Limitations and potential design risks when applying empirically derived coal pillar strength equations to real-life mine stability problems

The method of determining coal pillar strength equations from databases of stable and failed case histories is more than 50 years old and has been applied in different countries by different researchers in a range of mining situations. While common wisdom sensibly limits the use of the resultant pillar strength equations and methods to design scenarios that are consistent with the founding database, there are a number of examples where failures have occurred as a direct result of applying empirical design methods to coal pillar design problems that are inconsistent with the founding database. This paper explores the reasons why empirically derived coal pillar strength equations tend to be problem-specific and should be considered as providing no more than a pillar strength ‘‘index." These include the non-consideration of overburden horizontal stress within the mine stability problem, an inadequate definition of supercritical overburden behavior as it applies to standing coal pillars, and the non-consideration of overburden displacement and coal pillar strain limits. All of which combine to potentially complicate and confuse the back-analysis of coal pillar strength from failed cases. A modified coal pillar design representation and model are presented based on coal pillars acting to reinforce a horizontally stressed overburden, rather than suspend an otherwise unstable self-loaded overburden or section, the latter having been at the core of historical empirical studies into coal pillar strength and stability.     

应用有限单元法研究条带煤柱的稳定性

本文应用有限单元法分析了不同宽高比、不同顶底极岩性条带煤柱中的应力分布，并根据计算结果给出了条带煤柱强度计算公式，以及煤柱保持长期稳定的条件。     

基于能量理论的深埋矿山矿柱尺寸设计方法

随着资源开发步入到深部开采阶段,深埋矿山开采过程中的动力灾害问题日益突出,传统静力稳定分析方法在应对这些问题时表现出一定的局限性,研究适用于深部矿山的矿柱尺寸设计方法意义重大。本文基于面积承载理论和金属矿山矿柱强度估算方法,以一种动态的视角从功能转换角度重点探讨了瞬间回采方式下的矿柱应变能积聚和转化特征,对地下矿体阶段性分层回采这一过程进行简化,提出了一种基于可释放能理论的适应不同分层钻爆开挖方式下的矿柱尺寸参数设计方法,通过依托某工程实例进行了能量法的应用并与传统强度理论方法进行了比较分析,据此建议了5组矿柱尺寸参数方案,进一步利用有限差分软件（FLAC3D）对其优化从而最终确定了合理矿柱尺寸设计值。研究成果表明：矿柱体受动态开挖作用将产生一定程度的动力响应,诱发产生的动应力和动态变形一度可达静力分析时的两倍,同时也会伴随大量能量的积聚;与传统强度计算理论相比,应用能量法可有效地避免快速回采情况下矿柱动力失稳的可能,设计得到的矿柱尺寸参数更偏保守,随着开挖分层数的增多,能量校核法逐渐趋于和强度静力法等价。经数值模拟优化比选,最终建议该工程矿体分三层回采,矿柱合理宽度22m,高度70m,基本上可以满足回采过程中安全稳定和经济效益的需求,与工程实际契合较好。     

基于蒙特卡罗法的预应力锚索支护深基坑的可靠度分析

目的对预应力锚索支护深基坑的可靠性进行分析,建立其稳定可靠度计算公式.方法介绍预应力锚索支护深基坑设计时的稳定性设计计算,以土的密度γ和抗剪强度指标黏聚力C、内摩擦角为基本随机变量,建立预应力锚索支护深基坑的稳定可靠度计算公式,采用蒙特卡罗法进行计算,应用Matlab语言编制了计算程序“RAPADES”.结果建立了预应力锚索支护深基坑的稳定可靠性计算公式,结合实例计算预应力锚索支护深基坑的可靠指标,计算得可靠指标为4.32,满足规范安全要求.结论预应力锚索支护深基坑稳定可靠度计算公式合理、可靠,可为广大工程技术人员提供计算依据.     

基于非概率模型的星载天线展开机构可靠性分析

对某周边桁架式大型星载天线的展开运动机理进行了研究，建立了展开机构的力学分析和非概率运动可靠性的分析模型，综合考虑尺寸误差和太空环境因素的影响，将运动功能函数视为区间变量函数，利用优化算法推导出非概率可靠性计算公式，对机构在整个展开过程中的运动可靠性进行预测，并和将运动功能函数中的变量视为正态分布的概率模型下的可靠度相比较，概率可靠性指标约为非概率可靠性指标的3倍，两者的变化趋势相同，而且与试验过程比较吻合。     

隧道衬砌抗弯承载能力概率劣化模型

提出同时考虑时间效应与参数不确定性的隧道衬砌可靠度分析框架. 考虑衬砌受环境侵蚀引起的钢筋截面面积减少以及钢筋-混凝土黏结力下降,得到其抗弯承载能力时变模型. 考虑模型中参数不确定性,建立时变概率模型. 采用蒙特卡洛模拟（MCS）方法对理论模型的准确性以及计算效率进行验证. 分析模拟结果,对抗弯承载能力的分布进行讨论. 通过有限元分析,使用反转应力荷载释放法得到可靠度分析的荷载模型. 采用当量正态化（JC）法,构建隧道衬砌抗弯承载能力劣化可靠度分析框架. 通过算例对地下水氯离子侵蚀下衬砌抗弯承载能力的时变概率特征进行研究. 结果表明,随时间增长抗弯承载力的均值和标准差均减小;当初始计算变量同时存在正态变量与对数正态变量时,抗弯承载力计算结果更服从对数正态分布;衬砌负弯矩区域可靠度远高于正弯矩区域.     

随机参数压电桁架结构的稳定可靠性分析

在有限元分析方法基础上,基于稳定特征方程对随机参数压电桁架结构进行稳定可靠性分析.综合考虑电荷载和机械荷载联合作用的机电耦合效应,以杆元的物理参数和外荷载系数为随机变量,给出了压电桁架结构失稳的安全余量的表达形式和临界荷载系数对变量求导的方法.在此基础引入随机有限元法,对压电桁架结构进行结构稳定可靠性分析.最后由算例分析了机电耦合效应压对稳定可靠性指标的影响,分析表明考虑压电材料的机电耦合效应和利用外加电压可以提高结构系统的可靠性指标.该方法对含压电材料桁架在工程实际的稳定可靠性分析提供了一个较好的方法.     

Numerical investigation into the effect of backfilling on coal pillar strength in highwall mining

This paper attempts to quantify the effect of backfilling on pillar strength in highwall mining using numerical modelling. Calibration against the new empirical strength formula for highwall mining was conducted to obtain the material parameters used in the numerical modelling. With the obtained coal strength parameters, three sets of backfill properties were investigated. The results reveal that the behavior of pillars varies with the type and amount of backfill as well as the pillar width to mining height ratio(w/h). In case of cohesive backfill, generally 75% backfill shows a significant increase in peak strength, and the increase in peak strength is more pronounced for the pillars having lower w/h ratios. In case of noncohesive backfill, the changes in both the peak and residual strengths with up to 92% backfill are negligible while the residual strength constantly increases after reaching the peak strength only when 100%backfill is placed. Based on the modelling results, different backfilling strategies should be considered on a case by case basis depending on the type of backfill available and desired pillar dimension.     

Reliability analysis of earth slopes using hybrid chaotic particle swarm optimization

A numerical procedure for reliability analysis of earth slope based on advanced first-order second-moment method is presented, while soil properties and pore water pressure may be considered as random variables. The factor of safety and performance function is formulated utilizing a new approach of the Morgenstern and Price method. To evaluate the minimum reliability index defined by Hasofer and Lind and corresponding critical probabilistic slip surface, a hybrid algorithm combining chaotic particle swarm optimization and harmony search algorithm called CPSOHS is presented. The comparison of the results of the presented method, standard particle swarm optimization, and selected other methods employed in previous studies demonstrates the superior successful functioning of the new method by evaluating lower values of reliability index and factor of safety. Moreover, the presented procedure is applied for sensitivity analysis and the obtained results show the influence of soil strength parameters and probability distribution types of random variables on the reliability index of slopes.     

水电工程岩质高边坡安全度标准研究

综述了我国水电工程高边坡稳定性分析及设计研究现状,分析讨论了边坡安全度和目前边坡可靠性评价中常用的几种方法,参照国内外工程结构统一设计标准,结合国内外边坡和坝工方面的研究,通过工程类比法给出水电工程高边坡在正常荷载情况下安全度标准建议值,重要边坡β＝３．９０,普通边坡β＝３．１０,次要边坡β＝２．３３。     

Layout and support technology of entry for pillar face

In order to improve the recovery rate of coal, some mines have begun to recover the residual protective pillars in the form of short wall faces. However, it is difficult to control stability of the haulage entry and the ventilating entry under the mining influences of the pillar face and the two side faces. Thus the 4311 face, which was designed to recover the 57 m wide residual protective pillar in Guojiashan Coal Mine,was taken as engineering background. Distribution law of stress and plastic zone in the residual protective pillar was analyzed using the numerical simulation. Then the gob-side entry driving technology was proposed to layout the entries for the pillar face. Based on the analysis of stress distribution and deformation characteristics of surrounding rocks in gob-side entry driving with different width of narrow pillars, the width of the narrow pillar of the entries in the 4311 face was decided to be 4 m. In order to control stability of the gob-side entry driving, the mechanical model of the main roof was established and deformation characteristic of surrounding rock was analyzed. Then the bolt support technology with high strength and high pre-tightening force was proposed for entry support. Especially, the hydraulic expansion bolts were used to support the narrow pillar rib. The engineering results show that the width of the narrow pillar is reasonable and the entry support technology is effective. The research achievement can provide some references to pillar recovery for other coal mines.     

具有多随机因素结构系统的优化设计

提出了具有多随机因素的系统，即考虑结构元件面积，长度，弹性模量，结构强度和外载荷均为随机变量情况下，进行优化设计的方法，在这种结构中，极限状态方程是一个含有多随机变量的非线性函数，而且有些随机变量很难用显式表达，故采用随机有限元法进行可靠性分析，给出了系统可靠性指标的敏度表达式，用最佳矢量法求解系统可靠度约束下的最小重量设计问题，迭代过程中，采用梯度步和最佳矢量步进行计算，最后给出一个算例，表明该方法的有效性，该计教育处效率高，收敛稳定，适合工程应用。     

FRP筋混凝土梁裂缝控制验算方法的研究

在试验及国外有关成果的基础上，提出了FRP筋混凝土梁的最大裂缝宽度计算公式；给出了能够用于工程实际的FRP筋混凝土梁最大裂缝宽度限值及使用荷载作用下FRP筋的允许应变限值的取值建议；指出在进行FRP筋混凝土梁截面的配筋设计时，很多情况下起控制作用的将是裂缝宽度的允许值而不是其极限强度。     

现有堤坝地基渗透稳定可靠性研究及加固方案分析

针对现有堤防工程和土石坝工程防渗结构中常存在的下游设排水盖重层的结构形式,按照工程结构可靠性理论的基本原理,对其双层地基的渗透稳定可靠性评价中的基本变量和广义抗力及荷载效应进行了分析;基于现行设计规范中渗透稳定确定性计算方法,建立了现有堤防和土石坝工程的地基渗透稳定可靠性分析模型.根据建立的堤坝地基渗透稳定可靠性计算模型和方法,地基渗透稳定可靠性计算的结论能够反映现有堤坝的地基渗透稳定状态,可针对性地提出经济的加固方案.     

河冰抗压强度概率特征值的自助法估计

为了解决在小样本条件下河冰抗压强度概率特征值不稳定性及其概率模型确定难的问题.将增广样本统计方法——自助法应用于河冰抗压强度概率特征值的计算,解决了小样本情况下其概率特征值的不稳定性问题,从而确定其概率分布.试验数据表明:基于自助法计算得到了河冰抗压强度概率特征值优于常规方法和刀切法计算的结果.自助法能改善小样本条件下其概率特征值的稳定性.     

机械零件强度可靠性设计方法探讨

介绍了机械零件强度设计的应力一强度干涉理论，分析了机械零件强度可靠度计算的一般表达式，并给出了机械零件可靠度设计的工程实例分析。     

钢筋陶粒混凝土的锚固

本文根据试验统计回归建立的变形钢筋在陶粒砼中粘结锚固强度的计算公式，通过可靠度分析给出了钢筋的设计锚固长度，可供修订《轻骨料砼结构设计规程》和工程设计时参考。     

Earth slope reliability analysis under seismic loadings using neural network

σ2Z=∑ni=1(g Xi)2Var(Xi)(5)whereVar(Xi)isthevarianceofrandomvariableXi.AccordingtoEqn.(1),weobtainμZ=μF-1;σZ=σF(6)whereμFandσFarethemeanvalueandthestandarddeviationofthesafetyfactorF,respec tively.Consequently,thereliabilityindexinslopesafetyanalysiswasevaluatedasfollowsbasedontheconceptoftheFOSMmethod[1].β=μZσZ=μF-1σF(7)whereβisthereliabilityindexinslopestabilityanalysis.ThekeystepofEqn.(7)isthecalcula tionofthestatisticalmomentsofthesafetyfactor,i.e.themeanvalue(μF)an…     

公路桥梁中陶粒混凝土梁承载力的研究

目的研究陶粒混凝土梁的正截面受弯承载力和斜截面受剪承载力.方法进行6根陶粒混凝土梁和2根普通混凝土梁的正截面受弯承载力试验,分析陶粒混凝土梁正截面受弯的破坏特征,提出了陶粒混凝土梁正截面受弯承载力的计算方法,并将试验实测值与公式计算值进行了比较.基于陶粒混凝土梁斜截面受剪承载力的试验数据,按照目标可靠指标的要求,提出了陶粒混凝土梁斜截面受剪承载力的计算公式,并对该计算公式进行了可靠度分析.结果正截面受弯承载力的试验实测值与公式计算值的比值是1.064;斜截面受剪承载力计算公式的可靠指标为4.966.结论笔者提出的计算方法和计算公式用来计算公路桥梁中陶粒混凝土梁的承载力是安全可靠的.     

Uncertainty analysis and probabilistic design optimization of hybrid rocket motors for manned lunar landing

To obtain a conceptual design for a hybrid rocket motor(HRM)to be used as the Ascent Propulsion System in the Apollo lunar module,the deterministic design optimization(DDO)method is applied to the HRM design.Based on the results of an uncertainty analysis of HRMs,an uncertainty-based design optimization(UDO)method is also adopted to improve the design reliability.The HRM design process,which is a multidisciplinary system,is analyzed,and a mathematical model for the system design is established to compute the motor performance from the input parameters,including the input variables and model parameters.The input parameter uncertainties are quantified,and a sensitivity analysis of the model parameter uncertainties is conducted to identify the most important model parameter uncertainties for HRMs.The DDO and probabilistic UDO methods are applied to conceptual designs for an HRM to be used as a substitute for the liquid rocket motor(LRM)of the Ascent Propulsion System.The conceptual design results show that HRMs have several advantages as an alternative to the LRM of the Ascent Propulsion System,including nontoxic propellant combination,small motor volume,and comparable functions,such as restarting and throating.Comparisons of the DDO and UDO results indicate that the UDO method achieves more robust and reliable optimal designs than the DDO method.The probabilistic UDO method can be used to develop better conceptual designs for HRMs.