A methodology to describe spatial surface flux boundary conditions for solving tailings impoundment closure water balance problems

Abstract

This study deals with the closure water balance of a low-tonnage tailings impoundment in an arid climate that hosts a permanent pond on a portion of its surface. The calculation of surface fluxes from such an unsaturated tailings impoundment surface is difficult due to the fact that there is a spatially varying phreatic surface which determines the thickness of the vadose zone. This study presents a spatial flux hypothesis, which states that spatial flux boundary conditions on a generalized tailings impoundment cross-section (of this tailings facility) follow a characteristic shape that is governed by the depth to the phreatic surface. The hypothesis states that evaporation will be a minimum close to the tailings impoundment embankment wall where the depth to the phreatic surface is the greatest, and will increase to a maximum close to the pool. Inversely infiltration will be a maximum at the embankment and will decrease to a minimum close to the pool.

This study presents methodology to calculate the spatial flux boundary functions proposed in the hypothesis, and shows how these flux boundary functions can be used as a direct input for surface flux boundary conditions in multidimensional saturated/unsaturated flow seepage analysis models. This method effectively bridges the gap that currently exists between rigorous coupled soil/atmosphere one-dimensional surface flux boundary numerical models and multidimensional saturated/unsaturated flow seepage analysis models. The effective use of the calculated spatial flux boundary functions is proven through detailed evaluation modeling. The calculation of the flux boundary function stems from the development of a technique whereby the one-dimensional SoilCover surface flux boundary model can be used to solve a two dimensional cross section. The technique consists of a generalized non-dimensionalized tailings impoundment cross-section that comprises a beach profile and a phreatic level function. Material properties and the shape functions have been tested and calibrated through an extensive laboratory and field characterization program of the tailings. The generalized cross-section is divided into a number of equal zones and a SoilCover simulation is performed for each zone before being integrated to give a cumulative result. The cumulative result is tested and calibrated against a detailed transient tailings impoundment water balance. This cumulative result represents the spatial flux boundary function that is consistent with the spatial flux hypothesis. Effectively, what is presented in this thesis is a quasi-three-dimensional model for calculation of surface flux boundary conditions.