Closed-form expressions for a rigid passive pile in a two-layered soil

This study analyses a single unrestrained rigid passive pile embedded in a soil profile consisting of an unstable layer overlying a stable one. The paper focuses on the evaluation of pile response when in the unstable layer the ultimate pressure, which is assumed to increase linearly with depth, is fully mobilised in the direction of the soil movement (i.e. flow mode). The portion of the pile below the sliding surface is analysed by an elastic−plastic model using the Winkler approach assuming the horizontal subgrade reaction and soil resistance as constant with depth. For a given depth of the sliding surface three distinct mechanisms of pile response are identified; the occurrence of a particular failure mode is controlled by the pile embedment in the stable layer and the distribution of horizontal soil resistance with depth. For each failure mechanism a set of analytical expressions is derived to calculate the pile head deflection, pile rotation, maximum bending moment and soil movement required to generate the flow mode. A numerical example is presented to illustrate the application of the proposed procedure.