# Factors That Affect Liquefaction-Induced Lateral Spreading in Large Subduction Earthquakes
## 4 Parametric study using Nonlinear Site Response Analysis
### Results  
A total of 120 nonlinear site response analyses were performed. The numerical models were run in Cylic1D, and the primary purpose was to obtain, for each model, the maximum lateral displacement on the surface and correlate it with different intensity measures (IM). For the parametric study, the ground motions were scaled to 0.11 g, 0.22 g, and 0.33 g of PGA to measure the effect of PGA variability with lateral displacement. Figure 21 and Table 9 show the main results of the parametric analysis.  
The coefficient of determination (R\({}^{2}\)), the Pearson correlation coefficient (\(\rho\)), and the Spearman rank correlation coefficient (r\({}_{\rm{s}}\)) were used to quantify the correlation between lateral displacements at the surface (LD) and intensity measurements. These correlation coefficients can range from \(-1\) to \(+1\), where \(-1\) means total negative correlation, 0 means no correlation, and \(+1\) means total positive correlation. As Table 9 shows, the most influential parameters were CAV = cumulative absolute velocity (R\({}^{2}\) = 0.87, \(\rho\) = 0.93, r\({}_{\rm{s}}\) = 0.88), HI = Housner intensity (R\({}^{2}\) = 0.78, \(\rho\) = 0.88, r\({}_{\rm{s}}\) = 0.79) and SMV = Sustained Maximum Velocity (R\({}^{2}\) = 0.78, \(\rho\) = 0.88, r\({}_{\rm{s}}\) = 0.79). In this case, the three coefficients are the highest. On the other hand, the least influential parameters were Tp = predominant period (R\({}^{2}\) = 0.01, \(\rho\) = \(-0.05\), r\({}_{\rm{s}}\) = 0.17) and DRMS = root-mean-square displacement (R\({}^{2}\) = 0.01, \(\rho\) = \(-0.02\), r\({}_{\rm{s}}\) = 0.06).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Intensity Measures (IM)** & **R\({}^{2}\)** & \(\rho\) & **r\({}_{\rm{s}}\)** \\ \hline Cumulative absolute velocity (CAV) & 0.87 & 0.93 & 0.88 \\ Housner intensity (HI) & 0.78 & 0.88 & 0.79 \\ Sustained maximum velocity (SMV) & 0.78 & 0.88 & 0.79 \\ Peak ground velocity (PGV) & 0.77 & 0.88 & 0.78 \\ Velocity spectrum intensity (VSI) & 0.76 & 0.87 & 0.78 \\ Arias intensity (AI) & 0.73 & 0.85 & 0.77 \\ Specific energy density (SED) & 0.66 & 0.81 & 0.85 \\ Intensity characteristic (Ic) & 0.58 & 0.78 & 0.62 \\ Uniform duration (UD) & 0.55 & 0.76 & 0.72 \\ Room-mean square velocity (VRMS) & 0.48 & 0.46 & 0.48 \\ Significant duration (D\({}_{5.95}\)) & 0.48 & 0.69 & 0.60 \\ Mean period (Tm) & 0.47 & 0.68 & 0.60 \\ Bracketed duration (BD) & 0.30 & 0.55 & 0.69 \\ Effective design acceleration (EDA) & 0.29 & 0.54 & 0.53 \\ Sustained maximum acceleration (SMA) & 0.25 & 0.50 & 0.44 \\ Acceleration spectrum intensity (ASI) & 0.21 & 0.70 & 0.50 \\ Room-mean square acceleration (ARMS) & 0.21 & 0.46 & 0.63 \\ Parameter A95 (A95) & 0.03 & 0.18 & 0.34 \\ Predominant period (Tp) & 0.01 & \(-0.05\) & 0.17 \\ Room-mean square displacement (DRMS) & 0.01 & \(-0.02\) & 0.06 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Correlation between Intensity Measure (IM) and Lateral Displacement (LD).  
Figure 21: Relationship between the selected intensity measures (IM) and lateral displacement (LD).