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 Tgreater than 3, there is evidence that bells increase the
lateral resistance. The added ultimate resistance to uplift of a belled shaft Qut
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
Dand bell diameter Db.*
For the bearing-capacity solution,

(4.21)

The shear-strength reduction factor in Eq. (4.14) considers disturbance
effects and ranges from (slurry construction) to (dry construction). The cu
represents the undrained shear strength of the soil just above the bell surface,
andNcis a bearing-capacity factor.
The failure surface of the friction cylinder model is conservatively assumed
to be vertical, starting from the base of the bell. Qutcan then be determined for
both cohesive and cohesionless soils from

(4.22)

wherefutis the average ultimate skin-friction stress in tension developed on the
failure plane; that is, fut0.8ufor clays or tan for sands. WsandWp
represent the weight of soil contained within the failure plane and the shaft
weight, respectively.

SHAFT RESISTANCE IN COHESIONLESS SOILS

The shaft resistance stress is a function of the soil-shaft friction angle ,
degree, and an empirical lateral earth-pressure coefficient K:

(4.23)

At displacement-pile penetrations of 10 to 20 pile diameters (loose to dense
sand), the average skin friction reaches a limiting value fl. Primarily depending
on the relative density and texture of the soil, flhas been approximated conser-
vatively by using Eq. (4.16) to calculate.
For relatively long piles in sand, Kis 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,

fs

fsKvo tan fl

fs

c Kvo

Qul

bLfutWsWp

(^3) 
4
(^1) 
2
Qul
4
(Db^2 D^2 )Nc cuWp
*Meyerhof, G. G. and Adams, J. I., “The Ultimate Uplift Capacity of Foundations,” Canadian
Geotechnical Journal, 5(4):1968.