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<br /> <br /> <br /> <br />8 <br />Some of these alternate materials include articulated <br />concrete blocks, cellular concrete mats, and in some <br />low wave-energy sites, vegetation or geosynthetic <br />reinforced vegetation. This article focuses on the <br />design of riprap armoring, as it is the most commonly <br />preferred and installed material. <br />Procedure <br />In general terms and in TR-69, the procedure for the <br />design of riprap can be summarized as a flow chart as <br />shown on Figure 3. This procedure is described in the <br />following sections of this article and an example <br />(Example #2) is provided at the end of this article. <br />Example #2 is a continuation of Example #1 from the <br />previous article in this newsletter. <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br />Figure 3: Summary flow chart procedure for design of <br />riprap. <br />Determining Rock Weight <br />In accordance with TR-69, the equation to estimate the <br />required riprap rock weight (W50) can be given as: <br /> <br /> <br />( ) Eq.1 <br /> <br />GS = Specific Gravity <br />HS= Significant Wave Height (See previous article for <br />calculation method) <br />cot  = Horizontal Component of Embankment Slope <br /> <br />Rock weight can also be estimated using Figure 8 in TR- <br />69. As the embankment slope and or significant wave <br />height increases, the calculated rock weight also <br />increases. Conversely as the embankment slope and or <br />significant wave height decreases, the calculated <br />rock weight reduces. <br />Determining Type, Size, Thickness and <br />Gradation <br />There are two types of rock placement described in TR- <br />69: <br /> Type 1 – Dumped (Equipment-Placed) Rock <br /> Type 2 – Hand-Placed Rock <br />Dumped rock is regarded as superior to hand-placed <br />rock because of historically low maintenance costs. <br />Experience has also shown that in most cases dumped <br />rock provides the best upstream slope protection at <br />the lowest ultimate cost. For these reasons, only <br />dumped rock is discussed further in this article. <br />The procedure for determining the physical riprap <br />characteristics described in TR-69 for Type 1 (dumped) <br />rock is as follows: <br /> Size: using the W50 weight of rock, find rock <br />size (D50) using Figure 9 (TR-69) or the <br />equations provided with the figure. Usually the <br />equation for spherically shaped rock is used to <br />estimate rock size for riprap as follows: <br /> √ <br /> <br /> Eq.2 <br />Where, GS = Specific Gravity <br /> Gradation: using the rock size, find the <br />gradation limits using Figure 10 (TR-69). <br /> Thickness: two times the D50 rock size. <br /> <br />According to the hazard category of the dam a safety <br />factor can also be applied to the calculated D50 rock <br />size and this is described in “Slope Protection for Dams <br />and Lakeshores” (USDA 1989). Alternative methods for <br />determining riprap size, thickness, and gradation are <br />described in Chapter 7 of “Embankment Dams” (USBR <br />1992). <br />Generally riprap should be hard, dense angular stone, <br />graded as designed, comprising sound fragments <br />resistant to abrasion and weathering and be free of <br />cracks, seams, clay, organic material and other defects. <br />Rounded boulders or cobbles are not generally <br />acceptable as riprap. <br />Determine Rock Weight <br />Determine Type and Size of Riprap <br />Dumped Hand-Placed <br />Determine Gradation and Thickness of Riprap <br />and/or Bedding and/or Filter <br />Determine Limit of Riprap Protection