A packing generation scheme for the granular assemblies with 3D ellipsoidal particles

This paper introduces a new generator algorithm and computer program for 3-D numerical simulation of packing configuration in a granular assemblies composed of ellipsoidal particles of different a/b aspect ratios. Each ellipsoidal particle is approximated by the revolution of an ellipse, formed by four connected arcs, about the major axis passing through its centroid. The centroid co-ordinates, major axis direction and lengths of the major and minor axes are the essential data for the packing generation and associated contact detection. The domain to be filled with particles can be a polyhedron of any shape. The packing program was coded based on a newly proposed scheme which obeys the no interpenetration kinematics of solid bodies. New contact detection algorithms for any two ellipsoids in the packing space were developed. Though simple, these algorithms effectively determine the contact condition and contact point without solving the simultaneous equations of the two ellipsoidal surfaces. Each particle's packing location, contact-point co-ordinates, and three-dimensional graphs can be created using the packing domain given boundaries, along with numbers, and geometrical information of particles to be generated. Simulation results show that this new algorithm provides an effective packing model as a required initial input for analysing the mechanics of granular material. This generation scheme potentially can explore the complex 3-D behaviours of material composed of discrete particles. Copyright © 1999 John Wiley & Sons, Ltd.     

基于多视角二维图像的钙质砂颗粒三维重构方法

以多视角二维图像为基础进行复杂形状颗粒三维重构。以具有复杂形状的钙质砂颗粒为样本,针对块状、条状以及树枝状等典型复杂形状颗粒进行重构,并以凸度、圆形度以及长宽比等形状指标为依托对其最终重构精度进行表征。在重构过程中,以颗粒初始投影面为基础绕轴转动获取一系列颗粒二维投影图像,并提取其边界坐标值,而后利用三维点云与所获取的二维图像轮廓坐标进行定位匹配,并删除位于二维图像轮廓外部点集,最终得到使得所有点均位于所获取的系列二维图像轮廓内。在此基础上,进一步对点云实体化处理并构建得到三维实体。通过对150个不同形状颗粒展开重构,统计发现90%以上颗粒的重构误差在10%以内,其中,误差范围最大的为树枝状颗粒,最大误差为10.84%,最小误差则小于1.00%。该方法原理简单,可有效地构建得到精度较高的复杂形状颗粒三维模型。     

Investigating 3D geometry of porous media from high resolution images

We present spatial distributions for pore path length and coordination number, pore throat size and nodal pore volume obtained for a 1.5³ mm³ volume of 12.1% porosity Fontainebleau sandstone. The sandstone was imaged using Synchrotron X-Ray computed microtomography at 6 micron resolution. The spatial distributions were computed based upon three dimensional medial axis analysis of the void space in the image. We also present vesicle size and vesicle-vesicle contact surface area distributions for a 1.36 mm length of a 6.36 mm diameter core of basalt from a vesiculated lava flow imaged at 20 micron resolution.     

Transferable wavelet method for grain‐size distribution from images of sediment surfaces and thin sections,and other natural granular patterns

In images of sedimentary or granular material, or simulations of binary (two‐phase) granular media, in which the individual grains are resolved, the complete size distribution of apparent grain axes is well‐approximated by the global power spectral density function derived using a Morlet wavelet. This approach overcomes many limitations of previous automated methods for estimating the grain‐size distribution from images, all of which rely on either: identification and segmentation of individual grains; calibration and/or relatively large sample sizes. The new method presented here is tested using: (i) various types of simulations of two‐phase media with a size distribution, with and without preferred orientation; (ii) 300 sample images drawn from 46 populations of sands and gravels from around the world, displaying a wide variability in origin (biogenic and mineralogical), size, surface texture and shape; (iii) petrographic thin section samples from nine populations of sedimentary rock; (iv) high‐resolution scans of marine sediment cores; and (v) non‐sedimentary natural granular patterns including sea ice and patterned ground. The grain‐size distribution obtained is equivalent to the distribution of apparent intermediate grain diameters, grid by number style. For images containing sufficient well‐resolved grains, root mean square errors are within tens of percent for percentiles across the entire grain‐size distribution. As such, this method is the first of its type which is completely transferable, unmodified, without calibration, for both consolidated and unconsolidated sediment, isotropic and anisotropic two‐phase media, and even non‐sedimentary granular patterns. The success of the wavelet approach is due, in part, to it quantifying both spectral and spatial information from the sediment image simultaneously, something which no previously developed technique is able to do.     

二维粒状材料双轴压缩试验研究

为了研究粒状材料的各向异性力学行为与细观组构演化之间的关系,采用自主研发的双轴压缩试验系统,以圆形和椭圆形截面的金属棒状材料组成的二维堆积体为试验对象,对不同大主应力方向角?（沉积面与大主应力作用面的夹角）的试样进行了各向等压、常侧向压力、等p剪切3种应力路径试验,并通过分析试样在不同变形阶段的数字照片得到了其细观组构演化规律。发现对于椭圆形截面的试样存在一个卓越剪切方向,随剪应变增大,颗粒长轴呈现出向该方向偏转的趋势,并且在大变形条件下沿该方向形成剪切带;卓越剪切方向与沉积面方向关系不大,而与大主应力作用面方向夹角约为45°+ /2, 为残余内摩擦角;随卓越剪切方向与沉降方向夹角的不同,颗粒偏转程度的不同是导致剪胀特性和峰值强度各向异性的主要原因     

自然邻点插值算法及其在二维不规则数据网格化中的应用

由于观测数据的不足,对不规则散点数据的二维插值在地球物理中应用非常广泛。这里研究并实现了自然邻点二维插值算法,并以一个大地电磁测深反演数据为例,验证了该方法的可行性与效果。实际资料试算与成图结果表明,该方法具有精度高、插值效果好、速度快以及便于模拟地形数据等优点。     

3D mine pillar design information from 2D FEM analysis

This paper described a technique for obtaining three-dimensional mine design information using a two-dimensional finite element program where the mining geometry consists of an extensive array of underground rooms and pillars. The technique is based upon a simple augmentation of forces in a two-dimensional analysis to produce the same average pillar stress that would occur in a full three dimensional analysis. Detailed comparisons between a three-dimensional analysis, a two-dimensional analysis (plane stress and plane strain) and an augmented two-dimensional analysis (also plane stress and plane strain) of stress about a typical coal mine pillar are presented. A local factor of safety is defined and then mapped over the pillar midplane, the immediate roof and immediate floor using the results from the full three-dimensional analysis. Comparisons of roof and pillar safety factor distributions obtained by the three-dimensional, two-dimensional and augmented two-dimensional analyses show that the minimum safety factors in the pillar (at the pillar sides) are predicted quite closely by the augmented two-dimensional techniqe (plane stress). The same is true of the immediate roof, although the three-dimensional safety factor tends to be higher in the roof (over the room) than that calculated by the augmented twodimensional technique. The augmented loading procedure appears to hold considerable promise as a very efficient and cost reducing techniqe for mine pillar design.     

Correlation of fabric tensors for granular materials using 2D DEM

Acta Geotechnica - Soil fabric anisotropy can be quantitatively assessed by means of fabric tensors introduced as internal variables in constitutive models and defined by unit vectors along the...     

Size and shape effects in point load tests of irregular rock fragments

Summary Point-load tests were performed on three hard rocks of the Lake Superior district, ironformation, metadiabase, and ophitic basalt. More than 500 irregular, mine-run fragments ranging in diameter up to about 250 mm were tested in the field, using a specially designed, semi-portable test rig. Results were analyzed by multiple regression techniques, seeking a best expression for the point-load strength in terms of a size effect and shape effects. Standard unconfined compression tests and Brazilian tests were also performed on the metadiabase and the basalt, three core sizes of each, in order to determine their respective size effects. The size-effect exponents for compression were found to be a variable characteristic of rock type, as previously reported for other rocks by the senior author, whereas the size-effect exponent in the point-load test was constant over all three rocks.Notation A Load-bearing area of prismatic compression specimen, mm² - Probability level of a statistical significance test - b, w Long and short prism dimensions, mm, in plane perpendicular to load - c _i ,c _L Exponent in equation for strength (coefficient, in the log-linear form) - d Diameter, mm - D, H Initial and final (at rupture) distance between the load points, mm - E Young's modulus, MPa - F Axis of the fracture surface normal toD, mm, point-load test - G, J Semiminor, semimajor, specimen axis, mm, perpendicular to direction of point load - h Height of prismatic compression specimen, mm - K Constant in linear regression model, basic rock strength parameter - L, M, S Long, intermediate, and short axes, of point-load-test specimen - log Natural (Napierian) logarithm - n Number of tests - v Poisson's ratio - P Resistance of test specimen at rupture, Newtons - Q Compressive strength, MPa, determined from unconfined compression test - R Multiple correlation ratio for a multilinear regression analysis - SE Standard error of estimate for a multilinear regression analysis - T Tensile strength, MPa, determined from diametral compressive test of core - t Thickness, mm - U Geometric mean diameter, mm, of the minimum cross section through the load points=(DG)^1/2 - V Geometric mean diameter, mm, of point-load specimen=(LMS)^1/3 - W Geometric mean diameter, mm, of the specimen midsection perpendicular to the point-load direction=(GJ)^1/2 - X, Y Geometric mean diameter, mm, of the fracture surface, estimated by (DF)^1/2, by (HF)^1/2 - Z _LM ,Z _RA , ... Differences between values of logK, used to express category effects, those attributed to specimen orientation and/or rock type     

Gondwana: Its shape,size and position from Cambrian toTriassic times

Gondwana and the associated peri-Gondwana fragments cover an area which isabout two-thirds of the area of all continents above the 2000 m bathymetric contour. The Gondwana continents formed by break-up during a geologically short period (Jurassic to Tertiary times), coinciding with the eruption of flood basalts. The uplift caused by associated plumes probably provided the extra stresses necessary for continental separation. It is unclear whether plumes alone were able to fragment Gondwana. By contrast, the smaller, more numerous, peri-Gondwana fragments are generally elongate and their period of formation spans the whole of the Phanerozoic. Their shapes are tentatively attributed to trench suction and associated effects caused by south dipping slabs acting mostly on the northern margin of Gondwana; their migration to retreat of the hinge lines of the subduction zones generally northwards. Gondwana's position during the Cambrian to Triassic interval is uncertain. The most recent apparent polar wander paths (APWPs), based on high quality palaeomagnetic data, are incompatible with the distributions of corals, tillites and the Clarkeia shelly fauna of Silurian age. Somewhat surprisingly, a new APWP based on all available pal˦omagnetic poles is in much better agreement with the fossil and sediment distributions even though many poles have not been magnetically tested. A solution to the ‘Pang˦a problem’ is proposed, in which it is suggested that many of the Gondwana poles for the period 340-200 Ma have been remagnetised. However, all the APWPs give improbable polar positions for some Early Cambrian Moroccan archaeocyathids. Rates of change of pole position for the new modified APWP (‘apparent drift rates’) are similar to post-Triassic rates, implying that plate driving forces have not changed much during the Phanerozoic.     

Quantitative 3D imaging of partially saturated granular materials under uniaxial compression

Acta Geotechnica - Gauging the mechanical effect of partial saturation in granular materials is experimentally challenging due to the very low suctions resulting from large pores. To this end, a...     

Fluid inclusion modification by H2O and D2O diffusion: the influence of inclusion depth, size, and shape in re-equilibration experiments

The mobility of H₂O and D₂O by diffusion through quartz is illustrated with H₂O-rich fluid inclusions synthesized at 600 °C and 337 MPa, within the α-quartz stability field. Inclusions are re-equilibrated at the same experimental conditions within a pure D₂O fluid environment. Consequently, a gradient in volatile fugacities is the only driving force for diffusion, in the absence of pressure gradients and deformation processes. Up to 100 individual inclusions are analyzed in each experiment before and after re-equilibration by microscopic investigation, microthermometry, and Raman spectroscopy. Changes in fluid inclusion composition are obtained from the ice-melting temperatures, and density changes are obtained from total homogenization temperatures. After 1-day re-equilibration, inclusions already contain up to 11 mol % D₂O. A maximum concentration of 63 mol % D₂O is obtained after 40-day re-equilibration. D₂O concentration profiles in quartz are determined from the concentration in inclusions as a function of their distance to the quartz surface. These profiles illustrate that deep inclusions contain less D₂O than shallow inclusions. At equal depths, a variety of D₂O concentration is observed as a function of fluid inclusion size: Small inclusions are stronger effected compared with large inclusions. A series of 19-day re-equilibration experiments are performed at 300, 400, 500, and 600 °C (at 337 MPa), at the same conditions as the original synthesis. The threshold temperature of diffusion is estimated around 450 °C at 337 MPa, because D₂O is not detected in inclusions from re-equilibration experiments at 300 and 400 °C, whereas maximally 26 mol % D₂O is detected at 500 °C. Our study indicates that the isotopic composition of natural fluid inclusions may be easily modified by re-equilibration processes, according to the experimental conditions at 600 °C and 337 MPa.     

An experimental study on the time-dependent behavior of crushable granular materials using 3D-printed particles

Acta Geotechnica - This paper aimed to investigate the potential capability of using 3D-printed particles to study the time-dependent behavior of a typical crushable granular material, i.e.,...     

起伏地表二维瑞雷面波正演模拟及波场分析

采用高精度交错网格有限差分法,建立了在起伏地表条件下瑞雷面波数值模拟的自由边界条件,通过对倾斜二层模型模拟的结果与解析解对比,二者完全一致,由此证明了起伏地表下瑞雷面波数值模拟的正确性。在此基础之上,模拟并分析了小凸起与小凹陷模型条件下,瑞雷面波的波场传播特征。通过分析得出瑞雷面波在这二种地形传播时,都存在反射、波型转换,以及能量再分配。因此,在起伏地表条件下,利用瑞雷面波进行勘探时要考虑起伏地表对瑞雷面波波场的影响。     

三维稀疏反演多次波预测及曲波域匹配相减技术

传统的自由表面多次波压制(SRME)方法研究是基于二维假设的,这种算法对多次波贡献考虑过于局限,难以应对复杂地质构造的情况。3DSRME算法过于笨拙,对数据要求过于苛刻,很难有效推广和应用。三维稀疏反演多次波预测方法利用柯西概率密度函数,将垂直测线方向上稀疏的多次波能量贡献道集转换到模型空间,有效重构同相轴能量顶点——菲涅尔带,从而有效拾取多次波能量,准确预测多次波。采用曲波域匹配相减技术对多次波进行去除,相较于传统的最小平方匹配相减方法,Curvelet域具有多方向、多尺度的特性,能够更有效地压制多次波。建立三维倾斜层状速度模型,对模拟三维地震数据进行试算,并与常规2D SRME的处理结果进行对比,验证了本文所述方法的有效性。     

Modeling coupled erosion and filtration of fine particles in granular media

One of the major causes of instability in geotechnical structures such as dikes or earth dams is the phenomenon of suffusion including detachment, transport and filtration of fine particles by water flow. Current methods fail to capture all these aspects. This paper suggests a new modeling approach under the framework of the porous continuous medium theory. The detachment and transport of the fine particles are described by a mass exchange model between the solid and the fluid phases. The filtration is incorporated to simulate the filling of the inter-grain voids created by the migration of the fluidized fine particles with the seepage flow, and thus, the self-filtration is coupled with the erosion process. The model is solved numerically using a finite difference method restricted to one-dimensional (1-D) flows normal to the free surface. The applicability of the model to capture the main features of both erosion and filtration during the suffusion process has been validated by simulating 1-D internal erosion tests and by comparing the numerical with the experimental results. Furthermore, the influence of the coupling between erosion and filtration has been highlighted, including the development of material heterogeneity induced by the combination of erosion and filtration.

     

砂土颗粒三维形态的定量表征方法

颗粒形态是影响砂土力学特性的重要因素,特别是影响砂土在低应力状态下的抗剪强度、剪胀效应和临界状态行为,以及高应力状态下的颗粒破碎行为。因此,准确地重构砂粒的三维形态,并量化计算其形态表征参数是研究砂粒形态效应的前提工作。借助于高精度的CT扫描技术和图像处理技术,获得近海石英砂和风化花岗岩残积砂这两类砂土颗粒的三维形态信息。采用球谐函数序列实现两种砂颗粒三维形态的准确重构,并通过球谐函数分析计算砂土颗粒的体积来验证该方法的有效性。基于球谐重构的三维砂粒表面,提出了实用性的方法来计算砂粒的表面积、表面曲率和三维尺寸等,进而计算砂粒的三维球度、圆度和伸长率等形态表征参数。结果表明,当球谐函数阶达到15时,其重构的砂粒基本形状和表面纹理均与真实砂粒非常接近;近海石英砂在水流搬运和磨蚀的作用下颗粒形态较为规则和圆滑,球度和圆度较大,而风化花岗岩残积砂则在物理风化和剥蚀作用下颗粒形态较为复杂和粗糙,球度和圆度较小;而这两种地质作用对砂土颗粒的伸长率则没有明显的影响。     

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcak's fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.