Selective buckling of composite layers with contrasted rheological properties, a theory for simultaneous formation of several orders of folds

Ramberg, Hans

doi:10.1016/0040-1951(64)90020-4

Cited by 241 publications

(65 citation statements)

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“…This dominant wavelength solution was re-derived by Ramberg and Stephansson (1964) with a slightly different approach, and in addition was verified by them with laboratory experiments. In Eq.…”

Section: Lithospheric Foldingmentioning

confidence: 63%

“…Hudleston and Treagus, 2010). Ramberg and Stephansson (1964) performed laboratory experiments on folding of a viscous plate (made from molten mixtures of colophony and diethyl phthalate) floating on an aqueous solution of potassium iodide to verify the dominant wavelength for folding under gravity given in Eq. (34).…”

Section: Resultsmentioning

confidence: 99%

“…Ramberg, 1963Ramberg, , 1964Ramsay and Huber, 1987). As outlined above, studies have consistently shown that multilayers fold more strongly than individual single layers.…”

Section: Multilayer Foldingmentioning

confidence: 99%

“…This stress, if vertically integrated over the thickness of 20 km, corresponds to an unrealistically high force per unit length of ∼ 8 × 10 13 Nm −1 . All studies on elastic lithospheric folding have shown that the stress required for folding is unrealistically high and hence folding of the lithosphere was considered impossible (see, for example, the introductions in Ramberg and Stephansson, 1964;Lambeck, 1983a). However, McAdoo and Sandwell (1985) showed that for an elasto-plastic layer, with lithospheric strength based on experimental rock mechanics, the average stress required to fold the oceanic lithosphere is reduced to 600 MPa, which could be naturally realistic.…”

Section: Lithospheric Foldingmentioning

confidence: 99%

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Folding and necking across the scales: a review of theoretical and experimental results and their applications

Schmalholz

Mancktelow

2016

Solid Earth

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Abstract. The shortening and extension of mechanically layered ductile rock generates folds and pinch-and-swell structures (also referred to as necks or continuous boudins), which result from mechanical instabilities termed folding and necking, respectively. Folding and necking are the preferred deformation modes in layered rock because the corresponding mechanical work involved is less than that associated with a homogeneous deformation. The effective viscosity of a layered rock decreases during folding and necking, even when all material parameters remain constant. This mechanical softening due to viscosity decrease is solely the result of fold and pinch-and-swell structure development and is hence termed structural softening (or geometric weakening). Folding and necking occur over the whole range of geological scales, from microscopic up to the size of lithospheric plates. Lithospheric folding and necking are evidence for significant deformation of continental plates, which contradicts the rigid-plate paradigm of plate tectonics. We review here some theoretical and experimental results on folding and necking, including the lithospheric scale, together with a short historical overview of research on folding and necking. We focus on theoretical studies and analytical solutions that provide the best insight into the fundamental parameters controlling folding and necking, although they invariably involve simplifications. To first order, the two essential parameters to quantify folding and necking are the dominant wavelength and the corresponding maximal amplification rate. This review also includes a short overview of experimental studies, a discussion of recent developments involving mainly numerical models, a presentation of some practical applications of theoretical results, and a summary of similarities and differences between folding and necking.

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Section: Lithospheric Foldingmentioning

confidence: 63%

Section: Resultsmentioning

confidence: 99%

“…Ramberg, 1963Ramberg, , 1964Ramsay and Huber, 1987). As outlined above, studies have consistently shown that multilayers fold more strongly than individual single layers.…”

Section: Multilayer Foldingmentioning

confidence: 99%

Section: Lithospheric Foldingmentioning

confidence: 99%

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Folding and necking across the scales: a review of theoretical and experimental results and their applications

Schmalholz

Mancktelow

2016

Solid Earth

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“…In this paper we will discuss the nature of these patterns from the perspective of dynamical systems theory, and will derive a model in which we demonstrate that sinusoidal folding patterns are consistent with (low amplitude) periodic orbits arising at bifurcation points whereas non-smooth, chevron-type behaviour, in which we see zig-zag patterns with straight limbs, can be described in terms of near heteroclinic orbits, and that there is a continuous transition between these two types of behaviour. The focus of the existing modelling work has considered the buckling or folding of a single layered imbedded in a softer matrix [3,27,28,25] and has more recently received much interested from an engineering and mathematical perceptive on localised and sequential folding [19,23,6].…”

Section: Introductionmentioning

confidence: 99%

Chevron folding patterns and heteroclinic orbits

Budd

Chakhchoukh

Dodwell

et al. 2016

Physica D: Nonlinear Phenomena

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We present a model of multilayer folding in which layers with bending stiffness EI are separated by a very stiff elastic medium of elasticity k 2 and subject to a horizontal load P. By using a dynamical systems analysis of the resulting fourth order equation, we show that as the end shortening per unit length E is increased, then if k 2 is large there is a smooth transition from small amplitude sinusoidal solutions at moderate values of P to larger amplitude chevron folds, with straight limbs separated by regions of high curvature when P is large. The chevron solutions take the form of near heteroclinic connections in the phase-plane. By means of this analysis, values for P and the slope of the limbs are calculated in terms of E and k 2 .

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Influences of surface processes on fold growth during 3‐D detachment folding

Collignon

Kaus

May

et al. 2014

Geochem Geophys Geosyst

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In order to understand the interactions between surface processes and multilayer folding systems, we here present fully coupled three-dimensional numerical simulations. The mechanical model represents a sedimentary cover with internal weak layers, detached over a much weaker basal layer representing salt or evaporites. Applying compression in one direction results in a series of three-dimensional buckle folds, of which the topographic expression consists of anticlines and synclines. This topography is modified through time by mass redistribution, which is achieved by a combination of fluvial and hillslope erosion, as well as deposition, and which can in return influence the subsequent deformation. Model results show that surface processes do not have a significant influence on folding patterns and aspect ratio of the folds. Nevertheless, erosion reduces the amount of shortening required to initiate folding and increases the exhumation rates. Increased sedimentation in the synclines contributes to this effect by amplifying the fold growth rate by gravity. The main contribution of surface processes is rather due to their ability to strongly modify the initial topography and hence the initial random noise, prior to deformation. If larger initial random noise is present, folds amplify faster, which is consistent with previous detachment folding theory. Variations in thickness of the sedimentary cover (in one or two directions) also have a significant influence on the folding pattern, resulting in linear, large aspect ratio folds. Our simulation results can be applied to folding-dominated foldand-thrust belt systems, detached over weak basal layers, such as the Zagros Folded Belt.

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Selective buckling of composite layers with contrasted rheological properties, a theory for simultaneous formation of several orders of folds

Cited by 241 publications

References 5 publications

Folding and necking across the scales: a review of theoretical and experimental results and their applications

Folding and necking across the scales: a review of theoretical and experimental results and their applications

Chevron folding patterns and heteroclinic orbits

Influences of surface processes on fold growth during 3‐D detachment folding

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