Analysis of superposed strain: A case study from Barr Conglomerate in the South Delhi Fold Belt, Rajasthan, India

The structural geometry in the Barr conglomerate and the neighboring rocks in the western flank of the Meso- to Neoproterozoic South Delhi Fold Belt indicate superposed deformation, with structures developed by horizontal dextral simple shear deformation superimposed on earlier structures formed during approximately ESE-WNW compression and subvertical maximum elongation. The first deformation produced NNE-SSW trending subvertical schistosity, and associated steeply plunging isoclinal folds, mineral lineation and pebble elongation lineation having almost downdip alignment on the schistosity surface. The second deformation produced dextral folds both on bedding and schistosity surfaces and modified the shape of the pebbles already deformed by the first deformation. On vertical sections perpendicular to the schistosity trace the pebbles show sub-ellipsoidal shape with their mean elongation direction parallel to the schistosity trace. On the horizontal section the pebbles often show asymmetrical shape and asymmetrical deflection of the schistosity surface around the pebbles. The mean elongation direction makes a small angle (2°–8°) in the counter-clockwise sense with the schistosity surface. This obliquity is due to modification of post-first-deformation sub-ellipsoidal shape by later horizontal simple shear using the schistosity surface as the movement plane. Analytical expressions are derived for the modification of an original ellipse by simple shear parallel to the long axis of the ellipse. A family of curves has been generated to depict the change in axial ratio and orientation of long axis for different initial axial ratios, and for different values of shear strain (γ). Using these curves it has been possible to factorize the total strain into two components representing the earlier compression and the later simple shear. It is noted that the computed earlier shortening strain ellipsoids are consistently in the flattening field close to the line of pure oblate ellipsoids in the Flinn plot. There is no systematic spatial control on the variation in the values of shear strain (γ), strain ellipsoid shape parameter (k), and intensity of distortion (d) as one proceeds south to north along the strike of the conglomerate.

► In superposed deformation separation of strains of each deformation is difficult.
► Expressions are derived for an initial ellipse deformed by a simple shear parallel to its long axis.
► A family of curves has been generated with variable initial axial ratios and shear strain.
► These curves help to factorize the total strain into earlier compression and later simple shear.
► We apply these curves to compute the two strains in a deformed conglomerate.