Geometrical analysis of kink-bands seems to suggest that they are formed by consumption of least energy or less work . is done in the formation of kink-bands than in case of the formation of chevron folds. The axial plane normally bisects the angle between kinked and unkinked sectors but this is not true if there is dilation within the kinked zone (D ) so that the angles b1 and b2 are not equal(see Figure below). In this case the amount of orthogonal thickness is increased by an amount dt. The dilation D or d t/t is given by :

Delta =[(sin alpha)/(sin beta)]-1

If beta>alpha, then there is reduction in volume within the kink-band and dilation will take negative value. Positive dilation however is more common in naturally developed rocks. In extensional kink-bands since the shortening is layer normal, negative dilation is encountered. It is common to find tension gashes in the kinked sector suggesting the role of shearing. Conjugate or single kink-bands are developed by initiation of a

gentle buckle which develops into a kink-band by migration of axial surfaces of this buckle so the dip of the kink-band remains the same throughout the development of kink-bands. The total shortening in the development of kink-bands may not exceed 25 to 30 per cent. It is common to find faults developing along the axial surfaces of kink-bands since these are surfaces of shear and usually kink-bands, since formed during late stages of deformation may pass from ductile to brittle regime. The kink planes, to allow the brittle rupture and further displacement along them possible generally become curviplanar so that evenually a condition of s1 bisecting the acute angle may be reached.

but this is not true if there is dilation within the kinked zone (D ) so that the angles b1 and b2 are not equal(see Figure below). In this case the amount of orthogonal thickness is increased by an amount at. The dilation dt or dt/t is given by :

D =[(sin b2)/(sin b1)]-1

If b2> b1, then there is reduction in volume within the kink-band and dilation will take negative value. Positive dilation however is more common in naturally developed rocks.

Let us consider a kink-band of length l under a shortening of (l+e).l. If the angle of dip of kink-band is a and the the thickness t, then the overall slip on the surfaces in the kink-band is given by

2t.tan a /2 and the shear strain gt by

gt= 2 tan a /2.

Thus (see Ramsay, 1967, eq. 7-44):

(1+e) =(1- t/l) cos a + t/l sin ?

It is common to find tension gashes in the kinked sector suggesting the role of shearing. Note that eq. above is similar to that developed for chevron folds.Conjugate or single kink-bands are developed by initiation of a gentle buckle which develops into a kink-band by migration of axial surfaces of this buckle so the dip of the kink-band remains the same throughout the development of kink-bands. The total shortening in the development of kink-bands may not exceed 25 to 30 per cent. It is common to find faults developing along the axial surfaces of kink-bands since these are

surfaces of shear and usually kink-bands, since formed during late stages of deformation may pass from ductile to brittle regime. The kink planes, to allow the brittle rupture and further displacement along them possible generally become curviplanar so that eventually a condition of s1 bisecting the acute angle may be reached. The conjugate kink-bands may have a symmetry of low or high order. If two of the principal stresses (or the principal strains) lie within the pre-deformed layering and the third normal to it, the symmetry of conjugate kink-bands is orthorhombic or of high order. If only one of the principal stress directions is contained within the pre-deformed layers and the other two are at angles other than 90°, then the symmetry of resulting structures is monoclinic. If none of the principal stresses are symmetrically disposed relative to the layers before deformation, then the symmetry of the resulting conjugate kink-bands or single kink bands is said to be triclinic. We may conclude:

Case 1: s1 and s2 within layering= orthorhombic

Case 2: s1 within the layering, s2 and s3 not contained within the layers: Monoclinic

Case III; All three principal stresses neither parallel nor normal to layering: Triclinic

n the above three cases, s3 denotes the lease principal compressive stress, s2 denotes the intermediate principal compressive stress and s1 denotes the maximum principal compressive stress but in the figure shown the opposite or engineering convention is used. The symmetry can be known by direct observation or by plotting on an equal area net the orientations of axial planes of conjugate folds and the orientation of un-deflected layering. Depending on the variation in orientation of the pre-kink schistosity, only one set may be developed in an area with complete exclusion of the other set.

Complementary set may appear in another part of the same region where orientation of the layering is favourable to the general applied stress. Roberts (1971) showed this for the Flornes and Meraker area in a part of the Norwejian Caledonides. There is no evidence to suggest that chevron folds are produced from the original conjugate kink-bands but chevron folds may be found associated with conjugate kink-bands in the same sequence of strata because of anisotropy differences between parts of the same complex. Box folds or conjugate kink-bands may be associated with limb faults if such structures are produced over a surface of decollement in a thrusted sheet since ramp and flat geometry is common in such areas. The photograph he limb faults in fuchsite bearing quartzite of Archaean supracrustals occuring as enclaves within the granitoids batholith of Bundelkhand in Central India. Alongside the photograph are given the four diagrams from Ramsay (1967) which indicate possible stages of development of these limb faults or limb thrusts or high angle reverse faults.If the comprssion applied to laminated anisotropic medium is at an angle generally less than 25 degrees, then the conjugate or box folds developed may have a striking asymmetry with one kinked zone better developed than the other. The two photographs show the top asymmetrical conjugate kink-bands from Rhoscolyn anticline in North Wales and the lower one similar structures from the Delhi orogenic belt north of Khimpura near Masuda.