## 4 Results and Discussion  
### Interpretive Structural Modeling  
The set of liquefaction factors identified in Table 1 for soil liquefaction potential was used to develop the model which represented the correlation between fifteen soil liquefaction parameters. In the ISM model, the initial step was the development of the structure self-interaction matrix (SSIM) where the soil liquefaction factors of each pair were compared by the correlation criteria and four symbols V, A, X, or O were used (see Table 3). For example, relative density F8 (D\({}_{\mathrm{r}}\)) influences the standard penetration test blow counts, F11 (SPT N-value) so the symbol used is V. Depth of soil deposit F14 (D\({}_{\mathrm{s}}\)) influences the degree of consolidation, F10 (OCR) so the symbol used is A. Relative density F8 (D\({}_{\mathrm{r}}\)) and degree of consolidation, F10 (OCR) influence each other so the symbol used is X. Earthquake F1 (M) has no relation with the thickness of soil layer F15 (h) so the symbol used is O. SSIM is converted to a binary matrix called the initial reachability matrix by replacing the original symbols V, A, X, and O with 1 or 0 (Table A1) as per the rule illustrated in methodology Section 3.1. When pair of the same factor, i.e., F1 (M) with F1 (M) is formed, it is represented by 1. The concept of transitivity is introduced in Table A1 when the initial reachability matrix has been obtained and is presented in final reachability matrix (Table A2), wherein entries marked * show the transitivity. For example, in Table A1, the initial reachability matrix shows that F15 (h) is interrelated to F8 (D\({}_{\mathrm{r}}\)), and F8 (D\({}_{\mathrm{r}}\)) is interrelated to F11 (SPT N-value), then the interaction F15 (h) and F11 (SPT N-value) having 0 value is transformed into 1* in Table A2. The reachability sets are determined from the factor itself and other factors which have influence in the horizontal direction, while the antecedent sets consist of the factor itself and other factors which have influence in the vertical direction for each significant soil liquefaction factor. For example, in the case of F1 (M) in the final reachability matrix (Table A2), the reachability set will be all factors with values of 1 or 1* in the row intersections with F1 (M): F1 (M), F3 (t), F4 (a\({}_{\mathrm{max}}\)), and F16 (LP). The antecedent set will be all factors with values of 1 or 1* in the column intersections with F1 (M): F1 (M) only. When the intersection set and reachability set appear in the same intersection and reachability columns, then the corresponding soil liquefactionfactors are confirmed at a level (e.g., F16 (LP) as level 1) and the soil liquefaction factors in that level are separated out, e.g., F16 (LP) from the other factors for the next level-iteration process. The same level-iteration process is repeated until the level of each seismic soil liquefaction factor is established. Level partitioning of the soil liquefaction factors is accomplished in six iterations and shown in Tables A3-A8 (Appendix B). The ISM model is developed on the level partitions basis from Tables A3-A8. Each seismic soil liquefaction factor is positioned as per the consequent level and the relationships of the soil liquefaction factors are fixed from the bottom (level 6) to the top of the model (level 1). The multilevel hierarchy model developed with identified relations between the significant factors of seismic soil liquefaction potential (LP) is shown in Figure 4.  
Figure 4: Model depicting the relationships between soil liquefaction factors based on ISM. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline
**F1** & **F2** & **F3** & **F4** & **F5** & **F6 (Ca** & **F7** & **F8** & **F9** & **F10** & **F11 (  
The seismic soil liquefaction factors are connected by arrows from the bottom of the model (higher-level) to the top of model (lower-level). Seismic soil liquefaction factors on top of the Figure 4 are greatly influenced by the interconnection of left-over factors.