|FOLD PROPAGATION IN SINGLE EMBEDDED
Cobbold (1971, 1975) made extensive studies of single layer buckling andhe designed an apparatus called Cobbold IC Box. The plates x and y can be driven in by operating rotary arms a1,a2,a3 and a4, on rollers R-1, R-2, R-3 and R-4. The Z plates move outward and make room for extension. The temperature can be controlled in the apparatus and the displacement can be measured with a ruler. The internal displacement or distortion can be visually seen and photographed at various stages. The strain rate can be measured with the rotary drive from an instrument attached to it. Cobbold used paraffin wax in his experiments; it has advantages over other materials in that it deforms at low temperatures very easily and is able to suffer large deformation without rupturing. It is easy to use in that the model can be quickly made by just pouring it into a liquid. Besides, it is made up of polycrystalline aggregates of hydrocarbons and it is similar to the rocks in the sense that it behaves as the material following the laws of pressure solution, and diffusion and the grain boundary sliding observed in paraffin is similar to the one assumed to occur in rocks. Its stress/strain relationship is similar to the one for rocks.
Cobbold ran four experiments and in each he produced a linear extremely small amplitude ridge like inhomogeneity in a direction along the layer that would presumably become the future fold hinge. The geometry of these initial perturbations varied in the four models but in each the viscosity contrast between the layer and the matrix was the same of 10:1 at any given steady strain rate. He observed that initial folds always appeared at the initial induced deflection, in the form of an antiformal structure; new synforms appearing along side of the central antiform. Amplification of the folds occurred by two flow or perturbation cells. Cobbold's experiments showed that buckling, need rot occur simultaneously throughout a single layer but may initiate at a point of perturbation such as a sedimentary nodule and may propagate outwards from this point producing newer folds as the propagation continues. Establishment of flow cells achieves the propagation. In all experiments, spans converged towards a fixed value, perhaps controlled by the viscosity contrast. If rate of propagation is rapid, the folds tend to be more periodic; where this is slow, the periodicity is not distinct and folds have shapes that are not well marked. Cobbold predicted that if a number of initial deflections were present, their interference might produce complex fold shapes as found in naturally deformed rocks.
Shimamoto and Hara (1976) studied the single layer folds in the Sambagawa metamorphic suite of rocks in Japan and afforded a re-interpretation as to the mechanism of their formation. In their theoretical analysis. they assume an initial sinusoidal deflection, perfectly welded contact between layer and matrix, constant strain rate, steady state flow and negligible effect of gravity. They agree that the deformation is nearly homogeneous in the initial stages of up to 10-20 of limb dip. Wavelength selection is active soon after this, the hinges are fixed and the selection is no longer effective. Even if the wavelength is selectively fixed, the behaviour is not altered to any great extent because the strain field is still fairly homogeneous, i.e. neutral surface of strain is not yet established within the layer, fold wavelength is fixed in a relatively short period. Since hinges are fixed, folding of natural rocks is like that around an initial sinusoidal deflection. The results of such an analysis is strikingly similar to natural and experimentally produced single layer folds. Shimamoto and Hara noticed no indications of slip in Sambagawa folds, the contacts were therefore perfectly welded and folds formed by ductile flow. The constant strain rate is a geologically unrealistic assumption. But its change implies change of viscosity during folding. The assumption of constant viscosity ratio may be valid but at this stage of research the assumptions of constant viscosity ratio and constant shortening rate cannot be adequately tested.
Parrisch (1973) observed that no steady state flow can exist. This, together with the research done by Fletcher shows that the folds produced by linear or non-linear flow do not differ much in geometry. This explained the assumption of linear behaviour in Sambagawa folds. There is small relative thickening in the hinge area of Sambagawa folds which is difficult to account for by the numerical analysis of Shimamoto and Hara. This may be due to nonlinear behaviour or due to incompressibility of the material an shown by Stephansson and Berner(1971) and Hudleston and Stephansson by computer simulation (1973). No theoretical work has been done, as well as experimental except a few experiments run by Dubey (1978) as regards three dimensional folding. Recent studies of natural fold geometries suggest that three dimensional analysis is badly needed. Hara has observed that W/t ratio can vary widely from 6.1 to 12.6 along the fold axis even for a single fold. Dubey and Cobbold (1977) have shown in natural folds and by model analogue experiments that the amplitude is highest at the point of perturbation and that the fold progressively opens in either direction away from the point along the hinge as propagation along the fold axis occurs.
The buckling of a single viscous layer enclosed in less viscous matrix was investigated by Williams et al. (1978) by computer based finite-element analysis. They divided the perturbations into two categories : (i) those whose Wd is less than Biot's Wd and which do not play any significant role in determining finite fold shapes; and (ii) perturbations whose Wd is greater than Biot's Wd and which influence the entire fold evolution. In four experiments that Cobbold (1975) ran, the first two had less Wd than that of Biot's while the third was larger. In the Fig, it could be noticed how arc length or dominant wavelength grows with time in all model experiments. The first two folds acquire the same wavelength while the third has a pattern similar to that obtained by Williams et al. by finite element analysis. First a wavelength less than the initial wavelength of the first two models is reached and then it again begins to increase.
If natural rock strata contain banded perturbations longer and shorter than the characteristic dominant wavelength, then the resulting folds are, not predictable by present theories. Any computation of viscosity contrast from the mean fold wavelength wi11 yield a higher ratio as short perturbations may give characteristic wavelength but longer ones will not shorten to this characteristic wavelength. Williams et al. considered single isolated perturbations but natural rock strata may contain many perturbations not too much separated from each other. The experiments based on finite element analysis by Williams et al. also suggest that interference can also affect the development of folds.
Thus, it is not only the geometry of perturbations that counts in fold development but also the relative positions of different perturbations in the rock layers. They concluded that unless complete information about the geometric and distributional characteristics of initial perturbations is known, the viscosity ratios cannot be determined with a high degree of confidence level from the measurements of fold wavelengths and their thicknesses.