An improved 3D embedded beam element with explicit interaction surface

Abstract

Numerical modelling of pile foundations can be done in several ways. In commercial finite element packages two main options are available; using volume elements with interface elements between the pile and soil domains and the embedded beam approach. The embedded beam element was first proposed by Sadek and Shahrour (2004) and considers a beam element that can cross a solid element at any arbitrary location with any arbitrary inclination. This has several advantages to the volume pile method, such as the need for fewer elements and the mesh uncoupling of the pile and soil, which make this method much more efficient and leads to a significant reduction in calculation time. However, the embedded beam element also deals with a number of limitations and drawbacks. This research focuses on overcoming the mesh sensitivity, which is caused by the stress singularity that is introduced in the soil by the beam element. Also, the inability to take into account the pile surface will be resolved, aiming to improve the lateral pile-soil interaction.

The idea of Turello et al. (2016) of an embedded beam element with explicit interaction surface is extended and generalised leading to a new embedded beam formulation. In the proposed model the beam displacements at the interaction surface are obtained by a mapping scheme that takes into account Timoshenko beam theory and which is generalised to model inclined piles as well. A constitutive equation that describes the relation between the interface stresses and relative displacements between the pile and soil is defined along the shaft and at the foot of the pile. Along the shaft of the pile a shear stress limit is defined based on the Mohr-Coulomb failure criterion in order to incorporate plasticity in lateral direction. Furthermore, a more practical and efficient assembly procedure is proposed.

Validation of the proposed method proofs that the proposed model leads to a significant mesh sensitivity reduction in case of axially loaded models compared to the existing implementation. The overall response of laterally loaded piles is improved considerably as well. However, the proposed method is still unable to capture lateral interface behaviour in order to model soil slippage around the pile. Furthermore, it is recommended to formulate a generally applicable foot interface stiffness and to optimise the code in order to reduce the computation time. The description of the interaction surface opens up many new possibilities for future research, such as modelling the true cross-section shape.