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in magnitude (probably all fitting a controlling frequency spectrum). If this is combined
with other parametric studies then this implies a very large number of tests in order to
ensure that attribution of consequences issecure.
Inanextensivenumericalstudyoftheseismicresponseofareinforcedsoilretainingwall,
Hatami and Bathurst (2001) show that the response of the wall is influenced by, but not
correlated with, many different characteristics of the input motion including: predomi-
nantfrequency,peakgroundvelocity,earthquakeintensityanddurationofstrongground
motion, and whether the input is a harmonic motion or a recorded earthquake accelero-
gram. A similar conclusion is reached by Simonelli and Viggiani (1995) from sliding
block analyses (Newmark, 1965) of slope movement in earthquakes. Experimental stud-
iesofmuchsimplerphysicalsystemshaveshownclearevidenceofchaoticresponsewith
non-monotonic relationships between, for example, amplitude of input motion and mag-
nitude of permanent displacement response. This should also lead to caution in selecting
and relying on particular input time histories.
Numerical modelling using a full finite element or finite difference analysis may be a
heavy-handed way of seeking insight into some aspects of a problem of geotechnical
behaviour. Macroelement modelling can be a helpful intermediate way of introducing
some realistic geotechnical nonlinearity in order to compare different constitutive pos-
sibilities or to provide rapid 'order-of-magnitude' estimates of response against which
theresultsofmoreextensivenumerical—orphysical—modellingcanbecompared.Such
speedymodellingcanbeparticularlybeneficialwheretheconcernistostudythedynamic
responseofanonlineargeotechnicalsystem,and,inparticular,tostudythewayinwhich
that response is influenced by the nature of the dynamic input motion. This has been the
motivation behind the development of the macroelement model for a gravity retaining
wall that isdescribed here.
ThesystembeingconsideredisillustratedinFigure6.12(MuirWoodandKalasin,2004).
This system contains enough detail to have a realistic geotechnical 'feel' about it while
still retaining the simplicity associated with the macroelement approach. The wall inter-
actswiththegroundintwoways:thewallsitsonafoundationdescribedbyafoundation
macroelement or transfer function; the wall retains backfill soil and the interaction with
the retained soil isdescribed by the wall macroelement.
The foundation macroelement is subjected to simultaneous and interacting vertical,
horizontal and moment loading. The macroelement model adopted here has emerged
from several parallel experimental and theoretical studies of the response of footings
(e.g., Nova and Montrasio, 1991; Cremer et al., 2001). The incentive for these investiga-
tions came from the demands of offshore foundations which are subjected to horizontal
loads which areof magnitude comparable withthe vertical load.
The response of the footing can be described by a macroelement model with exactly
the same features as a constitutive model describing the behaviour of a single soil
element—replacing work-conjugate groups of strain increment and stress variables with
work-conjugate groups of displacement increments and force resultants. Constructing
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