Upper bound limit analysis of soils with a non-linear failure criterion

Limit analysis is a widely used technique for the analysis of geotechnical collapse states and there exists a significant body of literature covering its application to soils with a linear failure criterion. However, such a failure criterion is often an idealisation of an actual non-linear response for which available analytical techniques are limited. This paper presents a new fully general solution procedure for generating upper bound multi-wedge rigid block mechanisms for a soil with a non-linear failure criterion, utilising a curved interface that obeys the non-linear yield function flow rule along its full length. This work extends the long established kinematic sliding wedge approach for linear soils and is illustrated through application to active and passive retaining wall and anchor/trapdoor problems. Through additional consideration of the lower bound solution, close bounds on the retaining wall problem to within ~1% are established. The ability of the non-linear upper bound solution to predict the shear and normal stress at every point along the failure surface is discussed.