# Experimental and Empirical Studies to Evaluate Liquefaction Resistance of Partially Saturated Sands
## 3 Materials and Methods
### Testing Stages and Test Program  
The specimens were saturated using the back-pressure method in which the cell and back pressures were steadily increased with a 10 kPa difference (Figure 4a). The back pressures (\(u_{0}\)) applied to the nearly fully saturated sand specimens were high (300-400 kPa), while they were relatively low (100-200 kPa) for the partially saturated sand specimens. The final B values ([PERSON]'s pore pressure coefficient) were recorded; this was followed by the isotropic consolidation of the specimens (Figure 4b). The effective confining stress (\(\sigma_{c}^{\prime}\)) was in the range of 25-100 kPa in the tests. The consolidated specimens were cyclically sheared with a loading frequency of 0.1 Hz (Figure 4c). The applied cyclic-stress ratios (\(CSR\)) ranged from 0.1 to 0.45 depending on the test requirements. The cyclic loading was continued until the excess pore-pressure ratios (\(r_{u}\)) reached 1. Finally, excess pore pressures were allowed to dissipate (Figure 4d). The experiments were performed following the principles in ASTM, D5311/D5311M-13 [58]. Tables 2 and 3 present the testing parameters and typical experimental results obtained in the nearly /fully saturated and partially saturated tests. A total of 60 stress-controlled dynamic triaxial tests were conducted in undrained conditions; 16 of these tests were on nearly or fully saturated sand specimens, which provided a benchmark for the assessment of the influential parameters in partially saturated sand behavior. The rest of the 44 tests were carried out on partially saturated sand specimens. The target relative densities (\(D_{r}\)) were 40% and 85% for the loose and dense specimens, respectively; these were recalculated upon completion of the consolidation of the specimens. The degrees of saturation (\(S_{r}\)) of the partially saturated specimens were determined using the soil phase relationships while considering the amount of pore fluid leaving and entering the specimens during the saturation and/or desaturation process. Following the back- and cell-pressure ramp, the final degree of saturation was in the range of 99-100% and 79-96% for the nearly /fully saturated and partially saturated sand specimens, respectively. Figure 4: Schematic representation of test stages: (**a**) Saturation; (**b**) Consolidation; (**c**) Shearing; (**d**) Dissipation of excess pore pressures. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Test No.** & **Test ID** & \(D_{r}\) **(\%)** & \(S_{r}\) **(\%)** & **B** & \(\sigma_{3}\) **(kPa)** & \(u_{0}\) & \(\sigma^{{}^{\prime}}_{c}\) **(kPa)** & **CSR** & \(N_{liq}\) \\ \hline
1 & FS1 & 39 & 100 & 0.98 & 400 & 300 & 100 & 0.10 & 71 \\
2 & FS2 & 39 & 100 & 0.99 & 400 & 300 & 100 & 0.125 & 27 \\
3 & FS3 & 40 & 100 & 1.00 & 400 & 300 & 100 & 0.15 & 10 \\
4 & FS4 & 41 & 99 & 0.89 & 400 & 300 & 100 & 0.20 & 1 \\
5 & FS5 & 40 & 100 & 0.97 & 350 & 300 & 50 & 0.10 & 85 \\
6 & FS6 & 39 & 100 & 0.99 & 350 & 300 & 50 & 0.125 & 32 \\
7 & FS7 & 39 & 99 & 0.91 & 350 & 300 & 50 & 0.15 & 15 \\
8 & FS8 & 40 & 100 & 0.98 & 350 & 300 & 50 & 0.20 & 1 \\
9 & FS9 & 39 & 100 & 0.99 & 500 & 400 & 100 & 0.10 & 79 \\
10 & FS10 & 38 & 100 & 1.00 & 500 & 400 & 100 & 0.125 & 25 \\
11 & FS11 & 41 & 100 & 0.98 & 500 & 400 & 100 & 0.15 & 10 \\
12 & FS12 & 40 & 100 & 0.99 & 500 & 400 & 100 & 0.20 & 1 \\
13 & FS13 & 83 & 100 & 1.00 & 400 & 300 & 100 & 0.20 & 285 \\
14 & FS14 & 84 & 100 & 0.97 & 400 & 300 & 100 & 0.225 & 65 \\
15 & FS15 & 83 & 100 & 0.98 & 400 & 300 & 100 & 0.25 & 17 \\
16 & FS16 & 85 & 99 & 0.88 & 400 & 300 & 100 & 0.30 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test parameters and typical results for nearly or fully saturated sand specimens. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Test No.** & **Test ID** & **\(D_{r}\) (\%)** & **\(S_{r}\)** & **B** & \(\sigma_{3}\) **(kPa)** & **\(u_{0}\)** & \(\sigma^{{}^{\prime}}_{c}\)** & **CSR** & \(N_{liq}\) \\ \hline  
\hline \hline \end{tabular}
\end{table}