This section provides a description of the methodology for analysing the influence of
transitions on grass cover erosion. The general approach can be divided in two steps: (1) determining a representative parameter value for the strength of the grass cover and (2) calibrating a factor for the increase in load and/or the decrease in strength of the grass cover at the transition. The approach for modelling the effect of transitions is explained more specific for the hydrodynamic-erosion model (Subsection 3.2.1.) and the cumulative overload method (Subsection 3.2.2.).
3.2.1. Model 1: Hydrodynamic-erosion model
Two steps can be distinguished to analyse the influence of transitions on grass cover erosion using the cumulative overload method. First, a representative threshold flow velocity Ut needs to be determined and, next, the turbulence intensity parameter r0 needs to be calibrated (Figure 3.3).
Figure 3.3 Overview of the approach for determining influence factors for a transition on grass cover erosion using the hydrodynamic-erosion model.
The strength of the grass cover is included in the hydrodynamic-erosion model in terms of the threshold flow velocity Ut. To analyse the influence of transitions on grass cover erosion, it is
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first required to determine a representative value for Ut. From grass sod pulling tests is concluded that the grass cover strength generally varies along a dike profile (Bijlard, 2015). Therefore, it is difficult to determine parameters like the threshold flow velocity at a test section. In this research, it is assumed that a representative threshold flow velocity can be derived based on the measured erosion depth at a spot along the dike profile where no transition is present.
First, a range of threshold flow velocity values needs to be defined and, subsequently, the erosion depth at the spot along the dike profile is calculated for each threshold flow velocity value. The modelled erosion depths are compared to the measured erosion depth. The threshold flow velocity value for which the modelled erosion depth is closest to the measured erosion depth is selected as representative threshold flow velocity Ut. A minimum threshold flow velocity can be determined in case the grass cover did not erode during the wave overtopping test. This is the lowest Ut-value resulting in no erosion at the cross-dike coordinate. It is assumed that the derived threshold flow velocity is representative for each cross-dike coordinate.
The second step in the analysis using the hydrodynamic-erosion model is to calibrate the influence factors to account for increased hydraulic loads and/or decreased grass cover strength at transitions. The threshold flow velocity Ut and/or the inverse strength parameter
CE could be considered as calibration parameters to account for a lower grass cover strength at transitions. The increased hydraulic loads at transitions should be included in the model analysis using the depth-averaged turbulence intensity parameter r0 as calibration parameter. A range of values for the calibration parameter needs to be determined. Next, the model is used to calculate the erosion depth at the location of the transition for each value of the calibration parameter. The mean erosion depth at the transition is compared with the measured erosion depth near the transition. The value of the calibration parameter that results in the least difference between the modelled and measured mean erosion depth is assumed to be representative for the influence of the transition on grass cover erosion. This approach for the analysis of influence factors for transitions on grass cover erosion with the hydrodynamic-erosion model requires data from the wave overtopping tests. The input dike profile is defined in terms of the crest width, the length of the slope, the slope steepness and the berm width. The grass cover erosion needs to be expressed in terms of the mean erosion depth and the length of the eroded grass cover, while it is also required to know the cross-dike location at where erosion was observed.
3.2.2. Model 2: Cumulative overload method
The analysis of influence factors for transitions using the cumulative overload method is comparable to the analysis using the hydrodynamic-erosion model: the strength of the grass cover needs to be determined and, next, the influence factor(s) for the transition type are calibrated (Figure 3.4).
The grass cover strength is represented by the critical flow velocity Uc in the cumulative overload method. A range of Uc-values needs to be determined and, subsequently, a cumulative damage number D is calculated for each Uc-value. The modelled cumulative damage numbers for different Uc-values are compared to the damage number that corresponds to the observed damage category. The critical flow velocity that results in the least difference between the modelled damage number and the damage number for the
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observed damage category is selected as the representative critical flow velocity. It is again assumed that the derived critical flow velocity is representative for all cross-dike coordinates. The load factor αM and the strength factor αs in the cumulative overload method can be
considered as calibration parameters for transitions. A range of values for αM (αM≥ 1) or αs
(αs≤ 1) must be defined to determine the damage number for each value of the influence
factors. The modelled damage numbers for each value of the load factor αM is compared to
the damage number that corresponds to the observed damage category (Figure 3.4). The load factor for which the modelled damage number is closest to the damage number for the damage category is selected as the representative load factor for the transition.
Figure 3.4 Overview of the approach for determining influence factors for a transition on grass cover erosion using the cumulative overload method.
Data required for the analysis using the cumulative overload method consists of dike profile data (landward slope steepness) and erosion data (observed damage numbers and location of damage).