颗粒形态对离散介质剪切强度的影响

自然条件下,颗粒介质大多以非规则单元形态存在。非规则几何形态对颗粒介质的宏观力学性能有很大影响。针对颗粒单元的不同几何形态,采用团颗粒单元对离散介质的直剪试验过程进行了离散元数值计算,详细地讨论了颗粒形态对离散介质剪切强度的影响。该非规则颗粒由不同形态、不同数目、镶嵌尺寸、组合方位和颗粒大小的球形颗粒进行随机构造,其在局部与整体坐标之间的转动、力矩和方位关系通过4元素方法进行确定,基本球体颗粒之间的作用力采用具有Mohr-Coulomb摩擦定侓的Hertz-Mindlin非线性接触模型,并考虑了非线性法向粘滞力的影响。通过构造7种具有相同的质量概率分布的不同形态的团颗粒,在不同法向应力下,对团颗粒的直剪试验进行了离散元模拟,分析了不同形态颗粒的剪切强度。通过对不同形态颗粒介质剪切强度的数值分析,进一步揭示了非规则颗粒间的咬合互锁效应,为分析非规则颗粒的宏观动力特性提供了依据。     

Refined modeling and movement characteristics analyses of irregularly shaped particles

Irregularly shaped (IRS) particles widely exist in many engineering and industrial fields. The macro physical and mechanical properties of the particle system are governed by the interaction between the particles in the system. The interaction between IRS particles is more complicated because of their complex geometric shape with extremely irregular and co‐existed concave and convex surfaces. These particles may interlock each other, making the sliding and friction of IRS particles more complex than that of particles with regular shape. In order to study the interaction of IRS particles more efficiently, a refined method of constructing discrete element model based on computed tomography scanning of IRS particles is proposed. Three parameters were introduced to control the accuracy and the number of packing spheres. Subsequently, the inertia tensor of the IRS particle model was optimized. Finally, laboratory and numerical open bottom cylinder tests were carried out to verify the refined modeling method. The influence of particle shape, particle position, and mesoscopic friction coefficient on the interaction of particles was also simulated. It is noteworthy that with the increase of mesoscopic friction coefficient, the fluidity of IRS particle assembly decreases, and intermittent limit equilibrium state may appear. Copyright © 2014 John Wiley & Sons, Ltd.     

Equantcy versus sphericity

The shape of a particle is commonly characterized by its sphericity. In geology, sphericity is determined by comparing a grain's length, width and breadth diameters. This type of measurement does not indicate how close the particle is to a true spherical shape, and cubes, tetrahedrons, and true spheres all have the same degree of sphericity. Because the term sphericity is misleading, implying that its determination takes roundness into account, a different term should be used. I propose that whenever the shape of a grain is determined by measuring or estimating the lengths of its main axes, we regard this as determining its degree of equantcy.     

Laboratory measurements of pivoting angles for applications to selective entrainment of gravel in a current

Important to grain entrainment by a flowing fluid is the pivoting angle of the grain about its contact point with an underlying grain. A series of experiments has been undertaken to determine how this angle depends on grain shape (rollability and angularity), on the ratio of the size of the pivoting grain to those beneath, and on factors such as imbrication. The experiments involved gravel-sized spheres (ball-bearings and marbles), natural pebbles selected for their approximately triaxial ellipsoid shapes, and angular crushed basalt pebbles. The pivoting angles for these grains were measured on an apparatus consisting of a board which can be progressively inclined, the angle of the board being equal to the pivoting angle at the instant of grain movement. The pivoting angles of spheres showed reasonable agreement with a theoretically derived equation, showing much better agreement than in previous studies which utilized sand-sized spheres. A series of measurements with spheres ranging from sand to gravel sizes reveals that the pivoting angles decrease with increasing particle size. Our results are therefore consistent with the earlier studies limited to sand-size spheres. The cause of this size dependence is unknown since moisture and electrostatic binding can be ruled out. Similar size dependencies are also found for the ellipsoidal pebbles and angular gravel. The experiments with ellipsoidal pebbles demonstrated a strong shape dependence for the pivoting angle, being a function of the ratio of the pebble's smallest to intermediate axial diameters. This ratio controls the grain's ability to roll and pivot; with small ratios of these diameters the pebbles tended to slide out of position, whereas with ratios closer to unity (circular cross-section) true pivoting took place and the angles were smaller. Experiments with flat pebbles placed in an imbricated arrangement yielded much larger angles than when the pebbles lay in a horizontal position, the pivoting angle being increased approximately by the imbrication angle. The angular crushed gravel also required high pivoting angles, apparently due to interlocking of the grains resulting from their angularity. Other factors being equal, the measurements of pivoting angles demonstrate that the order of increasing difficulty of entrainment is spheres, ellipsoidal grains, angular grains, and imbricated grains. The results obtained here make possible the quantitative evaluation of these shape effects on grain threshold, as well as evaluation of the selective entrainment of grains from a bed of mixed sizes.     

Discrete simulations of a triaxial compression test for sand by DEM

A quasi‐static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three‐dimensional discrete element method. Grains were modelled by means of particle clusters composed of rigid spheres or spheres with contact moments imitating irregular particle shapes. Attention was paid to the effect of initial void ratio and grain shape mixture on the shear strength, volume changes, force chains, kinetic, elastic and dissipated energies. In addition, the effect of the mean grain size, grain size distribution, grain size range, specimen size and roughness and stiffness of boundaries was numerically analysed in initially dense sand. Some numerical results were compared with available experimental results. Copyright © 2014 John Wiley & Sons, Ltd.     

Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions

The undrained shear behaviour of sands has been a key topic after the devastating geo-disasters during the 1964 Niigata Earthquake in Japan. Extensive geo-technical soil tests, especially undrained triaxial compression tests, have revealed that the liquefaction phenomenon was the major cause for the disaster expansions. To numerically reproduce the liquefaction phenomenon, the pore-water pressure was coupled with a distinct element method. In this model, the dynamic changes in pore-water pressure were taken into consideration by the changes in volumetric strain and modulus of compressibility of water in the respective measurement spheres. Fluid-flows among the measurement spheres were controlled by Darcy’s law. The effective stress paths and steady state strengths in undrained triaxial compression tests associated with the wide ranges of initial void ratio were investigated. The effective mean stresses of medium-dense to dense numerical specimens at the steady state were negatively proportional to the initial void ratio. Loose numerical specimens reproduced quasi-liquefaction with the effective mean stresses that were less than 25% of the initial value. The medium-dense numerical specimens reproduced the phase transformation that was a typical characteristic of granular materials. The rolling restraints did not much influence of the effective angle of internal friction but strongly affected pore-water pressure behaviour within a certain range of initial void ratio.     

Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.     

基于离散元模拟的二元颗粒柱坍塌特性研究

常见的地质灾害如滑坡、泥石流、岩崩等通常都涉及不同形状的颗粒物质运动,这些形状不同的颗粒又多具有不同的尺寸和含量。基于典型的颗粒柱坍塌试验,首先根据试验方法确定了离散元模拟所需的各项参数,然后采用随机多面体方法生成了可控制长细比的大颗粒,利用离散元法就不同大颗粒含量下形态变化对二元颗粒柱坍塌特性的影响开展研究,研究结果表明:(1)利用离散元法可以较好地重现室内试验中小球和多面体组成的二元颗粒系统的颗粒柱坍塌过程;(2)在不同长细比的不规则大颗粒和小球组成的二元颗粒柱系统中,当大颗粒含量高于临界含量值20%时,二元颗粒柱坍塌持续的时间随非球形大颗粒长细比的增加而增加;(3)在不同长细比的不规则大颗粒和小球组成的二元颗粒柱中,当大颗粒含量高于临界含量值20%时,在相同百分比的大颗粒含量下,大颗粒长细比的增加会提高大颗粒平均配位数以及降低颗粒的运动能力,大颗粒间形成更强的互锁作用,降低了颗粒柱的整体流动性,使其最终堆积高度更高、最大跑出距离更短以及更小的归一化动能峰值。(4)在不同长细比的不规则大颗粒和小球组成的二元颗粒柱中,小颗粒可以较为明显降低大颗粒间摩擦及互锁作用,增加流动性,降低大骨料形态对坍塌过程的影响。     

The urban geography of underdevelopment: a case of petty commodity production

The study in urban geography of underdevelopment has serious inadequacies although there are numerous studies on unemployment, housing, transportation and poverty problems of the city in underdeveloped societies. Urban petty commodity production (a group of activities normally seen as lying outside the principal spheres of large-scale production in underdeveloped economies), for example, has been the focus of development economics and geography in the last two decades but the specific problem of appropriation of urban landscape by this group of activities, which in turn reproduce and transform the landscape has, at the very best, been only partially and indirectly addressed. This paper deals with this problem with particular reference to material derived from fieldwork in the Turkish city of Bursa.     

Pivoting analyses of the selective entrainment of sediments by shape and size with application to gravel threshold

Measured variations of pivoting angles with grain size, shape (‘reliability’ and angularity) and imbrication are employed in analyses of grain threshold to examine how these factors influence selective grain entrainment and sorting. With a bed of uniform grain sizes, as employed experimentally to establish the standard threshold curves such as that of Shields, the threshold condition depends on grain shape and fabric. The analysis demonstrates quantitatively that there should be a series of nearly-parallel threshold curves depending on grain pivoting angles. For a given grain size, the order of increasing flow strength required for entrainment is spheres, smooth ellipsoids (depending on their ‘reliability’), angular grains, and imbricated ellipsoids (depending on their imbrication angles). The relative threshold values for these different grain shapes and fabric are predicted according to their respective pivoting angles, but remain to be directly tested by actual threshold measurements. The pivoting angle of a grain also depends on the ratio of its size to those it rests upon. This dependence permits an evaluation of selective entrainment by size of grains from a bed of mixed sizes, the condition generally found in natural sediments. The pivoting model predicts systematic departures from the standard threshold curves for uniform grain sizes. Such departures have been found in recent studies of gravel threshold in rivers and offshore tidal currents. The pivoting model is compared with those threshold data with reasonable agreement. However, more controlled measurements are required for a satisfactory test of the model. It is concluded that variations in pivoting angles for grain entrainment are significant to the processes of selective sorting by grain size and shape.     

Numerical investigation of the opening effect on the mechanical behaviours in rocks under uniaxial loading using hybrid continuum-discrete element method

Openings including their size, shape and distribution in rock play a significant role in the performance of rock related structures. The well-established knowledge in this area can contribute to the engineering practices, for example, underground space design, planning and optimisation in Civil and Mining Engineering and wellbore stability in Drilling Engineering, among others. Thus, understanding the failure mechanism of rock with openings is theoretically and practically meaningful. Laboratory testing on rock or rock-like materials with openings have been studied extensively in the literature, which, however, primarily focuses on the cracks/fractures. In this paper, a comprehensive numerical study on the effect of non-banded openings, i.e., circular, rectangular, and triangular opening, on the rock mechanical behaviour is performed using a hybrid continuum-discrete element method. It is revealed that the proposed simulation method can reproduce reasonably the crack initiation and propagation, and predict well the change of the mechanical behaviour due to the openings. In addition, the influence of the opening shape and opening ratio (=area of opening/specimen area) on the mechanical behaviour is also investigated.     

A non-linear numerical model for soil mechanics

A new computer program (CONBAL-2) is developed for 2D numerical simulations of granular soil by random arrays of spheres. CONBAL-2 uses the discrete-element method and is based on 3D program TRUBAL, previously presented by Cundall. As in TRUBAL, the new program models a random array of elastic spheres in a periodic space. The main modification of TRUBAL is the implementation by the authors of a rigorous solution for the force–displacement relation at the interparticle contacts. This force-displacement relation is a function of the elastic constants, friction coefficient and sizes of the spheres, with the properties of quartz used to simulate sand. Other specific features of CONBAL-2 include its 2D character, the lack of particle rotation and its capability to simulate shear loading on any plane. Simulated laboratory test results are presented using CONBAL-2 and several random arrays of 531 spheres having two particle sizes. These simulations include monotonic loading drained and undrained (constant volume) ‘triaxial’ experiments, as well as a cyclic-loading, constant-volume ‘torsional shear’ test. The stress–strain curves, effective stress paths, volume changes, as well as the ‘pore water pressure’ build-up behaviour obtained in the simulations compare favourably—qualitatively and in some aspects quantitatively—with similar laboratory results on sands. However, the simulated soil is somewhat stiffer and stronger due to the perfectly rounded particles, limited range of grain sizes, lack of particle rotation and 2D character of the model.     

Intersecting dilated convex polyhedra method for modeling complex particles in discrete element method

This paper describes a new method for representing concave polyhedral particles in a discrete element method as unions of convex dilated polyhedra. This method offers an efficient way to simulate systems with a large number of (generally concave) polyhedral particles. The method also allows spheres, capsules, and dilated triangles to be combined with polyhedra using the same approach. The computational efficiency of the method is tested in two different simulation setups using different efficiency metrics for seven particle types: spheres, clusters of three spheres, clusters of four spheres, tetrahedra, cubes, unions of two octahedra (concave), and a model of a computer tomography scan of a lunar simulant GRC‐3 particle. It is shown that the computational efficiency of the simulations degrades much slower than the increase in complexity of the particles in the system. The efficiency of the method is based on the time coherence of the system, and an efficient and robust distance computation method between polyhedra as particles never intersect for dilated particles. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Normalized center-to-center strain analysis of packed aggregates

The resolution of conventional techniques of center-to-center strain analysis is limited by the degree of original anticlustering of centers on the analyzed plane. However, the three-dimensional anticlustering of packed objects does not result in equivalent anticlustering on two-dimensional planes through these aggregates. Size variations due to imperfect sorting further decrease the anticlustering of natural aggregates. For the Fry all-object-object separations method, these problems are manifested in vague point-density distributions and ambiguously defined strain ellipses.Normalization of center-to-center distances allows more precise determination of small initial and tectonic anisotropies in packed aggregates. On planes through packed aggregates, object spacing is a function of object size, shape and the distance between object margins. Dividing the center-to-center distance between two objects by the sum of their average radii eliminates variations due to object size and sorting. Analyses of synthetic aggregates of packed spheres and statically recrystallized iron show that normalized Fry diagrams form better-defined vacancy fields and sharper rims of maximum point density regardless of the original sorting and anticlustering in the aggregate. Normalized strain analyses of deformed aggregates also show greatly increased resolution, with variable initial and tectonic ellipticity resulting in a wider ring of high point-density.     

D’Orbigny: A non-igneous angritic achondrite?

D’Orbigny is the sixth and by far the largest angrite known. Its bulk chemical and mineral chemical compositions, rare gas abundances and oxygen and rare gas isotope compositions fit the compositional ranges known from other angrites. It is, however, peculiar with respect to three features: the abundance of hollow shells, the presence of abundant open druses and the abundant presence of glasses.The shape, structure and texture of D’Orbigny and its mineral and bulk chemical compositions indicate an unusual genesis under changing redox conditions. In our view, data and observations are incompatible with an igneous origin of this rock but are suggestive of a complex growth and metasomatism scenario. The sequence of events apparently began with the formation of spheres of a phase which later vanished and therefore is unknown but could have been CaS. On top of these spheres (sizes from < 1-30 mm) olivine-anorthite intergrowths precipitated forming compact shells and fluffy protrusions. Aggregation of these objects plus occasional large plates made of the same intergrowths led to formation of a highly porous object with abundant large open space between the olivine-anorthite intergrowths. The aggregate also included previously formed olivines, olivinite rocks and Al-spinels. The latter carry highly porous decomposition rims of Cr-enriched Al-spinel and record mildly oxidizing conditions prevailing very early in D’Orbigny’s history. Conditions changed (with falling T?) and became oxidizing causing the phase(s) that constituted the spheres to become unstable. Their breakdown liberated large amounts of Ca and trace elements which at least in part re-precipitated by reacting with Si and Mg from the vapor to form augites that grew into the open space thus forming augite druses. Also, some of the preexisting olivine was converted into augite, which is very rich in refractory lithophile trace elements (abundances ∼ 10 × CI). Augites grew mainly under oxidizing conditions leading to atomic Fe/(Fe+Mg) ratios of about 0.44. Finally, conditions became highly oxidizing and strongly mobilized Ca from a source that apparently became unstable. The high partial pressures of Ca and Fe (and also Ti) led to precipitation of Ca-olivine and kirschsteinite (∼Fo1La20 and ∼Fo1La33, respectively) and of titaniferous aluminous hedenbergite—atomic Fe/(Fe+Mg) ∼ 0.97. Ulvöspinel and sulfides were also precipitated. Because the original phase(s) forming the early spheres vanished during these oxidizing events, the shells remained empty.In this scenario, D’Orbigny provides us with a record of changing conditions ranging from extremely reducing to highly oxidizing and with a record of the formation of an achondritic rock from a chondritic source. Angrites bear many similarities with CAIs, texturally, mineralogically and chemically. Possibly, they can be seen as CAIs, which grew larger than the ones we know from carbonaceous chondrites. Thus, angrites may bear a record of rare and special conditions in some part of the early solar nebula. They reproduce most of the textures and structures of CAIs: crystallized liquids (Asuka 881371, LEW 87051), metasomatic granoblastic rocks (LEW 86010, Angra dos Reis?) and aggregates (D’Orbigny). In addition, all angrites record metasomatic alterations, subsolidus processing after formation, also similar to what is recorded by most CAIs. Obviously, they missed the alkali metasomatic event recorded by many CAIs but they record a siderophile—lithophile element separation event that is not recorded by CAIs.     

Three-dimensional random network model for thermal conductivity in particulate materials

This paper describes a three-dimensional random network model to evaluate the thermal conductivity of particulate materials. The model is applied to numerical assemblies of poly-dispersed spheres generated using the discrete element method (DEM). The grain size distribution of Ottawa 20–30 sand is modeled using a logistic function in the DEM assemblies to closely reproduce the gradation of physical specimens. The packing density and inter-particle contact areas controlled by confining stress are explored as variables to underscore the effects of micro- and macro-scales on the effective thermal conductivity in particulate materials. It is assumed that skeletal structure of 3D granular system consists of the web of particle bodies interconnected by thermal resistor at contacts. The inter-particle contact condition (e.g., the degree of particle separation or overlap) and the particle radii determine the thermal conductance between adjacent particles. The Gauss–Seidel method allows evaluation of the evolution of temperature variation in the linear system. Laboratory measurements of thermal conductivity of Ottawa 20–30 sand corroborate the calculated results using the proposed network model. The model is extended to explore the evolution of thermal conduction depending on the nucleation habits of secondary solid phase as an anomalous material in the pore space. The proposed network model highlights that the coordination number, packing density and the inter-particle contact condition are integrated together to dominate the heat transfer characteristics in particulate materials, and allows fundamental understanding of particle-scale mechanism in macro-scale manifestation.     

Terminal settling velocity of commonly occurring sand grains

Published measurements of terminal settling velocity for commonly occurring sands are used to develop three equations which join into a single segmented curve of dimensionless form. Results are noticeably different from those for spheres of similar diameter, and permit calculation of the settling velocity for usual sand grains without specification of exact grain shape. For quartz in water, the three equations of different settling regimes correspond approximately to: very fine sand; fine to coarse sand; and very coarse sand.     

Dynamic response of flexible rockfall barriers with different block shapes

Flexible rockfall barriers are commonly constructed on steep hillsides to mitigate rockfall. The evaluation of the dynamic response of proprietary flexible rockfall barriers is conventionally performed using full-scale field tests by dropping a block onto the barriers in accordance with the European test standard ETAG 027. The block typically has a spherical or polyhedral shape and cannot reproduce more complex rockfall scenarios encountered in the field. Little attention has been paid to the effects of the block shape on the impact force and structural response. This paper aims to quantitatively reveal the influence of the block shape on the dynamic response of flexible rockfall barriers. First, an ellipsoidal model is established to approximately simulate the block, and the sphericity is employed as the representative index of the block’s shape. A full-scale test on a typical flexible barrier system is carried out and then used to calibrate an advanced three-dimensional finite element model. Finally, the dynamic responses of flexible rockfall barriers are analyzed and discussed, focusing on the effects of the block’s shape. The numerical results show that the sphericity will obviously influence the maximum elongation of flexible barriers, the peak impact force, the peak force of the upslope anchor cable, the peak force of the lower main support cable, the axial peak force of the post, and the peak shear force at the post foundation. The assumption of spherical or polyhedral blocks in the test standard could lead to the defensive failure of flexible rockfall barriers in some impact scenarios.

     

我国土工离心模型试验技术发展综述

小尺寸物理模型试验是岩土力学与岩土工程研究的重要手段.常规小比尺模型由于其自重产生的应力远低于原型,以及原型材料明显的非线性,因而不能再现原型的特性.解决这一问题的唯一途径是提高模型的自重,使之与原型等效.提高模型的自重应力水平、增大材料自重的最简便的方法就是用离心机.本文在总结回顾大量文献资料的基础上,根据离心模型试...     

Practical representation of characteristic grain shape of sands: a comparison of methods

ABSTRACT A measure of grain shape is needed for incorporation in calculations of the behaviour of grain populations (for example during transport by fluids). Many shape measures have been proposed, most of them for application to single grains rather than to populations. In this paper three such shape parameters are evaluated for samples taken by size fraction from each of three parent sands. The chosen parameters are the maximum projection sphericity of Sneed & Folk (based on triaxial measurements made on the grains), the dynamic shape factor of Briggs (based on settling velocity in water), and rollability, after Winkelmolen (based on rolling behaviour in a specially mounted rotating cylinder).
It is shown that the Sneed & Folk parameter and rollability both discriminate clearly between the shape characteristics of the three sands over the size range 150-500 μm. Moreover the discrimination of the two parameters is mutually consistent. However, dynamic shape factor gives results which for sizes smaller than 300 μm are inconsistent with those of the other two methods and which do not discriminate reliably between the populations. This is inevitable because the differences between drag on spheres and on other shapes become very small at Reynolds Numbers corresponding to those which obtain in settling tests on grains smaller than 300 μm.