Modelling of the cross-shore mixed sand transport under sheet flow conditions

Abstract

Cross-shore sediment transport during extreme climate events (e.g. storm surges) may lead to significant morphological evolution and shoreline recession with drastic irreversible consequences. To protect sandy beaches against storm induced erosion issues, coastal engineering practices could be classified into hard/gray protecting coastal structures versus soft or environmentally friendly engineering measurements. Hard structures (e.g. seawalls) have usually been posed many problems during storm surges, which can be summarized as expensive reparation costs of structures after storm and damages of protected infrastructures as well as restriction of human access to beach for leisure activities, and consequently reduction of the tourist attraction. In contrast, the soft measurements for beach protection like beach nourishment can protect the sandy beaches against storms and preserves the beautiful beach scenes for tourists, and therefore provide financial support for people living along the coastline. The productivity as well as favorability of soft measurements for both nature and human parties lead to calling these activities in literature as building with nature in contrast to hard structures, which are known as building against nature. The high rate of beach erosion during storms and corresponding high costs for beach (re)nourishment to compensate the lost sand is one of the major issues in coastal zone management. To understand the erosion of sandy beaches under storm conditions, the associated erosion mode in literature is known as sheet flow, where the near bed current velocity is such great that sands are basically transported within highly concentrated sheets near the bed and therefore the bed forms are disappeared. The practical experiences on beach nourishment show that the new applied material (borrow material) have usually different properties, particularly grain size distribution, than the native sand. Moreover, this discrepancy between the grain size distribution of incorporated and native sand has an important role in increment/reduction of the erosion rate of (re)nourished beaches under future storms. To understand the erosion mechanisms of (re)nourished beaches, coastal engineers were interested to study the transport mechanisms of mixed sand versus uniform sand. Performed experiments in the Großer Wellenkanal (GWK) on mixed sands (well graded sand) with the same median grain size to a uniform sand (well sorted sand) in small scale experiments under storm induced transport mode (i.e. sheet flow) revealed that the erosion rate of the mixed sand is smaller than the uniform. This importance can approve the practical experiences, where the final sand mixture grain size distribution after (re)nourishment is a deciding parameter to reduce the erosion rate at future storms. Due to the natural heterogeneity of sand grains, coastal engineers tried to modify the effective shear stress or critical shear stress on grains using empirical/theoretical modification factors to include this in prediction formulas. These modification approaches are known in sediment transport as hiding/exposure factors. However, these are not able to include the detailed mechanisms of mixed sand transport in prediction formulas, and therefore depending on the applied formula for predicting the transport rate. The accuracy of transport formulas generally differs with respect to the applied modification factor. Moreover, the hiding/exposure factors are not able to provide detailed information about the concentration flux of constituting fractions in a mixed sand. Therefore, with regard to the positive economical property of mixed sand based on the performed experiments, detailed investigations like this thesis could be worthful to improve the protection performance of beach (re)nourishment as a sustainable environmentally friendly measurement in coastal engineering. In this study, the available experiments on mixed sand transport under sheet flow conditions are systematically compared. Then the capability of available (semi-) empirical formulas in coastal engineering for sheet flow induced sand transport in combination with available empirical equations for hiding/exposure coefficients are evaluated. Moreover, due to the importance of non-uniformity of mixed sand in reduction of the erosion rate after (re)nourishment under storm condition, a detailed RANS (Reynolds Averaged Navier Stokes) Eulerian two-phase numerical solver, mixedSedFoam, within the open-source CFD-toolbox framework OpenFOAM is developed, and with available experimental data calibrated and validated. This is the first time that accompanied with the sand concentration and velocity, the concentration of constituting fractions as well as their corresponding velocities are computed. This importance could improve the understanding of the transport mechanisms of mixed sand under sheet flow conditions and be implemented in the practice of coastal engineering, by deciding on the available borrow material with different grain size distribution for beach (re)nourishment. Moreover, due to the importance of inter-particle interactions within the sheet flow layer, in this thesis a new intergranular drag force coefficient based on the collision of particles (here sand grains) and the kinetic energy of granular system is developed. The developed new drag force coefficient can better than the previous describe the dynamics of different granular systems. Finally, a new formula for prediction of sheet flow layer thickness is presented, which improves the accuracy of available (semi-) empirical transport formula for mixed sand transport prediction.