*Elucidation of Seismic Soil Liquefaction Significant Factors DOI: http://dx.doi.org/10.5772/intechopen.97278*


**Table 4.**

*Initial reachability matrix.*


*Note: 1\* indicates the values after applying transitivity; Dep. represents dependence power; Dri. represents driving power.*

#### **Table 5.** *Final reachability matrix.*

when the initial reachability matrix has been obtained and is presented in final reachability matrix (**Table 5**), wherein entries marked (\*) show the transitivity. For example, in **Table 4**, the initial reachability matrix shows that F4 (*FC*) is related to F6 (*Ic*), and F6 (*Ic*) is related to F2 (*a*max), then the interaction F4 (*FC*) and F2 (*a*max) having 0 value is transformed into 1\* in **Table 5**. 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

pair-wise comparison were made by the correlation criteria and four symbols V, A, X, or O were used (see **Table 3**). For example, earthquake magnitude F1 (*M*)–row factor influences the peak ground acceleration, F2 (*a*max)– column factor so the symbol used is V. Groundwater table depth F9 (*Dw*)–column factor influences the

*Note: V–row factor influences the column factor; A–column factor influences the row factor; O–no relationship*

magnitude F1 (*M*)–row factor has no relation with the thickness of soil layer F11 (*Ts*)–column factor so the symbol used is O. Field experts' made consensus on the

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 4**) as per the rule illustrated in **Table 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 4**

pair-wise comparison and the results are shown in **Table 3**.

*Structural self-interaction matrix for seismic soil liquefaction factors.*

**Factor (F***i***) code Significant factor**

*Earthquakes - From Tectonics to Buildings*

F4 Fines content, (*FC*)

F1 Earthquake magnitude, (*M*) F2 Peak ground acceleration, (*a*max)

F6 Soil behavior type index, (*Ic*) F7 Vertical effective stress, (*σ*<sup>0</sup>

F8 Total vertical stress, (*σv*) F9 Groundwater table, (*Dw*) F10 Depth of soil deposit, (*Ds*) F11 Thickness of soil layer, (*Ts*)

*List of significant factors of seismic soil liquefaction.*

F3 Closest distance to rupture surface, (*R*/*rrup*)

F5 Equivalent clean sand penetration resistance, (*qc*1*Ncs*)

**F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F***<sup>i</sup>*

VOOOOOOO O O V F1 AOOAOOO O O V F2 OOOOOO O O V F3 VVOOO O O V F4 AAOA A O V F5 AAO O O V F6 AA A O V F7 OA OVF8

*v*)

OOVF9

O VF10

V F11 F12

*<sup>v</sup>*)–row factor so the symbol used is A. Earthquake

vertical effective stress, F7 (*σ*<sup>0</sup>

*between the row and column factors.*

**Table 3.**

**168**

**Table 2.**

factor. For example, in the case of F1 (*M*) in the final reachability matrix (**Table 5**), the reachability set will be all factors with values of 1 or 1\* in the row intersections with F1 (*M*): F1 (*M*), F2 (*a*max), and F12 (LP). The antecedent set is all factors with values of 1 or 1\* in the column intersections with F1 (*M*): F1 (*M*) only. When the intersection and reachability sets appear in the same intersection and reachability columns, then the corresponding factor is confirmed at a level (e.g. F12 (LP) as level 1) and the factor in that level is separated out, e.g. F12 (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 6**–**11**. The ISM model is developed on the level partitions basis from **Tables 6**–**11**.


### **Table 6.**

*Level partition—Iteration 1.*


The digraph is developed from final reachability matrix by removing the transi-

**Factor (F***і***) Reachability set R(F***і***) Antecedent set A(F***i***) Intersection set R(F***i***)∩A(F***i***) Level L***<sup>i</sup>* F10 F10 F10 F10 L6

**Factor (F***і***) Reachability set R(F***і***) Antecedent set A(F***i***) Intersection set R(F***i***)∩A(F***i***) Level L***<sup>i</sup>* F1 F1 F1 F1 L3 F3 F3 F3 F3 L3

F6 F6 F4,F6,F7,F8,F9,F10 F6 L3

**Factor (F***і***) Reachability set R(F***і***) Antecedent set A(F***i***) Intersection set R(F***i***)∩A(F***i***) Level L***<sup>i</sup>* F4 F4 F4 F4 L4 F7 F7 F7,F8,F9,F10 F7 L4

**Factor (F***і***) Reachability set R(F***і***) Antecedent set A(F***i***) Intersection set R(F***i***)∩A(Fi) Level L***<sup>i</sup>* F8 F8 F8,F10 F8 L5 F9 F9 F9 F9 L5

F4 F4,F6 F4 F4

*Elucidation of Seismic Soil Liquefaction Significant Factors*

*DOI: http://dx.doi.org/10.5772/intechopen.97278*

F7 F6,F7 F7,F8,F9,F10 F7 F8 F6,F7,F8 F8,F10 F8 F9 F6,F7,F9 F9 F9 F10 F6,F7,F8,F10 F10 F10

F8 F7,F8 F8,F10 F8 F9 F7,F9 F9 F9 F10 F7,F8,F10 F10 F10

F10 F8,F10 F10 F10

**Table 8.**

**Table 9.**

**Table 10.**

**Table 11.**

*Level partition—Iteration 3.*

*Level partition—Iteration 4.*

*Level partition—Iteration 5.*

*Level partition—Iteration 6.*

tivity links and on the level partitions basis from **Tables 6**–**11**. The digraph is converted in to an ISM-based hierarchical model by replacing nodes with statements. 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 seismic soil liquefaction factors are connected by arrows from the bottom of the model (higher-level) to the top of model (lower-level). The multilevel hierarchy model developed with identified relations between the significant factors of seismic soil liquefaction potential (LP) is

shown in **Figure 1**.

**171**

**Table 7.** *Level partition—Iteration 2.*
