The elastic deflections of piles in layered soils, each soil layer having its individual
constant modulus, have been analysed by Davisson and Gill(6.15)who have produced design
charts for this condition.
6.3.5 The use of p–y curves
The analytical methods of Reese and Matlock(6.14)and Davisson and Gill(6.15)that are
described in the previous section are applicable only to the deflections of piles which are within
the range of the elastic compression of the soil caused by the lateral loading on the piles.
However, these analytical methods can be extended beyond the elastic range to analyse
movements where the soil yields plastically up to and beyond the stage of shear failure. This
can be done by employing the artifice of ‘p–y’curves, which represent the deformation of
the soil at any given depth below the soil surface for a range of horizontally applied pres-
sures from zero to the stage of yielding of the soil in ultimate shear, when the deformation
increases without any further increase of load. The p–ycurves are independent of the shape
and stiffness of the pile and represent the deformation of a discrete vertical area of soil that
is unaffected by loading above and below it.
The form of a p–ycurve is shown in Figure 6.31a. The individual curves may be plotted on a
common pair of axes to give a family of curves for the selected depths below the soil surface,
as shown in Figure 6.31b. Thus for the deformed shape of the pile (and also the induced
bending moments and shearing forces) to be predicted correctly using the elastic analytical
method described above, the deflections resulting from these analyses must be compatible with
those obtained by the p–ycurves for the given soil conditions. The deflections obtained by the
initial elastic analysis are based on an assumed modulus of subgrade variation nhand this must
be compared with the modulus obtained from the pressures corresponding to these deflections,
as obtained from the p–ycurve for each particular depth analysed. If the soil moduli, expressed
in terms of the stiffness factor T, do not correspond, the stiffness factor must be modified by
making an appropriate adjustment to the soil modulus Esand from this to a new value of nh
and hence to the new stiffness factor T. The deflections are then recalculated from the Reese
and Matlock curves, and the corresponding pressures again obtained from the p–ycurves. This
procedure results in a new value of the soil modulus which is again compared with the second
trial value, and the process repeated until reasonable agreement is obtained.
342 Piles to resist uplift and lateral loading
P(a) (b)xy
yyyx=x (^4) y
x=x 3
x=x 2
x 5
x 4
x 3
x 2
x 1
Pile deflection Y
Soil resistance
P
x=x 1
Figure 6.31 p–ycurves for laterally loaded piles (a) Shape of curves at various depths xbelow soil
surface (b) Curves plotted on common axes.