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: H.G.Voortman@ct.tudelft.nl
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.
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H.G. VOORTMAN ET AL
Fig. 1: Pressure distribution according to Goda (1985)
The Goda formulae are written as:
*  0.751  cos 1 H
p1  0.51  cos  11   2* cos2 gH
p3   3 p1
p4   4 p1
(1)
pu  0.51  cos  31 3gH
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.
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CHAPTER 4.1
THE GODA MODEL FOR PULSATING WAVE FORCES
The -factors are given by:


4hs


L

1  0.6  0.5
 sinh  4hs  
L 



2
 
 1 d H 2

2d 

h
d
 2  min 
, 
3
H




1
 d  dc  
3  1  
 1 
 h 
2h
 cosh
L

4  1 





*
c
*
R

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
*
Rc :
min Rc , * 
When the wave pressures are know, the wave forces are given by:
Fh;Goda  12  p1  p4  Rc* 
1
2
p
1
 p3  d  d c 
(2)
Fu;Goda  12 pu Bc
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:
Rc*  p1  2 p 4    d  d c 
2
l h;Goda  d  d c 
3Rc*  p1  p 4   3 d  d c
p
 p
2
1
1
 2 p3 
 p3 
(3)
l v ;Goda  16 Bc
Using the expressions for the wave forces and the lever arms, the total moment due to the
wave forces can be calculated by:
MGoda  lh;Goda Fh;Goda  lv;Goda Fv;Goda
(4)
The calculated forces and moments serve as input in several limit state equations describing
the stability of the breakwater.
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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:
Fdesign  mFGoda
(5)
In which m denotes the model factor. Van der Meer et al found that m possesses a normal
distribution with parameters:
Horizontal force
Moment due to horizontal force
Uplift force
Moment due to uplift force
Mean
0.9
0.81
0.77
0.72
Standard deviation
0.25
0.40
0.25
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:
2
2
 total   Goda
  wave
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:
Horizontal force
Moment due to horizontal force
Uplift force
Moment due to uplift force
Mean
0.9
0.81
0.77
0.72
Standard deviation
0.20
0.37
0.20
0.34
REFERENCES
BRUINING, J.W (1994): Wave forces on vertical breakwaters, reliability of design formula.
Delft Hydraulics report, prepared for MAST II-MCS
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CHAPTER 4.1
THE GODA MODEL FOR PULSATING WAVE FORCES
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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