# Static Liquefaction Assessment Combining Shear Wave Velocity, Peak Strength and Soil Grading
## 4 Liquefaction Assessment Based on Stiffness/Strength Parameters  
### Definition of the Critical State Lines  
Following numerous studies published on soil liquefaction assessment (e.g., [6; 7; 8; 41]), it is recognized that the state parameter, \(\psi\), has a significant influence on liquefaction instability. For that purpose, this study initiated with the determination of the steady state line (SSL) for all the distinct soils (SSL is defined as the ultimate state achieved under undrained conditions, whilst CSL is defined as the ultimate state achieved under drained conditions).  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Test ID** & \(\sigma^{\prime}\)**\(\mu_{\text{B}}\)** & \(\sigma^{\prime}\)**\(\mu_{\text{B}}\)** & \(V_{\text{e}}\)**\(\mu_{\text{B}}\)** & \(V_{\text{e}}\)**\(\mu_{\text{B}}\)** & \(V_{\text{e}}\)**\(\mu_{\text{B}}\)** & \(q_{\text{peak}}\)**\(\mu_{\text{B}}\)** & \(V_{\text{e}}\)**\(q_{\text{Results obtained from both drained and undrained triaxial tests performed with Osorio sand are shown in Figure 8, where there are four different plots, including the stress-strain curves, the \(q\)-\(p^{\prime}\) and the \(e\)-log \(p^{\prime}\) paths followed by each triaxial test, as well as the identification of the SSL and CSL. For simplicity, only the plots associated with this soil are included. Any further reference to the other soils can be found in [34]. Similarly, further details concerning the other triaxial tests, namely non-CIU, are provided in [34]. The tables presented in this paper refer only to CIU triaxial tests.  
However, it was perceived that the state parameter per se could not be used to accurately determine the limit beyond which soils exhibit a stable behavior if it is based on a linear CSL obtained from drained tests at low confining stresses or undrained tests at medium stresses. Figure 9 shows, as an example, the critical and steady state lines obtained for the mixture while Figure 10 summarizes this idea, showing a sketch of the distinct ultimate state conditions.  
Additionally, the stress ratio at critical state (\(M=q/p^{\prime}\)) was obtained for the different soils and compared to the particle morphology classified in a qualitative way (Table 8). From these results, it is observed that Osorio sand, which has rounded particles, has a lower critical state friction angle (related with \(M=\frac{6\sin\phi}{3-\sin\phi}\)) than the silt, which shows more angular particles due to the grinding of Osorio sand. This is expected as particle angularity improves the interlocking of the particles.  
Figure 10: Normal state line, critical state line and steady state line for sands and silts; undrained shear strength of soils delimited in a diagram \(e\)-log \(p^{\prime}\); measurement of liquefaction potential through the state parameter \(\psi\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & \(M\)**Values** & **Particle Morphology** \\ \hline Gold tailings & 1.49 & sub-angular and angular \\ Osorio sand & 1.29 & rounded to sub-rounded grains \\ Silt & 1.46 & angular particles due to grinding \\ Mixture & 1.38 & angular particles due to grinding \\ Algeria sand & 1.28 & grains are generally relatively \\ Coimbra sand & 1.25 & sub-angular \\ \hline \hline \end{tabular}
\end{table}
Table 8: \(M\) values compared with soil morphology.  
Figure 9: Critical and steady state lines of the mixture.