# Analysis of Liquefaction in Tailings Deposits by Fem Modeling of Underained Cyclic Triaxial
## 6 Results and Discussion  
### Liquefaction Criterion  
For undrained CTX tests, the liquefaction criteria for clean sand in an isotropic consolidation state are divided into two types: one criterion based on pore pressure and another based on the axial strain. Several studies have used the axial strain to define the liquefied state in clean sands with a certain percentage of fines [16; 51]. However, the results of the present study show that the strains obtained from the modeling using UBC3D-PLM are lower than the experimental values, which was also observed in [22; 37]. This observation, coupled with the fact that the objective of the calibration is to represent the liquefaction cycle, suggests that defining a liquefaction criterion in terms of axial strain is inappropriate. In effect, the cyclic undrained triaxial test (CTX) allowed the application of controlled shear stresses to soil samples and the measurement of the response in terms of axial deformation and pore pressure. The soil's response was evaluated based on the increase in pore pressure and axial deformation under these controlled shear stresses. Therefore, to determine the point at which the soil begins to behave like a liquid, the liquefaction criterion based on the pore pressure ratio (Ru > 0.8) was used, which indicates that the pore pressure has reached 80% of the effective confining pressure, resulting in a significant loss of soil strength. This criterion, widely used in liquefaction studies [22; 24; 43; 52], was adjusted through the calibration of the UBC3D-PLM model, which ensured that the numerical results were consistent with the experimental findings.  
Considering the above, the evolution of pore pressure is used as an indicator to evaluate liquefaction in the modeled tests. The results show that the excess pore pressure ratio (\(R_{u}\)) exceeds 0.8 before complete liquefaction in both types of soil, and accordingly, \(R_{u}>0.8\) is defined as the liquefaction criterion.  
Although cyclic triaxial (CTX) tests conducted in the laboratory do not fully replicate the scale and complexity of in situ conditions, the experimental design allows for capturing the key soil responses, such as the development and progression of pore pressure increase and axial deformation under cyclic loads. Therefore, through a rigorous calibration process of the UBC3D-PLM model, the numerical results have been made consistent with the experimental outcomes, contributing to its applicability in real-world practical scenarios. Additionally, differences that may arise, such as variability in cyclic load levels and scale, were managed by adjusting the model parameters, aiming for the most accurate possible representation of soil behavior under different conditions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Silt (ML)** & **Sand (SM)** \\ \hline \(K_{G}^{p}\) & 757 & 974 \\ \(K_{G}^{p}\) & 1082 & 1392 \\ \(K_{G}^{p}\) & 880 & 4647 \\ \(m_{e}\) & 0.3 & 0.26 \\ \(n_{e}\) & 0.3 & 0.26 \\ \(n_{p}\) & 0.55 & 0.6 \\ \(c^{\prime}\ast\left(\text{kN/m}^{2}\right)\) & 0 & 0 \\ \(\phi_{p}\ast\left({}^{\circ}\right)\) & 37.7 & 39.8 \\ \(\phi_{\text{cv}}\ast\left({}^{\circ}\right)\) & 35.2 & 39.0 \\ \(f_{dens}\) & 0.68 & 0.55 \\ \(f_{post}\) & 5.0 & 0.3 \\ \(R_{f}\) & 0.95 & 0.95 \\ \(\gamma_{unsst}\ast\left(\text{kN/m}^{3}\right)\) & 17.4 & 19.3 \\ \(\gamma_{sat}\ast\left(\text{kN/m}^{3}\right)\) & 19.9 & 21.0 \\ \(\epsilon_{initial}\) & 0.71 & 0.88 \\ \(\text{N}_{1}^{60}\) & 15.5 & 36 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The calibrated parameters of the UBC3D-PLM model for each soil sample.