Numerical Analysis of the Effect of the Rheology Parameters in the Estimation of a Tailings Sand Dam Erosion Time due to Overtopping

Tailings dam failures are common disasters around the world. In fact, different authors indicate that the rate of failure of sand tailings dams are more than two orders of magnitude higher than the failure rate of conventional water retention dams. In Chile, this phenomenon has been produced mainly by earthquakes, which trigger seismic liquefaction of the stored tailings those that flow through the retention dam.

In mining, the tailings are usually transported as high density slurries through pipes or open channels to the storage facility, modeling the flow like that of a non-Newtonian fluid. In this work, the liquefied tailings were modeled in the same way, considering their behavior as that of a homogeneous hyperconcentrated suspension that fits a Hershel-Bulkley’s rheology. It was considered that the reservoir fails by the overtopping produced by an instantaneous deformation of its retention dam.

Tailings flow is calculated using the shallow water equations (SWE), considering the effects of the rheology in the bed shear stress source term. To describe the morphological evolution of the bed, this system of equations is weakly coupled with the Exner equation. The bed-load sediment transport is corrected by rheology and slope effects.

The system of equations was solved using finite volume schemes. The MUSCL-Hancock scheme was used for solving the SWE system, while a first-order Godunov scheme was used for the Exner equation. To avoid spurious oscillations, an essentially non oscillatory (ENO) slope limiter was used in the reconstruction step of MUSCL-Hancock scheme. In order to compute the intercell numerical flux, the well-known Riemann solver by Roe was used. The implementation of this model was done using OpenFOAM as a programming environment.

The effect of the rheological parameters over time erosion were parameterized according to the fluid consistency index, flow behavior index, yield stress and fluid density. A simplified geometry of a tailings dam was used, assuming a unidirectional flow over a typical cross-section built with non-cohesive material of uniform grain size.