## 3 Development of Seismic Soil Liquefaction Modeling
### Model Development Using BBNs  
A BBN structure is developed by using data fusion methodology based on an ML algorithm i.e., K2 learning from CPT case histories using FullBNT-1.0.7 tool in MATLAB, following which effective information is embedded as DK (deleting direct links of depth of soil deposit and thickness of soil layer to liquefaction potential) (see Figure 2). Consequently, the new BBN comprises of two separate networks as the thickness of soil layer has no relation to the other nodes, implying that the thickness of soil layer can be detached from the model. Thus, the network is composed of 11 nodes and several lines. The lines among these nodes represent the relationships. It can be seen from Figure 2 that soil liquefaction variables have counter-intuitive results by means of dependence. For example, \"peak ground acceleration\" is dependent on \"earthquake magnitude\", \"closest distance to rupture surface\", and others.  
\begin{table}
\begin{tabular}{l l c c c c} \hline \hline
**Seismic Soil Liquefaction Factors** & **Dataset** & **Minimum** & **Maximum** & **Mean** & **Standard Deviation** \\ \hline \multirow{2}{*}{Earthquake magnitude, \(M\)} & Training & 5.9 & 9 & 7.01 & 0.55 \\  & Testing & 5.9 & 9 & 6.88 & 0.56 \\ \multirow{2}{*}{Peak ground acceleration (PCA), \(a_{\text{max}}\) (g)} & Training & 0.09 & 0.84 & 0.32 & 0.14 \\  & Testing & 0.09 & 0.8 & 0.32 & 0.17 \\ \multirow{2}{*}{Closest distance to rupture surface, \(r_{\text{rnp}}\) (km)} & Training & 1 & 107.03 & 18.15 & 17.08 \\  & Testing & 1 & 100.36 & 18.57 & 17.92 \\ \multirow{2}{*}{Fines content, \(F_{c}\) (\%)} & Training & 0 & 85 & 18.65 & 19.92 \\  & Testing & 0 & 75 & 13.94 & 15.98 \\ \multirow{2}{*}{Equivalent clean sand penetration resistance, \(q_{\text{t1 Ncs}}\)} & Training & 16.1 & 311.9 & 93.83 & 38.82 \\  & Testing & 36.7 & 206.3 & 94.79 & 33.85 \\ \multirow{2}{*}{Soil behavior type index, \(l_{c}\)} & Training & 1.16 & 2.59 & 1.98 & 0.29 \\  & Testing & 1.34 & 2.5 & 1.90 & 0.25 \\ \multirow{2}{*}{Vertical effective stress, \(\sigma^{*}\) (kPa)} & Training & 19 & 147 & 56.60 & 24.12 \\  & Testing & 24 & 124 & 61.70 & 26.06 \\ \multirow{2}{*}{Total vertical stress, \(\sigma_{v}\) (kPa)} & Training & 24 & 210 & 79.90 & 36.48 \\  & Testing & 34 & 162 & 86.26 & 36.26 \\ \multirow{2}{*}{Groundwater table depth, \(D_{w}\) (m)} & Training & 0.2 & 7.2 & 2.00 & 1.20 \\  & Testing & 0.2 & 6.4 & 2.19 & 1.26 \\ \multirow{2}{*}{Depth of soil deposit, \(D_{s}\) (m)} & Training & 1.4 & 11.8 & 4.38 & 1.96 \\  & Testing & 1.9 & 8.7 & 4.71 & 1.93 \\ \multirow{2}{*}{Thickness of soil layer, \(T_{s}\) (m)} & Training & 0.3 & 6.5 & 1.79 & 1.19 \\  & Testing & 0.3 & 5 & 1.98 & 1.33 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Descriptive statistics of variables used in the model training and testing dataset.  
The network structure is created in Netica free version software (distributed by Norsys Software Corporation ([[https://www.norsys.com/](https://www.norsys.com/)]([https://www.norsys.com/](https://www.norsys.com/))) under Norsys License Agreement) to acquire conditional probability distribution of the nodes via parameter learning. Ultimately, a Bayesian belief network model was created to assess seismic soil \"liquefaction potential\", as shown in Figure 3.