Recent experimental work has concentrated on the study of resultant force and pressure distribution on the stepped barrier designated as Case 5 (W. M. Simpson, Serial 1057, 6 Aug 1953 / J. H . Carr). Case 5 barrier has

a plane vertical front face extending the two feet from bottom to still-water surface. Above still-water level are five steps, each of 2.4-in. rise and tread. These dimensions, to a 20:1 scale, represent the prescribed prototype depth of 40 feet and the rise and tread of four feet each.



The separate model barriers for resultant force and for pressure distribution measurements are each cast of aluminum. Vertical ribs at the rear provide rigidity and serve as convenient mounting surfaces

Elliott, J. G.

Meisels, Max

Stelzriede, M. E.

Caltech Authors - Main

/ 
Department of the Navy 
Bureau of Yards and Docks Contract NOy-12.561 
INTERIM REPORT 
November 1953 
Hydrodynamics Laboratory 
Hydraulic Structures Division 
California Institute of Technology 
Pasadena, California 
John H. Cad· 
Project Supervisor 
Report prepared by: 
J. C. Elliott 
Max Meisels 
M. E. Stelzriede 
I. INTRODUCTION 
Recent experimental work has concentr~ted on the study of resultant 
force a.nd pressure distribution on the stepped barrier designated a.~ Case 5 
(W. M. Simpson, Serial 1057, 6 Aug 1953 / J. H . Carr). Case 5 barrier has 
a plane vertical front face extending the two feet from bottom to ~till-water 
surface. Above still-water level are five steps, each of 2 . 4-in. ri~e and 
tread. These dimensions, to 01. 2.0:1 scale, represent the prescribed proto-
type depth of 40 feet and the rise and tread of four feet each. 
The separate model bar:riers for resultant force and for pressure dis· 
tribution measurements are each cast of aluminum. Vertical ribs at the 
rear provide rigidity and ~erve as convenient mounting surfaces. 
II. FORCE MEASUREMENTS 
A. Equipment 
The force balance (Interim Report, Dec. 1952.- March 1953) with the 
associated Case 5 barrier was installed in the two-foot channel in the same 
manner as were the plane barriers. The one -foot wide active section of 
the model which transmit~ wave forces to the balance frames was again 
located between two passive or dummy sections which were grounded to the 
channel. The 1/8-inch spaces between active and dummy sections were 
covered by neoprene tape cemented on either side of the gaps. The tape is 
made loose enough to provide a. tninimum restraining force on the balance, 
yet still prevents "breathing" through the gap. 
To determine the relative magnitude of forces acting on the barrier 
below and above still-water level, two additional tests were performed. 
The b~rrier was cut at the still-water line and the bottom part alone served 
as the active section, the stepped portion being grounded to the dummy sec-
tions . Finally, the forces on the stepped portion alone were measured 
while the lower part was grounded. This experimental determination was 
of interest because there exists no theory applying directly to stepped bar-
rier profiles. 
Figure 1 shows the barrier and balance a.!sembled for measuring 
.forces on the stepped portion only . 
-~-
B. Technique 
In the plane barrier tests, the wave system incident on the barrier was 
produced by a procedure of "tuning" the channel (Report E -11. 1, October 
1953). A stable standing wave was obtained by minute adjustment of the 
wave machine period in the vicinity of the three wave periods selected for 
testing. The incident progressive wave height was then assumed to be one-
half the standing wave height which was measured at an antinode seaward of 
the barrier. 
With the stepped barrier, however, the appreciable turbulence and 
dissipation of energy at the barrier results in a choppy and irregular stand· 
ing wave system, accurate measurements of which are impossible. 
It was necessary, therefore, to d etermine the incident wave height by 
some other method, and the procedure adopted was that of calibrating the 
crank arm of the wave machine in terms of the progressive wave heights 
produced. The balance was removed and an absorbing beach was con-
structed at the far end of the channel. Waves were then generated with a 
range of crank arm ~ettings for each of the three wave periods used, which 
were approximately l. 00, 1. 60, and 2.. 80 seconds, and the wave heights at 
the ultimate location of the barrier were recorded . 
Particular wave heights observed on these calibration runs were then 
correlated with corresponding waves on the later force runs. In the case 
of the 2. 8-second waves, for example, the fourth, fifth and sixth waves 
from start-up were found to be reasonably constant in height, and were 
correlated with the fourth, fifth and sixth fluctuation of the lift, thrust and 
moment records made at the same crank arm setting. The particular waves 
chosen occurred b~fore any re-reflections from the wave machine arrived at 
the barrier. 
C. Experimental Results 
The results of the balance measurernents are shown in Figs. 2 to 4. 
The wave heights along the abscissa are those of the incident progressive 
waves. All values are simultaneous readings at the time of maximum shore-
ward thrust, thu£~ the lift values are downwa rd and the moment given is the 
shoreward overturning mom e nt a'bout the s eaward toe of the barrier. Slight 
phase differences exist between thrust, lift and moment, but since the thrust 
-~-
is the major component, the values of maximum force and maximum shore-
ward overturning moment will not differ greatly from the values presented. 
As mentioned earlier, the above and below still-water portions of the 
barrier were tested both separately and together. The values of thrust 
given are the maximum for each part tested and do not consider any phase 
relationships. There exists, however, a definite phase difference between 
the time of maximum thrust for the top and bottom sections. For the 10. 5 -ft 
wave {1. 60 -second period) the maximum thrust for the above still-water por-
tion occurs approximately 15 ° after the maximum for the whole barrier. The 
maximum thrust on the below still-water portion occurs approximately 19° 
ahead of the maximum for the whole structure. This phase difference be-
tween top and bottom agrees fairly well with the differences found in the 
pressure measurements presented in Part III. The phase difference for the 
21.0-ft wave (2. SO-second period) was not obtained from the balance measure-
ments. 
Considering the phase difference between top and bottom, it is expected 
that the sum of the magnitudes of the force components for the top and bottom 
portions should be something greater than the magnitude for the whole barri;er 
In some cases, however, this result is not obtained. This anomaly can be 
attributed to the inability of the experimental technique to reproduce exactly 
the same wave conditions for the different test runs. This discrepancy, 
however, does not appreciably distort the over-all results. 
D. Discussion 
It is apparent from Fig. 3 that the major portion of the thrust on the 
barrier occurs on the portion below the still-water level. Neglecting any 
phase difference between top and bottom, this amounts to 82 per cent for the 
10. 5 -ft wave and 76 per cent for the 21. 0 -ft wave. This percentage is fairly 
constant throughout the range of the wave heights tested. There is no lift on 
the lower portion of the barrier and therefore the maximum thrust equals 
the maximum force. Since this portion is a vertical plane barrier, it is 
interesting to note that the theory for such a barrier agrees with the experi-
mental results. The dashed theory curves of Figs. 3 and 4 are computed 
using the combined momentum theory developed in Report E-11.1, October 
1953. These curves are computed for only the part below still water and 
use a reflection fa.::tor which was chosen to fit the experimental data. For 
-4-
the 21.0-ft wave the factor is 0. 85; for the 10.5-ft wave the factor is 0. 80. 
These factors, however, appear reasonable since observation of the bar-
rier shows some dissipation of energy in the form of turbulence and spray 
over the stepped portion. 
The lift and thrust components of force for the above still-water por-
tion of the barrier are nearly equal. Thus the resultant force vector acts 
at approximately 45 ° with the horizontal. Due to the relatively small 
magnitude of lift, it has little effect on the resultant force for the whole 
structure. Its effect on the moment, however, is appreciable. As can be 
seen from the curves (again neglecting any phase differences), the moment 
for the bottom portion due to the 10. 5-ft wave is nearly constant at 73 per 
cent of the total over the range of wave heights tested. For the 21.0-ft 
wave the percentage extends from 73 per cent for the smaller wave heights 
to 58 per cent for the larger waves. 
-5-
III. PRESSURE MEASUREMENTS 
A. Equipment 
The equipment used for the measurement of prest.ures resulting at 
the stepped barrier, Case 5, is the same as was described in the Interim 
Report for December 1952. to March 1953, with minor exceptions. In that 
report it was stated that the last six feet of the one -foot wide channel con-
sisted of 1/2-in. tempered plate glast. . One of the pane~ failed in early 
October, and rather than order additional material and construct a new 
wall section, it was considered more practical to shorten the channel 
six feet. In addition, one of the four pressure transducers ceased to 
function properly, so that it was necessary to remove it from the system. 
This necessitated the discontinuation of recordings at tap No. 0 which was 
located 2 . 5 in. from the bottom. 
The barrier had active pressure taps as follows: eight on 2. 5-in. 
centers from 4. 5 to 18.5 in. above the floor; four on 1-1/8-in. centers 
from 19-5/8 to 23 in. ; one each in the centers of the 2. 4 -in. wide treads 
at 24 . 0, 26. 4, 28. 8, and 31. 2 in.; and one each through the centers of 
the 2. 4-in. high risers at 25. 2, 27. 6, 30. 0, 32. 4, and 34.8 in. above the 
floor. The openings, 1/8-in. diameter on the seaward face, are connected 
to one of the three manifolds in groups as 1, 4, 7 ..... ; 2, 5, B ..... ; 3, 6, 
9 .... . , so that one of each group was valved into the corresponding mani-
fold at all times. Each manifold was connected to a pressure transducer. 
The movements of the transducer elements were recorded on the Heiland 
oscillograph. The transducers were calibrated once a week hydrostatically 
and twice daily electrically. 
B. Technique 
The experimental procedure for investigating the pressures against 
the barrier was the same as with the plane barriers described in Report 
E -11. 1 except for the measurement of wave heights. Due to the shortness 
of the one -foot wide channel, it was not possible to install there a sloping 
beach in order to calibrate the wave machine in terms of the height of the 
progressive waves produced as was done in the channel where the total 
force and moment against the bulkhead were measured. This inability to 
-6-
measure directly the height of the progressive wave at the barrier was not 
of great concern in the study of plane barriers, since in that case the heights 
could be obtained from the height of the standing wave. 
For the offset barrier study, the only method available was that of 
measuring the progressive waves at a point seaward of the barrier during 
the short interval before reflections from the barrier reached the mea sur-
ing station, and assuming these heights to be the same as the heights at the 
barrier. A submergence element was therefore installed 30ft from the 
barrier . In a 2-ft water depth a 20-ft long wave has a celerity of 7. 58 ft/ sec 
and a period of 2. 65 sec., and the corresponding values for a 10-ft long wave 
are 6. 60ft/sec and l. 52 sec., so that it was possible to obtain from the os-
cillograph records the values of the progressive wave, uninfluenced by re-
flections, by reading as late as the third and the fifth or sixth waves for the 
20- and 10-ft long waves, respectively. Each wave length was observed in 
triplicate runs, and an excellent agreement for both crest heights and total 
wave heights was obtained. 
C. Results 
The data obtained from the two sets of three runs each, which were 
averaged, are summarized in Figs. 5 and 6 for waves 10ft long, 5 in. high 
and 20 ft long, 5-1/4 in. high, respectively. The data shown represent 
positive pressures against the barrier, i.e., pressures in excess of the 
still-water hydrostatic head. The pressure -elevation curves shown may 
not be integrated for the calculation of total force and moment as was the 
case with plane barriers (Report E -11. 1} since the data points shown are 
individual maxima, not necessarily occurring simultaneously. The upper 
portion of each graph shows the phase relationship of the 18 readings. It is 
seen that fairly large phase differences exist, particularly with the 10-ft 
waves. It should, however, be emphasized that below the still-water surface, 
due to the rather flat peaks of the pressure-time records, the phase differ-
ences are of only slight concern and the data points in this region may well 
be treated as simultaneous values. Above the still-water level, the phase 
differences are more significant, and the values shown correlate with the 
total force phase differences referred to previously . 
Figures 5b and 6b show also theoretical curves based on the time rate 
of change of the horizontal and vertical components of momentum (with 
values of reflection factor as specified previously) as derived in Report 
-7-
E -11. 1. It appears that a very good cor relation exists between the theory 
and the experiments, with the exception of the vicinity of the still water 
surface where the experimental values are 43 per cent higher for the 10-ft 
long wave and 30 per cent in the case of the 20-ft long wave. Even with 
these local differences, the areas under the theoretical and experimental 
curves are seen to be nearly equal, which is the result obtained also from 
the force balance experiments. 
It is interesting to note also that the pressures at the still water level 
and above, as determined from the experimental runs, are approximately 
equal for the two wave lengths, while below the still water surface the longer 
wave length results in much higher pressures. This suggests that the pres-
sures on the stepped portion, where partial wave breaking occurs, is a 
function of wave height only, which supports the postulate that the pressures 
in this region of the barrier correspond to the velocity head (f-v 2 ) of the jet 
of water striking the barrier as the result of wave breaking. gThe jet ve-
locity for this special case of partial wave breaking cannot be calculated 
theoretically at this time, hence it is not possible to further substantiate 
thi;o assumption. Future work will be directed at more complete analysis 
of this question. 
-8-
IV. CONCLUSIONS 
In conclusion, it may be stated that this stepped barrier, Case 5, 
does not differ radically from a vertical plane barrier. Comparison of 
the results from this study with those of plane barriers (Report E-11.1, 
October 1953) shows that the force -height and moment-height curves for 
Case 5 are slightly less in general than those for a plane barrier. This 
is as expected since the reflection factor is less than unity. Use of the 
theory for plane barriers, therefore, should give conservative results. 
The shape and magnitude of the pressure di~tribution curves also con-
firms the above conclusion. 
Barrier designated Case 6, which is ~imilar to Case 5, will not 
be tested under the present schedule of experimental runs. Case 6 
differs from Case 5 in that the steps are smaller and more numerous. 
Instead of five steps, Case 6 has ten steps o£ 1 . 2 -in. rise and tread. 
It is the opinion of this Laboratory that the results from Case 6 will not 
differ appreciably from those o£ the barrier presented he rein. 
upporting Plates for 
Active Upper Section 
Fig . 1 - Force balance with Case 5 barrier 
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Interim Report November 1953

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Interim Report November 1953

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