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<br />contains no explicit attempt to account for resistive forces due to cables or rods. <br />Similarly, the additional stability which may arise from vegetative root anchorage or <br />mechanical anchoring devices, while recognized as significant, is ignored in the analysis <br />procedures for the sake of conservatism in selection and design. <br /> <br />Selection of Factor of Safety <br /> <br />The designer must determine what factor of safety should be used for a particular design. <br />Some variables which should affect the selection of the factor of safety used for final design <br />are: risks associated with a failure of the project, the uncertainty of hydraulic values used in <br />the design, and uncertainties associated with installation practices. Typically, a minimum <br />factor of safety of 1.5 is used for revetment design when the project hydraulic conditions are <br />well known and variations in the installation can be accounted for. Higher factors of safety <br />are typically used for protection at bridge piers, abutments and at channel bends due to the <br />complexity in computing shear stress at these locations. Research is being conducted to <br />determine appropriate values for factors of safety at bridge piers and abutments. <br /> <br />Stability of a single concrete block on a sloping surface <br /> <br />The stability of a single block on a sloping surface is a function of the magnitude and <br />direction of stream velocity and shear stress, the depth of flow, the angle of the inclined <br />surface on which it rests, geometric properties, and weight. Considering flow along a <br />channel bank as shown on Figure 4.2, the forces acting on a concrete block are the lift <br />force FL' the drag force Fo, and the weight of the block, W,.,. Block stability is determined by <br />evaluating the moments about the point 0 about which rotation can take place. The <br />components of forces relative to the plane of motion (assumed to act along the resultant <br />force R) are shown in Figure 4.1.c. The relationship that defines the equilibrium of the block <br />is: <br /> <br />f2 W,., cose = f1W,., sine cos~ + fsFo coso +f4FL <br /> <br />where the symbols are shown in Figure 4.1 and described below: <br /> <br />W,., = weight of the block <br />f 1 and f 2 = moment arms of the weight of the block (side slope and longitudinal slope) <br />Fo = drag force on the block <br />FL = lift force on the block <br />f sand f 4 = moment arms of the lift and drag forces on the block <br />a = side slope angle relative to the horizontal plane <br />A = angle between the horizontal and the velocity vector measured in the plane of the <br />side slope. This derivation is valid for "horizontal condition" where A = lX, where <br />lX = slope angle of a plane bed (i.e. uniform flow parallel to bed) <br />l) = angle between the drag force and particle movement direction = 90 - P - I.. <br />P = angle between the block movement direction and the vertical plane <br /> <br />The factor of safety, SF, for the block can be defined as the ratio of moments resisting <br />motion to those tending to rotate the block out of its resting position. Accordingly: <br /> <br />SF= f2W,.,COSe <br />fjW,., sine cos~ +fsFd coso + f4FL <br /> <br />(Factor of Safety) <br /> <br />4.5 <br />