Stability of Wide-Graded Rubble Mounds

The reshaping of temporary rubble mounds like the core of breakwaters or reclamation bunds is often a concern for contractorsi n the construction stages of marine structures. The formulas found in literature for the prediction of such behavior are few, and they do not provide clear insight on the influence of relevant parameters, in particular the small dimensions and wide stone-size gradation of the material involved, usually consisting of quarry run or resulting from dredging. The previous research in the field of dynamic stability focused on berm breakwaters and gravel beaches. These two typologies of structures define the range to which the rubble mounds considered in this study generally belong. An overview on the design tools provided by the technical literature shows that, whenever the grading was included as a governing parameter, some influence was recognized in the characteristics of the structure (e.g. the permeability) and in the dynamism of the different fractions of stone sizes. However, very wide ranges of the parameter grading were never investigated and a specific analysis in this direction constitutes the main significance of this study. The Delft University of Technology provided the laboratory facilities to carry out physical model tests on a wide graded rubble mound structure representative of the core of a breakwater. The parameter D85/D15, describing the stone-size gradation of the construction material, was varied between the values 2.71 and 17.7, and two different seaward slopes of the model structure were also tested. The reshaped cross-shore profiles measured during the tests showed how if the grading increases the stability of the structure is reduced. This is not always in accordance with the findings of previous researchers, showing how the extrapolation of existing empirical formulas to structures with high values of the ratio D85/D15 do not give reliable results. Instead, the formulas given by van de Meer (1992) to estimate the whole reshaped profile of a dynamic slope predict with good agreement the shape of the measured profiles, although the physical model shows a larger horizontal extension of the displacements. This difference is governed by the grading, being more noticeable as this parameter increases. This result leads to the definition of new formulas, some of them being modifications of the ones given by van der Meer, to describe the geometry of a reshaped profile. The formulas, all including the parameter grading, are derived through curve fitting of the measured data. Also a formula for the direct estimation of the crest recession is given. As a final step, a simple numerical model is proposed in which the new formulas are implemented, constituting a quick way to assess the shape of a slope after a wave attack. As a suggestion for further utilization of the results of physical modeling, a brief comparison is also carried out between the output of the tests and the prediction of the numerical model XBeach (developed mainly at UNESCO-IHE). In conclusion, this research points out how the formulas provided by the technical literature are not reliable in representing the effects of a very wide stone-size gradation in the stability of a rubble mound structure. Physical model tests proved to be a suited way to investigate these effects, as the nature of the phenomena who play a role in the stability does not allow a simple analytical representation. The tests carried out within the present study lead to the implementation of a numerical model of practical use for engineers and contractors: further investigations through laboratory tests are recommended to validate and extend the findings of this study. Another proposed direction for further research is the comparison between the results of physical model tests and the output of numerical models.