A New Analytical Solution for the Stress State in Inclined Backfilled Mine Stopes

There are several good reasons for using backfill in underground stopes, including a reduction of mine wastes on the surface and the improvement of ground stability. Backfilling is now commonly used in underground operations worldwide, so practical methods are required to assess the stress state in stopes, on the surrounding rock mass and on support structures. The majority of existing analytical solutions for the stresses have been developed for vertical openings. In practice, stopes often have inclined walls, and this affects the stress state. Recent numerical studies have shown how the stresses distribution in inclined backfilled stopes is influenced by stope geometry and backfill strength. It has also been shown that existing analytical solutions do not capture the essential tendencies regarding these influence factors. In this paper, a new solution is proposed for the vertical and horizontal stresses in backfilled stopes with inclined walls. This solution takes into account the variation of the stresses along the opening height and width, including the difference between the hanging wall and footwall, for various inclination angles of the walls. Key results are presented and validated using recently performed numerical simulations.     

Arching in Inclined and Vertical Mine Stopes

Hydraulic fills are one of the most common backfills used by mining industries to backfill the stopes (voids) created after extracting the ore. It is important to estimate the stresses within to the stope to design the drainage and barricades. Most of the existing analytical models for the estimation of stresses within the stopes consider flat rectangular elements to include the effects of arching, although a continuous compression catenary arch of principal stresses using intersections of shear lines is the reality in field situations. In this paper, a circular compression arch of principal stresses has therefore been used to derive a general expression for stress within the inclined stopes. The results have been compared with the existing analytical and numerical models for vertical stopes as well as inclined stopes. A methodology has been presented to determine the vertical stress variation along the width of stope at different depths. The variation of stresses along the width of stope is also presented graphically.     

Influence of an Inclined Rock Stratum on In-Situ Stress State in an Open-Pit Mine

In-situ stress plays a major role with respect to deformation and stability around underground or surficial excavations located at significant depth. Many sedimentary rock masses are more or less horizontally bedded. However, a possibility exists to have one or few inclined rock strata such as dikes in these horizontally bedded formations. It is important to know how the in situ stress changes from a purely horizontally bedded situation to a horizontally bedded rock mass that contains one or few inclined rock strata. This paper presents such an investigation using the largest open-pit metal mine in China—as a case study. This mine has a bedded rock mass with one steeply inclined rock stratum. For the bedded rock mass, the vertical stress was calculated based on the overburden above each lithology. The available in situ stress measurements conducted at the mine were used to estimate the ratios of horizontal to vertical stress. Numerical modeling was performed for the two scenarios: (a) the horizontally bedded system subjected to both the in situ and boundary stresses and (b) the mine lithological system that includes an inclined stiffer (denser) stratum intruding softer horizontally bedded system subjected to only boundary stresses to investigate the influence of an inclined rock stratum on the computed stress field. Thirty points were selected to compute the stresses on six planes of the inclined rock stratum. Due to the discontinuous nature of the geologic system at the interface between the stiffer inclined stratum and softer horizontally bedded system, one principal stress has become normal to the interface plane and the other two have become parallel to the interface plane with all three being perpendicular to each other. Presence of the stiffer inclined rock stratum has given rise to (a) increase in normal stresses up to about 120 % in the inclined rock stratum and (b) new shear stresses approximately in the range ?10.0 to 15.0 MPa. This means, because most of the rock masses are not purely horizontally bedded, estimation of in situ stress through measurements as well as application of in situ stress in numerical modeling associated with underground or surficial excavations located at significant depth is a difficult exercise. A better way to estimate the in situ stresses for complex geologic systems may be through application of appropriate boundary stresses to the geologic system in a numerical model.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Lateral Variation of the Vertical Stress in Underground Mine Stopes Filled with Granular Backfills

Marston’s theory and its modifications are widely used to predict the average vertical stress variation with depth within mine stopes. However, this does not model the lateral variation in vertical stress at a particular depth. In this study, a mathematical expression to simulate the vertical stress variation is developed using the experimental shear stress data of granular backfill. The developed model is validated against average vertical stress measured in the experiment. Therefore, the developed model has the advantage of determining both the average vertical stress and its distribution respectively, at a particular depth and a cross sectional area of the mine stope.     

GPR Signatures of Pipes and Walls with Emphasis on the Effect of Inclined Scanning Trajectory

This study investigates the effects of some commonly encountered constraints such as inclined scanning trajectory, multiple targets in the vicinity and material variation on GPR responses of pipes and walls. Further, the effects of wall inclination and broken walls are also explored in GPR signatures. Interpretation of such signatures in GPR data for archaeological and geotechnical surveys has been a challenge. A physical model was created to simulate buried pipes and walls under controlled conditions by maintaining density and moisture content of the soil medium. The presence of PVC pipes, plastered brick and stone walls buried in the dry sand have been investigated and major observations have been reported. The inclined scanning trajectory on buried pipes shows a change in curvature of hyperbola-like signatures. Inclined transects near the ends of pipes and walls manifest single limb GPR signatures. The responses of multiple pipes and walls show dependence on separation of targets and footprint of an antenna. One can discern stone walls from brick walls by recognizing the diffraction of waves by irregular stones in GPR responses. The signatures of walls differ from pipes with respect to the width of the apex and variation in the intensity in the limb.     

考虑格栅流变性的加筋挡土墙格栅等效应力计算

将土工格栅加筋土作为宏观均匀的各向异性材料 ,在考虑格栅与土之间变形协调、土为满足Mohr Coulomb破坏准则的理想弹塑性材料及格栅为粘弹性材料的条件下 ,假定格栅加筋土宏观应力由土和筋材两种微观应力所组成 ,通过引入格栅的流变模型 ,建立了筋土复合体中格栅的等效应力计算方法 ,并将结果与未考虑流变时的格栅应力法进行了对比分析。     

洛宁程家沟-沙沟银多金属矿中深斜孔钻探技术

洛宁程家沟-沙沟银多金属矿区矿床产状陡,矿体集中,钻探设计多为分支孔,钻孔中深、斜度大。如何要在保证效益的情况下确保钻孔质量成为关键技术。通过1550 m斜孔施工实例,介绍了矿区中深斜孔钻探工艺的选择及保证钻孔弯曲度的具体措施。     

中深孔直斜两用轻便钻塔的研制及应用

在调研国产立轴式岩心钻机的基础上,经过充分论证,提出了直、斜两用钻塔的设计方案。直、斜两用钻塔的成功研发,解决了国产立轴式岩心钻机不宜施工斜孔的问题,拓展了国产立轴式岩心钻机的使用空间。介绍了该钻塔的设计思路、结构设计及其生产试验效果。     

Analytical Solutions for Pore-Fluid Flow Focusing Within Inclined Elliptic Inclusions in Pore-Fluid-Saturated Porous Rocks: Solutions Derived in an Elliptical Coordinate System

Exact analytical solutions have been derived rigorously for the pore-fluid velocity, pore-fluid-flow focusing factor, stream function and excess pore-fluid pressure around and within a buried inclined elliptic inclusion in pore-fluid-saturated porous rocks. The geometric characteristics of the buried inclined elliptic inclusion are represented by the aspect ratio and dip angle of the inclusion, while the hydrodynamic characteristic is represented by the permeability ratio of the elliptic inclusion to its surrounding rock. Since an elliptic inclusion of any aspect ratio can be used to approximately represent geological faults and cracks, the present analytical solutions can be used to investigate the pore-fluid-flow patterns around buried faults and cracks within the crust of the Earth. Therefore, the present analytical solution not only provides a better understanding of the physics behind the pore-fluid-flow focusing problem around and within buried faults and cracks, but also provides a valuable benchmark solution for validating any numerical method in dealing with this kind of pore-fluid-flow focusing problem. The pore-fluid-flow focusing factor of a buried elliptic inclusion is demonstrated to be dependent on the aspect ratio, the permeability ratio and the dip angle.     

关于同位素地质测试数据的数据处理及结果表示

论述了同位素地质测试数据的数据处理及有效数字位数等问题,并根据现有分析方法及仪器的灵敏度、精密度和准确度等因素,对实施室报出同位素地质测试数据的有效位数进行了约定。意在促进我国同位素地质数据的规范化,从而更有利于不同实验室的测试数据之间的对比和应用,更充分地发挥同位素地质测试数据和作用。     

高含量铁水样中离子平衡及结果表示的探讨

讨论了在质量评估中,高含量铁水样的阴、阳离子平衡问题,认为应将测试原样瓶中离子态的铁含量计入离子平衡进行质量评估,而铁的含量采用加保护剂样品的检测结果报出。     

Analytical solution for the response of a flexible retaining structure with an elastic backfill

An extension of an existing analytical solution for the response of a flexible retaining wall subjected to seismic loading is presented. The solution is based on the assumption that the wall and the soil remain elastic and that there are no shear stresses at the wall–soil interface while the contact remains tied. In addition to the wall displacements due to bending, the wall can experience rigid‐body motions due to rotation and horizontal and vertical movements. The solution is verified by comparing its results with those of a finite element method. Results from the analytical solution together with those of the (FEM) are used to identify and quantify the relative importance of key parameters on the seismic response of a wall. The study shows that wall flexibility and horizontal rigid‐body motions of the wall and frequency content of the seismic input have a significant effect on the wall loads. The pressures behind a rigid wall decrease as the wall rotates about its base, whereas for a flexible wall, the soil pressures decrease as the friction between the backfill and the wall increases. The rigid‐body vertical movements of a wall have little impact on the dynamic pressures induced in the wall, except for a flexible wall where, when prevented, the dynamic loads may be reduced. Copyright © 2009 John Wiley & Sons, Ltd.     

Deep Cement Mixed Walls with Steel Inclusions for Excavation Support

Deep cement mixed (DCM) walls are widely used in supporting excavations in many parts of the world. In this paper, a case study of an excavation supported by a DCM wall with steel inclusions is analysed using a three-dimensional finite element model and based on the coupled theory of nonlinear porous media. The DCM wall is constructed with wide flange steel inclusions. The stress–strain behaviour of the DCM wall section is simulated using an extended version of the Mohr–Coulomb model, which considers the strain-softening behaviour of DCM columns beyond yield. The computed lateral deformations are compared with the field measurements to validate the numerical modelling procedure. Using the same case study, the internal stability of the wall against bending and shear failure modes is investigated. In addition, the lateral pressure distribution along the wall length is investigated because in practice design is carried out considering a uniform pressure distribution assuming rigid wall movements. A parametric study was carried out to investigate the viability of DCM walls in supporting excavations by varying the spacing between steel inclusions, wall thickness and initial lateral earth pressure. Based on the results of the parametric study, guidelines are proposed to select the most efficient geometric arrangement of steel inclusions within DCM walls.     

机械钻井法施工矿山竖井预制井壁漂浮法安放工艺技术

结合河北遵化铁矿Φ5.6 m、深286 m矿山竖井工程,介绍了钻井法施工矿山竖井采用漂浮法安放预制井壁的工艺原理,以及相邻两节井壁连接时的测量方法、工艺控制和井壁安放完成后井筒垂直度的测量技术等。     

Stability of an Embankment on Soft Consolidating Soil with Vertical Drains

Stability of an embankment constructed on soft consolidating soil improved with pre-fabricated vertical drains is investigated. The factor of safety of the embankment is obtained at various time intervals from the end of construction till the end of consolidation in order to check the embankment stability. Finite element method is used to obtain the effective stresses at required points in soil at various time intervals. Critical slip surface is obtained using two methods. In the first method, the critical slip surface is assumed as an arc of a circle selected among various probable slip circles with minimum factor of safety whereas, in the second method, a random walking type Monte Carlo technique is used to predict the critical slip surface. The effects of providing vertical drains on stability of an embankment is investigated by comparing the factor of safety of slope with vertical drains to the factor of safety of slope without vertical drains. It is concluded from the study that the installation of vertical drains enhances the factor of safety of the embankment from the end of construction till the end of consolidation.     

A Combined Analytical and Numerical Approach for the Evaluation of Radial Loads on the Lining of Vertical Shafts

The evaluation of the load acting on a shaft support is of fundamental importance for the correct dimensioning of the structure. The load acting on the support can appear somewhat complex. One approach to define the load on the lining may be to use the convergence-confinement method (CCM) normally used in the tunneling design. This process involves intersecting the convergence-confinement (CC) curve with the support reaction line. However, in order to be able to adopt this technique, it is necessary to know the radial displacement of the shaft wall at the point in which the support is to be installed. Using the equations of Vlachopoulos and Diederichs (Rock Mech Rock Eng 42:131–146, 2009) the reaction line of the support can be calculated. Numerical models developed with Flac 2D v.6.0 considering the Mohr–Coulomb criterion and an ideal elasto-plastic behavior simulating stepwise excavation and support installation were developed. The relation between applied internal stress and radial displacement of the wall shaft, obtained by the numerical simulation was compared with the CC curve obtained by the CCM and it showed a good match between the two methods. However, an iterative procedure has also been used to insert the reaction line in the CC graph. The result shows lower initial displacements (and therefore greater radial stress) when compared with the values obtained by numerical calculation with the axisymmetric model. It is therefore recommended the combined use of the CCM (analytical method) and the axisymmetric numerical model (step by step simulation) to obtain the values of the final load on the lining and the final plastic radius, necessary for the correct design of supporting structures on the shaft wall.     

非线性破坏准则下边坡稳定性极限分析斜条分法

考虑坡顶均布荷载和地震效应典型情况下,将边坡滑体进行任意斜条块划分,建立了具有倾斜界面的多块体破坏模型。基于极限分析上限法和非线性摩尔-库仑破坏准则,考虑岩体内正应力的不均匀性,引入多点切线法和强度折减法推导得出边坡临界破坏状态下的安全系数Fs通用计算公式。采用序列二次规划法对安全系数Fs的目标函数进行最优化计算,并与既有研究成果进行对比分析,其结果具有较好的一致性,相对误差不超过3.565%,表明了该方法的正确性。同时对比传统单点切线法计算结果,多点切线法较单点切线法获得的边坡安全系数值偏小,表明了多点切线斜条分法偏于保守,是安全的。参数分析表明坡顶均布荷载、地震效应和非线性参数均对边坡安全系数及潜在临界滑裂面有重要影响。多点切线法引入非线性摩尔-库仑破坏准则对边坡进行稳定性极限分析,为相关研究人员提供了一种新的思路与方法。