Page 166 - Numerical Analysis and Modelling in Geomechanics

MODELLING OF GROUND WAVES 147
The parameters can be conveniently expressed in dimensionless terms. The
frequency of the applied load, ω, is non-dimensionalised with respect to the
radius of the pile base, R, and the shear-wave velocity of the soil, c .
c

(5.13)

The static spring stiffness, k, is taken as

(5.14)

For convenience, non-dimensionalised mass and damping parameters α , α , β 0
1
0
and β , are defined as:
1
(5.15)

(5.16)

Further, Decks (1992) proposed the following expressions to accommodate
variations in Poisson’s ratio, v, as:

(5.17a)

(5.17b)

The pile shaft/soil interface described above is the frequency independent
transmitting boundary for axisymmetric shear waves derived by Deeks (1992).
This boundary is equivalent to viscous dashpots with a distributed damping
constant of ρ.c (identical to a viscous boundary) and a distributed spring constant
s
of G/ 2r , where p is the density of the soil, c is the shear-wave velocity in the
b
s
soil, G is the shear stiffness of the soil and r is the pile radius.
b
Stage 3
The third and final stage of the procedure is to impose the displacement-time
functions onto a large FE or FE/IE axisymmetric mesh of the surrounding soils.
The pile response is transferred to the ground model by way of an unrestrained
‘false’ pile made up of axisymmetric finite elements.