Page 176 - Civil Engineering Formulas

PILES AND PILING FORMULAS 113

These include elastic, semiempirical elastic, and load-transfer solutions for
single shafts drilled in cohesive or cohesionless soils.
Resistance to tensile and lateral loads by straight-shaft drilled shafts should
be evaluated as described for pile foundations. For relatively rigid shafts with
characteristic length T greater than 3, there is evidence that bells increase the
lateral resistance. The added ultimate resistance to uplift of a belled shaft Q ut
can be approximately evaluated for cohesive soils models for bearing capacity
[Eq. (4.14)] and friction cylinder [Eq. (4.15)] as a function of the shaft diameter
D and bell diameter D .*
b
For the bearing-capacity solution,

2
2
Q ul (D b D )N c c u W p (4.21)
4
The shear-strength reduction factor in Eq. (4.14) considers disturbance
1 3
effects and ranges from 2 (slurry construction) to 4 (dry construction). The c u
represents the undrained shear strength of the soil just above the bell surface,
and N is a bearing-capacity factor.
c
The failure surface of the friction cylinder model is conservatively assumed
to be vertical, starting from the base of the bell. Q can then be determined for
ut
both cohesive and cohesionless soils from
(4.22)
Q ul
b Lf ut W s W p
where f is the average ultimate skin-friction stress in tension developed on the
ut
failure plane; that is, f 0.8c for clays or K vo tan for sands. W and W
ut u s p
represent the weight of soil contained within the failure plane and the shaft
weight, respectively.

SHAFT RESISTANCE IN COHESIONLESS SOILS

is a function of the soil-shaft friction angle ,
The shaft resistance stress f s
degree, and an empirical lateral earth-pressure coefficient K:
(4.23)
f s K vo tan f l
At displacement-pile penetrations of 10 to 20 pile diameters (loose to dense
sand), the average skin friction reaches a limiting value f . Primarily depending
l
on the relative density and texture of the soil, f has been approximated conser-
l
vatively by using Eq. (4.16) to calculate . f s
For relatively long piles in sand, K is typically taken in the range of 0.7 to
1.0 and is taken to be about 5, where is the angle of internal friction,
*Meyerhof, G. G. and Adams, J. I., “The Ultimate Uplift Capacity of Foundations,” Canadian
Geotechnical Journal, 5(4):1968.