Extension of Mononobe–Okabe approach to unstable slopes

The resultant force of lateral earth pressure is commonly used in the design of nearly vertical walls while flatter slopes are designed to be internally stable using a factor of safety approach. An unstable slope is considered to have an unsatisfactory factor of safety unless supported by internal and/or external measures. However, from an analytical viewpoint, the distinction between walls and unstable slopes is unnecessary. Using a limit equilibrium analysis combined with a log spiral surface, a previous formulation is extended to deal with the pseudostatic instability of simple, homogeneous, cohesionless slopes. Hence, the original approach by Mononobe–Okabe (M–O) is extended to yield the resultant lateral force needed to stabilize an unstable slope. Given the slope angle, the design internal angle of friction, the backslope, the surcharge, the vertical and horizontal seismic coefficients, and the inclination of the resultant force, one can calculate the magnitude of this resultant force. The approach allows for the selection of a rational inclination of the resultant for cases where soil-face interaction is likely to develop along vertical segments only. The approach generalizes Coulomb’s (static) and M–O (pseudostatic) methods as all are in the same framework of limit equilibrium. While all methods yield identical results for vertical slopes, where the critical slip surface defining the active wedge degenerates to the same planar surface, the presented approach becomes more critical for flatter unstable slopes where the active wedge is augmented by a curved surface. Hence, the seamless extension of the M–O approach is produced.