EM 1110-2-1100 (Part II)
30 Apr 02
b. Reflection from structures.
(1) Most of the interior boundaries of many harbors are lined with structures such as bulkheads or reveted
slopes. Recent laboratory investigations (Seelig and Ahrens 1981; Seelig 1983; Allsop and Hettiarachchi
1988) indicate that the reflection coefficients for most structure forms can be given by the following
2
a Ir
Cr '
(II-7-8)
2
b%
Ir
where the values of coefficients a and b depend primarily on the structure geometry and to a smaller extent
on whether waves are monochromatic or irregular. The Iribarren number employs the structure slope and the
wave height at the toe of the structure.
(2) Table II-7-1 presents values for the coefficients a and b collected from the above references.
Table II-7-1
Wave Reflection Equation Coefficient Values Structure
Structure
a
b
Plane slope-monochromatic waves
1.0
5.5
Plane slope-irregular waves
1.1
5.7
Rubble-mound breakwaters1
0.6
6.6
Dolos-armored breakwaters - monochromatic waves
0.56
10.0
Tetrapod-armored breakwaters - irregular waves
0.48
9.6
1
This is an average conservative value. Seelig and Ahrens (1981) recommend a range of values for a and b that depend on the
number of stone layers, the relative water depth (d/L), and the ratio of incident wave height to breaker height.
EXAMPLE PROBLEM II-7-4
FIND:
The height of the reflected wave.
GIVEN:
A wave in deep water has a height of 1.8 m and a period of 6 sec. It propagates toward shore without
refracting or diffracting to reflect from a rubble-mound breakwater located in water 5 m deep. The breakwater
front slope is 1:1.75 (29.7 deg).
SOLUTION:
From linear wave theory shoaling calculations (Part II-1) the wave height at the structure would be 1.70 m
(this is Hi). From the linear wave theory, the deepwater wave length is L0 = 56.2 m. Then, from Equation II-7-6,
the Iribarren number is
tan 29.7o
' 3.28
Ir '
1.70 / 56.2
For the coefficient values a = 0.6 and b = 6.6 (from Table II-7-1), Equation II-7-8 yields
0.6 (3.28)2
Cr '
' 0.37
6.6 % (3.28)2
Thus, the reflected wave height Hr = CrHi = 0.37(1.70) = 0.63 m.
II-7-28
Harbor Hydrodynamics
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