Nonlinear Bending of Deep Foundation Piles
Authors: Bogard D. 
Published: October 2008

Abstract
Freeport McMoRan Resource Partners are planning to construct a number of offshore platforms for the purpose of extracting sulphur from a large deposit discovered in Block 299 of the Main Pass Area of the Gulf of Mexico.
Subsidence and lateral spreading of the near-surface sediments are expected to accompany the removal of the sulphur. As the soil moves laterally, the foundation piles will generally conform closely with the displaced shape of the soil, particularly in deep layers of sand. At some locations, the differential movement of sand layers separated by weaker clay layers produces very severe bending deformations in the piles.
The unique design problem for the Main Pass 299 platform foundations was not related to satisfying conventional safety factors, but rather, was concerned with selecting cross-sections which, although strained plastically, will remain in equilibrium with the imposed soil motions while retaining structural integrity.

Introduction
The predicted patterns of deformation of the near-surface soils accompanying the subsidence of the seafloor during extraction of the sulphur at the Main Pass 299 mine sites subject the foundation piles to lateral deflections and rotations which are of sufficient magnitude to yield the piles in bending.
The vertical soil settlements produce both uplift and downdrag forces on the piles, resulting in both tensile and compressive axiaI stresses.
While the magnitudes of the lateral loads generated by the subsiding soils are sufficiently large to deform the piles beyond yield, the available resisting forces are also large enough to prevent the piles from deflecting further under environmental loads. The design problems are thus not associated with instability and collapse, but are directed toward selecting material roper-ties and cross-sections which will tolerate the bending deformations with the plastic strains remaining at acceptable levels.
Conventional safety factors were not felt to be appropriate to the design of the pile foundations. For the deep-seated sod movements, which are generally greater than 150 ft below the seafloor, collapse of the Piling could not occur, since the piles are restrained b the stiff soils. With no physical mechanism for collapse, the design guidelines which were developed were based on estimates of the magnitudes of allowable strain, below which the piles can be expected to retain structural integrity, without buckling or fracture of the cross-section.
The limiting strain levels were selected after solving for the behavior of tubular cross sections in bending using the ABAQUS computer program. Once the tolerable strain levels had been established, the lateral load behavior of the piles was investigated using a much simpler program.
A computer program for the solution of nonlinear bending of beams using a discrete-element model was developed at the University of Texas at Austin in the late 1960's under the direction of Prof. Hudson Matlock. The computer program includes both axial and lateral solutions, each with nonlinear support capability. The axial thrust is transferred to the lateral solution to consider the p-delta effects on elastic bending.