Pages to print Enter page numbers and/or page ranges separated by commas. For example, 1,3,5-12. After downloading, print the document using a PDF reader (e.g. Adobe Reader).

<br />
<br />
<br />
<br />4
<br />
<br />Figure 3: Wind speed relationship – water to land
<br />Wind Setup, Wave Height, and Runup
<br />A sketch of waves striking an embankment slope is
<br />illustrated in Figure 4. When wind is blowing over a
<br />water surface, horizontal shear stress acts on the
<br />water surface, and the water surface is tilted in the
<br />direction of the wind. This wind effect is termed “wind
<br />setup” and can be estimated using the empirical
<br />equation from TR-69 shown below.
<br />
<br /> Eq. 4
<br />S = Wind Setup in feet
<br />Uw = Wind Speed in miles per hour
<br />F = Wind Fetch in miles (Approximately equal to Fe)
<br />D = An approximation of the average water depth
<br />along the fetch length in feet
<br />Slope protection is generally designed for what is
<br />known as the “significant wave height.” The significant
<br />wave height is the average height of the highest one-
<br />third of the wind-generated waves. This means that 33
<br />percent of the waves that hit the slope will be higher
<br />than this value. Based on the selected design
<br />overwater wind speed and the effective fetch, the
<br />significant wave height, Hs, and wave length, L, can be
<br />estimated using the following dimensionless equations
<br />from TR-69.
<br />
<br /> (
<br /> )
<br /> Eq. 5
<br /> √
<br />
<br /> (
<br /> )
<br /> Eq. 6
<br />g = Gravitational Acceleration, 32.2 ft/sec2
<br />Hs = Significant Wave Height in feet
<br />L = Wave Length in feet
<br />UL = Overland Wind Speed in ft/sec
<br />Fe = Effective Fetch in feet
<br />Equations 5 and 6 are empirical equations developed
<br />from deep-water waves, which are defined as waves
<br />having lengths equal to or less than 2D. They also give
<br />conservative wave height estimations for shallow-
<br />water waves.
<br />When waves reach a sloping embankment, the waves
<br />will eventually break on the slope and run up to a
<br />height governed by the angle of the slope, and the
<br />surface roughness and permeability. Wave runup
<br />height, R, is the difference between the maximum
<br />elevation reached by wave runup on a slope and the
<br />storm water level. The steeper the embankment slope
<br />the greater the wave runup height. Many studies have
<br />been published that provide guidance for determining
<br />the wave runup height on slopes. The runup from a
<br />significant wave on an embankment slope with riprap
<br />protection can be predicted using:
<br />
<br /> (
<br /> )
<br /> Eq. 7
<br />R = Wave Runup Height in feet
<br />Hs = Significant Wave Height in feet
<br />L = Wave Length in feet
<br />θ = Angle of the Dam Face from Horizontal
<br />Equation 7 should be used only for embankment
<br />slopes steeper than 5H:1V.
<br />
<br />
<br />
<br />The significant wave height defined above
<br />would be exceeded by approximately 33
<br />percent of the expected waves generated by the
<br />associated wind speed. If a lower potential of
<br />exceedance is desired, a wave height of 1.27Hs and
<br />1.67Hs have a corresponding potential for
<br />exceedance of 10 percent and 1 percent,
<br />respectively.
<br />Wi
<br />n
<br />d
<br />
<br />R
<br />a
<br />t
<br />i
<br />o
<br />
<br />(
<br />U w /U L )
<br />Figure 4: Sketch illustrating wave terms