Geotechnical Engineering

DHARM

852 GEOTECHNICAL ENGINEERING

Pine : 20,000 to 25,000 kN/m^2

Larch : 15,000 to 20,000 kN/m^2

20.6.4 Velocity of Anvil
The velocity of anvil after impact is required to be determined for the dynamic analysis of a
hammer foundation. This may be obtained as follows:
Velocity of Tup before Impact
For free fall hammer, the velocity v before impact is given by
v = α^2 gh ...(Eq. 20.90)
where h = height of fall,
and α = correction factor which characterises the resistance of exhaust steam (α = 1 for well
adjusted hammer according to Barkan, 1962).
For double-acting hammer, v is given by

v = α

2 gW pah

W

t

t

()+

...(Eq. 20.91)

where Wt = weight of tup,
p = pressure on the piston,
a = area of piston,
h = stroke,
and α = correction factor which varies from 0.5 to 0.8. Barkan (1962) recommends an
average value of 0.65.

Velocity of Tup and Anvil after Impact

Let v be the velocity of tup before impact,
v 1 be the velocity of tup after impact,
and va be the velocity of anvil after impact.
(It may be remembered the velocity of the anvil and foundation is zero before impact).
Applying the principle of conservation of momentum
Mtv = Mtv 1 + Mava ...(Eq. 20.92)
where Mt = mass of tup,
and Ma = mass of anvil (including the weight of frame, if mounted on it).

Another equation is obtained by using Newton’s hypothesis concerning the restitution
of impact which states that “the relative velocity after impact is proportional to that before
impact”. The ratio between these two, which is known as the coefficient of elastic restitution
(e) depends only on the materials of the bodies involved in the impact. Therefore we may write

e =

()vv

v

a− (^1) ...(Eq. 20.93)
or v 1 = (va – ev)
substituting for v 1 in Eq. 20.92 and simplifying,
va =
()
()
.
1
1

• 
  


• 
  

  e
  v
  λa
  ...(Eq. 20.94)