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Principles of Centrifuge Modeling
Typical Applications (top, reason, scaling, value, numerical)
A geotechnical centrifuge is used to conduct model tests to study geotechnical problems such as the strength, stiffness and capacity of foundations for bridges and buildings, settlement of embankments, 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.
Reason for Model Testing on the Centrifuge (top, reason, scaling, value, numerical)
Geotechnical materials such as soil and rock have nonlinear mechanical properties that depend on the effective confining stress and stress history. The centrifuge applies an increased "gravitational" acceleration to physical models in order to produce identical self-weight stresses in the model and prototype. The one to one scaling of stress enhances the similarity of geotechnical models and makes it possible to obtain accurate data to help solve complex problems such as earthquake-induced liquefaction, soil-structure interaction and underground transport of pollutants such as dense non-aqueous phase liquids. Centrifuge model testing provides data to improve our understanding of basic mechanisms of deformation and failure and provides benchmarks useful for verification of numerical models.
Scaling Laws (top, reason, scaling, value, numerical)
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 1 m x 50 = 50 m in the earth -- the 1 m deep model represents 50 m of prototype soil.
The reason for the centrifuge is to enable small scale models to feel the same stresses as a full scale prototype. This can be stated mathematically as
s* = smodel / sprototype = 1
Here s represents any quantity with units of pressure (modulus, shear strength, stress, pressure). The asterisk denotes a scale factor for that quantity.
The stress scales in proportion to the product of density (r), gravity (g), and depth (L). If we force s* = 1, it follows that
s* = r*g*L* = 1
If the same materials are used in model and prototype so that the scale factor for density is: r* = 1, then the gravity scale factor g* = 1/L*. In other words, if the model is 50 times smaller than the prototype, then the model gravity must be 50 times greater than the prototype gravity.
Various scale factors are summarized in the table below
Scale Factors for Various Quantities
Stress, Moduli s* = 1
Density r* = 1
Length, Displacement L* = L*
Gravity g* = 1/L*
Dynamic Time t* = L*
Dynamic Velocity v* = 1
Dynamic Acceleration a* = g* = 1/L*
Diffusion Time t* = (L*)2
Value of Centrifuge in Geotechnical Earthquake Engineering (top, reason, scaling, value, numerical)
Large Earthquakes are infrequent and unrepeatable but they can be devastating. All of these factors make it difficult to obtain the required data to study their effects by post earthquake field investigations. Instrumentation of full scale structures is expensive to maintain over the large periods of time that may elapse between major temblors, and the instrumentation may not be placed in the most scientifically useful locations. Even if engineers are lucky enough to obtain timely recordings of data from real failures, there is no guarantee that the instrumentation is providing repeatable data. In addition, scientifically educational failures from real earthquakes come at the expense of the safety of the public. Understandably, after a real earthquake, most of the interesting data is rapidly cleared away before engineers have an opportunity to adequately study the failure modes.
Centrifuge modeling is a valuable tool for studying the effects of ground shaking on critical structures without risking the safety of the public. The efficacy of alternative designs or seismic retrofitting techniques can compared in a repeatable scientific series of tests.
Verification of Numerical Models (top, reason, scaling, value, numerical)
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 the last two decades has revolutionized engineering analysis. Many computer models have been developed to predict the behavior of geotechnical structures during earthquakes. Before a computer model can be used with confidence, it must be proven to be valid based on experimental data. The meager and unrepeatable data provided by natural earthquakes is usually insufficient for this purpose. Verification of the validity of assumptions made by a computer program 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 claim to be able to simulate these phenomena are very complex and require extensive verification. The centrifuge is useful for verifying assumptions made by a computer model. If the results show the computer model to be inaccurate, the centrifuge test data provides some insight into the physical processes which in turn stimulates the development of better computer models.
(top, reason, scaling, value, numerical)