Low-mobility Transport of Coarse-grained Bed Material under Waves and Currents

Rubble mound near-bed structures are among the more common hydraulic structures. Examples include bottom protections to prevent scour near bridge piers, offshore structures, weirs and sluices and at the toe of bank protections or breakwaters, but also pipe covers on offshore pipelines. The cornerstone of the theory behind the design of these structures was laid by Izbash (1930) and, most notably, Shields (1936), who linked the stability of a stone in the near-bed structure to the shear stress exerted on the bottom by a flow. Even today, some 75 years later, the design of near-bed structures is still largely based on Shields' work. Shields postulated that for values of his stability parameter below a certain critical value (the socalled 'threshold of motion') the stones in the bed would not move at all. In reality stones do not exhibit this kind of behaviour; stones have been shown to move at any value of the Shields parameter, also below the 'threshold of motion'. The mobility of the stones does increase with higher values of the Shields parameter, indicating that this is really a mobility parameter rather than a stability parameter. In practice, this concept has given rise to a conservative ‘statically stable’ design approach: a threshold of motion is selected and the size and weight of the stones are chosen such that the Shields parameter does not exceed the critical value. Alternative, ‘dynamically stable’ design approaches in which some movement of stones is allowed in combination with an appropriate maintenance program may be more economical. However, these are not commonly adopted because the transport of the bed protection material cannot be accurately predicted and thus the rate of deterioration of the bed protection and the required intensity of the maintenance programme cannot be assessed. Research has been undertaken to investigate the transport of bed protection material and to improve the feasibility of a ‘dynamically stable’ design approach. Application in marine environments requires that the loading consists of waves and currents, or a combination of these.