## 2 Methodology
### Model Validation  
The performance of a proposed model can be validated through comparing the model results against the real field data, or the results of available software packages that are already validated through different benchmarks. The 1D model component of the proposed consolidation model is validated by [29; 30] through three sets of scenarios, based on the reported cases by [27] as the well-accepted benchmarks. The benchmark cases have been widely used in the literature for evaluation of numerical large strain consolidation models, and are the results of nine different models that predicted the consolidation behavior of four waste clay disposal scenarios [23]. In [29; 30], the authors simulated the tailings consolidation under different permeability and compressibility conditions for three types of tailings, i.e., untreated mature fine tailings (MFT), thickened tailings (TT) and phosphate tailings (PT). The authors considered a wide range of solid contents and initial deposit height to investigate the robustness of the model. The primary performance indicators used for validation include settlement over time, effective stress and void ratio profile. The commercial software FSCA is used to compare the key performance indicators for thickened tailings, based on the large strain consolidation theory. The interface height for the validation cases are illustrated in Figure 4. The 1D model component provides acceptable settlement predictions, labeled TMSim and TMSim-consol in Figure 4, when benchmarked against commercial software and laboratory datasets. Readers are directed to [29; 30] for comprehensive details about the validation of the 1D model. \begin{table}
\begin{tabular}{c l} \hline \hline \(\bullet\) & Maximum valley depth \\ \(\bullet\) & Average depth of N valleys \\ \(\bullet\) & Average distance between valleys \\ \(\bullet\) & Maximum peak height \\ \(\bullet\) & Average height of N peaks \\ \(\bullet\) & Average distance between peaks \\ \(\bullet\) & Average elevation of the surface \\ \(\bullet\) & Standard deviation of points’ elevation \\ \(\bullet\) & Average of absolute differences from the mean \\ \(\bullet\) & Maximum settlement \\ \(\bullet\) & Average distance between peaks and valleys \\ \(\bullet\) & Maximum slope withing search radius \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Differential settlement metrics. The quasi-3D model is tested for special conditions to verify its numerical results. As expected, it generates zero differential settlement (a flat surface) when all of the defined points follow a unique settlement curve. However, there are no available data about the actual surface of a deposit during the active life of a tailings storage facility or post deposition after the pond is filled. A review of the publicly available tailings reports published by oil sands operators clearly states that during the active life cycle of a tailings storage facilities, because the deposits are constantly filled with the tailings, the operators do not track the consolidation: \"Settlement and consolidation of fluid tailings are not tracked in active ponds, due to the complexity and inaccuracy inherent in measuring and calculating these values.\" [45]. Therefore, there are no valid data available to be compared against the results of the model. On the other hand, the developed model here generates a pseudo-3D estimation of the potential surface of the consolidated pond once the active deposition is over and the treated tailings has been consolidated. The model is not intended to predict the final surface profiles or for stage-volume predictions, but rather to inform the closure landform design process. In the literature, the 2D and 3D models are rarely validated independently from 1D models [46].