## 1 Introduction  
The presence of clay minerals in a fine-grained soil permits remolding without crumbling in the presence of some moisture. If a clay slurry is dried, the moisture content will gradually decrease, and the slurry will transform from a liquid state to a plastic state. With further drying, it will change to a semisolid state and finally to a solid state (Figure 1). [PERSON] [1] developed a method for describing the limit consistency of fine-grained soils on a moisture content basis. These limits are the liquid limit (_LL_), the plastic limit (_PL_) and the shrinkage limit (_SL_). The liquid limit is defined as the water content, in percent, at which the soil changes from a liquid state to a plastic state. The water contents at which the soil changes from a plastic to a semisolid state and from a semisolid to a solid state are defined as the plastic limit and the shrinkage limit, respectively [2]. These limits are generally referred to as the Attterberg limits [1]. The Atterberg limits of cohesive soil depend on the several factors, such as amount and type of clay minerals and type of adsorbed cation. The plasticity index is a parameter that is used to classify clayey and/or silty soils by use of a plasticity chart. The plasticity index (_PI_) is a measure of the plasticity of a soil. The plasticity index is the size of the range of water contents where the soil exhibits plastic properties. The PI is the difference between the liquid limit and the plastic limit (PI = LL \(-\) PL). The importance of the plasticity chart describes plasticity as a two-dimensional property. The chart is widely used to distinguish between clays and silts and further subdivide them based on their consistency properties. It was experimentally proven by many researchersthat plasticity index is highly correlated with many engineering properties, such as compaction characteristics, compression index, coefficient of consolidation, swelling potential, internal friction angle and undrained shear strength [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. The activity (\(A=PI/CF\)) of the soil can be defined as the ratio of the plasticity index to the clay fraction (\(CF\)) as a percentage. However, a plasticity index is also needed to obtain parameters such as activity, liquidity index and log liquidity index, which are well-correlated with the engineering properties of soils. Since it has wide applications in geotechnical engineering, it is desirable to determine it with reasonable accuracy. In other words, emphasis is placed on the correct determination of the liquid and plastic limits of fine-grained soils. Currently, there are two methods in the literature for determining the liquid limit of a fine-grained soil, namely, the Casagrande cup and the Fall cone methods. Compared to other factors, operator experience is one of the most important factors affecting the results of the Casagrande method. The Fall cone method is more advantageous than the Casagrande method due to its ease in application, simplicity and comparable reproducibility. However, for fine-grained soils with low plasticity, the Casagrande method is more difficult due to the difficulty of cutting the groove and sliding of the soil mass rather than the flow of the soil mass [3; 4; 5; 9; 12; 20; 22; 24]. Nowadays, since its use is more feasible, many European Union countries, Canada, England and India prefer to use the Fall cone method as one of the standard methods to determine the liquid limit of fine-grained soils [7; 8; 9; 10; 22; 24]. There are two types of cone penetration testers in the world in general use, namely, the British cone [25] and the Swedish cone. The British cone [25] specifies a \(30^{\circ}/80\) g cone and a \(20\) mm penetration depth at the liquid limit, while the Swedish cone specifies a \(60^{\circ}/60\) g cone and a \(10\) mm penetration depth at the liquid limit. However, both types of cone penetration tests provide approximately the same results [7; 26].