Use of Cycloidal Arcs for Estimating Ditch Safety

A method of analysis is presented for estimating the factor of safety of ditches and similar excavations taking into account the unit weight and shearing strength of the soil. The method is based on the theory that the shear failure, if it occurs, will occur along a surface which is cycloidal in shape. Equations for shear stress and strength are derived from Coulomb's shear strength equation and the equation for safety factor developed and results presented in tabular form. For cases where a soil will not stand vertically and must be sloped, a definition for critical slope is presented and the equation to determine critical slope is derived and presented in tabular form.