## 2 Methodology
### Training and Modelling
#### 2.4.4 Modelling Liquefaction Susceptibility  
In geotechnical engineering, particularly in earthquake-prone regions, the liquefaction susceptibility of soil is a crucial factor to consider. [PERSON] et al. (2004) [1] developed a multi-step method for determining the susceptibility of soil to liquefaction.  
First, the method classifies the soil as either clayey or sandy based on its Atterberg limits. Atterberg limits are the moisture contents at which a soil changes state from solid to liquid (liquid limit) and from liquid to semisolid (plastic limit). As shown in Figure 5, sandy soil is initially classified as liquefiable while clayey soil is classified as non-liquefiable.  
Figure 4: Process in modeling the unit weight of a soil layer.  
Figure 5: Initial considerations in determining liquefiable and non-liquefiable soil layers.  
Once classified as liquefiable, the initial input was the number of blows or penetration resistance (SPT N-value) registered for each penetration interval at a given depth. Due to the variety of hammer designs used in field research, corrections were made using hammers with an efficiency of approximately 60%, and an equation for the correction of SPT N-values was used. Once the corrected SPT N-value was determined, the equivalent clean sand value \(\left(\left(N_{1}\right)_{60 cs}\right)\) and cyclic resistance ratio (\(CRR_{7,5}\)) were computed. However, the \(CRR_{7,5}\) equation is only valid for \(\left(N_{1}\right)_{60 cs}<30\). Since there are clean granular soils that are too dense to liquefy, \(\left(N_{1}\right)_{60 cs}\geq 30\), it is further classed as non-liquefiable.  
After determining CRR, the seismic demand on a soil layer is further computed in terms of the cyclic stress ratio (CSR). The initial process is to analyze the Stress Reduction Coefficient (\(r_{d}\)) based on the depth of each soil layer, z, initially estimated. At a depth of more than 23 m below ground elevation, [PERSON] et al. noted that no occurrences of soil liquefaction were observed, thus, these depths were considered non-liquefiable.  
Aside from \(r_{d}\), the peak ground acceleration (PGA) is also an essential parameter for CSR. PGA is the maximum surface ground acceleration that occurred during an earthquake shaking at a particular location, a deterministic seismic hazard assessment (DSHA) approach was used to estimate PGA, wherein it is based on the expected earthquake magnitude for a specific seismic source and the minimum distance from the site to the fault source. Another essential parameter in determining CSR is the total and effective overburden stresses, the computation is based on the unit weight of the soil being analyzed and groundwater table elevation. Lastly, the factor of safety (FS) against soil liquefaction is computed in terms of CRR, CSR, and magnitude scaling factor (MSF).  
Once the factor of safety for each layer is determined, the calculated probability of liquefaction (PL) is shown in Equation (2). Consequently, the formula depicted in Equation (3) was used to determine the liquefaction severity index (LSI), which is used to evaluate the liquefaction hazard until 20 m below ground elevation. Thereafter, classifications of LSI from very low risk to very high risk were employed, as shown in Figure 6.  
\[P_{L}=\frac{1}{1+\left(\frac{FS}{0.96}\right)^{4.5}} \tag{2}\]  
where the probability of liquefaction (P\({}_{L}\)) is computed using the calculated factor of safety (FS).  
\[LSI=\int_{0}^{20}P_{L}(z)(10-0.5)dz \tag{3}\]  
where the liquefaction severity index (LSI) is computed using the probability of liquefaction (P\({}_{L}\)) and the depth of the soil layer (z, in m).  
Figure 6: Classification of LSI.