Folding of laterally compressed multilayers in the field of gravity, I

Details Folding of laterally compressed multilayers in the field of gravity, I Folding of laterally compressed multilayers in the field of gravity, I

Jun 1970

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1970pepi....2..203r&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 2, Issue 4, p. 203-232.

Physics

10

Scientific paper

Laterally compressed stratified rock complexes tend to develop folds with a defined wavelength (or sometimes several defined wavelengths). To the extent that solid rocks in the process of slow creep behave as Newtonian substances the characteristic wavelengths, when measured in proportion to the thickness of a selected reference stratum, depends upon the following dimensionless parameters: (a) the ratios between the thicknesses, (b) the ratios between the viscosities, (c) the ratios between the compressive stresses (buckling stresses) exerted on the different layers, and (d) the ratios between these stresses and the stresses due to gravity, viz. σb/Δρgh, where Δρ is the difference in density between adjacent layers. Of course, the number of layers in the complex, and the boundary conditions on top and bottom are significant (whether e.g. limited by infinite half spaces or finite layers with rigid surfaces). Though valid only for small amplitude/wavelength ratios the theoretical model developed is capable of determining the characteristic - or dominant - wavelength for complexes consisting of any number of layers. Each layer must be uniformly thick and exhibit uniform Newtonian viscosity and uniform density. All of these properties may, however, vary from layer to layer. Neither does the buckling stress need to be the same on each layer. To construct the multilayer theory equations for the buckling of a single free stratum are firstly developed. Some of these equations (eqs. 18, 20, 24, 25) relate the rate of growth of the buckles to the buckling stress; others (eqs. 27 a, b, c, d) show how the sinusoidally varying normal and shear stresses at the two surfaces of a buckling layer depend upon the buckling stress, the density of the layer and the rate at which the buckles amplify. In the equations the viscosity, the thickness and the wavelength are involved. The solution for a laterally compressed multilayer consisting of a stack of strata welded together at the interfaces is now found by applying the condition for dynamic equilibrium in terms of the normal stress and the shear stress being continuous at the contacts. Three cases are conveniently distinguished, viz. 1).The gravity is insignificant, realized when the terms Δρgh/σb are small (they vanish, of course, when the density contrasts vanish, but the gravity effect may also become negligible when the thicknesses are small even for appreciable density contrasts). The folding is a pure buckling process, with one or more characteristic wavelengths as measured in proportion to a given thickness, that depends only upon the viscosity ratio, the thickness ratio and the ratio between the buckling stresses exerted on the different layers. 2).The buckling stresses vanish or are negligible in relation to the gravity term, i.e. the terms Δρgh/σb are relatively large. Now the folds develop solely due to buoyancy of one or more of the layers which must be less dense than their superincumbent strata. This situation is treated in Ramberg (1968). 3).Both the gravity term and the buckling stress assume appreciable magnitudes. One may distinguish between the case of normal density stratification (i.e. the density increases downward) and the case of inverted density (the density at least in part of the system increases upward). With normal density stratification the characteristic wavelength tends to be less than for pure buckling in the same system (i.e. if the density contrast was disregarded, point 1). With inverted density stratification the characteristic wavelength may be larger than under pure buckling in the same system.

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