## 3 Development of Seismic Soil Liquefaction Modeling  
### Dataset, Date Preprocessing, and Predictor Variables  
The dataset used in this study is based on an updated version of cone penetration test case history records compiled by [PERSON] and [PERSON] [37]. The dataset consists of 253 cases with soil behavior type index, \(I_{c}\) < 2.6; 180 of them are liquefied cases, 71 are non-liquefied cases, and the remaining 2 are doubtful cases (margin between liquefaction and non-liquefaction), which have been eliminated in this study to reduce epistemic uncertainty (an individual case record can have only one performance outcome--either liquefaction or non-liquefaction). These case history records are derived from CPT measurements at sites and field performance observations of 17 different earthquakes--7 in the United States of America, 4 in New Zealand, 3 in Japan, and 1 each in China, Taiwan, and Turkey. Readers can refer to [PERSON] and [PERSON] [37] for details of the CPT case histories. Soil liquefaction is influenced by seismic parameters, soil properties, and site geometry conditions that contain a diversified set of factors. Previous studies [25; 26; 38; 39; 40; 41] offer a detailed understanding of the process, leading to appropriate selection of variables, discretization, and classification in this study. Therefore, 11 influence factors or variables--earthquake magnitude (\(M\)), peak ground acceleration (\(a_{max}\), \(g\)), closest distance to rupture surface, (\(r_{rupt}\), km), fines content (\(F_{c}\), %), equivalent clean sand penetration resistance (\(q_{c1N\text{s}}\)), soil behavior type index (\(l_{c}\)), vertical effective stress (\(\sigma\)', kPa), total vertical stress, (\(\sigma_{v}\), kPa), groundwater table depth (\(D_{w}\), m), depth of soil deposit (\(D_{s}\), m), and thickness of soil layer (\(T_{s}\), m)--are used for evaluation of liquefaction potential. The new earthquake factor i.e., closest distance to rupture surface, (\(r_{rup}\)), was estimated through an attenuation equation derived by [PERSON] et al. [42]; it considers the influence of an earthquake's causative fault type and the effect of an earthquake near a fault zone. It has a range of 4 to 8+ for earthquake magnitude (\(M\)) and up to 100 km for closest distance to rupture surface, (\(r_{rup}\)); in this paper, it is proposed for use for a maximum earthquake magnitude (\(M\)) of 9 with a range of 1 to 107.03 km for closest distance to rupture surface, (\(r_{rup}\)). A BBN has a strong ability to deal with discrete variables, albeit weak in processing with continuous variables. The K2 machine learning (ML) algorithm, meanwhile, requires variables to be discrete; thus, it is necessary to convert the 11 influence factors into discrete values before building the BBN models. The liquefaction potential (output) was given a binary value of 0 for non-liquefied sites and a value of 1 for liquefied sites. Table 2 presents the grading standards for seismic soil liquefaction factors. To construct the models, the dataset was divided into two data subsets:  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  
* A training dataset is required to train the models. In this research work, the authors used 80% of the data i.e., 201 out of 251 CPT case histories are considered for the training set. * A testing dataset is needed to predict the developed models' performance. In this study, the remaining 20% of data i.e., 50 out of 251 CPT case histories are considered as the testing dataset. Data division for training and testing datasets was performed with due attention to statistical aspects, such as minimum, maximum, mean, and standard deviation of the datasets. The statistical consistency of the training and testing datasets optimizes the models' performance and subsequently assists in evaluating them better.