CIVIL ENGINEERING FORMULAS

108 CHAPTER FOUR

group. The efficiency factorEgis defined as the ratio of the ultimate group
capacity to the sum of the ultimate capacity of each pile in the group.
Egis conventionally evaluated as the sum of the ultimate peripheral friction
resistance and end-bearing capacities of a block of soil with breadth B, width
W, and length L, approximately that of the pile group. For a given pile, spacing
Sand number of piles n,

(4.11)

where is the average peripheral friction stress of block and Quis the single-pile
capacity. The limited number of pile-group tests and model tests available suggest
that for cohesive soils, Eg 1 if Sis more than 2.5 pile diameters Dand for cohe-
sionless soils, Eg 1 for the smallest practical spacing. A possible exception
might be for very short, heavily tapered piles driven in very loose sands.
In practice, the minimum pile spacingfor conventional piles is in the range
of 2.5 to 3.0D. A larger spacing is typically applied for expanded-base piles.
A very approximate method of pile-group analysis calculates the upper limit
of group drag load, Qgdfrom

(4.12)

whereHf,f,andAFrepresent the thickness, unit weight, and area of fill con-
tained within the group. P,H, and cuare the circumference of the group, the

QgdAFFHFPHcu

fs

Eg

2(BLWL)fsBWg

nQu

35° 40° 45° 50°

Angle of internal friction, φ

25° 30°

10

50

100

Bearing capacity factor,

N

q

500

1000

FIGURE 4.1 Bearing-capacity factor for granular soils related to angle of

internal friction.