CHEVRON FOLDS, THICKNESS VISCOSITY RELATIONS
Ramsay (1974) also studied the speed of development of chevron folds by theoretical analysis. His results show that when the critical threshold value of shear stresses acting along the layers is crossed (i.e. at a certain value of limb dip or amount of shortening), the speed of development of folds accelerates but after about 50 percent shortening has been achieved for folds with very small t/l ratio, the speed decelerates and eventually the fold structure locks up. Further stress might lead to the formation of flattened chevron folds.
In chevron folds the ratios of shear strain rates in the competent and incompetent material can be computed if their thicknesses and limb dips at each stage are known (Ramsay 1974, eq. 22). Thus
gt1/gt2=[(t1/t2+1)sec2a+t1/t2]-1 Thus the ratio of rates of shear is dependent exclusively on the thickness ratio of layers at any stage since this thickness ratio is again dependent upon the limb dip. Fig shows the relations expressed by equation given above in terms of a set of standard curves. The figure illustrates that as the fold grows, the ratio of shear strain rates becomes less and less, this implies that the shear strain rate in the incompetent layers must increase with growth of fold to keep the ratio low. Because incompetent material is more liable to flow, the ratio of shear strain rate is proportional to the reciprocal of the viscosity ratio of a competent-incompetent pair. If the equation given below holds good, the shear strain rates in layers are proportional to their viscosities otherwise, the equation given before the beginning of this paragraph holds good.
This relationship is also graphically illustrated in figure. At low limb dips or less amount of shortening the shear strains in competent layers are high but under greater shortening reverse is the case. Under these conditions, extension cracks in outer area of competent layers appear during advanced stages of fold development with tension gash veins in less competent layers and development of cleavage in the inner arc region and hinge area of less competent material. If shortening further increases, the shear strain rate in the less competent layer exceeds that in the competent layer. This produces extension fissures in the inner are region of the competent layer and concentric cracks at the outer arc. Depending on the actual ratio of viscosities and thicknesses the structures of the first or second category may be predominant as illustrated in the figure. In general, it may be concluded that if the viscosity ratio is high, the model on left in figure is stable, else the structures of model to the right may be more preferentially developed. Four diagrams show the four cases, two for high viscosity ratio but high or low t1/t2 and two for low viscosity ratio but high or low t1/t2.