3.4 Test design

A geotechnical centrifuge test is normally designed to model a generic prototype situation. As with many other reduced-scale modelling techniques, such as hydraulic modelling, not every aspect of the prototype behaviour can be correctly modelled. Attention must be made to model directly those factors which are expected to dictate the prototype behaviour, such as the effective stress conditions in the soil. For those factors which cannot be directly modelled, the modeller must still ensure that the correct class of behaviour is simulated if possible. A commonly occurring example is modelling the flow of pore fluid through the soil skeleton. If the same pore fluid and soil are used in the model and the prototype then the Reynolds number is larger by the scaling factor, n in the model.

Laminar flow conditions in the model soil skeleton can still be maintained by ensuring that the Reynolds number in the model is less than unity (Bear, 1972).

Although the model may not be an exact replica of the prototype, it is still a unique physical event. In prototype terms, the engineer can view the model as

‘the site next door’ where conditions are very similar if not identical to their own.

In the centrifuge model only those processes which are dominated by gravitational effects will be automatically enhanced. To verify the effects that these processes have on the prototype behaviour, the technique of ‘modelling of models’ can be employed as described by Schofield (1980). Similarities between the different models can be attributed to these processes. Differences in behaviour can assist in separating the effects of different processes: Miyake et al.

(1988) modelled the process of soft-clay sedimentation and consolidation and separated the two effects by modelling of models techniques.

The principle of ‘modelling of models’ was discussed by (for example) Ko (1988) and is demonstrated in Figure 3.3: the same 10m high prototype could be modelled at full scale, at 1/10th scale, or at 1/100th scale at points A1, A2 and A3, respectively. Normally the range of scales used for modelling of models is narrower than indicated and does not include full-scale tests; more care is then required to extrapolate the results to prototype scale. The effects of stress and size must also be considered when comparing tests (Ko, 1988).

For small-size models the effect of particle size is also important. Soil is a particulate medium. Modellers, for example Fugslang and Ovesen (1988), have found that at least 30 particles must be in contact with each linear dimension of the model structure for the observed behaviour to be representative of the prototype behaviour. Care must be taken before scaling down the particle size in

the model to ensure that the mechanical properties of the particles are not changed, including their angularity and crushing strength, as demonstrated by Bolton and Lau (1988).

The geometric scale factor for the model is selected to fit the prototype situation under study into the model container with minimal boundary effects.

The choice of scale factor will be constrained by the maximum model size, which is related to the payload capacity of the centrifuge, and the operational domain of the centrifuge. In general, the scale factor should be as small as possible to maximise the size of the model: small models are more difficult to instrument and more sensitive to the presence of the instrumentation and the model making procedure. Small models of simple boundary value problems are, however, valuable for performing parametric studies with multiple models in one soil sample.

Some prototype situations may be too large for direct centrifuge modelling.

For deep problems, the effective stress levels in the soil can be increased by downward seepage (Zelikson, 1969). This technique was used by Nunez and Randolph (1984) in centrifuge model tests of long piles.

The appropriate centrifuge acceleration level is normally identical to the geometric scaling factor, but may be different when equivalent materials and partial similarity are required as described by Craig (1993). The Figure 3.3 Modelling of models principle. (After Ko, 1988).

CENTRIFUGE MODELLING: PRACTICAL CONSIDERATIONS 41

centrifuge acceleration level is not constant but increases linearly with centrifuge radius. Schofield (1980) showed that the appropriate centrifuge acceleration level should be selected at one-third the depth of interest in the soil model, and that provided the overall soil depth did not exceed 10% of the effective centrifuge radius the error in assuming that this acceleration level is constant with depth is tolerable.

Ideally soil strata within the soil model should be formed at the same curvature as that of the centrifuge. The majority of centrifuge model tests are conducted with level strata. If the package width is about 20% of the centrifuge radius in the circumferential direction, then a lateral acceleration of 10% of the centrifuge acceleration will be induced at the outside edge of the level strata.

This effect can be minimised by placing the area of interest along the centre-line of the strongbox.

The time scaling factors are determined from the appropriate centrifuge acceleration level, N, using the scaling laws. From these time factors the actuation frequency of the soil model can be determined. The method of actuation and required actuation power can then be selected.

In many cases, the actuation frequency required to directly model diffusion events is too fast for the available means of actuation or may require too much power. The higher actuation frequency may also induce inertial effects that are not present in the prototype. The actuation frequency must then be reduced to more manageable levels. This reduced actuation frequency must not cause a significant change in the dissipation of pore pressure occurring during the actuation.

Where significant pore pressure changes would occur in granular materials, the modeller can choose to increase the viscosity of the pore fluid to retard pore pressure dissipation. Increasing pore fluid viscosity by the scaling factor is common when modelling dynamic events in sand to match the time scaling factors for inertia and diffusion. The modeller must also ensure that changing the pore fluid does not significantly affect the mechanical behaviour of the soil medium. Wilson (1988) has shown that damping within the soil medium is increased close to resonance when viscous fluids are used.

The instrumentation for monitoring the model test can be selected knowing the type and expected range of measurands and the required monitoring frequency.

The selection of modelling materials, actuators and instrumentation are discussed in sections 3.5 to 3.8.

The model structure is normally scaled to have the same external geometry as the prototype. Other scaling requirements might include the bearing stress, the stiffness and the strength of the structure relative to the soil medium. Frequently, these model structures are manufactured from different materials than the prototype to satisfy the selected scaling criteria.

The model test must be integrated with the centrifuge. The design should include how communication is established with the test package and how the model will be affected by the centrifuge environment. As the centrifuge rotates,

most of the power required to rotate the centrifuge is dissipated in aerodynamic drag creating heat and a potential increase of temperature within the centrifuge chamber. For tight temperature control within the model test, the test package may have to be enclosed within thermal control barriers. The heat may be partly dissipated by ventilation of the rotating mass of air within the chamber. Air movements may cause undesirable effects to the exposed model such as buffeting and high evaporation rates which should be controlled by protecting the exposed model.

3.5