Upper bound limit analysis using finite elements and linear programming

This paper describes a technique for computing rigorous upper bounds on limit loads under conditions of plane strain. The method assumes a perfectly plastic soil model, which is either purely cohesive or cohesive-frictional, and employs finite elements in conjunction with the upper bound theorem of classical plasticity theory. The computational procedure uses three-noded triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the grid. The finite element formulation of the upper bound theorem leads to a classical linear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power and is expressed in terms of the velocities and plastic multiplier rates. The unknowns are subject to a set of linear constraints arising from the imposition of the flow rulé and velocity boundary conditions. It is shown that the upper bound optimization problem may be solved efficiently by applying an active set algorithm to the dual linear programming problem. Since the computed velocity field satisfies all the conditions of the upper bound theorem, the corresponding limit load is a strict upper bound on the true limit load. Other advantages include the ability to deal with complicated loading, complex geometry and a variety of boundary conditions. Several examples are given to illustrate the effectiveness of the procedure.     

A useful technique for metallurgical mass balances — Applications in grinding

The simple yet powerful steady state data analysis algorithm and software described herein have proven most useful in industrial grinding circuit studies at ANAMAX. Examples are drawn from that work. A process configuration can include up to 50 process streams connecting up to 30 pieces of equipment. “Steady state” plant data (e.g., solids, water, slurry flow rates, percent solids; sieve analyses) are collected where feasible, input, analyzed for consistency and, if the process is “overdefined”, adjusted in a least squares sense to achieve overall mass balance as well as mass balance within each size fraction. The combined sampling and analysis errors are assumed random with a weighting factor based upon whether the specific data point is believed to be “fair”, “good” or “excellent”. Extension of the technique to overall plant material balances is straightforward.     

An expression for the permeability of anisotropic granular media

There are many expressions proposed for the permeability of isotropic media based on flow channel and pore size distribution concepts, but there are no such expressions for anisotropic media. In this paper an expression for the permeability of an anisotropic medium is proposed, which has been verified in the laboratory. The mechanism behind fluid flow through soil was investigated using microscopic computer simulations to propose an expression for macroscopic permeability. The soil was assumed to be a spatially periodic porous medium, and the Navier-Stokes equation was solved using the FEM with appropriate boundary conditions for several different arrangements of the porous medium. The basic variables influencing flow through soil at the microscopic level were identified as specific surface area, void ratio, particle shape, material heterogeneity and the arrangement of particles in a porous medium. A sensitivity analysis was carried out to obtain an expression for the permeability in terms of the above variables. The corresponding macroscopic variables for the above microscopic variables are average specific surface area, average void ratio, anisotropy, tortuosity due to material heterogeneity, and the arrangement of particles respectively. An expression for the directional permeability is proposed in terms of these variables for the most common occurrence of particles in a porous medium. For the verification of the proposed equation, the permeability values of a fine-grained sand were measured at different void ratios and were compared with those predicted by the proposed equation. The results show that the predicted permeability values from the proposed equation are very close to the measured values.     

北京十三陵中元古代串岭沟期地质事的探索

宏观、微观和地球化学研究结果证明在北京十三陵中元古界长城系串沟组有地质事件层。宏观标志包括一系列地震滑塌、砂体液化、层内错断和角砾化构造等;微观标志包括火山晶屑,火山玻璃的假象,显微层内错位等。地球化学资料表明,Ｒｅ、０ｓ及其同位素和Ｉｒ含量异常,某些稀有元素含量的对比等等,都有可能说明地质事件引起了异常现象的出现,笔者认为串岭沟组的地质事件是由于燕山裂陷槽形成早期的火山活动及由其引发的地震事件产     

宏细观缺陷对岩体力学特性及边坡稳定影响研究

岩体是同时含有宏、细观缺陷的天然损伤地质体,如何更好地反映该两类缺陷对岩体力学特性的共同影响是亟待解决的一个重点和难点问题。采用FLAC3D中的弹脆性模型和Null模型分别描述完整岩石和上述两类缺陷的力学行为,用超细单元剖分计算模型的方法模拟岩体破坏,同时提出一个利用岩石孔隙率反映细观缺陷的新方法,研究细观缺陷即岩石孔隙率、裂隙倾角及长度等对裂隙岩体力学特性的影响。利用该方法研究了上述两类缺陷对岩质边坡临界滑面(CFS)及安全系数(FS)的影响。结果表明,宏观缺陷对岩体单轴压缩破坏模式、峰值强度和弹性模量起控制作用,同时控制岩质边坡的破坏模式和安全系数;尽管细观缺陷并不能改变宏观缺陷对岩体力学行为的控制作用,但其对这种控制作用将产生一定影响,宏细观缺陷以不同的作用机制对岩体力学特性产生影响。     

综合考虑宏微观复合损伤的节理岩体本构模型

针对目前节理岩体损伤本构模型中仅考虑节理等宏观缺陷造成的损伤,而没有考虑岩块中微裂纹等微观损伤的不足,提出了综合考虑宏微观损伤的节理岩体本构模型。其中微观损伤模型采用基于应变强度理论和岩石微元强度服从Weibull分布假定的统计损伤模型,把其应用于被节理切割而成的岩块。而宏观损伤模型主要基于连续介质力学原理,把节理对岩体性质的劣化作为损伤来考虑。在考虑节理传压及传剪系数的基础上,提出了综合考虑宏微观复合损伤的节理岩体本构模型。算例表明宏观节理的存在大大削弱了岩体的强度,降低了其刚度,增大了其柔性。所提出的模型能够较好地反映宏微观两类损伤对岩体应力-应变关系及强度的影响,较为合理。      

The optimisation of flotation networks

The generalised optimisation of a flotation network is studied by means of using variable connections (structural parameters) and variable enhancement factors which are used instead of a flotation model to describe the separation process. The enhancement factors are functions of variables affecting the flotation process. These functional relationship may be derived by means of using a flotation model. Bounds are placed on the enhancement factors by means of either using a flotation model or by inspection of existing pilot or commercial plant data. These bounds, together with external, system and mass balance constraints and an appropriate objective function, define the general optimisation problem for a flotation network.The optimisation problem above may be solved by non-linear programming methods, however, it is easily transformable into a Linear Programme which is easy to solve. The procedure has been applied to a flotation circuit comprising three banks of cells for which an optimal set of connections and enhancement factors has been computed for varying constraints.A simulation procedure based on a gamma flotation model has been applied to one of the optimal circuits so as to compute the flotation variables.     

Micro- and macro-behaviour of fluid flow through rock fractures: an experimental study

Microscopic and macroscopic behaviour of fluid flow through rough-walled rock fractures was experimentally investigated. Advanced microfluidic technology was introduced to examine the microscopic viscous and inertial effects of water flow through rock fractures in the vicinity of voids under different flow velocities, while the macroscopic behaviour of fracture flow was investigated by carrying out triaxial flow tests through fractured sandstone under confining stresses ranging from 0.5 to 3.0 MPa. The flow tests show that the microscopic inertial forces increase with the flow velocity with significant effects on the local flow pattern near the voids. With the increase in flow velocity, the deviation of the flow trajectories is reduced but small eddies appear inside the cavities. The results of the macroscopic flow tests show that the linear Darcy flow occurs for mated rock fractures due to small aperture, while a nonlinear deviation of the flow occurs at relatively high Reynolds numbers in non-mated rock fracture (Re?>?32). The microscopic experiments suggest that the pressure loss consumed by the eddies inside cavities could contribute to the nonlinear fluid flow behaviour through rock joints. It is found that such nonlinear flow behaviour is best matched with the quadratic-termed Forchheimer equation.     

Analysis of the gold recovery profile through a cyanidation plant

Leaching in the grinding circuit is currently practiced in plants that process gold ores with low content of cyanide consuming minerals. The high gold recovery observed in the grinding–classification section of the plant is commonly explained by the inherent high initial dissolution rate of gold observed in gold ore cyanidation, or by the intense agitation prevailing in grinding mills. For understanding this leaching behavior of gold ores, the grinding, classification and leaching sections of a gold processing plant are analyzed through reconciliation of operating data. It is found that gold circulation in the grinding circuit is quite different from the flow behavior of other species due to the strong gold separation effect in the hydrocyclones, which produces quite large residence time for gold-rich particles. The results presented in this study demonstrate that the residence time of these particles in the grinding circuit can be as long as in the leaching tanks and might be the dominant factor in explaining the high dissolution of gold in this section.     

钙质砂一维蠕变分形破碎特性宏微观试验研究

钙质砂是远洋地区港口、机场和民用建筑等构筑物的天然地基材料。通过钙质砂一维压缩蠕变试验和微观结构测试,发现了蠕变前后表面孔隙面积减小且呈分散分布的规律以及试验过程中试样瞬时变形、快速变形和衰减变形特征与粒径的高度相关性;利用基于分形理论改进的相对颗粒破碎率和质量分形维数描述了蠕变前后颗粒破碎程度,得到了分形维数和蠕变与时间的衰减形态曲线关系以及宏观质量分形维数和微观表面分形维数的线性关系,并在此基础上对单一粒径组钙质砂蠕变过程中的分形破碎行为进行了多尺度分析和宏微观跨尺度关联性研究,获得了蠕变过程中颗粒破碎发展以及微观孔隙变化规律,证明了钙质砂蠕变过程中的颗粒重组排列、破碎和研磨行为,揭示了钙质砂蠕变机制。     

Resource Model Updating For Compositional Geometallurgical Variables

In the field of mineral resources extraction, one main challenge is to meet production targets in terms of geometallurgical properties. These properties influence the processing of the ore and are often represented in resource modeling by coregionalized variables with a complex relationship between them. Valuable data are available about geometalurgical properties and their interaction with the beneficiation process given sensor technologies during production monitoring. The aim of this research is to update resource models as new observations become available. A popular method for updating is the ensemble Kalman filter. This method relies on Gaussian assumptions and uses a set of realizations of the simulated models to derive sample covariances that can propagate the uncertainty between real observations and simulated ones. Hence, the relationship among variables has a compositional nature, such that updating these models while keeping the compositional constraints is a practical requirement in order to improve the accuracy of the updated models. This paper presents an updating framework for compositional data based on ensemble Kalman filter which allows us to work with compositions that are transformed into a multivariate Gaussian space by log-ratio transformation and flow anamorphosis. This flow anamorphosis, transforms the distribution of the variables to joint normality while reasonably keeping the dependencies between components. Furthermore, the positiveness of those variables, after updating the simulated models, is satisfied. The method is implemented in a bauxite deposit, demonstrating the performance of the proposed approach.

     

A micromechanically derived anisotropic micropolar constitutive law for granular media: Elasticity

In the present work, it is attempted to derive a macroscopic constitutive law for the elastic deformation of granular materials, based on microscopic considerations. For the sake of simplicity, the solution is restricted to two dimensions, that is, a random assembly of infinitely extended cylinders. After examining pairwise contact interactions, the elastic energy rate of the assembly is retrieved in a discrete form. Introducing the probability density function of the contact orientations, the continuum form of the elastic energy density rate is evaluated as a function of generalized strains and curvatures, and their rates. The stresses and couple stresses result as dual variables to the generalized strain and curvature rates. Some properties of the resulting model are discussed, examples are presented and conclusions are drawn.Copyright © 2014 John Wiley & Sons, Ltd.     

Untersuchungen zur kreislaufmahlung in einer aufbereitung für komplexe sulfidische erze

Circuit grinding was investigated in the Rammelsberg ore dressing plant. From short-interval sampling it was possible to make a statement about the non-stationary and stationary state of grinding. The objective of these investigations was to establish the distribution curves of the quantitative flow, of the grain sizes and of the mineralogical components in the individual streams of the circuit grinding.     

Optimal lower bound of passive earth pressure using finite elements and non-linear programming

The present study pertains to the finding of the lower bound solution, formulating it as a non-linear programming problem using the generalized method developed by Lysmer with certain variations to incorporate the non-linear no-yield condition constraints directly in the analysis. The method considers the family of plane stress fields having the property that all stresses vary linearly within each triangular element of some mesh which covers the soil mass under study. For this type of stress field it is possible to express all equilibrium conditions as a set of linear constraints and the no-yield as a set of non-linear constraints. The boundary condition constraints may be of linear equality or inequality type. By expressing some of the design variables in terms of the remaining variables the linear equality constraints are implicity satisfied. Such a technique minimizes the complexity of the problem by eliminating the equality constraints and reduces the dimensionality of the problem, saving much, computational effort. The optimal lower bound is isolated by formulating it as a non-linear programming (NLP) problem subjected to both linear and non-linear inequality constraints. The sequential unconstrained minimization technique using the extended penalty function method as suggested by Kavlie has been used to isolate the optimal lower bound. The method has successfully been applied to the passive earth pressure and bearing capacity problem. Numerical results are obtained and compared with Lysmer's solution to show the effectiveness of the present approach.     

自适应BP算法及其在河道洪水预报上的应用

提出一种改进的BP算法,即自适应BP算法。该方法采用两种策略:一是在权重修改公式中加动量项;二是学习率随总误差的变化作自适应调整,亦即总误差增加时,学习率将减小,反之学习率增大。以上两种策略能有效的抑制网络陷于局部极小并缩短了学习时间。实例研究表明,该算法用于河道洪水的预报,能取得令人满意的结果。     

Simultaneous optimization of the performance of flotation circuits and their simplification using the jumping gene adaptations of genetic algorithm

The elitist non-dominated sorting genetic algorithm with the modified jumping gene operator (NSGA-II-mJG) is used to optimize the performance of froth flotation circuits. Four example optimization problems (Mehrotra and Kapur, 1974; Green, 1984; Dey et al., 1989) [Mehrotra, S.P., Kapur, P.C., 1974. Optimal–sub-optimal synthesis and design of flotation circuits. Sep. Sci. 9, 167–184; Green, J.C.A., 1984. The optimization of flotation networks. Int. J. Miner. Process. 13, 83–103; Dey, A.K., Kapur, P.C., Mehrotra, S.P., 1989. A search strategy for optimization of flotation circuits. Int. J. Miner. Process. 26, 73-93.] of varying complexity are solved using single-objective functions. In one example, the overall recovery of the concentrate stream is maximized for a desired grade of the concentrate and a fixed total cell volume. The interconnecting cell linkage parameters (fraction flow rates) and the mean cell residence times are the decision variables. In all these cases, the optimal solutions obtained using NSGA-II-mJG are superior to those obtained by earlier techniques (which converged to local optimal solutions). Thereafter, a few two-objective optimization problems are solved. In these, the performance of the circuit is optimized, and simultaneously, the number of connecting streams is minimized so as to give simple circuits. Pareto optimal sets of equally good (non-dominating) solutions are obtained. This is probably the first study involving the multi-objective optimization of flotation circuits with one aim being to simplify them.     

Microscopic characteristics of partially saturated dense sand and their link to macroscopic responses under triaxial compression conditions

Acta Geotechnica - This paper presents a set of triaxial compression tests on partially saturated dense sands to clarify the microscopic characteristics and their link to the macroscopic responses....     

计算流体地球化学研究的进展

成矿作用的化学机理可以通过实验和计算机模拟进行研究。随着计算机运算能力的不断增强 ,在地球化学中正在形成一门新兴学科———计算地球化学。其中热质输运模拟、化学质量迁移数值模拟和流体输运化学反应耦合动力学研究取得了显著进展。建立在Darcy定律和守恒方程基础上的多孔介质热质输运模拟通过流函数图、等温线图及速率矢量图等 ,从古水文学和流体地球化学方面高度动态研究成矿作用。根据化学和热力学原理进行的化学质量迁移数值模拟则通过矿物和流体中化学物种的热力学数据 ,预测多组分体系中发生的流体岩石相互作用 ,定量揭示经历了复杂化学反应进程的成矿作用的化学行为。将上述两方面结合的流体输运化学反应耦合动力学 ,可以从时间和空间上模拟真实成矿流体系统复杂的动力学行为 ,是计算流体地球化学的发展方向。     

Potential use of model predictive control for optimizing the column flotation process

A constrained model predictive control (MPC) strategy is proposed to deal with the problem of optimizing flotation column operation using secondary variables. Froth depth, collection zone gas hold-up and bias rate are selected as secondary variables to be controlled whereas tailing, wash-water and gas flow rate are used as manipulated variables. The control problem was formulated in order to minimize the tracking error of the gas hold-up and bias rate by maintaining gas flow rate, wash-water flow rate and bias rate within their operational limits. In particular, a strategy was conceived to optimize the column flotation process based on establishing an unreachable high set point for the gas hold-up (which is equivalent to maximizing the bubble surface area available for particle collection at a given flotation reagent dosage and thus recovery), while simultaneously satisfying operational constraints (such as ensuring a positive bias rate to prevent gangue entrainment and therefore concentrate grade deterioration). Several other operational constraints on wash-water, gas rate, gas hold-up and bias rate were considered, their use being justified from a processing point of view. Since this study deals with the hydrodynamic characteristics of flotation columns, a pilot flotation column working with a two-phase system is sufficient to demonstrate the advantages of using predictive control for this process optimization.