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Hudson's equation

Hudson's equation, also known as Hudson formula, is an equation used by coastal engineers to calculate the minimum size of riprap (armourstone) required to provide satisfactory stability characteristics for rubble structures such as breakwaters under attack from storm wave conditions.

The equation was developed by the United States Army Corps of Engineers, Waterways Experiment Station (WES), following extensive investigations by Hudson (1953, 1959, 1961a, 1961b)[1][2][3]

Initial equation

The equation itself is:

where:

  • KD = around 3 for natural quarry rock
  • KD = around 10 for artificial interlocking concrete blocks

Updated equation

This equation was rewritten as follows in the nineties:

where:

  • KD = around 3 for natural quarry rock
  • KD = around 10 for artificial interlocking concrete blocks

The armourstone may be considered stable if the stability number Ns = Hs / Δ Dn50 < 1.5 to 2, with damage rapidly increasing for Ns > 3. This formula has been for many years the US standard for the design of rock structures under influence of wave action [4] Obviously, these equations may be used for preliminary design, but scale model testing (2D in wave flume, and 3D in wave basin) is absolutely needed before construction is undertaken.

The drawback of the Hudson formula is that it is only valid for relatively steep waves (so for waves during storms, and less for swell waves). Also it is not valid for breakwaters and shore protections with an impermeable core. It is not possible to estimate the degree of damage on a breakwater during a storm with this formula. Therefore nowadays for armourstone the Van der Meer formula or a variant of it is used. For concrete breakwater elements often a variant of the Hudson formula is used.[5]

See also

References

  1. ^ Hudson, Robert Y. (1959). "transaction paper 3213". Laboratory investigation of rubble-mound breakwaters. ASCE. pp. 25 p.
  2. ^ CIRIA, CUR, CETMEF (2007). "chapter 5". The rock manual : the use of rock in hydraulic engineering. London: CIRIA C683. pp. 567–577. ISBN 9780860176831.{{cite book}}: CS1 maint: multiple names: authors list (link)
  3. ^ Coastal Engineering Manual EM 1110-2-1100, part VI, chapter 5. US Army Corps of Engineers. 2011. p. 73.
  4. ^ "Vol II". Shore Protection Manual. US Army Corps of Engineers. 1984.
  5. ^ CIRIA, CUR, CETMEF (2007). "chapter 5". The rock manual : the use of rock in hydraulic engineering. London: CIRIA C683. pp. 585–596. ISBN 9780860176831.{{cite book}}: CS1 maint: multiple names: authors list (link)