Numerical Simulation of Damage Accumulation and Seismic Energy Release During Brittle Rock Failure-Part II: Rib Pillar Collapse

This paper presents an application of the numerical model presented in the companion paper (Part I) in which, by using a newly developed numerical code, RFPA^2D (Rock Failure Process Analysis), a fundamental approach for the simulation of damage initiation and propagation causing seismic energy release during an unstable failure of brittle rock was presented. The influence of material and loading system properties including stiffness and strength on pillar failure and associated seismic patterns is studied. The results confirm that soft loading systems promote unstable failure or collapse of pillars. Weak pillar foundations and shear stresses on the pillar drastically reduce the pillar's load bearing capacity, and the related seismic activity and seismic energy release is significantly altered by these factors. As expected, for a high strength pillar, shear failure occurs in the floor and roof close to the edges of the pillar, whereas failure zones inside the pillar are found for low strength pillars. It is demonstrated that the proposed model properly simulates the pillar failure process.     

The Äspö Pillar Stability Experiment: Part II—Rock mass response to coupled excavation-induced and thermal-induced stresses

A 1-m-thick pillar was subject to coupled excavation- and thermal-induced stresses to induce brittle rock mass yielding. The yielding strength of the heterogeneous and fractured rock mass consisting of Äspö diorite was evaluated at eighteen discrete locations using data from the displacement, acoustic emission, and thermal monitoring systems. The average rock mass yielding strength was determined to be 0.59 of the uniaxial compressive strength.The onset of dilation in uniaxial laboratory tests, determined from strain gauge data, was found to occur at approximately 0.45 of the uniaxial compressive strength. It was shown that that the onset of acoustic emission events in situ also occurred when the tangential stress exceeded 0.43 of the uniaxial compressive strength. For sites with absence of in situ data it is recommended that this lower-bound value determined from laboratory data may be used for assessing the in situ rock mass yielding strength.Visual observation and displacement monitoring showed that extent of rock mass yielding is sensitive to small changes in the tangential stress magnitudes. It was determined using three-dimensional modelling that changes in the tangential stress magnitude of approximately 1 MPa was sufficient to cause yielding of the pillar to propagate in what appeared to be intact rock. Observations suggest that without this small stress change yielding of the rock mass would not occur. In other words, there appeared to be a well defined boundary, and if the stresses reached this boundary yielding was observed. However, if stresses were only slightly below this boundary yielding or time-dependant processes were not observed over the monitoring period used in the experiment.     

非充分采动采空区与煤岩柱(体)耦合作用机制及应用

 以镇城底矿为工程背景,通过理论分析、相似模拟、数值模拟和现场实测,研究了非充分采动采空区和煤岩柱(体)耦合作用机制。得出如下结论：(1) 不同的工作面布置产生不同的工作面构型、采空区形态和煤岩柱(体)形态,进而造成不同的耦合作用结果,采空区响应对实体煤岩柱(体)的应力及岩体破坏影响很大,数值模拟不可忽略采空区作用;(2) 推导出煤柱极限平衡区宽度表达式,分层开采单一分层时采高降低、大采高和错层位开采存在斜坡均导致煤柱极限平衡区宽度下降;(3) 垮落角对采空区和煤岩柱(体)耦合作用有重要影响,通过相似模拟确定了垮落角并用于数值模拟,得出非充分采动条件下工作面宽度L、最上部关键层跨度L1与垮落角θ之间的关系式;(4) 数值模拟显示非充分采动采空区承载增加,则支承压力相应降低,反之亦然,验证了非充分采动采空区和煤岩柱(体)的耦合作用,数值模拟若忽略采空区承载作用会造成支承压力偏大,应力集中区高度偏大,且位置降低,岩体破坏范围偏大;(5) 根据研究结果,现场将进风巷布置于采空区边缘下方,形成巷顶沿空巷道,该巷道处于整个回采系统应力最低区;而回风巷沿顶板布置,工作面两侧顺槽矿压问题均得到良好控制。     

Reliability of numerical modelling predictions

The accuracy of all predictions made using numerical modelling is strictly limited by the natural variability of geologic materials. In this paper, an attempt is made to quantify this accuracy through the straightforward application of probability and statistics. It is shown how the contributions from variability of the input parameters and also errors introduced by the modelling procedure can be combined into a single representative coefficient of variation C_p. This parameter is a characteristic that quantifies how well the entire modelling procedure is performing. It includes contributions from the variability of the pre-mining stress and rock mass strength, material heterogeneity and also errors introduced by the modelling procedure (e.g. elastic versus inelastic), and represent the uncertainty one has in predictive capability.In the paper, a lower limit for C_p of 30% is estimated for use with the conventional empirical approach (i.e. measurement of pre-mining in situ stress state, laboratory testing, and subsequent strength degradation to rock mass scale). Realistic values are most likely higher than this since some contributions have not been included and others are not known with any certainty. Various methods to reduce the magnitude of this parameter are then investigated. It is shown how this parameter can be evaluated by back-analysis of field observations. An example is detailed where a series of pillar failures are back analysed to calculate a site-specific value of 10%. This allows predictions to be made with greatly improved confidence and accuracy, and demonstrates why the back-analysis approach is so appealing. The paper presents a rational means for improving on existing empirical procedures for design of underground excavations.     

Modelling fracture propagation and failure in a rock pillar under mechanical and thermal loadings

The spPillar Stability Experiment (APSE) was conducted to study the rock mass response in a heated rock pillar between two large boreholes. This paper summarizes the back calculations of the APSE using a two-dimensional (2D) fracture propagation code FRACOD. To be able to model all the loading phases of the APSE, including the thermal loading, the code was improved in several ways. A sequential excavation function was developed to model promptly the stepwise changing loading geometry. Prior to the mod-elling, short-term compressive strength test models were set up aiming to reproduce the stress-strain behaviour observed for the sp diorite in laboratory. These models simulate both the axial and lateral strains of radial-controlled laboratory tests. The volumetric strain was calculated from the simulations and compared with the laboratory results. The pillar models include vertical and horizontal 2D models from where the stress in the pillar wall was investigated. The vertical model assesses the stability of the experimental rock volume and suggests the resultant stress below the tunnel floor in the pillar area. The horizontal model considers cross-sections of the pillar between the two large boreholes. The horizontal model is used to simulate the evolution of the stress in the rock mass during the excavation of the boreholes and during and the heating phase to give an estimation of the spalling strength. The modelling results suggest that the excavation-induced stresses will cause slight fracturing in the pillar walls, if the strength of the APSE pillar is set to about 123 MPa. Fracture propagation driven by thermal loading leads to minor spalling. The thermal evolution, elastic behaviour and brittle failure observed in the experiment are well reflected by the models.     

Coal pillar load calculation by pressure arch theory and near field extraction ratio

A method for calculating the load acting on a pillar of coal in a bord-and-pillar mine is described for the purpose of back analysing pillar failure or assessing the stability of a panel of pillars. The method is applicable to pillars of arbitrary plan shape and accounts for the spatial position of the pillar with respect to the other pillars, un-mined coal, and the network of roadways. Calculation of the extraction ratio within the pillar’s zone of influence defined by the depth dependent load transfer distance accounts for the pillar’s spatial position in the mine layout. An advantage of this approach is its suitability for computer programming for the automated analysis of hundreds of pillars. In this paper, pillars are analysed by the new method, and by tributary area theory, with the results from the new method comparing favourably to elastic three dimensional numerical analysis. Finally, an example of coal mine pillar failure from the literature that neither could be satisfactorily back-analysed by the traditional factor of safety approach nor by two-dimensional numerical modelling is considered. With the proposed, approach 42 of the 54 pillars in the observed failed pillar region are predicted to have a safety factor below the recommended value for long term stability and of these, three pillars are predicted to have an FoS of 1.18. With tributary area theory every pillar, including all those outside the failed pillar region, is predicted to have an FoS less than 1.2.     

Comparison between controlled laboratory experiments and discrete particle simulations of the mechanical behaviour of rock

Discrete particle modelling offers the possibility for performing grain-scale modelling of rock mechanical behaviour. An important step in turning this kind of numerical modelling into a more quantitative tool is to perform a calibration of the numerical model against controlled laboratory experiments. In this paper, a strategy for calibration is outlined and results from tests with artificial rock-like materials are presented. The rock-like materials consist of spherical grains (glass beads) while the numerical simulations were performed with PFC^3D (PFC: Particle Flow Code), which uses spherical particles as its basic elements.

Stress dependent P- and S-wave velocities in uncemented assemblies of glass beads were computed using a Hertzian contact law, and a satisfactory correspondence with laboratory data was obtained without any fitting parameters. The discrete particle model was able to reproduce the observed dependence of unconfined strength and Young's modulus on cement content. The initial experiments presented here demonstrate the potential of using discrete particle modelling as a numerical laboratory for studies of rock mechanical behaviour.     

Numerical simulation of coal pillar strength

The present paper describes an approach for estimation of strain-softening constitutive behaviour of coal-mass through calibration of a numerical model with field cases. A three-dimensional finite element model was used, in which the coal-mass was considered to be a Hoek–Brown strain-softening material. Dilation behaviour was considered to be a function of confinement and plastic shear strain. The numerical model was calibrated by satisfying the (1) various failed/stable cases of coal pillar of Indian coal mines and (2) post-failure behaviour of large-scale coal pillars determined by various researchers through conducting in-situ tests. The calibration of the model was done by taking various permutation and combination of strain-softening parameters. It has been concluded that the yielding of the pillars start almost at 2/3 of the peak strength. The statistical expressions for estimation of pillar strength for Indian coal mines and post-failure modulus have been developed by analyzing the results of the simulations. For Indian coal pillars having width-to-height ratio (w/h) less than five, the pillar strength was almost linearly dependent on w/h, and non-linearly dependent on uniaxial compressive strength of the coal specimen. The post-failure modulus of coal pillars was non-linearly dependent on w/h, and not significantly dependent on the uniaxial compressive strength.     

Ground subsidence observations and a modified influence function method for complete subsidence prediction

The results of surface subsidence investigations carried out in different coal fields in India are presented in this paper. Important differences are seen to exist between the subsidence norms given in the Subsidence Engineers Handbook, UK and those obtained in Indian conditions. Differences also exist for extraction below unfractured or uncaved rock and below pre-existing caved goaf(s). The subsidence is higher in the latter case and also in the slopes and strains. Consequently separate equations and guidelines have been given for these two conditions of mining.Since Indian coal mining is mostly under shallow to moderate cover, several cases of discontinuous subsidence have been observed. A demarcation limit for discontinuous subsidence is given, seeing that discontinuous subsidence causes severe surface damage.Since room and pillar mining is the principal underground method of extraction, panels of irregular shapes often occur making complete subsidence prediction difficult. The influence function method with a new function and additional functions for modelling subsidence asymmetry and the effect of extraction edges are given in this paper. The method for extraction below goaf(s) is also examined. Four cases are given for the comparison of observed and predicted subsidence contours and two cases for comparison of the slopes and strains.     

谦比希矿深部开采隔离矿柱稳定性分析

 隔离矿柱是地下开采矿山浅部转深部开采的衔接部分,其合理尺寸选择及其稳定性对深部开采安全极其重要。针对谦比希矿浅部转深部开采的实际情况,采用极限跨度法、经验公式法以及极限平衡分析方法,对原设计的隔离矿柱尺寸进行验算,提出合理的隔离矿柱厚度为21 m;根据隔离矿柱尺寸,修正原隔离矿柱留设方案,对所修正的方案应用FLAC3D对其稳定性进行分析计算。结果表明,当隔离矿柱下部回采高度达到33 m时,此隔离矿柱将完全失去其稳定性,而此时在深部开采采用无底柱分段崩落法回采时,其覆盖层厚度已达到28 m以上,这就不能对深部无底柱分段崩落法开采的采场内人员和设备安全造成威胁,满足浅部转深部开采平稳过渡安全生产要求,为谦比希矿隔离矿柱设计与施工提供依据和指导,同时也为相关矿山的浅部向深部开采平稳过渡提供一定的借鉴意义。     

Rock mass—mine workings interaction model for Polish copper mine conditions

Geological and mining conditions characteristic for the Polish Legnicko–Glogowski Okreg Miedziowy (LGOM) copper mines as well as various exploitation systems utilized in that area are presented. The historical background of mining systems development as well as their classification are also reviewed.Presently, due to difficult mining conditions, a new more universal analytical tool for mine workings geometry selection is required. Therefore, a very useful in design process multi-plate analogy based physical model of rock mass—mine workings interaction has been developed and presented in the paper. The model utilizes the analytical approximation of pillar compression including the effect of pillar critical and residual strength on roof strata deflection resulting in the definite bump hazard level.The research performed in the past which dealt with the effect of size and slenderness on pillar strength is reviewed. A new approach for pillar strength calculation and its utilizing in a general problem of overburden–mine workings interaction is proposed. The problem has been illustrated by numerical examples concerning a rock mass static and dynamic behavior in the area of one of the underground Polish copper mines. By solving the numerical model based on the finite element method formulated in three dimensions, the effect of extraction path on mine workings safety in a static load domain has been proved. The dynamic load transfer from mine workings to a shaft lining has also been determined.     

Structural modelling of support scaffold systems

In this paper, accurate three-dimensional advanced analysis models are developed to capture the behaviour of support scaffold systems, as observed in full-scale subassembly tests consisting of three-by-three bay scaffold systems with various combinations of lift height, number of lifts and jack extension. The paper proposes methods for modelling spigot joints, semi-rigid upright-to-beam connections and base plate eccentricities. Material nonlinearity is taken into account in the models based on the Ramberg-Osgood expression fitted to available experimental data. Actual initial geometric imperfections including member out-of-straightness and storey out-of-plumb are also incorporated in the models. The ultimate loads from the nonlinear analyses were calibrated against failure loads and load-deflection responses obtained from full-scale subassembly tests. The numerical results show very good agreement with tests, indicating that it is possible to accurately predict the behaviour and strength of complex support scaffold systems using material and geometric nonlinear analysis. The paper highlights the main difficulties in the numerical modelling of support scaffold systems, and describes mechanical models for implementing base plate, U-head and spigot joints in the analysis.     

深井特厚煤层综放工作面区段煤柱合理宽度研究

 留设合理宽度的区段煤柱是确保深井特厚煤层综放工作面顺利接续和安全回采的关键。以新巨龙矿井一采区区段煤柱宽度的确定为工程背景,首先采用微地震监测、应力动态监测和理论计算等方法确定深井特厚煤层综放工作面侧向支承压力分布特征,得出低应力区宽度约为20 m;其次,采用工程类比、数值模拟等方法确定深井特厚煤层综放工作面侧向煤体不完整区宽度约为3 m;最后,综合考虑资源回收、冲击地压防治、次生灾害控制和巷道支护等因素,确定深井特厚煤层综放工作面区段煤柱合理宽度为5.0～7.2 m。应用沿空巷道表面位移观测结果验证区段煤柱宽度的合理性。该研究结果对类似开采条件下的区段煤柱宽度确定具有参考意义。     

Uncertainty modelling in plate buckling

A brief account is given of the basic principles of uncertainty modelling with first-order second-moment methods. The main features of the behaviour of plates subjected to compressive loads are considered and various prediction methods are compared. The governing parameters of plate behaviour are used to construct probabilistic models for the laboratory test situation, for the analysis and for the design of plates. The uncertainty of the strength predictions is quantified in the different cases. Special attention is given to the implications of problem formulation and to the methodology of uncertainty modelling.     

OFDR光纤传感技术在十字岩柱暗挖法物理模型试验中的应用

 现阶段岩土工程模型试验围岩变形监测多采用点式传感器,仅能获得部分测点的应变,而光纤传感作为一种迅速发展的分布式监测技术,能很好地解决这一问题。对于岩土工程室内试验,现有光纤传感技术无法满足试验对空间分辨精度的高要求。对一种新型光纤传感技术光频域反射技术(OFDR)的测量原理和优点进行介绍,并将其应用于浅埋超大断面圆形隧道十字岩柱开挖模型试验中,对整个模型不同断面进行水平向应变连续监测。根据试验结果,结合有限元分析,表明OFDR能准确记录试验过程中模型内部的应变变化,揭示围岩在十字岩柱开挖方法下的变形规律,反映十字岩柱对围岩的支撑作用,为今后隧道工程开挖提供参考。另外通过算法将应变结果转化为位移结果,并与多点位移计的监测结果进行对比分析,偏差在10%以内。结果表明,该技术可应用于岩土工程试验中的变形监测。     

Exploitation of developed coal mine pillars by shortwall mining—a case example

The shortwall mining technique is similar to longwall mining but with shorter face lengths, ranging between 40 and 90 m, with the aim of controlling the caving nature of the overlying upper strata, the load on support and the overall operation of the supports applied at the face. Field observations and three-dimensional numerical modelling studies have been conducted for the longwall panel extraction of the Passang seam at Balrampur Mine of SECL to understand the caving behavior of the overlying upper strata. A large area of the Passang seam adjacent to the longwall panels has already been developed via bord and pillar workings. In this paper, numerical modelling studies have been conducted to assess the cavability of the overlying strata of the Passang seam in the mine over developed bord and pillar workings along with the support requirement at the face and in the advance gallery. The caving nature of the overlying rocks characterized by the main fall is predicted for varying face lengths, strata condition and depths of cover. The support resistance required at the face, the load in the advance gallery and its optimal obliquity were estimated for faster exploitation of the developed pillars in the Balrampur mine by shortwall mining.     

双矿柱体系变形破坏及承载特性的试验研究

 为揭示外部载荷作用下矿柱体系的力学响应特性,开展单矿柱及双矿柱试样组的压缩试验,监测并分析矿柱变形破坏过程中的荷载、变形及声发射信息。研究表明：单矿柱压缩过程中,随着裂纹演化,其承载能力逐渐弱化,当其不足以承担外部荷载时,试验机储存的弹性能将迅速释放并导致矿柱突然破坏;相同力学性能矿柱组压缩过程中,两矿柱基本能均匀承载,协调变形且几乎同时丧失承载能力;不同力学性能矿柱组压缩过程中,低强度矿柱先出现裂纹,承载能力缓慢下降,与此同时荷载向高强度矿柱转移,当高强度矿柱出现宏观滑移时,双矿柱试样组整体随之丧失承载能力;单个矿柱的承载能力、应力状态及外部荷载与能量环境均对双矿柱体系的整体稳定有着显著的影响;进行地下矿床开采时,在设计常规矿柱基础上预留高承载能力边界矿柱,将能有效预防矿柱群大规模突发性失稳灾害。     

The strength of hard-rock pillars

Observations of pillar failures in Canadian hard-rock mines indicate that the dominant mode of failure is progressive slabbing and spalling. Empirical formulas developed for the stability of hard-rock pillars suggest that the pillar strength is directly related to the pillar width-to-height ratio and that failure is seldom observed in pillars where the width-to-height ratio is greater than 2. Two-dimensional finite element analyses using conventional Hoek–Brown parameters for typical hard-rock pillars (Geological Strength Index of 40, 60 and 80) predicted rib-pillar failure envelopes that did not agree with the empirical pillar-failure envelopes. It is suggested that the conventional Hoek–Brown failure envelopes over predict the strength of hard-rock pillars because the failure process is fundamentally controlled by a cohesion-loss process in which the frictional strength component is not mobilized. Two-dimensional elastic analyses were carried out using the Hoek-Brown brittle parameters which only relies on the cohesive strength of the rock mass. The predicted pillar strength curves were generally found to be in agreement with the observed empirical failure envelopes.     

动力扰动下深部高应力矿柱力学响应研究

对深部矿柱在承受高静载应力时的动力扰动力学模型进行应力波传播力学响应分析，采用FLAC^3D有限差分程序对深部开采圆形矿柱进行高应力下动力扰动数值计算。研究高径比为4的圆形矿柱在承受不同静载作用时对动力扰动的力学响应特性，通过改变矿柱所受静载应力的大小，来考察承压不同的矿柱对外界动力扰动的响应情况；通过改变扰动应力波峰值的大小，来考察动力扰动强度的变化对承受高应力矿柱稳定性的影响。矿柱的数值分析结果表明：承受高应力的岩体，随着所受初始静载应力的增大，外界的动力扰动对其影响就越明显；承受高静载应力的矿柱，较小的动力扰动可能会使其发生塑性破坏而导致深部开采时的“多米诺骨牌”效应。     

云冈石窟立柱岩体长期强度研究

 基于分级加载单轴抗压蠕变试验,研究世界文化遗产云冈石窟9,10,12窟窟前立柱岩体的长期强度,并对其长期承载力学性能进行评价。研究结果表明：(1) 云冈石窟9,10,12窟窟前立柱岩体的岩性主要为砂岩,岩性单一,结构面不发育,属整体块状岩体结构类型,工程地质条件良好。(2) 立柱岩体中粗粒砂岩的长期强度低于中粒、中细粒砂岩的长期强度。其根本原因在于,中粗粒砂岩的胶结物类型是泥质胶结;其中含有微量的蒙脱石,在长期的风化过程中,与水作用后,易发生淋滤作用和溶蚀作用,次生裂隙相对较发育。(3) 高含水量状态下,中粗粒砂岩的长期强度为20.22 MPa,比其在低含水量状态下的长期强度降低44.31%。按云冈石窟立柱应力最大值出现在10窟西柱的上部(1.31 MPa)计,中粗粒砂岩立柱岩体的安全系数为15.4。因此,9,10,12窟窟前立柱岩体的长期承载力学性能良好。建议尽快修复和搭建窟檐,避免雨水对石窟的冲刷,同时还能调节窟内温度与湿度,减轻风化剥蚀。计算9,10,12窟窟前立柱最大可以承载的窟檐质量,供有关建筑设计和文物保护部门参考。这些研究结果和建议对于云冈石窟的保护具有一定的指导意义。