An analytical solution for the nonlinear distribution of effective and total stresses in vertical backfilled stopes

The increasing use of backfill in underground mines requires a proper evaluation of the stress state in and around the filled openings. This is, however, a relatively complex issue due, in part, to the large contrast in strength and stiffness between the backfill material and surrounding rock mass. In recent years, it has been shown that arching theory, based on limit equilibrium analysis, can be used to estimate the stress distribution in backfilled stopes. Nonetheless, many simplifications are involved in such analytical solutions and this affects the precision and significance of the calculated results. In this paper, a previously developed solution is enhanced by introducing the combined effects of non-uniform vertical stress distribution and positive pore water pressure. This leads to a more representative analytical solution, as demonstrated by successful comparisons with numerical simulations. The results indicate that the proposed solution can be used to estimate the effective and total stress state in submerged or partially submerged backfilled stopes with a simple geometry.     

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.     

A solution to estimate the total and effective stresses in backfilled stopes with an impervious base during the filling operation of cohesionless backfill

Mining backfill is commonly used in underground mines. A critical concern of this practice is to evaluate the pressures and total stresses in backfilled stopes to ensure a safe and economic design of barricades, constructed to retain the backfill. When a slurried backfill is placed in a mine stope, excess pore water pressure (PWP) can instantaneously generate and progressively dissipate. The dissipation of the excess PWP and consolidation lead to the development of effective stresses, which in turn lead to an arching effect in the backfilled stope. Until now, arching effect has been largely considered for stress estimation in dry or submerged backfill. The former corresponds to the final state at the end process of the drainage and consolidation of the backfill with a pervious while the latter with an impervious barricade. However, previous studies have shown that the most critical moment for the stability of barricades is during the stope filling. Therefore, the design of barricades requires a proper estimation of the pressure and total stresses during the filling operation. This in turn needs joint consideration of the arching effect and consolidation of the backfill. In this paper, a new solution is developed to evaluate the pressures and stresses in backfilled stopes during the filling operation of cohesionless backfill by considering the self-weight consolidation and arching effect. The proposed solution is validated by numerical modeling with Plaxis2D. It can thus be used to evaluate the pressures and stresses in backfilled stopes during the stope filling with an impervious barricade.     

A Three-Dimensional Analysis of the Total and Effective Stresses in Submerged Backfilled Stopes

The determination of the stress state in backfilled stopes is an important step for assessing the behaviour of mine openings and for designing barricades. Most previous analyses have considered only the 2D case (plane strain condition) and neglected the effect of pore water pressure. In this paper, a three-dimensional solution is proposed for totally or partly submerged backfill. The new solution gives the normal stresses along the vertical and horizontal axes, with the effect of a surface load on the backfill. The solution is validated using laboratory experimental results taken from the literature. The good agreement obtained between the proposed analytical solution and laboratory test results indicates that this new solution provides a realistic evaluation for both the total and effective stresses in vertical backfilled stopes.     

A three-dimensional analytical solution to the arching effect in inclined backfilled stopes

The stress state in backfilled mine stopes is an important issue to assess the behavior of the interaction between the backfill and the surroundings or barricades. Most previous arching analyses have considered only the vertical backfilled stopes in both 3D and 2D conditions, and the 3D stress distribution that results from the arching effect in inclined mine stopes remains unclear. In this paper, based on the limit equilibrium theory, a 3D stress solution that is applicable to vertical and inclined backfilled stopes is proposed to further examine the arching effect. The solution is validated against an available centrifuge model by changing the inclination of the model. The proposed analytical solution is consistent with the numerical simulations, and it is suggested that neglecting the wall inclination causes one to underestimate the arching phenomenon. In other words, the vertical stresses at the bottom of the stope can decrease when the wall inclination is considered. Hence, when the stope is assumed in plain strain conditions, both the vertical and horizontal stresses exerted on the barricades are overestimated.     

Analytical Expression for Vertical Stress within an Inclined Mine Stope with Non-parallel Walls

Arching is a phenomenon that occurs in many situations in geotechnical engineering. When underground mine stopes are backfilled, a significant fraction of the self-weight of the backfill is carried by the side walls. As a result, the vertical stress at the bottom of the stope is significantly less than its overburden pressure. Few analytical expressions published in the literature can be used to determine the vertical stresses of stope with parallel walls. The objective of this paper is to extend the analytical solution previously developed by the authors to long plane-strain stopes with non-parallel walls with both slopes leaning to the same side. Different combinations of wall inclination are examined using the new analytical expression developed. To validate the analysis, the proposed results are compared with numerical model results. The results show that the proposed analytical expression is capable of estimating the vertical stress within mine stopes when the inclination of the hangingwall to the horizontal (α) is less than that of footwall (β). An important behavioural trend for the stress distribution is observed, where with the same overburden pressure and base width, the stress magnitude experienced by fill material significantly varies depending on the wall inclination.     

Arching within hydraulic fill stopes

Arching is a well known phenomenon, which effects stress developments which were investigated and compared using analytical and numerical solutions. Marston’s (1930) solution was extended to a generalised 3-dimensional rectangular stope and later modified for square and circular stopes for comparison with FLAC results. Aubertin et al. (2003) & Li et al. (2003) models were improved significantly by placing the backfill within narrow stopes as lifts or layers in numerical modelling where the normal stress variation with depth were found to be more realistic. The FLAC results were compared with analytical solutions which were developed by previous researchers and modified by the authors to evaluate the arching effects in backfilled placed in narrow and circular stopes. It appeared from the investigation herein that δ = 0.67 ϕ and K = K _o condition gives a very close match with the numerical model solutions obtained from FLAC. Many laboratory tests were conducted to find out friction angles for four Australian mines, which were between 30 and 49 degrees.     

An Extension of Marston’s Solution for the Stresses in Backfilled Trenches with Inclined Walls

Infrastructure rehabilitation and development are very active fields around the world. Many of these activities involve the installation of conduits buried in trenches. The analysis and design of such conduits often rely on a solution developed by Marston and his coworkers who used the basic arching theory proposed by Janssen. This solution is theoretically only valid for vertical trenches, but it has been used for trenches with different wall inclinations, which sometimes leads to non-conservative stresses. In this paper, a more general solution for the stress state in backfilled trenches is developed based on the approach adopted by Marston and his coworkers. The effects of wall inclination and of a surcharge on top of the backfill are introduced in the analytical solution. Numerical modeling is performed and the results are used to adjust some components of the equations, leading to a more general solution. The good correlation between the vertical stress distributions given by the proposed solution and additional numerical simulations indicates that this new solution is representative of the stress state in backfilled trenches, and can thus be used for the design of infrastructure rehabilitation and development.     

Applications of numerical modelling in underground mining and construction

Numerical modelling has been used to investigate a variety of problems in underground mining and tunnelling: subsidence induced by longwall coal mining; stresses generated when an open stope is filled cemented backfill and the stability of exposures created during subsequent mining of adjacent stopes; the interaction of two tunnels; and the effects of under-mining a pre-existing tunnel and shaft. In each case, results from nonlinear stress analyses can be used to guide the design of excavations and rock support mechanisms.     

Geochemical constraints on underground disposal of uranium mill tailings

A three phase investigation has been conducted on groundwater quality impacts of the underground disposal of tailings from acid-leach milling of uranium ores. These phases included field collection and analysis of samples obtained during backfilling of mill tailings in empty underground mine stopes, collection of soil samples from mill tailings piles and previously backfilled stopes, and evaluation of thermodynamic constraints on possible geochemical transformations. Contaminants of principal concern include As, Mo, Se, U, V and Ra-226.The investigation has shown that short-term degradation of groundwater due to backfill disposal of the sand fraction of uranium tailings is negligible. Long-term effects, defined as those occurring after mining operations cease and the mine fills with water, are predicted to also be very small. This is attributed to immobilization of pollutants through chemical reduction and precipitation, as well as adsorption onto aquifer materials. This conclusion is substantiated, in part, by observation of high concentrations of most of the contaminants on the silt and clay fraction of the soil samples collected, in contrast to the concentrations found on the sand fraction.     

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.     

金川二矿区大体积充填体变形的三维数值模拟

充填法采矿是维护矿山稳定、控制地压变化以及限制围岩变形的最有效的手段方法,这种方法被大量地应用于金属矿山的开采工程当中。充填体作为矿体采出后的替代物,充入地下采空区后经过相变-固结-承压-提供反力-与围岩相互作用等阶段,与上覆岩层、下部矿体以及周围围岩形成了一个共同抵抗外部压力又相互作用的系统。这个系统在矿山开采状态下如何维护自身稳定以及相互作用所产生的变形破坏等都是需要进行研究的问题。金川镍矿二矿区已经进行了几十年的充填开采作业,逐渐形成了体积非常巨大的充填体,而进入深部开采工程后,上覆巨大充填体的受力稳定问题直接关系到矿山的安全生产。本文结合金川二矿区开采实际,在精确刻画充填体三维形态特征的基础上,采用数值模拟方法分析了大型充填矿山充填体的力学行为。模拟结果表明:充填体在开采时会出现整体受压变形,最大剪应力是导致充填体与围岩发生局部破坏的主要因素,对此根据充填体整体塑性屈服区域的分布和剪应力分布情况,确定了破坏失稳的危险区域。     

尾砂胶结充填体损伤模型及与岩体的匹配分析

分别对灰砂配比为1:4,1:8,1:10和1:12的4种尾砂胶结充填体进行了力学试验,得出了其应力-应变曲线。分析了不同配比充填体变形与破坏特征,用损伤力学建立了4种不同配比充填体损伤本构方程。经验算对比,所建立的损伤本构方程与试验结果吻合。尾砂胶结充填体损伤研究表明,不同配比的充填体表现出不同的损伤特性,充填体配比越低,达到峰值应力时的损伤值越小;峰值应力后,损伤增长越快,破坏过程越突然。根据岩体开挖释放能量与充填体蓄积应变能相近的原则,探讨了充填体与岩体的合理匹配。充填体与岩体的匹配系数与原岩应力、岩体弹性模量、充填体弹性模量及充填体损伤参数相关。为了便于工程实际应用,对充填体力学试验结果进行了回归分析,得出了充填体强度设计公式,并研究了深部矿床不同开采深度所要求的充填体强度。     

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.     

三峡库区箭穿洞危岩体变形破坏模式与防治效果分析

本文以三峡库区箭穿洞危岩体为例,对涉水厚层危岩体的变形破坏模式和防护措施进行了研究。根据现场调查和长期监测数据可知,干湿循环作用下基座岩体的劣化是加速箭穿洞危岩体变形破坏的主导因素,并判定其破坏模式为基座滑移式崩塌。在此基础上,将危岩体的防护治理定为两部分,分别是基座软弱岩体的补强加固,以及中上部危岩体的锚索加固。通过数值模拟对防护前后危岩体的位移场以及应力场进行了分析,结果表明危岩体上部的锚索加固能够有效控制岩体的变形,基座补强能够有效控制危岩体的最大剪应力,综合防护可以显著提高箭穿洞危岩体的稳定性。该防护措施的理念及方法,可以为库区涉水危岩体的治理提供重要的参考价值。     

Design and Application of Underground Mine Paste Backfill Technology

This paper reviews the design and application of paste backfill in underground hard rock mines used as ground support for pillars and walls, to help prevent caving and roof falls, and to enhance pillar recovery for improved productivity. Arching after stope filling reduces vertical stress and increases horizontal stress distribution within the fill mass. It is therefore important to determine horizontal stress on stope sidewalls using various predictive models in the design of paste backfill. Required uniaxial compressive strength (UCS) for paste backfill depends on the intended function, such as vertical roof support, development opening within the backfill, pillar recovery, ground or pillar support, and working platform. UCS design models for these functions are given. Laboratory and backfill plant scale designs for paste backfill mix design and optimization are presented, with emphasis on initial tailings density control to prevent under-proportioning of binder content. Once prepared, paste backfill is transported (or pumped) and placed underground by pipeline reticulation. The governing elements of paste backfill transport are rheological factors such as shear yield stress, viscosity, and slump height (consistency). Different models (analytical, semi-empirical, and empirical) are given to predict the rheological factors of paste backfill (shear yield stress and viscosity). Following backfill placement underground, self-weight consolidation settlement, internal pressure build-up, the arching effect, shrinkage, stope volume, and wall convergence against backfill affect mechanical integrity. An erratum to this article can be found at     

台阶式加筋土挡墙的原型试验研究

对一座台阶式钢筋混凝土串联拉筋加筋土挡墙的筋带应力、土侧向压力、土竖向压力及挡墙变形进行了实测和分析, 所得结论可供设计类似支挡结构时参考。     

TBM隧道回填层-管片受力特征模型试验研究

回填层作为围岩和管片之间的连接部分,起到稳定衬砌、传递荷载、吸收变形等作用。护盾式TBM隧道施工过程中,回填层存在未注浆松散、注浆固结两个主要状态。回填层状态不同,回填层作用及管片受力特点也不同。研究采用相似模型试验分析不同状态下的回填层作用机制,通过研究得到了以下结论：回填层未注浆松散状态下,由于碎石的径向压缩与环向移动,围岩传递到管片上的荷载量值降低且分布较为均匀,此时回填层作为“可压缩层”,具有让压和均匀荷载的作用,能明显降低管片的受力和变形;回填层注浆固结后,回填层虽然能够承担少量的荷载与变形,但承载能力有限,主要作为围岩与管片之间的“传递层”,传递荷载与变形;对于挤压性围岩护盾式TBM隧道施工可适当应用回填层未注浆时的“可压缩性”,减小施工过程中管片受力与变形;对于浅埋及地铁隧道则应尽早注浆,使衬砌与围岩形成稳定的受力体系;回填层弹性模量的增加可提高回填层-管片组合体系支护刚度,但增加效果不明显。     

多因素组合影响下向进路充填顶板稳定性计算

下向分层进路充填采矿法中,进路充填顶板的稳定对回采过程安全性至关重要,而分层充填体叠加载荷计算一直是顶板稳定性分析的难点。在充分考虑采动岩体荷载、矿体倾角、相邻分层间回采进路的交错布置、充填体与围岩的接触等工程实际后,推导了进路顶板平衡微分方程,求解得到进路顶板静荷载的理论值。结合回采工艺建立了“多跨梁”力学模型,并得到了回采进路顶板拉应力的理论计算公式,分析得到影响进路顶板稳定性的4个重要理论因素：顶板上部载荷σ v、回采进路跨度l、1:4充填体的厚度h、充填体自身抗拉强度[σt]。为充分考虑进路顶板静载荷和回采爆破动载荷影响,利用FLAC^3D对多因素影响下的顶板稳定性进行了数值模拟正交计算。根据模拟结果,分析了各因素对顶板拉应力的影响规律,利用多元非线性回归的方法建立了多因素组合影响下顶板稳定性评价模型。该模型应用到某铜矿试验采场的实际生产,具有较好的指导作用。