Incipient motion of riprap on steep slopes

Langmaak, Kai Rainer (2013-12)

Thesis (MEng)--Stellenbosch University, 2013.

Thesis

ENGLISH ABSTRACT: Riprap is commonly used as an erosion protection measure around the world. In some cases, for example when constructing bed arrestors, riprap has to be designed to be stable on steep slopes. The literature shows that the problem of incipient motion is reasonably well understood, but existing hydraulic design methods are found to be largely unreliable. The main objective of this study is to improve the understanding of the different factors affecting incipient motion in order to furnish the prospective design engineer with a reliable method for sizing riprap on steep slopes adequately. Eight existing theories dealing with the threshold of incipient motion are reviewed, of which Liu’s work (1957) seems most promising. Naturally, the required median rock diameter of the riprap is reasonably large (due to the steep slopes), with high particle Reynolds numbers. However, little data is available for these flow conditions. Data collected from 12 large scale laboratory tests carried out for this research indicate that the dimensionless Movability Number is in fact constant for large particle Reynolds numbers. For design purposes, the recommended Movability Number which emerged from this study is 0.18, provided that the steep bed slope is taken into account, and that the theoretical settling velocity is calculated using an accurate drag coefficient and the d90 sieve size. A comparison of the laboratory data with design equations showed that a large variety of results are obtained, which supports the need for this study. Finally, it was shown that a calibrated one dimensional hydrodynamic model can be used by the practicing engineer to extract the hydraulic properties needed for applying Liu’s theory. It was found that the ratio ks/d90 = 0.81 may be applied to estimate the bed roughness for the grading used in this study.

AFRIKAANSE OPSOMMING: Stortklip is ‘n metode wat wêreldwyd gebruik word om erosie te voorkom. In sommige gevalle, byvoorbeeld vir die konstruksie van erosietrappe, moet stortklip teen steil hellings spesifiek ontwerp word om stabiliteit te verseker. Die literatuur beskryf die probleem van aanvanklike beweging redelik goed, maar dit is bevind dat die bestaande ontwerpmetodes grotendeels onbetroubaar is. Die hoofdoelwit van hierdie ondersoek was om die faktore wat beweging van stortklip veroorsaak, beter te verstaan en ‘n betroubare metode te ontwikkel wat ’n ingenieur kan aanwend om stortklipbeskerming wat op steil hellings geplaas word te ontwerp. Agt verskillende metodes wat die begin van beweging beskryf is bestudeer, en dit wil voorkom asof die Liu teorie van 1957 die grootste potensiaal het. As gevolg van die steil hellings wat ondersoek word, is die benodigde klipgroote redelik groot wat weereens die oorsaak is vir ‘n hoë deeltjie Reynolds getal is. In die literatuur kon geen data gevind word vir so ‘n vloeitoestand nie. Daarom is 12 laboratoriumtoetse gedoen en daar is gevind dat die Mobiliteitsgetal redelik konstant is vir groot deeltjie Reynoldsgetalle. Vir onwerpdoeleindes word ‘n Mobiliteitsgetal van 0.18 aanbeveel, met die voorwaarde dat die bodemhelling in ag geneem word, en dat die teoretiese valsnelheid bereken word met die d90 klipgroote en ‘n akkurate sleurkoëffisiënt. Verder is gevind dat die labaratorium data die voorspellings van die bestaande ontwerpvergelykings nie bevredigend pas nie. Dit ondersteun die behoefte vir hierdie studie. Om die bogenoemde bevindings vir praktiese probleme bruikbaar te maak, is daar gewys dat ‘n gekalibreerde een dimensionale hydrodinamiese rekenaarmodel gebruik kan word om die nodige hidrouliese eienskappe te verkry om die Liu teorie toe te pas. Dit is bevind dat die verhouding ks/d90 = 0.81 ‘n goeie benadering vir die hidrouliese ruheid kan voorsien.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/85816
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