Beach nourishment

Definition of Beach nourishment: Beach nourishment is the artificial supply of sediment, usually sand, to restore or enlarge a beach. This is the common definition for Beach nourishment, other definitions can be discussed in the article

Purpose of beach nourishment

Beach nourishments can be applied in various cases; e.g.:

• To broaden the beach (recreation purposes);
• To create entirely new beaches (recreation purposes);
• To increase coastal safety by providing a larger sand buffer that protects dunes, seawalls or other landward assets against storm waves;
• To compensate losses because of structural erosion.

The first three cases can be regarded as applications to improve an existing undesirable situation that does not necessarily imply an ongoing supplementation program. In the fourth case, coastal nourishments are used as an instrument in coastal protection projects. Due to structural erosion, sediments are lost more or less continuously from a stretch of coast; regular nourishments are required to compensate for the losses that occur on average.

Non-equilibrium coastal profile

Fig. 1. Schematic profile adjustment after beach nourishment. If sand is placed mainly on the subaerial beach, cross-shore redistribution towards the submerged profile occurs until a profile compatible with the sediment characteristics and hydrodynamic conditions is approached. Part of the added sand may also be transported landward by wind and incorporated into the foredune.

When borrow sand is placed in a coastal profile, the initial profile and sediment distribution will generally differ from those that are compatible with the prevailing hydrodynamic conditions. Cross-shore sediment transport will therefore redistribute the nourishment towards a profile better adapted to these conditions, as illustrated in Fig. 1. There will also be changes caused by alongshore distribution of the nourishment, by a possible trend of sustained long-term erosion or by the response to extreme weather events. On a structurally eroding coast, nourishment does not remove the cause of erosion. The added sediment will therefore gradually be redistributed and the nourishment must eventually be repeated unless the sediment deficit is eliminated. The need for repeated nourishment is therefore not evidence of failure; it is an inherent consequence of using nourishment to compensate an ongoing sediment deficit. As environmental concerns and requirements for sustainability gain in importance, the share of nourishment in coastal management schemes has gradually increased in recent decades.

When a beach suffers from structural erosion, artificial nourishments can be applied as a soft remedy. The losses occurring from a stretch of coast are replenished from time to time. The regular application of nourishments with borrow sand with the same grain size as the native beach material will not strongly disturb the existing longshore sediment transport and thus will not change the occurring losses. Therefore the erosion will not stop; this means that after a certain period of time (the nourishment lifetime) the nourishment must be repeated.

Nourishment design: Experience from Denmark

The performance of a nourishment scheme very much depends on the grain size of the borrow material relative to the grain size of the native material. The influence of grain size on cross-shore sediment transport processes is discussed in the article Coastal Hydrodynamics And Transport Processes.

If the borrow sand is finer than the native sand, it will tend to form a flatter profile than the natural one. The equilibrium reshaping of the nourished sand will reach out to the closure depth. If the objective of the nourishment is to obtain a wider beach, this will require large volumes of sand, as illustrated in the upper part of Fig. 2.

If the objective is to reduce the required nourishment volume while retarding subsequent erosion (increasing the nourishment lifetime) it is advantageous to apply sand with a larger grain size than that of the native sand into a coastal profile. This will produce a steeper profile than the natural profile. Furthermore, coarser sand will be more stable in terms of longshore loss. This nourishment efficiency of the nourished sand has been studied by the Danish Coastal Authority based on many years of nourishment along the Danish North Sea Coast. The nourishment efficiency is defined as the ratio between the erosion rate for the natural sand (theoretical) and that of the nourished sand. The nourishment efficiency has been analysed as function of the ratio between the mean grain size of the borrow sand and that of the native sand:

[math]GSR_{Nourishment}=d_{50,Borrow}/d_{50,Native}[/math]

The analysis covers effects of cross shore as well as longshore effects. Experience along the Danish North Sea coast showed a strong empirical relationship between nourishment performance and the ratio of median borrow and native grain sizes (Fig. 3).

Fig. 2. Schematic equilibrium conditions for nourished beaches required to obtain an additional beach width of [math]\Delta w[/math] with borrow sand, which is finer and coarser than the native sand (upper and lower, respectively).

Fig. 3. Empirical relationship between Nourishment Efficiency and the Grain Size Ratio derived from nourishment experience along the Danish North Sea coast; it should not be interpreted as a general nourishment-design formula.

Instead of only considering the median grain size, the full grain-size distribution is more usually taken into consideration in nourishment design. Coarser nourishment sand is less mobile than finer native sand and will therefore reduce both cross-shore and longshore sediment losses. The magnitude of this effect depends on the resulting beach profile and local wave climate and cannot be inferred from grain size alone. If a limited coastal section is nourished with substantially coarser sand, the resulting reduction in longshore sediment supply can increase erosion farther downdrift.

Nourishment design: Experience from the Netherlands

Fig. 4. Lifespan of beach nourishments compared to the nourishment volume.

Beach nourishments are regularly carried out along the Dutch coast in order to maintain the coastline in all sections subject to erosion. In total 258 beach nourishments have been carried out since 1990. From the experience of these nourishments some rules of thumb have been derived to optimize their effectiveness.

Sand is borrowed from the seabed of the southern North Sea where thick sand layers are present. Sand is mined within a distance of 12 miles from the coast to limit shipping distances, but below the 20 m depth contour to avoid an influence on coastal processes. Borrow sites are selected for grain size distributions similar to the sand of the beach where the nourishment is to be applied. Nourishment sand is distributed over the beach from the dune foot (at approximately 3 m above mean sea level) to the low-water shoreline, such that the original natural slope (around 1:30) is maintained. The average volume of beach nourishments is 200 m³/m and the average length is 2.3 km with a gradual decrease in volume towards both ends of the nourishment in the alongshore direction to minimize side effects. These design rules reflect Dutch North Sea conditions and should not be transferred directly to coasts with different wave climates, tides, sediment characteristics or profile geometry.

The evaluation of beach nourishments along the Dutch coast shows that the average nourishment lifetime is about 3 years. The lifetime is defined with respect to the Dutch coastline definition (see Coastline), which is based on the sand volume in the most dynamic part of the active coastal zone. A lifetime of 3 years means that after 3 years the coastline is back to its initial position. At the nourishment site, approximately 40–50% of the nourished volume is lost in the first year from the most dynamic cross-shore zone. When considering the entire active coastal zone the loss is likely smaller. As shown in Fig. 4, no clear relationship between nourishment volume and nourishment lifetime is observed.

An extreme and fundamentally different strategy is the Sand Motor mega-nourishment (Fig. A4), in which 21.5 million m³ of sand was placed at one location and allowed to spread naturally along the coast over several decades. The Sand Motor mega-nourishment has an estimated lifetime that exceeds 20 years.

Nourishment on a littoral drift coast

Under certain simplifying conditions, an approximate analytical expression can be obtained for the evolution of a nourishment on an initially uniform coast under the influence of a constant small wave incidence angle, see the Appendix. According to this simplified linear model, the evolution of an initial Gaussian-shaped nourishment has the following characteristics:

• The nourishment is not displaced along the shoreline, despite net unidirectional littoral drift.
• The nourishment retains its symmetric Gaussian shape, while the squared longitudinal spread increases linearly with [math]P \, t / D[/math], where [math]P[/math] is the wave power (wave energy flux), [math]t[/math] is the elapsed time and [math]D[/math] is the sum of closure depth and height of the beach berm.
• For small wave incidence angles, the nourishment evolution does not depend on this angle.

These characteristics are largely due to the linearity of the simplified model. More realistic non-linear models show deformation and displacement of the nourishment, but the alongshore spreading of the nourishment is the prevailing characteristic, as in the simplified linear model.

Appendix: Analytical solution for a Gaussian-distributed sand nourishment

The simplifying conditions for which an approximate analytical expression can be obtained for the evolution of a beach nourishment on an alongshore uniform coast are:

(i) The cross-shore profile of the nourishment in the active coastal zone is all the time close to morphological equilibrium (i.e. cross-shore sediment exchange processes can be neglected compared to longshore processes) and follows displacements of the shoreline by simple cross-shore translation.

(ii) The breaker line is and remains parallel to the shoreline

(iii) The wave incidence angle [math]\alpha_b[/math] at the breaker line is small (< 30°).

Fig. A1. The one-line model schematization of shoreline evolution.

With these simplifications, the displacement of the shoreline position [math]y(x,t)[/math] can be described by the one-line model (see Fig. A1 and Littoral drift and shoreline modelling)

[math]\dfrac{\partial y}{\partial t} + \large\frac{1}{(D_B + D_C)(1-p)} \frac{\partial Q}{\partial x}\normalsize = 0 \; . \qquad (1) [/math]

Symbols have the following meaning:

[math]x=[/math] the alongshore coordinate along the fixed [math]x-[/math]axis,

[math]y(x,t)=[/math] the position of the shoreline at time [math]t[/math], measured perpendicularly from the [math]x-[/math]axis,

[math]D_C=[/math] the closure depth (seaward limit of the active coastal zone),

[math]D_B=[/math] the berm height (landward limit of the active coastal zone),

[math]p=[/math] the porosity of the seabed,

[math]Q=[/math] longshore sand transport (littoral drift).

With the conditions (i)-(iii), the dependence of the longshore sand transport on the wave incidence angle [math]\alpha_b[/math] is given by (Fig. A2)

[math]Q = Q_0 \sin \alpha_b \cos \alpha_b \, , \qquad (2)[/math]

where [math]Q_0[/math] depends on wave climate parameters and shoreface characteristics (e.g. slope, grainsize). In the following we will assume that [math]Q_0[/math] has been empirically determined for the nourishment site.

Fig. A2. Wave incidence angles in a 1-line model where the breaker contour line is parallel to the shoreline. [math]\alpha_b[/math] is the angle of the wave front with the breaker line, [math]\alpha'_b[/math] is the angle of the wave front with the [math]x-[/math]axis, [math]\delta[/math] is the angle of the shoreline with the [math]x-[/math]axis.

For wave incidence angles [math]\alpha_{b}[/math] (the angle between the wave front and the breaker line, Fig. A2) smaller than 30° we approximate [math]\sin \alpha_b \approx \alpha_b[/math] and [math]\cos \alpha_b \approx 1[/math].

The wave incidence angle [math]\alpha'_b[/math], the angle between the wave front and the [math]x-[/math]axis, is assumed constant. It is related to the shoreline angle [math]\; \tan \delta = \partial y / \partial x \;[/math] by [math]\; \alpha'_b=\alpha_b+\delta[/math]. The gradient of the longshore transport is then given by

[math]\dfrac{\partial Q}{\partial x} = Q_0 \dfrac{\partial \sin \alpha_b \cos \alpha_b}{\partial x} \approx Q_0 \dfrac{\partial \alpha_b}{\partial x} = - Q_0 \Large\frac{\partial \delta}{\partial x}\normalsize \approx - Q_0 \Large\frac{\partial^2 y}{\partial x^2}\normalsize . \qquad (3) [/math]

The one-line littoral drift model Eq. (1) then becomes

[math]\Large\frac{\partial y}{\partial t}\normalsize = \epsilon \Large\frac{\partial^2 y}{\partial x^2}\normalsize , \quad \epsilon = \Large\frac{Q_0}{(1-p) D}\normalsize ,\qquad (4) [/math]

where [math]D=D_B+D_C[/math] is the sum of berm height and closure depth. Equation (4) is a diffusion equation: initial deviations from a straight shoreline will be gradually spread along the coast. If the initial shoreline position [math]y(x,0)[/math] is known, the solution of Eq. (4) for the shoreline position [math]y(x,t) , \, t\gt 0 [/math] is given by

[math]y(x,t) = \Large\frac{1}{2 \sqrt{\pi \epsilon t}}\normalsize \int_{-\infty}^{\infty} y(x+\xi, 0) \exp\big(-\large\frac{\xi^2}{4 \epsilon t}\normalsize \big) d \xi . \qquad (5)[/math]

Fig. A3. Evolution of Gaussian-shape nourishment ([math]a = 100 \, m, \; \sigma_0 = 1000 \, m[/math]) with littoral drift ([math]Q_0 = 4 \, 10^5 \, m^3/yr[/math]) and berm height + closure depth [math]D = 8 \, m[/math]. Blue curve: [math]t=0[/math], red curve [math]t=10 [/math] year. No cross-shore sediment transport.

This expression can be integrated analytically for simple shapes of the initial shoreline. An example is the evolution of an initial Gaussian-distributed sand nourishment with cross-shore amplitude [math]a[/math] and longitudinal spread [math]\sigma_0[/math],

[math]y(x,0) = a \exp \big(-\large\frac{x^2}{2 \sigma_0^2} \normalsize \big) . \qquad (6)[/math]

We assume [math]a \lt \lt \sigma_0[/math], to ensure that the wave incidence angle [math]\alpha[/math] is small over the entire nourishment. We also assume that the cross-shore profile of the nourishment is in morphological equilibrium (no cross-shore sediment transport). The shoreline will then evolve according to

[math]y(x,t) = a \Large\frac{\sigma_0}{\sigma}\normalsize \exp \big(-\large\frac{x^2}{2 \sigma^2}\normalsize \big) , \quad \sigma^2 = 2 \epsilon t +\sigma_0^2 .\qquad (7) [/math]

The nourishment is not displaced along the shoreline, despite the unidirectional longshore sediment transport [math]Q = Q_0 \, \cos \alpha_b \sin \alpha_b[/math] (Fig. A3). It retains its symmetric Gaussian shape, while the squared spread increases linearly with [math]Q_0 t / D[/math]. The spreading rate in this linearized small-angle approximation does not depend on the constant wave incidence angle [math]\alpha'_b[/math].

The small angle condition is important. For sufficiently large wave-incidence angles and shoreline perturbations, nonlinear shoreline response can become important. A strongly protruding nourishment can then behave morphodynamically like a sandy headland and may develop an asymmetric downdrift extension, as discussed in the article Sand spit. Despite this theoretical possibility, no flying spit developed on the Sand Motor, the largest beach nourishment in history (21 million m³), see Fig. A4. Due to the dominant northward littoral drift, the amount of sand spread to the adjacent northern coast was about twice the amount spread to the south.

Eq. (5) can provide estimates of shoreline evolution for many other initial shapes. Several examples are shown in Larson et al. (1987). This report also provides analytical expressions for situations where the longshore sediment transport is modified by the presence of groynes and detached breakwaters. Analytical expressions for the case of beaches of finite length (embayed beaches) are given by Ciccaglione et al. (2023, 2024).

Fig. A4. The evolution of the 21.5 million m3 ‘Sand Motor’ nourishment on the Dutch coast from 2011 (initial state) to 2021. During this period about 10% of the sand was transported outside the analysed coastal sections, 10% was spread to the north (dominant littoral drift direction) and 5% to the south. Image from Huisman et al. (2021).

Related articles

• Experiences with beach nourishments in Portugal
• Shore nourishment
• Shoreface nourishment
• Ecological impacts of seabed sand mining
• Shoreface profile
• Coastal Hydrodynamics And Transport Processes
• Coastline

References

The main authors of this article are Mangor, Karsten, Jan van de Graaff, Anna Kroon and Job Dronkers Please note that others may also have edited the contents of this article. For other articles by this author see Category:Articles by Mangor, Karsten For other articles by this author see Category:Articles by Jan van de Graaff For other articles by this author see Category:Articles by Anna Kroon For other articles by this author see Category:Articles by Job Dronkers