Geometry and Internal Structures of Flexural Folds (Ⅰ) Folding of a Single Competent Layer Enclosed in Thick Incompetent Layer

Some problems on folding of a single competent layer enclosed in thick incompetent layer, with regard to the variation in competency difference between the related rocks, have been examined on natural flexural folds, i. e., folds of quartz-rich layers in pelitic schist in the Kune district and the Oboke district, folds of quartz-rich layers in psammitic schist in the Oboke district, and folds of psammitic schist in pelitic schist in the Oboke district.
Shape and orientation of the strain ellipsoid of mean strain of small domain in the Oboke and the Kune district, at the time when the buckle folding of competent layers and the cleaving (the formation of strain-slip cleavage) of incompetent matrix in that domain occurred, have been determined. The strain-slip cleavage in the incompetent matrix is correlated with the plane normal to the direction of maximum shortening, i. e., the principal plane XY of the mean strain ellipsoid.
Geometric relationships between the strain ellipsoid of mean strain of a domain and geometric elements of buckle folds have been examined, especially where the enveloping surfaces of folded competent layers are inclined at angles of between 50° and 60° to the principal plane XY. At the initial stage of folding the axial surface shows a tendency to be normal to the layer being folded. For some folds the axial surfaces are completely rotated toward the principal plane XY when the interlimb angle becomes 90°-100°, but for some other folds they remain normal to the layer even when the interlimb angle becomes 700-80°. When the interlimb angle becomes smaller than 70-80°, the axial surfaces of all folds tend to rotate toward the principal plane XY. Although geometric relationship between the fold axes and the mean strain ellipsoid has not been strictly determined, the former does not appear to lie on the principal plane XY.
The intensity of folding of competent layers, which is estimated by interlimb angle, is maximum for the layers parallel to the schistosity of the incompetent matrix and to the principal axis Z, and minimum for those normal to the schistosity and parallel to the axis Z, that showing the competency difference between different directions in the incompetent matrix, that is, the maximum competency in a direction parallel to the schistosity and the minimum in a direction normal to it.
It has been clarified that for the folds of quartz-rich layers in pelitic schist of the Kune district and the Oboke district and those in psammitic schist of the Oboke district a linear relationship exists between the length of arc (L) and the thickness of the quartz-rich layer (T). In the former cases, the average L/T ratios are 14.9 (Kune) and 16.2 (Oboke), and the minimum L/T ratios are 9.1 and 11.6, while in the latter case the average L/T ratio is 11.6 and the minimum L/T ratio 5.8, respectively. Folds of psammitic layers in pelitic schist show frequently L/T ratios smaller than 1.00.
On the assumption that during the folding pelitic schist, psammitic schist and quartz-rich layer behaved mechanically as Newtonian substance, the ratios of viscosity coefficient between those rocks have been esti-mated by using the average L/T ratios according to the wavelength equation of BIOT (1961). In the Oboke district, the viscosity ratio between the quartz-rich layer and the psammitic schist is ca. 38, that between the quartz-rich layer and the pelitic schist ca. 102, and that between the psammitic schist and the pelitic schist ca. 3 (indirectly estimated). In the Kune district, the viscosity ratio between the quart-rich layer and the pelitic schist is ca. 80.
The relationship between the mechanisms of buckle folding and the internal structures, between the folding mechanisms and the viscosity ratios of the related rocks and between the folding mechanisms and the orientational relation of the buckled layer to the mean strain ellipsoid of the domain concerned have also been examined.
Internal structure of buckle fold appears to be commonly characterized by the cleavage which is correlated with the principal plane XY of mean strain ellipsoid at any position of the fold. When buckled competent layer is a schistose rock, the cleavage is referred to the type of strain-slip cleavage, while for non-schistose rock it is referred to the type of flow cleavage.
The strain pictures developed during the buckle folding of competent layers which arc parallel or subparallel to the principal axis Y (the intermediate axis = constant) have been classified into the following five types; Type I — the neutral axis is located at or near the middle part of fold knee, and the part of no-distortion is further developed at the inflection point and on the outermost side of the limbs. The principal axes X (the maximum extension axis) and Z(the maximum contraction axis) arc oriented normal to the fold axis. Type II — the neutral axis is developed at the outermost part of fold knee, and the part of no-distortion is rarely developed on the limbs. The principal axes X and Z are oriented normal to the fold axis, and the principal axis X is radially arranged through the fold. Type III — the neutral axis is not developed within the layer. The principal axes X and Z are oriented normal to the fold axis, though at the outermost part of fold knee X = Y. The principal axis X is radially arranged through the fold. Type IV— the neutral axis is not developed within the layer. At any position of the fold the mean strain ellipsoid is of the triaxial type. The principal axes X and Z arc oriented normal to the fold axis. The principal axis X is radially arranged through the fold. Type V —although the strain picture of this type may be essentially the same as that of Type IV, the angle β (angular deviation of the principal axis X beween both limbs) for the former is much smaller than that for the latter. The change of the strain picture from Type I to Type V corresponds to the decrease of the angle β. The strain pictures of Type I, Type II, Type III, Type IV and Type V are never the end member.
The folds of quartz-rich layers in politic schist of the Kune district show the strain pictures of Type I, Type II and Type III, while those in psammitic schist show the strain pictures of Type II, Type III and Type IV. The folds of psammitic layers in pelitic schist show the strain picture of Type V. A definite relationship exists between the mechanisms of folding and the viscosity ratios of the related rocks, that is, the change of the strain picture from Type I to Type V corresponds to the decrease in the viscosity ratio, that showing a good agreement with RAMBERG'S theory (1964). Namely, the decrease of viscosity ratio of the related rocks corresponds to the increase of distance of between the neutral axis and the bottom surface of fold knee of the competent layer, and to the decrease of the angle β, when compared between the folds with the same inter-limb angle and the same initial thickness of layer. It has been pointed out that, if any fold is characterized the fan-like arrangement of cleavage with downward convergence, buckling instability played in general the by important role in the development of the fold.
The nature of change of layer-thickness due to buckling has also been examined. For folds which show orthorhombic or near orthorhombic symmetry and larger interlimb angles, the competent layers show generally a tendency to be thickened at all positions of the folds and the amount of thickening appears to be maximum at the fold knee and minimum at the inflection point. The nature of change of layer-thickness due to buckling appears to be closely related to the type of strain picture (Type I to Type V) which is controlled by the viscosity ratio of the related rocks: with respect to the whole amount of layer shortening, the amount of layer thickening at the fold knee and the inflection point, and the difference in the amount of layer thickening between these two positions, Type I <Type II<Type III <Type IV <Type V, when compared between the folds with the same interlimb angle. Roughly speaking, the layer shortening due to the folding (interlimb angle = ca. 65°), which is characterized by the formation of the strain picture of Type I, may be less than ca. 10 per cent. That due to the folding for the strain picture of Type II may be between ca. 10 per cent and ca. 15 per cent. And, that due to the folding for the strain picture of Type IV—Type V may be larger than ca. 15 per Cent. For the fold of competent layer, therefore, the present length of arc is not always equal to the initial fold wavelength. From the measurement of the layer shortening for the folds of quartz-rich layers in the Kune district and the Oboke district, the average L/T ratios and the viscosity ratios between the related rocks have been re-estimated.