Design of pile groups - Piling Engineering - page 208

while the proportion of load carried by the raft, P r and the pile group, P p is given by

k r 1 − α rp

P r
P r +

k r 1 α rp

P p =

(5.28)

k p + − 2

The stiffnesses of the pile cap and pile group may be evaluated conventionally,
while the interaction factor, α rp , may be obtained from the approximate expression

(Randolph, 1983)

ln 2 r m / d r ln d r / d

ln 2 r m / d =

α rp = 1 − (5.29)

ζ

where r m is the radius of influence of the piles (see section 4.2.1) and d r is the effective
diameter of the element of raft associated with each pile. This may be calculated so
that, for a group of n piles, n d r /

4 equals the actual area of the raft. More rigorous
analyses reported by Clancy and Randolph (1993) show that, as the pile group size
increases, the value of

π

α rp tends towards a constant value of about 0.8.
Figure 5.22 shows how the stiffness of a single pile under vertical load is increased
by the presence of a pile cap in contact with the ground. The approximate method
outlined here is compared with results from Poulos and Davis (1980) and shows good
agreement. The results show that a small pile cap ( d r /

4) has very little effect on
the stiffness of the foundation, although a significant proportion of the overall load
may be carried by the pile cap (see Figure 5.23). Comparison of the approximate
analysis with a more rigorous numerical analysis for the case of a 5

d ≤

× 5 pile group

Figure 5.22 Effect of pile cap on single pile stiffness.