# Static Liquefaction Assessment Combining Shear Wave Velocity, Peak Strength and Soil Grading
## 4 Liquefaction Assessment Based on Stiffness/Strength Parameters
### Liquefaction Assessment  
Whilst the state parameter \(\psi\) has the limitations previously mentioned, both stiffness (expressed by the shear wave velocity, \(V_{S0}\)) and the peak undrained deviatoric stress (\(q_{peak}=\sigma_{V}-\sigma_{H}\)) are controlled (although differently) by the void ratio, mean stress state, contractiveness and soil structure. For this reason, these parameters were found to be particularly useful for predicting soil behavior [19]. The peak deviatoric stress occurs before the onset of complete (\(q_{ult}=0\) kPa) or partial (\(q_{ult}>0\) kPa) instability. It should be noted that \"complete\" or \"true\" liquefaction is achieved when a null mean effective stress is reached whilst \"partial instability\" is typically achieved by specimens which exhibit strain hardening and/or strain softening after reaching the phase transformation line and therefore always exhibit an ultimate deviatoric stress. A sketch comparing these distinct behaviors is shown in Figure 10.  
\(V_{S0}\) is the shear wave velocity, measured after consolidation and prior to shearing. The respective normalized parameters \(q_{1}\) and \(V_{S1}\) have been defined as follows:  
\[q_{1}=\bigg{(}\frac{q_{peak}}{p_{a}}\bigg{)}\bigg{(}\frac{p_{a}}{\sigma^{ \prime}_{v0}}\bigg{)}^{0.5}=\bigg{(}\frac{q_{peak}}{p_{a}}\bigg{)}\bigg{(} \frac{1+2K_{0}}{3}\bigg{)}^{0.5}\bigg{(}\frac{p_{a}}{\sigma^{\prime}_{m}} \bigg{)}^{0.5} \tag{2}\]  
\[V_{S1}=V_{S0}\bigg{(}\frac{p_{a}}{\sigma^{\prime}_{v0}}\bigg{)}^{0.25}=V_{S0} \bigg{(}\frac{1+2K_{0}}{3}\bigg{)}^{0.25}\bigg{(}\frac{p_{a}}{\sigma^{\prime}_ {m}}\bigg{)}^{0.25} \tag{3}\]  
Figure 11: Instability line of all soils on a log–log scale. where \(p_{a}\) is the atmospheric pressure (approximately 100 kPa), \(K_{0}\) is the coefficient of earth pressure at rest, \(\sigma^{\prime}_{m}\) is the mean effective confining pressure \(\left(\sigma^{\prime}_{m}=\frac{\sigma^{\prime}_{V0}+2\pi\sigma^{\prime}_{imb}}{ 3}\right)\) and \(\sigma^{\prime}_{V0}\) is the vertical effective stress. Figure 12 correlates \(q_{1}\) and the ratio \(V_{S0}/q_{peak}\) for all the studied materials in a single plot, showing that it is possible to define the boundaries between true liquefaction and strain softening for finer materials as well as between true liquefaction and strain hardening for uniformly graded sands. The adopted symbols aim to distinguish true liquefaction (open symbols) from a strain softening behavior (grey symbols) and from a stable behavior, characterized by strain hardening (black symbols). This figure clearly distinguishes the boundaries of soil behavior, which correspond to the ratios for true liquefaction triggering provided in Table 9 for the soils under study. As shown in Figure 12, it is clear that low \(V_{S0}/q_{peak}\) and high \(q_{1}\) correspond to a stable condition. This framework is particularly suitable for predicting liquefaction potential, overcoming the limitations of other approaches. Figure 13 shows that stability increases both with increasing shear wave velocity, \(V_{s0}\), (or stiffness) and with increasing peak undrained deviatoric stress, \(q_{peak}\), for all soils. Thus, stability increases with both increasing \(V_{s1}\) and \(q_{1}\), reflecting greater contact between grains, due to the dual effect of the increase in confining pressure and the decrease in the void ratio. Figure 12: Correlation between the normalized peak undrained deviatoric stress and the ratio between shear wave velocity and peak undrained deviatoric stress.