Geotechnical centrifuge modeling: Difference between revisions

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====Scaling of other quantitites====
(this section obviously needs work!)
 
scale factors for energy, force, pressure, acceleration, velocity, etc.
If a 1 m deep model container is filled with soil, placed on the end of a centrifuge and subject to a centrifugal acceleration of 50 g, the pressures and stresses are increased by a factor of 50. So, the vertical stress at the base of the model container is equivalent to the vertical stress at a depth of 50 m below the ground surface on earth -- the 1 m deep model represents 50 m of prototype soil.
Note that stress has units of pressure, or force per unit area. Thus we can writeshow that
 
With a centrifuge model, we scale down the length (L) of the model and we scale up gravity (g) [or acceleration (a)]. We use the same soil at the same mass density (r) to ensure we get similar behavior. That is, for a given scaling factor N,
 
and
 
Note that stress has units of pressure, or force per unit area. Thus we can write
 
Substituting F = m∙a (Newton’s law, force = mass ∙ acceleration) and r = m/L3 (from the definition of mass density),
 
Substituting from above,
 
Therefore, if we build a reduced-scale model using the same soil at the same mass density, reduce the length by a factor of N while simultaneously increasing gravity by the same factor N, then we ensure that the stress in the model is the same as it would be in the prototype.
 
Scale factors for many other quantities can be derived from the above relationships. The table below summarizes common scale factors for centrifuge testing.