Abstract
The upper bound theorem of the generalized theory of perfect plasticity has been employed to estimate the stability of a vertical cut with a variable corner angle; the driving forces are the self-weight of the soil comprising the back-slope and a concentrated surcharge load that acts in the vertical plane of symmetry of the cut. The solution is based on a three-dimensional collapse mechanism in which the failure plane is allowed to pass through or above the toe of the cut, and results involving the functional relationship between the critical surcharge load and a normalized distance are presented graphically in dimensionless form. Both the internal angle of friction of the soil and the normalized height of the cut are treated as parametric quantities. The critical surcharge load was found to vary nonlinearly with respect to normalized distance from the corner, the friction angle, and the normalized height of the cut.
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