IN HIS recent doctoral thesis, Dr Neil Armitage of the Department of Civil Engineering has come up with a number of innovations as he designed and developed a mathematical model that predicts the commencement of riverbed erosion around manmade structures.

Working with Albert Rooseboom, Professor of Hydraulics at the University of Stellenbosch, and basing his work on an oeuvre of international research compiled over the past 85 years, Armitage came up with a number of modifications to existing models in his thesis on A unit stream power model for the prediction of local scour. This model describes energy utilisation in rivers, and how this affects the rate of scour in rivers, i.e. the erosion of the riverbed.

Local scour is usually associated with particular features or obstacles in a river, be it a boulder, an island or just a sharp bend, explains Armitage. "But the prime interest for engineers – historically, at any rate – has been the local scour that's come about as a result of man-made structures."

Because of scour, holes are dug around structures – such as bridge piers and abutments – that are built on or below the riverbed. "Those holes can be exceptionally deep, e.g. they can easily run to 20 or 30 metres," notes Armitage.

"Scour can result in the sand around the pier being removed to such a depth that the pier ends up being supported on nothing – the sand's just washed away." Because of this, the pier will fail and the structure will collapse.

This happens far more often than desired, especially in KwaZulu Natal, a province that experiences many large floods, says Armitage. But this is a worldwide phenomenon, he adds, and of great concern to engineers, both from a financial and communications aspect.

"The simple premise of my thesis was, firstly, that there is a direct connection between unit stream power – the stream power that is dissipated in unit volume – and scour," he notes. "But it's a very complex relationship that is subject to a whole host of very complex influences."

"What I had to do was to build a relatively simple model that could be run on a PC and that would enable us to make some sort of prediction about local scour around any arbitrary engineering structure." To do this, Armitage and Masters student Caroline McGahey adapted a commercial computational fluid dynamics (CFD) programme, which models the physical behaviour of a fluid, to help predict the rate of local scour.

Here, Armitage's main challenge was to try and determine the criteria under which sand will just stop to move, a point that is called the incipient motion criterion. This criterion has been the subject of considerable debate and study, and there is no agreement on the best way to determine it, Armitage says.

He did manage however, to come up with a modified criterion, which improves on one developed by his supervisor some 30 years ago. He was also able to show the relationship between the rate of movement of sand (intensity of motion) and the unit stream power, something that had not been done before.

"I basically came up with a new criterion for describing the boundary between scour and no scour," he says. His model also stood up pretty well when tested against experimental data.

Armitage's project was funded by Water Research Commission (WRC), who will reproduce the thesis in report form shortly. The thesis has also been the basis of a conference paper that was presented at the 10th South African National Hydrology Symposium (SANCIAHS) in Pietermaritzburg at the end of 2001.

The problem with PhDs, says Armitage, is that you inevitably end up with more questions than you started off with. Questions he hopes to answer as he continues his work on the subject over the next few years, he adds.

Armitage graduated from the University of Stellenbosch in March.

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