## 3 Experimental Results
### Variation of Flow Index with Atterberg Limits  
Flow index can be obtained with both Casagrande and Fall cone test results. In the Casagrande method, firstly, a graph of the water content versus the logarithm of number of blows is obtained. The resulting line is called the flow curve, and the slope of the flow curve gives the flow index. In the Fall cone method, the linear relationship between the water content and the \(log_{10}\) penetration depth (mm) is called the flow curve. However, many studies showed that the use of a semi-logarithmic plot gives much more consistent results than an arithmetic plot in experimental relationships regarding soil behavior [31]. From this point of view, it is stated that the flow index, which is the slope of the semi-logarithmic graph, is dimensionless, unlike the slope of the flow curve plotted at natural scale [31; 32]. Within the scope of this study, a correlation has been developed between the flow index and both the liquid limit and plasticity index without the need for any assumptions. In this study, commercially available _NaM_-_CaM_, _NaM_-_K_ and _NaM_-_S_ mixtures were used on clay blends with a 10% increase in clay content, ranging from 0% to 100% and covering a wide range of liquid limit and plasticity indices. Additionally, liquid limit-flow index plots and plasticity index-flow index plots obtained by both Fall cone and Casagrande methods are presented comparatively. Figure 7a,b shows the relationship between the liquid limit and the flow index obtained from the Casagrande and Fall cone methods on 31 clay-clay mixtures, respectively. Correlation coefficients of 0.71 and 0.78 were obtained for Equations (9) and (10) by using Casagrande and Fall cone methods between liquid limit and flow index. According to test results, a strong correlation exists between the liquid limit and the flow index obtained by Casagrande cup and Fall cone methods:  
\[LL_{p}=5.82\times\left(I_{fp}\ \right)\ +23.48 \tag{9}\]  
\[LL_{c}=1.20\times\left(I_{fc}\ \right)-5.93 \tag{10}\]A number of soils along with commercially available _NaM_-_CaM_, _NaM_-_K_ and _NaM_-_S_ mixtures covering a wide range of plasticity index (9.6% < \(I_{p}\) < 521.5) were used in the present study. In the study, the lowest plasticity index was found to be 9.6 for 100% \(S\), while the plasticity index for 100% _NaM_ was 521.5%. Figure 8a shows the relationship between the plasticity index and the flow index, \(I_{fp}\), obtained from the Casagrande cup method on 31 clay mixtures. The following relationship with a correlation coefficient of 0.72 has been obtained. In addition, the data obtained by performing the Casagrande cup experiment in [PERSON] et al. (2018) are presented in Figure 8a. In the study of [PERSON] et al. (2018), no correlation was found between the plasticity index and the flow index. \[PI_{p}=5.52\times\left(I_{fp}\right)-10.55 \tag{11}\]  
Figure 8b shows the plasticity indices plotted against corresponding flow indices. A good correlation is found to exist between the plasticity index and the flow index obtained  
Figure 7: Relationship between flow index and liquid limit using the (**a**) Casagrande cup method and the (**b**) Fall cone method. by the cone method, \(I_{fc}\), with the correlation coefficient being 0.76. The relationship between these parameters can be expressed as:  
\[PI_{c}=1.16\times\left(I_{fc}\right)-34.91 \tag{12}\]  
Figure 8: Relationship between flow index and plasticity index using the **(a)** Casagrande cup method and the **(b)** Fall cone method. Figure 8b shows the correlation for the data from the literature and from the present investigation put together. It is quite interesting to note that from the correlation equation obtained by [PERSON] et al. (2018), the data also result in a good correlation coefficient. These experimental results also support the claim that the cone penetration method has a very good reproducibility and is, for all practical purposes, free of errors.