# Effect of Characteristics of Ground Motion on Seismically Induced Sliding Surface of Slopes
## 3 Parametric Study  
A parametric study was performed to evaluate the influence of the input motion, slope geometry and soil properties. The matrix of the dynamic analyses performed for the parametric analysis is summarized in Table 1. A total of twelve slope models were used. Three slope angles were used, which are 25\({}^{\circ}\), 35\({}^{\circ}\), and 45\({}^{\circ}\). Two friction angles (\(\phi^{\prime}\)) were used, which are 30\({}^{\circ}\) and 40\({}^{\circ}\). Two cohesion values were assigned, which are 6 kPa and 12 kPa. The \(V_{S}\) profile was generated using the following empirical correlation:  
\[Vs=57.372\ \sigma_{c}^{0.2751} \tag{4}\]  
where \(Vs\) is shear wave velocity (m/s) and \(\sigma_{c}\) is the confining pressure (kPa). The equation was developed from the results of a series of resonant column test using silty sand specimens. The calculated shear wave velocity from the empirical relationship are in line with the typical range for granular soil, as reported in [PERSON] et al. (2019). \(Vs\) was not correlated with the shear strength because the unavailability of the strength and confining pressure dependent correlation to estimate \(Vs\). Additionally, the influence of \(Vs\) on the failure surface is estimated to be marginal. The shear modulus was calculated from \(Vs\), where the density was set to 1.784 g/cm\({}^{3}\). The Poisson's ratio was set to 0.30.  
Among twelve slope models, the baseline characterization is Case 9.  
Four recorded ground motions were used, as listed in Table 2. The baseline corrected motions were amplitude scaled to four peak ground accelerations (PGaAs), which are 0.25 g, 0.50 g, 0.75 g, and 1.0 g, resulting in sixteen motions. The acceleration time history and response spectra of these motions scaled to PGA = 0.25 g are shown in Figure 3. Table 2 lists the characteristics of the input ground motions. The motions are listed in the order of mean period (\(T_{m}\)).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Slope Angle (\({}^{\circ}\))** & **Friction Angle (\(\phi^{\prime}\)) (\({}^{\circ}\))** & **Cohesion (\(c^{\prime}\)) (kPa)** & **Static Factor of Safety** \\ \hline
1 & & & 6 & 1.8 \\
2 & & 30 & 12 & 2.2 \\
3 & & & 6 & 2.5 \\
4 & & 40 & 12 & 2.9 \\ \hline
5 & & & 6 & 1.4 \\
6 & & 35 & 30 & 12 & 1.7 \\
7 & & & 6 & 1.8 \\
8 & & & 40 & 12 & 2.1 \\ \hline
9 & & & 6 & 1.1 \\
10 & & 45 & 30 & 12 & 1.4 \\
11 & & & 6 & 1.4 \\
12 & & & 40 & 12 & 1.7 \\ \hline \hline \end  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Earthquake** & **PGA (g)** & **Predominant Period (s)** & **Mean Period (s)** \\ \hline Whititer Narrows & 0.188 & 0.156 & 0.159 \\ Northridge & 0.221 & 0.20 & 0.250 \\ Ofunato & 0.186 & 0.195 & 0.317 \\ Kobe & 0.25 & 0.34 & 0.646 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristics of input ground motions selected for dynamic analyses.  
Figure 3: Acceleration time histories and 5% damped response spectra of earthquake ground motions used in the analyses (**a**,**b**) Whititer Narrows (**c**,**d**) Northridge (**e**,**f**) Ofunato (**g**,**h**) Kobe.