# Analysis of Liquefaction in Tailings Deposits by Fem Modeling of Underained Cyclic Triaxial
## 5 Strategy and Characteristics of Numerical Modeling  
To represent the geometry of the cylindrical experimental specimens, an axisymmetric model was used. The specimen was modeled with regular dimensions of \(1\) m \(\times\) 1 m in order to use a single geometrical configuration for all simulated laboratory tests since the results are the same regardless of the geometry ([PERSON] and [PERSON], 1993; [PERSON], 1993). Figure 5 shows the specimen configuration used with its strain, dynamic, and flow boundary conditions. The left side and bottom are the axes of symmetry; at these boundaries, the displacements normal to the boundary are fixed and the tangential displacements are kept free to allow \"smooth\" motion.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Function** & **Parameter** & **Formulation** \\ \hline Elastic domain & \(K_{B}^{e}\), \(K_{G}^{e}\), \(m_{e}\), \(n_{e}\) & Nonlinear stress–strain dependence, \\ Failure criterion & \(c^{\prime}\),\(\phi_{p}\) & Oakr–Coulomb \\ Hardening rule & \(K_{G}^{p}\), \(n_{p}\), \(Rf\) & Hyperbolic hardening rule (Beaty and Byrne) \\ Flow rule & \(\phi_{cv}\) & Unassociated (Rowe) \\ Plastic potential & \(\theta\) (\(Lode\)\(angle\)) & Based on Drucker–Prager \\ Densification rule & \(n_{rev}\), \(f_{dens}\), \(f_{hard}\) & Densification with the number of cycles \\ Post-liquefaction factor & \(f_{post}\) & Degradation of stiffness \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the UBC3D-PLM model.  
The undrained CTX test phases were simulated using the stepwise construction process integrated into the software. In the first phase, the \"\(K_{0}\) Procedure\" calculation type is used, which allows the initial stress state in the specimen to be calculated. The objective of the second phase (see Figure 5c) is to simulate the consolidation phase of the experimental test; the calculation type is set as \"_Plastic_\", where the confining stress is applied by activating load A. In this phase, water flow is allowed by setting the state of the edges as \"Open\" to generate a drained condition.  
In the third phase of the stepwise construction (see Figure 5d), the \"Dynamic\" calculation type is used, this time incorporating the UBC3D-PLM constitutive model. To represent the deviatoric stress, a vertical load B is used by inputting a harmonic signal with a frequency equal to that determined experimentally. This sine wave is valid for symmetric loading and unloading cycles, which are suitable for the densification rule of the model [32]. In this phase, the water flow was restricted to maintain the undrained condition. The \"None\" condition using standard fixtures was applied to the dynamic edges since the model has a small-dimensional and finite geometry.  
Likewise, the dynamic time must be configured and must coincide with the duration of the test to be represented. Additionally, the \"_Max steps_\" parameter must be modified to obtain an adequate response since it greatly influences the simulation. Following various tests to optimize the time efficiency and the fit to the experimental curve, this parameter was calculated using an approximation of \(10*N_{c}\), where \(N_{c}\) is the number of cycles in each experimental test to be simulated. As shown in Figure 6a, which shows the experimental results for silt, when there is an insufficient number of steps, the model cannot apply the constant cyclic load, in contrast to what is observed in Figure 6b, where the number of \"_Max Steps_\" was adjusted.  
Figure 5: (**a**) Three-dimensional model of the specimen. (**b**) Dynamic boundary conditions. (**c**) Drained flow conditions and strain boundary conditions. (**d**) Undrained flow condition and strain boundary conditions.  
Figure 6: (**a**) Insufficient adjustment of the Plaxis numerical control parameter “_Max Steps_”. (**b**) Results when the “_Max Step_” parameter is adjusted using the approximation \(10*N_{c}\).