# Factors That Affect Liquefaction-Induced Lateral Spreading in Large Subduction Earthquakes
## 3 Validation of the Numerical Methodology
### Validation with Centrifuge Tests
#### 3.1.1 General Description of the Centrifuge Tests  
The project Verification of Liquefaction Analysis by Centrifuge Studies (VELACS) was a cooperative research effort involving eight universities to study soil liquefaction problems ([PERSON] and [PERSON] (1993) [32]). In that project, a series of dynamic centrifuge tests was performed on a variety of different saturated soil models ([PERSON] and [PERSON] (1993) [32]). In this section, we present the simulation of the centrifuge model 2 of the VELACS project conducted at Renneselaer Polytechnic Institute (RPI) by [PERSON] and [PERSON] (1998) [27] and numerically validated by [PERSON] et al. (2002) [9]. In this test, the soil profile consisted of submerged 20 cm high (physical model) uniform Nevada sand, of Dr = 40%-45%, inclined by 2\({}^{\circ}\) with respect to the horizontal (more details in Table 4). The experiment was conducted at 50 g centrifugal acceleration. A sketch of the laminar box and the instrumentation is shown in Figure 7. The lateral input shaking applied to the base of the model and its corresponding 5% damped pseudo acceleration response spectra are shown in Figure 8. \begin{table}
\begin{tabular}{c c} \hline
**Property** & **Value** \\ \hline Specific gravity & 2.68 \\ Maximum dry density & 17.33 kN/m\({}^{3}\) \\ Minimum dry density & 13.87 kN/m\({}^{3}\) \\ Maximum void ratio & 0.894 \\ Minimum void ratio & 0.516 \\ D\({}_{50}\) & 0.15 mm \\ Hydraulic conductivity & 0.0021 cm/s \\ \hline \end{tabular}
\end{table} 
Table 4: Characteristics of Nevada Sand ([PERSON] and [PERSON] (1998) [27]). \begin{table}
\begin{tabular}{l c c c c c} \hline
**Parameter** & **Nevada Sand** & **Ottawa F65** & **Mean Value 1** & **Standard** & **Coefficient of** \\  & **Dr = 40\%** & **Dr = 65\%** & **Deviation 1** & **Variation 1** [\%] \\ \hline Mass density [\(\rho\)] (kg/m\({}^{3}\)) & 1800 & 1900 & 1570 & 270 & 9\% \\ Reference shear wave & & 203.3 & 203.3 & 242.5 & 16.5 & 28\% \\ velocity [Vs ref] (m/s) & & & & & \\ Confinement & 0.5 & 0.5 & & & \\ coefficient of lateral & & 0.5 & 0.67 & & \\ Friction angle [\(\varphi\)] (\({}^{\circ}\)) & 31.4 & 31.4 & 40.5 & 2.1 & 5\% \\ Peak shear strain & & 5 & 5 & & \\ [\(\gamma\) max] (\%) & & & & & \\ Number of yield surfaces & & 20 & 20 & & \\
[NYS] & & & & & \\ Phase transformation angle & 26.5 & 26.5 & 32.9 & 2.2 & 7\% \\
[PT angle] (\({}^{\circ}\)) & & & & & \\ Contraction parameter 1 [c1] & 0.19 & 0.19 & 0.12 & 0.04 & 32\% \\ Contraction parameter 2 [c2] & 0.2 & 0.2 & & & \\ Dilatation parameter 1 [d1] & 0.2 & 0.2 & 0.11 & 0.04 & 42\% \\ Dilatation parameter 2 [d2] & 10 & 10 & & & \\ Liquefaction parameter [Liq] & 0.015 & 0.015 & & & \\ Permeability coefficient & & & & & \\
[Perm k] (m/s) & \(3.3\times 10^{-3}\) & \(6.6\times 10^{-5}\) & & & \\ \hline \end{tabular} \({}^{1}\) Mean value and standard deviation from [PERSON] et al. (2019) [30] and [PERSON] et al. (1995) [31].  
\end{table} 
Table 3: Input variables for Cyclic1D’s numerical model. Similarly, the Liquefaction Experiments and Analysis Project (LEAP) was a cooperative effort among several universities and research institutes to investigate liquefaction and its effects on geostructures ([PERSON] et al. (2018) [33]). The data are available on the Network for Earthquake Engineering Simulations (NEES) website ([PERSON] et al. (2017) [34]). In this section, we show the simulation of the centrifuge LEAP project conducted at Renneselaer Polytechnic Institute (RPI) ([PERSON] et al. (2018) [33]). In this test, the soil layer was 4 m high at the center of the model (prototype dimension), and a uniform medium dense sand (Ottawa F-65) was used. The soil had a relative density of \(\mathrm{Dr}=65\%\) and a \(5^{\circ}\) slope (more details in Table 5).