FOLDING OF ANISOTROPIC MEDIA

See buckling of laminated media.

__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 ans 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 ratiosgoverned 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.