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<br />Hydraulic Design Example (Factor of Safety Method) <br /> <br />The following example illustrates the use of the factor of safety method in the selection of <br />block sizes for ACB's for revetment or bed armor. Two generic block sizes are used to <br />illustrate the use of design charts and the factor of safety equations. A design example <br />using design charts similar to those which would be provided by a block manufacturer is <br />presented and a design example using the factor of safety equations, directly, are <br />presented. The examples assume that hydraulic testing has been performed for the block <br />system to quantify a critical shear stress and to develop the design charts. <br /> <br />Given: <br /> <br />A trapezoidal channel with a bed slope of 0.039 mlm, side slopes 1V:2.5H, and the following <br />hydraulic conditions: <br /> <br />Block Size 1 Block Size 2 <br />n = 0.032 n = 0.026 <br />Depth = 616 mm Depth = 549 mm <br />Velocity = 3.78 mls Velocity = 4.36 mls <br />Hyd. Radius = 475 mm Hyd. Radius = 433 mm <br />Bed Shear, 'to = 235.2 Pa Bed Shear, 'to = 209.8 Pa <br /> <br />Block Size 1 has a greater open area and therefore yields a higher Manning's n value. <br /> <br />Design Chart Example <br /> <br />Design charts can be developed from the factor of safety method given block properties and <br />hydraulic test results. These are normally developed by the ACB manufacturer for use by <br />the design engineer. Typically these curves relate the allowable shear stress or velocity to <br />channel bed slope for a given factor of safety as shown in Figure 4.4. This chart represents <br />the stability of the ACB's placed flat on the channel bed neglecting the influence of the side <br />slope. Charts which account for the effect of channel side slope on the factor of safety are <br />also provided by the manufacturer (see Figure 4.5). The factor of safety can then be <br />computed by taking the ratio of the allowable shear stress or velocity to the design <br />conditions as follows: <br /> <br />SF=~(SF.)K, or <br />'to <br /> <br />SF = Va (SFa) K1 <br />Vo <br /> <br />where: <br /> <br />1:a and V. = the allowable shear stress and velocity for the factor of safety for which the chart <br />was developed (SF.). 1:a and V. are synonymous to critical shear stress and velocity for a <br />factor of safety of one. <br /> <br />1:0 and V 0 = the design shear stress and velocity. <br /> <br />K, = side slope correction factor. <br /> <br />4.9 <br />