Sediment Transport Rates
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SANDS calculates the alongshore sediment transport rates for the CERC, Kamphuis and Damgaard & Soulsby formulas, results are presented as a year-on-year summary of average quantity and direction of material transported.
This feature will allow users to estimate the volume of beach material traveling in which direction along a shoreline.
The sediment transport rate calculations are intended for use only by users with a sound understanding of the CERC formula or Kamphuis equation for fine grain sizes (< 0.5mm) and the Damgaard and Soulsby formula for coarse grain sizes (> 0.5mm) and a full appreciation of there limitations.
The CERC formula is the most widely used method to calculate the total sediment transport integrated across the width of the surf zone, The formula, originally given in Shore Protection Manual (CERC 1984) in US units, can be converted to a dimensionally consistent form (eg. Fredsoe and Deigaard, 1992). A variety of versions have been used, differencing in chiefly in their treatment of the wave group celerity and the wave breaking criterion. Taken these as and in the surf zone. together with , leads to the simple formula:
= sediment transport rate (m3 s-1) integrated across the surf zone, in volume of sediment (excluding pore space) per unit time.
= acceleration due to gravity.
= significant wave height at breaker line
= angle between wave crest and shoreline at breaker line.
= relative density of sediment
This is the simplest form of the CERC Equation, obtained by applying shallow-water linear wave theory to the full expression.
Kamphuis (1991) derives an expression that includes the effects of wave period (or wave steepness), beach slope and grain size.
Shingle (Damgaard & Soulsby)
Damgaard an Soulsby (1997) defined a physics-based formula for bedload longshore sediment transport. It is intended primarily for use on shingle beaches, although it is also applicable to the bedload component on sand beaches.
'Inshore' wave data, this can be transformed/calculated/imported. (Kamphius, CERC & Shingle)
Water levels (either recorded or predicted via SANDS). (Kamphius & Shingle)
Definitions for the Beach Parameters required when using the calculations:
Beach Contour (mOD) The lowest water level at which waves will influence beach movement. For transformed wave data this must be the depth of the inshore point. The depth of the Beach Contour is then used to calculate the breaking wave height. (Kamphius, CERC & Shingle)
Beach Slope expressed as a number (i.e. a 1/100 slope would be 0.01, a 1/25 would be 0.04 etc) (Kamphius & Shingle)
Beach Normal Offshore facing Deg (N) This is the offshore bearing of the beach profile from land out to sea from north. (i.e. a typical bearing for a profile on the east coast might be 90deg, or on the South coast 180deg etc)
This bearing is required in order for the user to interpret the results (i.e. if the drift is north south , east west etc) (Kamphius, CERC & Shingle)
Sediment Size - D50 (m) This is the median grain diameter for the sediment. For fine grain size, D50 < 0.0005 (0.5mm), the Kamphuis or CERC equation should be used, for coarse grain sizes, D50 > 0.005, then the Damgaard and Soulsby formula should be used.
Note: This is expressed in metres (i.e. 50mm = 0.05, 30mm = 0.03 etc) (Kamphius, CERC & Shingle)
Wave Breaking Criteria used to calculate the wave breaking point. (Kamphius, CERC & Shingle)
Data Interval (mins) used in the pivot table for displaying the resulting Q per interval.
It is likely the user will want to undertake multiple runs. E.g. to determine the differences of varying the sediment size or slope. It is also sensible to undertake sensitivity tests by varying the offshore bearing.
Multiple runs can be quickly setup via the ‘Input Data’ tab.
Multiple runs can be set running via selecting and highlighting from the setup list.
The results summary can be seen via the ‘Sediment Transport Rates’ tab.
Results are presented annually, the volumes are expressed as cubic metres per hour and per year.
The values will be positive or negative, to relate this in to true directions we should compared to the beach normal.
Waves approaching from the left of the offshore facing beach normal are -ve = Q Right.
Waves approaching from the right of the offshore facing beach normal are +ve = Q Left.
Negative values indicate waves approaching from the left of the offshore facing beach normal = Q Right.
Positive values indicate waves approaching from the right of the offshore facing beach normal = Q Left
E.g If we have a location on the east coast the bearing could be 90deg.
Here negative values would indicate material travelling south and positive values would indicate material travelling north.
E.g If we have a location on the south coast the bearing could be 180deg.
Here negative values would indicate material travelling west and positive values would indicate material travelling east.
Interpreting results via the Results Pivot Table
The ‘Results Pivot Table’ is allows the user to examine the sediment transport results in great detail.
The variables can be dragged and dropped to display or hide data as required.
The user may also calculate results with a specific interval (i.e. in addition to the hourly default) via the ‘Data Interval’ box.
Variables available via the Results Pivot Table
Qk (m3/hr) Quantities via Kamphuis equation
Qc (m3/hr) Quantities via CERC equation
Qs (m3/hr) Quantities via Shingle equation
If the user specifies an interval via the ‘Data Interval’ box additional data will be available;
Qk (m3/Int) Quantities via Kamphuis equation
Qc (m3/Int) Quantities via CERC equation
Qs (m3/Int) Quantities via Shingle equation
Here the Int (Interval) will relate to the specified interval.
The letter following the Q will indentify results as either Kamphuis, CERC, or Shingle
Qk (m3/hr) Net quantities (values will be either + or - )
-Qk (m3/hr) Quantities travelling right of the offshore facing normal
+Qk (m3/hr) Quantities travelling left of the offshore facing normal
Why use the Results Pivot Table?
The pivot table can be used to represent the sediment transport results in many user specific formats.
Ref: Coastal Engineering Research Center (CERC) (1984). Shore protection manual. Washington, D.C., U.S. Army Corps of Engineers.
Ref: Dynamics of Marine Sands (Soulsby)
Ref: Introduction to Coastal Engineering and Management (j. William Kamphuis)