Polygonal deformation bands

We report for the first time the occurrence of polygonal faults in sandstone, which is compelling given that layer-bound polygonal fault systems have been observed so far only in fine-grained sediments such as clay and chalk. The polygonal faults are shear deformation bands that developed under shallow burial conditions via strain hardening in dm-wide zones. The edges of the polygons are 1–5 m long. The shear deformation bands are organized as conjugate faults along each edge of the polygon and form characteristic horst-like structures. The individual deformation bands have slip magnitudes ranging from a few mm to 1.5 cm; the cumulative average slip magnitude in a zone is up to 10 cm. The deformation bands heaves, in aggregate form, accommodate a small isotropic horizontal extension (strain <0.005). The individual shear deformation bands show abutting T-junctions, veering, curving, and merging where they mechanically interact. Crosscutting relationships are rare. The interactions of the deformation bands are similar to those of mode I opening fractures. The documented fault networks have important implications for evaluating the geometry of km-scale polygonal fault systems in the subsurface, top seal integrity, as well as constraining paleo-tectonic stress regimes.     

Geometric analysis and scaling relations of deformation bands in porous sandstone

Displacement, length and linkage of deformation bands have been studied in Jurassic sandstones in southeastern Utah. Isolated deformation bands with lengths (L) that span more than three orders of magnitude show similar displacement (D) profiles with more or less centrally located maxima and gently increasing gradient toward the tips. Soft- and hard-linked examples exhibit steeper displacement gradients near overlap zones and immature hard links, similar to previously described fault populations. The deformation band population shows power-law length and displacement distributions, but with lower exponents than commonly observed for populations of larger faults or small faults with distinct slip surfaces. Similarly, the D_max-L relationship of the deformation bands shows a well-defined exponent of ca 0.5, whereas the general disagreement for other fault populations is whether the exponent is 1 or 1.5. We suggest that this important difference in scaling law between deformation bands and other faults has to do with the lack of well-developed slip surfaces in deformation bands. During growth, deformation bands link to form zones of densely spaced bands, and a slip surface is eventually formed (when 100 m < L < 1 km). The growth and scaling relationship for the resulting populations of faults (slip surfaces) is expected to be similar to ‘ordinary’ fault populations. A change in the D_max-L scaling relationship at the point when zones of deformation bands develop slip surfaces is expected to be a general feature in porous sandstones where faults with slip surfaces develop from deformation bands. Down-scaling of ordinary fault populations into the size domain of deformation bands in porous sandstones is therefore potentially dangerous.     

Finite strain analysis of nonuniform deformation inside shear bands in sands

A methodology has been developed to extend the incremental (Eulerian) Digital Image Correlation (DIC) technique to enable a Lagrangian‐based large‐strain analysis framework to examine the nature of strain and kinematic nonuniformity within shear bands in sands. Plane strain compression tests are performed on dense sands in an apparatus that promotes unconstrained persistent shear band formation. DIC is used to capture incremental, grain‐scale displacements in and around shear bands. The performance of the developed accumulation algorithm is validated by comparing accumulated displacements with two sources of reference measurements. A comparison between large and infinitesimal rotation is performed, demonstrating the nature of straining within shear bands in sands and the necessity of using a finite strain formulation to characterize ensuing behavior. Volumetric strain variation along the shear band is analyzed throughout macroscopic postpeak deformation. During softening, volumetric activity within the shear band is purely dilative. During the global critical state, the shear band material is seen on the average to deform at zero volumetric strain; however, locally, the sand is seen to exhibit significant nonzero volumetric strain, putting into question the current definition of critical state. At the softening‐critical state transition, a spatially periodic pattern of alternating contraction and dilation along the shear band is evidenced, and a preliminary evaluation indicates that the periodicity appears to be a physical phenomenon dictated only in part by median grain size. Copyright © 2011 John Wiley & Sons, Ltd.     

Characteristics of plastic deformation of quartz

The fold-thrust tectonics in the Northern Tarim Basin, oriented roughly parallel to the South Tianshan orogenic belt, consists of two large-scale tectonic regimes: (1) the foreland-basin, thin-skinned deformation belt; and (2) the foreland-craton, thick-skinned-dominated (i.e., basement-involved) deformation belt. Variations in the degree of deformation in these tectonic belts and style along the regional tectonic strike can be accounted for by longitudinal (progressive) transfer or transverse (abrupt) transfer. Longitudinal transfer maintains the overall displacement or shortening within the fold-thrust belts as uniform or with gradual change along the tectonic strike. This includes the tectonic transfer between en echelon master thrusts and from the individual master thrust to terminal fold (s) or distributive thrusts. Transverse transfer resulted from an abrupt change in overall displacement or shortening along the tectonic strike. Within the transverse transfer zone, various tectonics—such as strike-slip faults, strike-slip thrusts, transverse anticlines, and en echelon folds—are developed.

The development of longitudinal transfer zones can be attributed to the gradual variation of intrinsic and extrinsic deformational conditions along the tectonic strike. The initiation of transverse transfer may be related to variations in the thickness of sedimentary layers, detachment-layer distribution limits, and variation along strike of the degree and mode of the South Tianshan orogenic belt's effect on the basin, as well as the variation of the boundary conditions of the deformation, such as in the geometry of plate margins.     

Dynamic analysis and two types of kink bands in quartz veins deformed under subgreenschist conditions

In order to clarify deformation mechanisms and behaviours of quartz in a low-temperature regime in the earth's crust, microstructural analyses, particularly on kink bands have been carried out for quartz veins moderately deformed under subgreenschist conditions. Both the dominance of subbasal deformation lamellae and geometry of kink bands suggest that basal (0001) slip was the sole active slip system in the deformed quartz. On a morphological basis, kink bands in the quartz were classified into two types: type I is characterized by conjugate and narrow bands with angular hinge zones, and type II by a wide monoclinal band. Dynamic analyses using deformation lamellae and kink bands have revealed that type I kink bands were formed in grains with basal plane (sub-)parallel to the compression axis, whereas type II kink bands were formed in grains with basal planes inclined to it. Using a numerical model of kinking of elastic multilayers modified after Honea and Johnson (Tectonophysics 30, 197–239, 1976), changes of the level of yielding stress for kinking and the width of kink bands as a function of the angle θ between the slip plane and the compression axis have been examined. The theory predicts that type I kink bands were formed at a higher stress level than type II kink bands, and hence occurrence of type I kink bands suggests that a significant strain hardening occurred in the deformed quartz veins. The theory also well explains the fact that the width of type I kink bands (θ=0 to 10°) is narrower by an order of magnitude than type II kink bands (θ=10 to 80°).     

Strain analysis using deformed line distributions

This paper describes a new technique of strain analysis using passively deformed linear markers which were initially uniformly or symmetrically distributed in a plane. The axial ratio of the strain ellipse is determined from the quartiles or other percentiles of the deformed distribution. The technique permits statistical testing of assumptions and rapid reconstruction of the undeformed state.     

Plastic deformation of quartz at ultrahigh pressures

The authors' experimental studies show that quartz crystals will flow plastically at temperatures of approximately 1000° C, and pressures of the order of 1000 kg/cm². The 84° rotation of the major optic axis is taken as evidence of this.     

Chemical etching of deformation sub-structures in quartz

Chemical etching of dislocations has been studied in natural and synthetic quartz single crystals, in deformed synthetic quartz and in naturally and experimentally deformed quartzites. The ability of different etchants to produce polished or preferentially etched surfaces on quartz is described. Dislocation etching was achieved on all crystal planes examined by using a saturated solution of ammonium bifluoride as the etchant. Appropriate etching times were determined for etching quartzites for grain size, subgrain boundaries, deformation lamellae, dislocations and twins. Growth and polished surfaces of synthetic single crystal quartz were similarly etched and dislocation etch pits, characteristic of various orientations were found. The use of ammonium bifluoride proved to be expecially advantageous for the basal plane, producing a polished surface with etch pits, suitable for dislocation etch pit counting. “Double” etch pits have been found on Dauphiné twin boundaries on the basal plane and the first order prism, using this etchant. Slip lines and deformation bands were suitably etched on deformed synthetic crystal surfaces for identification of the slip planes. Other acidic etchants have been explored and their application to the study of deformation structures in quartz crystals is discussed.     

Influence of deformation bands on sandstone porosity: A case study using three-dimensional microtomography

This study presents a qualitative and quantitative analysis of porosity in deformation bands by applying X-ray micro-computed tomography in conjunction with microstructural analysis. Samples of compactional cataclastic bands and shear compactional bands identified in Early Cretaceous aeolian sandstones of the Paraná Basin were analyzed. The application of X-ray micro-computed tomography expanded the view of features in the porous framework of each type of deformation band studied and provided information that are not clear or was not observable with optical microscopy. The compactional cataclastic bands and shear compactional bands differ in geometry, thickness, microstructures and, mainly, in the distribution, shape and orientation of the remaining pores. Porosity analysis was also performed by comparing values of porosity (total, open and closed pores) of the parental rock and the deformation band in each sample. Results of these analyses show a reduction of total porosity and open pores and therefore an increase in the amount of closed pores in all types of deformation bands in relation to parental rock. In addition, it is observed that changes in porosity characteristics are related to the effect of different deformation mechanisms that operated in each type of deformation band.     

Shear bands and related extensional structures in a mylonitized quartz dyke

Chiefly monomineralic quartz dykes in the Canigó massif (Eastern Pyrenees) are affected by mylonitic deformation. Deformation took place under low-temperature conditions and produced incipient to well-developed mylonitic foliation. In the deformed quartz, grainsize reduction was mainly achieved by brittle failure of crystals along two conjugate sets of cracks. Two sets of conjugate shear bands are also present even in samples with poorly developed mylonitic foliation. Cracks and shear bands are consistent with an extension parallel to foliation. Both are simultaneously present in all the studied samples. Hydrolytic weakening may have aided the development of ductile structures.     

In situ TEM observations of plastic deformation in quartz crystals

With in situ nanocompression experiments in a transmission electron microscope, we investigated plastic deformation in natural quartz crystals and observed both dislocation plasticity as well as mechanical twinning. Through this experimental method, we are able to provide direct evidence of Dauphiné twin nucleation and could measure the intrinsic twinning stress. The twinning phenomena appear to include a memory effect, where the same twin can reappear upon successive loading and unloading events. The data provide insight into this twin generation mechanism and can be used as a benchmark for the use of twins in quartz for paleopiezometry. Together, the observation of room-temperature dislocation plasticity and reversible twinning adds new insight into the extensive field of quartz plasticity and demonstrates the usefulness of small-scale testing techniques for mineral physics.     

基于OpenMP的非连续变形分析并行计算方法

非连续变形分析（DDA）方法严格满足平衡要求和能量守恒,具有完全的运动学及数值可靠性,但对大规模岩土工程问题的数值模拟耗时太长,尤其是线性方程组求解,并行计算可以很好地解决该问题。首先基于DDA方法的基本理论,阐述了适用于DDA方法中的基于块的行压缩法和基于“试验-误差”迭代格式的非零位置记录;其次,引入块雅可比迭代法并行求解DDA方法的线性方程组,并改进了相应的非零存储方法;最后,基于OpenMP实现了DDA线性方程组求解并行计算,并将其应用于地下洞室群的破坏过程分析,以加速比为并行效率的指标评价,结果表明,该并行计算策略可以极大提高DDA的计算效率,而且适合各种规模的问题。     

Strain-rate estimation using fractal analysis of quartz grains in naturally deformed rocks

The area-perimeter fractal dimension (D) of quartz grains has earlier been proposed as a strain-rate gauge based on experimental deformation of quartz aggregates. To test the application in naturally deformed rocks, D is calculated in (a) three quartzites belonging to the Lunavada Group of rocks (Aravalli Mountain Belt, NW India) that developed textures between 420–600°C and (b) one quartz reef sample from the Malanjkhand Granite (Central India), which underwent dynamic recrystallization between 250–400°C. Using the above T ranges and calculated D values, strain-rates are calculated for the two sets of samples. A 10^−12.7 s⁻¹ strain rate at 250°C is calculated for the quartz reef sample. However, at higher temperatures the calculated strain-rate is >10⁻¹⁰ s⁻¹ for the quartz reef and the quartzite samples. The quartzites show evidence of dynamic recrystallization by grain boundary migration (GBM) and subgrain rotation (SGR), while the quartz reef is replete with evidence of bulging (BLG) recrystallization. T and calculated strainrates are plotted on available recrystallization map of quartz. It is demonstrated that whilst the T/strain-rate of the quartzites does not fall in the region of GBM and SGR, the T/strain-rate of the quartz reef falls in the BLG region. The problems with strain-rate calculations using area perimeter fractal dimension are discussed. It is concluded that the method of strain-rate calculation can be used only for lower T.     

Spatio-temporal analysis of rockfall pre-failure deformation using Terrestrial LiDAR

We present a long-term spatio-temporal analysis of rock slope evolution using a Terrestrial LiDAR aiming to improve our understanding of the link between pre-failure deformation and the spatial prediction of rockfalls. We monitored the pilot study area located at the Puigcercós cliff (Catalonia, Spain) over a period of 1,705 days and detected the deformation of nine different cliff regions together with a high rockfall activity. An exact match was observed between the progressively deformed areas and the regions recently affected by three of the highest magnitude rockfall events, demonstrating a causal relationship between pre-failure deformation and rockfall occurrence. These findings allowed us to make a forward spatial prediction of future failures, hypothesizing a high probability of failure in the six remaining regions. We observed an exponential acceleration of the deformation close to failure, in accordance with tertiary creep theory. However, the temporal analysis of the deformed areas showed a complex and variable behavior, so no exact prediction of the date of failure can yet be made. Our findings have broadened our understanding of the pre-failure behavior of rockfalls and have clear implications for the future implementation of early warning systems.     

石英显微变形机制及流变学特征研究进展

石英是组成地壳的主要矿物之一,其物理性质与地壳的变形行为及流变学属性密切相关,因此石英的显微变形机制及流变学特征研究意义重大。随着石英显微变形机制及流变学属性实验学研究的深入,我们对石英在地壳变形过程中重要作用的认识也随之提升。本文从石英结构入手,对升温过程中石英主滑移系的转换进行了总结,并且升温过程中显微变形机制也发生了改变,对流变学内涵也不同,所以分述了石英的主要变形机制,及其流变学参数;由于应变局部化为地壳变形的研究热点,并且石英对应变局部化具有一定的指示意义,所以本文对石英在应变局部化过程中的表现进行了深入讨论。考虑到地壳变形的研究过程中,石英不常作为单矿物发生变形,所以本文对多相矿物的变形表现也进行了讨论。最后我们将简单介绍一些现今主流的石英显微变形机制的研究手段。     

Distribution of impurities in deformed quartz and its implications for deformation studies

The distribution of impurity atoms (At. No.> 11) in two naturally deformed quartzites has been determined by microchemical analyses in a scannling transmission electron microscope. The study reveals impurity segregations at sub-grain boundaries and dislocations. The importance of the presence and segregation of impurities other than OH to quartz deformation studies is discussed. It is suggested that the potential role of these impurities on the development and behaviour of deformation microstructures warrants the inclusion of this previously neglected topic into future quartz deformation studies.     

Strain and vorticity analysis using small-scale faults and associated drag folds

Small-scale faults with associated drag folds in brittle-ductile rocks can retain detailed information on the kinematics and amount of deformation the host rock experienced. Measured fault orientation (α), drag angle (β) and the ratio of the thickness of deflected layers at the fault (L) and further away (T) can be compared with α, β and L/T values that are calculated with a simple analytical model. Using graphs or a numerical best-fit routine, one can then determine the kinematic vorticity number and initial fault orientation that best fits the data. The proposed method was successfully tested on both analogue experiments and numerical simulations with BASIL. Using this method, a kinematic vorticity number of one (dextral simple shear) and a minimum finite strain of 2.5–3.8 was obtained for a population of antithetic faults with associated drag folds in a case study area at Mas Rabassers de Dalt on Cap de Creus in the Variscan of the easternmost Pyrenees, Spain.     

Strain variation with progressive deformation in basement-involved trishear structures

Basement-involved structures associated with reverse, vertical and normal faults commonly involve non-parallel shear within a triangular deformation (trishear) zone located on the front limbs of the structures. Deformation within the trishear zone is characterized by shear gradients and an associated decrease in the dips of the beds in stratigraphically higher units. Geometric models suggest that the layer-parallel strain within the trishear zone depends on the type of fault (normal, reverse, or vertical), the dip and throw of the fault, the dip of the anticlinal or synclinal axial surfaces, and the distance of any unit above the initial tip of the trishear zone, located at the basement-sediment contact. At any given location, reverse faults typically show increasing layer parallel shortening, followed by decreasing layer parallel shortening and a transition to extension, with increasing throw. The transition from contraction to extension occurs at lower values of throw for stratigraphically lower units and also for faults with smaller dips. Vertical and normal faults exhibit increasing layer-parallel extension of all units with increasing throw, with larger extension for stratigraphically lower units. Experimental models suggest that the trishear zone can expand with increasing fault throw. The strain within the trishear zones is accommodated largely by secondary faults, which are rotated with progressive deformation. The strain variations in the experiments closely mimic those predicted by the geometric models for reverse, vertical, and normal faults.     

Spatial distribution of deformation bands in damage zones of extensional faults in porous sandstones: Statistical analysis of field data

The distribution of deformation bands in damage zones of extensional faults in porous sandstones has been analyzed using 106 outcrop scanlines along which the position and frequency of deformation bands have been recorded. The analysis reveals a non-linear relationship between damage zone width and fault throw, a logarithmic decrease in deformation band frequency away from the fault core, as well as a fractal spatial distribution associated with clustering of the deformation bands. Furthermore, damage zones appear wider in the hanging wall than in the footwall, although the deformation band density is similar on both sides. Statistical trends derived from the database imply that fault growth in porous sandstones can be considered as a scale invariant process. From an initial process zone, the damage zone grows by a constant balance between the development of new deformation bands in the existing damage zone and the creation of new bands outside. Moreover, as the width of the damage zone increases throughout the active lifetime of a fault, the distribution of the deformation bands in the damage zone remains self-similar. Hence band distribution and damage zone width for seismically mapped faults can be predicted from the relationships found in this paper.