Most (maybe all) the references I've seen for design of cantilevered retaining walls show the stabilizing effect of the weight of soil behind the wall based on a straight vertical extrusion of the heel width. E.g., if the heel width is 4 feet, the stabilizing weight of soil behind the wall is 4' x (wall height) x (soil unit weight). But the "failure plane" of the wedge of soil behind the wall, which is driving the overturning effect, is basically projected at some diagonal angle from the end of the heel (e.g., an angle alpha from the horizontal, where alpha = 45 + phi/2, projected from the end of the heel). My question is, if the active soil pressure is defined by this soil wedge, why wouldn't the stabilizing weight of soil also be derived from this wedge-shaped (and larger) geometry, rather than the straight vertical extrusion above the heel? It seems like the straight vertical extrusion significantly underestimates the potential stabilizing weight of soil behind the wall.
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