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R.H. Charlier and Chr. P. De Meyer
Another mathematical model requires calculation of a renourishment factor.
This factor provides an estimate of the frequency of renourishment with a specific
fill required to maintain a beach's dimensions. The frequency is function of the
difference in composite grain-size distributions between the original and the fill
material.
The model allows an evaluation of different nourishment materials suitability in
regards to maintenance costs. As coarser materials have a longer "on-beach"
residence time, comparing grain-size distributions enables to predict a fill's longterm performance. A simplified mass-balance equation embodying arriving and
departing materials, size and amount is :
(7)
with :
R
I1
b
n
A
the renourishment factor
the mean diameter in ~p units
the sorting coefficient in ~ units
indicates nourishment material
indicates original beach material
dimensionless parameter related to winnowing
The renourishment factor, or relative retreat rate is the ratio of the respective
retreat rates of fill to original materials. Winnowing is selective sorting in the
environment.
A value of 1 indicates that residence time of nourished and original material is
the same ; values larger than 1 indicate the fraction of time the nourished
material will be retained as compared to the original material ; inversely, a
fractional value of R indicates how many times less often such fill will have to be
replaced than the original materials.
This model establishes the frequency of renourishments needed to maintain a
stable beach. On the other hand the fill-factor model attempts usually to
determine the quantity of fill material needed for a unit volume of grain-size
distribution as the natural material. Both aim at providing beach stability, but the
latter method considers the original material as optimal for the beach and thus
thinks in terms of such size material as fill, in other words to maintain or reestablish the status-quo lsf
R.H. Charlier and Chr. P. De Meyer
Another mathematical model requires calculation of a renourishment factor.
This factor provides an estimate of the frequency of renourishment with a specific
fill required to maintain a beach's dimensions. The frequency is function of the
difference in composite grain-size distributions between the original and the fill
material.
The model allows an evaluation of different nourishment materials suitability in
regards to maintenance costs. As coarser materials have a longer "on-beach"
residence time, comparing grain-size distributions enables to predict a fill's longterm performance. A simplified mass-balance equation embodying arriving and
departing materials, size and amount is :
(7)
with :
R
I1
b
n
A
the renourishment factor
the mean diameter in ~p units
the sorting coefficient in ~ units
indicates nourishment material
indicates original beach material
dimensionless parameter related to winnowing
The renourishment factor, or relative retreat rate is the ratio of the respective
retreat rates of fill to original materials. Winnowing is selective sorting in the
environment.
A value of 1 indicates that residence time of nourished and original material is
the same ; values larger than 1 indicate the fraction of time the nourished
material will be retained as compared to the original material ; inversely, a
fractional value of R indicates how many times less often such fill will have to be
replaced than the original materials.
This model establishes the frequency of renourishments needed to maintain a
stable beach. On the other hand the fill-factor model attempts usually to
determine the quantity of fill material needed for a unit volume of grain-size
distribution as the natural material. Both aim at providing beach stability, but the
latter method considers the original material as optimal for the beach and thus
thinks in terms of such size material as fill, in other words to maintain or reestablish the status-quo lsf