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PART THREERetaining Wall Design TheoryCOULOMB EARTH PRESSURE THEORYThe reader should note that for horizontal surfaces (level surcharge) or infinite sloping surfaces (extendingbeyond the theoretical Coulomb failure plane), a closed-form equation solution is applicable and easilyderived. For geometries where the slope changes within the zone of failure (broken back slope), the simpleequations are no longer applicable and may be unnecessarily conservative. For example, if a short brokenback slope is modeled as an infinite slope, the design may require significantly more reinforcement andexcavation than if modeled correctly. For these conditions, the trial wedge method is used in the analysis.This is an iterative trial wedge process where successive failure surfaces are modeled until a maximumearth pressure force is calculated for the geometry and loading given (See Figure 3:4).The earth pressure behind the wall face or at the back of the reinforced zone is represented by a triangularpressure distribution for active soil pressure and a rectangular distribution for uniform surcharge pressureas is shown in Figure 3:1.qP qHP aH/2H/3Figure 3:1 Earth Pressure DiagramCOULOMB EARTH PRESSURE EQUATIONThe appropriate Coulomb earth pressure equations for earth and surcharge pressure are as follows:Equation (3a) P a = ½ γ H²k aEquation (3b) P q = qHk awhere:k a = coefficient of active earth pressureγ = moist unit weight of the soilH = total design height of the wallq = uniform surcharge3.4