_{f_{score}}-min_{R_{f_{score}}}}{max_{R_{ f_{score}}}-min_{R_{f_{score}}}}\times 100 \tag{4}\]  
Here, the standardized \(R_{f_{score}}\) is the plasticity potential of soils. This expression assigns a particular value between 0 and 100 to each soil. As this value increases, soil plasticity also increases. Therefore, the soil with the least plasticity potential should yield zero, and the soil that shows the most plasticity should be assigned 100. The validation of this model is critical for the purpose of this research. Considering the plasticity index is a direct approach for measuring plasticity and is widely accepted in practice, this model should coincide if the soils are ranked based on only using the PI. Meaning that if the PI increases, the plasticity potential should also increase in a parallel way. However, the theory of this study is clear; the PI measures the plasticity but does not incorporate the effect of other soil properties. That is the reason that other soil properties related to PI, but not PI itself, were included in the analysis and eventually reduced to a standardized definition of soil plasticity. These facts should be clearly observed in order to validate the theory. Therefore, all the soils were ranked based on the plasticity potential from top-to-bottom and bottom-to-top order. This study's ranking is then compared to the PI ranking for validation. Tables 5 and 6 represent the most and the least plastic soils based on these rankings, respectively.