Page 160 - Numerical Analysis and Modelling in Geomechanics

MODELLING OF GROUND WAVES 141
Infinite elements
The use of infinite elements to model continua has been developed particularly
by Bettess (1992). The standard infinite element method available within
Abaqus, see Figure 5.5, is very effective in preventing spurious reflection when a
single wave type and transmission velocity strikes the boundary. However, it is
less effective when the wave pattern contains components of different velocities
and/ or directions.
A further difficulty may arise if static forces such as self-weight are to be
applied prior to the dynamic analysis. The formulation of the dynamic damper is
in terms of resistance to velocity, not displacement, with the result that the
configuration of a pile in an elastic half-space has no resistance to rigid body
movement of the FE mesh. Geostatic stresses are necessary when considering
Coulomb slip at the interface between pile and soil, but would cause unrestrained
extreme displacements, Figure 5.9.
A number of strategies were used to achieve satisfactory analyses:

1 The viscous boundary developed by Lysmer and Kuhlemeyer (1969) was
programmed into Abaqus as a ‘user-defined’ element. With respect to pure P
or S-waves, this performed as well as the Abaqus element (Ramshaw, 1999)
but caused significant extensions in run time, because of the toggling
between formulations. However, it also had limitations with respect to
Rayleigh waves (Lysmer and Kuhlemeyer, 1969).
2 Lysmer and Kuhlemeyer also proposed a Rayleigh wave damper where
dashpots are tuned to the frequency of the incoming waves. This was also
programmed in as user-defined, and produced a substantial improvement
over the Abaqus element, albeit at the expense of extended run times
(Ramshaw, 2001).
3 A combination of IEs was used, where geostatic stress was not required, as
in Figure 5.10, which was found to give satisfactory performance.
4 When considering interface slip at the pile-soil interface, it was necessary to
generate normal stress between the pile and soil, which increases with
depth. Application of soil self-weight caused the above problem of gross
rigid-body movement. A device to generate the normal stresses was
developed, in which a ‘pseudo-pile’ was expanded non-uniformly against
the soil to generate the necessary stresses. Application of a Coulomb friction
factor, µ, was then feasible.
5 Experience of actual wave patterns due to impact driving led to the
conclusion that the most time-efficient computational model was a large FE
mesh with rigid boundaries, eliminating the need for IEs. Careful scrutiny of
the wave patterns showed that the significant waves were the first outgoing
P-wave, followed by an S-wave which degenerated into an R-wave at the
surface. Following wave bands were of much smaller amplitude.
Consequently, the significant disturbance within say 20 m of the pile could