FOLDS, SINGLE LAYER

Since buckling of a "Single" more viscous layer enclosed in a less viscous matrix has been very extensively studied by theoretical analyses, model analogue experiments and by computer based finite element analysis, a special section is included here to discuss the development of such folds. We have briefly discussed the development of a single layer into buckle folds in fold profile, Biot's (1959,1960- thin plate theory) previously briefly alluded to, in this regard was the most pioneering work. Ramberg (1960) arrived at the same conclusion in Uppsala but the approach of the two workers and the constraints considered by the two were slightly different. Sherwin and Chapple (1968) based on measurements on naturally developed "single" layer folds, most of these being quartz veins in phyllitic matrix (Sprague Upper Reservoir group), of slaty matrix (Martinsburg slate) or sandy matrix (Vermont Group), found the W/t ratios were actually lower than the Biot-Ramberg theory had predicted. The total amplification at the dominant wavelength was also found to be considerably less than that predicted by the Biot-Ramberg theory. In the light of their studies they modified the existing equation

Wd=2pt(m1/6m2)1/3

to

Wd=2pt[m1(s-1)/6m2(2s2)]1/3

where S is the bulk strain ratio involved and which Sherwin and Chapple were able to compute accurately. The equation above is the same as given by Sherwin and Chapple (1968) except that uses the notations similar to that of Biot for immediate ready comparison.

Biot had predicted on the basis of his theoretical analysis, the thin plate theory, that no significant buckling would occur if the viscosity contrast was less than 100:1. Sherwin and Chapple however showed that the dominant wave number ld which is the ratio of 2pt to Wd is an important factor and determines the amount and rate of amplification. Thus folds can form even if the viscosity contrast was just around 4.0. In other words, folds of the same amplitude can be produced under different viscosity contrasts but this will be controlled by the amount of shortening of the material under as assumed plane strain condition.