# Viscosity of Clayey Soils: Experimental Studies
## 3 Results
### Effect of Shear Rate on Ultimate Shear Resistance of Clay Soil  
According to the well-known concept of [PERSON] [3,4], the ultimate shear resistance of clay soil (\(\tau^{*}\)) can be represented as the sum of Coulomb friction (\(\sigma tg\varphi\)), structural cohesion (\(c_{c}\)) and cohesion of water-colloid bonds (\(c_{w}\)), which depend on moisture content, i.e.,  
\[\tau^{*}=\sigma tg\varphi+c_{c}+c_{w}, \tag{2}\]  
Agreeing with this representation of the ultimate shear resistance of clay soil (\(\tau^{*}\)), it should be noted that it does not take into account the effect of the shear rate (\(\dot{\gamma}\)). Indeed, under kinematic shear (\(\dot{\gamma}=const\)) in a soil medium possessing viscosity, viscous resistance may manifest (\(c_{\dot{\gamma}}\)). Assuming that the viscous resistance is due to the viscosity of the soil as a whole, then under kinematic shear, viscous resistance will arise (\(c_{\dot{\gamma}}=\dot{\gamma}\eta\)). Based on the above, the total cohesion (\(c\)) in clay soil can be represented as the sum of structural cohesion (\(c_{c}\)), cohesion of water-colloid bonds (\(c_{w}\)) and viscous resistance (\(c_{\dot{\gamma}}\)), i.e.,  
\[c=c_{c}+c_{w}+c_{\dot{\gamma}}, \tag{3}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Vertical** & **Shear Displacement** & **Soil Viscosity at the First** & **Soil Viscosity at the** \\
**Stress, kPa** & **Rate, mm/min** & **Section, kPa-min** & **Second Section, kPa-min** \\ \hline \(\sigma_{n}\) & \(\dot{u}\) & \(\gamma_{1}\) & \(\gamma_{2}\) \\ \hline  & 5 & 539 & 418 \\  & 0.5 & 5680 & 4466 \\
600 & 0.05 & 55,264 & 61,732 \\  & 0.005 & 576,840 & 610,720 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 3: Characteristic graph of the dependence of shear stresses on shear strains (\(\tau-\gamma\)) with division into characteristic sections. It is clear that in order to account for the influence of shear rate (\(\dot{\gamma}\)) on the shear resistance of a clay soil, it is necessary to conduct at least three tests at different shear rates (\(\dot{\gamma}_{1}<\dot{\gamma}_{2}<\dot{\gamma}_{3}\)). In the laboratory of the REC \"Geotechnics\" named after [PERSON] (National Research Moscow State University of Civil Engineering) experimental studies were conducted on samples of fluid-plastic loam using a simple shear device in a kinematic loading mode (\(\dot{\gamma}=const\)) (at a constant shear displacement rate equal to \(\dot{u}=\dot{\gamma}h\)) at four different shear rates (\(\dot{\gamma}_{1}>\dot{\gamma}_{2}>\dot{\gamma}_{3}>\dot{\gamma}_{4}\)) and under three different constant vertical loads (\(\sigma_{1}<\sigma_{2}<\sigma_{3}\)) applied to the soil sample during testing. Figures 4-7 show the results of the tests of flow-plastic loam in the simple shear device in the kinematic loading mode (\(\dot{\gamma}=const\)). Figure 4: Graph of the dependence of acting shear stresses on shear strains (\(\tau-\gamma\)) and graph of the dependence of ultimate shear stresses on normal stresses (\(\tau^{*}-\sigma\)) during testing of clay soil in a simple shear device in the kinematic loading mode at a constant shear displacement rate of \(\dot{u}=5\) mm/min and at different values of \(\sigma_{n}\). Figure 5: Graph of the dependence of acting shear stresses on shear strains (\(\tau-\gamma\)) and graph of the dependence of ultimate shear stresses on normal stresses (\(\tau^{*}-\sigma\)) during testing of clay soil in a simple shear device in the kinematic loading mode at a constant shear displacement rate of \(\dot{u}=0.5\) mm/min and at different values of \(\sigma_{n}\). the work of [PERSON]. [33], showed (Figure 8) that the ultimate lines at different shear rates (\(\dot{\gamma}_{1}>\dot{\gamma}_{2}>\dot{\gamma}_{3}>\dot{\gamma}_{4}\)) have the same slope equal to \(\varphi=const\), and this angle does not depend on the shear rate (\(\dot{\gamma}\)). The ultimate shear resistance of clay soil (\(\tau^{\ast}\)) significantly depends on the internal friction angle (\(\varphi\)) and the cohesive strength (\(c\)).