Geoscience Reference
In-Depth Information
u
M
e
, J
H
e
stiffness, k
K
f1
M
0
J
0
K
f2
d
θ
u
0
K
0
Fig. 10.7. Foundation-structure model for computation of system earthquake response
A method of representing the foundation and attached structure is shown in Figure 10.7.
Thisreducestheattachedstructuretoasingledegreeoffreedomandmodelsthefounda-
tion as a rigid block with three displacement degrees of freedom. Although the model in
Figure 10.7 is a simplification of a real foundation-structure system there are still many
parametersrequiredtosetupthemodel:twomasses,twomomentsofinertia,thedimen-
sions
h
K
θ
as well as the damping values associated
with each stiffness. The outputs from the model are the displacements
u
,
d
,
H
e
, the stiffnesses
k
,
K
f
1
,
K
f
2
,
,as
well as the actions in the various springs. Shallow foundation stiffness and damping val-
ues are frequency dependent. Usually the values associated with the first mode period of
the system are used. Mylonakis et al. (2006) show how combining stiffness and damp-
ing within a complex impedance leads to efficiencies in the calculation of the system
response.
,
u
o
, and
θ
Theaboveparagraphsrefertoelasticsoilbehaviour.Itiswellknownthatsoilisnotelastic
for other than very small shear strains. Fully nonlinear dynamic numerical analyses are
possible, but they are hardly design tools. One approach uses an approximate equivalent
linearcalculationinwhichthestiffnessofthesoilisdecreasedandthedampingincreased
as the level of earthquake excitation increases, but the calculations are still performed
assumingelasticbehaviour.SuggestionsalongtheselinesaregivenintheEC8Part5and
FEMA273(FEMA,1997).ThosefromEC8arerepeatedhereinTable10.2andthosein
FEMA 273 inTable 10.3.
