Geoscience Reference
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ofsmallbutsignificantparasiticundesiredmotionsincludingverticalandlateralmotion,
yawing and pitching which need tobeactively controlled tobe zero.
Thelinearscalefactorformodeldesignwasdrivenbytheneedtopermitthefulldevelop-
ment of a seismic bearing capacity failure mechanism on either side of the model when
installed within the shear stack. A foundation width of 120mm was chosen, giving a
length scale factor of
n
=
3500. The width of the model foundation (440mm) is
closetothewidthoftheshearstack(550mm).Noattempthasbeenmadetoapplyscaling
relationstotheprototypefoundationsoilprofileortothefootingload.Ifthefootingload-
ing were to be scaled together with the length scale, the load applied would be low and
possiblyinsufficienttorevealtheeffectofanyputativemitigationscheme.Amodelmass
of 130kg distributed over the model foundation reproduces the prototype 25kPa bear-
ing pressure and promotes soil-structure interaction effects in the shaking table model.
To preserve the structure/foundation mass ratio of the prototype, 80kg of the total mass
are attributable to the 'foundation' and the remaining 50kg to the 'structure'. The height
of the model structure above the model foundation is the scaled distance between the
centre of mass of theprototype structure and the prototype foundation.
120
/
In the model structure (Figure 6.8) the foundation and structural mass are connected by
aseriesofflexiblesteelcolumns,hingedtothestructure.Thenaturalresonantfrequency
ofthemodelstructurecanbetunedbetween4.4Hzand22.5Hzbychangingthenumber
and thickness of these columns. The lowest value in this range reproduces the natural
frequency(firstmode)oftheprototype;thehighestisclosetothescalednaturalfrequency
of the prototype when modelled at 120/3500 scale (24Hz).
Thus the design of the model represents a compromise. It is supposed that, because of
the uncertainties of the stress level dependency of the soil behaviour, there is an advan-
tage in working with stress levels around the foundation which are similar in model and
prototype.Itisnotpossiblesimultaneouslytomatchthegravitationalgradientofvertical
stress. The increase in stress at a depth equal to the width of the foundation is of the
order of 60kPa in the prototype (more than twice the applied foundation loading) but is
negligibleinthemodel.However,theshakingtablemodelissufficientlylargetoprovide
a useful set of observations from which extrapolation to prototype scale can be made by
means of numerical modelling—with an appropriate constitutive model. For scaling of
frequency, the dominant effect is the length scale, and, in the region of interest around
thefoundation,thestresslevelandhencethesoilstiffnessareroughlythesameinmodel
and prototype. Frequency then scales with square root of the inverse of the linear scale:
theresonantfrequencyanddampingofthemodelmeasuredbysecuringthemodelfoun-
dation to the shaking table ('fixed-base') are 22.5Hz and 2.4% respectively, close to the
fundamental frequency of the prototype (4.4Hz) when scaled with the model/prototype
length scale factor of 120/3500 (
≈
23
.
9Hz).
The mitigation scheme studied in the NEMISREF project involved the construction of
a 'soft caisson' around and beneath an existing foundation (Figure 6.9). By inserting a
horizontal slip layer at some moderate depth (for example around 10m), and also insert-
ing soft trenches around the foundation, the foundation can be somewhat isolated from
