Nibir Mandal

Modes of superposed buckling in single layers controlled by initial tightness of early folds

In a series of experiments with soft test models, superposed buckling folds were produced in a competent layer resting on a slab of incompetent painters putty. The angle between the hinge lines of the first set of cylindrical folds (F1) and the direction of the second compression (P2) was varied in the different experiments. The experiments showed that with an increase in the initial tightness of F1 there was a transition from one mode of superposed buckling to another. When the interlimb angle of F1 was very large the superposed deformation gave rise to a dome-and-basin pattern (the first mode of superposed buckling). The second mode, with small F2 folds riding over larger F1 folds, developed when the initial interlimb angle ranged roughly between 135° and 90°. The third mode was observed when the F1 interlimb angle was less than about 90° but the fold was not very tight. In the third mode a set of non-plane non-cylindrical folds developed; however, the sinuous hinge line of the non-cylindrical structure was newly created by replacing the old F1 hinge. When F1 was very tight or isoclinal the fourth mode of superposed buckling led to the development of non-plane non-cylindrical folds without concomitant hinge replacement.

Evidence for a non-linear relationship between fracture spacing and layer thickness

In experiments, extension fractures were generated in rigid layers of Plaster of Paris resting on a viscous substratum (pitch). The experimental results predict a non-linear relationship between the spacing of fractures in uniform brittle layers and layer thickness for fractures generated by the tractional force of embeddins weak rocks. We derive an equation which relates the critical fracture spacing (λc) with layer thickness (b), tensile strength of the layer material/viscosity of the embedding medium ratio (τo/η) and bulk strain rate (eb). The equation shows that the spacing increases as a function of the square root of the layer thickness. The theory also predicts that the fracture spacing depends on the strain rate when the embedding weak medium is viscous.

Superposed buckling in multilayers

Experiments with soft models indicate that, just as in the case of a single-layer, the mode of superposed buckling in multilayers is essentially controlled by the shape of the early folds. A thin multilayer embedded in an incompetent host may undergo superposed buckling in any one of the four standard modes observed in single-layers. In general, however, the geometry of superposed folds is more varied in multilayers. A fifth mode appears only in multilayers, whereas the other four standard modes may be modified during refolding in multilayers. When different orders of buckling folds develop, the interference pattern of the smaller folds is distorted by that of larger disharmonic folds. There are several consequences of this distortion: (i) the degree of complexity of outcrop may vary in layers of different lithology; (ii) a morphology similar to that produced by three or more generations of superposed folds may develop even when there are only two distinct events of deformation; and (iii) there may be a significant lowering of the axial direction stability of the new folds. The experiments also indicate that the type 1 interference pattern may be produced in mode 1, mode 2, modified mode 2 and mode 5 folding. In addition, the experiments show that there are some special features associated with superposed buckling of parallel flexural-slip folds in thick multilayers.

Boudinage in multilayered rocks under layer-normal compression: a theoretical analysis

Abstract This paper presents a dynamic analysis of boudinage in multilayers of alternate brittle and ductile layers under layer-normal compression. Based on the mode of fracturing of individual brittle layers, boudinage is classified into three types: tensile fracture boudinage (Type 1), shear fracture boudinage (Type 2a) and extensional shear fracture boudinage (Type 2b). The layer-thickness ratio, T r (= t b / t d ), and the strength ratio, F (= T /2 ηe ), between the brittle and the ductile units are the principal physical factors determining the type of boudinage. Type 1 boudinage develops rectangular boudins and occurs when T r is low ( F is high (>0.8). In contrast, Type 2a boudinage takes place when T r is high (>8.5) or F is low ( A r ) of all the types of boudins is inversely proportional to layer-thickness ratio ( T r ). However, Type 1 and Type 2 boudins, have contrasting aspect ratios, which are generally greater and less than 1, respectively.

Imbricate thrust spacing: experimental and theoretical analyses

With the help of model experiments and theoretical analyses we evaluate the relationships of imbricate thrust spacing (a) with the bed thickness (H), basal friction (μb), initial taper (mw), and the magnitude (normalized to bed-weight per unit area) of horizontal stress (n). Imbricate thrust spacing increases linearly with bed thickness when mw = 0 and initial-stage thrust imbricates are taken into account. For general cases (mw≠0) the variations are nonlinear. In nonlinear variations thrust spacing steadily increases but approaches a stable value. The variations for large mw are complex, where thrust spacing increases to a maximum and then decreases down to a near-stable value. Thrust spacing shows a positive relationship with the dynamic factor, n. With increase in basal friction, thrust spacing decreases. Steepening of early frontal thrusts and formation of back-thrust also depend on the basal friction.

Numerical modeling of heterogeneous flow fields around rigid objects with special reference to particle paths, strain shadows and foliation drag

Abstract With the help of two-dimensional numerical models this paper investigates three aspects of heterogeneous deformation around rigid objects: (1) the nature of particle paths ; (2) the development of strain shadow zones; and (3) the drag patterns of passive markers. In simple shear, spherical objects develop typically a concentric vortex motion, showing particle paths with an eye (double-bulge)-shaped separatrix. The separatrix has no finite dimension along the central line, parallel to the shear direction. Under a combination of pure shear and simple shear, the particle paths assume a pattern with a bow-tie shaped separatrix. With increase in the ratio of pure shear to simple shear ( S r ), the separatrix around the object shrinks in size. The axial ratio of the object ( R ) is another important factor that controls the geometry of particle paths. When R R , the loci form a doublet elliptical shell structure. Objects with R >3 do not show closed particle paths, but give rise to elliptical or circular spiral particle paths. The development of strain shadow zones against equant rigid bodies depends strongly on the strain ratio S r . When S r =0 (simple shear), they develop opposite to the extensional faces of the object, forming a typical σ -type tail. The structure has a tendency to die out with an increase in the pure shear component of the bulk deformation ( S r ). The initial angle of the long axis of the object with the shear direction ( φ ) and the axial ratio of the object ( R ) determine the development of strain shadow zones near inequant rigid objects. Objects with large R and φ between 60 and 120° form pronounced zones of low finite strain, giving rise to strain shadow structures. A geometrical classification of diverse drag patterns of passive markers around rigid objects is presented along with their conditions of formation.

Rotation, offset and separation of oblique-fracture (rhombic) boudins: theory and experiments under layer-normal compression

Abstract Boudinage structures are generally produced by extension fracturing of competent rocks normal to layering. Boudin-like structures may also develop by shear fracturing of competent rocks oblique to layering. In such structures boudins of rhomboid shape are rotated and offset with respect to each other. It is usually considered that shear fracture boudins do not get separated until a critical rotation is attained, when they can just touch each other. However, the experiments under layer-normal compression and the theoretical analysis of the present study indicate that the layer-segments produced by a set of parallel shear fractures may undergo rotation with separation or rotation with interfacial slip depending upon their geometry. The thickness to length ratio ( G T ) of layer-segments and the orientation of fractures (Φ) are the parameters that could control the rate of rotation versus rate of displacement of layer-segments.

Flow patterns around rigid inclusions in a multiple inclusion system undergoing bulk simple shear deformation

Abstract During deformation of an inclusion-matrix system, the velocity fields around individual inclusions mutually interfere with one another. Such interacting inclusions rotate at slower rates than non-interacting, single inclusions. This paper presents a theoretical model that describes the flow pattern of matrix (viscous) material around interacting rigid inclusions of spherical shape in bulk simple shear deformation. Numerical simulations based on the velocity functions reveal that the volume concentration of inclusions is a crucial parameter controlling the flow pattern around rotating inclusions under interacting conditions. At low volume concentrations (ρv 0.1), transforms into a pattern with a bow-tie shaped separatrix. At a large volume concentration (ρv=0.4) the separatrix assumes the geometry of a super-ellipse. We also present numerical models that illustrate the influence of volume concentration on the (1) nature of strain distribution, (2) distortion patterns of passive foliations ,and (3) mantle structures around inclusions in an interacting state. Based on this theory, it is shown that the rotational retardation of the inclusions slightly enhances the bulk viscosity of the inclusion-matrix system.

Progressive development of mantle structures around elongate porphyroclasts: insights from numerical models

Abstract This paper presents a generalized theoretical approach towards two-dimensional numerical modeling of the mantle geometry of inequant porphyroclasts of varying shapes within a Newtonian matrix during progressive, general type of bulk deformation. The analysis takes into account the effects of synkinematic size reduction of the porphyroclast with concomitant mantle development in response to dynamic recrystallization. Numerical simulations reveal that the principal factors governing the geometry of mantle structures are: (1) the initial aspect ratio of the porphyroclast (a/b), (2) the rate of clast-size reduction, and (3) the ratio of the rates of pure shear and simple shear (Sr) or the kinematic vorticity (Wk) in the general type of non-coaxial deformation. In general, porphyroclasts develop δ-, φ- and finally, σ-type mantle structures, as the rate of clast-size reduction is progressively increased. The tails of equant porphyroclasts tend to be characterized by wings with increase in bulk shear during progressive deformation. In contrast, inequant objects (a/b>1) develop composite tails with multiple wings, even at low finite shear strains. However, with increase in aspect ratio δ geometry tends to dominate the overall mantle structure. Porphyroclasts with a large aspect ratio (a/b=3) form tails with overturned δ-wings, as described in Passchier, C.W., Simpson, C., 1986. “Porphyroclast system as kinematic indicators”, Journal of Structural Geology 8, 831–844. In general the type of non-coaxial deformation, with decrease in kinematic vorticity (or increase in Sr), porphyroclasts irrespective of their initial shapes, tend to form atypical δ-like tails that do not cross the central reference plane.

Mg doping in wurtzite ZnO coupled with native point defects: A mechanism for enhanced n-type conductivity and photoluminescence

From first-principles calculations, we show that Mg energetically prefers to substitute Zn atoms rather than occupying interstitial octahedral or tetrahedral sites in ZnO structure. The Mg substitutions significantly reduce the formation energies of Zn/O vacancy and Zn interstitial defects, which consequently promotes the n-type conductivity and photoluminescence in ZnO. The defects form complexes with moderate binding energies, as supported by the shorter Mg-O bonds relative to Zn-O bonds. In agreement with available experimental data, Mg substitutions result in contraction along c-axis and extension along a-axis in wurtzite ZnO.