Geotechnical Engineering

DHARM

PILE FOUNDATIONS 681

or a block. The limiting value of the spacing for which the group capacities obtained from the

two criteria—block failure and individual pile failure—are equal is usually considered to be

about 3 pile-diameters.

Negative skin friction Qng may be computed for a group in cohesive soils as follows:

Individual pile action:

Qng = nQnf = nP. Dn. c ...(Eq. 16.42)

Notations are the same as for Eq. 16.39.

Block action:

Qng = c. Dn. Pg + γ. Dn. Ag ...(Eq. 16.43)

Here, Pg and Ag are the perimeter and area of the pile block.

[Pg = 4B and Ag = B^2 , where B is the overall width of the block].

The larger of the two values for Qng is chosen as the negative skin friction.

16.6.3 Pile Group Efficiency
The ‘efficiency’, ηg, of a pile group is defined as the ratio of the group capacity, Qg, to the sum
of the capacities of the number of piles, n, in the group:

ηg =

Q

nQ Q

g

(. ) ( )ppor Σ

...(Eq. 16.44)

where Qp = capacity of individual pile.

Obviously, the group efficiency depends upon parameters such as the types of soil in

which the piles are embedded and on which they rest, method of installation, and spacing of

piles.

Vesic (1967) has shown that end-bearing resistance is virtually unaffected by group

action. However, skin friction resistance increases with increase in spacing for pile groups in

sands. For pile groups in clay, the skin friction component of the resistance decreases for

certain pile spacings. Thus, in general, efficiencies of pile groups in clay tend to be less than

unity. Interestingly, Vesic’s experimental investigations on pile groups in sands indicate group

efficiencies greater than unity.

Sowers et al. (1961) have shown that the optimum spacing at which the group efficiency

is unity for long friction piles in clay is given by

So = 1.1 + 0.4n0.4 ...(Eq. 16.45)

where So = optimum spacing in terms of pile diameters; So is 2 to 3 pile diameters centre to

centre,

and n = number of piles in the group.

The actual efficiency, ηg, at the theoretical optimum spacing is

ηg = 0.5 +

04

09 0.1

.

(.)n−

...(Eq. 16.46)

This has been found to be 0.85 to 0.90, rather than unity. Since a factor of safety is used

for design, the error in assuming the real efficiency to be 1 at optimum spacing is inconsequential.

A number of empirical equations for pile group efficiency are available. There is no

acceptable formula and these should be used with caution as they may be no better than a good