# Static Liquefaction Assessment Combining Shear Wave Velocity, Peak Strength and Soil Grading
## 4 Liquefaction Assessment Based on Stiffness/Strength Parameters
### Liquefaction Assessment
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{\(V_{s0}/q_{peak}\)} \\ \cline{2-3}  & **True Liquefaction Triggering** & **Behavior Limiting Boundary \({}^{*}\)** \\ \hline Gold tailings & \(>\)5 to 6 & \(>\)0.8 to 1 \\ Osorio sand & \(>\)2 to 3 & \(>\)2 to 3 \\ Silt & \(>\)2 to 3 & \(>\)0.5 \\ Mixture & \(>\)2 to 10 & \(>\)0.2\({}^{*}\) \\ Algeria sand & \(>\)2 & \(>\)2 \\ Coimbre sand & \(>\)1 & \(>\)1 \\ \hline \end{tabular} \({}^{*}\) between strain softening and strain hardening for finer soils and between true liquefaction and strain hardening for monogranular sands; \({}^{*}\) due to limited \(V_{S}\) data, there is greater uncertainty for this soil.  
\end{table} 
Table 9: \(V_{s0}/q_{peak}\) ratios for true liquefaction triggering for the different tested materials. From both Figures 12 and 13, further conclusions can be drawn. For instance, Figure 12 indicates that among the three sands, Algeria sand is the most stable one since the \(V_{s0}\) boundary separating liquefaction from a stable behavior is obtained for low \(V_{s0}\). This is believed to be associated with the greater roundness of its particles. On the contrary, Coimbra sand is the soil with higher brittleness due to its highly meta-stable structure created by the small contact bridges between its angular grains. It can also be observed that both Coimbra sand and the mixture can only reach full stability (i.e., a strain hardening behavior) for very high initial confining stresses (and/or low void ratios), as stability was not verified within the wide range of confining pressures applied during the triaxial tests (Table 7). Finally, both the gold tailings and the silt are the least prone to liquefaction, yet this was not reflected in a higher stability, since these soils display a strain softening behavior within a wide range of shear wave velocities. Despite the robust correlations obtained with the laboratory results, good reasoning must be applied since a strong statistical correlation exists between both variables (i.e., between \(V_{s0}/q_{peak}\) and \(q_{1}\)). In fact, a higher relevance should be given to the limiting effects of \(V_{s0}/q_{peak}\) when distinguishing liquefiable and non-liquefiable conditions than the correlation between \(V_{s0}/q_{peak}\) and \(q_{1}\), particularly under laboratory conditions. Making use of the same parameters, a different approach may be adopted. This framework derives from a concept based on the simplified procedure proposed by [46], initially adopted for cyclic conditions [47], as shown in Figure 14. In this case study, instead of the cyclic resistance ratio (CRR), the normalized peak undrained deviatoric stress under monotonic conditions, \(q_{peak}/(2\sigma^{\prime}h)\), is taken (Equation (4)). Although this chart was initially proposed for determining the cyclic resistance of sands with low fines content, an analogy can be made to identifying the boundary that separates liquefiable from non-liquefiable conditions. It should also be pointed out that [PERSON] and [PERSON]'s equation was not corrected for fines content, instead it was decided to adjust both the \(b\) and \(V_{s1}\)* parameters. The main disadvantage of this framework is the existence of distinct boundaries, specific to each soil, which in this case, are a function of \(b\) and \(V_{s1}\)*. Table 10 summarizes these values for the studied soils, where it becomes clear that \(b\) is around 3.0 but \(V_{s1}\)* varies between  
Figure 13: Peak undrained deviatoric stress as a function of the shear wave velocity. 150 and 240 depending on the soil type. This is also observed in Figure 14 where the lines have approximately the same shape but their vertical asymptotes move to the right with increasing instability potential.