# Factors That Affect Liquefaction-Induced Lateral Spreading in Large Subduction Earthquakes
## 2 Background of Lateral Spreading in Subduction Earthquakes
### Current Models and Large-Magnitude Subduction Earthquakes  
[PERSON] (2014) [7] evaluated six empirical models used in practice ([PERSON] et al. (2002) [5]; [PERSON] and [PERSON] (1995) [2], [PERSON] et al. (2006) [3], [PERSON] et al. (2012) [4], and [PERSON] et al. (2004) [17]) with three case-histories from the 2010 Maule Mw 8.8 subduction earthquake. He found that site-to-source distances are difficult to define accurately for large subduction zone earthquakes. They can vary significantly between seismic regions, making it difficult to recommend a method for calculating such an \"R\" value. Figure 4 shows a summary of different distance terms that can be considered: D1 = hypocentral distance, D2 = epicentral distance, D3 = closest distance to high-stress zone, D4 = closet distance to the edge of the fault rupture, D5 = closest distance to the surface projection of the rupture (Joyner Boore distance). In large subduction earthquakes, although there is a small area where the earthquake begins (hypocenter), there are multiple zones on the contact between plates (\"patches\") where energy is released at different times and with different intensities. Hence, although distances D1, D2, and D3 could be defined, they do not necessarily have a reasonable correlation with the intensity of the ground motion at the site of interest. Additionally, for seismically active countries, such as Chile and Peru, D4 and D5 are very small or even zero. From a design point of view, estimating these distances before an earthquake occurs is very difficult. Similarly, [PERSON] (2015) [8] used two case-histories from the 2010 Maule Mw 8.8 earthquake to evaluate the empirical methods developed by [PERSON] et al. (2002) [5] and by [PERSON] and [PERSON] (1995) [2], concluding that they are extremely sensitive to the distance term, R, and that the current definition of R for these two methods (the Joyner Boore distance) resulted in predictions that were more than two times the measured values. The semi-empirical models by [PERSON] et al. (2004) [17] and [PERSON] et al. (2006) [3] also over predicted the displacement but in these cases due to the depth weighting factor of their models. In particular, the empirical model of [PERSON] et al. (2004) [4] predicted displacements roughly six to eight times larger than the measured displacements. On the other hand, [PERSON] et al. (2017) [22] studied one case history (Caleta Lo Rojas) from the 2010 Maule Mw8.8 earthquake. They used the [PERSON] et al. (2002) [5] methodology with different distances, finding that the \begin{table}
\begin{tabular}{l l} \hline \hline
**Author(s)** & **Variables** \\ \hline [PERSON] and [PERSON] (2014) [19] & Ground slope, thickness of the liquefiable layer, fines content, average grain size, earthquake magnitude, horizontal distance from the site to the seismic energy source. \\ [PERSON] et al. (2019) [20] & Ground slope, thickness of the liquefiable layer, fines content, average grain size, earthquake magnitude, cumulative absolute velocity, peak ground acceleration. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 4: Distances from an earthquake source to the site of interest (adapted from [PERSON] (1988) [21]). distance to the zone that bounds 10% of the largest slips resulted in satisfactory values when compared against in-situ post-earthquake measurements. In this study, we analyzed 13 lateral spread cases from six sites affected by the 2010 Maule Mw 8.8 earthquake, where lateral spreading took place (Figure 5). Figure 6 shows a comparison between observed and calculated lateral spreading using [PERSON] et al. 's (2002) [5] methodology with three R-value definitions. The first one is the original R from [PERSON] et al. 's (2002) [5] methodology, the second one is the distance to the maximum observed coastal uplift, and the third one is the distance used by [PERSON] et al. (2017) [22], which is defined as the distance to the zone that bounds 10% of the largest slips.