A comparison of intracrystalline deformation in naturally and experimentally deformed quartzites

A relatively undeformed quartzite sample from the Weverton formation was experimentally deformed in plane strain at a temperature of 700° C, a confining pressure of 15 kb and a constant strain rate of 10⁻⁶/sec, in a modified Griggs apparatus. A comparison of the known experimental strain for the sample with that measured from deformed rutile needles within the quartz grains shows fairly close agreement between the two values. This confirms the validity of using the needles as intracrystalline strain markers. A comparison has been made of the microstructures and preferred orientations in the experimentally deformed sample and a naturally deformed sample of the same quartzite which has undergone the same strain. The experimentally deformed sample exhibits more inhomogeneous intragranular deformation and a “double funnel” pattern of c axes, while the naturally deformed sample exhibits more homogeneous intragranular deformation and a broad great circle girdle of c axes normal to the foliation and lineation.     

Removal of finite deformation using strain trajectories

A technique is described for removing the effects of finite deformation, given the principal values and orientations of strain at a number of points throughout a deformed body.Using the principal orientations, strain trajectories are constructed for the deformed state. The body is divided into finite elements bounded by these trajectories. Each element is then unstrained without changing its orientation or position. This process creates artificial voids and overlaps, which are minimized by imparting rigid translations and rotations to the elements according to a least squares method.The result is the pattern of strain trajectories for the undeformed state. It is shown that the trajectories for the deformed and undeformed states may be used as reference coordinates in order to map the change in shape of any body as it passes from the deformed to the undeformed state or vice versa. The technique is tested using models of a folded layer and a shear zone. It is suggested that the technique is versatile enough to allow for errors in original strain data. Although the technique has so far been applied to two-dimensional deformations, a similar method should be usable in three dimensions.     

A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain

An adaptively stabilized finite element scheme is proposed for a strongly coupled hydro‐mechanical problem in fluid‐infiltrating porous solids at finite strain. We first present the derivation of the poromechanics model via mixture theory in large deformation. By exploiting assumed deformation gradient techniques, we develop a numerical procedure capable of simultaneously curing the multiple‐locking phenomena related to shear failure, incompressibility imposed by pore fluid, and/or incompressible solid skeleton and produce solutions that satisfy the inf‐sup condition. The template‐based generic programming and automatic differentiation (AD) techniques used to implement the stabilized model are also highlighted. Finally, numerical examples are given to show the versatility and efficiency of this model. Copyright © 2013 John Wiley & Sons, Ltd.     

The significance of stretching lineations in terms of progressive deformation and finite strain

Abstract

For a given increment of deformation, stretching lineations can be defined either by old grains or by new grains.

Progressive strain accumulated in a matrix causes reorientation of old grains. The velocity field acting within a grain depends on the degree of non-coaxiality of the progressive strain in the matrix, and on the competence contrast between grain and matrix (e.g. Lister & Williams, 1983). Deformed populations of old grains do not systematically track the principal directions of finite stretch; this depends on the mechanical behavior of the grains. On the other hand, these populations may be good markers of finite strain magnitude, provided that the initial distribution is known.

In contrast, the statistical shape orientation distribution of population of new grains cannot be related in a simple way to the finite strain magnitude, but their preferred orientation is considered to be the best indicator of the principal directions of finite stretch.

An example is considered from the schistes lustrés near Kenestrelle (Val Chisone, Western Alps), where the observed mineral lineation is attributed to a late E-W stretching event in the alpine orogenic history.     

Bulk finite tectonic strain estimates from the deformation of neptunian dykes

Large sedimentary dykes, which penetrate down through their host sediments for several metres, are described from the Late Precambrian Dalradian sediments of Islay in the southwest Scottish Highlands. The sediments and their neptunian dykes have suffered a single penetrative deformation which produced a slaty cleavage during the evolution of the Islay nappe. Ratios of the three principal finite strains are calculated for the bulk or large-scale, homogeneous deformation of the sediments and their neptunian dykes using the method of Borradaile and Johnson (1973) and a new, more general method. Since the neptunian dykes result from the infilling of fractures in already consolidated sediments, subsequent considerable volume changes are unlikely to have occurred. Accepting constant volume post-diagenetic deformation the bulk tectonic strain is shown to have, in round figures: 70% shortening normal to slaty cleavage and extensions of 50% and 120% within the cleavage. The deformation accompanying the slaty cleavage lies within the field of true flattening.     

Qualitative and quantitative analysis of vorticity,strain and area change in general non-isochoric 2D deformation

A scale free representation of a general non-isochoric 2D deformation is presented which is amenable to mathematical analysis. By describing deformation in 2D in terms of polar coordinates the stretching and rotational histories of linear elements separate and are easily analysed both qualitatively and quantitatively. An analysis of finite strain combined with dynamical considerations allows the derivation of equations which may be used to estimate finite strain, area change and kinematic vorticity number. Numerical investigation of method developed here was carried out and it was found to perform well unless large area changes occur in combination with large components of simple shear. A re-analysis of natural data indicates the method is consistent.     

Chemical and physical responses to deformation in micaceous quartzites from the Tauern Window, Eastern Alps

Micaceous quartzites from a subvertical shear zone in the Tauern Window contain abundant quartz clasts derived from dismembered quartz‐tourmaline veins. Bulk plane strain deformation affected these rocks at amphibolite facies conditions. Shape changes suggest net shortening of the clasts by 11–64%, with a mean value of 35%. Quartz within the clasts accommodated this strain largely via dislocation creep processes. On the high‐stress flanks of the clasts, however, quartz was removed via solution mass transfer (pressure solution) processes; the resulting change in bulk composition allowed growth of porphyroblastic staurolite + chlorite ± kyanite on the clast flanks. Matrix SiO₂ contents decrease from c. 83 wt% away from the clasts to 49–58% in the selvages on the clast flanks. The chemical changes are consistent with c. 70% volume loss in the high‐stress zones. Calculated shortening values within the clast flanks are similar to the volume‐loss estimates, and are greatly in excess of the shortening values calculated from the clasts themselves. Flow laws for dislocation creep versus pressure solution imply large strain‐rate gradients and/or differential stress gradients between the matrix and the clast selvages. In a rock containing a large proportion of semirigid clasts, weakening within the clast flanks could dominate rock rheology. In our samples, however, weakening within the selvages was self limiting: (1) growth of strong staurolite porphyroblasts in the selvages protected remaining quartz from dissolution; and (2) overall flattening of the quartz clasts probably decreased the resolved shear stress on the flanks to values near those of the matrix, which would have reduced the driving force for solution‐transfer creep. Extreme chemical changes nonetheless occurred over short distances. The necessity of maintaining strain compatibility may lead to significant localized dissolution in rocks containing rheologic heterogeneities, and overall weakening of the rocks may result. Solution‐transfer creep may be a major process whereby weakening and strain localization occur during deep‐crustal metamorphism of polymineralic rocks.     

A case study on the characteristics of footwall ground deformation and movement and their mechanisms

Natural Hazards - The characteristics of ground deformation induced by the excavation of underground orebodies are summarized based on an analysis of over 10 years of deformation data...     

Evaluation of a regional strain gradient in mylonitic quartzites from the footwall of the Main Central Thrust Zone (Garhwal Himalaya,India): Inferences from finite strain and AMS analyses

The footwall of the Main Central Thrust (MCT) Zone along the Bhagirathi valley comprises a wide zone of mylonitic quartzite and deep-level tectonites. The systematic variation of finite strain parameters (Es, k and v) in the mylonites indicates heterogeneous deformation, which is determined to vary between, simple shear and non-coaxial flattening type. In such a strain regime the outer boundary of the quartz clasts are no longer preserved thus leading to an error in finite strain measurement.In order to supplement the finite strain studies, Anisotropy of Magnetic Susceptibility (AMS) analyses were carried out on the mylonitic quartzites. A systematic variation in degree of anisotropy (P′) with distance from the MCT is documented and is interpreted to be tectonic in origin. Based on these results it is concluded that P′ can be used as a strain-intensity gauge at least on an outcrop scale, where a systematic variation in P′ values from one part of the outcrop to the other can be established. However, the quantitative relation between principal axes of finite strain ellipsoid and AMS axes, magnitude of principal susceptibility difference (ΔK₁ and ΔK₃) and finite strain magnitude (ε₁=ln 1 + e₁ and ε₃=ln 1 + e₃) were related by a logarithmic relationship with a correlation coefficient of 0.844.     

An edge-based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

To solve large deformation geotechnical problems, a novel strain-smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge-based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node-based smoothed PFEM when lower-order triangular element is used. Compared with the node-based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super-convergent and very accurate solutions due to the implementation of edge-based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.     

Relationships between strain and quartz crystallographic fabrics in the Roche Maurice quartzites of Plougastel,western Brittany

An integrated microstructural and petrofabric study of the plastically deformed and partially recrystallized Roche Maurice quartzites of Plougastel, western Brittany, has revealed a clear correlation between the pattern of c-axis fabrics displayed by detrital quartz grains and the symmetry of the calculated strain ellipsoid. In specimens with flattening (k = 0) strains, c axes lie on a small circle girdle (opening angle 28–42°) centred about the principal finite shortening direction (Z). For specimens that exhibit approximate plane strain (k = 1), cross-girdle c-axis fabrics consisting of a small circle girdle centred about Z and connected through the intermediate principal extension direction (Y) were detected.Within individual specimens c-axis fabrics of syntectonically recrystallized new quartz grains within the matrix are similar to those of detrital quartz grains. c axes of new grains located within the relatively undeformed sections of the host detrital grains are commonly orientated at angles between 10 and 40° to the host c axis and are, in addition, statistically orientated at a higher angle to Z than their host c axes. These relationships are interpreted as indicating that both host grain control and the local strain (and/or stress) field may have influenced the process of recrystallization; the relative influence of these factors is, however, unknown.Microstructural and petrofabric studies indicate that the Roche Maurice quartzites have been subjected to essentially coaxial strain histories. The role of syntectonic recrystallization in facilitating continued plastic deformation in quartzites subjected to such strain histories is considered.     

碎石垫层强度与变形特性试验研究和有限元分析

碎石垫层已广泛应用于土木工程各个领域,但碎石垫层的强度与变形特性尚不十分清楚,需要进一步研究。通过对5种不同厚度碎石垫层在高应力下的室内模型试验和有限元分析,揭示了不同厚度碎石垫层的强度特性和变形特征。通过有限元分析与试验结果的对比分析,得出了不同厚度的碎石垫层荷载与沉降变形、竖向应力与侧向约束力都近似呈线性变化。碎石垫层的厚度对沉降大小有一定影响,在其他条件相同的情况下,碎石垫层越厚,沉降越大。在一定荷载作用下,碎石垫层在较短的时间内自身压缩变形已基本趋于稳定,而后随时间的增加,其压缩变形量很小。提出了一种测定碎石类土侧压力系数、泊松比及变形模量的试验测定方法,以期为测定其他类别土的侧压力系数、泊松比及变形模量提供参考。     

The Effect of finite strain and deformation history of HALABAN area,eastern Arabian shield,Saudi Arabia

The present study aims to evaluate a relationship between the mineralogy and structural analysis in the Halaban area and to document the tectonic evolution of Halaban and Al Amar faults. The collected samples were taken from deformed granitiods rocks (such as granite, gneisses and tonalite), metasedimentary, metavolcanic, metagabbro and carbonate rocks are trend to NE-SW with low dip angle in the Halaban area. These samples were 8 from granite, 14 metagabbro, 6 metavolcanics, 5 tonalite, 6 metasedimentary, 10 gneisses and 8 carbonate rocks. Our results are described for the different axial ratios of deformed rocks as the following: XZ sections range from 1.10 to 4.60 in the Fry method and range from 1.70 to 2.71 in the Rf/? method. YZ sections range from 1.10 to 3.34 in the Fry method and range from 1.62 to 2.63 in the Rf/Phi method. In addition, XY sections range from 1 to 3.51 in the Fry method and range from 1 to 1.27 in the Rf/? method for deformed granite rocks, metasedimentry rocks, and metagabbro. The stretch axes for measured samples in the X direction axes (S_X) variety from 1.06 to 2.53 in the Fry method and vary from 1.20 to 1.45 in the Rf/? method. The values of the Y direction axes (S_Y) vary from 0.72 to 1.43 in the Fry method, which indicates contraction and extension in this direction and vary from 1.13 to 1.37 in the Rf/? method which indicates extension in this direction. Furthermore, the Z direction axes (SZ) varies from 0.09 to 0.89 in the Fry method and from 0.52 to 0.71 in the Rf/? method. The stretches axes in the Z direction (SZ) show a vertical shortening about 11% to 91% in the Fry method and show vertical shortening about 29% to 48% in the Rf/? method. The studied rock units are generally affected by brittle-ductile shear zones, which are sub-parallel to parallel NW or NNW trend. It assumed that different rock types of have similar deformation behavior. Based on these results, it is concluded that the finite strain is accumulated during the metamorphism after that was started the deformation by thrusting activity. The contacts between the different rock types were deformed during thrusting under semi-brittle to ductile deformation conditions by simple shear. A component of vertical shortening is also involved causing subhorizontal foliation in the Halaban area.     

Structural mechanisms of ice deformation

New results of experimental studies into ice deformation and structural changes are presented. A sequence of structural mechanisms of deformation from polygonization to formation of cracks, cavities and shattering of crystals that replace each other primarily relatively to the load value and the deformation rate is developed. The principal mechanism of creep deformation is crack formation and crystal shattering. A brittleness index for ice deformation is proposed. It is shown that the vesicular texture of ice can be the result of the regeneration of open cracks during deformation.     

平面应变条件下粗粒土的变形特性试验研究

使用河海大学TSW－40型真三轴仪,对粗粒土分别进行平面应变和常规三轴压缩试验,研究了粗粒土在平面应变条件下的应力-应变关系及各种应变之间的关系,包括：主应力差? 1-? 3(? 2-? 3)与大主应变?1、主应力比? 1 /? 3(? 2 /? 3)与大主应变?1、球应力p与体积应变?v、偏应力q与偏应变? s、广义应力比q/p与广义剪应变? s、小主应变? 3与大主应变?1、体积应变? v与广义剪应变? s之间的关系。试验结果表明,对于相同的? 3,平面应变试验的(? 1-? 3)(或? 1 /? 3)-ε1曲线位于常规三轴压缩试验相应曲线的上方;? 3大的(? 1-? 3)(或? 2-? 3)-? 1曲线在上方,而? 3大的? 1 /? 3(或? 2 /? 3)-? 1曲线在下方;对于相同的? 3,在相同的? 1下,平面应变条件下的小主应力方向膨胀量要比常规三轴压缩条件下的大;产生相同的? s时,? 3越大,? v越大,对于相同的? 3,平面应变条件下的? v要比常规三轴压缩条件下的大;粗粒土在平面应变和常规三轴压缩条件下加荷时,具有归一化的双曲线应力-应变关系。研究表明,采用非线性弹性模型计算粗粒土的平面应变问题时,有必要考虑弹性模量E和泊松比? 的各向异性。     

土工有限元计算中如何剔除先期固结变形

土体在重力作用下的固结变形历史上大多已经完成,土体内的自重应力场和重力场处于相互平衡状态。以此为初始条件的土工有限元计算,如果直接在模型上施加重力作外载,将产生一个较大固结变形,而这个变形对土体来说是先期完成了的,所以计算会产生不合理的结果。为此,先把初应力作为一种载荷进行理论推导,并据此提出一个如何剔除先期固结变形的方法,即先加重力,通过求解,导出土体自重应力场;然后重新开始分析,把自重应力场当初始应力导入土体单元中,再加重力进行求解,这样就剔除了先期固结变形;最后进行了算例对比分析,证明其是一种合理的方法。     

A finite element method for modeling coupled flow and deformation in porous fractured media

Modeling the flow in highly fractured porous media by finite element method (FEM) has met two difficulties: mesh generation for fractured domains and a rigorous formulation of the flow problem accounting for fracture/matrix, fracture/fracture, and fracture/boundary fluid mass exchanges. Based on the recent theoretical progress for mass balance conditions in multifractured porous bodies, the governing equations for coupled flow and deformation in these bodies are first established in this paper. A weak formulation for this problem is then established allowing to build a FEM. Taking benefit from recent development of mesh‐generating tools for fractured media, this weak formulation has been implemented in a numerical code and applied to some typical problems of hydromechanical coupling in fractured porous media. It is shown that in this way, the FEM that has proved its efficiency to model hydromechanical phenomena in porous media is extended with all its performances (calculation time, couplings, and nonlinearities) to fractured porous media. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite strain and progressive deformation in models of diapiric structures

The distribution of strain within and around gravitationally produced diapiric structures was studied through the use of experimental models which were deformed in a large-capacity centrifuge. A new method of model construction was developed which is equivalent to building the model of initially square 1-mm elements. After deformation the elements assume shapes which approximate parallelograms and their finite strains can easily be calculated. If several initially identical models are deformed to different extents, the finite strain states of an element in each of the models define points on the deformation path of that element. The deformation path can be used to make estimates of the nature of the internal fabric which would be expected in the equivalent element of the natural structure.This method was applied to the study of the finite strain in diapiric ridges. The models demonstrate that the highest strain is always in the region above the diapir. Within the diapir initial vertical stretching is followed by vertical flattening. Large portions of the structure can be seen to suffer what would in natural examples be called polyphase deformation, even though all of the deformation was due to a single buoyant overturn of unstable density stratification. The strain patterns within the models support the contention that in salt diapirs the buoyant salt has a lower viscosity than the overlying sediments, but that in mantled gneiss domes the reverse is true.