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


#### **Table 8.**

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

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

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

accomplished in six iterations and shown in **Tables 6**–**11**. The ISM model is

F8,F9,F10,F11,F12

**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>*

F2 F2 F1,F2,F3,F4,F6,F7,F8 F2 L2

F5 F5 F4,F5,F6,F7,F8,F9,F10 F5 L2

F11 F11 F11 F11 L2

F12 L1

developed on the level partitions basis from **Tables 6**–**11**.

F1 F1,F2,F12 F1 F1 F2 F2,F12 F1,F2,F3,F4,F6,F7,F8 F2 F3 F2,F3,F12 F3 F3 F4 F2,F4,F5,F6,F12 F4 F4 F5 F5,F12 F4,F5,F6,F7,F8,F9,F10 F5 F6 F2,F5,F6,F12 F4,F6,F7,F8,F9,F10 F6 F7 F2,F5,F6,F7,F12 F7,F8,F9,F10 F7 F8 F2,F5,F6,F7,F8,F12 F8,F10 F8 F9 F5,F6,F7,F9,F12 F9 F9 F10 F5,F6,F7,F8,F10,F12 F10 F10 F11 F11,F12 F11 F11 F12 F12 F1,F2,F3,F4,F5,F6,F7,

F1 F1,F2 F1 F1

F3 F2,F3 F3 F3 F4 F2,F4,F5,F6 F4 F4

F6 F2,F5,F6 F4,F6,F7,F8,F9,F10 F6 F7 F2,F5,F6,F7 F7,F8,F9,F10 F7 F8 F2,F5,F6,F7,F8 F8,F10 F8 F9 F5,F6,F7,F9 F9 F9 F10 F5,F6,F7,F8,F10 F10 F10

for the next level-iteration process.

*Earthquakes - From Tectonics to Buildings*

**Table 6.**

**Table 7.**

**170**

*Level partition—Iteration 2.*

*Level partition—Iteration 1.*

*Level partition—Iteration 3.*


#### **Table 9.**

*Level partition—Iteration 4.*


#### **Table 10.**

*Level partition—Iteration 5.*


#### **Table 11.**

*Level partition—Iteration 6.*

The digraph is developed from final reachability matrix by removing the transitivity 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**.

**Figure 1.**

*Model depicting the relationships between seismic soil liquefaction significant factors based on ISM technique.*

*3.2.2 Cluster II: dependence factors*

*MICMAC Analysis of seismic soil liquefaction factors.*

*Elucidation of Seismic Soil Liquefaction Significant Factors*

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

influence soil liquefaction.

stable.

**173**

**Figure 2.**

*3.2.3 Cluster III: linkage factors*

*3.2.4 Cluster IV: independent/driving factors*

factor in this model fall in this cluster.

Dependence factors have a strong dependence power and weak driving power. This dependence cluster has two seismic soil liquefaction factors (18%) except liquefaction potential that including peak ground acceleration F2 (*a*max) and equivalent clean sand penetration resistance F5 (*qc*1*Ncs*), while, the liquefaction potential F12 (LP) falls in this cluster is not an influence factor of earthquake liquefaction, but a discriminate index. It is just proved that the driving power is poor and needs to rely on other factors to discernment liquefaction. In the ISM model, these factors form the top levels which need other soil liquefaction factors that collectively act to

Linkage factors have a strong driving power as well as strong dependence power. The factors affect each other and directly affect the liquefaction system. Therefore, the factors in this cluster are unstable. No factor in this model fall into this cluster, which indicates that the liquefaction influencing factors in this model are relatively

In this cluster, factors have strong driving power but weak dependence power. It

A special case can be observed on factors that are depth of soil deposit F10, (*Ds*) and total vertical stress F8, (*σv*), on the middle between independent and autonomous factors whereas soil behavior type index F6, (*Ic*), on the middle between dependence and autonomous factors. Factors that are depth of soil deposit F10, (*Ds*) and total vertical stress F8, (*σv*), are lower on dependence but higher on driving

is often the most critical factors of the system and also the essential factors. No
