The Centrifuge Laboratory

Physical-Modelling Technique and Scaling

Analogue modelling using the centrifuge technique (Ramberg 1967, 1981) and appropriate model materials (Dixon & Summers 1985) can achieve considerable geometric and dynamic similarity between the models and the natural prototype system. The models are placed in a large-capacity centrifuge where the radial centrifugal force field simulates the Earth's gravitational field. By this means the stress distribution in a model, arising from both body and surface forces, is scaled to that in the natural prototype, and in consequence the model structures evolve kinematically in the same way as their natural prototypes. A great advantage is that the kinematic evolution of structures can be documented while a model is deformed in stages. The 20,000-g centrifuge at the Experimental Tectonics Laboratory at Queen's University and details of the experimental technique have been presented elsewhere along with previous results from our investigations of fold-thrust tectonics (Dixon & Summers 1985; Dixon & Tirrul 1991; Dixon & Liu 1992; Liu 1990; Liu & Dixon 1990, 1991, 1995; Dixon, 1995, 1996). A brief summary is given here to familiarize the reader with the process. 

The models are constructed of laminae of Harbutt's Plasticine® and Dow-Corning silicone putty (dilatant compound 3179), materials which are suitable mechanical analogues for limestone (or sandstone) and shale, respectively, under conditions expected within a deforming fold-thrust belt and for the scale-model ratios chosen (Dixon & Summers 1985; Dixon & Tirrul 1991; see below and Table 1). Each stratigraphic unit is constructed of finely interlayered sheets of Plasticine (representing competent rock such as carbonates and coarse clastics) and silicone putty (representing incompetent rock such as shale). Because the individual stratigraphic units are internally laminated they retain a mechanical anisotropy that simulates bedding. Varying the relative thicknesses of alternating laminae of the two materials yields stratigraphic units with different bulk competencies, simulating prototype units with different limestone/shale (or sandstone/shale) ratios.

Models can be constructed with laterally uniform "layer-cake" stratigraphic sequences or the strata can be assembled with heterogeneities that simulate lateral thickness variations resulting from growth-faulting. The present paper describes the structural evolution of folds and thrusts in plane-layered strata, in strata offset by primary normal faults with growth-stratal geometry, and in strata disrupted by pre-cut thrust ramps. 

Each model is subjected to horizontal compression from one end by a "hinterland wedge" of Plasticine which begins to undergo gravitational collapse and lateral spreading while the acceleration in the centrifuge is climbing from about 2500 g to the set level of 4000 g. A model can be shortened in several stages if the wedge is rebuilt after each stage to renew its gravitational potential. Transverse sections (parallel to the shortening direction) are cut between the shortening stages so that the structural evolution can be monitored in some detail. 

The acceleration ratio (the g level for the centrifuge run) is chosen as follows (see Table 1). The length ratio is selected first, on the basis of the fixed size of the model and the prototype dimension appropriate to the problem under study. The specific gravity (or mass) ratio is essentially fixed because the prototype rock densities are known and the model material densities can not be varied significantly. The model ratio of viscosity is based on estimates of the effective viscosity of the prototype rocks under the conditions of the tectonic process under consideration, and estimates of the effective viscosity of the selected model materials obtained by physical testing. The time ratio is based on estimates of the strain rates that are typical of the relevant orogenic process and those obtained during deformation of a model. These ratios together define the appropriate acceleration ratio that achieves dynamic scaling between model and prototype.

Table 1. Typical Model Scaling Ratios. 

Several notes of caution must be expressed concerning application of the model results to natural systems such as the Canadian Rocky Mountain Foothills fold-thrust belt. There is considerable uncertainty in our knowledge of the rheological behaviour of rocks under orogenic conditions, and this, together with the limited scope for manipulating the properties of the model materials, limits the accuracy of rheological scaling. Recognizing this uncertainty, we have shown (Dixon & Summers 1985; Dixon & Tirrul 1991) that the materials we are using for fold-thrust modelling achieve a reasonable degree of rheological analogy. Certain variables that apply in the natural prototype cannot be reproduced in the models; examples include the geothermal gradient and its effect on rock properties with depth, the effect of pore-fluid pressure on effective stress, and the effect of syntectonic surface erosion. Another uncertainty arises from imprecise knowledge of the initial configuration of a prototype, including the presence of heterogeneities that may have considerable influence on its structural evolution. Given these uncertainties, as a rule it is safer to investigate general principles rather than to attempt to simulate the precise structural evolution of a specific prototype example. Finally, the models rest on a planar, rigid baseplate that is not involved in the deformation.

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