Bearing Capacity of Footings Placed Adjacent to $c^{\prime }\text{-}{\varphi }^{\prime }$ Slopes

Conventional bearing capacity analyses for shallow foundations placed on slopes use a modified set of bearing capacity factors based on soil properties, footing geometry, and slope configuration, but are restricted to purely cohesionless or purely cohesive soils. This approach is adequate for establishing bearing capacity on engineered fills with controlled foundation properties, yet does not adequately address design for bearing capacity on soils that have both cohesion and internal frictional resistance—a common scenario for native soils. This role becomes increasingly important in design for mechanically stabilized earth walls, which are often placed on slopes of native $c^{\prime }\text{-}{\varphi }^{\prime }$ soils in which the bearing capacity can often be the critical design constraint. Prior approaches to bearing capacity on horizontal ground for $c^{\prime }\text{-}{\varphi }^{\prime }$ soils utilize principles of limited state plasticity in their formulation, yet the most commonly applied bearing capacity approaches on slopes use semiempirical formulations that employ mutually exclusive soil strength parameters. In this work, results are attained using upper-bound limit state plasticity failure discretization scheme, known as discontinuity layout optimization (DLO), which uses nonassumptive failure geometry (under translational kinematics) in its formulation. The values presented demonstrate important components in consideration of bearing capacity for strip footings placed adjacent to slopes of $c^{\prime }\text{-}{\varphi }^{\prime }$ soils, in particular, the relationship between soil strength properties, slope height to footing width ratio, slope angle, and critical collapse mechanism. A set of reduction coefficients that can be directly applied to the classical bearing capacity formulation is presented for ease of application.