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Graphic representation of Sorby's ideas (Sorby, 1853) on the superposition of the deformation caused by volume loss (only possible normal to bedding) on the deformation due to general shortening of the rock and how this causes different but compatible finite strain ellipses in each lithology. Cleavage parallels the finite strain ellipses, being thus refracted. Figure based on Ramsay and Huber (1987, Fig. 21.24).
Source publication
High-quality research developed during the 19th century
established the foundations of rock strain investigations. Careful
observation and description of rock fabrics and deformed objects in rocks
allowed early researchers to obtain mathematical expressions that are still
used today to quantify strain. Thus, in a span of a few decades, and
applying...
Contexts in source publication
Context 1
... plane; in his words, "the amount of elongation in the line of dip [of bedding] could not vary" (since no detachment was observed; Sorby, 1853, p. 145). Therefore, the shale can accommodate more contraction (with volume loss) than the sandstone only in a direction normal to bedding, resulting in a cleavage plane more inclined towards the interface (Fig. 1). We will see how Harker (1886) further explained this concept, but still Sorby's theory remained as one of the possible explanations for strain refraction in multilayers: the difference in bedding-normal compaction across the surface ( Ramsay and Huber, ...
Context 2
... this point, Sorby incorporated the action of pressure-solution into his mechanical theory of cleavage, at least in calcareous rocks. A beautiful example of his understanding of rock strain is given in a paper published in 1879, in which he describes a deformed limestone band from Ilfracombe, reproduced in Fig. 3a (his Fig. 10). The description states the ...
Context 3
... Fisher (1884a) proposed that the rock strain associated with cleavage, including a flattening perpendicular to cleavage and a lengthening parallel to its dip, was the result of "a pressure combined with a shear" (p. 269), which would explain the lineations parallel to the cleavage dip often seen in slates. He illustrated this concept with his Fig. 1 (reproduced in Fig. 4a), which is the first diagram of simple shear applied to rock strain that I have record of. He argued that this shear was due to the "sinking" of an elevated region after folding (cf. Sharpe, 1847; Phillips, 1857) and showed mathematically how vertical movements of the crust would generate velocity differences in adjacent portions of ...
Context 4
... his aim was to evaluate whether the cleavage was formed by flattening (compression perpendicular to cleavage planes) or by shear (cf. Fisher, 1884b, 1885), and he simplified the problem to the question "whether the cleaved rocks have or have not suffered a total diminution of bulk" (Harker, 1885b, p. 266). ...
Context 5
... the packing reaches a limit, volume loss by this process is hampered; thus "continued pressure would give rise to a vertical expansion of the mass compensating the horizontal compression" (Harker, 1885b, p. 267). The deformation in this stage is of constant volume, with an increase of the long axis of the ellipsoid and a proportional decrease of the short axis (a > b > c), and the cleavage is best developed due to the more perfect arrangement of the long and flat particles perpendicular to the compression (cf. ...
Context 6
... constant volume. The related ellipsoid would turn out as an "excessively elongated and flattened" one (a c). This model as put forward by Harker (1885b), like the model mentioned above by Sorby (1880), is remarkably still valid today, as a description of the progressive strain in sedimentary rocks (see Ramsay and Huber, 1983, pp. 185- 188, fig. ...
Context 7
... cleavage formation. Van Hise (1896) considered that the parallel alignment of old and new particles, either flattened (cf. Sharpe, 1947) and/or rotated (cf. Sorby, 1853), was the main cause of the cleavage, the latter understood as the property of some rocks to part in Figure 5. Geometry of the strain ellipses of the sandstone and shale layers of Fig. 1, which are rotated ellipses with reference to the Cartesian x, y coordinates. µ is the ratio between the volumetric stretches of both ...
Context 8
... OP makes an angle ϕ with the x coordinate axis, and this line transforms after deformation in line Op at an angle ϕ with the same axis (Fig. A1). Equation (1) establishes the relationship of the tangent of angle ϕ with the tangent of angle ϕ . In the example of Fig. A1 it is clear that the length from the x axis to point P is tan ϕr. This distance becomes tan ϕr √ λ 2 after deformation, which is the length from the x axis to point p. Therefore, this allows us to conveniently ...
Context 9
... OP makes an angle ϕ with the x coordinate axis, and this line transforms after deformation in line Op at an angle ϕ with the same axis (Fig. A1). Equation (1) establishes the relationship of the tangent of angle ϕ with the tangent of angle ϕ . In the example of Fig. A1 it is clear that the length from the x axis to point P is tan ϕr. This distance becomes tan ϕr √ λ 2 after deformation, which is the length from the x axis to point p. Therefore, this allows us to conveniently ...
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