Pile Design and Construction Practice, Fifth edition

Methods of drawing sets of p–y curves have been established for soils which have a
linearly increasing modulus, that is, soft to firm normally consolidated clays and coarse
soils. Empirical factors were obtained by applying lateral loads to steel tubular piles driven
into soft to firm clays and sands. The piles were instrumented to obtain soil reactions and
deflections over their full embedded depth.
The method of establishing p–y curves for soft to firm clays is described by Matlock (6.17) .
The first step is to calculate the ultimate resistance of the clay to lateral loading. Matlock’s
method is similar in concept to those described in Section 6.3.1. but the bearing-capacity
factor N c is obtained on a somewhat different basis.
Below a critical depth x r the coefficient is taken conventionally as 9 as in Section 6.3.1.
Above this depth it is given by the equation:
N c � 3 � �x
c u � Jx
B
(6.36)
where � is the density of the overburden soil, x is the depth below ground level, c u is the
undrained cohesion value of the clay, J is an empirical factor, and B is the width of the pile.
The experimental work of Matlock yielded values of J of from 0.5 for a soft clay to 0.25
for a stiffer clay. The critical depth is given by the equation:
x r � 6B
�B
c u � J
(6.37)
The ultimate resistance above and below the critical depth is expressed in the p–y curves as
a force p u per unit length of pile, where p u is given by the pile width multiplied by the
undrained shear strength c u and a bearing capacity factor N c, usually taken as 9.
Up to the point a in Figure 6.32 the shape of the p–y curve is derived from that of the
stress/strain curve obtained by testing a soil specimen in undrained triaxial compression, or
from the load/settlement curve in a plate loading test (Figure 5.15). The shape of the curve
is defined by the equation:
p
p � 0.5� u 3 y
yc p
p a 5p u
p b 50.72p u
b
y53y c
a
y58y c
Curve defined by :
x50
Piles to resist uplift and lateral loading 343
5 0.5 3 p /pu y /yc
Ultimate resistance for static loading
x ≥ x r
Ultimate resistance for cyclic loading
x < xr y515y c
p5p b ×
Figure 6.32 Determining shape of p–y curve in soft to firm clay (after Matlock (6.17) ).
x
xr y
(6.38)