## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**References**} & \multirow{2}{*}{**Sand**} & \multirow{2}{*}{\begin{tabular}{c} **Test** \\ **Method** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(\alpha^{\prime}_{\rm e}\) \\ **(x)a** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **D\({}_{\rm r}\)** \\ **(x)a** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Failure** \\ **Criteria** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **N\({}_{\rm Liq}\)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(f\) (Hz)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Frequency** \\ **Effect** \\ \end{tabular} } \\ \hline
1 &
\begin{tabular}{c} [PERSON] and \\ [PERSON] [2] \\ \end{tabular} & Bandajima & CTOR & 33 & 37 & \(\tau_{\rm u}=1\) & NA & 1–12 & None \\ \hline
2 & [PERSON] et al. [4] & Toyoura & CTX & 98 & 50–80 & \(\iota_{\rm a}=10\)\% DA & 10 & 0.05, 0.5 & \\ \hline
3 & Polito [6] & Monterey & CTX & 100 & 74 & \(\tau_{\rm u}=1\) & 10, 15 & 0.5, 1 & \\ \hline
4 & [PERSON] et al. [3] & Monterey & CTX & 100 & 60 & \(\tau_{\rm u}=1\) & NA & 0.067, 0.33 & Negligibly \\ \hline
5 &
\begin{tabular}{c} Sae [8] \\ \end{tabular} & Toyoura & CTX & 100–500 & 10–70 & \(\iota_{\rm a}=5\)\% DA & 10 & 0.01, 1 & \\ \hline
6 &
\begin{tabular}{c} Peacock and Seed \\ [9] \\ \end{tabular} & Monterey & SS & 500 & 50 & \(\tau_{\rm u}=1\) & 10 & 0.17-4 & Very small \\ \hline
7 & [PERSON] et al. [5] & Toyoura & CTX & 100 & 50 & \(\iota_{\rm a}=10\)\% DA & 10 & 0.05, 1 & \\ \hline
8 & [PERSON] and Zhou [7] & Dongtinghu & CTX & 150 & 58 & \(\iota_{\rm a}=10\)\% DA & NA & 1, 3, 5 & \\ \hline
9 & Lee and Fitton [10] & \
\begin{tabular}{c} EI Monte \\ sand and Silt \\ \end{tabular} & CTX & 100 & 50,75 & \(
\begin{tabular}{c}\iota_{\rm a}=5,10,\\ 20\%\) DA \\ \end{tabular} & 30 & 0.17, 1 & Higher \\ \hline
10 &
\begin{tabular}{c} Feng and Zhang \\ [11] \\ \end{tabular} & Fujian & CTX & 100 & 30 & \(\iota_{\rm a}=5\)\% DA & 20, 30 & 0.05–2 & \\ \hline
11 & [PERSON] et al. [12] & Gravel sand & CTX & 100–300 & 25 & \(\tau_{\rm u}=1\) & NA & 0.5–2 & \\ \hline
12 & [PERSON] and [PERSON] [13] & Sandy soil & CTX & 100–300 & 28,70 & \(\tau_{\rm u}=1\) & 12, 30 & 0.05, 0.1, 1 & \\ \hline
13 & [PERSON] et al. [14] & Monterey & CTX & 100 & 50 & \(\iota_{\rm a}=5\)\% DA & 10 & 0.017, 1 & Higher \\ \hline \hline \end{tabular} Note: (1) confining stress (\(\alpha^{\prime}_{\rm e}\)); relative density (D\({}_{\rm r}\)); number of cycles to liquefactions (\({\bf N_{\rm Liq}}\)); loading frequency (\(f\)). (2) Cyclic triaxial (CTX); cyclic torsional shear (CTOR); simple shear (SS). (3) Axial strain (\(\iota_{\rm a}\)); double amplitude (DA); excess pore pressure ratio (\(\tau_{\rm u}\)). Not available (NA).  
\end{table} 
Table 1: Literature review on loading frequency effect. tests. In the cyclic triaxial tests, the major principal stress is always parallel or perpendicular to the vertical direction. Cyclic direct simple shear loading causes the continuous rotation of principle stress axes, which can be better to simulate the rotation of principal stress caused by earthquakes. Due to the contradictory conclusions and limited data on CDSS tests on the effect of the loading frequency on the liquefaction prediction of sand, the effect of loading frequency on the liquefaction prediction of sand requires further attention. In this study, a series of CDSS tests were performed on loose and dense clean dry sand obtained from Nakdong River. Loading frequencies of 0.05, 0.1, 0.5, and 1 Hz were considered for evaluating the effect of the loading frequency on the liquefaction resistance of the sand.