Centrifuges in modelling: principles and scale effects
2.5 Model tests
Centrifuge testing concerns physical modelling of geotechnical events. However, it is not restricted to studying a particular prototype with a view to improving design but rather it is a means by which the general understanding of geotechnical events and processes can be better understood. Centrifuge test series can be designed with different objectives in mind; the following categories of model tests are similar to those identified by James (1972).
● The study of a particular problem (for example an embankment) for which there are some difficult design decisions to be made. In such a study, there is clearly a need to replicate sufficient of the essential features of the prototype so that the model test data can be extrapolated to the prototype scale and so give a sensible assessment of its behaviour.
● The study of a general problem with no particular prototype in mind. The investigation is directed at making general statements about a particular class of problem, for example the long-term stability of retaining walls or the patterns of settlement caused by tunnel construction. Each model is a prototype in its own right and the results of a series of tests can be correlated by making good use of dimensional analysis. The purpose of using the centrifuge is then to generate realistic stress distributions so that overall the model test data can be sensibly applied to field situations and can also assist in developing new analyses.
● The detailed study of stress changes and displacements relevant to a particular class of problem. The purpose of such tests is to gain information on soil
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behaviour which can then assist with developing constitutive models and so improving analysis.
Of these categories, the second is the most applicable to the majority of centrifuge studies. This is, in part, because most centrifuge facilities are established in research institutions and a significant proportion of the centrifuge income comes from research-based programmes. It is pleasing to note that good progress has been made in Japan in using centrifuge tests for more routine design work.
Many of the early programmes of centrifuge studies were essentially investigations of mechanisms of collapse. The centrifuge is particularly useful in these studies since there is proper replication of self-weight effects and realistic failures can be observed, particularly if two-dimensional models are tested with viewing of a vertical section through the Perspex side wall of a model container.
There is special merit in centrifuge tests since real soil is used with proper modelling of behaviour. Therefore mechanisms developed in the model will be realistic rather than predetermined as in other forms of analysis. The scope of tests is now much more advanced and serviceability as well as collapse can be studied. This is particularly useful since in geotechnical engineering details of pre-failure patterns of deformation are often just as valuable as factors of safety against failure. Also, centrifuge studies now extend well beyond the traditional problems and centrifuge projects have included studies on burial of heat-generating waste (Maddocks and Savvidou, 1984), stability of iron ore concentrates cargoes during shipping (Atkinson and Taylor, 1994) and the generation of ice-floe forces on offshore structures.
In many problems, as well as studying mechanisms of collapse it is important to assess the relative effects of key parameters, often related to geometry, which influence the mechanism of deformation or collapse. Parametric studies can be successfully undertaken using a centrifuge since it is possible to have good control over the soil models. In this way, it is possible to determine the relative significance of certain parameters which may not be possible by other forms of analysis.
Model studies can, and should, be treated as prototypes in their own right.
They embody details directly comparable to prototypes, in particular the correct distribution of stress and stress-strain behaviour. Therefore, they can give excellent data for validation of numerical codes and analysis. These range from predictions of collapse to detailed modelling of deformations. The latter is particularly difficult numerically due to the problems of realistic representation of the small strain behaviour of soils. However, recent research is encouraging and centrifuge test data have been found to provide useful comparisons with detailed finite-element calculations. Also, centrifuge data can be useful even if, for some reason, the models do not fully replicate a particular prototype situation. The numerical code can still be validated against the model test data and that code
can then be used for analysis of the full-scale prototype taking into account its special features and boundary conditions.
Site-specific studies are the most difficult type of test to undertake and are the least common. Usually, major decisions are required on what details should be included in the model and on how best to incorporate natural variations across a site within the small-scale model. In studies of the Oosterschelde storm surge barrier, Craig (1984) commented on the importance of soft-sand pockets in the foundation sea-bed soils. These occurred randomly in the field but in the model it was decided to account for them by including a number of evenly spaced sand inclusions occupying a fixed percentage of the total volume of foundation soil. In this way it was possible to quantify to some extent the influence of the sand pockets.
Modelling of specific sites requires the recovery of field samples. This could be in the form of intact blocks which are then trimmed to size and loaded in centrifuge containers for subsequent reconsolidation on the centrifuge and testing. Alternatively, the site soil could be reconstituted and consolidated such that the profile of effective stress history in the model corresponded to the prototype. Reproducing the consolidation history is not especially difficult using consolidation presses with a downward hydraulic gradient consolidation facility.
However, effects of ageing and some degree of cementing at grain contacts may have an important influence on behaviour and should be recreated. A promising technique for reproducing ageing effects by consolidation at elevated temperatures is described by Tsuchida et al. (1991).
If an intact block is recovered for later modelling of a site, some thought needs to be given as to the reconsolidation process such that the profile of stress history in the model properly represents the site. If the block is recovered from near the top of the strata of interest and reconsolidated on the centrifuge using a surcharge load to represent any soil eroded from the site in geological time, then all elements of the model with depth will experience the same maximum pre-consolidation stress profile as the in situ site. The centrifuge can then be stopped, the surcharge removed and the sample then reconstituted in centrifuge flight. In this way, the prototype effective stress profile and effective stress history will be correctly represented in the model. (It should be noted that this would not be the case for a sample recovered from the bottom of the strata.) However, any ‘structure’ or
‘fabric’ present in the field sample is likely to be destroyed by this process and some attempt at ageing of the sample may be necessary if all aspects of the prototype behaviour are to be replicated.
2.6 Summary
The general background to centrifuge modelling has been presented. This has involved derivation of the most fundamental scaling laws using standard methods based either on dimensional analysis or the governing differential
CENTRIFUGES IN MODELLING: PRINCIPLES AND SCALE EFFECTS 33
equations. In any modelling study, it is important to investigate sources of potential error and for centrifuge modelling the most commonly identified errors have been considered and shown, in general, to be of minor significance.
Centrifuge model testing is a technique of increasing relevance to engineering design and practice and some examples of the types of study undertaken have been presented. The increasingly wide variety of centrifuge studies to engineering applications can be examined by reference to the specialist international conferences.
References
Atkinson J.H. and Taylor, R.N. (1994) Drainage and stability of iron ore concentrate cargoes. Centrifuge ’94. Singapore, pp. 417–422. Balkema, Rotterdam.
Cooke, A.B. and Mitchell, R.J. (1991) Evaluation of contaminant transport in partially saturated soils. Centrifuge ’91, Boulder, Colorado, pp. 503–508. Balkema, Rotterdam.
Craig, W.H. (1983) Simulation of foundations for offshore structures using centrifuge modelling. In Developments in Geotechnical Engineering (ed. P.K. Banerjee), pp. 1–27. Applied Science Publishers, Barking.
Craig, W.H. (1984) Centrifuge modelling for site-specific prototypes. Symp. Application of Centrifuge Modelling to Geotechnical Design, University of Manchester, pp. 473–489. Balkema, Rotterdam.
Fuglsang, L.D. and Ovesen, N.K. (1988) The application of the theory of modelling to centrifuge studies. In Centrifuges in Soil Mechanics (eds W.H.Craig, R.G.James and A.N.Schofield), pp. 119–138. Balkema, Rotterdam.
Goforth, G.F., Townsend, F.C. and Bloomquist, D. (1991) Saturated and unsaturated fluid flow in a centrifuge. Centrifuge ’91, Boulder, Colorado, pp. 497–502. Balkema, Rotterdam.
James, R.G. (1972) Some aspects of soil mechanics model testing. In Stress-Strain Behaviour of Soil, Proc. Roscoe Mem. Symp., Foulis, pp. 417–440.
Langhaar, H.L. (1951) Dimensional Analysis and Theory of Models. John Wiley, New York.
Maddocks, D.V. and Savvidou, C. (1984) The effects of heat transfer from a hot penetrator installed in the ocean bed. Symp. Application of Centrifuge Modelling to Geotechnical Design, University of Manchester, pp. 336–355. Balkema, Rotterdam.
Ovesen, N.K. (1979) The scaling law relationship—Panel Discussion. Proc. 7th Eur.
Conf. Soil Mech. Found. Eng., Brighton, No. 4, pp. 319–323.
Tatsuoka, F., Okahara, M., Tanaka, T., Tani, K, Morimoto, T. and Siddiquee, M.S.A.
(1991) Progressive failure and particle size effect in bearing capacity of a footing in sand. ASCE Geotechnical Engineering Congress 1991, Vol. II (Geotechnical Special Publication 27), pp. 788–802.
Tsuchida, T., Kobayashi, M. and Mizukami, J. (1991) Effect of ageing of marine clay and its duplication by high temperature consolidation. Soils and Found., 31(4), 133–147.