Theory of Folding of Stratified Viscoelastic Media and Its Implications in Tectonics and Orogenesis
This paper presents an introduction to the theory of folding of stratified viscoelastic media under compression and discusses its significance in the context of tectonics and orogenesis. Simplified derivations are given for results obtained earlier by the writer as particular cases of more elaborate theories. The writer emphasizes the mechanism involved in folding. The paper begins with a discussion of the buckling of an elastic rod that is under axial compression and is restrained laterally by viscous dashpots. The analysis then proceeds to the analogous problem for an elastic and a viscous plate surrounded by a viscous medium. Results of some of the more complex problems previously analyzed by the writer are also applied and discussed. Experimental verification of the theory by model tests is presented in a companion paper (Biot, Ode, and Roever, 1961). A new feature of the present approach is the emphasis on rate phenomena and time histories in tectonic folding. In purely static problems of elastic buckling, a sharply defined wavelength is associated with the instability. By contrast, for viscoelastic media, the present theory leads to the concept of dominant wavelength and band width selectivity in analogy with the theory of electric wave filters. This is well illustrated by the gradual appearance of near-regular folds when a purely viscous layer surrounded by a viscous medium of lower viscosity is subjected to a compression in a direction tangent to the layer. The theory is applied to specific examples of geological interest. These include the case of a single layer or a superposition of layers. Previous theoretical work by the writer is applied to the discussion of folding, under the simultaneous action of gravity forces and a horizontal compression, for a single layer or a superposition of layers lying at the surface of a deep substratum of lower viscosity. The case of a continuously inhomogeneous medium under similar forces is also included. Using accepted values of rock viscosity and elastic moduli, the writer finds that the time required for significant folding to take place agrees very well with the geological time scale. Folding may occur under tectonic stresses that are small in comparison with the crushing strength of the, rock. The time history of folding depends, of; course, on initial irregularities of the layers, but9 after sufficient time the folding becomes fairly! insensitive to the magnitude and the distribution of the initial disturbances. The writer concludes ; that the viscous mechanism tends to predominate in tectonic folding. As a theoretical consequence, the wavelength of the folds will, in general, not be sensitive to the magnitude of the tectonic stresses unless gravity forces become important. The calculated wavelengths are in good agreement with the range of observed values. The point at which plastic or brittle failure occurs is found to depend primarily not on the magnitude of the strain but on deformation rates. The theory can be applied to materials with nonlinear stress-strain characteristics, and the procedure to accomplish this is briefly discussed. Certain nonlinear features resulting from the geometry of deformation are shown o t have a bearing on the regularity of the folds.