Laserfiche WebLink
<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