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Beaches downcoast of harbours in bays
Coastal Engineering, 19 (1993) 163-181
163
Elsevier Science Publishers B.V., Amsterdam
Beaches downcoast of harbours in bays J o h n R.C. H s u a, T a k a a k i U d a b a n d R i c h a r d Silvestera aDepartment of Civil and Environmental Engineering, Universityof Western Australia, Nedlands, Perth, W.A. 6009, Australia bCoastal Engineering Division, Public Works Research Institute, Ministry of Construction, Tsukuba 305, Japan (Received 4 March 1992; accepted after revision 30 June 1992 )
ABSTRACT Hsu, J.R.C., Uda, T. and Silvester, R., 1993. Beaches downcoast of harbours in bays. Coastal Eng., 19: 163-181. In spite of beach berms being removed during each storm sequence the waterline may be retained constant either by a constant supply of littoral drift or static equilibrium bays being formed between headlands. The construction of salients behind offshore breakwaters may be at the expense of the adjoining coast, which resembles the ubiquitous bay shapes formed between headlands that can be either in dynamic or static equilibrium. This is the same silting situation in the lee of breakwaters extending from the coast where beach erosion results downcoast. Ports constructed upcoast of a bay in dynamic equilibrium can have their breakwaters so located that the bay can become statically stable. In the case of the bay being already in static equilibrium breakwater extension often causes massive accretion in its lee and concomitant erosion further downcoast, thus demanding prodigious expense for beach protection installations. Appropriate procedures are now suggested to minimise this undesirable effect of beach erosion associated with the construction and extension of breakwaters to ports upcoast of a bay.
INTRODUCTION
Before equilibrium plan forms of the coastline can be understood there is need for discussion o f beach processes associated with fine to coarse sands in which lateral as well as longshore transport o f these materials takes place. This involves the alternate action of storm waves and swell on the beach profile. The former move berm material offshore forming a bar, while the latter return it to the shore. During this process longshore movement may occur. This introduces the phenomenon o f pulsative rather than a uniform littoral drift along the coast. Once the bar, which has limited the original erosion, is replaced on the berm within a few days by the following swell after any storm Correspondence to: J.R.C. Hsu, Department of Civil and Environmental Engineering, University of Western Australia, Nedlands, Perth, W.A. 6009, Australia.
0378-3839/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
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J.R.C. HSU
event, this drift may become minimal as only the beach face and narrow surf zone can contribute to the transport. Where natural headlands occur on a mobile shoreline with predominant waves arriving persistently and oblique to the general coastline, a bay which has a specific shape is sculptured between them. Sediment may bypass the downcoast structure where the beach line is almost parallel to the crests of the incoming swell. Behind the upcoast headland a curved segment of the bay exists whose curvature has been likened to a logarithmic spiral. The indentation of the bay is dictated by the amount of sediment passing through it from upcoast or from a river debouching into it. In this condition the bay is said to be in dynamic equilibrium and its waterline can vary with fluctuations in littoral drift. Where this ceases altogether, due to natural or man-made causes, the indentation increases to some limit when static equilibrium is reached. This infers that littoral drift within the bay has become zero due to the incessant swell waves arriving normal to the beach around its periphery. It is for this final condition that equations can be derived defining the shape of the bay. When harbours are established on a coast, by the construction of breakwaters to provide shelter for ships, it is like inserting a new headland that results in shorelines that differ on the upcoast and downcoast sides of it. On the upstream side accretion takes place as sediment attempts to bypass this impediment, whilst at the downcoast side erosion will occur as a bay tends to form in its lee. The larger or longer the breakwater the greater these effects will be. The resulting erosion is generally fought by the installation of seawalls, groynes, or offshore breakwaters, sometimes all three, but these have not always been successful against the persistent swell, not to mention the infrequent storm occurrences. Many natural headlands, acting as breakwaters, have provided reasonable shelter for ships but as industry develops there is demand for more calm areas which involves breakwaters being run from them at various angles many years after the original construction. This intercepts littoral drift, if only temporally, which causes erosion of beaches within the bay and beyond. It can also cause accretion leewards of the headland and its subsequent extension by the breakwater, so reducing the area of desired calm water due to siltation. Komar (1983) has observed: "Many occurrences of destructive coastal erosion have resulted directly from the construction of jetties, breakwaters, and other engineering structures." Moutzouris (1990) has commented: "Coastal erosion a n d / o r accretion are sometimes a result of the construction of harbour or coastal works in an area. Most of the time these side-effects are undesired and engineers have to cope with them." It will be shown in the present context that by selective positioning and length of such structures no deleterious effects may be suffered in this downcoast region. The static equilibrium bay shape, implying zero littoral drift due to its interception by the new break-
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BEACHES DOWNCOAST OF HARBOURS IN BAYS
water, could well match the original shoreline which was in dynamic equilibrium with the passage of sediment through it. For the case of a bay already in static equilibrium the installation or extension of a new breakwater can only result in serious erosion downcoast and undesired accretion in different segments of it. The knowledge herein envisaged would benefit the planning of harbour construction on a bay and its subsequent extension, in minimising any potential beach erosion downcoast. BAY F O R M A T I O N
Bays along a coast are ubiquitous and are in all sizes and indentations, be they on oceanic margins, enclosed seas, lakes or river margins. As seen in Fig. 1, they are crenulate shaped with a curved segment in the lee of the upcoast headland (breakwater) and straighter in orientation towards the downcoast limit. Whilst sediment is still passing through the bay or fed to it internally, the bay can be said to be in dynamic equilibrium, since it could become more indented should the littoral drift be reduced in the longer term by natural reduction of supply or by man-induced impediments. In the event of complete cut-off the bay will recede to a limiting indentation, as indicated in the figure, by the waterline termed static equilibrium (Hsu et al., 1989a). It is only for this stage that a precise relationship can be found between the parabolic shape and the wave obliquity fl to the control line from the upcoast headland to the downcoast limit of the bay. At the former it is the point at which diffraction takes place, while at the latter it is generally the limit of the straightening beach. Waves within the bay not only diffract but also refract to arrive normal to the shoreline around the shore periphery of this static equilibrium bay shape. It is seen that fl alters very little for this and the dynamic equilibrium shape as the varying indentation is normally very slight. bay in
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In checking a bay from an aerial photograph or hydrographic chart for stability the control line is first determined from which fl can be measured (Hsu et al., 1989a, b). As seen in Fig. 2, the length of the control line is given as Ro at angle fl to the wave crest line. Other radii R from the diffraction point to the beach line at angles 0 to the wave crest line are then related to fl by the equation:
R/Ro = Co + Ct ( b~ O) + 6/2 ( b/O) 2
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where coefficients Co, CI and C2 are given in Fig. 3 (Hsu and Evans, 1989). For an existing bay in static equilibrium, the curved waterline will remain sensitively unchanged despite the variation of the chosen fl from its true value, so long as the downcoast extremity is located at a point along the straight segment. In fact, it has been found that fl and Ro compensate with each other. This renders Eq. 1 a simpler procedure for field applications and yet also retains its desirable accuracy. If the existing shoreline is seawards of the predicted bay shape it is in dynamic equilibrium and may be unstable, since it could recede back to the static equilibrium condition but no further, should sediment supply cease. The possible recession is not uniform around the bay, as is generally assumed in setting limits to encrouchment on coastal margins. More permanent infrastructure should be restricted to landwards of the static equilibrium waterline as predicted, plus an allowance for the loss of the berm during normal storm sequences and a margin of safety for the severe cyclones arriving less infrequently.
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SALIENT BEHIND PROTRUDING BREAKWATERS
Another application to the formation of equilibrium bay shapes is that of studying salients and tombolos in the lee of offshore breakwaters (Hsu and Silvester, 1990). As seen in the definition sketch of Fig. 4, the same nomenclature can be used for which Eq. 1 is applicable. The simple case is of normally approaching waves to an original shoreline distance S from the breakwater which is parallel to it. When waves diffract into the shadow zone of the breakwater they break at an angle to the original shoreline and hence transport sand towards the centre line of the structure, aided by nearshore current circulation. Initially double salients may form, but with adequate wave duration and sediment supply these will coalesce into a single salient.
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Except for apex positions and the accreted sand volume associated with the salients behind a single offshore breakwater, no previous authors have given scientific attention to the shapes of beaches so accreted until Hsu and Silvester (1990). When the bays either side of the predicted salient apex is considered to be in static equilibrium, the material required for the formation of this salient must come from the adjoining beaches generally beyond the limits of the breakwater extremities. The tangent to these eroded beaches parallel to the original shoreline is landward of it (S~ in Fig. 4). Dimensionless parameters from the many variables involved have been derived in order to predict salient characteristics (Hsu and Silvester, 1990 ), including the conditions for tombolo formation, but the present issue is to look at half the picture as depicted in Fig. 4, from the breakwater centre line outwards. If a natural headland should exist up to the breakwater center line and it is extended to the limit of the other extremity, then ultimate accretion will take place in its lee similar to the salient as depicted, which can be predicted by employing the concept of the static bay shape given by Eq. 1 previously. This infers that the calm water area planned as a port in the lee of the new breakwater will be partially filled in with a curved shoreline. If shore-protection structures, such as seawalls, groynes and offshore breakwaters, are installed consequently, the curved salient planform is most unlikely to be reached as readily as predicted. It also indicates that the adjacent berm or sandy cliff downcoast will be denuded as material is shifted towards this developing salient. Should a river debouch in the lee of the aforesaid natural headland serving as an original port location then exit channels from it will be silted and so require dredging until the stable salient has formed. When this stage is reached no further littoral drift will occur so that any access channel so dredged will not continue to silt up, except for local refraction at the entrance which will be minimal. H A R B O U R ON S T R A I G H T S H O R E L I N E
Many harbours are constructed on straight segments of sandy coast or even within large bays in dynamic equilibrium, which have similar bypassing requirements. Any breakwater of substantial proportions extending out to sea will disturb the continuity of the littoral drift and act like a headland in the manner previously discussed. This involves accretion on the upcoast side of the structure and concomitant erosion on the downcoast side as a bay attempts to form. Komar (1983) recognized this tendency for cases of littoral drift, but states: "In other cases, however, it is not initially apparent why the engineering structure produced significant erosion. For example, jetties have induced erosion on coasts where no net littoral drift exists." The case of salients discussed above may give an answer to this anomaly. A typical case is exhibited in Fig. 5, where the main breakwater is angled to
BEACHES DOWNCOAST OF HARBOURS IN BAYS
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Fig. 5. Typical port development on a straight sandy shoreline. and then parallels the shoreline. The secondary breakwater at A provides shelter from waves diffracting around the tip of the first and storm waves that arrive from many directions. The sediment accreting against the main breakwater could eventually silt up the harbour entrance and then bypass it as shown, welding to the coast at point C one or many kilometres downcoast from B, where some accretion may be experienced from A to B, as a salient tends to form in the lee of the main breakwater. It is between these points that erosion will occur, which generally promotes the construction of seawalls, groynes or offshore breakwaters. However, it is recommended that headland control (Hsu and Silvester, 1989 ) be utilised to form stable bays which retain sand in position. In fact, it is suggested that these structures be inserted prior to the construction of the main breakwater, because erosion is very swift. Initially the resulting bays will be in dynamic equilibrium and not so indented but later will become fully stable, with their waterlines oriented to the new direction of the approaching waves within the embayment downcoast. H A R B O U R IN D Y N A M I C E Q U I L I B R I U M BAY
A modest port may be constructed in the form of breakwaters AB and CD as in Fig. 6, with the former connected to a natural headland at A. The control line A E to the downcoast limit of the bay at headland E (or a point along the relatively long and straight section downcoast) has a length Ro and angle to the beach tangent or wave crest line fl= 32 °. The static equilibrium shape of bay A E can thus be drawn utilising Eq. 1. From the existing shoreline as drawn it can be seen that should littoral drift around the headland at A cease the bay should suffer severe erosion. Previously sufficient sediment was bypassing point A to maintain this shoreline. Once breakwater AB is inserted a new diffraction point B reduces the previous Ro to give a new stable shape marked as "bay for BE". This again is for
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Fig. 6. Effects of positioning breakwaters upcoast of a bay in dynamic equilibrium.
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/ Fig. 7. Map of Japan showing harbour locations discussed in the text. no littoral drift. Should an additional breakwater FG be constructed fl= 38 ° and a new Ro results, which provides the bay denoted "bay for GE" in Fig. 6. This seems to match the existing shoreline quite well, although with slight accretion adjacent to CD and slight erosion further downcoast. In time sediment would bypass point G, traverse the bay and weld to the coast in the eroded region. The bay, in fact, may accrete seawards o f the static equilib-
BEACHES DOWNCOAST OF HARBOURS IN BAYS
171
Fig. 8. Aerial photograph showingshoreline downcoastof Oarai harbour, Japan, in 1961 (see Fig. 10 for the N-direction). rium waterline predicted should upcoast sediment supply continue. It is seen that the alternative diffraction point G rather than B has almost solved the erosion problem of this bay in dynamic equilibrium, with some downcoast segment of the bay suffering transient erosion, when only the action of the persistent waves is considered.
172
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Fig. 9. Aerial photograph showing shoreline of the bay at Oarai harbour in 1976 (see Fig. 10 for thc N-direction ).
The structure between A and F could be set back in order to accrete a beach in front of it, which means it does not have to be so massive and its armour units smaller in size. Should it be desired to make the coast from A to E completely stable, due to imminent interception of all littoral drift upcoast of headland A, then point H may be chosen as the new diffraction point. As seen fl= 40 ° and the control line HE, which results in the stable bay shown with large dots which follows the original shoreline periphery perfectly. This will occur even with no input of sediment, should it eventuate in the future. The port of Oarai on the Japanese Kashima coast facing the Pacific Ocean, (see Fig. 7), is an example of the above concept. As seen in the aerial photography of Fig. 8, two angled breakwaters formed a small harbour during 1911 and 1916, which was quickly silted. No further construction was carried out until 1961. Application of Eq. 1 to the curved section of this coast in 1961 showed that the predicted bay shape was landwards of the existing shoreline. This was due to continued littoral drift to the coast at that time, implying that it was in dynamic equilibrium, or could be eroded if a dearth of sediment
173
BEACHES DOWNCOAST OF HARBOURS IN BAYS
Oarai "~, harbour
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Fig. 10. Breakwaterconstruction and resulting bay shape at Oarai harbour in 1976.
Fig. 11. Aerial photograph showingshoreline of the bay at Oarai harbour in 1988 (see Fig. 12 for the N-direction). supply were available. By 1976, the tip of the main breakwater for the new harbour was about 650 m out into the sea from its original shoreline at point G marked with a + on Fig. 8, as shown in Figs. 9 and 10. This established a new diffraction point A with Ro = 1.92 km and fl= 45 °. It is seen that the pre-
174
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D
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Fig. 12. Actual and predicted salient formation downcoast of Oarai harbour in 1988.
dicted static bay shape matched the existing shoreline extremely well, indicating that the beach downcoast would remain stable if no further breakwater extension were made, considering only persistent swell. An extension of this breakwater to B was completed in early 1981 as shown in Figs. 11 and 12 where Ro= 3.48 km and fl= 35 °, giving the static equilibrium shape denoted bay shape for BE. The 1976 shoreline is also shown for comparison. Severe beach erosion had occurred to some 3 km south of the harbour, which has initiated the installation of seawalls and concrete block revetments (Mizumura, 1982; Kraus et al., 1984; Uda et al., 1986). From 1981 to 1985 the detached breakwater CD (totalling 800 m, shown in Fig. 12 ) was constructed for which the bay shapefor CE applies. This is far seaward of the 1988 shoreline in spite the two large groynes (900 and 300 m in length respectively, with the former serving as the second breakwater) inserted to prevent sand incursion into the harbour from the accreting land from 1981 to 1984 and 1985 to 1988, respectively. As noted in the previous section on salients it is such an accumulation that is taking place out to the predicted shape for no further littoral drift. Should this drift continue in the future the waterline could be slightly seawards of this mark, although the bulk of it will weld to the coast in proximity to point E. At the moment, however, erosion is taking place some 2 to 7 km south of the harbour, causing beach profile steepening in front of the seawalls and their subsequent failures (Ibaraki Prefecture, 1991 ). It is thus clear that the effects of changing the upcoast control points due to breakwater extension, from point G in 1961, to point A in 1976,
17 5
BEACHES DOWNCOAST OF HARBOURS IN BAYS
then to point B in 1981 and later to point D by 1985, have shifted the originally dynamic equilibrium bay to a stable bay in static equilibrium (in 1976 ), and then into a series of dynamically unstable conditions, accompanied by undesirable erosion further downcoast.
HARBOUR IN STATIC EQUILIBRIUM BAY
In this case it is difficult to locate a new diffraction point that will prevent erosion on some part of the periphery of a stable bay. Iwafune harbour, located as shown in Fig. 7, on the Sea of Japan, was originally in a river mouth some 50 m wide, as seen in Fig. 13. It received sand from this outlet as well as from a river 6 km to the north. A groyne and detached breakwater were installed in 1929 to stop siltation, but later was connected to the mainland in 1934. Inner revetments and wharf were added in 1957 (Haruta, 1961 ), which became the original outer breakwater for this river mouth harbour. An aerial photograph of 1965 exhibited wide beaches upcoast of the main breakwaters as most sediment had come from the north. To correlate the existing waterline with static bay shape, a downcoast position (F) along the straight segment is selected as the limit of the bay, as noted in Fig. 14. This provides a control line AF, with Ro= 1.35 km and fl= 30 °. The location o f F is not crucial as the predicted bay shape differs very little for changes in fl of
SEA OF JAPAN ,-detached O,,,j breakwoter
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Fig. 14. Shoreline downcoast of lwafune harbour showing a stable bay shape in 1965.
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S Fig. 15. Salient advancement in the lee of breakwater extensions at Iwafune harbour from 1976 to 1984, showing also the survey lines So and N2 to be discussed in Fig. 16 (Uda and Noguchi, 1991 ).
_+5 ° and concurrent changes in Ro, as explained previously after applying Eq. 1. The predicted static equilibrium shape fits the 1965 shoreline and hence no erosion downcoast could be expected. However, mammoth extensions to the outer breakwater then took place in stages between 1965 and 1984, as depicted in Fig. 15, resulting in the salient shoreline along the survey line So in the vicinity of the inner breakwater being
177
BEACHES D O W N C O A S T O F H A R B O U R S IN BAYS
advanced some 280 m over this period (Uda and Noguchi, 1991 ). As seen in Fig. 16, the development of these salients adjacent to the inner breakwater (survey line So in Fig. 15 ) is directly proportional to the length of the breakwater extension, while the shoreline position just north of it (survey line N2 in Fig. 15 ) remains essentially steady. Hence, the sand volumes required for the construction of these salients must have been supplied mainly by the erosion of the beach berm and cliff downcoast, accompanied by profile steepening. Material supplied from the river, either at upcoast or from within the embayment, is minimal.
. o 700 C
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Fig. 17. Predicted and actual shorelines in 1988, after breakwater extension at Iwafune harbour.
178
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Fig. 18. Groynesystemand offshorebreakwatersdowncoastof Iwafuneharbour in i 988. The correlation between the salients thus formed with the breakwater extension from points A to B and then to C is seen in Fig. 17. With an appropriate value offl= 40 ° and selected Ro = 1.63 and 1.75 km respectively, the stable salient shapes for BD and CE are noted in the figure, where D and E are again arbitrary points on the straight segment downcoast. Both of these are well seaward of the 1988 shoreline, inferring that much more material will be removed from the southern beaches to meet this demand of salient built-up. Although the present beach line has been used as the downcoast limit of the bay it could well be landward of this, as noted in the previous section on salients behind an offshore breakwater. The expected erosion has been dealt with without much success by installation ofgroynes, as seen in the figure. Beyond the limit of E other more formidable structures, such as a field of short groynes and offshore breakwaters, have been employed in an attempt to stop the erosion (see Fig. 18 ). These will be left stranded in the sea as Nature carries out its reshaping of the coastline to some static equilibrium condition. PREDICTION OF SHORELINECHANGES The application of the parabolic shapes to the salients formed behind single breakwaters, as exemplified by using two Japanese harbours, suggests that this geomorphological concept is useful in harbour planning. Although the knowledge offers the reasons for erosion downcoast and its concomitant salient development leewards of a breakwater and its extensions, it also provides information on possible siltation and the need for dredging. The sediment transport may still be taking place so that the ultimate equilibrium shoreline may not have been reached, hence with further consequent erosion downcoast.
BEACHES DOWNCOAST OF HARBOURS IN BAYS
179
In the case of Oarai harbour, seawalls and revetments have been installed from some 2 kms southward of the second breakwater. They have been subject to frequent collapse, becoming almost an annual event. No field data were available so that the downcoast points were chosen from this artificially "stabilized" tangent. At Iwafune harbour sandy cliffs exist downcoast, with beach retreat monitored. However, data were limited, so requiring an empirical model to be utilised. Although the beach plan behind a single offshore breakwater with normal waves can be predicted (Hsu and Silvester, 1990), its extension to oblique waves and breakwater extension from a natural headland requires further attention. The obliquity of persistent waves should not prove difficult once the wave crest alignment is established, since the arcs from the diffraction point can be drawn to the stable shoreline. The exclusion of waves from one side of the equivalent offshore breakwater should not greatly influence the single bay facing the opening from the exposed end of the breakwater. The waves from the alternate side of the single breakwater have little influence on the apex of the salient so forming, except that in this case it will continue to form what is virtually a tombolo in the lee of the breakwater extension. However, in using the formulae the equivalent length of the "offshore breakwater" (B) cannot be determined, or its centreline fixed. Further research is required in models, either physical or numerical, to solve this problem. Because of the engineering significance of beach evolution downcoast of extending harbours, the coastal engineering profession needs to apply itself to the erosion and silting problems related thereto. In time, new relationships should be available for the landbacked extension of breakwaters. CONCLUSIONS
( 1 ) The removal of the berm by storm waves for the construction of the protective offshore bar cannot be prevented by man but it is during its refurbishment back to the beach by subsequent swell waves within days that the greatest littoral drift occurs. (2) When waves are persistently inclined to a coast with headlands, bays are sculptured to crenulate shape that can be either in dynamic or static equilibrium. A parabolic shape can be determined for the latter. (3) Salients formed in the lee of an offshore breakwater have bay shapes either side of their apexes which may ultimately become in static equilibrium and are hence predictable. (4) The salients as in (3) above can be equated to the sedimentation that occurs in the shadow of a breakwater extended from the mainland to provide calm water for a port. (5) Littoral drift impediments such as breakwaters running seawards from a sandy coast will cause accretion and erosion on opposite sides of them.
180
J.R.C. HSU
Headland control is suggested as a remedial measure for the latter, with its implementation prior to, or not later than, the construction of the main breakwater. (6) In the development of a port upcoast of a bay in dynamic equilibrium the breakwater locations can be so chosen to make the existing shoreline stable. (7) Such a port in (6) above, but within a bay already in static equilibrium, will produce a salient in its lee at the expense of the beaches being eroded further downcoast. This may result in the need for annual dredging of the navigation channel or river mouth within the embayment, as depicted in Figs. 1 and 17. (8) It is strongly recommended that the concept of static bay shape and salient formation, which are ubiquitous features in coastal geomorphology, be employed in harbour planning, in order to minimise the erosive effect on beaches. ACKNOWLEDGMENT
This study is the result of a theme project under Japan/Australia Science and Technology Agreements 1989-90 and 1991-92, of which the authors are the Australian and Japanese Contacts respectively. The authors are grateful to the Reviewers' comments on the original draft, as well as to the Geographical Research Institute, Ministry of Construction, Japan, for the aerial photographs used in this paper.
REFERENCES Haruta, T., 1961. Recent coastal processes in Niigata Prefecture. Coastal Eng. Jpn., 4: 73-83. Hsu, J.R.C. and Evans, C., 1989. Parabolic bay shapes and applications. Proc. Inst. Civil Eng., 87: 557-570. Hsu, J.R.C. and Silvester, R., 1989. Comparison of various defense measures. Proc. 9th Aust. Conf. Coastal and Ocean Eng., pp. 143-148. Hsu, J.R.C. and Silvester, R., 1990. Accretion behind single offshore breakwater. J. Waterway Port Coastal Ocean Eng., ASCE, 116(3): 362-380. Hsu, J.R.C., Silvester, R. and Xia, Y.M., 1989a. Generalities on static equilibrium bays. Coastal Eng., 12: 353-369. Hsu, J.R.C., Silvester, R. and Xia, Y.M., 1989b. Static equilibrium bays: new relationships. J. Waterway Port Coastal Ocean Eng., ASCE, 115 (3): 285-298. Ibaraki Prefecture Government, Japan, 1991. Master Plan on Coastal Management: Evaluation of Beach Changes. Report, Civil Eng. Dept., 38 pp. (in Japanese). Komar, P.D., 1983. Coastal erosion in response to the construction of jetties and breakwaters. In: P. D. Komar (Editor), CRC Handbook of Coastal Processes and Erosion. CRC Press, Boca Raton, FL, pp. 191-204. Kraus, N.C., Hanson, H. and Harikai, S., 1984. Shoreline changes at Oarai beach: past, present and future. Proc. 19th Int. Conf. Coastal Eng., ASCE, 2: 2107-2124.
BEACHES DOWNCOAST OF HARBOURS IN BAYS
181
Mizumura, K., 1982. Shoreline change estimates near Oarai, Japan. J. Waterway Port Coastal Ocean Div., ASCE, 108(WWl ): 65-80. Moutzouris, C.I., 1990. Effect ofharbour works on the morphology of three Greek coasts. Proc. 27th Int. Nav. Congr., pp. 17-21. Uda, T. and Noguchi, K., 1991. Beach changes around lwafune port in northern Niigata Prefecture. Tech. Notes Civil Eng. Jpn., 33( l l ): 28-33 (in Japanese). Uda, T., Sumiya, M. and Kobayashi, Y., 1986. Beach change along the Ibaraki coast, Japan. Trans. Jpn. Geomorphol. Union, 7(3): 141-163 (in Japanese).
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Elsevier Science Publishers B.V., Amsterdam
Beaches downcoast of harbours in bays J o h n R.C. H s u a, T a k a a k i U d a b a n d R i c h a r d Silvestera aDepartment of Civil and Environmental Engineering, Universityof Western Australia, Nedlands, Perth, W.A. 6009, Australia bCoastal Engineering Division, Public Works Research Institute, Ministry of Construction, Tsukuba 305, Japan (Received 4 March 1992; accepted after revision 30 June 1992 )
ABSTRACT Hsu, J.R.C., Uda, T. and Silvester, R., 1993. Beaches downcoast of harbours in bays. Coastal Eng., 19: 163-181. In spite of beach berms being removed during each storm sequence the waterline may be retained constant either by a constant supply of littoral drift or static equilibrium bays being formed between headlands. The construction of salients behind offshore breakwaters may be at the expense of the adjoining coast, which resembles the ubiquitous bay shapes formed between headlands that can be either in dynamic or static equilibrium. This is the same silting situation in the lee of breakwaters extending from the coast where beach erosion results downcoast. Ports constructed upcoast of a bay in dynamic equilibrium can have their breakwaters so located that the bay can become statically stable. In the case of the bay being already in static equilibrium breakwater extension often causes massive accretion in its lee and concomitant erosion further downcoast, thus demanding prodigious expense for beach protection installations. Appropriate procedures are now suggested to minimise this undesirable effect of beach erosion associated with the construction and extension of breakwaters to ports upcoast of a bay.
INTRODUCTION
Before equilibrium plan forms of the coastline can be understood there is need for discussion o f beach processes associated with fine to coarse sands in which lateral as well as longshore transport o f these materials takes place. This involves the alternate action of storm waves and swell on the beach profile. The former move berm material offshore forming a bar, while the latter return it to the shore. During this process longshore movement may occur. This introduces the phenomenon o f pulsative rather than a uniform littoral drift along the coast. Once the bar, which has limited the original erosion, is replaced on the berm within a few days by the following swell after any storm Correspondence to: J.R.C. Hsu, Department of Civil and Environmental Engineering, University of Western Australia, Nedlands, Perth, W.A. 6009, Australia.
0378-3839/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
164
J.R.C. HSU
event, this drift may become minimal as only the beach face and narrow surf zone can contribute to the transport. Where natural headlands occur on a mobile shoreline with predominant waves arriving persistently and oblique to the general coastline, a bay which has a specific shape is sculptured between them. Sediment may bypass the downcoast structure where the beach line is almost parallel to the crests of the incoming swell. Behind the upcoast headland a curved segment of the bay exists whose curvature has been likened to a logarithmic spiral. The indentation of the bay is dictated by the amount of sediment passing through it from upcoast or from a river debouching into it. In this condition the bay is said to be in dynamic equilibrium and its waterline can vary with fluctuations in littoral drift. Where this ceases altogether, due to natural or man-made causes, the indentation increases to some limit when static equilibrium is reached. This infers that littoral drift within the bay has become zero due to the incessant swell waves arriving normal to the beach around its periphery. It is for this final condition that equations can be derived defining the shape of the bay. When harbours are established on a coast, by the construction of breakwaters to provide shelter for ships, it is like inserting a new headland that results in shorelines that differ on the upcoast and downcoast sides of it. On the upstream side accretion takes place as sediment attempts to bypass this impediment, whilst at the downcoast side erosion will occur as a bay tends to form in its lee. The larger or longer the breakwater the greater these effects will be. The resulting erosion is generally fought by the installation of seawalls, groynes, or offshore breakwaters, sometimes all three, but these have not always been successful against the persistent swell, not to mention the infrequent storm occurrences. Many natural headlands, acting as breakwaters, have provided reasonable shelter for ships but as industry develops there is demand for more calm areas which involves breakwaters being run from them at various angles many years after the original construction. This intercepts littoral drift, if only temporally, which causes erosion of beaches within the bay and beyond. It can also cause accretion leewards of the headland and its subsequent extension by the breakwater, so reducing the area of desired calm water due to siltation. Komar (1983) has observed: "Many occurrences of destructive coastal erosion have resulted directly from the construction of jetties, breakwaters, and other engineering structures." Moutzouris (1990) has commented: "Coastal erosion a n d / o r accretion are sometimes a result of the construction of harbour or coastal works in an area. Most of the time these side-effects are undesired and engineers have to cope with them." It will be shown in the present context that by selective positioning and length of such structures no deleterious effects may be suffered in this downcoast region. The static equilibrium bay shape, implying zero littoral drift due to its interception by the new break-
165
BEACHES DOWNCOAST OF HARBOURS IN BAYS
water, could well match the original shoreline which was in dynamic equilibrium with the passage of sediment through it. For the case of a bay already in static equilibrium the installation or extension of a new breakwater can only result in serious erosion downcoast and undesired accretion in different segments of it. The knowledge herein envisaged would benefit the planning of harbour construction on a bay and its subsequent extension, in minimising any potential beach erosion downcoast. BAY F O R M A T I O N
Bays along a coast are ubiquitous and are in all sizes and indentations, be they on oceanic margins, enclosed seas, lakes or river margins. As seen in Fig. 1, they are crenulate shaped with a curved segment in the lee of the upcoast headland (breakwater) and straighter in orientation towards the downcoast limit. Whilst sediment is still passing through the bay or fed to it internally, the bay can be said to be in dynamic equilibrium, since it could become more indented should the littoral drift be reduced in the longer term by natural reduction of supply or by man-induced impediments. In the event of complete cut-off the bay will recede to a limiting indentation, as indicated in the figure, by the waterline termed static equilibrium (Hsu et al., 1989a). It is only for this stage that a precise relationship can be found between the parabolic shape and the wave obliquity fl to the control line from the upcoast headland to the downcoast limit of the bay. At the former it is the point at which diffraction takes place, while at the latter it is generally the limit of the straightening beach. Waves within the bay not only diffract but also refract to arrive normal to the shoreline around the shore periphery of this static equilibrium bay shape. It is seen that fl alters very little for this and the dynamic equilibrium shape as the varying indentation is normally very slight. bay in
........., Y " ~ ' r Z r z T #. V~=Q~II~I'I(~
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.
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Fig. 1. Dynamic and static equilibrium shape of bay formed between two headlands.
16 6
J.R.C. HSU
In checking a bay from an aerial photograph or hydrographic chart for stability the control line is first determined from which fl can be measured (Hsu et al., 1989a, b). As seen in Fig. 2, the length of the control line is given as Ro at angle fl to the wave crest line. Other radii R from the diffraction point to the beach line at angles 0 to the wave crest line are then related to fl by the equation:
R/Ro = Co + Ct ( b~ O) + 6/2 ( b/O) 2
(1)
where coefficients Co, CI and C2 are given in Fig. 3 (Hsu and Evans, 1989). For an existing bay in static equilibrium, the curved waterline will remain sensitively unchanged despite the variation of the chosen fl from its true value, so long as the downcoast extremity is located at a point along the straight segment. In fact, it has been found that fl and Ro compensate with each other. This renders Eq. 1 a simpler procedure for field applications and yet also retains its desirable accuracy. If the existing shoreline is seawards of the predicted bay shape it is in dynamic equilibrium and may be unstable, since it could recede back to the static equilibrium condition but no further, should sediment supply cease. The possible recession is not uniform around the bay, as is generally assumed in setting limits to encrouchment on coastal margins. More permanent infrastructure should be restricted to landwards of the static equilibrium waterline as predicted, plus an allowance for the loss of the berm during normal storm sequences and a margin of safety for the severe cyclones arriving less infrequently.
g \\\
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167
BEACHES D O W N C O A S T O F H A R B O U R S 1N BAYS
3
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Fig. 4. Definition sketch of salient development in the lee of an offshore breakwater with waves normal to the coast.
SALIENT BEHIND PROTRUDING BREAKWATERS
Another application to the formation of equilibrium bay shapes is that of studying salients and tombolos in the lee of offshore breakwaters (Hsu and Silvester, 1990). As seen in the definition sketch of Fig. 4, the same nomenclature can be used for which Eq. 1 is applicable. The simple case is of normally approaching waves to an original shoreline distance S from the breakwater which is parallel to it. When waves diffract into the shadow zone of the breakwater they break at an angle to the original shoreline and hence transport sand towards the centre line of the structure, aided by nearshore current circulation. Initially double salients may form, but with adequate wave duration and sediment supply these will coalesce into a single salient.
168
J.R.C. HSU
Except for apex positions and the accreted sand volume associated with the salients behind a single offshore breakwater, no previous authors have given scientific attention to the shapes of beaches so accreted until Hsu and Silvester (1990). When the bays either side of the predicted salient apex is considered to be in static equilibrium, the material required for the formation of this salient must come from the adjoining beaches generally beyond the limits of the breakwater extremities. The tangent to these eroded beaches parallel to the original shoreline is landward of it (S~ in Fig. 4). Dimensionless parameters from the many variables involved have been derived in order to predict salient characteristics (Hsu and Silvester, 1990 ), including the conditions for tombolo formation, but the present issue is to look at half the picture as depicted in Fig. 4, from the breakwater centre line outwards. If a natural headland should exist up to the breakwater center line and it is extended to the limit of the other extremity, then ultimate accretion will take place in its lee similar to the salient as depicted, which can be predicted by employing the concept of the static bay shape given by Eq. 1 previously. This infers that the calm water area planned as a port in the lee of the new breakwater will be partially filled in with a curved shoreline. If shore-protection structures, such as seawalls, groynes and offshore breakwaters, are installed consequently, the curved salient planform is most unlikely to be reached as readily as predicted. It also indicates that the adjacent berm or sandy cliff downcoast will be denuded as material is shifted towards this developing salient. Should a river debouch in the lee of the aforesaid natural headland serving as an original port location then exit channels from it will be silted and so require dredging until the stable salient has formed. When this stage is reached no further littoral drift will occur so that any access channel so dredged will not continue to silt up, except for local refraction at the entrance which will be minimal. H A R B O U R ON S T R A I G H T S H O R E L I N E
Many harbours are constructed on straight segments of sandy coast or even within large bays in dynamic equilibrium, which have similar bypassing requirements. Any breakwater of substantial proportions extending out to sea will disturb the continuity of the littoral drift and act like a headland in the manner previously discussed. This involves accretion on the upcoast side of the structure and concomitant erosion on the downcoast side as a bay attempts to form. Komar (1983) recognized this tendency for cases of littoral drift, but states: "In other cases, however, it is not initially apparent why the engineering structure produced significant erosion. For example, jetties have induced erosion on coasts where no net littoral drift exists." The case of salients discussed above may give an answer to this anomaly. A typical case is exhibited in Fig. 5, where the main breakwater is angled to
BEACHES DOWNCOAST OF HARBOURS IN BAYS
169
:-.''; .'...
. // breakwate/~ main
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Fig. 5. Typical port development on a straight sandy shoreline. and then parallels the shoreline. The secondary breakwater at A provides shelter from waves diffracting around the tip of the first and storm waves that arrive from many directions. The sediment accreting against the main breakwater could eventually silt up the harbour entrance and then bypass it as shown, welding to the coast at point C one or many kilometres downcoast from B, where some accretion may be experienced from A to B, as a salient tends to form in the lee of the main breakwater. It is between these points that erosion will occur, which generally promotes the construction of seawalls, groynes or offshore breakwaters. However, it is recommended that headland control (Hsu and Silvester, 1989 ) be utilised to form stable bays which retain sand in position. In fact, it is suggested that these structures be inserted prior to the construction of the main breakwater, because erosion is very swift. Initially the resulting bays will be in dynamic equilibrium and not so indented but later will become fully stable, with their waterlines oriented to the new direction of the approaching waves within the embayment downcoast. H A R B O U R IN D Y N A M I C E Q U I L I B R I U M BAY
A modest port may be constructed in the form of breakwaters AB and CD as in Fig. 6, with the former connected to a natural headland at A. The control line A E to the downcoast limit of the bay at headland E (or a point along the relatively long and straight section downcoast) has a length Ro and angle to the beach tangent or wave crest line fl= 32 °. The static equilibrium shape of bay A E can thus be drawn utilising Eq. 1. From the existing shoreline as drawn it can be seen that should littoral drift around the headland at A cease the bay should suffer severe erosion. Previously sufficient sediment was bypassing point A to maintain this shoreline. Once breakwater AB is inserted a new diffraction point B reduces the previous Ro to give a new stable shape marked as "bay for BE". This again is for
170
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.
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Fig. 6. Effects of positioning breakwaters upcoast of a bay in dynamic equilibrium.
N
k.
/
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/ Fig. 7. Map of Japan showing harbour locations discussed in the text. no littoral drift. Should an additional breakwater FG be constructed fl= 38 ° and a new Ro results, which provides the bay denoted "bay for GE" in Fig. 6. This seems to match the existing shoreline quite well, although with slight accretion adjacent to CD and slight erosion further downcoast. In time sediment would bypass point G, traverse the bay and weld to the coast in the eroded region. The bay, in fact, may accrete seawards o f the static equilib-
BEACHES DOWNCOAST OF HARBOURS IN BAYS
171
Fig. 8. Aerial photograph showingshoreline downcoastof Oarai harbour, Japan, in 1961 (see Fig. 10 for the N-direction). rium waterline predicted should upcoast sediment supply continue. It is seen that the alternative diffraction point G rather than B has almost solved the erosion problem of this bay in dynamic equilibrium, with some downcoast segment of the bay suffering transient erosion, when only the action of the persistent waves is considered.
172
J.R.C. HSU
Fig. 9. Aerial photograph showing shoreline of the bay at Oarai harbour in 1976 (see Fig. 10 for thc N-direction ).
The structure between A and F could be set back in order to accrete a beach in front of it, which means it does not have to be so massive and its armour units smaller in size. Should it be desired to make the coast from A to E completely stable, due to imminent interception of all littoral drift upcoast of headland A, then point H may be chosen as the new diffraction point. As seen fl= 40 ° and the control line HE, which results in the stable bay shown with large dots which follows the original shoreline periphery perfectly. This will occur even with no input of sediment, should it eventuate in the future. The port of Oarai on the Japanese Kashima coast facing the Pacific Ocean, (see Fig. 7), is an example of the above concept. As seen in the aerial photography of Fig. 8, two angled breakwaters formed a small harbour during 1911 and 1916, which was quickly silted. No further construction was carried out until 1961. Application of Eq. 1 to the curved section of this coast in 1961 showed that the predicted bay shape was landwards of the existing shoreline. This was due to continued littoral drift to the coast at that time, implying that it was in dynamic equilibrium, or could be eroded if a dearth of sediment
173
BEACHES DOWNCOAST OF HARBOURS IN BAYS
Oarai "~, harbour
-\
PacificOcean
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,,
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Fig. 10. Breakwaterconstruction and resulting bay shape at Oarai harbour in 1976.
Fig. 11. Aerial photograph showingshoreline of the bay at Oarai harbour in 1988 (see Fig. 12 for the N-direction). supply were available. By 1976, the tip of the main breakwater for the new harbour was about 650 m out into the sea from its original shoreline at point G marked with a + on Fig. 8, as shown in Figs. 9 and 10. This established a new diffraction point A with Ro = 1.92 km and fl= 45 °. It is seen that the pre-
174
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D
1981-1985
,Jextens'~9 ,,
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Fig. 12. Actual and predicted salient formation downcoast of Oarai harbour in 1988.
dicted static bay shape matched the existing shoreline extremely well, indicating that the beach downcoast would remain stable if no further breakwater extension were made, considering only persistent swell. An extension of this breakwater to B was completed in early 1981 as shown in Figs. 11 and 12 where Ro= 3.48 km and fl= 35 °, giving the static equilibrium shape denoted bay shape for BE. The 1976 shoreline is also shown for comparison. Severe beach erosion had occurred to some 3 km south of the harbour, which has initiated the installation of seawalls and concrete block revetments (Mizumura, 1982; Kraus et al., 1984; Uda et al., 1986). From 1981 to 1985 the detached breakwater CD (totalling 800 m, shown in Fig. 12 ) was constructed for which the bay shapefor CE applies. This is far seaward of the 1988 shoreline in spite the two large groynes (900 and 300 m in length respectively, with the former serving as the second breakwater) inserted to prevent sand incursion into the harbour from the accreting land from 1981 to 1984 and 1985 to 1988, respectively. As noted in the previous section on salients it is such an accumulation that is taking place out to the predicted shape for no further littoral drift. Should this drift continue in the future the waterline could be slightly seawards of this mark, although the bulk of it will weld to the coast in proximity to point E. At the moment, however, erosion is taking place some 2 to 7 km south of the harbour, causing beach profile steepening in front of the seawalls and their subsequent failures (Ibaraki Prefecture, 1991 ). It is thus clear that the effects of changing the upcoast control points due to breakwater extension, from point G in 1961, to point A in 1976,
17 5
BEACHES DOWNCOAST OF HARBOURS IN BAYS
then to point B in 1981 and later to point D by 1985, have shifted the originally dynamic equilibrium bay to a stable bay in static equilibrium (in 1976 ), and then into a series of dynamically unstable conditions, accompanied by undesirable erosion further downcoast.
HARBOUR IN STATIC EQUILIBRIUM BAY
In this case it is difficult to locate a new diffraction point that will prevent erosion on some part of the periphery of a stable bay. Iwafune harbour, located as shown in Fig. 7, on the Sea of Japan, was originally in a river mouth some 50 m wide, as seen in Fig. 13. It received sand from this outlet as well as from a river 6 km to the north. A groyne and detached breakwater were installed in 1929 to stop siltation, but later was connected to the mainland in 1934. Inner revetments and wharf were added in 1957 (Haruta, 1961 ), which became the original outer breakwater for this river mouth harbour. An aerial photograph of 1965 exhibited wide beaches upcoast of the main breakwaters as most sediment had come from the north. To correlate the existing waterline with static bay shape, a downcoast position (F) along the straight segment is selected as the limit of the bay, as noted in Fig. 14. This provides a control line AF, with Ro= 1.35 km and fl= 30 °. The location o f F is not crucial as the predicted bay shape differs very little for changes in fl of
SEA OF JAPAN ,-detached O,,,j breakwoter
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~.
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~
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176
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Sea of Japan
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Fig. 14. Shoreline downcoast of lwafune harbour showing a stable bay shape in 1965.
Sea of Japan
~:~ tOr t^ 0
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.1984
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S Fig. 15. Salient advancement in the lee of breakwater extensions at Iwafune harbour from 1976 to 1984, showing also the survey lines So and N2 to be discussed in Fig. 16 (Uda and Noguchi, 1991 ).
_+5 ° and concurrent changes in Ro, as explained previously after applying Eq. 1. The predicted static equilibrium shape fits the 1965 shoreline and hence no erosion downcoast could be expected. However, mammoth extensions to the outer breakwater then took place in stages between 1965 and 1984, as depicted in Fig. 15, resulting in the salient shoreline along the survey line So in the vicinity of the inner breakwater being
177
BEACHES D O W N C O A S T O F H A R B O U R S IN BAYS
advanced some 280 m over this period (Uda and Noguchi, 1991 ). As seen in Fig. 16, the development of these salients adjacent to the inner breakwater (survey line So in Fig. 15 ) is directly proportional to the length of the breakwater extension, while the shoreline position just north of it (survey line N2 in Fig. 15 ) remains essentially steady. Hence, the sand volumes required for the construction of these salients must have been supplied mainly by the erosion of the beach berm and cliff downcoast, accompanied by profile steepening. Material supplied from the river, either at upcoast or from within the embayment, is minimal.
. o 700 C
"--'
Outer breokwoter length
-- x~ --~--
Survey Line So (salient widthl
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Survey line N2 (beoch wid
123 c- 500 t2l r~ ~ 400 30o
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~
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Fig. 16. Smoothed curves of salient width advancement and breakwater extension at Iwafune harbour along survey lines So and N2 in Fig. 15, from data presented by Uda and Noguchi (1991).
E
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Fig. 17. Predicted and actual shorelines in 1988, after breakwater extension at Iwafune harbour.
178
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Fig. 18. Groynesystemand offshorebreakwatersdowncoastof Iwafuneharbour in i 988. The correlation between the salients thus formed with the breakwater extension from points A to B and then to C is seen in Fig. 17. With an appropriate value offl= 40 ° and selected Ro = 1.63 and 1.75 km respectively, the stable salient shapes for BD and CE are noted in the figure, where D and E are again arbitrary points on the straight segment downcoast. Both of these are well seaward of the 1988 shoreline, inferring that much more material will be removed from the southern beaches to meet this demand of salient built-up. Although the present beach line has been used as the downcoast limit of the bay it could well be landward of this, as noted in the previous section on salients behind an offshore breakwater. The expected erosion has been dealt with without much success by installation ofgroynes, as seen in the figure. Beyond the limit of E other more formidable structures, such as a field of short groynes and offshore breakwaters, have been employed in an attempt to stop the erosion (see Fig. 18 ). These will be left stranded in the sea as Nature carries out its reshaping of the coastline to some static equilibrium condition. PREDICTION OF SHORELINECHANGES The application of the parabolic shapes to the salients formed behind single breakwaters, as exemplified by using two Japanese harbours, suggests that this geomorphological concept is useful in harbour planning. Although the knowledge offers the reasons for erosion downcoast and its concomitant salient development leewards of a breakwater and its extensions, it also provides information on possible siltation and the need for dredging. The sediment transport may still be taking place so that the ultimate equilibrium shoreline may not have been reached, hence with further consequent erosion downcoast.
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In the case of Oarai harbour, seawalls and revetments have been installed from some 2 kms southward of the second breakwater. They have been subject to frequent collapse, becoming almost an annual event. No field data were available so that the downcoast points were chosen from this artificially "stabilized" tangent. At Iwafune harbour sandy cliffs exist downcoast, with beach retreat monitored. However, data were limited, so requiring an empirical model to be utilised. Although the beach plan behind a single offshore breakwater with normal waves can be predicted (Hsu and Silvester, 1990), its extension to oblique waves and breakwater extension from a natural headland requires further attention. The obliquity of persistent waves should not prove difficult once the wave crest alignment is established, since the arcs from the diffraction point can be drawn to the stable shoreline. The exclusion of waves from one side of the equivalent offshore breakwater should not greatly influence the single bay facing the opening from the exposed end of the breakwater. The waves from the alternate side of the single breakwater have little influence on the apex of the salient so forming, except that in this case it will continue to form what is virtually a tombolo in the lee of the breakwater extension. However, in using the formulae the equivalent length of the "offshore breakwater" (B) cannot be determined, or its centreline fixed. Further research is required in models, either physical or numerical, to solve this problem. Because of the engineering significance of beach evolution downcoast of extending harbours, the coastal engineering profession needs to apply itself to the erosion and silting problems related thereto. In time, new relationships should be available for the landbacked extension of breakwaters. CONCLUSIONS
( 1 ) The removal of the berm by storm waves for the construction of the protective offshore bar cannot be prevented by man but it is during its refurbishment back to the beach by subsequent swell waves within days that the greatest littoral drift occurs. (2) When waves are persistently inclined to a coast with headlands, bays are sculptured to crenulate shape that can be either in dynamic or static equilibrium. A parabolic shape can be determined for the latter. (3) Salients formed in the lee of an offshore breakwater have bay shapes either side of their apexes which may ultimately become in static equilibrium and are hence predictable. (4) The salients as in (3) above can be equated to the sedimentation that occurs in the shadow of a breakwater extended from the mainland to provide calm water for a port. (5) Littoral drift impediments such as breakwaters running seawards from a sandy coast will cause accretion and erosion on opposite sides of them.
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Headland control is suggested as a remedial measure for the latter, with its implementation prior to, or not later than, the construction of the main breakwater. (6) In the development of a port upcoast of a bay in dynamic equilibrium the breakwater locations can be so chosen to make the existing shoreline stable. (7) Such a port in (6) above, but within a bay already in static equilibrium, will produce a salient in its lee at the expense of the beaches being eroded further downcoast. This may result in the need for annual dredging of the navigation channel or river mouth within the embayment, as depicted in Figs. 1 and 17. (8) It is strongly recommended that the concept of static bay shape and salient formation, which are ubiquitous features in coastal geomorphology, be employed in harbour planning, in order to minimise the erosive effect on beaches. ACKNOWLEDGMENT
This study is the result of a theme project under Japan/Australia Science and Technology Agreements 1989-90 and 1991-92, of which the authors are the Australian and Japanese Contacts respectively. The authors are grateful to the Reviewers' comments on the original draft, as well as to the Geographical Research Institute, Ministry of Construction, Japan, for the aerial photographs used in this paper.
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