Suction profiles and scale factors for unsaturated flow under increased gravitational field
Dell'Avanzi, Eduardo; Zornberg, Jorge G.; Cabral, Alexandre
Abstract: Scale factors for centrifuge modelling have been traditionally defined using dimensional analysis concepts. This is the case, for example, of centrifuge modelling of unsaturated water flow. However, scale factors governing suction, discharge velocity, and time obtained using dimensional analysis have often differed from those obtained from methodologies not based on dimensionless groups. In this paper, a consistent framework is developed for analytic determination of suction profiles for steady-state unsaturated flow under both natural and increased gravitational fields. This framework allows deduction of the scale factors, which emerge from direct comparison of the analytic solutions for model and prototype without the need to use dimensionless groups. For centrifuge conditions leading to an approximately uniform acceleration field, the suction profile in the prototype is found to be the same as that in the model, while the discharge velocity is found to be properly scaled by 1/N and time by N2, where N is the average acceleration ratio between model and prototype. If acceleration field is not uniform, the scale factors should be defined as a function of the centrifuge radius and model length. In addition, evaluation of the effect of different test conditions allows identification of the suction profiles and test setup best suited for hydraulic conductivity determination using centrifuge techniques.
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