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BUCKLING OF LAMINATED MEDIA

This concept given by Biot(1965) but considerably developed by Cobbold et al. (1971). They considered the average rheologic properties of the rock composing the multilayer complex rather than the individual properties of each layer as done by Ramberg. This was extension of the theoretical analysis put forward by Biot in 1965 but supported by model analogue experiments using materials such as soft and hard plasticene. Biot had suggested that the anisotropy is highest when N and Q the compressive and shear moduli are widely different. That is the anisotropy is high if N>>Q and N<<Q but least when N=Q which occurs when the applied stress is at 45 to the planes  of anisotropy. They found that two ratios governed the formation of structures in homogeneous anisotropic material, one of these being the ratio M/L or the ratio of compressive to shearing stress modulus and the other P/L ratio which is non-dimensional and indicates critical stress difference. M/L is plotted on the abscissa and P/L on the ordinate constructed at (M/L)/2 value. The ordinate at zero M/L indicates the initial stress. Three fields could be noticed in the accompanying diagram which indicate three different types of instabilities in a multilayered complex consisting of statistically homogeneous anisotropic material. In case of type 1 instability the ratio M/L exceeds 0.5 and the ratio P/L exceeds unity. The structures formed under this type of instability are usually sinusoidal folds. If M/L ratio is less than 0.5 and P/L ratio less than unity but greater than 4M/L(1-M/L), then the complex has high anisotropy and the structures developed are conjugate kink-bands, box folds, single kink-bands or chevron folds or mitre folds. These are known as type 2 instability structures. If M/L ratio is less than 0.5 and P/L ratio greater than unity then type 3 instability is said to develop producing structures intermediate between conjugate kink-bands and sinusoidal folds. Thus Cobbold et al.(1971) have shown that in homogeneous anisotropic media, there are two ends of a spectrum one of which represents material of high anisotropy and in which conjugate kink-bands are developed and at the other end in material of low anisotropy, sinusoidal folds are developed.