A continuum mechanics‐based framework for optimizing boundary and finite element meshes associated with underground excavations‐framework

Many field problems, from stress analysis, heat transfer to contaminant transport, deal with disturbances in a continuum caused by a ‘source’ (defined by its discrete geometry) and a ‘region of interest’ (where a solution is sought). Depending on the location of ‘regions of interest’ in relation to the ‘sources’, the level of geometric detail necessary to represent the ‘sources’ in a model can vary considerably. A practical application of stress analysis in mining is the evaluation of the effects of continuous excavation on the states of stress around mine openings. Labour intensive model preparation and lengthy computation coupled with the interpretation of analysis results can have considerable impact on the successful operation of an underground mine, where stope failures can cost tens of millions of dollars and possibly lead to closure of the mine. A framework is proposed based on continuum mechanics principles to automatically optimize the level of geometric detail required for an analysis by simplifying the model geometry using expanded and modified algorithms that originated in computer graphics. This reduction in model size directly translates to savings in computational time. The results obtained from an optimized model have accuracy comparable to the uncertainty in input data (e.g. rock mass properties, geology, etc.). This first paper defines the optimization framework, while a companion paper investigates its efficiency and application to practical mining and excavation‐related problems. Copyright © 2005 John Wiley & Sons, Ltd.     

A framework for automatic modeling of underground excavations and optimizing three‐dimensional boundary and finite element meshes derived from them—framework

Many problems in mining and civil engineering require using numerical stress analysis methods to repeatedly solve large models. Widespread acceptance of tunneling methods, such as New Austrian Tunneling Method, which depend heavily on numerical stress analysis tools and the fact that the effects of excavation at the face of a tunnel are distinctively three–dimensional (3D), necessitates the use of 3D numerical analysis for these problems. Stress analysis of a practical mining problem can be very lengthy, and the processing time can be measured in days or weeks at times. A framework is developed to facilitate efficient modeling of underground excavations and to create an optimal 3D mesh by reducing the number of surface and volume elements while keeping the result of stress analysis accurate enough at the region of interest, where a solution is sought. Fewer surface and volume elements mean fewer degrees of freedom in the numerical model, which directly translates into savings in computational time and resources. The mesh refinement algorithm is driven by a set of criteria that are functions of distance and visibility of points from the region of interest, and the framework can be easily extended by adding new types of criteria. This paper defines the framework, whereas a second companion paper will investigate its efficiency, accuracy and application to a number of practical mining problems. Copyright © 2012 John Wiley & Sons, Ltd.     

‘Infinite domain’ elements in finite element analysis of underground excavations

The Finite Element Method is frequently used to analyse problems involving an ‘infinite domain’. A typical problem is an underground excavation in prestressed infinite medium in either tunnelling or mining operations or a foundation in an infinite half space. This paper examines the implications of mesh truncation on the accuracy of the accuracy of the solution. At the same time, a more economical and accurate method of analysing these problems using special ‘infinite domain’ Finite Elements is presented.     

地下隧洞开挖和支护的三维数值分析计算

根据地下工程锚固支护原理,采用隐含锚杆柱单元的三维有限元和混凝土喷锚支护的三维数值计算方法,对复杂的地下泄洪隧洞的开挖和支护进行了分析计算。该方法不仅能够有效地反映锚杆的长度、密度、倾角对洞室开挖的影响,而且能够较好地模拟钢拱架和锚杆的时间施加效应。由于隐含锚杆柱单元和喷层单元是隐含在岩体单元中的,所以锚杆和喷层单元不受岩体单元划分的影响,能够有效地模拟各种支护方案,加快计算速度,合理反映锚固支护所作用的位置和时间影响。通过对构皮滩泄洪洞施工开挖和锚固支护的模拟计算,论证了施工开挖的稳定性和锚杆、喷层、钢拱架的支护作用,提出了洞室结构的加固措施,为工程施工开挖提供了有效的设计依据。     

Computing derivative information of sequentially coupled subsurface models

A generic framework for the computation of derivative information required for gradient-based optimization using sequentially coupled subsurface simulation models is presented. The proposed approach allows for the computation of any derivative information with no modification of the mathematical framework. It only requires the forward model Jacobians and the objective function to be appropriately defined. The flexibility of the framework is demonstrated by its application in different reservoir management studies. The performance of the gradient computation strategy is demonstrated in a synthetic water-flooding model, where the forward model is constructed based on a sequentially coupled flow-transport system. The methodology is illustrated for a synthetic model, with different types of applications of data assimilation and life-cycle optimization. Results are compared with the classical fully coupled (FIM) forward simulation. Based on the presented numerical examples, it is demonstrated how, without any modifications of the basic framework, the solution of gradient-based optimization models can be obtained for any given set of coupled equations. The sequential derivative computation methods deliver similar results compared to FIM methods, while being computationally more efficient.     

电法测井的三维有限元模拟

研究了不同测量方式(井-地,地-井,井-井)下点源场井中电法的三维有限元数值模拟。考虑到深度方向上大范围的网格剖分和井眼的影响及井-井测量等因素,采用放射状三棱柱单元的网格剖分方式,以提高网格质量,减少剖分单元数;给出了三棱柱单元的坐标变换公式,进行精确的单元积分,减少了单元积分时间;结合非结构化网格技术,实现了复杂模型的模拟;开发出相应的程序实现了复杂条件下(如考虑井眼影响、井井测量、倾斜井情形、地形起伏等)电法测井的三维有限元模拟,数值算例验证了方法的可靠性及计算效率,并对不同情形下的异常响应进行了分析,为进一步的反演工作奠定了基础。     

基于自适应差分克里金的煤质指标估算

煤炭质量核心指标的估算有利于煤炭质量的管控,并为智能开采、分质开采提供科学依据。将克里金插值法引入到煤质指标估算模型的建立,利用差分进化算法求解其变差函数的模型参数;针对在差分进化过程中因"早熟"现象导致最优解被破坏的问题,在变异过程中设计可动态修正变异方向的缩放因子,提出修正变异方向的自适应差分进化算法(UMDE)来确定变差函数的模型参数,并用该方法对煤矿井下未开采区域的全水分进行克里金插值。通过交叉验证与对比实验,证明基于自适应差分克里金方法(UMDE-Kriging)构建的煤质指标估算模型较其他优化方案在估算精度上有显著提升。     

起伏地表下的复杂三维地质模型建立与重力异常计算

由于地质体和矿体的形态非常复杂，使用长方体网格离散建立正演模型时可能和真实情况有很大差别，因此计算结果可靠性差。本文提出一种基于约束Delaunay网格剖分的方法对地质体进行离散并进行重力建模，在模型边界等复杂区域使用网格自适应加密技术，将三维地质体离散为有限个四面体；并详细推导出针对四面体网格的重力正演公式，实现了基于约束Delaunay网格剖分技术的三维重力数值模拟；最后，针对一个合成数据模型，将计算解与解析解对比。结果表明，细化网格的模拟结果比粗糙网格更好，满足数值模拟的精度要求。将该方法应用到金川矿区实际地质体建模中，根据局部需要，建立各处网格密度不均匀的三维模型，并计算该模型的地表重力场，而后对比模拟数据与实测数据，结果表明Delaunay网格建模方法具有很强的适用性，能够模拟复杂的地质体重力异常。     

Mining Method Selection and Optimization for Hanging-Wall Ore-Body at Yanqianshan Iron Mine,China

In order to smooth ore production during the transition from open pit to underground mining at Yanqianshan Iron Mine, China, it is necessary to select an appropriate mining method to operate simultaneously open-pit mining and underground mining for inner-slope (hanging-wall) ore-body. Based on practical geologic setting of the hanging-wall ore-body, a comprehensive evaluation model for selecting the underground mining method to extract handing-wall ore-body was proposed, which is constituted by 3 sub-systems of safety factors, production factors and technical–economic factors. This evaluation model could be analyzed by the mutation progression method, which based on catastrophe theory and fuzzy mathematics. In addition, the FLAC^3D is employed to simulate the mining process of hanging-wall ore-body, and finally the optimal mining scheme is determined. By using mutation progression analysis and numerical modeling, some useful conclusions for hanging-wall ore-body mining have been drawn, which will be beneficial to mining safety during transitional period from open-pit to underground mining.     

A Symmetrical Streamline Stabilization scheme for high advective transport

An overview of numerical techniques and previous investigations related to the solution of advection‐dominated transport processes is presented. In addition a new Symmetrical Streamline Stabilization (S³) scheme is introduced. The basis of the technique is to treat the transport equation in two steps. In the first step the dispersion part is approximated by a standard Galerkin approach, while in the second step the advection is approximated by a least‐squares method. The two parts are reassembled, resulting in one system of equations. The resulting coefficients' matrix is symmetric. Only half of a sparse matrix needs to be stored. Robust iterative algorithms for symmetrical systems of equations such as the preconditioned conjugate gradient method (PCG) can be successfully used. The new method leads to an implicit introduction of an ‘artificial diffusion’ term. Solute transport with high Peclet and Courant numbers does not lead to oscillations due to an inherent upwind damping. The upwind effect acts only in flow direction. The efficiency of the new formulation in terms of accuracy and computation time is shown in comparison with the Galerkin approach for mesh parallel and mesh oblique high advective solute transport. Copyright © 2000 John Wiley & Sons, Ltd.     

浅埋隧道掌子面稳定性二维自适应上限有限元分析

为研究浅埋隧道掌子面稳定性及获取精细化的破坏模式,提出了一种上限有限元非结构化网格自适应加密策略。以单元耗散能权重指标作为网格自适应加密评判准则,该策略同时兼顾了单元尺度与塑性应变。应用高阶的6节点三角形单元并建立上限有限元线性规划模型,以多次反复计算和网格加密的方式实现了二维自适应上限有限元分析并编制了计算程序。利用条形基础地基极限承载力课题,从上限解精度和网格加密形态方面验证了该程序的有效性。针对浅埋隧道掌子面稳定性问题,展开多参数条件下的自适应上限有限元计算,分析了网格加密过程中单元总数与上限解精度的关系,列出不同隧道埋深和内摩擦角对应的隧道掌子面稳定性临界值的上限解,揭示出掌子面稳定性变化规律及精细化的破坏模式。     

Assessing precision and accuracy of atmospheric emission inventories

Assuming that state-of-the-art air quality models are accurate, then the precision and accuracy of their results directly depend on the precision and accuracy of their geographical, meteorological and emission input data. There are important applications, such as open pit mining, in which emission data are the main source of uncertainty. In such cases, historical air quality experimental data are typically available. The present work proposes a backward air quality simulation approach to assess the accuracy of emission inventories for these applications, with the goal of identifying sources that are over or underestimated. This approach consists of finding constants of the linear combination of the estimated emission that maximize R ² and make the slope equal to one in the linear correlation analysis when the results from the air quality model are compared to the experimental measurements of air quality. This methodology was applied to the case of the mining region in northern Colombia. As one of the largest open pit coal mining regions in the world, this region consists of seven independent mines with no relevant additional sources of emission. Use of the proposed methodology allowed quantification of the amount by which companies over or underestimated their emission, as well as quantification of uncertainties due to sources not considered in the model but that locally affect each monitoring station.     

Underground excavation shape optimization considering material nonlinearities

The shape of an underground opening is a major factor influencing the stability of the underground excavation. Obtaining an optimized shape is significant in civil and mining engineering applications for increasing stability and reducing costs. This paper presents an updated method for finding the optimal shape of an underground excavation using the latest bi-directional evolutionary structural optimization (BESO) techniques considering material nonlinearities. Recent development in the BESO applications to underground excavation is discussed through illustrated examples. Details are given of the BESO method used to finding the optimal shape based on the global stiffness. The methodology of the stiffness based optimization techniques is described with examples of applications to underground excavation. Applications to underground void structures, such as cavern and tunnel, as well as underground solid structure such mine pillar are demonstrated. It is concluded that stiffness based optimization techniques are applicable to underground excavations and practical shape of an excavation can be generated as a result of the BESO application.     

Induced seismicity in potash mining — a finite element study

Summary A number of earthquakes have been recorded in strata above underground potash mines in Saskatchewan, Canada. These seismic events are widely understood to be generated in the carbonate Dawson Bay Formation and, possibly, other superincumbent beds, and are believed to be directly related to mining operations. The mechanical response of these higher strata to mining is not observable andin situ instrumentation for measuring post-mining stresses and strains in the carbonate beds is sparse. Numerical models are believed to be the most effective option for investigating the response of these higher strata to potash mining. In this regard a realistic finite element model based on elasto-plastic material behaviour is developed in this paper. Special capabilities added to this general elasto-plastic model permit simulation of the post-failure behaviour of the rock mass. Possible modes of failure in the Dawson Bay are investigated and the brittle failure of intact limestone is affirmed as the possible mode of failure producing major seismicity. Slip along existing discontinuities in overlying strata is also demonstrated to be another possible mechanism, though with lower energy levels.     

地下水数值模拟过程中的误差分析

分析了从模型建立到输出过程中的误差来源,得出概念模型误差来源极大依靠资料的详实程度,三维的数学模型仿真程度最高,数值模型是将数学模型的精确解转化为近似解的过程,存在着不可避免的截断误差,模型构建过程中由于剖分尺度的不同而产生误差的程度不同,模型输入过程中定解条件和各项参数的选取较大影响了模型的输出精度。     

Superiority of neural networks for pillar stress prediction in bord and pillar method

Estimation of pillar stress is a crucial task in underground mining. This is used to determine pillar dimensions, room width, roof conditions, and general mine layout. There are several methods for estimating induced stresses due to underground excavations, i.e., empirical methods, numerical solutions, and currently artificial intelligence (AI). AI based techniques are gradually gaining popularity especially for problems involving uncertainty. In this paper, an attempt has been made to predict stresses developed in the pillars of bord and pillar mining using artificial neural network. A comparison has also been done to compare the obtained results with the boundary element method as well as measured field values. For this purpose, a multilayer perceptron neural network model was developed. A number of architectures with different hidden layers and neurons were tried to get the best solution, and the architecture 5-20-8-1 was found to be an optimum solution. Sensitivity analysis was also carried out to understand the influence of important input parameters on pillar stress concentration.     

Development of a framework of automated water quality parameter optimization and its application

This paper presents a methodology and framework for the development of an automated least-squares optimization tool for calibrating water quality parameters in QUAL2E. The method has been applied to estimate the optimal water quality parameters in simulation of stream water quality for the Anyang stream in Korea. The Monte Carlo analysis is used to assess the relative importance of model parameters for water quality constituents. It is found that μ_max and ρ are the most influential parameters for Chlorophyll-a modeling and K ₁ and K ₃ are critical parameters for variation of DO and BOD in the Anyang stream. A computer program for automated parameter calibration has been developed using a nonlinear GRG optimization algorithm. The application framework provides an intuitive and easy-to-use interface and allows visual evaluation of results. According to the simulation results, the automated approach is computationally efficient for evaluation of model parameters and converges on a best fit more rapidly and reliably than a trial and error method. The methodology proposed herein can be extended to other models to obtain the best possible parameter values.     

Block fracturing analysis using nodal‐based discontinuous deformation analysis with the double minimization procedure

As a hybrid method, the nodal‐based discontinuous deformation analysis (NDDA) greatly improves the stress accuracy within each DDA block by coupling a well‐defined finite element mesh inside the DDA block; at the same time, the NDDA inherits the unique block kinematics of the standard DDA method. Each finite element mesh line inside the DDA block is treated as a potential crack, which enables the transformation of the block material from continuum to discontinuum through the tensile and shear fracturing mechanism. This paper introduces a double minimization procedure into the NDDA method to further improve the accuracy of the stresses evaluated at the finite element mesh lines and thus to obtain a more realistic fracture model. Three numerical examples are employed to demonstrate the improved stress accuracy by the implemented double minimization procedure and the accuracy and capability of the enhanced NDDA method in capturing brittle fracturing process. Copyright © 2013 John Wiley & Sons, Ltd.     

Vertical drain consolidation analysis in one,two and three dimensions

A new method, the η or ‘eta’ method, for modeling consolidation by vertical and horizontal drains is presented. The approach is applicable in one, two and three dimensional as well as axisymmetric cases. Material and geometry properties are familiar from unit cell vertical drain analysis and are consistent across dimensions. An uncoupled finite element method (FEM) program is used to test the efficacy of the new approach. Because drains are not explicitly modeled in the finite element mesh, mesh complexity and computational time are greatly reduced. Unlike existing plane strain matching methods there is no special transformation of permeability or drain properties. The analyses conducted indicate that the η method provides an efficient and consistent means of modeling drains in any dimension.     

PARAMETER AND VARIANCE ESTIMATION IN GEOTECHNICAL BACKANALYSIS USING PRIOR INFORMATION

A probabilistic framework to perform inverse analysis of geotechnical problems is presented. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the error structure of field measurements and prior information. The difficulty of ascribing definite values to the uncertainties associated with the various types of observations is overcome by including the corresponding variances in the set of parameters to be identified. The inverse analysis results in a minimization problem that is solved by coupling the optimization technique to the finite element method. Two examples are presented to illustrate the performance of the method. The first one corresponds to a synthetic case simulating the excavation of a tunnel. Young's modulus, K₀ value and measurements variances are identified. The second case concerns the excavation of a large underground cavern in which again Young's modulus and K₀ are identified. It is shown that introduction of prior information permits the estimation of parameters more consistent with all available informations that include not only monitored displacements but also results from in situ tests carried out during the site investigation stage.