A simple visual field method of determining,the

amount of flattening of a flattened flexure fold is

described. The method allows estimation of the

pre-flattening thicknesses and dips of the deformed

beds, so that original thicknesses of sequences and

the total shortening of the layers by folding may

be calculated

Williams, E

University of Tasmania Open Access Repository

PAPERS AND PROCEEDINGS OF THE ROYAL SOCIETY OF TASMANIA, VOLUME 10!. NOTES ON THE DETERMINATION OF SHORTENING BY FLEXURE FOLDING MODIFIED BY FLATTENING By EMYR WILLIAMS Geological Survey, Mines· Department, Hobart, Tasmania. (With six text figUl'CS.) ABSTRACT A simple visual field method of determining ,the amount of fiattening of a flattened flexure fold is described. The method allows estimation of the pre-flattening thicknesses and dips of the deformed beds, so that original thicknesses of sequences and the total shortening of the layers by folding may be calculated, INTRODUCTION Van Rise (1894) recognised two fundamental groups of folds-the flexure (also known as parallel or concentric) type and the similar folds. The geo-metrical characters of the two groups differ marl~edly. With flexure folds the thicknesses of the beds measured at right angles to the bedding surfaces remain constant throughout the fold, whereas with similar folds the thicknesses of the beds measured parallel to the axial surface to the fold are constant but thicknesses measured per-pendicular to bedding are variable (fig. 1). In general, it appears that folds usually en-countered in the field are of a flexure type modified by flattening, which when extensive results in folds that superficially resemble those of similar type (de Sitter, 1958, Ramsay. 1962), Only flattened flexure folds are considered in these notes. Flattened flexure folds are usually readily dis-tinguished especially where variations in the thick-ness of some layers are significantly less than adjacent ones. Again, acutely pinched lower bound-aries of beds are characteristic of this type of fold (fig. 2). Where doubt exists as to whether the examined fold is of the type considered here, marked variations in thicknesses of beds measured parallel to the axial plane of the fold are diag-nostic (see Ramsay. 1962). In the following geometrical analysis it is assumed that layers were initially of uniform thickness. Deformation is divided into two distinct types~ flattening and pure flexure folding-for geomet-rical analysis only. In the actual fold development parts may be undergoing flexure folding whilst other parts are being flattened (Williams, 1965). ES'I'IMATION OF' FLATTENING Ramsay (1962, p. 314-15) has presented a graph-ical method whereby the percentage of fiattening of a flexure fold may be determined. The method in volves the comparison of thicknesses measured perpendicular to bedding of a competent horizon 37 A B FIG.I A. Protl1f.' or flexure fold illustrating unjfol'm thickness of layer normal to beckling. t =::= e .:-::: t". B. Profile of similar fo1d Ivith uniforul thickness of layer measnred ·parallel to axial surface. t ~-= t/ =: t". of known dins with the thickness of that bed at the fold hinge. - However, where difficulties are en-countered in measuring with sufficient accuracy thicknesses of compet.ent horizons, due perhaps 38 NOTES ON DETERMINATION OF SHORTgNING BY FLEXURE FOLDING to well developed sale markings or tectonically frayed boundaries, Ramsay's graphical method is unsatisfactory, Furthermore, with folds exhibit-ing differential flattening Ramsay's method is uncertain, for this phenomenon may be attributed to inaccurate fleld measurements. In order to determine the shortening of strata by folding an estimation of the amount of flatten-ing in a fold is of use only if the form of the profile of the pre-flattened fold is known. Therefore, in using Ramsay's method it is necessary to recon-struct the original fold proflle by trial and error before any further calculations can be made. I-o o ... w Z o 1\, \ FIG. 2 Profile of lIattened flexure fold of sandstone (8) and lutE'''-bedded mudstone (M). Location neal' Tullo"bgornm on the South Esk Highway, North-East Tasmania. Field orientation: fold axes plunge 28° in direction 145°, axial surface dips approximately 56° in direction 205°. Note marked difference in competence of sandstone and mudstone, and acute pinch at lower boundaries of sand-stone. FIG.3 Send-circular area flattened by 10, 20, 30 and 40 per cent. Corres~ ponding points on the CUrves are indicated by broken line. See text for fu]·ther explanation. In the writer's experience pre-flattened fold pro-files correspond to arcs of circles, and this appears to be the experience of many others in that it is the underlying assumption of the treatment given to flexure folds in text-books (e.g., de Sitter, 1964) and in Ramsay's paper. Nevertheless, it is con-sidered necessary that in any method used in the calculation of shortening by folding, pre-flattened fold profiles which do not correspond to arcs of circles are immediately recognised, for in such cases the calculation of shortening is unique for each fold and they are therefore not considered in this paper. During routine mapping activities it appears advisable to use methods for determining flattening in folds which do not depend on numerous accurate measurements of the thicknesses of layers, flnd no difficulties with differential fia.ttening and give an immediate indication as to whether the pre-flattened fold profile is of an arc of a circle. With these points in mind simple graphs, based directly on the theoretical consideration of de Sitter (1958), have been constructed for visual comparison with the folds encountered. Figure 3 shows an area bounded by a semi-circle flattened by 10, 20, 30 and 40 per cent. Corresponding points on the curves are indicated by a broken line. The flgure, with a semi-circle of three inches radius, is engraved on a perspex sheet of 1/l2th inch thickness. This sheet is used in the fleld by holding, preferably mounted on a light tripod, at a suitable distance between eye and out-crop perpendicular to the direction of the fold axis. The distance between eye and perspex sheet is varied until the fold proflle flts the set of engraved curves. Quicker results are obtained when the method is used with folds in layers showing acute pinches at a boundary surface so that the approxi-EMYR WILLIAMS 39 mate centres of folding during the flexural defor-mation are known. By comparing the fold profile with the set of engraved curves on which corres-ponding points have been superimposed the pre-flattened dips of the sectors of the fold can be readily determined. Figure 4A illustrates the use of this method. ONE FOOT '------ ,----~.---' FIG. 4A A. Profile (thkk line) of syncline in sandstone (3) '\vith an10unts of flattening iietermilled by superimp0sed graph (thin Hne) shown on outer arc. Brok~n line indicates unftaUened fold pyofile. Location near Tullochgorum, on South E8k Highway, North-East Tasmania. Field odenta~ tion: fold axis plunge 14° in direction 125°, axial surface dips arJpl'O:ximate1y 61 Co in direction 200 0 Q FIG.4B B. Misfit folds (thick and hroken lines) indicating pre-flattened fold forms are not of al'CS of a circle. Misfitting fold profiles (fig. 4E) and differences in the percentage flattening determined by com-paring both upper and lower surfaces of a bed with the curves inscribed on a perspex sheet, indicate that the pre-flattening fold proflles are not of a circular arc. It must be emphasised that pre-fiattened fold forms which are not oj an arc of a circle are readily recognised by using the method described. Having determined the percentage of fiattening of a fold of a pre-flattened profile of an arc of a circle, it remains to determine the amolmt of shortening by pure flexure folding. ESTIMATION OF SHORTENING BY FLEXURE FOLDING For simplicity let the angle of the arc of uniform curvature be the same in both anticline and adjacent syncline, and let the limbs be straight. Then in fig. 5, where the radius of curvature of the hinges is greater or equal to the thickness of the competent unit folded, it is evident that the percentage shortening is~-1(1--008(1.) + (r' 11') (",'=--Sinrt.) \ I· 2 180 JOO ........ (1) lj ;~) (l'j + rz) where l is the length of the fold limb, (1. half the angle of uniform curvature, T, the radius of curva-ture of the synclinal are and T, the radius of curvature of the anticlinal arc. FIG.5. Geumetry of profile of flexure fold of competent unit where IX is half angle of uniform eUl'vature.. r 1 radius of curvature of synclinal are, r 2 radius of anticlinal arC', and I length of fold limb. In the special case of simple flexure folding. where arcs are of constant curvature (fig. 6) and l is zero, the percentage shortening is-(I -- ~80;;~nc:) . 100 ......................... (2) In simple fiexure folding, shortening is constant for each value of rt., and when centres are colinear is approximately 36.6% (fig. 6E), which is the amount often incorrectly quoted for the maximum amount of shortening by flexure folding (see Ramsay, 1962, p. 313), for in the more general cases it is evident by inspection of equation (1) that considerably more shortening can occur. 40 NOTES ON DETERMINATION OF SHORTENING BY FLEXURE FOLDING ii A B FIG. 6 GeOtnetry of pt'ofiles of simple flexure folds of competent units fen' varying values of tJ.~ half angle of UnifOl"m CUlv'atUl'e, anfl R. distance between centres of curvature. Shortening in A is 100/0 and 13 36.6!j(). 0) R = thiekness of layer. (ii) R > thickness of layer. Note R == r1 .f- r:!~ where r1 is radius of curvature of synclinal al'C, and r 2 radius of anticlinal are. ESTIMATION OF TOTAL SHORTENING If the shortening by pure flexure folding is X% and by flattening Y%, then the total shortening is- XY) (X Y -100 %.. .." .. ,."",.,"',.". (3) With accordian or concertina folds of long straight limbs it is essential to study the hinges in order to determine the amount of flattening (see Williams, 1965). However, the folds may be neglected in the flnal calculations of shortening, Using the visual comparison method both the flattening percentage and the pre-flattened dip of the limbs can be determined (flg. 4A), and the total shortening is given by---X) -, [ 1 -- (1 - .. -- - GOS Cl.J ' I , 100 % ' , . , ,. .,.,',.,' (4) 100 . where X is the percentage flattening, C(. the dip of the pre-flattened limb and ! the length. CONCLUSIONS Usually folds encountered in the fleld are of a flattened flexure type whieh when unflattened have profiles of arcs of circles. The visual graphical method described above is constructed to analyse these folds, but it is designed so as to allow immediate recognition of a fold with a pre-flattened profile of curves not of arcs of circle>' in the event of one being encountered, A comparison of fold profiles in the fleld with a set of curves representing various percentages of flattening of a semi-circular area inscribed on a perspex sheet, allows a calculation to be made of not only the original thicknesses of the deformed layers but also the horizontal extent of the beds before folding, Determinations such as these will give true variations in stratigraphic thicknesses from one locality to another and greatly help in building up a picture of the amounts of structural deformation in regions. EllIYR WILLIAMS 41 ACKNOWLEDGMENTS The methods described have been available for use in the Geological Survey since early 1964, This account has benefited much from discussions with Mr. R. D. Gee and ML D. Leaman. I thank Mr. 1. B. Jennings, Mr. G. Everard, Mr. R. D. Gee. Mr. D. Leaman and Mr. P. Legge for reading and commenting on the manuscript. I also wish to record my gratUude for discussion of the subdect-matter of this paper when it was presented in a seminar in the Geology Department, University of Tasmania, in July. 1966. RAMSAY, J. tion REFERENCES 1962.-The Geometry and Mechanics of Forma· Similar" Type folds. .I. Geol., 70, 309-327. SrTl'ER. L. U. DE~ 1964.--Stru:ctural Geology~ 2nd Edition, London. 1958.-Boudins and Parasitic Folds Relation to and Folding. ((eol. en ]Ylijnb.~ 277-286. V AN HIER, C. R.. 1894.--Principles North American Pre.., Cambrian Geology. U.S. Geol. 16th Ann. Rep., 581-843. WU.I.Il\MS. E .• 1965.-The Defornlation of Competent Gl'anUlal' Layers in Folding. Amer. ,1. So£., 263, 229-237. 

Determination of shortening by flexure folding modified

by flattening

http://eprints.utas.edu.au/14253/1/1967_Williams_Determination_of_shortening.pdf

Determination of shortening by flexure folding modified by flattening

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