layer is proportional to the critical shear stress of noncohesive sediment during live-
bed equilibrium, Hughes (1999) derived a formula for the maximum discharge per unit
width. The maximum equilibrium discharge is the maximum flow rate that can be
maintained for a given water depth without causing additional scour. An empirical
constant in the formula was established using data from two tidal inlets. (See the
Appendix of this paper for a summary of the development).
The maximum equilibrium discharge per unit width that occurred during forma-
tion of the original scour hole formation is estimated by substituting the maximum
scour depth (9.5 m) and the sediment grain-size (0.2 mm = 0.0002 m) into Eqn. 10 in
the Appendix, i.e.,
(0.0002 m) 3/8 (9.5 m)9/8 = 10.6 m2/s
qe = 5.12 9.807 m/s ) (2.65 - 1)
This estimate of qe can be substituted into Eqn. 1, along with the gap width of
a ≈ 38 m, to estimate the total discharge as Q ≈ 400 m3/s. The mean velocity
corresponding to the maximum equilibrium discharge per unit width is found to be
= 1.1 m/s
This estimate assumes that the scour hole had reached maximum depth, and that no
infilling had occurred between the scour event and subsequent survey.
Placement of the rock sill reduced the maximum depth in the gap to just 4.5 m.
Therefore, the mean velocity over the sill for a storm that produces the same maximum
discharge will be
= 2.4 m/s
Velocities this high are expected to carry across the sill, and erode the sand adjacent
to the detached breakwater toe.
Due to the uncertainty of the scour potential, the Los Angeles District of the Corps
of Engineers planned to install toe protection along selected regions of the breakwater
south of the rock sill. The initial toe protection design was based on engineering
judgment and past experience, and this design was tested and refined in movable-bed
laboratory tests conducted at the Waterways Experiment Station during AprilJune,
The movable-bed physical model study was conducted with two primary objectives:
1. Determine if flow conditions similar to the flow that caused the original scour
hole were likely to cause additional scour downstream of the rock sill, thus
endangering the detached breakwater leeside armor. The outcome of this test
would support the decision on whether or not to fund construction of a protective
toe berm along the leeside toe of the detached breakwater.