EI 02C097
01 Jul 97
Chapter 4 1
load. As shown later, the computational procedure allows the
Lateral Loads
detrmination of the axial load at which the pile will buckle.
1. Description of the Problem
c. Soil representation. The soil around the pile is
replaced by a set of mechanisms indicating that the soil
a. Design philosophy. Deep foundations must often
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 = x1 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 = x2 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.
b. Cause of lateral loads. Some causes of lateral loads are
d. The p-y curve method. The p-y method is extremely
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).
2. Nonlinear Pile and p-y Model for Soil.
(1) Definition of p and y. The definition of the quantities
a. General concept. The model shown in Figure 4-1 is
p and y as used here is necessary because other approaches have
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
b. Axial load. An axial load is indicated and is considered
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.
4-1
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