(4)
Shi-Leng Xie
China Communications First Design Institute of Navigation Engineering,
Tianjin 300222, China
Fax: +86(22)28341925 E-mail: fdine@public.tpt.tj.cn
Abstract: The design of semi-circular breakwaters and estuary jetties at Tianjin Port and in Deep Water Channel Improvement Project of Yangtze Estuary is introduced in the present paper. A new calculation method for the wave forces acting on a submerged semi-circular structure is given based on physical model tests. The development of the structure of semi-circular breakwater and estuary jetty is also discussed.
Keywords: semi-circular breakwater, estuary jetty, wave forces
The semi-circular breakwater or estuary jetty is mainly a precast reinforced concrete structure composed of a circular arch and a bottom slab. The prefabricated structure is placed on a prepared rubble mound foundation. This new type composite structure was first developed in Japan at the beginning of the nineties. A test semi-circular breakwater with a length of 36m was built at Miyazaki Port of Japan during 1992 to 1993.
The main advantages of the semi-circular breakwater are as follows:
(1) The wave force acting on a semi-circular breakwater is smaller than that on a vertical breakwater. Therefore, the engineering cost can be reduced.
(2) The wave pressure on the semi-circular surface passes through the centre of the circle. The overturning moment is small. Therefore, the vertical load acting on the foundation is almost uniformly distributed, which is advantageous to the soft soil foundation.
(3) The internal stress induced by the load applied is relatively small for an arch structure.
(4) Unlike the construction of conventional reinforced concrete caisson structure, there is no rock filling inside the semi-circular structure. As long as the semi-circular structure is placed on the rubble foundation, it can withstand the attack of large waves. Thus this type of breakwater is specifically suitable to rough sea areas.
(5) There is also no in-situ concrete casting work for the semi-circular structure. The construction process is relatively simple.
(6) It is easy to re-lift the erected semi-circular structure in case of necessity.
(7) The arch configuration of the breakwater has nice scenery effect.
In China, the preliminary design of a semi-circular breakwater for the New North Breakwater Project of Tianjin Port was performed in 1995. Then a semi-circular breakwater was designed for protecting the south harbour area of Tianjin Port. This breakwater, 527m in length, was completed in September, 1997.
The semi-circular estuary jetty structure was first proposed to use for the Deep Channel Improvement Project of Yangtze Estuary in 1996. This estuary jetty is essentially a submerged breakwater. During 1998 to 2000, semi-circular jetty and groin structures with total length of about 18km were built for the first phase works of that deep channel improvement project.
The jetty at Yangtze estuary will be submerged at high water level. For design application, an empirical method for calculating the wave forces on submerged semi-circular breakwater and similar structures was proposed by the present author ( Xie, 1999).
According to the master plan of Tianjin Port, a new north breakwater shall be constructed on the north of the original north breakwater to protect the new harbour basin.
The slope of the sea bottom is very mild, which is about 1/1500 at the construction site. The depth of the sea bed along the axis of the proposed breakwater is about –1.0m calculated from the lowest tide level.
The soil layers underneath the sea bed are as follows: First layer is mud, the elevation of the bottom of layer being –7m to –11m. The water content of this layer is 62% on the average. Second layer is muddy clay with water content of 44.8%, the elevation of the bottom of layer being –12.7m to –14.3m. The soil under the second layer is relatively compact, which is sandy clay or loam.
The design high and low water levels are 4.30m and 0.5m respectively. The maximum high tide level with return period of 50-year has been adopted for checking.
According to the wave statistics, the design wave height for high water level being H=3.2m with mean wave period of T=8.1s. The wave height for maximum high water level being H=4.1m. All the wave heights mentioned are breaking wave heights due to the effect of shallow water. Several structure types of breakwater have been compared. The engineering cost of rubble mound breakwater is relatively high due to lack of rock material in the locality. The conventional type of composite breakwater is also not economic because the foundation soil should be treated and compacted. The option of semi-circular breakwater was recommended in the preliminary design of New North Breakwater Project in 1995. The structure weight of the semi-circular element is relatively light, the stability of the foundation can be satisfied by simple foundation treatment using sand underlayer and geotextile sheet.
The cross section of the semi-circular breakwater for the New North Breakwater Project is shown in Fig.1. The crest elevation of the breakwater is 5.2m and the radius of the semi-circular element is 4.5m. The thicknesses of reinforced concrete arch and bottom slab are 55cm and 80cm respectively. There are circular holes on the front part of the arch as well as on the bottom slab. The latter is mainly for relieving the wave uplift. The design length of the semi-circular element is 4.8m with weight of 176.6t.
The wave forces acting on semi-circular breakwater were calculated using modified Goda formula (Tanimoto and Takahashi, 1994). Then, the design section of the breakwater was tested in two harbour and coastal engineering laboratories. The New North Breakwater Project has not been executed yet due to the adjustment of the construction plan.
However, a 527m long semi-circular breakwater was constructed for protecting the new reclamation area in the south part of the Port in 1997. The elevation of the sea bed along the axis of this breakwater is about –1.8m. The foundation condition underneath the breakwater is better than that of the new north breakwater. Other design conditions are almost the same with those of the new north breakwater. Therefore, the cross section of this breakwater is similar to that shown in Fig.1. The crest elevation of this breakwater is 5.5m and the radius of the semi-circular element is 4.5m. The thickness of bottom slab is 75cm. The length of the semi-circular element is 2.5m in order to use floating crane with smaller lifting capacity.
According to the comparison, the engineering cost of the semi-circular breakwater is 21.4% lower than that of the conventional rubble mound structure.
There are two long estuary jetties with some inside groins to direct and confine the flow for the Deep Water Channel Improvement Project of Yangtze Estuary. The lengths of the south and north jetties of the first phase works of the Project are 20 and 16.5 km respectively. The semi-circular structure option is adopted for the south jetty and one inside groin with total length of about 18km.
The crest elevation of the jetties is determined as 2.0m calculated from local datum. Different cross sections of the south jetty are designed according to the different depths of the bed. A section of the jetty suitable for water depths of –3.0m to –3.5m is given in the following (Fig.2). The wave height being H1%=3.9m with mean wave period of T=7.5s for the design high water level condition. H1% refers the wave height with the probability of exceedance of 1% in a random wave train. For checking condition, i.e. the high water level with return period of 50-year, H1% = 5.3m and T = 7.6s.
According to the geotechnical exploration, the soil layers underneath the south jetty are as follows: First layer is silt, the thickness of which is 3m~5m with N=2~4 for standard penetration test. Second layer is soft saturated silty clay, the thickness of which is 3m~5m. There are muddy clay and clay with total thickness of 15m~19m under the second layer.
As shown in the Figure, the radius of the semi-circular jetty structure is 4.0m, the height of the precast element is 4.5m, and the thicknesses of reinforced concrete arch and bottom slab are 75cm and 125cm respectively. The longitudinal length of the semi-circular element is 4.0m. The perforation ratios of the front part of arch and bottom slab are 4.7% and 11.3% respectively. The structure weight of the precast element is 180t. Mattresses composed of geotextile and sand as well as geotextile and small concrete blocks are placed on bed to prevent scouring. It has been found in physical model tests that the modified Goda’s wave force formula (Tanimoto and Takahashi, 1994) is not appropriate to the submerged semi-circular structure. Therefore, a new calculation method for the wave forces acting on submerged semi-circular breakwater and similar structures was proposed (Xie, 1999), which is based on Goda formula and new experimental data. This calculation method will be given in Section 4. The safety factors against sliding of the south jetty obtained from the above mentioned empirical method, mathematical analysis based on fifth order Stokes wave (Jia, 1999) as well as physical model tests are listed in Table 1.
Table 1 Comparison of safety factors Ks for sliding
|
Water Level |
Ks |
||
|
Empirical method |
Mathematical analysis |
Model test |
|
|
Design high water 4.02m |
1.75 |
1.43 |
1.80 |
|
Checking high water 5.32m |
1.34 |
1.24 |
1.29 |
The results calculated from empirical method are close to those measured from model tests on the whole.
An empirical wave force formula for semi-circular breakwater based on the modification of Goda formula for vertical breakwater is generally used in Japan ( Tanimoto and Takahashi, 1994). The calculation procedures are as follows:
The wave pressures on a vertical breakwater with the same water depth h, water depth above the rubble foundation h’ and crest elevation of breakwater above the still water level hc as those for a semi-circular breakwater are calculated. The well-known Goda formula will not be cited here. It should be pointed out that a factor l2 related to impulse pressure in Goda formula is taken as zero in the present case.
The horizontal wave force on a vertical breakwater under the action of wave crest is determined mainly by three parameters h, p1, and p3. h is the elevation of zero pressure point above the still water level in wave pressure diagram. p1 and p3 are wave pressures at still water level and at wall bottom level respectively.
The action of wave crest on various positions of a semi-circular surface has phase difference. Therefore, a phase modification coefficient should be introduced into the related formula. For a semi-circular breakwater:
h'=h (1)
p1'= p1 (2)
p3'=lpp3 (3)
in which the phase modification coefficient is expressed as
(4)
where Dl is the horizontal distance between the application points of p1' and p3' on the semi-circular surface, and the application points of p1' is the intersection point of the curve surface and the still water level. L is the wave length.
The modified wave pressure is indicated as p’(z), z being the vertical height above the bottom level of semi-circular element.
The direction of wave pressure acting on a semi-circular structure is perpendicular to the curve surface. Therefore, angle modification of wave pressure should be taken into consideration. The wave pressure on curve surface is
p( q ) = p' (z) cosq (5)
in which q is the central angle of the application point of wave pressure.
In general, there are vertical holes on the bottom slab for relieving the wave uplift. Experimental data show that the wave uplift acting on the bottom can be neglected when the opening ratio of the bottom slab is larger than 10%. Then the wave uplift pressure at the toe of wall will be
pu=p3', for eb =0 (6)
pu = 0, for eb≥0.1 (7)
in which eb is the opening ratio of bottom slab.
The aforementioned formulas are suitable for the case of crest elevation hc exceeding about 1.0Hs, Hs being the significant wave height.
The fourth step will be used only for submerged semi-circular structure. According to the physical model tests for the different cross sections of semi-circular jetty of Yangtze estuary using both regular and irregular waves, it was indicated that the submerged structures would be unsafe when the aforementioned empirical wave force formula for semi-circular breakwater was adopted in design. Therefore, a new calculation method for the wave forces on a submerged semi-circular structure was proposed ( Xie ,1999), which will be given as follows:
(1) First, the current wave force formula is still used. However, the wave pressure on the inside circumference of the arch, i.e. p0 = pu/2 should be applied when the wave uplift on bottom is neglected.
(2) Second, a new phase modification
coefficient lp1
derived from the experimental data should be used in Eq.
(3) instead of lp
of Eq.
(4). lp1
is expressed as
(8)
This new calculation method has been verified by seven cases of submerged semi-circular structures tested in different harbour and coastal engineering laboratories.
The front and rear sides of the semi-circular arch can be perforated either on one side or on both sides in accordance with specific requirements.
The test breakwater at Miyazaki Port is perforated on both sides of the arch, and the opening ratios are 25% and 1% for the rear and front sides respectively. Wave ovetopping is significantly dissipated by the large opening on rear part of the arch.
For the front perforated type structure, it was expected at first that a wave chamber would be formed to dissipate the energy. However, experiment showed that wave force on structure with front opening ratio of about 5% was almost the same with that on structure without front opening. For submerged case, larger wave force would act on rear part inside the arch when the front opening ratio was increased. And this situation had an adverse effect on the stability of the structure.
Test results show that the stability of the submerged semi-circular structures with and without the opening on bottom slabs are almost the same. This is because the wave pressures on the inside circumference of the arch become rather small when there is no opening on bottom slab. The arch and bottom slab of the semi-circular structure with radius of 9.8m at Miyazaki Port are prefabricated separately. Then, the separative elements are assembled as an integrated structure. The semi-circular structures used in Tianjin Port and at Yangtze estuary with radii of 4.5m and 4.0m are precasted as whole elements.
The application and development of semi-circular breakwater and similar structures in China are briefly introduced in the present paper. The current wave force formula for semi-circular structures has been modified further to accommodate the submerged case.
The superiority of the semi-circular structures, especially for rough sea area and soft soil condition, has been proved further by the execution of two projects mentioned above. It is expected that the semi-circular structures will be utilized for the Second Phase of Yangtze Estuary Project in an even larger scope.
References
Jia, Donghua (1999), Study on the Interaction of Water Waves with Semi-Circular Breakwater, China Ocean Engineering, Vol.13, No.1, pp.73-80.
Tanimoto, K. and S.Takahashi (1994), Japanese Experiences on Composite Breakwaters, Proc. International Workshop on Wave Barriers in Deepwaters, Yokosuka, Japan, pp.1-22.
Xie, Shileng(1999), Wave forces on Submerged Semi-Circular Breakwater and Similar Structures, China Ocean Engineering, Vol.13, No.1, pp.63-72.
Fig. 1 Cross section of semi-circular breakwater at Tianjin Port
Fig. 2 Cross section of semi-circular jetty at Yangtze Estuary