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.

 

WARNING

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.

 

CERC

The CERC formula is the most widely used method to calculate the total sediment transport clip0007 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 clip0006 and the wave breaking criterion. Taken these as clip0003and clip0004in the surf zone. together with clip0005, leads to the simple formula:

 

clip0002

 

where

clip0008= sediment transport rate (m3 s-1) integrated across the surf zone, in volume of sediment (excluding pore space) per unit time.

clip0009  = acceleration due to gravity.

clip0010= significant wave height at breaker line

clip0011 = angle between wave crest and shoreline at breaker line.

clip0012 = 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

 

Kamphuis (1991) derives an expression that includes the effects of wave period (or wave steepness), beach slope and grain size.

 

clip0013

 

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.

 

clip0014

 

 

Inputs:

 

'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.

 

SedimentTransportRate

 

 

Multiple runs

 

 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.

 

Viewing results

 

 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.

 

Interpreting results

 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.
E.g. the user can switch the year and month variables to examine data monthly, perhaps to identify trends and examine increased transport of material in stormy months.

 

 

 

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)