EM 1110-2-1100 (Part III)
30 Apr 02
4 ε tan2 (αb )
where Y = length of structure.
(11) Pelnard-Considre (1956) also provides a second solution for times after the structure has filled to
capacity and bypassing of sediment begins to occur naturally. The boundary conditions for his second
solution are that y = Y at x = 0 and y = 0 at x = 4 for all t > 0. The initial conditions are as in the previous
solution y = 0 at t = 0 for x > 0. The solution to these specific boundary conditions is as follows:
, t > tf
y ' Y erfc
2 ε t2
which can be made dimensionless by dividing the above equation by the length of structure Y. The
dimensionless solution is presented graphically in Figures III-2-34a, III-2-34b, and III-2-34c (at different
scales). Pelnard-Considre (1956) used a time = t2 in Equation 2-30 such that areas of shoreline above the
x axis would be equal at the time t = tf when the structure is just filled to capacity (Equation 2-29), i.e.,
matched solution plan areas. In this manner t2 was found to be t2 = t - 0.38tf , where t is the initial solution
time at which the structure begins to trap sand. Although the planforms do not match at time t = tf for the two
solutions of Pelnard-Considre, the formulations are still useful for conceptual preliminary design and
evolution of projects.
(12) The solution of Pelnard-Considre prior to bypassing (as given by Equation 2-28 and Fig-
ure III-2-31) may also be utilized for the situation in which erosion occurs on the sand-starved beach down-
drift of an impermeable coastal structure that has no bypassing (natural or man-made). In this specific
instance the solution would provide shoreline recession values as opposed to shoreline progradation values.
In this scenario the solution should only be utilized far enough downdrift of the structure (i.e., beyond the
immediate "shadow" of the structure) such that diffraction and refraction effects due to the structure do not
influence the wave field and shoreline geometry.
(13) When applied in this scenario, the solution of Pelnard-Considre suggests that the ultimate downdrift
extent of erosion caused by the structure is infinite. In practice, Equations III-2-28 and III-2-29 may be
applied to estimate the theoretical downdrift extent of erosion, prior to bypassing, in terms of the structure
length Y. That is, the distance downdrift of a structure at which the shoreline recession is less than or equal
to some fraction of the structure's length (i.e., y / Y) can be expressed as a multiple of the structure's length
(i.e., x / Y). Example III-2-10, below, illustrates this application. It is important to note that this solution is
idealized and assumes that the breaking wave angle αb can be approximated as an average, quasi-steady value.
At present, the actual downdrift extent of erosion associated with a structure or other sediment sink is not well
(14) The second case to be considered is that of a rectangular beach fill as shown in Figure III-2-35.
Figure III-2-36 is a nondimensionalized solution graph that can be utilized in estimating plan area change for
the rectangular beach nourishment fill on an initially straight reach of beach. Fill exists from -a < x < +a and
extends Y distance seaward from the original beach. The solution for this specific case is as follows:
Longshore Sediment Transport