## 2 Research Methods and Results
Laboratory experiments with sandy soils were complemented by strength tests performed using the direct shear apparatus GPP-30, designed by Institute \"Hydroproject\". For this purpose, the consolidated drained method of shear strength testing was used. It  
Figure 5: Scatter plots of the permeability coefficient for conditionally pure and contaminated sands versus their density: (**a**) loose structure; (**b**) dense structure. implies shearing previously consolidated samples in compression at a slow rate, which allows pore pressure built up during the experiment to dissipate. The method is widely used for the determination of a sand's shear strength [22; 23; 24; 25; 26]. For experiments to be conducted, 12 air-dried samples of pure and contaminated sands were prepared--6 of both loose and dense types of structures. In accordance with the recommendations outlined in normative documents, a set of three samples was subjected to controlled normal stress (\(\sigma\))--100 kPa, 150 kPa, and 200 kPa in each experiment. After that, inducing strain lateral load was applied until samples failed. Thus, peak stresses (\(\tau\)) were found (Table 2). Test results produced graphs of shear stress as a function of normal stress (Figure 6). They were used to determine shear strength parameters--cohesion c (kPa) and angle of internal friction \(\phi\) (deg. ). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Laboratory**} & \multicolumn{2}{c}{**Conditionally Pure Sand**} & \multicolumn{2}{c}{**Conaminated Sand**} \\ \cline{2-6}  & \multicolumn{2}{c}{**Stress, kPa**} & \multirow{2}{*}{**Laboratory**} & \multicolumn{2}{c}{**Stress, kPa**} \\ \cline{2-6}  & **Normal** & **Shear** & **Sample** & **Normal** & **Shear** \\  & **(Confining),** & **(Tangential),** & & **(Confining),** & **(Tangential),** \\  & \(\sigma\) & \(\tau\) & & \(\sigma\) & \(\tau\) \\ \hline \hline \multicolumn{6}{c}{**Loose structure**} \\ \hline
1 & 100 & 65 & 7 & 100 & 75 \\
2 & 150 & 99 & 8 & 150 & 119 \\
3 & 200 & 130 & 9 & 200 & 170 \\ \hline \hline \multicolumn{6}{c}{**Conditionally Pure Sand**} & \multicolumn{2}{c}{**Contaminated Sand**} \\ \cline{2-6}
**Laboratory** & \multicolumn{2}{c}{**Stress, kPa**} \\ \cline{2-6}
**sample** & \multicolumn{2}{c}{**Normal**} & **Shear** & **Laboratory** & **Stress, kPa** \\  & **(Confining),** & **(Tangential),** & **sample** & **Normal** & **Shear** \\  & \(\sigma\) & \(\tau\) & & **(Confining),** & **(Tangential),** \\  & \multicolumn{2}{c}{Dense structure**} \\ \hline
4 & 100 & 95 & 10 & 100 & 85 \\
5 & 150 & 126 & 11 & 150 & 126 \\
6 & 200 & 160 & 12 & 200 & 190 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Shear strength test results for sands. Figure 6: _Cont._  
Shear strength parameters were determined using a straight-line equation describing the linear curve fitting the test result points. The equation is also known as [PERSON]'s shear strength equation:  
\[\tau=\sigma\cdot\tan\ \phi+c, \tag{2}\]  
where \(\sigma\) is an effective normal stress on the rupture plane, kg/cm\({}^{2}\); \(\tan\ \phi\) is termed as the coefficient of internal friction of the soil; \(\phi\) is the angle of internal friction; the intercept \(c\) is the cohesion of the soil, kPa. Figure 6 shows that in conditionally pure loose sand (Figure 6a), \(\phi\) is 33\({}^{\circ}\) and the c value is at a near-zero level. For dense sand (Figure 6b), \(\phi\) remains the same, whereas c increases significantly up to 30 kPa. In contaminated sands, another pattern is detected. An observation can be made that \(\phi\) of sand with loose structure (Figure 6c) is 37\({}^{\circ}\), \(c=2\) kPa. In the case of a dense structure, \(\phi\) increases by 2\({}^{\circ}\) (39\({}^{\circ}\)), and c increases to 5 kPa. The results suggest that the increase in the density of contaminated sands has less impact on change in strength parameters compared to conditionally pure sands.