Cress Help - Wind waves and swell - Wave / structure interaction - Overtopping - Vertical structures - Z16.1

Overtopping over sloping dike
Calculation of run-up according to Van der Meer

Background information

Van der Meer [] has developed an equation for overtopping over a sloping structure. This equation is quite similar to the equations for run-up.

The dimensionless overtopping is given by:

Q is the dimensionless overtopping discharge and R is the dimensionless freeboard.

The coefficients a and b depend on the breakertype:

The values of a and b are determined by curve-fitting from measurements:

{bmc dik055301.bmp}

Measured data from plunging wave experiments

{bmc dik055302.bmp}

Meaured data from surging wave experiments

As usual

In cress the value for b is calculated using

The value u follows from the normal distribution. For standard design an exceedence of 10% is recommended, which results in a value of u = 1.28.

The non-dimensional overtopping is defined as:

(for surging waves the second root has to be set to 1).

In this equation h is the water depth just in front of the structure.

The discharge q is in m³/sec per running meter of dike. Realise that q is a time averaged value. The instantaneous amount of water in one wave gives instantaneously is much higher discharge.

The non-dimensional freeboard is defined as:

(for surging waves the second term has to be set to 1). In this equation h_k is the freeboard

Effect of berm, etc is included in the correction factor:

The total reduction of the overtopping is:

{button gamma f, KLink("friction;")}{button gamma b, KLink("berm reduction;")}{button gamma beta, KLink("oblique waves;")}

References

Al state of the art knowledge regarding run-up and overtopping is summarised in:

TAW [2002] Calculation of run-up and overtopping over sloping structures (in Dutch)

Other background information:

Van der Meer J.W. and Stam, C.J.M. [1992] Wave run-up on smooth and rock slopes of coastl structures, ASCE journal of WPC&OE, vol 118, (5) pp534-550

#K$allowable overtopping

Allowable overtopping

Note that q in this rule is the average overtopping in time. The instantaneous amount of water flowing over the dike is much more. For the individual amount of water in one overtopping wave see the relevant rule in Cress.

According to Dutch standards the allowable overtopping is:

For any inner dike slope             q<0.1 l/s

For normal inner dike slopes       q<1    l/s

For high quality inner slopes       1<10  l/s

Other information:

For safe walking                         q<0.1 l/s

Structural damage to buildings    q<10  l/s

Damage to protected sea walls   q<100 l/s

References

Van der Meer [1993] Conceptual design of rubble mound breakwaters, originally published by Delft Hydraulics; also reprinted in newer versions as lecture note by IHE and publications of Infram.

TAW [1998] Guidelines on the design of sea and lake dikes

#K$equivalent slope

In case of a berm, and different slopes above and below the berm, Van der Meer suggests the following calculation for the effective slope:

in which h_b is the depth of the berm below Still Water Level; n₁ is the slope above the berm, n₂ is the slope below the berm.

In case of shallow water in front of the slope, the wave height is automatically reduced, using

in which d_h is the depth in front of the slope.

#K$berm reduction

A berm will also reduce the overtopping; this is calculated using (b = berm width, n_b is berm slope):

            in this equation n_eq is the equivalent slope  {button details, KLink("equavalent slope;")}

#K$oblique waves

Oblique waves also will reduce the overtopping:

For short-crested waves, the equations of Van der Meer are used (approach angle ):

For long crested waves, the old equations for regular waves are recommended (TAW):

#K$friction

Also the roughness of the slope gives a reduction: