INCREMENTAL STRAIN SUPERIMPOSED ON
FINITE STRAIN
Any finite strain state is built by addition of gradual infinitesimally small increments of strain to build up the next finite strain state. The diagram below shows a sequence like the series of figures which could be likened to a series of stills from a continuous motion picture. If we introduce a circle at the 5th stage of deformation, it will be deformed into an ellipse which is known as the INFINITESIMAL OR INCREMENTAL STRAIN ELLIPSE. The incremental strains when added on to the 5th stage finite strain state then produce the next finite strain state or the 6th state. In reality the process can be far too complex than that shown in the figure. We know that the strain ellipse, whether finite or infinitesimal, contains areas of positive extension (with elements getting increased in length, or the boudinage as the naturally occurring phenomenon) and the negative extension (which implies folding or contraction or negative extension). When the incremental strain ellipse is superimposed onto a finite strain ellipse with the principal strains of both not being coincident, four distinct zones or areas of overlap are produced. The diagram given below shows this feature. |
Top left is the finite strain ellipse or the strain that has occurred while the one at top right shows the incremental strain ellipse or what might happen if this is superimposed on preexisting finite strains on lines or planes oriented differently with respect to both, the principal finite strains and principal incremental strains. Zone I: is bounded by lines of ef=0 and ei=0 or the one of +ve ef and positive ei. This implies that the lines were extended by +ve finite extension and will further extend by +ve incremental extension. Geologic situation is that of planes that are broken by boudinage and will continue to suffer boudinage on superimposition of incremental strain. Further boudinage may occur or the boudins may be separated by further extension. As it may require tremendous amount of mechanical work to further break a layer which is already broken by boudinage, the natural situation might be the separation between the individual boudins. This zone is therefore the one of ACTIVE BOUDINAGE. Zone II :is of -ve finite extension followed by +ve incremental extension. The lines that were contracted (or planes folded) now fall in the +ve extensional area of the incremental and the lines must therefore extend or planes unfold and then give rise to boudins. As the rocks are very heterogeneous in nature, it is not possible for folded layers to get unfolded; rather they get disrupted by boudinage. This zone is therefore one of BOUDINAGED FOLDS. Zone III :shows the one f -ve finite and -ve incremental extension. This implies continuous contraction or folding. The gentle folds generated by finite -ve extension get tight and highly amplified by further -ve incremental extension. This zone is the one of ACTIVE FOLDING. Zone IV: is one of +ve finite extension but -ve incremental extension. The lines that were extended are now going to contract because of -ve incremental extension. The result which is geologically realistic is the development of structures that could best be described as FOLDED BOUDINS. |