Analytical solutions of Gibson’s model for estimating the pore water pressures in accreting deposition of slurried material under one-dimensional self-weight consolidation

Jian Zheng, Li Li, Mamert Mbonimpa, Thomas Pabst

In the proceedings of: GeoOttawa 2017: 70th Canadian Geotechnical Conference; 12th joint with IAH-CNC

Session: Mining - Underground and Backfill

ABSTRACT: It is a critical concern to evaluate the total pore water pressure (PWP) and excess PWP associated with the self-weight consolidation of slurry deposition for the safety and stability of the confining structures (tailing dams and mine backfill barricades). To this end, the Gibson (1958) solutions are particularly interesting and useful. However, the equations cannot be directly applied because the Gibson (1958) solutions contain an integral that cannot be treated by hand calculations. The Gibson (1958) solutions are not analytical expressions. In this paper, transformation was made to the integral contained in the Gibson (1958) solutions. This leads to truly analytical expressions of the Gibson (1958) solutions that can readily be used through calculations with commonly available computing tools like Microsoft Excel. The proposed analytical solutions have been validated by numerical modeling with SIGMA/W. They can thus be used to estimate the (excess) PWP of slurry deposition confined in mine backfilled stopes or tailings dams with a pervious or impervious base. Résumé Il est primordial d'évaluer la pression interstitielle totale et la pression interstitielle en excès associées à la consolidation résidus et barricades de remblais miniers). À cette fin, les solutions de Gibson (1958) sont particulièrement intéressantes et utiles. Cependant, les équations de Gibson (1958) ne peuvent pas être directement appliquées car elles impliquent une intégrale qui ne peut pas être calculée manuellement. Les solutions de Gibson (1958) ne sont pas des expressions analytiques. Dans cet article, une transformation a été faite à l'intégrale contenue dans les solutions de Gibson (1958). s analytiques à partir des solutions de Gibson (1958) qui peuvent facilement être utilisées pour faire des calculs avec des outils informatiques couramment disponibles comme Microsoft Excel. Les solutions analytiques proposées ont été validées par des modélisations numériques avec SIGMA/W. Elles peuvent donc être utilisées pour estimer la pression interstitielle (en excès) de dépositions de coulis confinées dans des chantiers miniers ou dans des digues à résidus avec une base perméable ou imperméable. 1. INTRODUCTION The huge amount of mine wastes, in terms of tailings and waste rock, resulted from mine operations need to be properly managed. In most cases, tailings are transported by pipelines and confined in tailings dams. Stope backfilling using tailings as the main solid material has also become a common practice in most modern mines as a way of the mine waste management. For both cases, the backfill contains a lot of water and in a state of oversaturation. The grain-grain contacts are absent or non-effective and the effective stresses are zero. Once deposited in a confining structure, the solid particles tend to settle down under the effect of the gravity. This movement of the particles tends to reduce the volume of the backfill and expel the water toward the outside of the backfill. As the backfill usually has a low permeability, the water flow is hindered and results in the generation of excess pore water pressure (PWP). As the water is in an unstable state due to the presence of the excess PWP, water flow takes place as long as the hydraulic boundary condition favours the water flow, resulting in drainage of water and dissipation of the excess PWP. This phenomenon is called self-weight consolidation (Been and Sills 1981; Toorman 1996, 1999; Pedroni 2011; Li 2013; Li et al. 2013; El Mkadmi et al. 2014; Zheng et al. 2017a, 2017b).

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Jian Zheng; Li Li; Mamert Mbonimpa; Thomas Pabst (2017) Analytical solutions of Gibson’s model for estimating the pore water pressures in accreting deposition of slurried material under one-dimensional self-weight consolidation in GEO2017. Ottawa, Ontario: Canadian Geotechnical Society.

@article{geo2017Paper393,author = Jian Zheng; Li Li; Mamert Mbonimpa; Thomas Pabst,title = Analytical solutions of Gibson’s model for estimating the pore water pressures in accreting deposition of slurried material under one-dimensional self-weight consolidation,year = 2017}