load. As shown later, the computational procedure allows the

detrmination of the axial load at which the pile will buckle.

replaced by a set of mechanisms indicating that the soil

resistance *p *is a nonlinear function of pile deflection *y*. The

support substantial lateral loads as well as axial loads. While

mechanisms, and the corresponding curves that represent their

axially loaded, deep foundation elements may be adequately

behavior, are widely spaced but are considered to be very close

in the analysis. As may be seen in Figure 4-1, the *p-y *curves are

designed by simple statis methods, design methodology for lateral

fully nonlinear with respect to distance *x *along the pile and pile

loads is more complex. The solution must ensure that

deflection *y*. The curve for *x *= *x*1 is drawn to indicate that the

equilibrium and soil-structure-interation compatability are

satisfied. Nonlinear soil response complicates the solution.

pile may deflect a finite distance with no soil resistance. The

curve at *x *= *x*2 is drawn to show that the soil is deflection-

Batter piles are included in pile groups to improve the lateral

capacity when vertical piles alone are not sufficient to support the

softening. There is no reasonable limit to the variations that can

loads.

be employed in representing the response of the soil to the lateral

deflection of a pile.

wind forces on towers, buildings, bridges and large signs, the

centripetal force from vehicular traffic on curved highway

versatile and provides a practical means for design. The method

bridges, force of water flowing against the substructure of

was suggested over 30 years ago (McCelland and Focht 1958).

bridges, lateral seismic forces from earthquakes, and backfill

Two developments during the 1950's made the method possible:

loads behind walls.

the digital computer for solving the problem of the nonlinear,

fourth-order differential equation for the beam-column; and the

remote-reading strain gauge for use in obtaining soil-response

(*p-y*) curves from field experiments. The method has been used

loaded deep foundations depends on stiffness of the pile and soil,

mobilization of resistance in the surrounding soil, boundary

by the petroleum industry in the design of pile-supported

conditions (fixity at ends of deep foundation elements), and

platforms and extended to the design of onshore foundations as,

duration and frequency of loading.

for example by publications of the Federal Highway

Administration (USA) (Reese 1984).

(1) Definition of *p *and *y*. The definition of the quantities

emphasized in this document. The loading on the pile is general

been used. The sketch in Figure 4-2a shows a uniform

for the two-dimensional case (no torsion or out-of-plane

distribution of unit stresses normal to the wall of a cylindrical

bending). The horizontal lines across the pile are intended to

pile. This distribution is correct for the case of a pile that has

show that it is made up of different sections; for example, steel

been installed without bending. If the pile is caused to deflect a

distance *y *(exaggerated in the sketch for clarity), the distribution

pipe could be used with the wall thickness varied along the

length. The difference-equation method is employed for the

of unit stresses would be similar to that shown in Figure 4-2b.

solution of the beam-column equation to allow the different

The stresses would have decreased on the back side of the pile

values of bending stiffness to be addressed. Also, it is possible,

and increased on the front side. Both normal and a shearing

but not frequently necessary, to vary the bending stiffness with

stress component may developed along the perimeter of the

bending moment that is computed during interation

cross section. Integration of the unit stresses will result in the

quanity *p *which acts opposite in direction to *y*. The dimensions

of *p *are load per unit length along the pile. The definitions of *p*

and *y *that are presented are convenient in the solution of the

in the solution with respect to its effect on bending and not in

regard to computing the required length to support a given axial

differential equation and are consistent with the quantities used

in the solution of the ordinary beam equation.

1

(2) Nature of soil response. The manner in which the soil

Portions of this chapter were abstracted from the writings

responds to the lateral deflection of a pile can be examined by

of Dr. L. C. Reese and his colleagues, with the permission

examined by considering the pipe pile shown

of Dr. Reese.

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