(^618) „„„„„ A Textbook of Engineering Mechanics
30.22. PILE AND PILE HAMMER
A pile, in its simplest form, is a body of conical shape which is driven into the ground by the
impact of a pile hammer. The pile hammer is a body which is released from some height over the pile
head as shown in Fig 30.11.
The pile hammer has potential energy before it is released. After
release, the potential energy is converted into kinetic energy, with which
the pile hammer strikes the pile head. After impact, both the pile and pile
hammer move together with a common velocity. This movement is retarded
by the resistance of the soil, into which the pile is driven.
Let m = Mass of the pile hammer
M = Mass of the pile
h = Height through which the pile ham
mer falls before striking the pile,
x = Distance through which the pile is
driven into the ground
v = Velocity of the pile hammer just before impact (i.e. after fall
ing through a distance h. It is equal to^2 gh).
V = Common velocity of the pile and pile hammer after impact
(which is reduced to zero in a distance x ), and
R = Average resistance of the soil.
We know that the momentum of the pile hammer and pile just before impact
= mv ...(i)
and momentum just after impact = (m + M) V ...(ii)
Equating equations (i) and (ii),
mv = (m + M) V
∴
mv
V
mM

• 
  

  ...(iii)
  Now consider B as the datum level. We know that kinetic energy of pile and pile hammer
  immediately after impact
  ()^2
  2
  mMV+

  
  

  and potential energy of pile and pile hammer immediately after impact
  = (m + M) gx
  ∴ Total energy,
  ()^2
  ()
  2
  mMV
  E mMgx

  
  


• 
  

  =++
  Substituting the value of V from equation (iii),
  2
  ()
  ()
  2
  mv
  mM
  mM
  EmMgx
  ⎛⎞

  
  


• ⎜⎟
  ⎝⎠+
  =++
  22
  ()
  2( )
  mv
  mMgx
  mM
  =++


• 
  

  Fig. 30.11.