Geotechnical centrifuge modeling: Difference between revisions

Revision as of 21:06, 6 January 2021

Revision as of 22:16, 7 January 2021

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The scale [[Physical model|model]] is typically constructed in the laboratory and then loaded onto the end of the [[centrifuge]], which is typically between {{convert|0.2|and|10|m|ft|1}} in radius. The purpose of spinning the models on the centrifuge is to increase the [[g-force]]s on the model so that stresses in the model are equal to stresses in the prototype. For example, the stress beneath a {{convert|0.1|m|ft|adj=mid|-deep|1}} layer of model [[Soil mechanics|soil]] spun at a centrifugal acceleration of 50 g produces stresses equivalent to those beneath a {{convert|5|m|ft|adj=mid|-deep|0}} prototype layer of soil in earth's [[gravity]].

The idea to use centrifugal acceleration to simulate increased gravitational acceleration was first proposed by Phillips (1869).<ref name=phillips1869>{{Citation

| last1=Phillips | first1=Edouard | year=1869

| title=De l’equilibre des solides elastiques semblables

| publisher=C. R. Acad. Sci., Paris

| volume=68 | pages=75–79

}}</ref>. Pokrovsky and Fedorov (1936)<ref>{{Citation

| last1=Pokrovsky | first1=G. Y. | last2=Fedorov | first2=I. S. | year=1936

| title=Studies of soil pressures and soil deformations by means of a centrifuge

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===Typical applications===

[[File:Centrifuge Model of a Port Structure.png|thumb|Model of a port structure loaded on the UC Davis centrifuge]]

A geotechnical centrifuge is used to test models of geotechnical problems such as the strength, stiffness and capacity of foundations for bridges and buildings, settlement of embankments,<ref> {{Citation

| last1=Malushitsky | year=1975

| title=The centrifugal modelling of waste-heap embankments

| publisher=Russian edition, Kiev, English translation edited by A. N. Schofield, Cambridge University Press (1981)

}}</ref>, stability of slopes, earth retaining structures ,<ref>{{cite book

| last1=Mikasa | first1=M. | last2=Takada | first2=N. | last3=Yamada | first3=K.| year=1969

| chapter=Centrifugal model test of a rockfill dam.

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| pages=325–333

| publisher=México: Sociedad Mexicana de Mecánica de Suelos.

}}</ref>, tunnel stability and seawalls. Other applications include explosive cratering,<ref name=schmidt1988>{{cite book

| last1=Schmidt | first1=Robert M. | year=1988

| chapter=Centrifuge contributions to cratering technology

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| pages=199-202

| publisher=Balkema

}}</ref>, contaminant migration in ground water, frost heave and sea ice. The centrifuge may be useful for scale modeling of any large-scale nonlinear problem for which gravity is a primary driving force.

===Reason for model testing on the centrifuge===

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===Scaling laws===

Note that in this article, the asterisk on any quantity represents the scale factor for that quantity. For example, in <math>x^* = \frac{x_{m}} {x_{p}}</math>, the subscript m represents "model" and the subscript p represents "prototype" and <math>x^* \,</math> represents the scale factor for the quantity <math>x \,</math> .<ref name=garnier2007/>.

The reason for spinning a model on a centrifuge is to enable small scale models to feel the same effective stresses as a full-scale prototype. This goal can be stated mathematically as

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:<math>\sigma^t = \rho g H \,</math>

where <math> \rho </math> represents the density of the layer and <math> g</math> represents gravity. In the conventional form of centrifuge modeling,<ref name=garnier2007/>, it is typical that the same materials are used in the model and prototype; therefore the densities are the same in model and prototype, i.e.,

:<math> \rho^* = 1 \,</math>