Rec/8/4 Section 4 the Coastal Zone

The University of the West Indies Organization of American States

PROFESSIONAL DEVELOPMENT PROGRAMME: COASTAL INFRASTRUCTURE DESIGN, CONSTRUCTION AND MAINTENANCE

A COURSE IN COASTAL DEFENSE SYSTEMS I

CHAPTER 8

SEDIMENT BUDGETS AND MODELLING

By PATRICK HOLMES, PhD Professor, Department of Civil and Environmental Engineering Imperial College, England

Organized by Department of Civil Engineering, The University of the West Indies, in conjunction with Old Dominion University, Norfolk, VA, USA and Coastal Engineering Research Centre, US Army, Corps of Engineers, Vicksburg, MS, USA. St. Lucia, West Indies, July 18-21, 2001

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8. SEDIMENT BUDGETS AND MODELLING.

P.Holmes, Imperial College, London

8.1 Introduction. It is always necessary to prepare a sediment budget when planning engineering work in the coastal zone. Various sources of sediment supply to the area are identified together with the points where sediment is either trapped or is lost, these latter points being known as sinks. An estimate is then made of the effect which each of the sources, sinks and traps has on the balance of sediment within the area.

8.1.1 Sources, Sinks and Traps. The sediments in a particular area may come from a number of sources:

(a) from inland – carried by rivers or glaciers or (to a lesser extent) by the wind; (b) from cliffs – weathering and direct removal by waves; (c) from offshore – carried landward by wave action; (d) from artificial beach nourishment; (e) from alongshore – the material moved alongshore will originally have been derived from one of the other sources.

The ways in which sediment may be removed from the area (sinks) include:

(i) by alongshore transport; (ii) by deposition offshore during a storm – much of this material comes back to the beach during swell conditions but some (especially the finer sediment) may be permanently lost; (iii) by being driven by the flood of the tide into estuaries, inlets and harbours where it accumulates in the quieter waters – even if the ebb flow carries back some of this sediment it may be transported into the offshore zone; (iv) by deposition into a depression in the bed of the inshore zone or nearshore canyon; (v) by the wind carrying it inland to dunes or seaward to the offshore zone; (vi) by dredging or mining.

Even when the sediment remains within a particular stretch of beach it may be trapped for long periods at certain features. These sediment traps include spits and tombolos; man-made structures such as breakwaters may also act as traps. However, during storms some of the trapped material may be eroded and then it may once more enter the sediment transport system.

8.1.2 An Example of a Shoreline budget.

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Figure 1 shows an imaginary stretch of coastal zone which incorporates some of the features described earlier. 3 At A there is a net drift of sand westwards : Q1 = 3,000 m /year. However, at B this material is prevented from moving further west by the headland and most of the sand is lost to the very deep water which comes close to the shore at that point. The headland itself has been stable for many years and so the quantity of beach material supplied by this source is negligible. However, immediately to the west of it the beach has been retreating at an average rate of 0.5 m/year from which it is estimated that Q2 = 10,000 m3/year.

N Incident Waves

Q1

Q7 Q4 Q2 Q5 B cliffs A F D E Q3 C cliffs dunes Q6

Q8 river rivers

Figure 1. Example of a Sediment Budget.

Measurements of the sediment in the river at C indicates that the river carries a total sediment load of 100,000 m3/year but that only 20% of this material is sufficiently coarse to remain in the coastal zone; the remaining very 3 fine sediment is lost offshore. Thus Q3 = 0.2 x 100,000 = 20,000 m /year. At D the dunes have been increasing in volume at a rate, Q4, of about 5,000 m3/year whilst the beach between C and E has remained in equilibrium for

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many years. Thus the net longshore transport rate, Q5, in the vicinity of the proposed harbour may be estimated as:

3 Q5 = Q2 + Q3 – Q4 = 25,000 m /year.

Beach material is supplied by the river at E at an estimated rate of 12,000 m3/year whilst surveys of the beach and spit near F have shown that 3 sand is accumulating in this region at a rate Q7 of 34,000 m /year. These 3 figures suggest that Q5 = Q7 – Q6 = 22,000 m /year. 3 The discrepancy of 3,000 m /year between the two estimates for Q5 is reassuringly small compared with each of the individual values and may be accounted for in a number of ways. For example, no allowance has been made for the loss of sand from the spit. Consequently, the first estimate of 25,000 m3/year is probably the more correct. This budget will then form the basic context for coastal works and any effects of those works, e.g., trapping of sand, can be taken into account in an up-dated budget.

8.2 Modelling Shoreline Changes.

8.2.1 A “One Line” Shoreline Model. Figure 2 illustrates the concept of a “one line” model of shoreline

Q IN ∆y ∆x

QOUT dc

Qn+1 E Qn N LI RE O SH evolution.

Figure 2. Prediction of Longshore Shoreline Evolution.

If the longshore transport rate into the region (QIN) is greater than that out (QOUT) then in time ∆t sediment will accumulate and the shoreline will move seaward a distance ∆m:

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∆m ∆x h = (QIN - QOUT)∆t 1.

If QOUT is greater than QIN then ∆m will be negative; erosion will occur. The volume balance is taken between the top of the beach and the level below which there is little significant movement of beach material - the closure depth, dC, in figure 4. Note also that in these models the “equilibrium beach profile” – see below – is used. Writing ∆Q in place of (QIN – QOUT) in equation 1 gives:

∆m/∆t = (1/h). ∆Q/∆x 2. which shows that the rate,∆m/∆t, at which the shoreline position changes depends on the longshore variation in Q, the longshore transport rate. Q is given by well-known equations which require wave height and wave direction at the breaker line, αb. Then, equations 1 and 2, may be used to study the development of a stretch of beach by dividing it into a series of cells of uniform length ∆x, Figure 2. Each of the longshore transport rates, Q1, Q2, ...Qn... etc., may be computed from the alongshore sediment transport equations. However, the αb, which the breaking waves make with the shoreline in each cell, will, in general, be changing. To allow for these changes and to prevent sudden alterations in the shoreline position it is necessary to ensure that values of ∆m remain small by selecting a suitable time step, ∆t, between successive computations. In addition, ∆x must be small in order that the series of cells provides a reasonable approximation to the actual shoreline. It is most important that every effort is made to “calibrate” the alongshore sediment transport equations because they contain empirical coefficients. Any location along a coastline where there is a complete barrier to the alongshore sediment transport is a potential calibration point. It is possible to calculate volumes of sediment accumulated up-drift of the barrier if a number of beach surveys are available but note that the surveys have to extend to the offshore limiting depth for sediment transport under wave action.

If a part of the beach has a source of sediment other than that coming alongshore then its effect may be readily accounted for, provided it can be quantified. For example, if a cell in Figure 6 has sand supplied to it by a river at a rate Qr, then:

∆mn = (Qn – Qn+1 + Qr) ∆t/h∆x 3.

Similarly, if a cell represents an area where sand is mined from the beach at a rate Qm then:

∆mn = (Qn – Qn+1 – Qm) ∆t/h∆x 4.

This outlines a one-dimensional model of coastline evolution.

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In a two-dimensional model onshore/offshore movement would be included and an x,y grid used to cover the area for application of sediment mass balance to each cell. Such 2-D models have been used to explore the sea bed level changes at the mouth of a river – a combination of river and wave induced transport, and to the mouth of a tidal lagoon – a combination of tidal and wave induced transport. Relatively simple models have an advantage that they can by run to simulate longer periods of coastal evolution, for example, five to ten years, but because of the simplification care must be taken in the interpretation of the results. In fact, with all numerical models of coastal evolution it is almost always necessary to collect full scale data to validate the model for use in a design context.

8.2.2 “N”–Line Shoreline Models.

These models are an extension of the “one line” models that allow cross-shore sediment transport to be taken into account, in effect they are two-dimensional with the region normal to the shore divided into “N” increments. Then the sediment transport into and out of each ∆x,∆y cell is calculated to determine the increase or decrease in bed level in each computational time increment. As illustrated by figure 3, the numerical

q OUT

Q OUT

Q IN

q IN

SHORELINE

Lim iting Depth of Sedim ent Transport

Figure 3. Concept of an “N”-Line Shoreline Model.

“housekeeping” in such models is not trivial because of the irregular geometry involved but such models are used in advanced coastal engineering design. In addition to the geometric and equation validity problems it ahs to be noted that a predictive model must be run to represent long-term changes in the beach and nearshore region. This requires the simulation of the wave

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climate in terms of HS, TZ and angle of wave approach (to give αb, the breaker angle) for, say five years. If the sediment transport equations are simplified these simulations can be carried out on a fast desk-top computer but it is essential to calibrate the results in some way. Such models have been run for specific locations, for example, a river exit onto a coastline, which required an additional simulation of the river discharge and its sediment load; and tidal lagoon interaction with a coastline, which required a tidal model and associated sediment transport to be included, although the tides are deterministic.

8.3 Pocket Beaches. A “pocket beach” is defined as one situated between barriers, which might be natural or man-made, that prevent transport of sediment past them. In such a case it is relatively simple to predict the equilibrium shoreline configuration for particular incident wave conditions. According to equation 2 – which, of course, accounts only for longshore movement of sediment – a beach is in equilibrium when the alongshore variation in the longshore transport rate (i.e. ∆Qx/∆x) is zero. But in the case of a pocket beach Qx is zero at each of its ends. Consequently, its equilibrium state is reached when the breaker angle αb (and thus Qx) is everywhere zero (if dHsb/dx = 0): the shoreline has approximately the same shape in plan as the breaker crests. Obviously the shape of the beach will change as the incident wave direction changes but no sediment will be lost from the bay. Recent discussions about pocket beaches in the West Indies indicate that pocket beaches may not lose their total sand volume (by definition) but they may lose beach width. If the wave climate is relatively bi-modal, i.e., it consists of limited periods of high wave action and long periods of significantly lower wave action, under high waves the beach will be drawn offshore – probably forming an underwater sand berm or bar. It may then be quite possible that the lesser wave action is not sufficient to mobilise all of that sand to bring it back to the shore, thus resulting in a loss of beach width. Visual inspection only or beach surveys only out to just beyond low water level may lead to the conclusion that the beach is eroding. In fact it is but the sand is not lost irrevocably. Relatively small-scale dredging could recover the sand from the berm and replace it on the beach, but the implication is that this would be a repetitive need at some time interval that would depend on the wave climate and its annual variablility.

8.4 SOME EFFECTS OF COASTAL ENGINEERING WORKS Section 1.2 gave an example of the preparation of a sediment budget. In this section some of the possible effects of engineering works on the coastal zone are described. 8.4.1 Shore-connected Breakwater. Figure 4 shows an offshore breakwater and a harbour created by enclosing an area of water behind a breakwater extending from the shoreline.

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N Dominant Wave Direction Tombolo

EROSION ACCRETION

Beach Changes at an Offshore Breakwater Dominant Wave Direction

ACCRETION EROSION

Beach Changes at a Barrier to Longshore Transport

Figure 4. Two Examples of Coastal Structure Interaction with Lonshore Transport.

The effect of the breakwater would be to trap sediment on its up-drift side. As a result the down-drift beach would be deprived of its source of sediment and it would be eroded. Eventually the up-drift region would reach its impounding capacity and sediment carried into the region would be balanced by material transported out of it. Sediment would then be driven along the outer face of the breakwater until it reached the tip of the breakwater where some of it would be deposited as a spit in the relatively calm water in the lee of the structure. In practice, to maintain harbour operations, dredging would be carried out to remove the spit. This material could be deposited on the down-drift beach to compensate for erision; this process is known as sand bypassing. Note that although longshore transport of sediment may take place in both directions it is usually necessary only to bypass material in the direction of net longshore transport.

8.4.2 Dredged Inlet Channel. Instead of enclosing an area of water behind a long breakwater, the harbour could be built landward of the existing shoreline with access from the sea provided by a channel dredged through the beach. Siting the harbour here could be particularly worthwhile if the land behind the beach was very low- lying, the material removed to form the basin being used to raise land levels behind the quays. Unfortunately, the increased water depths in the dredged channel would reduce wave breaking in that area and sediment would tend to deposit in the updrift side of the channel with corresponding erosion of the beach downdrift of it. Tidal motion might prevent the entrance to the harbour being completely closed (if the size of the basin were sufficiently large). In

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that case sediment would be moved into the harbour during the flood flow and offshore during the ebb flow. Even so, the channel would tend to move down the coast. To stabilise the channel and reduce sediment deposition in it, training walls could be constructed Sand bypassing operations would be necessary to prevent material eventually passing round the end of the wall (or over it if it were submerged during part of the tidal cycle) and to replenish the down-drift beach. If no training walls were built it might be necessary to dredge the channel at up to the gross longshore transport rate.

8.4.3 Detached Breakwater. A detached or offshore breakwater could also be used to provide a protected area of water or to combat coastal erosion Figure 4. However, reflection and dissipation of incident wave energy by the structure would mean that, although waves would diffract into the protected zone, the power available for longshore transport in this region would be less than that available up-drift or down-drift of it. The design basis here is to modify the wave field to reduce the longshore sediment transport rather than attempting to contain the sediment directly. Consequently, sediment would accumulate in the lee of the structure whilst the beach on the down-drift side would erode. Eventually the sediment deposited behind the breakwater might form a tombolo connecting the structure to the shore. Further erosion and accretion would then be similar to that for the shore-connected breakwater. A series of short detached breakwaters may be used to stabilise an eroding beach or to encourage a beach to widen. The breakwaters act as artificial headlands with the wave energy being spread by refraction and diffraction in the bays between the headlands.

8.4.4 Groynes. Groynes are structures built approximately perpendicular to the shoreline to trap sediment carried by longshore transport. Their purpose is to widen a beach or to maintain its position if it is eroding. The shoreline between adjacent groynes tends to align itself more closely than the original shoreline with the crests of the breaking waves. Since they are designed to trap sediment that would otherwise be moved alongshore, some erosion down- drift of a system of groynes must be expected unless the groyned region is filled by artificial beach nourishment. Even then, if the groynes had been built to maintain a beach which was previously eroding, any measure to reduce that erosion will rob the down-drift beaches of some of their previous source of sediment. In that case continuous nourishment of the down-drift beaches may also be necessary unless they had previously been accreting. Groynes will offer little protection against the general offshore movement of sediment associated with storm waves and may, under certain circumstances, actually enhance this movement. For example, if the groynes project well above the beach level they will tend to deflect the longshore current seaward as a series of rip currents which carry sediment seaward. This effect will be enhanced by any reflection of wave energy from the sides of the groynes. Even if groynes are adjustable so that they may be maintained at an elevation which is only just above beach level, the above problem may

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arise when storm waves are not approaching from the predominant wave direction but from the opposite quadrant. In this case the lower beach level on a groyne’s down-drift side may expose a considerable part of it to wave action. Nowadays it would be difficult to commit expenditure on man-power to monitor the heights of groynes and to adjust them according to need. More recent developments involve building large, rock armoured groyne structures, sometimes with exaggerated roundheads, to provide fixed control points on long exposed beaches, essentially man-made headlands.

8.4.5 Sea-walls. During storm conditions a beach is eroded and sediment is transferred to a longshore bar which then protects the shore from the larger waves. Most of the sediment is returned to the beach during subsequent swell conditions. Vertical sea-walls are built to protect coastal assets and to prevent the offshore movement of sediment during storms. Unfortunately, since the wall limits the landward extent of the material available for the building of a longshore bar, it encourages greater erosion immediately in front of the wall than would otherwise occur. The ability of the waves to erode the beach is considerably enhanced by reflection from the structure. Even if the erosion at the toe is limited by suitable scour protection, the presence of the wall may accelerate the longshore transport rate in front of it as a result of the increase in wave activity caused by the reflections. This increased transport rate could lead to a general lowering of the beach levels and eventually result in the wall being undermined. For these reasons it is often desirable to design a wall or slope with a reflection coefficient as low as possible, < 0.3. This would generally require that it has a relatively flat seaward slope or be constructed of voided man- made units to maximise energy loss. Special care should also be taken in designing the ends of the structure to ensure that it is not outflanked by erosion of the beach at its ends. Construction of vertical sea-walls is best confined to rocky coasts (perhaps to protect the base of a cliff from erosion) where a firm foundation will prevent the wall from being undermined.

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8.5 Artificial Beach Nourishment A shoreline configuration depends on the rates at which sediment was supplied to and removed from each section of the beach. Consequently, in order to stabilise an eroding shore it is necessary either to reduce the rate at which the sediment is being removed or to increase the rate at which it is being supplied. The first option usually involves the construction of sea- walls, groynes or offshore breakwaters, that is, control structures. The second involves periodically supplying material to the beach from some outside source. This process is known as artificial beach nourishment (or replenishment). If a suitable source of material is readily available, beach nourishment may be less expensive than the alternative structural solutions. The borrow material chosen for beach nourishment should preferably be coarser than the native beach sediment because it has a higher threshold of movement and consequently will be more stable. The new foreshore slope will then be steeper than the original. Possible sources of borrow material are the sediment sinks and traps described in Section 1.1. If material is taken from the offshore zone, care must be taken to ensure that the resulting modifications to the wave refraction patterns do not have undesirable effects. Three types of nourished profile can be defined: “Intersecting”, “Non- intersecting” and “Submerged” as shown in figure 5.

W* ∆y

B

h* Added Sand

Intersecting Profile AF > AN

Virtual Origin of Nourished Profile

y1

h*

Added Sand Added Sand

Non-intersecting Profile Submerged Profile AF < AN

Figure 5. Types of Beach Nourishment Scheme.

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The “equilibrium beach profile” is given by:

h(x) = Ay-2/3 5. where A is a function of grain size and we denote AN as the native and AF as the fill profile parameters. The volumes of sand required for each case differ, with an impact on cost and it is often difficult to find a local source of sand of a larger grain size. The volume required per unit length of beach can be calculated from the equilibrium profile and will depend on the width of “new” beach required at the shoreline. In the West Indies beach nourishment options for solving coastal problems are not favoured, largely because of the high cost of mobilising dredging equipment. However, it must be noted that low volume dredging plant is not expensive, it can be assembled locally, and high production rates are not required. The density of a pumped sand/water mixture is usually about 1200 to 1250kg/m3 so that for every cubic metre pumped some 200 to 250 kg of sand is placed on the beach. A major factor in beach nourishment options is the reluctance of governments to accept a solution that implies maintenance costs in the future, i.e., additional nourishment from time to time. Thus a combination of nourishment and control structures is most likely to find favour, unless the latter would constitute a significant visual detraction and amenity loss.

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