chapter 4.1the goda model for pulsating wave forces

CHAPTER 4.1: THE GODA MODEL FOR

PULSATING WAVE FORCES

H.G. VOORTMAN, P.H.A.J.M. VAN GELDER, J.K. VRIJLING

Delft University of Technology, Hydraulic and Offshore Engineering Section,
Stevinweg 1, NL-2628 CN, Delft, The Netherlands
E-mail:

ABSTRACT

The Goda model for pulsating wave loads is introduced. Some considerations concerning model uncertainties are given.

Key words: Pulsating wave loads, Goda model, Model uncertainties, Vertical breakwaters

1.INTRODUCTION

Once the wave height and wave period in front of the structure are known, a model is needed to transform wave heights into loads on the structure. In case of pulsating loads, the model proposed by Goda (1985) can be used. Section 2 introduces the Goda model.

Every model includes some imperfections due to simplifications or lack of knowledge. These imperfections can be treated in a probabilistic sense by including model uncertainty. Considerations regarding model uncertainty in the Goda model are treated in section 3.

2.THE GODA MODEL FOR PULSATING WAVE LOADS

The basis of the Goda model is an assumed pressure distribution over the height and width of the caisson. Fig. 1 shows this pressure distribution.

Fig. 1: Pressure distribution according to Goda (1985)

The Goda formulae are written as:

(1)

In which:

H:incident wave height in front of the structure;

:angle of incidence of the wave attack with respect to a line perpendicular to the structure;

:density of the water;

g:acceleration of gravity;

1, *, 3, 4:multiplication factors dependent on the wave conditions and the water depth (see below);

1, 2, 3:multiplication factors dependent on the geometry of the structure.

The -factors are given by:

In which:

hs:water depth in front of the structure;

L:wave length;

d:depth in front of the caisson;

dc:height over which the caisson protrudes in the rubble foundation

:

When the wave pressures are know, the wave forces are given by:

(2)

In which Bc denotes the width of the caisson bottom.

The lever arms of the wave forces with respect to the centre of the caisson bottom are given by:

(3)

Using the expressions for the wave forces and the lever arms, the total moment due to the wave forces can be calculated by:

(4)

The calculated forces and moments serve as input in several limit state equations describing the stability of the breakwater.

3.MODEL UNCERTAINTIES REGARDING THE GODA MODEL

In Van der Meer et.al., 1994, the model uncertainty of Goda's formula has been studied. The model uncertainty Is given as a multiplicative error. The force to be used in a design calculations was defined as:

(5)

In which m denotes the model factor. Van der Meer et al found that m possesses a normal distribution with parameters:

Mean / Standard deviation
Horizontal force / 0.9 / 0.25
Moment due to horizontal force / 0.81 / 0.40
Uplift force / 0.77 / 0.25
Moment due to uplift force / 0.72 / 0.37

The model bias and -uncertainty were based on the calculated and measured values of the average of the highest of 250 waves. However, the average of the highest of 250 waves has inherent uncertainty, as described in Volume IIa, chapter 4.4. Goda's model uncertainty should be corrected for uncertainty of the highest wave in the following way:

In case of the horizontal forces it follows by

Total = 0.25 and Wave = 0.15 that

Goda = 0.20; a reduction of 5% in the model uncertainty.

Application of a similar procedure to all force components leads to modified values of the model factor:

Mean / Standard deviation
Horizontal force / 0.9 / 0.20
Moment due to horizontal force / 0.81 / 0.37
Uplift force / 0.77 / 0.20
Moment due to uplift force / 0.72 / 0.34

REFERENCES

BRUINING, J.W (1994): Wave forces on vertical breakwaters, reliability of design formula. Delft Hydraulics report, prepared for MAST II-MCS

GODA Y (1985): Random seas and design of maritime structures. University of Tokyo press, Tokyo

TAKAHASHI, S (1996): Design of vertical breakwaters. Port and Harbour Research Institute

VRIJLING, J.K;.VAN GELDER, P.H.A.J.M (1998): Statistical analysis of wave heights, Proceedings Delft Workshop 27/28 August 1998.

VAN DER MEER, J.W., D'ANGREMOND, AND JUHL, J., (1994): Probabilistic calculations of wave forces on vertical structures, Coastal Engineering 1994, pp.1754-67.

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