In this paper, Bentley Systems specialists Marina Trevizolli, Murray Fredlund, and Hai Hua Lu illustrate the importance of using 3D limit equilibrium (LE) analysis for complex open pit sidewalls, while they emphasize the concept of column resolution in LE calculation. Then, they present analysis scenarios of complex sidewalls of a real open pit case, using the concept of column ratio concept for setting the modelling criteria. Finally, they provide recommendations on the analysis procedure for producing reliable results.
The paper was recently presented at #GeoNiagara2021. You can watch the video of the full presentation in the Media section below.
The common presence of geometry effects (concave or convex geometries), and related anisotropic geo-strata effects on open pit factors of safety, increase the need of understanding the real influence of column resolution in a 3D slope stability analysis. Reliable 3D modeling of open pit slope stability enhance the safety, accuracy, and mining optimization.
In 2D, the sliding mass is typically subdivided in slices. 3D LEM subdivide the model into columns while all parameters, such as material properties, water pressure, normal stress, and others are evaluated at the column base discretization (Figure 1). Indeed, the differences in the factor of safety result may occur from different ways of discretizing the failure mass into soil columns.
Trevizolli et al., then presented a real case history; i.e., an open pit located in Australia utilized for iron ore extraction was modeled to apply the proposed methodology. The 3D model presents complex geometry involving uneven benched topology and faults (Figure 2).
PLAXIS 3D LE was used for the analysis. PLAXIS 3D LE includes the capability of adjusting grid resolution in details at convergence options, while also providing the option for features such as oriented search planes and multiplane analysis. The latter was an important aspect for the study in question.
Different scenarios of square and rectangular grid were defined, and the reference point on column refinement was based on the column ratio concept, which was computed as:
Examples of different column resolutions, based on the column ratio, are shown in Figure 2.
Results associated with the square and rectangular grid resolution were analyzed (column ratio of 1.0 and 0.4, respectively), and the results are presented in Figure 3. Based on Figure 3, it can be seen that the factor of safety reaches a plateau in a certain stage of the analysis, i.e., the slope stability analysis converged to an (almost) constant factor of safety, regardless of any increase in column resolution and calculation time.
Moreover, the authors emphasize that graphing and visual checking were key aspect for mapping the most appropriate column resolution. In the example analyzed, the rectangular grid surface used was used for the better understanding of the lateral geometry that is represented in the concavity of the open pit.
Subsequently, the selected, optimal, grid resolutions were considered for a larger verification area around the entire pit.
Using the multi plane analysis (MPA) concept, 31 searching planes were located having an approximate 60-meter distance from each other (Figure 4). Moreover, the calculation and search methods used were based on previous analyses.
Based on Figure 4, the authors mention that the engineer should understand by the shadings if the grid resolution would interfere critically on failure zones, which are not potentially identified with a lower column resolution. Furthermore, it was emphasized that large open pit models require slope stability analyses around several regions. Finally, it was documented that increasing the column resolution significantly increases the calculation time.
In this paper, Bentley Systems specialists Marina Trevizolli, Murray Fredlund, and Hai Hua Lu, reached the following conclusions:
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