## 3 Experimental Results
### Variation of Undrained Shear Strength with Log Liquidity Index and Water Content  
Figure 6 shows the relationship between undrained shear strength, water content and log liquidity index on a linear scale for the _NaM-CaM_, _NaM-K_ and _NaM-S_ mixtures. While confirming the findings of studies by various researchers that there is a definite relationship between undrained shear strength and water content variables for fine-grained soils, the three-dimensional undrained shear strength, water content and log liquidity index relationships are exhibited together for the first time. More importantly, the experimental results obtained show that the trend of the relationship undergoes a transition at a low value of _log_ (_Li_), which proves that the water content is close to the plastic limit; this behavior is followed by a drastic increase in shear strength, and a further increase in water content is accompanied by a decreased _Su_ and a subsequent increase in _log_ (_Li_). This behavior is unique, but the observed values are different for _NaM-CaM_, _NaM-K_ and _NaM-S_ mixtures. It should be noted that the experimental study was carried out on clay blends that included commercially available mixtures of _NaM_, _CaM_, \(K\) and \(S\) clays with different mineralogical properties. Therefore, the tested soil mixtures were grouped under various categories of fine-grained soils according to the Unified Soil Classification System (USCS). All tested soils appear to range from very high to low plasticity levels.  
Figure 6: Relationship among undrained shear strength, water content and log liquidity index for (**a**) _NaM–CaM_, (**b**) _NaM–K_ and (**c**) _NaM–S_ mixtures.  
In the study, _NaM_-clay, which has the highest plasticity among all three types of mixtures, was chosen as the main material. In this case, in 100% _NaM_ clay, the undrained shear strength was close to 200 kPa, and the water content was close to 400%. However, it has been observed that there are serious differences between the log liquidity index values of all three mixtures. For example, while the highest and lowest log liquidity index values of 1.48 and \(-\)1.30 were obtained in 100% _CaM_ clay, respectively, in _NaM_-_CaM_ mixtures (Figure 6a), in _NaM_-_K_ mixtures, the highest and lowest log liquidity index values of 2.04 and \(-\)2.91 were at 100% \(K\) clay (Figure 6b). Finally, in _NaM_-_S_ mixtures, the highest and lowest log liquidity index values of 3.22 and \(-\)6.85 were obtained for 100% \(S\). These results show that the water content, undrained shear strength and log liquidity index behaviors of clays with different mineralogical properties vary in a very narrow band in _NaM_-_CaM_ mixtures and in a wide band in _NaM_-_S_ mixtures. For example, for 100% _NaM_ clay, the water content was up to 400%, while this value was 225% for 100% _CaM_, 90% for 100% \(K\) clay, and only 41% for 100% \(S\) clay.  
Data points based on _NaM_-_CaM_ mixtures were found to be located within a narrow band of two distinct regions with almost indistinguishable slopes (Figure 6a). Data points for _NaM_-_K_ mixtures were also found to be located in a wider band consisting of several distinct regions with different slopes (Figure 6b). Finally, it can be observed that the data points for _NaM_-_S_ mixtures are located in a much wider band consisting of several separate regions with very different slopes (Figure 6c). Furthermore, the boundary between the two zones has a log liquidity index value of about 0, which corresponds to the plastic limit water content. This behavior can be defined as the transition state of the soil from the plastic state to the semisolid state. For this reason, the discovery of the behavior of \"undrained shear strength plotted against log liquidity index relationships\" in four consistencies, namely, solid, semisolid, plastic and liquid states, has been attempted for _NaM_-_CaM_, _NaM_-_K_ and _NaM_-_S_ mixtures.