## Consulting Solutions: 1D/2D/3D Consolidation

### Introduction:

Industry standard of practice is to perform a 1D numerical model at the deepest part of the tailings facility. Possibly in some cases 2-3 additional 1D models may be run. Models typically involved a solution of Gibson’s saturated 1D formulation. Behavior of the facility (i.e. dewatering, settlement, pwp dissipation, strength gain) is inferred in 3D from the 1D model through approximate correlations. The problem is that the estimations of tailings pit capacities from this methodology have historically resulted in over-optimistic pit capacities over time.

There are a number of difficulties with this approach which are:

• Depositional modeling is ignored (i.e. upper surface is assumed flat)
• Effects of surface ponding are ignored
• Lateral stresses/strains are ignored (Impossible to consider with Gibson’s formulation)
• 3D surface shape is not adequately calculated (impacts landform design for closure)

SoilVision Systems Ltd. Can consider modeling tailings consolidation / capacity in 1D, 2D, Pseudo 3D and full 3D

### 1D MODELING

1D numerical models can be run by placing multiple points randomly around the tailings management facility (TMF). Corrections can be handled by relating the 1D capacities back to 3D space within SoilVision Systems Ltd. Software.

### 2D MODELING

2-D models can be run by taking sections through the TMF and adding layers of tailings on at reasonable time-frames.

Figure 1: 2D cross section of tailings facility

### Pseudo 3D MODELING

Pseudo 3D numerical modeling divides the depositional area up into a grid of 1D numerical models. Each “cell” of the grid represents a full 1D large-strain consolidation numerical model and is solved based on the depositional method selected. The advantage of this method is that it is robust — each 1D numerical model is relatively easy to solve and solution is just a function of time. This methodology does not consider lateral seepage or deformations. Depositional strategies and even evaporation can be handled with this methodology. This methodology is ideally suited for facilities with a high horizontal to vertical ratio in their geometry.

Figure 2: Pseudo 3-D example numerical model solving tailings deposition

### 3D MODELING

SoilVision Systems Ltd. has developed technologies for the solution of full 3-D numerical models using large-strain consolidation formulations. These solutions are particularly well suited for narrow or relatively deep TMFs. Lateral seepage and deformations are considered in this methodology. The 3-D influence of complex strains underlying a deposit can also be modeled with this methodology.

Figure 3: Example of 3-D numerical model solution