Analysis of Laterally Loaded Piles in Sand
Authors: Reese Lymon C. , Cox William R. , Koop Francis D. 
Published: October 2008

Abstract
Data were taken during the lateral loading of two 24-in. diameter test piles installed at a site where the soils consisted of clean fine sand to silty fine sand. Two types of loading were employed, static loading and cyclic loading. The data were analyzed and families of curves were developed which showed the soil resistance p as a function of pile deflection y.
With theoretical studies as a basis, a method was devised for predicting the family of p-y curves based on the properties of sand and pile dimension. Procedures are suggested or both static loading and cyclic loading. While there is some basis for the methods from theory, the behavior of sand around a laterally loaded pile does not yield to a completely rational analysis; therefore, a considerable amount of empiricism is involved in the recommendations.
The procedure was employed for predicting p-y curves at the experimental sire and computed results are compared with experimental results. The agreement is good.

Foreword
This paper is a companion to the paper entitled, "Field Testing of Laterally Loaded Piles in Sand," by William R. Cox, Lymon C. Reese and Berry R. Grubbs. The research described in fund set up by the following oil companies: Amoco Production Company, Chevron Oil Field Research, Esso Production Research Company, Mobil Oil Corporation, and Shell Development Company. Shell Development Company was the operator of the project.

Introduction
There are a relatively small number of papers in the technical literature which give recommendations for predicting the behavior of the soil around the piles subjected to lateral loading. With regard to sand, such recommendations are made in two papers, Terzaghi1 and Parker and Reese.2 Terzaghi presents no experimental evidence for the parameters which he recommends; the paper by Parker and Reese is based on lateral load tests of small diameter piles. The method presented below is based on the results of full-scale tests of instrumented piles and should be a useful addition to the literature.
The differential equation, Eq.1, for the problem of the laterally loaded pile is well known and its solution has been discussed by a number of authors. 3,4,5,6,7
(Mathematical Equation Available in Full Paper)
It should be noted that Eq. 1 does not include a term to account for the effect of axial load on bending. If the axial load is sizable, Eq. 1 should be expanded.
As indicated in the referenced papers, appropriate solutions can sometimes be obtained by the use of non-dimensional relationships. A more favorable approach is to write the differential equation in difference form and to obtain solutions by use of the digital computer.
In the solution of the differential equation, appropriate boundary conditions must be selected at the top of the pile to insure that the equations of equilibrium and of compatibility are satisfied at the interface between the pile and the superstructure. The selection of the boundary conditions is a simple problem in some instances; for examples, where the superstructure is simply a continuation of the pile.