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bounding surface
horizontal
force or
moment
yield
surface
vertical
force
Fig. 6.16. Kinematic 'ice-cream cone' yield surfaceinsidebounding surface
of macroelement foundation model ofDiPriscoet al. (2003)
surface is reached. Exactly the same arguments apply to the macroelement modelling.
For the wall macroelement this can be achieved by modifying the Winkler springs to
have the hysteretic characteristics of the dashed lines in Figure 6.14, so that whenever
thedirectionofrelativemovementofwallandretainedsoilchangesthelocalresponseis
elastic. For the foundation macroelement DiPrisco et al. (2003) have added a kinematic
yieldsurfaceinsidethe'bounding'surfaceofFigure6.13(Figure6.16).Amacroelement
that neglects the plasticity that occurs almost throughout the loading history will not be
satisfactory.
Earthquakemotiontendstobeofquiteshortdurationwithaveryfewcyclesofhighaccel-
eration and many cycles of much lower acceleration with a typical duration of 10-20 s
depending on the location and nature of the earthquake. Once the motion becomes large
enough to move into the regimes of nonlinear response of the wall interacting with the
foundation and the retained soil, then the detail of the movement of the wall depends on
the exact time within the earthquake that particular large pulses of ground acceleration
occur. This can be illustrated by showing the dependence of the translation and rotation
ofthewallontheamplitudeoftheearthquakerelativetothecriticalsteadyunidirectional
acceleration required to generate active failureofthe wall (Figure6.17).
Thesystembeinganalysedisextremelynonlinear. Theinputmotionthatisgenerated by
an earthquake is extremely irregular. Put together, the overall system response is some-
what chaotic. There is no linear variation of displacement or rotation of the wall with
this relative magnitude of the input motion (Figure 6.17). In fact, for some time histo-
ries of input motion there is not even a monotonic variation of movement with relative
acceleration input magnitude.
The response of this simple macroelement system confirms rather clearly that, so far as
performance
of the system is concerned—the permanent displacement developed during
the seismic event—the occurrence of high acceleration pulses of short duration is not
necessarily devastating. The macroelement model also allows us to explore parametric
variations of both the geotechnical features of the system and the input motion itself in
