Geotechnical Engineering

DHARM

666 GEOTECHNICAL ENGINEERING

where C =^1

2

(c 1 + c 2 + c 3 )

c 1 = elastic compression of pile

c 2 = elastic compression of pile cap

c 3 = elastic compression of soil.

This is on the assumption of gradual application of the load.

2. The loss of energy during the impact of the pile and hammer:
   This depends upon the coefficient of restitution, Cr, for the system which may vary
   between 0.25 and 0.90, depending upon the materials involved. The available energy after
   impact is given by multiplying the energy of the hammer by
   WCW
   WW

hrp

hp

+

+

F

H

G

I

K

J

2

The loss of energy is therefore given by

Wh. Hη 1

2

−

+

+

L

N

M

M

O

Q

P

P

WCW

WW

hrp

hp

,

or

WW H C

WW

ph r

hp

..( )

()

η 1 −^2

+

Substituting these losses into the energy Eq. 16.18, and simplifying, one obtains

Qup =

WH

sC

CR

R

hr..

()

()

()

η

+

× +

+

1

1

2

...(Eq. 16.23)

where R = Wp/Wh.

This is referred to as the Hiley formula.

The allowable load Qap may be obtained by dividing Qup by a suitable factor of safety,

which may be 2 to 2.5. (The formula is dimensionally homogeneous).

For long and rigid piles, the Hiley formula is conservative since a fraction of the total

weight of the pile is accelerated at one time, as demonstrated by wave analysis. The weight Wp

in the formula is then taken as the weight of pile cap plus the weight of the top portion of the

pile; Chellis suggests that di 21 Wp be taken for Wp.

The Hiley formula is considered to be reasonably accurate for piles driven in cohesionless

soil.

The various quantities used in Eq. 16.23 are obtained as follows:

(i) Elastic compression of pile (c 1 )

This is computed from the equation

c 1 =

QL

AE

up e ...(Eq. 16.24)

where Le = embedded length of pile,

A = cross-sectional area of pile, and

E = modulus of elasticity of the material of the pile.