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 Coastal Defense Systems 1 8-1 CDCM Professional Training Programme, 2001 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. Coastal Defense Systems 1 8-2 CDCM Professional Training Programme, 2001 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 Coastal Defense Systems 1 8-3 CDCM Professional Training Programme, 2001 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: Coastal Defense Systems 1 8-4 CDCM Professional Training Programme, 2001 ∆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. Coastal Defense Systems 1 8-5 CDCM Professional Training Programme, 2001 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.