The limitation of closed form solutions, such as the Coulomb and Rankine equations, is that only simple level and infi nite sloping surcharges with uniform loadings can be analyzed. It is necessary to look at a “trial wedge” method or “approximation” method when attempting to analyze broken back slopes or other slope/load combinations. AASHTO and NCMA suggest an approximation method for broken-back slope conditions that defines equivalent design slopes for the external analysis. However, the internal analysis is not well defi ned for unusual slopes and loading conditions and the designer is expected to use engineering judgement with the simplifi ed methods. The KeyWall program uses a “trial wedge” analysis for determining the internal and external forces in order to provide the “correct” results for more complicated design geometries. The “trial wedge” calculation is an iterative process that determines the loading at successive failure plane orientations until a maximum loading is determined for the geometry and surcharge loading. The KeyWall “trial wedge” analysis used is consistent with the fundamental assumptions of the applicable Coulomb and Rankine theoriesby setting δ = β. “Trial wedge” results match the equation solutions for the level and infinite slope conditions, but will determine the “correct” internal and external values for broken back slope conditions and offset live and dead loads. This method of analysis permits the designer to properly model many typical design conditions and not overly simplify the analysis due to limitations of equation solutions and other design software.
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