# Viscosity of Clayey Soils: Experimental Studies
## 1 Introduction
In simple shear, the cubic specimen takes the shape of an inclined parallelepiped at the end of the test. Depending on the design and assembly method of the simple shear device, it is possible to determine not only the usual strength (specific cohesion (\(c\)), angle of internal friction (\(\varphi\)), angle of dilatancy (\(\psi\))) and deformation (ground shear modulus (\(G\)), shear strain (\(\gamma\))) characteristics of tested soil samples, but also to determine rheological parameters (ground viscosity (\(\eta\))). The concept of viscosity originates from [PERSON]'s discovery in 1687 of the basic law of viscous liquids, according to which the internal friction in the flow of a fluid, arising <<due to insufficient slip of the fluid particles>>, is proportional to the shear rate at which these fluid particles move relative to each other. A fluid obeying this law is called an ideal viscous (Newtonian) fluid. In a Newtonian fluid at any shear stress different from zero, a viscous flow develops in time with a constant shear strain rate \(\left(\dot{\gamma}=const\right)\), and this shear rate is directly proportional to the shear stress. The viscosity coefficient of the soil can be determined from tests in which the relationship between the angular strain rate and the acting shear stress on the soil specimen can be determined. Thus, it can be concluded that the viscosity coefficient or, in other words, dynamic viscosity defines a measure of the resistance of the soil to its deformations. Soil viscosity is measured in Poise (1 Poise = 0.1 Pa-sec). The viscosity of different media varies over a fairly wide range. For example, the viscosity of air is \(1.8\cdot 10^{-4}\) Poise, the viscosity of water is--\(1.0\cdot 10^{-2}\) Poise, the viscosity of various oils generally ranges from 0.5 to 10 Poise and the viscosity of the Earth's crust reaches about \(5.0\cdot 10^{22}\) Poise. Based on the performed experimental studies, as well as the analysis and generalization of both his results and the results obtained by other researchers, [PERSON]. [3] determined the following average values of the dynamic viscosity coefficient of melted clay depending on its state (consistency): soft plastic clay--\(\eta\) = \(10^{10}\)-\(10^{11}\) Poise; tight plastic clay--\(\eta\) = \(10^{12}\)-\(10^{13}\) Poise; semi-hard clay--\(\eta\) = \(10^{14}\)-\(10^{15}\) Poise; and hard clay--\(\eta\) = \(10^{15}\)-\(10^{17}\) Poise. The methodology of determining the coefficient of viscosity of soil, as well as the great variety of properties of the soils themselves have a great influence on the obtained values of viscosity coefficients for different soils, which can explain the large variation in the obtained values. In most cases, according to [PERSON], there is a misinterpretation of the value itself. Indeed, taking viscosity as a constant quantity \((\eta=const)\) is valid only for a perfectly viscous (Newtonian) medium. In soils, the relationship between stress and flow rate is nonlinear, and as a consequence, the viscosity coefficient of the soil will be a variable value depending on both the magnitude of the applied load and the time of its action. For example, at the beginning of the test, when the ground deformations are still small, the viscosity of the ground may be \(10^{13}\) Poise and closer to the end of the deformation stage, the viscosity coefficient value may increase to \(10^{14}\) Poise. This phenomenon was confirmed by [PERSON] in his work [29] based on experimental studies on sandy soil samples in a triaxial compression device in the kinematic loading mode. Based on the results of the performed studies, the dependences of sandy soil viscosity on the angular strain rate were obtained. The presented work also described a methodology that allows the determination of the viscosity of air-dry and water-saturated sandy soil based on triaxial tests in kinematic loading mode. This methodology is based on the application of [PERSON]'s elastic-viscous rheological model [29].