EM 1110-2-1100 (Part III)
30 Apr 02
Figure III-2-30.
Structure placed perpendicular to shore
with the boundary condition at the structure being tan αb = dy/dx, and the boundary condition at x = 4 being
y = 0 for all times. The initial condition for this solution is that y = 0 for t = 0. This particular solution graph
can be utilized to estimate planform shapes on the updrift side of coastal structures where bypassing does not
take place.
(9) The dimensionalized solution for these conditions is given by Pelnard-Considre (1956) to be
2
1
x
x
x
y ' 2 ε t tan(αb)
exp &
erfc
, for t < tf
(III-2-28)
&
2 εt
2 εt
2 εt
π
where tf is the time at which the structure fills to its capacity via this solution and where erfc( ) is the
complementary error function defined as erfc( ) = 1 - erf( ) where erf( ) is the error function and
2
π m0
()
2
e &z dz
erf ( ) '
Both erfc ( ) and erf ( ) are tabulated in various mathematical handbooks. Figures III-2-32 and III-2-33
provide graphs of erfc ( ) and erf ( ).
(10) The time required for the structure to fill to capacity t = tf can be found from the previous solution
with ordinate x = 0; i.e.,
III-2-60
Longshore Sediment Transport
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