Coeval folding and boudinage under plane strain with the axis of no change perpendicular to the layer

Plane-strain coaxial deformation of a competent plasticine layer embedded in an incompetent plasticine matrix was carried out to improve our understanding about the evolution of folds and boudins if the layer is oriented perpendicular to the Y-axis of the finite strain ellipsoid. The rock analogues used were Beck’s green plasticine (matrix) and Beck’s black plasticine (competent layer), both of which are strain-rate softening modelling materials with a stress exponent n=ca. 8. The effective viscosity η of the matrix plasticine was changed by adding different amounts of oil to the original plasticine. At a strain rate of 10⁻³ s⁻¹ and a finite strain e of 10%, the effective viscosity of the matrix ranges from 1.2×10⁶ to 7.2×10⁶ Pa s. The effective viscosity of the competent layer has been determined as 4.2×10⁷ Pa s. If the viscosity ratio is large (ca. 20) and the initial thickness of the competent layer is small, both folds and boudins develop simultaneously. Although the growth rate of the folds seems to be higher than the growth rate of the boudins, the wavelength of both structures is approximately the same as is suggested by analytical solutions. A further unexpected, but characteristic, aspect of the deformed competent layer is a significant increase in thickness, which can be used to distinguish plane-strain folds and boudins from constrictional folds and boudins.An erratum to this article can be found at     

Shear-zone deformation and bulk strain in granite-greenstone terrain of the Western Superior Province,Canada

The later Archaean history of the granite-greenstone terrain of the western Superior Province in Manitoba was marked by the development of numerous shear zones with varying orientation and sense of movement. Data are presented on the orientation, width and displacement of 15 shear zones in a 61,000 km² area east of Lake Winnipeg. By making simplifying assumptions, estimates are made of the orientation of the maximum compressive stress (N-S) and the bulk shortening strain caused by the shear zone displacements (39–45%).The estimates of shear zone displacement strain are compared with estimates of bulk strain obtained by analysing the granite-greenstone shape pattern over a large area of the western Superior Province, again making simplifying assumptions. As expected, the contribution of the more ductile greenstones to the bulk strain is proportionately greater. A value of around 40% is indicated for the bulk shortening strain.Estimates of mean shear strain obtained both from shear zone displacement/width measurements and from strain profiles show a wide range in values from around 10 in some narrow zones to around 1 in very wide zones.     

Uniform investigation of hydraulic fracturing propagation regimes in the plane strain model

The hydraulic fracturing propagation regimes in the plane strain model are uniformly investigated using a numerical method based on the finite element method. The regimes range from toughness‐dominated cases to viscosity‐dominated cases, covering zero leak‐off situations and small leak‐off situations. Unlike the asymptotic solutions, the numerical method is independent of the energy dissipation regimes and fluid storage regimes. The numerical method pays no special attention to the fracture tip, and it simulates fracture tip behaviors by increasing the number of functions in a natural and uniform manner. The numerical method is verified by comparing its results with the asymptotic solutions. The effect of the model sizes on the numerical method is discussed along with the robustness of the numerical method. Copyright © 2014 John Wiley & Sons, Ltd.     

Impacts of the plane strain ratio on excavations in soft alluvium deposits

Acta Geotechnica - Due to tool, time and budget limitations, 2-dimensional analyses of deep excavation are often adopted for engineering practice; thus, the 3-dimensional behaviour is ignored....     

减围压平面应变压缩试验条件下丰浦砂中剪切带特性研究

不同于常规土体单元试验中恒定围压的应力路径,进行了减围压（卸载）应力路径下丰浦砂的平面应变压缩试验,研究了初始围压和初始相对密度对砂土的剪切强度和剪切带特性的影响。结合二维数字图像（DIC）相关方法,分析剪切带的形成过程,对剪切带的厚度和倾角及其影响因素进行定量地分析。研究结果表明,剪切带形成于峰值剪切强度之前;对于密实丰浦砂试样,随着围压的增加,其剪切强度(最大有效主应力比)减小且峰值强度出现越晚,剪切带厚度减小而剪切带倾角变化不大;丰浦砂试样的相对密度越高,剪切强度越大且峰值强度出现越早,剪切带厚度越小而剪切带倾角越高。此外,基于峰值内摩擦角的Coulomb公式可以较好地预测平面应变试验条件下丰浦砂的最大剪切带倾角。     

Semi-analytical solutions of two-dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary

The study presents semi-analytical solutions of two-dimensional plane strain consolidation problem in unsaturated soils incorporating the lateral semipermeable drainage boundary by adopting Fourier sine series and Laplace transform. The two-dimensional plane strain consolidation equations in the form of two-order partial differential equations with three variables are firstly converted to two-order partial differential equations with two variables, which are similar to those of one-dimensional consolidation problem. The four-order ordinary differential equations about excess pore-air and excess pore-water pressures are got by applying Laplace transform and the substitution method. Then, the solutions of excess pore pressures and settlement are achieved in the Laplace transform domain. Afterwards, on the basis of Crump's method, the inverse Laplace transform is conducted to obtain the analytical solutions in time domain. The comparison is conducted to verify the exactness of the obtained solutions, and the two-dimensional plane strain consolidation property with the lateral semipermeable drainage boundary is illustrated and discussed. Parametric studies are demonstrated for the excess pore pressures and normalized settlement with the change of the boundary parameters, air-water and lateral-vertical permeability coefficients, and the distance and depth. It can be found that the lateral semipermeable drainage boundary impedes the consolidation rate obviously, and when different investigated parameters are adopted, the consolidation property is similar to each other under the later permeable and semipermeable drainage boundary conditions.     

Anorthosite-adamellite-troctolite layering in the Barth Island structure of the Nain complex, Labrador

The Barth Island structure is an oval, 9 by 6 km body of layered igneous rocks. The central part contains a rhythmically layered troctolite-adamellite sequence. The sequence is repeated outward, but appears overturned, strongly sheared and reduced in thickness. Outward follows an adamellite-anorthosite sequence in which the effects of shear gradually diminish. In both sequences cryptic layering is evidenced by gradual change in mineral compositions. Isopleth maps based on the compositions of plagioclase, orthopyroxene and olivine show a circular high of An, En and Fo percentages in troctolite, gradually decreasing inward to a low in adamellitic rock. Between the highs in troctolite and the surrounding anorthosite occurs a low-temperature trough where both sequences grade into adamellitic rock. The structure may represent a deformed portion of pre-existing igneous layering. An alternative explanation would involve mixing of successive magma batches of gradually more sodic and ferrous composition.     

Application of a unified linear yield criterion in plane strain to study the strength theory effect in geotechnical engineering

The plane strain condition is a common, but polyaxial stress state for geotechnical structure designs, in which the selection of an appropriate yield or failure criterion is crucial to reasonably account for the intermediate principal stress. Under plane strain condition, a unified linear yield criterion for seven commonly used geotechnical yield criteria is presented in conjunction with the inductive method. These seven yield criteria considered in this study are the Mohr–Coulomb, Tresca, Drucker–Prager, Mogi–Coulomb, Extended Matsuoka–Nakai, Extended Lade–Duncan criteria, and the Unified Strength Theory. The generalized analytical solutions for earth pressure of retaining walls, critical load of strip foundations as well as stress and displacement of circular tunnels are derived on the basis of the proposed unified yield criterion, and their respective theoretical significance is analyzed. Thereafter, the critical load of strip foundations obtained herein is compared with two numerical results from the literature. Furthermore, the effect of strength theory on result differences of the three typical geotechnical problems by simply selecting constants, which conform to different yield criteria, is explored through a parametric study. It is found that the proposed unified yield criterion is convenient for investigating analytical solutions of the aforementioned geotechnical structures. The strength theory effect due to adopting different yield criteria is considerably significant, which cannot be ignored. Additionally, recommendations are provided on how to make use of these seven yield criteria for an optimum design.     

Dynamic analysis of ground with rigorous use of strain dependency and its application to seismic microzonation of alluvial plane

Seismic microzonation is one of the most important measures to mitigate earthquake hazards in urban areas. Because the ground motion varies significantly with the subsurface geology, it is needed for microzonation to account as much as possible for the local soil conditions. Noteworthy is that nonlinear deformation properties of soil play essential roles in amplification of strong ground motion. It is desired furthermore to focus on the expected damage extent in addition to the calculated maximum acceleration and/or velocity. The present study first developed a computer code for one-dimensional response analysis of ground that reasonably takes into account nonlinear dynamic soil properties. Second, correlations between the calculated ground motion and damage extent were obtained by examining seismic damages during the past earthquakes. By combining these two issues, seismic microzonation was carried out, and detailed damage distribution was assessed. The product of this study covers not only the damage caused by ground shaking but also liquefaction problem and lifeline damage.     

The strain history of a dalradian slide: Using pebbles with low fluctuations in axis orientation

The strain associated with the Horn Head Slide, a major tectonic break in the Dalradian rocks of NW Ireland, is recorded by pebbles in an adjacent quartzite horizon. Mean X/Y ratios of the deformed pebble shapes in excess of 8.0 are seen closest to the slide and the field of three-dimensional shapes lies along the K = 1 line. The usual methods of separating initial shape ratio (R_i) and tectonic strain ratio (R_s) from the deformed shape ratio (R_f) of ellipsoidal markers are based on measurements of variation in fluctuation (e.g., the (R_f/φ technique). However, due to the high X/Y strains in this situation and since the pebbles initially lay parallel to bedding and to a principal plane of the finite strain ellipsoid, fluctuation is generally very low. Thus, except for the least deformed X/Y data, the R_f/φ technique is inapplicable and other methods are used. For X/Y data with mean (R_f > 4.0: R_s is calculated as the harmonic mean of R_f; maximum R_i values only are obtained from the range of R_f data. For all Y/Z and X/Z data: R_i is calculated from the logarithmic range (ω_log) of R_f; R_s is simply obtained from the geometric mean of R_f modified by R_i. It is concluded from this that a varying prolate tectonic strain (K - 1.5) reaching X/Y values in excess of 8.00 was coaxially superimposed on an initial oblate shape fabric to produce the present field of deformed pebbles in the quartzite near the slide.     

The effect of the plastic potential in boundary value problems involving plane strain deformation

A large proportion of the constitutive models currently employed in Geomechanics are based on the theory of plasticity. Owing to the limitations of the data obtained from conventional testing equipment, arbitrary assumptions are often made about the behaviour of the material in generalized stress space. In this paper it is shown that the Lode angle of the stress state at failure in plane strain deformation is dependent on the shape adopted for the plastic potential. The influence of the shape of the plastic potential in the deviatoric plane on the predicted behaviour of two boundary value problems both prior to and at failure is then considered. In both cases a form of the Modified Cam Clay model is employed to describe the soil behaviour, and numerical predictions are obtained using a finite element computer code. For drained situations it is shown that the Lode angle of the stress state at failure has a dominating influence on the predicted behaviour. However, for undrained cases the effects are not so important as long as the correct undrained strength at failure is enforced.     

Influence of relative density,particle shape,and stress path on the plane strain compression behavior of granular materials

Two types of stress path-controlled plane strain compression tests were performed on both loose and dense specimens of angular and sub-angular sands and two rounded glass beads with different particle sizes. Digital image correlation method was used to analyze local deformation developments, especially shear band patterns. The material behavior in response to shearing has been found to be dependent on the relative density, particle shape, and stress path. The results of analysis on local deformation developments showed that the onset of shear bands occurred prior to their peak strengths in both dense and loose specimens. The growth rates of local maximum shear strain along a shear band were approximately consistent with an increasing global axial strain after the onset of shear band. The shear band width was influenced by both the mean particle size and the particle shape. The measured shear band inclination angles were in between those estimated by Coulomb’s and Roscoe’s formulas.     

Wavelength-amplitude characteristics of polyphase folds in the Precambrian bundelkhand complex, India

On the basis of wavelength-amplitude measurements on minor folds in a Precambrian complex of Central India, it is demonstrated that the folds related to a particular generation are characterised by some definite values of their wavelength/amplitude ratio. The wavelength-amplitude plots show that the folds related to a particular generation are all confined to certain definite fields.     

Grain boundary plane populations in minerals: the example of wet NaCl after low strain deformation

Many physical properties of rocks are sensitive to grain size and hence to the structure of grain boundaries. Depending on their properties, such as deformation and transport behaviour, boundaries may be divided into two broad types, namely special and general grain boundaries. Electron backscattered diffraction (EBSD) is used to investigate the misorientation distributions of grain boundaries and, more recently, to determine the population of grain boundary planes. Studies on metals and ceramics suggest that the grain boundary plane, rather than the misorientation, is the key parameter when defining special and general grain boundaries. In this study, the distribution of grain boundary plane orientations has been successfully determined using EBSD for a slightly deformed, synthetic NaCl material containing 22 ppm water. Boundaries showed a preference for {100} planes, which occurred with twice the frequency of a random distribution. The grain boundary plane distributions found in NaCl were largely in agreement with studies on MgO. Grain boundaries, with a coincident site lattice (CSL) misorientation, also showed a preference for {100} planes, rather than the planes of high coincident density associated with the CSL. Three main types of boundary were identified, namely {100} twist boundaries, boundaries with {100}{hkl} planes and general {hkl}{hkl} boundaries. As the properties of these three types of boundary differ, then the transport and creep properties in wet NaCl will depend on the fraction of the different boundary types found in the grain boundary population.     

Measurement of the deformation of sand in a plane strain compression experiment using incremental digital image correlation

Acta Geotechnica - This work presents the results from a series of plane strain compression experiments on medium-density sands. In these experiments, a new type of plane strain experimental...     

Late Cretaceous to Miocene and Quaternary deformation history of the Chalk: Channels,slumps, faults,folds and glacitectonics

Late Cretaceous Chalk sedimentation history across the British Isles included (i) fault controlled uplift and subsidence in Northern Ireland and the Inner Hebrides and (ii) uplift along the lines of en echelon folds in Southern Britain and northern France. Synsedimentary slump folds and downslope displacement structures are compared with penecontemporaneous interbed slides and later tectonic folds and faults. Compressional strike-slip tectonic processes at Flamborough Head, Yorkshire, illustrate intra-Chalk slump beds in a half-graben setting. Progressive ‘growth’ of structures characterises early downslope slump folding, interbed sliding and some listric faulting. Sheet-flints replacing slide shear planes and early fractures provide evidence for early movements. Availability of open-slopes or the depth of burial under which the range of structures developed is reflected in the degree of disruption and fragmentation of chalk and flint. Fragmentation provides clues to the timing of events and origin of the Late Campanian Altachuile Breccia (Northern Ireland) and the Coniacian Hope Gap slides (Sussex). Fragmentation and formation of sheet flints together help distinguish intra-Chalk tectonics from Quaternary glacitectonic structures.The role of marl seams, high porosity chalk beds and hardgrounds on bed-sliding, décollement zones and disruption of chalk blocks from bedrock in glacitectonics is discussed. Chalk formations with marl seams develop a special style of fracturing related to early interbed sliding and pore-fluid escape structures. Marl-seams are shown to be primary sedimentary features and not the products of post depositional pressure-solution. More than any other formation the Late Santonian – Early Campanian Newhaven Chalk contains extensive sheet-flints and shows great lateral variation in thickness and lithology across the fold belts of southern England and northern France.