Elastic–Plastic Analysis of Rigid Passive Piles in Two-Layered Soils

Abstract

The paper analyses the behavior of a rigid passive pile embedded in a soil profile consisting of a stable layer underlying an unstable layer subjected to a uniform soil displacement. Pile-soil interaction is considered by modeling the soil by a series of elastic–plastic springs along the pile shaft. The modulus of horizontal subgrade reaction is assumed to linearly increase with depth in the unstable layer and constant in the stable one. The ultimate soil resistance is assumed increasing with depth in both layers. The results of analysis are presented in dimensionless form in terms of shear force developed at the slip surface as a function of the pile embedment into the stable layer and the distribution of soil characteristics over depth. The method allows capturing pile response not only at the soil ultimate state but also at the intermediate states. Specifically, the governing equations for the elastic, elastic–plastic and plastic cases are discussed and, whenever possible, a set of closed-form expressions is provided to estimate the maximum bending moment along the shaft and the pile head deflection, so that for an assigned value of the required stabilizing force both ultimate and serviceability limit state of the pile can be checked. A numerical example is given to illustrate the application of the proposed procedure.

Practical Considerations in the Design of Passive Free Piles in Sliding Soil

“…For this purpose, the design approach is simplified in three main steps: This procedure refers to the ultimate state only and gives no indication on pile response prior to the ultimate state, nor on displacements required to achieve the ultimate state. To overcome this limitation, a model of rigid passive piles was proposed, embedded in a landslide with both subgrade reaction modulus and strength linearly increasing with depth [16,17]. In addition, a model of flexible piles embedded in cohesive layered soils was proposed, where both the subgrade reaction modulus and the strength are constant with depth [18].…”