Geotechnical centrifuge modeling: Difference between revisions

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[[File:Geotechnical centrifuge at the University of California, Davis..png|thumb|{{convert|9|m|ft|adj=mid|-radius|0}} geotechnical [[centrifuge]] at the University of California, Davis]]
 
'''Geotechnical centrifuge modeling''' is a technique for testing physical scale models of [[geotechnical|geotechnical engineering]] systems such as natural and man-made slopes and earth retaining structures and building or bridge foundations.<ref name=craig2001>{{cite book
| last1=Craig | first1=W.H. | year=2001
| titlechapter=The seven ages of centrifuge modelling
| publishertitle=Proc. Workshop on constitutive and centrifuge modeling: two extremes
| pages=165-174
}}</ref>
 
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 Pokrovsky and Fedorov (1936) in the Soviet Union and Bucky (1931) in the United States were the first to implement the idea. [[Andrew N. Schofield]] (e.g. Schofield 1980) played a key role in modern development of centrifuge modeling.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
| publisher=Proc. 1st Int. Conf. On Soil Mechanics & Foundation Engineering
| volume=1
}}</ref> in the Soviet Union and Bucky (1931) <ref>{{Citation
| last1=Bucky | first1=P.B. | year=1931
| title=The use of models for the study of mining problems
| publisher=New York: Am. Inst. Of Min. & Met. Engng.
| volume= Technical Publication 425
}}</ref> in the United States were the first to implement the idea. [[Andrew N. Schofield]] (e.g. Schofield 1980)<ref>{{Citation
| last1=Schofield | first1=A. N. | year=1980
| title=Cambridge geotechnical centrifuge operations
| publisher=Géotechnique | volume=30 | issue=3 | pages=227–268
}}</ref> played a key role in modern development of centrifuge modeling.
 
==Principles of centrifuge modeling==
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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> stability of slopes, earth retaining structures, tunnel stability and seawalls. Other applications include explosive cratering, 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.{{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=Garnier Mikasa | first1=JM. | last2=GaudinTakada | first2=CN. | last3=Yamada | first3=K.| year=1969
| chapter=Centrifugal model test of a rockfill dam.
| title=Proc. 7th Int. Conf. Soil Mechanics & Foundation Engineering 2:
| 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
| title=Centrifuges in Soil Mechanics
| veditors=Craig et al.
| 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> (Garnier et<ref al. 2007)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 (Garnier et al. 2007)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>
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:<math>T^* = L^{*2} \,</math>
 
For model tests involving both dynamics and diffusion, the conflict in time scale factors may be resolved by scaling the permeability of the soil (Garnier<ref et al. 2007)name=garnier2007>{{Citation
| last1=Garnier | first1=J. | last2=Gaudin | first2=C.
| last3=Springman | first3=S.M. | last4=Culligan | first4=P.J.
| last5=Goodings | first5=D.J. | last6=Konig | first6=D.
| last7=Kutter | first7=B.L. | last8=Phillips | first8=R.
| last9=Randolph | first9=M.F. | last10=Thorel | first10=L.
| year=2007
| title=Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling
| journal=International Journal of Physical Modelling in Geotechnics
| volume=7 | issue=3 | pages=1–23
}}</ref>
 
====Scaling of other quantitites====
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Scale factors for many other quantities can be derived from the above relationships. The table below summarizes common scale factors for centrifuge testing.
 
Scale Factors for Centrifuge Model Tests (from Garnier et al., 2007 <ref name=garnier2007/>)
(Table is suggested to be added here)
 
Line 106 ⟶ 157:
 
==References==
<references/>
{{refbegin}}
* {{Citation
| last1=Bucky | first1=P.B. | year=1931
| title=The use of models for the study of mining problems
| publisher=New York: Am. Inst. Of Min. & Met. Engng.
| volume= Technical Publication 425
}}
* {{Citation
| last1=Garnier | first1=J. | last2=Gaudin | first2=C.
| last3=Springman | first3=S.M. | last4=Culligan | first4=P.J.
| last5=Goodings | first5=D.J. | last6=Konig | first6=D.
| last7=Kutter | first7=B.L. | last8=Phillips | first8=R.
| last9=Randolph | first9=M.F. | last10=Thorel | first10=L.
| year=2007
| title=Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling
| journal=International Journal of Physical Modelling in Geotechnics
| volume=7 | issue=3 | pages=1–23
}}
* {{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)
}}
* {{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
| publisher=Proc. 1st Int. Conf. On Soil Mechanics & Foundation Engineering
| volume=1
}}
* {{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
}}
* {{Citation
| last1=Schofield | first1=A. N. | year=1980
| title=Cambridge geotechnical centrifuge operations
| publisher=Géotechnique | volume=30 | issue=3 | pages=227–268
}}
* {{Citation
| last1=Craig | first1=W.H. | year=2001
| title=The seven ages of centrifuge modelling
| publisher=Workshop on constitutive and centrifuge modeling: two extremes
}}
 
* Schmidt (1988), in Centrifuges in soil mechanics; Craig, James and Schofield eds. Balkema.
 
*Schofield (1993), From cam clay to centrifuge models, JSSMFE Vol. 41, No. 5 Ser. No. 424 pp 83– 87, No. 6 Ser. No. 425 pp 84–90, No. 7, Ser. No. 426 pp 71–78.
 
* Mikasa M., Takada N. & Yamada K. 1969. Centrifugal model test of a rockfill dam. Proc. 7th Int. Conf. Soil Mechanics & Foundation Engineering 2: 325–333. México: Sociedad Mexicana de Mecánica de Suelos.
{{refend}}