Geoscience Reference
In-Depth Information
The response of the structure-foundation system is what the designer needs to predict.
If a response spectrum approach is being used, one aspect of this is to evaluate the way
the stiffness of the structure and foundation contribute to the first mode period of the
system. Similarly the soil damping, both radiation and hysteretic, need to be combined
with the structuraldamping.
These two factors, variability of the soil properties relative to those of the structure, and
combination of damping values, need structural engineering and geotechnical engineer-
ing teamwork to arrive at the appropriate design model. It is of note that the FEMA 273
document makes thispoint inthe Chapter4 dealing with foundations.
Figures 10.1 and 10.2 deal with the ultimate bearing strength of the foundation. In this
section we are considering dynamic response of the foundation under the assumption
that the soil contribution can be modelled by assuming that the soil behaves “elasti-
cally”. In other words what is envisaged here is a two stage process. First check to see
that the foundation actions do not violate the bearing strength surface. Then evaluate the
deformationsofthefoundationassuming“elastic”behaviour.Thetwo-stepnatureofthis
process may be perceived as a disadvantage and so one wonders if there might be an
alternative. Given the magnificent computing resources available today a fully nonlin-
ear dynamic analysis of the structure-foundation system could be suggested. However,
asstatedabove,thisisnotadesignapproach.Whatisattractiveistheconceptofamacro-
elementtorepresenttheelasticandnonlinearbehaviourofthefoundationblockshownin
Figure 10.7 in one computational entity. This has the elastic vertical, lateral and rocking
stiffnesses of the foundation to represent the response of the foundation at low levels of
excitation. In addition the bearing strength surface acts as yield boundary and so a plas-
tic method is used to estimate permanent deformations of the foundation. The criterion
for satisfactory foundation response is then based on the residual permanent displace-
ments and rotations. Macro-elements have been developed by Paolucci (1997), Cremer
et al. (2001) and Gajan et al. (2005a). Centrifuge model testing also provides informa-
tionaboutthelikelyearthquakeresponseofshallowfoundationsonidealisedsoilprofiles.
DataobtainedbyGajanetal.(2005b)indicatesthatthelimitingfactorontheperformance
of shallow foundations might be theresidual deformation at the end of the earthquake.
Further insight into foundation-structure interaction during earthquakes can be obtained
by analyzing data from the recorded response of structures during earthquake shaking,
particularlywheredatafromseveralinstrumentslocatedatdifferentpositionsinthestruc-
ture and the surrounding ground are available. A comprehensive study of this type has
been reported by Stewart et al. (2001). Some of the results are presented in Figure 10.9
in which the period lengthening attributed to soil-structure interaction is plotted against
a dimensionless parameter involving the shear wave velocity of the soil and the first
mode period and height of the structure. The results indicate that soil-structure induced
period lengthening is usually less than 20% of the first mode period (that is
T
2)
although there may be some cases where the lengthening is considerably greater. From
this one concludes that, from the perspective of foundation design, the effects modelled
by the foundation block in Figure 10.7 are generally modest. Possibly more significant
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