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.. I I I I I I I , I I I I I I I I I I I I Hydrostatic forces (F u & F d) on the monolith consist of the static head of the water on the surface, or the pressure due to the depth. Water flowing around an obstruction will first rise up immediately in front of the object as velocity head is converted into potential energy. It then accelerates around the obstruction, lowering the water surface on the other side. This creates a static head differential with a resultant hydrostatic force in the direction of the flows (Reference 5). This differential varies as a function of velocity and flow regime, and generally creates a small resultant which is considered nivial for the purposes of this analysis and therefore ignored. Base Analysis While the average individual subjected to average conditions during a flood event is very difficult to quantify, a "base configuration" was assumed as part of this analysis for purposes of comparison (Figure 5). This base configuration consists of a 120 pound monolith, one foot wide across the face and 1/2 foot thick with a coefficient of drag of 1.0. This monolith was assumed to be resting on a horizontal surface with a coefficient offriction of 0.5, and a safety factor of 1.5 d was used to reflect uncertainty. Slippage The horizontal stability of the monolith is based upon the point at which the force of the oncoming water exceeds the force of friction exerted by its contact with an assumed horizontal surface (Figure 4). Summing forces in the horizontal direction: ~ 1:Fh = Ff - P 0.5 It B p Figure 4 Setting this equation equal to zero and solving for f-- 1/2 Thickness velocity at an appropriate range of depths under the base conditions produces a curve which shows the hazard due to slippage (Figure 6). Each data point on this curve represents a combination of depth and velocity which produces a hydraulic force exactly balancing the horizontal stability of the design monolith due to friction. For example, at a depth of 2 feet, a velocity of 3.15 feet per d second (fps) produces a force exactly equal to, but l in the opposite direction of the force available to the design monolith in the fonn of friction (Figure 6, Table I). Note that at a depth of 2 feet, a velocity greater than 3.15 fps produces a force Ff greater than the available friction force and slippage occurs. Likewise, at a velocity of 3.15 fps, a depth greater than 2 feet reduces the available frictional force because of the effect of buoyancy also resulting in slippage. Using this line of reasoning the region above the curve represents hazardous conditions, while the area below the curve represents less hazardous conditions. -..=- Point "0" w Figure 5 -7-