A novel coupled FDM-DEM modelling method for flexible membrane boundary in laboratory tests

Difficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress-strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM-DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.     

Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

An approximate method for evaluating the shear band thickness in saturated soils

A formula for the thickness of a shear band formed in saturated soils under a simple shear or a combined stress state has been proposed. It is shown that the shear band thickness is dependent on the pore pressure properties of the material and the dilatancy rate, but is independent of the details of the combined stress state. This is in accordance with some separate experimental observations. Copyright © 2004 John Wiley & Sons, Ltd.     

Application of micropolar plasticity to post failure analysis in geomechanics

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy–Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

Experimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd     

Paleoproterozoic Extensional Structure and Its Controlling on Mineralization in the East of Liaoning Province

IntroductionThe area of eastern Liaoning is an importantmetal and nonmetal metallogenetic district in China,and the Liaohe group is one of the most importantstrata that hosts Pb, Zn, Au, B and Mg etcstratabound deposits. Up to now many geo1ogistssuch as Z…     

康古尔塔格缝合带的变形机制

北天山东段康古尔塔格带是晚古生代塔里木板块和准噶尔板块碰撞的结果。它是一条复杂的、强烈的高应变带．并具有独特的变形机制、应变序列以及构造变形。本文运用构造－地层研究方法对该碰撞带的构造特征加以分析和研究。     

High-pressure eclogites in northern Jiangsu – southern Shandong province, eastern China

Abstract Eclogites are distributed for more than 500 km along a major tectonic boundary between the Sino-Korean and Yangtze cratons in central and eastern China. These eclogites usually have high-P assemblages including omphacite + kyanite and/or coesite (or its pseudomorph), and form a high-P eclogite terrane. They occur as isolated lenses or blocks 10 cm to 300 m long in gneisses (Type I), serpentinized garnet peridotites (Type II) and marbles (Type III). Type I eclogites were formed by prograde metamorphism, and their primary metamorphic mineral assemblage consists mainly of garnet [pyrope (Prp) = 15–40 mol%], omphacite [jadeite (Jd) = 34–64 mol%], pargasitic amphibole, kyanite, phengitic muscovite, zoisite, an SiO₂ phase, apatite, rutile and zircon. Type II eclogites characteristically contain no SiO₂ phase, and are divided into prograde eclogites and mantle-derived eclogites. The prograde eclogites of Type II are petrographically similar to Type I eclogites. The mantle-derived eclogites have high MgO/(FeO + Fe₂O₃) and Cr₂O₃ compositions in bulk rock and minerals, and consist mainly of pyrope-rich garnet (Prp = 48–60 mol%), sodic augite (Jd = 10–27 mol%) and rutile. Type III eclogites have an unusual mineral assemblage of grossular-rich (Grs = 57 mol%) garnet + omphacite (Jd = 30–34 mol%) + pargasite + rutile. Pargasitic and taramitic amphiboles, calcic plagioclase (An₆₈), epidote, zoisite, K-feldspar and paragonite occur as inclusions in garnet and omphacite in the prograde eclogites. This suggests that the prograde eclogites were formed by recrystallization of epidote amphibolite and/or amphibolite facies rocks with near-isothermal compression reflecting crustal thickening during continent–continent collision of late Proterozoic age. Equilibrium conditions of the prograde eclogites range from P > 26 kbar and T= 500–750°C in the western part to P > 28 kbar and T= 810–880°C in the eastern part of the high-P eclogite terrane. The prograde eclogites in the eastern part are considered to have been derived from a deeper position than those in the western part. Subsequent reactions, manifested by (1) narrow rims of sodic plagioclase or paragonite on kyanite and (2) symplectites between omphacite and quartz are interpreted as an effect of near-isothermal decompression during the retrograde stage. The conditions at which symplectites re-equilibrated tend to increase from west (P < 10 kbar and T < 580°C) to east (P > 9 kbar and T > 680°C). Equilibrium temperatures of Type II mantle-derived eclogites and Type III eclogite are 730–750°C and 680°C, respectively.     

The second order characteristic condition for plastic flow

In this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd.