Geotechnical centrifuge modeling: Difference between revisions

Revision as of 15:15, 11 January 2015

Revision as of 01:14, 14 March 2015

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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). 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.

==Principles of centrifuge modeling==

===Typical applications===

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

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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 al. 2007).

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

:<math>\sigma'^* = \frac{\sigma'_{m}} {\sigma'_{p}} = 1</math>

where the asterisk represents the scaling factor for the quantity, <math>\sigma'_{m}</math> is the effective stress in the model and <math>\sigma'_{p}</math> is the effective stress in the prototype.

In [[soil mechanics]] the vertical effective stress, <math>\sigma'</math> for example, is typically calculated by

:<math>\sigma' = \sigma^t - u\,</math>

where <math>\sigma^t </math> is the total stress and <big><math> u </math></big> is the pore pressure. For a uniform layer with no pore pressure, the total vertical stress at a depth <math>H </math> may be calculated by:

:<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 (Garnier et al. 2007), 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>g^* = \frac{1} {L^*}</math>

The above scaling law states that if lengths in the model are reduced by some factor, n, then gravitational accelerations must be increased by the same factor, n in order to preserve equal stresses in model and prototype.

====Dynamic problems====

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:<math>T^* = L^* \,</math>

Frequency has units of inverse of time, velocity has units of length per time, so for dynamic problems we also obtain

:<math>f^* = \frac{1} {L{*}}</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 et al. 2007)

====Scaling of other quantitites====

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Centrifuge tests can also be used to obtain experimental data to verify a design procedure or a computer model. The rapid development of computational power over recent decades has revolutionized engineering analysis. Many computer models have been developed to predict the behavior of geotechnical structures during earthquakes and other loads. Before a computer model can be used with confidence, it must be proven to be valid based on evidence. The meager and unrepeatable data provided by natural earthquakes, for example, is usually insufficient for this purpose. Verification of the validity of assumptions made by a computational algorithm is especially important in the area of geotechnical engineering due to the complexity of soil behavior. Soils exhibit highly non-linear behavior, their strength and stiffness depend on their stress history and on the water pressure in the pore fluid, all of which may evolve during the loading caused by an earthquake. The computer models which are intended to simulate these phenomena are very complex and require extensive verification. Experimental data from centrifuge tests is useful for verifying assumptions made by a computational algorithm. If the results show the computer model to be inaccurate, the centrifuge test data provides insight into the physical processes which in turn stimulates the development of better computer models.

==See also==

{{Portal| Engineering }}

{{multicol}}

* [[Geotechnical engineering]]

* [[Soil Mechanics]]

* [[Network for Earthquake Engineering Simulation]]

* [[Civil engineer]]

{{multicol-break}}

* [[Physical model]]

* [[Scale model]]

* [[Andrew N. Schofield]]

{{multicol-end}}

==References==

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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 83-83– 87, No. 6 Ser. No. 425 pp 84-9084–90, No. 7, Ser. No. 426 pp 71-7871–78.

Mikasa M., Takada N. & Yamada K. 1969. Centrifugal model test of a rockfill dam. Proc. 7th Int. Conf.

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Suelos.

{{refend}}

==See also==

{{Portal| Engineering }}

{{multicol}}

* [[Geotechnical engineering]]

* [[Soil Mechanics]]

* [[Network for Earthquake Engineering Simulation]]

* [[Civil engineer]]

{{multicol-break}}

* [[Physical model]]

* [[Scale model]]

* [[Andrew N. Schofield]]

{{multicol-end}}

==External links==

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* [http://nees.org/sites-mainpage/laboratories/centrifugelabs NEES Centrifuge Facilities - Network for Earthquake Engineering Simulation]

* [http://www.asce.org/asce.cfm American Society of Civil Engineers]

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