# Calibration of Finn Model and UBSCAN Model for Simplified Liquefaction Analysis Procedures
## 4 Results and Discussion  
### Finn Model  
Tables 4 and 5 list the calibrated inputs for all four simplified liquefaction analysis procedures. The friction angle (\(\varphi\)) was \(\varphi_{peak}\) in Table 3 with a small modification, and the dilation angle, \(\Psi\) (\(=\varphi-\varphi_{cv}\)), is the difference between \(\varphi\) and \(\varphi_{cv}\). Cohesion (\(C\)) was assigned a value of 1 kPa for numerical simulation stability. The model parameters \(C_{1}\) and \(C_{3}\) followed the suggested equations and values of [PERSON] (1996). The Finn model was combined with a FLAC built-in hysteretic model (the Hardin hysteretic model) ([PERSON], 1996) to model the shear modulus degradation curve of sand (1996). The shear modulus reduction equation of the Hardin hysteretic model is expressed as follows:  
\[G/G_{max}=1/(1+(\gamma/\gamma_{ref})), \tag{13}\]  
where \(G\) is the current shear modulus under the cyclic loading, \(G_{max}\) is the small strain shear modulus (i.e., \(G\) in Table 4), \(\gamma\) is the current shear strain under the cyclic loading, and \(\gamma_{ref}\) is the reference shear strain corresponding to \(\gamma\) when the shear modulus reduction ratio is 0.5 (=\(G/G_{max}\)). Table 5 shows that for NCEER and HBF procedures, the values of \(C\_Finn\) at (N\({}_{1}\))\({}_{60\text{cs}}\) = 25 could not be determined because the excess pore pressure ratio, \(\tau_{u}\), was not able to meet \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value or** & **Parameter** & **Value or** \\  & **Relationship** & **Parameter** & **Relationship** \\ \hline \(\varphi\) & \(\varphi_{cv}+0.1\)(N\({}_{1}\))\({}_{60\text{cs}}\) & \(C_{1}\) & 8.7((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{-1.25}\) \\ \(C\) & 1 kPa & \(C_{2}\) & \(C_{1}\times C_{2}\) = \(C\_Finn\) \\ \(T_{cut}\) & 0 & \(C_{3}\) & 0.005\% \\ \(\Psi\) & \((\varphi-\varphi_{cv})\) & \(\varphi_{cv}\) & 33\({}^{\circ}\) \\ \(G\) (= \(G_{max}\)) & Equation (11) & hysteretic model & \(\gamma_{ref}\) = 0.06\% \\ \(B\) & 1.33\(G\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calibrated parameters of the Finn model–[PERSON] formulation in FLAC. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value or Relationship** & **Parameter** & **Value or Relationship** \\ \hline \(K_{G}\)\({}^{e}\) & 21.7 \(\times\) 20 \(\times\) ((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{0.333}\) & \(\varphi_{cv}\) & 33\({}^{\circ}\) \\ \(K_{B}\)\({}^{e}\) & 0.7\(K_{G}\)\({}^{e}\) & \(R_{f}\) & 1.1((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{-0.15}\) \(<\) 0.99 \\ \(K_{G}\)\({}^{p}\) & \(K_{G}\)\({}^{e}\times\) ((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{2}\times\) 0.003 + 100 & \(m\_{flac}1\) & \(a\times(\sigma^{\prime}/P_{a})^{b}\) \\ \(ne/me/np\) & 0.5/0.5/0.4 & \(m\_{flac}2\) & 1 \\ \(\varphi_{peak}\) & \(\varphi_{cv}+0.1\)(N\({}_{1}\))\({}_{60\text{cs}}\) + max(0, ((N\({}_{1}\))\({}_{60\text{cs}}\) \(-\) 15)/5) & \(m\_{flac}3\) & 1 \\  & \(m\_{flac}4\) & 1 \\ \hline \hline \end{tabular} \({}^{1}\)\(a\) = 1.05 \(-\) 0.03(N\({}_{1}\))\({}_{60\text{cs}}\) + 0.004((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{2}\) - 0.000185((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{3}\) + 2.92 \(\times\) 10\({}^{-6}\)((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{4}\); \(b\) = 1/(\(-\)0.424 \(-\)0.299(N\({}_{1}\))\({}_{60\text{cs}}\) + 0.00763 ((N\({}_{1}\))\({}_{60\text{cs}}\))\({}^{2}\)).  
\end{table} 
Table 3: Calibrated parameters of the UBCSAND model (1996). \begin{table} \begin{tabular}{c c c c} \hline \hline
**(N\({}_{1}\))\({}_{60\text{cs}}\)** & **NCEER** & **HBF** & **JRA96** & **T-Y** \\ \hline \(5\) & 0.35 & 0.90 & 0.80 & 0.56 \\ \(10\) & 0.35 & 0.50 & 0.34 & 0.34 \\ \(15\) & 0.35 & 0.43 & 0.29 & 0.19 \\ \(20\) & 0.35 & 0.40 & 0.21 & 0.13 \\ \(25\) & N.A. & N.A. & 0.11 & 0.10 \\ \hline \hline \end{tabular}