Geoscience Reference
In-Depth Information
The specially developed foundation element used in the Ruaumoko calculations has ver-
tical, horizontal and rotational stiffness, all of which are coupled so at uplift all three
are detached from the underlying soil. In addition all three springs can exhibit nonlinear
behaviour.
Initiallythestiffnessofthespringswaselasticandgavethesettlementundergravityload.
To estimate the foundation stiffnesses formulae for the vertical, horizontal and rotational
stiffness of rigid rectangular foundations on an elastic soil from Gazetas (1991) were
used.
A single earthquake record was used in the analysis and was applied parallel to the
longestplandimensionofthestructure.ThisrecordwasfromtheLaUnionevent,N85W
Michoacan,Mexico1985.TheearthquakespectrumwasscaledusingthemethodinNZS
1170.5 to the spectrum representing an earthquake in the Wellington region of New
Zealand for a 1 in 500 year return period event. The resulting earthquake time history
had a peak ground acceleration of 3
s
2
. The response spectrum with 5% damping
gives aspectral acceleration at thenatural period of thestructureof 5
.
46m
/
s
2
.
.
6m
/
Initially three methods were used to size the shallow foundations: (i) all footings with
adequate bearing strength from static LFRD ultimate limit state considerations, (ii) all
footings to have equal static settlement, and (iii) all footings to have equal vertical
stiffness with the most heavily loaded footings having adequate static LRFD bearing
strength.However,asthebearingcapacityofshallowfootingsdecreasesrapidlywiththe
application of moment this was found to be the critical design consideration. Whether
the structure remains elastic or is designed as ductile, moments are generated at the
base of the ground floor columns, and these moments are transferred to the foundation.
Itwasfoundthatonlytheequalstiffnessfootingswereofsufficientsizetoaccommodate
thesemoments.Thisappearstogivetheexteriorfootingssizeswhichareextravagant,but
althoughthesefootingscarrythesmallestgravityloadstheyhavethelargestcyclicverti-
calloadsduringtheearthquakeaswellascyclicshearandmoment.Duringtheunloading
partofthecyclethingsbecomecriticalasitisthenthatthemomenthasthemostadverse
affect on the bearing strength of the footing. Results below were taken from the equal
stiffnessfooting design method.
5.3. ELASTIC STRUCTURAL RESPONSE WITHFIXED COLUMN-FOOTING
CONNECTIONS
Figure 10.15 shows the time history of the vertical load and vertical displacement of the
corner footing, footing number 1 in Figure 10.14, during the earthquake. As the corner
footingscarrythesmallestgravityloaditisthesethataremostaffectedbytheearthquake.
It is seen that there are five brief instances of uplift during the earthquake. These are
indicated by zero vertical load on the footing and positive vertical displacement. The
upperpartofFigure10.15showsthatthegravityloadonthefootingisabout680kNand
the static settlement is about 2mm (the sign convention being negative for compressive
