## 1 Introduction
While the liquid limit values are calculated with greater confidence, it is hard to make the same comment for the plastic limit. In the plastic limit method, a soil mass is rolled into a thread at a certain rate under sufficient pressure. This method is quite laborious and depends on the personal experience of the operator. Only experienced people can achieve reproducible results. If the tests are performed by different operators, experimental results are significantly affected. Many researchers [27; 28] in the literature performed studies to obtain the plastic limit using results of the Fall cone method. Nevertheless, some researchers [5; 6; 29; 30] attempted to recover the plastic limit by fixing the ratio of strength in the plastic limit to the liquid limit at a certain value, which ranged between \(70\) and \(100\). Furthermore, it is known that the Casagrande test is more user-dependent than the Fall cone test because the Fall cone test uses a more standardized methodology, which requires user experience at a minimal level. In this regard, the Casagrande test suffers from many disadvantages, including rigidity of the base, cup material, frequency of blows, base resilience, disturbance of soil caused by the groove and application of \"dynamic effect\" to  
Figure 1: Consistency of cohesive soils [2]. cause \"flow\" of a plastic soil. Apart from proposing an error coefficient, which is dependent on the type of Casagrande device, the experience of the user, clay type and content in the soil tested, liquid limit of the material, as well as the water content range with which the user is working, ambient temperature and time elapsed during testing (time elapsed up to determination of a penetration depth of 20 mm or number of blows of 25) can influence the results obtained. In this regard, variations as low as 0.2\(\sim\)0.4% between two tests [31; 32] and as high as 25% [33; 34] can be observed, and it is hard to propose an error coefficient for the psychological or experience-based influence factor. The flow index (\(I_{f}\)), which measures the plasticity of soils, is the slope of the water content versus \(\log_{10}(N)\) plot in the percussion cup method, or the slope of the water content versus \(\log_{10}(d)\) plot in the cone penetration method [31; 32; 33; 34]. Analysis of experimental data on clays with widely varying plasticity properties and mineralogical origins shows that there is a good correlation between the plasticity index and the flow index in both the Fall cone and the Casagrande methods. The flow index can be calculated using Equations (1) and (2) for the Casagrande method and the Fall cone method, respectively. \[I_{f,p}=\frac{(w_{1}-w_{2})}{\log(N_{1})-\log(N_{2})} \tag{1}\]  
\[I_{f,FC}=\frac{(w_{1}-w_{2})}{\log(D_{1})-\log(D_{2})} \tag{2}\]  
Using previous experimental data, [PERSON] and [PERSON] [35] found that the undrained shear strengths at the liquid limit and plastic limit are 1.7 and 170 kPa, respectively. [PERSON] et al. [36] showed that a unique strength value should not be assigned to the undrained shear strength at the liquid limit and proved that the undrained shear strength ranges measured by different methods at the liquid limit are also different. However, the Fall cone test method is often used to calculate the undrained shear strength for fine-grained soils. [PERSON] [37] proposed the following equation for estimating the undrained shear strength (\(c_{u}\)) of fine-grained soils with Fall cone tests:  
\[c_{u}=K\times\left(\frac{mg}{d^{2}}\right) \tag{3}\]  
where \(K\) is the cone factor, \(m\) is the Fall cone mass, \(g\) is the gravitational acceleration and \(d\) stands for Fall cone penetration. Many researchers [6; 38; 39; 40] carried out several experimental studies to show the variation in the undrained strength of soil with water content. Equation (4) shows the liquidity index (\(I_{L}\)) obtained using both the Fall cone and the Casagrande methods.