Calculations to determine the ultimate resistance per unit depth of the pile shaft at a given
depth xare obtained by using the angle of shearing resistance and density of the sand as
determined by field or laboratory tests. The procedure for obtaining the shape of the curve,
and the trial and adjustment process using various assumed values of the coefficient of
subgrade modulus variation nhto obtain the stiffness factor Tare more complex than those
described above for piles in normally consolidated clays. The reader is referred to the rec-
ommendations of the American Petroleum Institute(4.31)and reference 6.18 for guidance.
It will be evident from the foregoing account of the construction and use of p–ycurves for
laterally loaded piles in clays and sands that the procedure using longhand methods is
extremely time-consuming (see Worked Example 8.2). However, computer programs have
been established from which the required data on pile deflections, bending moments and soil
resistances can be readily determined. The programs can deal with cyclic loading and prede-
termined variations in pile width or wall thickness over the depth of the shaft. A widely used
program Lpile plus(6.19)was developed by the work of Reese and others at the University of
Texas at Austin, and the ALP program(6.20)is available from OASYS Limited.
The use of p–ycurves as described above is strictly applicable to piles in soils having a
linearly increasing modulus (i.e. coarse soils and normally consolidated clays). In the case
of stiff clays having a constant modulus of subgrade reaction k 1 equation 6.36 can be used to
obtain values of Ncabove the critical depth. The latter can be calculated from equation 6.37
using a value of 0.25 for coefficient J. Values of nhare obtained by plotting the soil modulus
Esagainst the depth, but the trial line is a vertical one passing through the plotted points,
again with weight being given to depths of 0.5Ror less. Cyclic loading can be a critical
factor in stiff clays. The relationship in equation 6.40 should preferably be established for
the particular site by laboratory and field tests, but the factor of 0.72 may be used if results
of such studies are not available.
Instead of relating the deflection ycto the strain ‡cat a stress corresponding to the maxi-
mum stress obtained in the laboratory stress–strain curve for use in equation 6.38, Reese and
Welch(6.18)adopted the following relationship for stiff clays:
(6.41)
where pand puare as previously defined, and y 50 is the deflection corresponding to the strain
‡ 50 at one-half of the maximum principal stress difference in the laboratory stress–strain
curve.
If no value of ‡ 50 is available from laboratory tests a figure of between 0.005 and 0.010
can be used in equation 6.39 but substituting y 50 for ycand ‡ 50 for ‡c. The larger of these two
values is the more conservative. Reese and Welch(6.18)have described a method for
establishing p–ycurves for cyclic loading on piles in stiff clay.
6.3.6 Effect of method of pile installation on behaviour under
lateral loads and moments applied to pile head
The method of installing a pile, whether driven, driven-and-cast-in-situ or bored and cast-
in-situ, has not been considered in Sections 6.3.1 to 6.3.4. The effect of the installation
method on the behaviour under lateral load, can be allowed for by appropriate adjustments
to the soil parameters. For example, when considering the resistance to lateral loads, of piles
p
pu^ 0.54 y
y 50Piles to resist uplift and lateral loading 345