Page 171 - Civil Engineering Formulas

108 CHAPTER FOUR

1000

500

Bearing capacity factor, N q 100

50

10
25° 30° 35° 40° 45° 50°
Angle of internal friction, φ
FIGURE 4.1 Bearing-capacity factor for granular soils related to angle of
internal friction.

group. The efficiency factor E is defined as the ratio of the ultimate group
g
capacity to the sum of the ultimate capacity of each pile in the group.
E is conventionally evaluated as the sum of the ultimate peripheral friction
g
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
S and number of piles n,

E g 2(BL WL) f s BW g (4.11)
nQ u
where is the average peripheral friction stress of block and Q is the single-pile
f s
u
capacity. The limited number of pile-group tests and model tests available suggest
that for cohesive soils, E 1 if S is more than 2.5 pile diameters D and for cohe-
g
sionless soils, E 1 for the smallest practical spacing. A possible exception
g
might be for very short, heavily tapered piles driven in very loose sands.
In practice, the minimum pile spacing for 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, Q from
gd
(4.12)
Q gd A F F H F PHc u
where H , , and A represent the thickness, unit weight, and area of fill con-
f
f
F
tained within the group. P, H, and c are the circumference of the group, the
u