# Behaviour of Uniform Drava River Sand in Drained Condition--A Critical State Approach
## 4 Results of Laboratory Tests
\[v=\Gamma-\lambda\cdot\left(\frac{p^{\prime}}{p_{a}}\right)^{\kappa} \tag{5}\]  
where \(v\) is the specific volume, \(\Gamma\) is the value of specific volume at \(p^{\prime}=1\) kPa, \(p^{\prime}\) is the mean effective stress, \(p_{a}\) is the atmospheric pressure of 101.25 kPa and \(\kappa\) is the exponent factor. From the presented compression and extension tests, the elastic soil parameters were determined, Table 5.  
Figure 5: Triaxial test results on sample with relative density 33%: (**a**) mean stress \(p^{\prime}\) vs. deviatoric stress \(q\), (**b**) axial strain \(\epsilon_{a}\) vs. deviatoric stress \(q\), (**c**) mean stress \(p^{\prime}\) vs. specific volume \(v\) and (**d**) axial strain \(\epsilon_{a}\) vs. specific volume \(v\). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Relative Density, \(D_{r}\) (\%)** & \(\Gamma_{c}\) & \(\lambda_{c}\) & \(\kappa_{c}\) & \(\Gamma_{CS}\) & \(\lambda_{CS}\) & \(\kappa_{CS}\) \\ \hline
33 & 1.844 & 0.016 & 0.7 & 1.80 & 0.016 & 0.7 \\
50 & 1.789 & 0.02 & 0.7 & 1.775 & 0.02 & 0.7 \\
80 & 1.692 & 0.016 & 0.7 & 1.725 & 0.016 & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of Equation (4) fit parameters. Figure 6: Triaxial test results on sample with relative density 50%: (**a**) mean stress \(p^{\prime}\) vs. deviatoric stress \(q\), (**b**) axial strain \(\epsilon_{a}\) vs. deviatoric stress \(q\), (**c**) mean stress \(p^{\prime}\) vs. specific volume \(v\) and (**d**) axial strain \(\epsilon_{a}\) vs. specific volume \(v\). \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Relative Density, \(D_{r}\) (\%)** & \(M_{C,f}\) & \(M_{E,f}\) & \(M_{C,cs}\) & \(M_{E,cs}\) & \(\phi^{\prime}_{C,peak}\) & \(\phi^{\prime}_{E,peak}\) & \(\phi^{\prime}_{C,cs}\) & \(\phi^{\prime}_{E,cs}\) \\ \hline
33 & 1.3349 & 0.936 & 1.3109 & 0.9221 & 33.09 & 33.68 & 32.54 & 33.01 \\
50 & 1.3547 & 0.9541 & 1.2326 & 0.7657 & 33.54 & 34.56 & 30.75 & 26.03 \\
80 & 1.4468 & 1.0443 & 1.2114 & 0.7113 & 35.65 & 39.21 & 30.26 & 23.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary strength parameters. From the presented compression and extension tests, elastic soil parameters were determined. Values obtained are summarised in Table 5.  
The values for Young modulus (\(E\)) were obtained during the stress-strain ratios from Figures 5b, 6b and 7b based on a general relation between deviatoric stress (\(q\)) and axial strain (\(\epsilon_{a}\)), Equation (6). The shear modulus was calculated using the relation between deviatoric stress and deviatoric strain, [6], (Equation (7)). The plots of deviatorc stress and deviatorc strain are not presented here. Poisson ration (\(\
u\)) was calculated based on the relation between axial strain and volumetric strain (\(\epsilon_{v}\)), (Equation (8)), while the bulk modulus was calculated using the values of Young modulus (\(E\)) and Poisson's ratio (\(\
u\)). The values of strength ratio in compression and extension, along with effective friction angle are presented in Table 3. These values are based on Figures 5a, 6a and 7a, as described earlier. \[E=\frac{q}{\epsilon_{a}} \tag{6}\]  
\[G=\frac{q}{\epsilon_{q}} \tag{7}\]  
\[\
u=\frac{\epsilon_{v}}{\epsilon_{a}} \tag{8}\]  
Figure 7: Triaxial test results on sample with relative density 80%: (**a**) mean stress \(p^{\prime}\) vs. deviatoric stress \(q\), (**b**) axial strain \(\epsilon_{a}\) vs. deviatoric stress \(q\), (**c**) mean stress \(p^{\prime}\) vs. specific volume \(v\) and (**d**) axial strain \(\epsilon_{a}\) vs. specific volume \(v\). The data from Figures 5c, 6c and 7c are plotted in Figure 8 where filled square marks present the values of specific volume \((v)\) after isotropic consolidation stage while the empty square marks present the specific volume at the assumed critical state. Densely dotted curves are presenting the isotropic consolidation curves, while the dashed curve present the critical state. The data in Figure 8 present a tendency toward a critical state.