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Technical Note (National Research Council of Canada. Division of Building Research), 1968-06-01
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Possible Dynamic Causes of Settlement of Perforated Concrete
Breakwaters at Saulnierville, N.S.
Rainer, J. H.
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.,.
No.
DIVISION OF BUILDING RESEARCH
NATIONAL RESEARCH COUNCIL OF CANADA
523
NOTlE
'Jr
E
C
JH[
N II CAlL
L I M I T E D D I S T R I B U T I O N
PREPARED BY J. H. Rainer CHECKED BY T. D. N. APPROVED BY N. B. H. DATE June 1968
PREPARED FOR l-A:r. C. D. ThoITlpson
Testing Laboratories, Soil Mechanics Section Dept. of Public Works
SUBJECT POSSIBLE DYNAMIC CAUSES OF SETTLEMENT OF PERFORATED
CONCRETE BREAKWATERS .AT SAULNIER VILLE, N. S.
A perforated breakwater has been shown to possess desirable hydraulic chara.cteristics in ITlodel tests in the laboratory as well as in a successful full-scale application at Baie Carneau, Quebec. A siITlilar perforated structure built at Sal.llnierville, Nova Scotia, however, exhibited large fOlmdation settlements, of the order of 1 to 3 ft, smne ｮｾｯｮｴｨｳ after con-struction was cOITlpleted. Settlements of approxiITlately 1 it
occurred one day during wbich sea wave action could perbaps be described as·ITloderate. The Division of Building Research was asked by Mr. C. D. ThoITlps on of the Testing Laboratories, Department of Public Works, to investigate the dynaITlic be-haviour of the breakwater structure as a possible cause of
foundation settlement. Otber possible causes of such settleITlent, such as scour and shear failure, are not considered here.
The layout of tbe breakwater consists of a series of 80-ft-long cribs forITling roughly an L- shaped wharf in the water. Tbe individual cribs adjoined each other and were con-nected by open keys and a filler ma.terial. Differential settle-ment, however, has separated the units. A typical cross:-section through a c:rib is shown in Fig. 1.
- 2 .;
Theoretical Considerations
Possible vibrational phenomena may arise from: (a) vibrations of structural components, which for these
cribs are essentially plates restrained by adjacent wall elements;
(b) vibrations of the crib if the structure is considered as an elastic unit;
(c) vibration of the whole crib on the elastic foundation material, commonly termed structure-ground inter-action.
Initially, items (a) and (b) can be dismissed as possible sources of vibration problems since the relevant natural
periods of vibrations are very short compared with the nominal 8-sec wave period. The possibility of a resonance condition as a result of (a) or (b) can thus be excluded. A detailed in-vestigation of item (c) follows.
Analysis
The main assumptions contained in the theoretical analysis are:
(l) The foundation material is elastic and homogeneous. (A substantial change in material property at a depth greater than the width of the crib would have little effect on the results. )
(2) The contact area between structure and foundation is circular. To convert the rectangular base to an equivalent circle, the radius of a circle was determined which gives the same second moment of area about a diameter as a square with sides equal to the crib width. The tributary mass of the crib was then also considered to be that bounded by this square base.
(3) Possible dynamic effects due to the water flowing through the perforations are neglected.
- 3
The required data are:
(a) Foundation material: ...
supplied by Mr. C. D. Thompson = 330 psi = 1000 psi)
ｾ
\I=
0.5 E Shear modulus, G = -2(1+\1) Young- s modulus, E Poisson1s ratio, (b) Crib:Unit weight of concrete = 150 lb/ft3
Unit weight of ballast including entrapped water = 120 1b/ft3•
8 .
=
150 x 10 m. lb = 1 2n 8 G r 3 3(1 - \I) = rocking s tiffne s s = Natural frequency of rocking, f. r
Partial submersion of the crib in water has no effect on the calculation of the natural frequency since the relevant quantities are those of mass inertia of the structure and deformational stiff-ness of the ground. These are not affected by buoyancy.
4 g 4 b4
Equivalent radius, r = ; for b = 30 ft, r = 17. 1 ft. 12n
J
kt
where k
r
I
=
mass polar moment of inertia about a horizontal axis through point A (Fig. 1).Neglecting the perforation openings and other small irregularities, one obtains I Thus, f = 550 x 106 in. lb sec2
=
_1_ (15000 = 0.84 cycles/sec 2n \)550
and the period T = 1
If
=1.
19 sec ｾ 1.2 sec.4
-The sensitivity of the results to changes in material properties may be assessed, for instance, by varying Young's modulus. For E
=
2000 psi, T=
12/fi
=
O. 85 sec; for E=
500 psi, T = 1. 7 sec.-Similarly, for horizontal motion alone, the natural frequency
f
h = 2n1/\
V-!;
r;;:
where ｾ
=
horizontal stiffness=
32 (l - v) Gr o 7 -8v
= 36 x 104 Ib/in.. .
m
=
mass of structure=
0.7 x 104 lb sec2/in. : . fh = 1. 14 cycles/sec.
The rocking and horizontal deformations will produce coupled vibrational modes for which the natural frequencies can be calculated approximately 1 from from which + y f 2 r =
o
f 1 ｾ 1.9 and f2 .z' 0.53 cycles/sec. , or T = 0.53 and T=
1. 9 .sec. , y=
I /1 0 whereI = mass polar moment of inertia about the centre of gravity. The amplitudes of vibration associated with the period T, are considered to be small; thus only the effects giving rise to the period T 2 will be discussed further. At present no theoretical results are available for good estimates of magnification factor s for coupled motion, but a
•
5
-reasonable value one might use is the magnification factor for rocking alone, which can vary from about 7 to 10. This means that the foundation stresses induced by the dynamic forces of the waves having that period would be multiplied by factors of 7 to 10 relative to the effects of the same wave forces applied statically. According to Dr. S. Ince of the Division of Mechanical Engineering at NRC, for wave periods of about 2 sec the static design force of the waves at that frequency range is approximately 13 per cent of the full lateral design wave load, so that the design stresses in the foundation material might be exceeded by approximately 30 per cent under conditions of resonance.
The possible interaction of other factors with the dynamic
effects should not be overlooked. If, for instance, scouring had removed some foundation material, the effective contact area of the crib would be reduced and consequently the natural period of vibration would inc:ease. With higher natural periods the dynamic amplification factors rise signi-ficantly. At the same time, the natural period of the structure approaches the periods of waves with greater energy. The calculations performed are admittedly approximate, but they are not very sensitive to changes in foundation properties nor to small changes in the effective base radius assumed. The results are of course limited by the available theoretical solutions and the field data. More accurate answers could only be ob-tained by vibration measurements on site, but this does not seem war-ranted here.
R ecomm endations
Specific recommendations for remedial work at the Saulnierville breakwater are beyond the scope of this report. Generally speaking, unless specific provisions have been made, the natural period of vi-bration of the structure should be removed from resonance conditions with the incoming waves. Possible methods to achieve this are:
6
-(b) effectively widening the foundation.
Both of these will result in shorter periods of vibration of the given structure.
It must be pointed out that the nominal 8 -s ec wave period is not a sufficiently accurate design criterion against such a resonance condition. The actual wave spectrum should be examined and the sig-riificant bounding periods determined. The period of vibration of the structure should then be kept away from the wave period bounds by at least a factor of 1/2, but preferably less for the lower bound, and by a faetor of 2 or more for the upper bound. For the particular struc-tur
e
under consideration the natural period of the structur e -soil system should not exceed1.
0 sec.It is also urged that the possibility of resonance of the structure-ground system be investigated in any future design of a marine struc-ture.
REFERENCE
Barkan, D. D. Dynamics of Bases and Foundations., McGraw-Hill, N. Y., 1962, p.112.
