Improvements in Blast Fragmentation Models Using Digital Image Processing

One of the fundamental requirements for being able to optimise blasting is the ability to predict fragmentation. An accurate blast fragmentation model allows a mine to adjust the fragmentation size for different downstream processes (mill processing versus leach, for instance), and to make real time adjustments in blasting parameters to account for changes in rock mass characteristics (hardness, fracture density, fracture orientation, etc). A number of blast fragmentation models have been developed in the past 40 years such as the Kuz-Ram model [1]. Fragmentation models have a limited usefulness at the present time because: 1. The input parameters are not the most useful for the engineer to determine and data for these parameters are not available throughout the rock mass. 2. Even if the input parameters are known, the models still do not consistently predict the correct fragmentation. This is because the models capture some but not all of the important rock and blast phenomena. 3. The models do not allow for 'tuning' at a specific mine site. This paper describes studies that are being conducted to improve blast fragmentation models. The Split image processing software is used for these studies [2, 3].     

New Prediction Models for Mean Particle Size in Rock Blast Fragmentation

The paper refers the reader to a blast data base developed in a previous study. The data base consists of blast design parameters, explosive parameters, modulus of elasticity and in situ block size. A hierarchical cluster analysis was used to separate the blast data into two different groups of similarity based on the intact rock stiffness. The group memberships were confirmed by the discriminant analysis. A part of this blast data was used to train a single-hidden layer back propagation neural network model to predict mean particle size resulting from blast fragmentation for each of the obtained similarity groups. The mean particle size was considered to be a function of seven independent parameters. An extensive analysis was performed to estimate the optimum value for the number of units for the hidden layer for each of the obtained similarity groups. The blast data that were not used for training were used to validate the trained neural network models. For the same two similarity groups, multivariate regression models were also developed to predict mean particle size. Capability of the developed neural network models as well as multivariate regression models was determined by comparing predictions with measured mean particle size values and predictions based on one of the most applied fragmentation prediction models appearing in the blasting literature. Prediction capability of the trained neural network models as well as multivariate regression models was found to be strong and better than the existing most applied fragmentation prediction model. Diversity of the blasts data used is one of the most important aspects of the developed models.     

Modelling dynamic breakage in rock blocks with different elongation and flatness ratios upon impact

The two crucial shape factors (elongation ratio and flatness ratio) of brittle particles may influence the dynamic breakage of brittle particles upon impact. Hence, three-dimensional discrete element method simulations of brittle rock blocks with different shapes upon normal impact were performed. The simulated results indicate that the elongation ratio, that is, ratio of width to length and flatness ratio, that is, ratio of thickness to width can significantly affect the breakage of brittle rock blocks. Three fracture mechanisms, that is, fragmentation, horizontal tensile fracture and vertical tensile fracture, were revealed, which determine the dynamic breakage of rock blocks. The fragmentation results in numerous single-sphered fragments with velocities even larger than 2 times of the initial velocities. Fragmentation can provide a buffering effect at high impact velocities of larger than 4 m/s. With an increasing elongation ratio or flatness ratio, the phenomenon of fragmentation gradually disappears. The reflection of a compression stress wave results in horizontal tensile fracture. The expansion in the plane perpendicular to the impact velocity results in vertical tensile fracture.     

On size and boundary effects in scaled model blasts spatial problems

This paper addresses size and boundary effects on wave propagation, fracture pattern development and fragmentation in small scale laboratory-size specimens for model blasting. Small block type specimens are centre-line loaded by linear explosive charges and supersonically detonated. Using elastic wave propagation theory and fracture mechanics it is shown that the type of boundary conditions which prevail at the outer boundary of the cylinder control the extension of bore-hole cracking and fragmentation within the body of the cylinder. In the case of a composite block where a cylindrical core of different material is embedded, the level of fracturing and fragmentation is controlled by the separation of the interface which in turn depends on the relative dimensions of the core and the block. The most important parameter is the ratio between the length of the pulse (space-wise or time-wise) and the characteristic dimensions of the models, i.e. in this case the dimensions of the core and the mantel. Stress wave superposition effects occur in the corner sections of the mantel. Theoretical results are in good agreement with recent experimental findings.     

TBM滚刀破岩的广义粒子动力学数值模拟

提出了一种新的无网格数值模拟计算方法--广义粒子动力学法(GPD),并在GPD算法中引入了粒子损伤理论。运用GPD方法,建立了TBM单滚刀、双滚刀作用下的完整岩体破岩模型,成功模拟了TBM滚刀破岩过程。通过与数值模拟结果及室内试验结果的对比分析,验证了GPD法模拟TBM滚刀破岩过程的有效性。同时,运用GPD方法建立了含节理岩体及高围压条件下岩体的TBM滚刀破岩模型,研究了节理及围压条件下TBM滚动破岩过程。得到了节理对TBM滚刀破岩效率的影响,既可能是促进作用又可能是抑制作用,高围压对TBM滚刀破岩过程中裂纹的起裂及扩展和破岩深度有较大的影响。     

Fracture step structure: geometrical characterization and effects on fluid flow and breakthrough curve

Groundwater flow and solute transport through fractured rock is highly responsive to the hydraulic anisotropy and heterogeneity that are specific to every major fracture. A major fracture is modeled as the combination of some primal master fractures and several splay fractures that branch out from primal master fractures: step structures (or jog parts). Step structures are commonly observed along a major fracture on various scales. Master fractures were formed and developed by shear movement while some splay fractures were formed by extension normal to their wall. This difference in fracturing process may lead to a permeability difference between master fractures and splay fractures which seems to be one of the major factors controlling flow and solute transport through the fracture networks due to its hydraulic anisotropic and heterogeneous features. This study is composed of two major components: (1) identification and characterization of a step structure from borehole data; (2) evaluation of effect of some idealized step structures on breakthrough curve by numerical simulations. The fracture data of four 1000-m boreholes were used to make clear fracture patterns in the Tono area of Japan. Some major fractures were identified using stereographic projection technique. On the basis of these results, several idealized models of a major fracture having a step was constructed for the numerical study. The obtained results from numerical simulations clearly imply that geometry of step structure plays an important role in flow and transport through the fracture networks.     

Understanding size and boundary effectsin scaled model blasts - plane problems

This contribution addresses model blasting and focuses on size and boundary effects on wave propagation, fracture pattern development and fragmentation in small scale laboratory size specimen. Small cylindrical specimens are centre-line loaded by linear high velocity of detonation explosive charges and detonated.

Using elastic wave propagation theory and fracture mechanics it is shown that the type of boundary conditions which prevail at the outer boundary of the cylinder control the extension of bore-hole cracking and fragmentation within the body of the cylinder. In the case of a composite cylinder with dissimilar mantel and core materials, the level of fracturing and fragmentation is controlled by the delamination of the interface. This, in turn, depends on the relative diameters of the core and the mantel. The most important parameter though is the ratio between the length of the pulse (space-wise or time-wise) and the characteristic dimensions of the models, i.e. in this case the diameters of the core and the mantel.

The theoretical basis for a simplified two-dimensional plane treatment is developed. Simple or composite, thin, plate-like specimens are centrally loaded; whereas the core is always a circle, the mantel can be either a circle or a square.     

A Discrete Element Model for Predicting Shear Strength and Degradation of Rock Joint by Using Compressive and Tensile Test Data

A discrete element model is proposed to examine rock strength and failure. The model is implemented by UDEC, which is developed for this purpose. The material is represented as a collection of irregular-sized deformable particles interacting at their cohesive boundaries. The interface between two adjacent particles is viewed as a flexible contact whose constitutive law controls the material fracture and fragmentation properties. To reproduce rock anisotropy, an orthotropic cohesive law is developed for the contacts, which allows their shear and tensile behaviors to be different from each other. Using a combination of original closed-form expressions and statistical calibrations, a unique set of the contact microparameters are found based on the uniaxial/triaxial compression and Brazilian tension test data of a plaster. Applying the obtained microparameters, joint specimens, made of the same plaster, are simulated, where the comparison of the obtained results to laboratory data shows a reasonable agreement.     

A Method to Estimate In Situ Block Size Distribution

This paper presents a new technique for estimating the in situ block size distribution in a jointed rock mass. The technique is based on Monte Carlo simulations using more realistic fracture geometry as its input compared to other block size estimation methods described in the literature. This geometry represents fractures as either polygons or triangulated surfaces and therefore models persistence and truncation of fractures accurately. Persistence has been shown to be critically important for the accurate prediction of block size and shape. We show that for rock masses with relatively small discontinuities, the results of our predictions differ markedly from previous methods which over-predict fragmentation.     

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.     

On size and boundary effects in scaled model blasts—fractures and fragmentation patterns

This contribution is the third part of a paper addressing size and boundary effects on explosively induced wave propagation, fracturing and fracture pattern development in small scale laboratory specimens, which are frequently used for model blast tests. Small cylindrical and block type specimens fabricated from concrete, sandstone and amphibolite are centre-line loaded by linear explosive charges and supersonically detonated. Using shock wave theory, elastic wave propagation theory, and fracture mechanics it is shown that the type of boundary conditions prescribed at the outer boundary of the cylinder controls the extension of stem cracking and the development of the fragmentation pattern within the body of the cylinder and the cube specimens. In the case of a composite specimen, where a cylindrical core of different material is embedded in a cylinder or in a cube, the level of fracturing and fragmentation is controlled by the conditions and possible de-lamination of the interface which, in turn, depends on the relative dimensions of the core and the block. Using known results from the theory of wave interaction with free boundaries and interfaces it will be shown that the fracture strain and the notch sensitivity of the material expressed by imperfections play an important role. Equally important is the ratio between the length of the pulse (space-wise or time-wise) and the characteristic dimensions of the models. Axi-radial boundary cracks and spalling will be explained on the basis of earlier wave propagation studies associated with supersonic blasting. Theoretical results are in good agreement with numerical simulations and recent experimental findings.     

The Hydro-Mechanically Coupled Response of Rock Fractures

Summary. In a fractured rock mass, variations in stress and fluid pressure induced by engineering activities can significantly affect the hydrogeological properties. A significant change in fracture transmissivities can also be experienced in the far-field. The simulation of this kind of change requires a Hydro-Mechanical (HM) coupled model. The purpose of this paper is to show how such a model can be used to analyse the evolution of deformation and pressure in a fracture subjected to fluid injection. A 2D BEM-FEM code is used to solve the non-linear system of equations that describe the dependency of transmissivity on local fracture closure. The results of a sensitivity analysis of the essential fracture parameters allow one to gain insight into the importance of the HM models in the framework of the hydrogeology of fractured rock masses. Results obtained from a system of two impervious blocks and a saturated fracture are reported, in order to show the possibilities offered by this technique.     

爆炸作用下岩石破裂块度分布特点及其物理机理

就岩石在爆炸载作用下破坏块度分布的物理机理进行了分析。从分析可以看出,岩石破坏块度的对数正态分布与材料的多重破坏有关。在封闭爆炸情况下这种分布描述爆心附近岩石破坏块度的分布,此处材料处于静水压力状态,应变率很高,材料的破坏为多重破坏。而Rosin-Rammler分布主要描述离爆心较远处岩石破坏的块度分布,此处岩石的破坏主要是由环向拉力引起的径向裂纹所致,以单重破坏为主。     

Regional fracture network permeability using outcrop scale measurements

Estimating the hydraulic properties of fractured aquifers is challenging due to the complexity of structural discontinuities that can generally be measured at a small scale, either in core or in outcrop, but influence groundwater flow over a range of scales. This modeling study uses fracture scanline data obtained from surface bedrock exposures to derive estimates of permeability that can be used to represent the fractured rock matrix within regional scale flow models. The model is developed using PETREL, which traditionally benefits from high resolution data sets obtained during oil and gas exploration, including for example seismic data, and borehole logging data (both lithological and geophysical). The technique consists of interpreting scanline fracture data, and using these data to generate representative Discrete Fracture Network (DFN) models for each field set. The DFN models are then upscaled to provide an effective hydraulic conductivity tensor that represents the fractured rock matrix. For each field site, the upscaled hydraulic conductivities are compared with estimates derived from pumping tests to validate the model. A hydraulic conductivity field is generated for the study region that captures the spatial variability of fracture networks in pseudo-three dimensions from scanline data. Hydraulic conductivities estimated using this approach compare well with those estimated from pumping test data. The study results suggest that such an approach may be feasible for taking small scale fracture data and upscaling these to represent the aquifer matrix hydraulic properties needed for regional groundwater modeling.     

X-ray CT based numerical analysis of fracture flow for core samples under various confining pressures

The X-ray CT based numerical analysis of fracture flow for core samples, recently developed by the authors, was applied to two granite core samples having either a mated artificial or a mated natural fracture at confining pressures of 5 to 50 MPa. A third-generation medical X-ray CT scanner was used to image the samples within a core holder consisting of an aluminum liner and a carbon fiber overwrap. Fracture models (i.e., aperture distributions) were obtained by the CT images, the resolution of which was coarser than the apertures, and a single-phase flow simulation was performed using a local cubic law-based fracture flow model. Numerical results were evaluated by a fracture porosity measurement and a solution displacement experiment using NaCl and NaI aqueous solutions. These numerical results coincided only qualitatively with the experimental results, primarily due to image noise from the aluminum liner of the core holder. Nevertheless, the numerical results revealed flow paths within the fractures and their changes with confining pressure, whereas the experimental results did not provide such results. Different stress-dependencies in the flow paths were observed between the two samples despite the similar stress-dependency in fracture porosity and permeability. The changes in total area of the flow paths with confining pressure coincided qualitatively with changes in breakthrough points in the solution displacement experiment. Although the data is limited, the results of the present study suggest the importance of analyzing fluid flows within naturally fractured core samples under in situ conditions in order to better understand the fracture flow characteristics in a specific field. As demonstrated herein, X-ray CT-based numerical analysis is effective for addressing this concern. Using a multi-phase flow model, as well as a core holder constructed of an engineered plastic, should provide a useful, non-destructive, and non-contaminative X-ray CT-based fracture flow analysis for core samples under in situ conditions in future studies.     

开采扰动下考虑损伤破裂的深部煤体渗透率模型研究

为了研究深部煤体在开采扰动影响下的渗透率演化规律,以三向应力条件下的煤体渗透率模型为基础,从吸附解吸作用引起裂隙变形和损伤破裂造成煤基质弹性模量劣化的角度进行理论推导,引入内膨胀应变系数的概念,同时基于Drucker-Prager破坏准则的损伤本构关系建立了两种考虑煤体损伤破裂的渗透率演化模型——指数型和立方型,并且对常规三轴加载、开采扰动加卸载和改变气体压力下的瓦斯渗透试验结果进行了拟合分析。结果表明：所构建的两种模型可以较好地反映常规三轴加载和开采扰动加卸载下煤体渗透率的分区段变化特征,也可以描述有效围压恒定条件下煤体渗透率随气体压力升高而降低的规律。在开采扰动加卸载和改变气体压力的试验中,指数型的拟合效果略优于立方型。研究结果可为深部煤炭开采及瓦斯抽采的工作提供指导。     

New data on seismic wave attenuation in the lithosphere and upper mantle of the northeastern flank of the Baikal rift system

The investigation data on seismic wave attenuation in the lithosphere and upper mantle of the northeastern flank of the Baikal rift system obtained with a seismic coda envelope and sliding window are considered. Eleven local districts were described by one-dimensional attenuation models characterized by alternation of high and low attenuation layers, which are consistent with the results obtained previously by Yu.F. Kopnichev for the southwestern flank of the Baikal rift system [9]. The subcrust of the lithosphere contains a thin layer with high attenuation of seismic waves likely related to higher heterogeneity (fragmentation) and occurrence of fluids. The lithosphere basement depth varies from 100–120 km in the west within the Baikal folded area to 120–140 km in the east within the Siberian Platform. It is concluded that there are two asthenosphere layers. Based on specific features of the lithosphere and upper mantle structure, it can be assumed that they were subject to gradual modification involving fluidization processes and partial melting in the Late Cenozoic extension under the influence of distant tectogenesis sources.