Validation of a model for impact breakage incorporating particle size effect

Investigation of a breakage probability model published by Vogel and Peukert [Vogel, L. and Peukert, W., 2004. Determination of material properties relevant to grinding by practicable labscale milling tests. Int. J. Miner. Process., 74S, 329–338.] has led to a modification of their model to describe the degree of impact breakage, t₁₀. The modified model takes a form similar to the JKMRC prior art breakage model, but with particle size and breakage properties incorporated explicitly in the model.     

Role of feed moisture in high-pressure roll mill comminution

The application of high-pressure roll mills (HPRM) for industrial comminution has been growing, particularly because of its energy efficiency. Many aspects of HPRM comminution have not been fully characterized because the performance of the machine is affected by numerous parameters that still need to be investigated and optimized. The present paper is concerned with the effect of feed moisture on HPRM performance. The comminution of minus 8-mesh dolomite feed at several different moisture levels was conducted with a laboratory HPRM to delineate the effect of feed moisture on product characteristics, specific energy consumption, and such mill operating parameters as applied load, roll gap and roll speed. The results showed definite effects of moisture on these parameters and the product size distribution, most likely because of lubrication of the particles in the compacting bed as they pass through the roll gap.     

Discrete element modeling for predicting breakage behavior and fracture energy of a single particle in a jaw crusher

In the present study, Discrete Element Method (DEM) technique was applied to model the fracture behavior of a single spherical and cubic rock in a laboratory jaw crusher. The rocks studied were modeled as granular assemblies located between two jaws, and their fracture mechanism was studied. To verify the obtained results, the spherical and cubic specimens produced from Dokoohak Limestone and Dehbeed Granite were studied and the energy applied by the jaws was compared to those of the fracture energy estimated by the single particle breakage analysis. There is fairly good agreement between the energy acquired from the DEM model and the single particle fracture energy of the spherical rocks. It appears that DEM is a suitable method for predicting the crushing energy of the spherical rocks in the jaw crusher. The fracture behavior of the crushed rocks was examined and compared by the results obtained from the DEM model. The tensile mode of fracture occurring in the spherical rocks is well presented by the discrete element modeling. However, the DEM technique is not capable of modeling the delamination mode occurring in the cubic rocks.     

Models of breakage and selection for particle size distributions

It is generally agreed that particle size distributions of sediments tend ideally to approximate the form of the lognormal probability law, but there is no single widely accepted explanation of how sedimentary processes generate the form of this law. Conceptually, and in its simplest form, sediment genesis involves the transformation of a parent rock mass into a particulate end product by processes that include size reduction and selection during weathering, transportation, and deposition. The many variables that operate simultaneously during this transformation can be shown to produce a distribution of particle sizes that approaches asymptotically the lognormal form when the effect of the variables is multiplicative. This was first shown by Kolmogorov (1941). Currently available models combine breakage and selection in differing degrees, but are similar in treating the processes as having multiplicative effects on particle sizes. The present paper, based on careful specification of the initial state, the nth breakage rule and the nth selection rule, leads to two stochastic models for particle breakage, and for both models the probability distributions of particle sizes are obtained. No attempt is made to apply these models to real world sedimentary processes, although this topic is touched upon in the closing remarks.     

Modeling the particle breakage of rockfill materials with the cohesive crack model

A practical combined finite–discrete element method was developed to simulate the breakage of irregularly shaped particles in granular geomaterials, e.g., rockfill. Using this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted cohesive interface elements (CIEs) with a progressive damage model. The Mohr–Coulomb model with a tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode occurs at the particle scale. Two series of biaxial tests were simulated for both the breakable and unbreakable particle assemblies. The two assemblies have identical configurations, with the exception that the former is inserted with CIEs and is breakable. The simulated stress–strain–dilation responses obtained for both assemblies are in agreement with experimental observations. We present a comprehensive study of the role of particle breakage on the mechanical behavior of rockfill materials at both the macroscopic and microscopic scales. The underlying mechanism of particle breakage can be explained by the force chain in the assemblies.     

考虑颗粒强度尺寸效应的原型堆石料破碎特性研究

高土石坝中,堆石体颗粒破碎是导致坝体变形的主要因素之一。但是由于原型坝料的颗粒尺寸较大,其破碎程度难以直接通过室内试验度量,因此通常要将原型级配缩尺为60mm以下的小粒径级配堆石料,然后才能进行室内试验。而由于原型和试验级配差异较大,导致试验测得的参数往往和原型坝料实际参数有较大差异,因而影响了原型坝料力学特性的深入研究。这里提出了一种新的实时预测原型坝料破碎的方法。首先在颗粒尺度上,基于单粒强度的Weibull分布理论和颗粒分形破碎理论,阐述了原型堆石料级配演化的推求过程;然后通过单粒强度试验测得了相关参数,并与三轴试验测得的试样级配曲线对比,验证了参数选取的合理性;之后分析了颗粒强度离散程度对于原型坝料级配曲线形状的影响;最后,讨论了加载过程中原型级配和试验级配堆石体的相对破碎参量和受力状态的关系。     

非均质含水层中地下水年龄数值模拟

地下水年龄数值模拟是近年来国际地下水领域的一个全新研究方向。在简单介绍地下水年龄数值模拟相关理论和方法基础上,通过一个简单算例模拟对比了稳定流条件下不同非均质含水层中的水流运动和年龄分布,探讨了夹层透水性的强弱对地下水年龄分布的影响。结果表明,在地下水系统保持补径排通量不变的前提下,弱透水夹层的存在对于特定区域地下水的深部循环和更新具有积极作用。同时,在模拟区域深部含水层的年龄分布时,不能忽略其弥散作用。地下水年龄模拟为研究区域尺度上的地下水循环和地下水资源可持续利用提供了一种新的途径。     

Modeling of a Multiply Jointed Voussoir Beam in the Centrifuge

Summary The mechanics and kinematics of a multiply jointed Voussoir beam have been studied based on the response of small scale beams tested in the centrifuge. The model beams were made up of six blocks, confined between fixed abutments. The tests included monitoring of beam deflection, development of axial thrust and distribution of strain within the beam. The models were subjected to accelerations of up to 90 g, depending upon the beam geometry. Two different beam geometries were considered. The test data were analysed in the light of pseudo analytical algorithms accepted in the analysis of singly jointed Voussoir beams. The data show that small translations and rotations of the block at the beam-abutment interface are required for a stable compression arch to set up in the beam. The computations and physical models indicate that the development of thrust is in linear proportion with the applied acceleration and is independent of beam thickness. The distribution of strains along the beam leads to the conclusion that the depth of the compression arch varies from the total beam thickness, to approximately one half of the beam thickness, under stable conditions. The data should be of considerable use to researchers looking to calibrate/validate numerical techniques used in describing the response of discontinuous rock masses.     

Implicit integration under mixed controls of a breakage model for unsaturated crushable soils

This paper discusses a series of stress point algorithms for a breakage model for unsaturated granular soils. Such model is characterized by highly nonlinear coupling terms introduced by breakage‐dependent hydro‐mechanical energy potentials. To integrate accurately and efficiently its constitutive equations, specific algorithms have been formulated using a backward Euler scheme. In particular, because implementation and verification of unsaturated soil models often require the use of mixed controls, the incorporation of various hydro‐mechanical conditions has been tackled. First, it is shown that the degree of saturation can be replaced with suction in the constitutive equations through a partial Legendre transformation of the energy potentials, thus changing the thermomechanical state variables and enabling a straightforward implementation of a different control mode. Then, to accommodate more complex control scenarios without redefining the energy potentials, a hybrid strategy has been used, combining the return mapping scheme with linearized constraints. It is shown that this linearization strategy guarantees similar levels of accuracy compared with a conventional strain–suction‐controlled implicit integration. In addition, it is shown that the use of linearized constraints offers the possibility to use the same framework to integrate a variety of control conditions (e.g., net stress and/or water‐content control). The convergence profiles indicate that both schemes preserve the advantages of implicit integration, that is, asymptotic quadratic convergence and unconditional stability. Finally, the performance of the two implicit schemes has been compared with that of an explicit algorithm with automatic sub‐stepping and error control, showing that for the selected breakage model, implicit integration leads to a significant reduction of the computational cost. Such features support the use of the proposed hybrid scheme also in other modeling contexts, especially when strongly nonlinear models have to be implemented and/or validated by using non‐standard hydro‐mechanical control conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Improvements for the smooth joint contact model of the particle flow code and its applications

This paper deals with two shortcomings of the smooth-joint contact model (SJCM) used in the particle flow code (PFC). The first shortcoming is the increase of the shear strength of the joint when the shear displacement of the joint exceeds a specific value that is related to the particle size. This problem is named as the interlocking problem, which is caused by the interlocking particles. It occurs due to a shortcoming of the updating procedure in the PFC software related to the contact conditions of the particles that lie around the intended joint plane during high shear displacements. This problem also increases the dilation angle and creates unwanted fractures around the intended joint plane. To solve this problem two new approaches are proposed in this paper: (1) joint plane checking (JPC) approach and (2) joint sides checking (JSC) approach. These approaches and the regular approach are used to model: (a) the direct shear test using the PFC^2D and PFC^3D, (b) the biaxial test on a sample having a persistent joint with a dip angle varying from 0° to 90° at an interval of 15° using the PFC^2D and (c) the polyaxial test on two samples, one of them having a joint with a dip direction of 0° and the dip angle varying from 0° to 90° at an interval of 15°, and the other sample having a joint with a dip angle of 60° and the dip direction varying from 0° to 90° at an interval of 15° using the PFC^3D. All numerical results show that the JPC and JSC approaches can solve the interlocking problem. Also, they proved to be more consistent with the theory compared to the regular approach. However, the JPC approach leads to a slightly softer joint. Therefore, the JSC approach is suggested for jointed rock modeling using the PFC. The other shortcoming of the SJCM dealt within this paper is its inability to capture the non-linear behavior of the joint closure varying with the joint normal stress. This problem is solved in this paper by proposing a new modified smooth-joint contact model (MSJCM). MSJCM uses a linear relation between the joint normal stiffness and the normal contact stress to model the non-linear relation between the joint normal deformation and the joint normal stress observed in the compression joint normal stiffness test. A good agreement obtained between the results from the experimental test and the numerical modeling of the compression joint normal test shows the accuracy of this new model.     

堆石料颗粒破碎特征的大型三轴试验研究

针对多个堆石料进行的大型三轴剪切试验,研究了颗粒破碎情况。结果表明,在试样制备过程所发生的颗粒破碎不可忽视。为了在固结开始前保持初始设计的级配,应将设计级配相应下调一定数值来制备试样。分析试验数据表明,大颗粒主要发生的是表面破碎,而整个试验过程中在剪切完成后的颗粒破碎率与围压之间呈线性增加关系,且风干样的颗粒破碎率小于饱和样的破碎率。     

Object and Pixel-Based Reservoir Modeling of a Braided Fluvial Reservoir

To assess differences between object and pixel-based reservoir modeling techniques, ten realizations of a UK Continental Shelf braided fluvial reservoir were produced using Boolean Simulation (BS) and Sequential Indicator Simulation (SIS). Various sensitivities associated with geological input data as well as with technique-specific modeling parameters were analyzed for both techniques. The resulting realizations from the object-based and pixel-based modeling efforts were assessed by visual inspection and by evaluation of the values and ranges of the single-phase effective permeability tensors, obtained through upscaling. The BS method performed well for the modeling of two types of fluvial channels, yielding well-confined channels, but failed to represent the complex interaction of these with sheetflood and other deposits present in the reservoir. SIS gave less confined channels and had great difficulty in representing the large-scale geometries of one type of channel while maintaining its appropriate proportions. Adding an SIS background to the Boolean channels, as opposed to a Boolean background, resulted in an improved distribution of sheetflood bodies. The permeability results indicated that the SIS method yielded models with much higher horizontal permeability values (20–100%) and lower horizontal anisotropy than the BS versions. By widening the channel distribution and increasing the range of azimuths, however, the BS-produced models gave results approaching the SIS behavior. For this reservoir, we chose to combine the two methods by using object-based channels and a pixel-based heterogeneous background, resulting in moderate permeability and anisotropy levels.     

Modeling and calculating for the compaction characteristics of waste rock masses

Bearing and deformation behaviors of waste rock masses (WRM) are more usually considered in stress distribution in caved waste. As WRM is widely located in hidden and dangerous environments, herein, numerical calculation is the preferred research method, but there are no modules specifically designed to simulate WRM, and the distribution of blockiness size, void, and properties of WRM in existing programs is still immature. A construction and subdivision method for modeling WRM is proposed in this paper. That is on the basis of the intact rock mass numerical model established in 3D Voronoi, the blocks in the intact rock mass are removed at random to achieve the purpose of retrieving the WRM structure by means of predetermined porosity. Also, the Weibull distribution is introduced to describe the properties of joints randomly, and a uniaxial compression experiment is used to research the compaction characteristics of WRM. The modeling and parametric methods can more accurately reflect fragmentation characteristics, bulking characteristics, and compaction characteristics of WRM. Compared with the existing theoretical and experimental results, this method has a high degree of consistency with them. This experimental study provides a new and effective method for the safety control of backfilling technics of WRM in coal mines.     

On the role of particle breakage in the shear failure behavior of granular soils by DEM

This article presents a fundamental study on the role of particle breakage on the shear behavior of granular soils using the three‐dimensional (3‐D) discrete element method. The effects of particle breakage on the stress ratio, volumetric strain, plastic deformation, and shear failure behavior of dense crushable specimens undergoing plane strain shearing conditions are thoroughly investigated through a variety of micromechanical analyses and mechanism demonstrations. The simulation of a granular specimen is based on the effective modeling of realistic fracture behavior of single soil particles, which is demonstrated by the qualitative agreement between the results from platen compression simulations and those from physical laboratory tests. The simulation results show that the major effects of particle breakage include the reduction of volumetric dilation and peak stress ratio and more importantly the plastic deformation mechanisms and the shear failure modes vary as a function of soil crushability. Consistent macro‐ and micromechanical evidence demonstrates that shear banding and massive volumetric contraction depict the two end failure modes of a dense specimen, which is dominated by particle rearrangement–induced dilation and particle crushing–induced compression, respectively, with a more general case being the combination and competition of the two failure modes in the medium range of soil crushability and confining stress. However, it is further shown that a highly crushable specimen will eventually develop a shear band at a large strain because of the continuous decay of particle breakage. Copyright © 2011 John Wiley & Sons, Ltd.     

基于夜间灯光辐射数据的张掖市甘州区GDP空间分布建模

尽管近年来统计数据的生成技术有了很大提高, 但可用的详细GDP空间分布数据始终难以得到满足. 以夜间灯光辐射数据、 官方统计数据和已有空间化人口分布数据构建了一种GDP空间化建模方法, 得到张掖市甘州区2000年的GDP空间分布. 首先, 分析基于乡镇单元的GDP与对应的夜间灯光辐射数据DN值之间的关系, 得到GDP模拟模型; 然后结合人口空间分布数据和三次产业的比例, 得到基于500 m×500 m栅格的GDP空间分布图. 各乡镇的GDP平均值为372×10⁴元, 标准差为34×10⁴元.     

基于多元自适应回归样条的青藏高原温泉区域的冻土分布制图

以探地雷达、电磁测深、钻探等技术方法获得野外数据及数字高程（DEM）遥感数据为基础,通过聚类分析和相关性分析对高程、坡度、坡向等因素对多年冻土分布的影响进行了定量化研究.利用非线性的多元自适应回归样条（MARS）方法建立了基于高程、太阳辐射的多年冻土分布模型,通过自身的交叉验证及对比年平均地温模型和逻辑回归模型的总体分...     

浅层气藏流体相控属性参数建模及应用

对钻井资料较少的莺歌海盆地某气田采用流体相控属性建模,利用叠前纵横波速度比反演预测储层含气性和储层测井综合解释成果,用随机模拟方法建立储层的流体相模型;用流体相模型进行间接相控,建立了用波阻抗约束的随机模拟孔隙度模型,解决了浅层气藏由于受含气效应影响导致模拟的气层孔隙度偏高而难以正确反映储层物性分布的问题。在此基础上求得连通因子平面分布,勾出孔隙度分隔带,解释了研究区压力和气体类型分区特征。     

南海北部深水西区中中新世混合沉积模式及控制因素

以新采集的地震资料为基础,对南海北部深水西区的混合沉积作了初步研究。混合沉积在地震剖面上表现为平行—亚平行,振幅强—中,频率中等及连续性中等的反射特征。混合沉积分布在研究区地震资料覆盖范围的西北角,发育规模较大,最大长度达44.7km,最大宽度33.2km,面积1084km2,最大厚度为138m,纵向上分布在中中新统梅山组。综合南海北部构造演化、地震勘探等研究成果,建立了混合沉积模式。该混合沉积分布于半深海沉积区,由其南东东方向的西沙—广乐台地提供碳酸盐岩碎屑(同时也提供部分硅质碎屑),由其西侧的中南半岛提供主要的硅质碎屑。在南海北部深水西区,控制混合沉积分布的主要因素为构造作用(包括海平面变化)、物源供给及水动力条件等三个方面,这三者之间又具有密切的内在联系。     

两花岗岩体接触带铀系核素迁移的初步模拟

随着世界各国大力发展核电,放射性废料的安全处置已成为当今研究热点和前沿学科。高放废物深地质处置的安全性主要取决于处置库内放射性核素向生物圈的迁移程度。在侵入岩中,放射性核素主要是通过地下水沿岩石孔隙从处置库向生物圈迁移的。为了理解放射性核素在花岗岩体接触带的迁移行为,本文根据两花岗岩体接触带中样品的铀系核素放射性活度比值（^234U/^238U,^230Th/^234U,^226Ra/^230Th,^230Th/^238U),利用 α-反冲（弹射）作用引起的放射性不平衡理论,计算了铀系核素子体^234U,^230Th,^226Ra在后期地下水的作用下在花岗岩体接触带及其裂隙内的迁出率、迁入率、并进行了质量平衡的计算。结果表明,经α-反冲作用进入流体的核素的迁出率要远大于因核素自然衰变的消亡率;裂隙充填物及裂隙能阻滞大量核素的迁移,其沉淀核素来自接触带花岗岩;花岗岩能强烈阻滞核素的迁移,可作为阻止放射性核素从核废料地下处置库向外迁移的有利天然屏障。     

Kinetics of fine wet grinding of zeolite in a steel ball mill in comparison to dry grinding

Batch wet grinding of zeolite was studied with emphasis on a kinetic study in a laboratory size steel ball mill of 200 mm diameter. The breakage parameters were determined by using the single sized feed fractions of − 850 + 600 µm, − 600 + 425 µm and − 425 + 300 µm for the zeolite samples. The S_i (specific rate of breakage) and B_i,j (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. The specific rates of breakage values for wet grinding in the first-order breakage region were higher than the dry values reported previously by a factor 1.7 at the same experimental conditions, but the primary breakage distribution (B_i,j) values were approximately the same. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The wet grinding of zeolite was subjected to slowing-down effect in the mill at 2 min of grinding, corresponding to an 80% passing size of about 400 µm. On the other hand, the slowing down effect in the dry grinding of zeolite was also seen at 4 min of grinding. In addition, effects of some operational parameters on dry and wet grinding of zeolite were determined by simulation using the breakage parameters obtained experimentally.