Incremental shortening calculation of the mixed-shear fault-bend folds

2021 ◽  
Author(s):  
Weiheng Zhang ◽  
Jie Chen ◽  
Tao Li
Keyword(s):  
Simple Shear ◽  
Quantitative Methods ◽  
Pure Shear ◽  
Kink Band ◽  
Growth Strata ◽  
Fluvial Terraces ◽  
Fault Bend ◽  
Shortening Rate ◽  
Dip Angle ◽  
Two Parameters

<p>Shear fault-bend folds are characterized by a long back-limb that dips more gently than the fault ramp [1]. During the folding growth, the back limb rotates and widens progressively through a combination of limb rotation and kink-band migration. Two end-member models of shear fault-bend folding theories, including simple-shear fault-bend folding (C=0.5) and pure-shear fault-bend folding (C=1), have been developed and widely applied. Mixtures of pure and simple shear (0.5<C<1) are possible and have been found in the natural. Few quantitative methods to limit the shear-index (C) of the shear fault-bend folds so far. The incremental shortening can be calculated based on a simplified equation that assumes the linear relationship between the shortening and the limb rotation angle of the back limb [2]. However, the relationship of these two parameters is nonlinear according to the shear fault-bend folding theory [1]. Calculation results of the linear model have large uncertainty.</p><p>Here, we develop a method to calculate the shear-index (C), providing an idea to improve the mixed-shear fault-bend fold models, and establishing a formula to calculate the incremental shortening based on the nonlinear relationship between the back-limb dip angle and the shortening. It is a more general method to calculate the incremental shortening of the shear fault-bend folds.</p><p>This model has been applied to the Tugulu anticline in the northern foreland of Chinese Tian Shan, which is a mixed-shear fault-bend fold based on previous studies [3]. Through an analysis of deformed fluvial terraces and growth strata, we develop the shortening history of the Tugulu anticline along the Hutubi River using our developed nonlinear model. Our results show that the Tugulu anticline has a shear-index of ~0.91 and a steady shortening rate of ~1.5mm/yr over the last 500ka.</p><p>References:</p><ul><li>[1] Suppe et al. (2004) AAPG Memoir 82: 303-323.</li> <li>[2] Yue et al. ( 2011) AAPG Memoir 94: 153–186.</li> <li>[3] Qiu et al. ( 2019) Tectonophysics 772:228209.</li> </ul>

Reorientation of inclusions by combination of pure shear and simple shear

1976 ◽  
Vol 34 (1-2) ◽  
pp. 1-70 ◽  
Author(s):  
S.K. Ghosh ◽  
H. Ramberg
Keyword(s):  
Simple Shear ◽  
Pure Shear

scholarly journals An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Elsiddig Elmukashfi
Keyword(s):  
Crack Propagation ◽  
Viscous Dissipation ◽  
Simple Shear ◽  
Elastic Energy ◽  
Classical Method ◽  
Pure Shear ◽  
Dissipated Energy ◽  
Dynamic Experiments ◽  
Unloading Rate ◽  
Tearing Energy

AbstractA method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of $$0.01~{\rm {s}}^{-1}$$ 0.01 s - 1 and for different unloading rates, i.e. $$0.01$$ 0.01 , $$0.1$$ 0.1 and $$1.0~{\rm {s}}^{-1}$$ 1.0 s - 1 . The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. $$0.5$$ 0.5 -$$18~{\rm {Hz}}$$ 18 Hz which corresponds to unloading rates $$0.46$$ 0.46 -$$16.41~{\rm {s}}^{-1}$$ 16.41 s - 1 , using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. $${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$ λ ˙ U < 1.0 s - 1 ), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate $$125.2~{\rm {s}}^{-1}$$ 125.2 s - 1 , the viscous dissipation is significant such that the amount of dissipated energy increases approximately by $$125.4\%$$ 125.4 % from the lowest unloading rate. The critical tearing energy is obtained to be $$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$ 7.04 kJ / m 2 using classical method and $$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$ 5.12 kJ / m 2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately $$37.5\%$$ 37.5 % .

scholarly journals Crystal rotations and alignment in spatially varying magma flows: Two-dimensional examples of common subvolcanic flow geometries

2021 ◽  
Author(s):  
Rémi Vachon ◽  
Mohsen Bazargan ◽  
Christoph F Hieronymus ◽  
Erika Ronchin ◽  
Bjarne Almqvist
Keyword(s):  
Shear Flow ◽  
Magma Chamber ◽  
Simple Shear ◽  
Thermal Convection ◽  
Pure Shear ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Crystal Orientations ◽  
Volcanic Plumbing System ◽  
Spatially Varying

Summary Elongate inclusions immersed in a viscous fluid generally rotate at a rate that is different from the local angular velocity of the flow. Often, a net alignment of the inclusions develops, and the resulting shape preferred orientation (SPO) of the particle ensemble can then be used as a strain marker that allows reconstruction of the fluid’s velocity field. Much of the previous work on the dynamics of flow-induced particle rotations has focused on spatially homogeneous flows with large-scale tectonic deformations as the main application. Recently, the theory has been extended to spatially varying flows, such as magma with embedded crystals moving through a volcanic plumbing system. Additionally, an evolution equation has been introduced for the probability density function (PDF) of crystal orientations. Here, we apply this new theory to a number of simple, two-dimensional flow geometries commonly encountered in magmatic intrusions, such as flow from a dyke into a reservoir or from a reservoir into a dyke, flow inside an inflating or deflating reservoir, flow in a dyke with a sharp bend, and thermal convection in a magma chamber. The main purpose is to provide a guide for interpreting field observations and for setting up more complex flow models with embedded crystals. As a general rule, we find that a larger aspect ratio of the embedded crystals causes a more coherent alignment of the crystals, while it has only a minor effect on the geometry of the alignment pattern. Due to various perturbations in the crystal rotation equations that are expected in natural systems, we show that the time-periodic behavior found in idealized systems is probably short-lived in nature, and the crystal alignment is well described by the time-averaged solution. We also confirm some earlier findings. For example, near channel walls, fluid flow often follows the bounding surface and the resulting simple shear flow causes preferred crystal orientations that are approximately parallel to the boundary. Where pure shear deformation dominates, there is a tendency for crystals to orient themselves in the direction of the greatest tensile strain rate. Where flow impinges on a boundary, for example in an inflating magma chamber or as part of a thermal convection pattern, the stretching component of pure shear aligns with the boundary, and the crystals orient themselves in that direction. In the field, this local pattern may be difficult to distinguish from a boundary-parallel simple shear flow. Pure shear also dominates along the walls of a deflating magma chamber and in places where the flow turns away from the reservoir walls, but in these locations, the preferred crystal orientation is perpendicular to the wall. Overall, we find that our calculated patterns of crystal orientations agree well with results from analogue experiments where similar geometries are available.

Superposed structures in the Mona Complex at Rhoscolyi Ynys Gybi, North Wales

1992 ◽  
Vol 129 (4) ◽  
pp. 475-490 ◽  
Author(s):  
H. Roper
Keyword(s):  
Simple Shear ◽  
Large Scale ◽  
Axial Direction ◽  
Kink Band ◽  
Alternative Interpretation ◽  
First Episode ◽  
Band Model ◽  
Kink Bands ◽  
The North ◽  
Island Group

AbstractThe Bedded Series of the Mona Complex at Rhoscolyn comprises two groups of clastic metasediments: the Holy Island Group, consistingof quartzites, impure psammites and pelites, with well-preserved bedding, is overlain conformably by the New Harbour Group, which is for the most parthomogeneously semi-pelitic without surviving bedding. Both groups have undergone the same two major tectono-metamorphic episodes, but with differing response. In the Holy Island Group the first episode (Dx) produced nearly upright and upward-facing folds (Fx) with an axial planar foliation (Sx), which varies from an anastomosing or rough-spaced cleavage in quartzites to a penetrative phyllitic schistosity in pelites. In the New Harbour Group Dx has generally obliterated original bedding surfaces, replacing them with a composite foliation (Sx) of fine compositional banding and a penetrative schistosity, together with a stretching lineation (Lx), the latter being at a high angle to the Fx axial direction. The Dx structures are attributed to a major episode of compressional tectonics.The structures attributed to the second deformation (Dy) includestrata-bound sets of quartz-filled tension fractures (attributed by most previous authors to an earlier episode), abundant NNW-verging asymmetric folds (Fy) of Sx, and a sporadically developed set of shear fractures which constitute a crenulation cleavage (Sy) axial planar to the folds. It is suggested that all these structures were produced by a single agency. One interpretation is that the observed shear fractures and folded tension fractures correspond fairly closely to and provide a natural analogy of those obtained in the classical simple shear experimentsof Riedel. In this case all the Dy structures can be accounted for by the action of a large-scale simple shear couple (Cy), whose vergence and shallow dip were both towards the NNW. Such a mechanism may imply a gravity-dominated regime of net horizontal extension in a NNW-SSE direction, with extension being less constrained to the north than to the south. J. W. Cosgrove has suggested an alternative interpretation, that all the Dy structures can be explained as reverse kink bands; the simple shear interpretation is here preferred because the angle between Sy and the estimated direction of Pmax during Dy was < 45°; the kink band model would require an angle > 45°.The fact that cleavage vergence boundaries for both Sx and Sy occur close to the hinge zone of the Rhoscolyn Antiform is consistent with either Dx or Dy age for the initiation of this fold. However, when fold limb length (or limb rotation) vergence is considered, the presence of an Fx0 vergence boundary but absence of an Fxy vergence boundary (and by implication of an Fy0 boundary) is consistent with a Dx age but difficult to reconcile with a Dy age.

A quantitative analysis of lithospheric subsidence due to thinning by simple shear

1988 ◽  
Vol 25 (1) ◽  
pp. 20-29 ◽  
Author(s):  
Brett S. Mudford
Keyword(s):  
Simple Shear ◽  
Pure Shear ◽  
Shear Thinning ◽  
Dominant Mode ◽  
Basin And Range Province ◽  
Passive Margins ◽  
Metamorphic Core Complexes ◽  
First Case ◽  
Major Fault ◽  
Brittle Zone

Kinematic simple-shear models have recently been used to provide qualitative explanations for tectonic features in the Basin and Range Province of the southwestern United States and on passive margins. In this paper, a general kinematic simple-shear model is presented. Explicit expressions for the subsidence and stretching factors across a simple-shear zone are derived for two important cases. The first case is one in which simple-shear rifting occurs along a major fault that cuts through the whole lithosphere. In the second case, simple-shear thinning takes place in a brittle zone overlying a regional ductile zone that is undergoing pure-shear thinning. In these cases the subsidence and stretching factors both have characteristic distributions across the stretched region, which can indicate the dominant mode of rifting. It is also shown that simple-shear rifting under the assumption of local isostatic compensation cannot lead to the production of uplifted metamorphic core complexes unless some additional mechanism such as crustal underplating is operating.

Signs of polichnous deformations in microstructures of carbonate rocks of the Katav-Yuryuzan zone of transpression (Southern Urals)

2020 ◽  
pp. 13-21
Author(s):  
A. V. Tevelev ◽  
A. A. Borisenko ◽  
M. I. Erokhina ◽  
S. S. Popov ◽  
I. A. Kosheleva ◽  
...  
Keyword(s):  
Simple Shear ◽  
Carbonate Rocks ◽  
Pure Shear ◽  
Southern Urals ◽  
Second Stage ◽  
The Third ◽  
The North ◽  
Third Stage ◽  
Three Stages ◽  
Two Stages

The Katav-Ivanovsk transpression zone experienced at least two stages of tectonic deformations, and the sequence of deformations was approximately the same throughout the entire zone — from the Bakal-Satka fault in the south to the Suleimsky fault in the north. Three stages of the formation of parageneses were identified. The parageneses of the first and the second stages were formed in a pure shear environment, and the paragenesis of the third stage — in a simple shear environment. There are stylolites (S1) parallel to bedding, and mineral veins (V1) in the paragenesis of the first stage. Paragenesis of the second stage combines stylolites (S2), mineral veins (V2) and intergranular cleavage (S2). In paragenesis of the third stage were distinguished schistosity (S3), milonites (S3), cataclasites, mica packets (SC-textures), and the rotation structures of porphyroblasts.

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