Along with global climate changing, the disaster caused by overtopping from breakwater or revetment seems further serious. There are many factors which related with wave overtopping flux, one is wave period, some researches have big gap on it. Three formulas of overtopping flux were compared on wave period influence. Eight\ud
sections of single sloping breakwater without super structure were tested in wave flume. The overtopping was measured under different wave periods. The measured values were compared with calculation results. Wave run-up was calculated to analyze the difference of overtopping between measurement and calculation, and it showed that the cases which had much difference were splashing. The factor L/H was adopted to improve the existed formula as multiple 

Bao, C.H.

Ping, L.L.

Wu, Z.H.

Zai, G.L.

Hasanuddin University Repository

 415 
 
 
Proceedings of the 7th International Conference on Asian and Pacific Coasts  
(APAC 2013) Bali, Indonesia, September 24-26, 2013 
 
 
 
EXPERIMENT STUDY ON OVERTOPPING OF SLOPING  
BREAKWATER BY SWELL 
 
C.H. Bao 
1
, Z.H. Wu 
2
 ,G.L Zai
1
 and L.L Ping 
2
 
 
 
ABSTRACT: Along with global climate changing, the disaster caused by overtopping from breakwater or revetment 
seems further serious. There are many factors which related with wave overtopping flux, one is wave period, some 
researches have big gap on it. Three formulas of overtopping flux were compared on wave period influence. Eight 
sections of single sloping breakwater without super structure were tested in wave flume. The overtopping was measured 
under different wave periods. The measured values were compared with calculation results. Wave run-up was 
calculated to analyze the difference of overtopping between measurement and calculation, and it showed that the cases 
which had much difference were splashing. The factor L/H was adopted to improve the existed formula as multiple . 
 
Keywords: Wave period, swell, breakwater, overtopping . 
 
 
                                                 
1 Tianjin Research Institute for Water Transport Engineering Ministry of Transport, Tianjin 300456, CHINA 
2CCCC Second Harbor Consultants,Co.,Etd.,Wuhan 430071,CHINA  
INTRODUCTION 
Global climate changing, storm strengthen, sea 
level rising, coastal city ground settlement, we have to 
face serious risk of disaster by overtopping, 
unfortunately came true. The breakwaters and 
revetments would not overtopping in design before, will 
overtopping now, and it will impact its stability. 
The breakwaters and revetments were constructed for 
resisting storm, keeping the land and activity safety in 
back side. The top elevation is very high if without 
overtopping, and always be expensive. Some coast 
defenses were designed in lower standard, permitted 
overtopping, reduced the height of breakwater and cost 
of construction. The factors related with overtopping 
include the parameter of structure and hydrodynamics 
condition, such as the top elevation, the slope, armor 
block type, the width of breakwater, the slope of sea bed, 
the water depth of breakwater, wave height, wave period, 
wave direction, wave spectrum and wind velocity.  
Summarizing from site experience, physical model 
and numerical model are the important three 
methodologies for estimating overtopping flux. Because 
there are several factors related with overtopping flux, 
the formula is based on one, two or three factors and 
under certain condition. The relationship between 
overtopping flux and wave period was researched in this 
paper, the formula of swell with long wave period was 
provided. It is approved that the very long period wave 
as tsunami would cause huge run-up in shallow water, 
the overtopping is difficult to estimate, there is abundant 
water running over breakwater and causing damage. One 
objective of this paper is to arouse people to pay close 
attention to the disaster by overtopping. 
 
 THE FORMULA OF OVERTOPPING 
In Chinese Standard, a formula for overtopping was 
provided. The parameter includes slope, armor block 
type, wave height, wave period, water depth and top 
elevation. Assumed other parameters constant, except 
wave period, the one wave overtopping quantity is 
directing ratio with nature logarithm of wave period. The 
average overtopping flux decreased when the wave 
period increased according to the formula. 
 
   TT
Q pp /ln                                                           (1) 
Here, Q is average overtopping flux，m3/m/s; Tp is 
period of spectrum peak, s. 
 Owen obtained the formula from the experiments of 
unidirectional wave for sloping breakwater with different 
slope. 
 
  
)exp(
HgT
R
BA
HgT
Q
s
c
s

                                          (2) 
Here, Q is average overtopping flux,m3/m/s; T is 
average wave period,s; g is gravity acceleration，m/s2; 
Hs is significant wave height, m; Rc is the height of 
breakwater top from water level, m; A,B is experience 
factors related with slope. The relation of overtopping 
and wave period shows: 
 
  
)
1
exp(
T
TQ 
                                                           (3) 
 
Experiment Study On Overtopping Of Sloping Breakwater By Swell 
 
416 
 
YU Y X and Wei D  obtained the formula based on 
experiment studies of sloping breakwater by wave flume. 
    
HgT
R
BA
gH
Q
s
c
s
33
3
ln 
                                          (4) 
Here, A3，B3 is experience factors related with slope. 
The relation of overtopping and wave period shows: 
 
   
)
1
exp(
T
Q 
                                                          (5) 
Fig. 1 shows the trend of overtopping compared with 
wave period in three formulas. The difference is obvious. 
 
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25
T(Tp)
Q
/
Q
T
(
T
p
)
=
1
0
s
CS
Owen
YU and WEI
 
Fig.1 Sketch map on relation between wave overtopping 
flux and wave period 
 
 PHYSICAL MODEL 
Experiment condition 
Experiment studies were performed in wave flume, 
as Fig.2. The length of wave flume is 68 m, width is 1.0 
m, and height is 1.5m. Wave generator is active 
absorption irregular type. The effective stroke is 1 200 
mm, it can generate long period wave to 4s in model, 
and with fine wave absorbed function. The wave 
generator consists of machinery, electricity servo control 
system, computer and active absorption module. 
 
 Overtopping measurement 
The overtopping water is collected at the back of 
breakwater top, measures the volume or weight, and then 
calculates wave overtopping flux. The whole wave series 
are collected for irregular waves, divided by total 
duration time, obtained average overtopping flux. 
According to similarity criterion, the model results will 
be calculated to prototype value. The formula is as 
follows: 
 
  bt
V
q 
                                                                         (6) 
Here, 
q
is average overtopping flux in one meter，
m3/（m·s） ; V is total overtopping volume of one 
irregular wave series, m3；b is the width of overtopping 
collection, m; t is the duration time of one irregular wave 
series, s. 
Wave-absorption
Devices
Fan
Semi-circle Structural Closed-cover
Wave-absorption
Devices
Gage 2~6
23456
Gage 1
Wave Generation
Location of
Model
▽+2.0m
▽+1.5m
▽+0.0m
 
Fig. 2 Wave flume
 
Experiment results 
Eight cross sections were tested in physical model 
with the scale of 1:29~1:35. The major parameters were 
showed in following table. Two layer DOLOS blocks 
were armored in these sections and without upper 
structure. 
 
 CALCULATION RESULTS AND COMPARISON 
 
The comparison of overtopping flux between 
calculation and measurement 
 
Here, the overtopping was calculated by formula in 
CS, the differences were analyzed in table 2. From the 
data, obvious differences occurred in the cases of 
Hc/Hs>1.2. Along with the increasing of Hc/Hs, the less 
of overtopping, the less of measured value comparing 
with calculation. When Hc/Hs closing to 1, the calculated 
overtopping is closed to measured value. But the rule is 
different, the wave period longer, the calculation less, the 
measured value more. 
 
 
 
 
C. H. Bao, et al. 
  
417 
 
 
 
                          Tab. 1 Experiment results of wave overtopping flux  
No Section Bottom  
elevation 
(m) 
Slope Top 
 elevation 
(m) 
Water 
 level 
(m) 
Hs 
(m) 
Ts 
(s) 
Overtopping  
flux 
(m3/m.s) 
1 1 -9.0 1.5 8.184 1.13 5.28 20.8 0.009 
2 1 -9.0 1.5 8.184 0.43 5.25 20.8 0.005 
3 1 -9.0 1.5 8.184 -0.33 5.21 20.8 0.002 
4 2 -8.0 1.5 7.713 1.13 5.23 20.8 0.008 
5 2 -8.0 1.5 7.713 0.43 5.20 20.8 0.005 
6 2 -8.0 1.5 7.713 -0.33 5.17 20.8 0.004 
7 3 -4.0 1.5 5.986 1.13 4.01 20.8 0.001 
8 4 -5.0 1.5 6.986 1.13 4.77 20.8 0.012 
9 4 -5.0 1.5 6.986 0.43 4.24 20.8 0.003 
10 5 -2.33 2.0 4.39 1.13 2.48 20.8 0.007 
11 6 -17 1.5 8.563 1.92 5.34 13.8 0.0161 
12 6 -17 1.5 8.563 1.92 5.34 18.0 0.0245 
13 6 -17 1.5 8.563 3.46 5.76 13.8 0.3184 
14 6 -17 1.5 8.563 3.46 5.76 18.0 0.4176 
15 7 -18.5 1.5 8.984 1.92 5.45 13.8 0.0174 
16 7 -18.5 1.5 8.984 1.92 5.45 18.0 0.0304 
17 7 -18.5 1.5 8.984 3.46 5.87 13.8 0.3831 
18 7 -18.5 1.5 8.984 3.46 5.87 18.0 0.4609 
19 8 -3.403 1.5 8.5 3.46 4.84 13.8 0.076 
20 8 -3.403 1.5 8.5 3.46 4.84 18.0 0.089 
 
Tab.2 Overtopping flux comparison between calculation and measurement 
No A KA m 
d 
(m) 
Hc 
(m) 
Calculation 
overtopping
（m3/m.s） 
Measured 
Overtopping 
（m3/m.s） 
1 0.035 0.4 1.5 10.13 7.054 0.0545 0.009 
2 0.035 0.4 1.5 9.43 7.754 0.0483 0.005 
3 0.035 0.4 1.5 8.67 8.514 0.0420 0.002 
4 0.035 0.4 1.5 9.13 6.583 0.0642 0.008 
5 0.035 0.4 1.5 8.43 7.283 0.0550 0.005 
6 0.035 0.4 1.5 7.67 8.043 0.0467 0.004 
7 0.035 0.4 1.5 5.13 4.856 0.0459 0.001 
8 0.035 0.4 1.5 6.13 5.856 0.0615 0.012 
9 0.035 0.4 1.5 5.43 6.556 0.0336 0.003 
10 0.06 0.4 2.0 3.46 3.26 0.0273 0.007 
11 0.035 0.4 1.5 18.92 6.643 0.0738 0.0161 
12 0.035 0.4 1.5 18.92 6.643 0.0632 0.0245 
13 0.035 0.4 1.5 20.46 5.103 0.1513 0.3184 
14 0.035 0.4 1.5 20.46 5.103 0.1298 0.4176 
15 0.035 0.4 1.5 20.42 7.064 0.0802 0.0174 
16 0.035 0.4 1.5 20.42 7.064 0.0687 0.0304 
17 0.035 0.4 1.5 21.96 5.524 0.1572 0.3831 
18 0.035 0.4 1.5 21.96 5.524 0.1349 0.4609 
19 0.035 0.4 1.5 6.863 5.04 0.1059 0.076 
20 0.035 0.4 1.5 6.863 5.04 0.0905 0.089 
 
 
 
Experiment Study On Overtopping Of Sloping Breakwater By Swell 
 
418 
 
Run-up analysis 
Tab.3 Wave run-up calculation 
 
The overtopping is very small in some cases, and 
shows splashing in model testing. The results were 
influenced by surface tension, breaking shape as scale 
effect. Here, according the run-up formula in CS, the 
run-up of all cases was calculated and showed in Table 3. 
 
It is cleared that the splashing cases are less 
overtopping, and the run-up is less than or close to top 
elevation. So the cases of 13,14,17,18 were analyzed in 
this paper. 
As the results of calculation results, the run-up of 
long period is less than longer period wave, and it is 
different in physical model. The results of case 15 and 
case 16 showed that the run-up of long period would not 
decrease obviously. Actually, there are large water body 
overtopping the top of breakwater of long period wave, 
the overtopping flux of one wave is significant increased. 
Especially, the long period wave will be collapsing 
broken on slope or top of breakwater, the serious 
overtopping occurs when the top elevation is not high 
enough. Overtopping the top of breakwater is different 
between laboratory and in-situ tests of the new seat is 
shown as Fig.3 and Fig.4. 
 
 
Fig. 4 Photo of overtopping on site 
 
Correction on overtopping formula for long period 
swell 
The disaster on breakwater is always strong storm, 
the wave were mixed by storm wave and swell. Some 
destroyed examples showed that the long period wave 
have larger breaking force. In order to connecting with 
CS formula, here adopted the parameter of H0/L0. In 
physical model, the run-up is not only wave run-up, but 
also the shoaling of long period wave in shallow water, 
as the extreme phenomena of tsunami. Here, the Ho is 
significant wave height in deep water, Lo is wave length 
of significant wave period in deep water. The factor of 
（L0/12H0）2/3 is multiples with the original formula in 
CS. The wave period has stable relation with wave 
height in storm wave, and the factor of （L0/12H0）2/3 
is close to 1.0. So the corrected formula is: 
 )12/(exp 00
3/2'
HLQQ                                      (7) 
Here, Q’ is corrected overtopping flux, m3/m/s；Q is 
the overtopping flux calculated by formula in CS, 
m3/m/s；L0 is wave length in deep water, m；H0 is wave 
height in deep water, m. 
The overtopping flux was calculated by corrected 
formula, the results were listed in Table 4. The corrected 
calculation values were close to measured data.. 
 
 
Fig. 3 Photo of overtopping in experiment study  
No 
Hs 
(m) 
Ts 
(s) 
d 
(m) 
Hc 
(m) 
R 
(m) 
Measured 
Overtopping 
（m3/m.s） 
1 5.28 20.8 10.13 7.054 3.82 0.009 
2 5.25 20.8 9.43 7.754 3.61 0.005 
3 5.21 20.8 8.67 8.514 3.37 0.002 
4 5.23 20.8 9.13 6.583 3.51 0.008 
5 5.2 20.8 8.43 7.283 3.29 0.005 
6 5.17 20.8 7.67 8.043 3.04 0.004 
7 4.01 20.8 5.13 4.856 1.84 0.001 
8 4.77 20.8 6.13 5.856 2.39 0.012 
9 4.24 20.8 5.43 6.556 2.00 0.003 
10 2.48 20.8 3.46 3.26 0.80 0.007 
11 5.34 13.8 18.92 6.643 7.39 0.0161 
12 5.34 18 18.92 6.643 6.18 0.0245 
13 5.76 13.8 20.46 5.103 8.15 0.3184 
14 5.76 18 20.46 5.103 6.86 0.4176 
15 5.45 13.8 20.42 7.064 7.70 0.0174 
16 5.45 18 20.42 7.064 6.48 0.0304 
17 5.87 13.8 21.96 5.524 8.45 0.3831 
18 5.87 18 21.96 5.524 7.16 0.4609 
19 4.84 13.8 6.863 5.04 3.86 0.076 
20 4.84 18 6.863 5.04 3.04 0.089 
 
C. H. Bao, et al. 
  
419 
 
 
Tab. 4 Calculation results by improved formula 
No. m d(m) Hc(m) Hs(m) Ts(s) 
CS calculated  
overtopping
（m3/m.s） 
Corrected 
calculatedovertopping 
（m3/m.s） 
Measured 
overtopping
（m3/m.s） 
13 1.5 20.46 5.103 5.76 13.8 0.1513 0.3999 0.3184 
14 1.5 20.46 5.103 5.76 18 0.1298 0.4890 0.4176 
17 1.5 21.96 5.524 5.87 13.8 0.1572 0.4104 0.3831 
18 1.5 21.96 5.524 5.87 18 0.1349 0.5020 0.4609 
 
  
CONCLUSIONS 
(1) The average overtopping flux of longer period wave 
is larger in physical model test results, when the other 
conditions are the same. 
(2) Some formulas shows the overtopping flux is less of 
longer wave period, it is different from experiments. 
(3) The corrected formula was obtained by multiplying 
one factor as （L0/12H0）2/3, it represents the 
influence of wave period, the corrected calculation 
results are close to measured values. 
 
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Experiment study on overtopping of sloping breakwater by swell

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Experiment study on overtopping of sloping breakwater by swell

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