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DESIGN MANUAL& KEYWALL OPERATING GUIDECOULOMB EARTH PRESSURE EQUATIONThe active earth pressure coefficient, k a , is determined from an evaluation of the Coulomb wedge geometryshown in Figure 3:2 and results in the following k a coefficient:Equation (3c) k a =sin² (α + φ)⎡⎢⎣sin² α sin (α − δ) 1 +sin(φ + δ) sin(φ – β) ⎤²√ sin(α – δ) sin(α + β) ⎦ ⎢where:α = angle of batter from horizontalφ = angle of internal friction of soilβ = slope angle above wallδ = angle of friction at back of wallThis equation is found in differing forms in other texts due to the trigonometric assumptions made in theformula derivation. The derivation of this Coulomb formula can be found in geotechnical textbooks such asFoundation Analysis and Design by Bowles (1996).βWHδPaφRαρFigure 3:2 Coulomb Wedge Diagram3.5