Geotechnical Engineering

DHARM

872 GEOTECHNICAL ENGINEERING

Initial Velocity of Anvil after Impact

va =

()

()

1

(^11)

• 
  


• 
  

  e v
  λ
  λ 1 =
  M
  M
  W
  W
  a
  t
  a
  t
  ==^1000
  50
  = 20
  Substituting e = 0.5, v = 6.2 m/s, and λ 1 = 20,
  va =
  (.)
  ()
  .
  105
  120
  62

  
  


• 
  


• 
  

  × = 0.443 m/s
  Amplitudes
  The amplitude for the foundation-soil system
  A 1 = −
  −−
  −
  ()()
  ()
  ωωωω
  ωω ω ω
  anan
  an n n
  va
  2
  2
  22
  1
  2
  2
  1
  2
  2
  2
  2
  Substituting ωa^2 = 45.126 × 10^3 , ωn 12 = 67.7744 × 10^3 , ωn 22 = 15.666 × 10^3
  and va = 0.443 m/s,
  A 1 = −
  −−
  ×−
  10 45 126 15 666 45 126 67 7744 0 443
  10 45 126 67 7744 15 6660 125 164
  6
  6
  (.. )(.. )(. )
  .(.. )(.)
  m
  = 1.00 mm
  The amplitude of the anvil
  Aa = −
  −
  −
  ()
  ()
  .
  ωω
  ωωω
  an
  nnn
  va
  2
  1
  2
  1
  2
  2
  2
  2
  = − −
  −
  10 45 126 67 7744 0 443
  10 67 7744 15 6660 125 164
  3
  3
  (.. )(. )
  (.. )(. )
  m
  = 1.54 mm
  Stress in the Elastic Pad
  σp =
  kA A
  A
  a
  p
  21 ()−
  Substituting k 2 = 46 × 10^5 kN/m, Aa = 1.54 × 10–3m, A 1 = 1.00 × 10–3 m,
  and Ap = 5.5 m^2 ,
  σp =
  46 10 1 54 1 00 10
  55
  ×−×^5 (.. )
  .
  –3
  kN/m^2
  = 451.64 kN/m^2
  Final Values of Salient Quantities
  The Size of foundation: 7.5 m × 6.5 m × 1.5 m high.
  Estimated amplitude of motion of the foundation: 1.00 mm
  Estimated stress in the elastic pad: 452 kN/m^2.