Unformatted text preview: st and the second terms of Eq.(11):
(11)
are the solutions of the equations below:
(12)
and
(13) The mechanics of Eq.(12) :
(12)
can be explained by Fig.5: And also, the mechanics of Eq.(13):
(13) can be explained by Fig.6. In Eq.(12):
(12)
Eq.(122) is:
(122)
and the displacement vector {XSf} is obtained as:
(14)
Substituting Eq.(14) into Eq.(121) leads to: (15) Because {XFf} is the displacement vector and {F} is the
force vector in Eq.(15):
(15)
the term in the parenthesis in the left hand side refers
to the stiffness matrix.
Putting:
(16)
Then, Eq.(15) can be expressed by:
(17) The matrix [KF] in Eq.(17):
(17)
indicates the dynamic stiffness matrix of the soil with
the void which is evaluated at the interface F.
The mechanics of Eq.(17) is illustrated by the figure: The matrix [KF] is called "Dynamic Impedance matrix of
soil at the interface F". Because Eq.(111) in Eq.(11):
(11)
is:
(18)
the interaction force vector {F} of Eq.(17) :
(17)
can be expressed by:
(19) Substituting Eq.(19):
(19)
into Eq...
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This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.
 Summer '14
 DrGRD

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