Evaluation of the effect of geometrical parameters on stope probability of failure in the open stoping method using numerical modeling

Stress-induced failure is among the most common causes of instability in Canadian deep underground mines.Open stoping is the most widely practiced underground excavation method in these mines,and creates large stopes which are subjected to stress-induced failure.The probability of failure(POF)depends on many factors,of which the geometry of an open stope is especially important.In this study,a methodology is proposed to assess the effect of stope geometrical parameters on the POF,using numerical modelling.Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines.A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D,to generate model realizations containing stopes with different geometrical features.The probability of failure(POF)for different categories of stope geometry,is calculated by considering two modes of failure;relaxation-related gravity driven(tensile)failure and rock mass brittle failure.The individual and interactive effects of stope geometrical parameters on the POF,are analyzed using a general multi-level factorial design.Finally,mathematical optimization techniques are employed to estimate the most stable stope conditions,by determining the optimal ranges for each stope’s geometrical parameter.

Reliable Failure Restoration with Bayesian Congestion Aware for Software Defined Networks

SoftwareDefined Networks(SDN)introduced better network management by decoupling control and data plane.However,communication reliability is the desired property in computer networks.The frequency of communication link failure degrades network performance,and service disruptions are likely to occur.Emerging network applications,such as delaysensitive applications,suffer packet loss with higher Round Trip Time(RTT).Several failure recovery schemes have been proposed to address link failure recovery issues in SDN.However,these schemes have various weaknesses,which may not always guarantee service availability.Communication paths differ in their roles;some paths are critical because of the higher frequency usage.Other paths frequently share links between primary and backup.Rerouting the affected flows after failure occurrences without investigating the path roles can lead to post-recovery congestion with packet loss and system throughput.Therefore,there is a lack of studies to incorporate path criticality and residual path capacity to reroute the affected flows in case of link failure.This paper proposed Reliable Failure Restoration with Congestion Aware for SDN to select the reliable backup path that decreases packet loss and RTT,increasing network throughput while minimizing post-recovery congestion.The affected flows are redirected through a path with minimal risk of failure,while Bayesian probability is used to predict post-recovery congestion.Both the former and latter path with a minimal score is chosen.The simulation results improved throughput by(45%),reduced packet losses(87%),and lowered RTT(89%)compared to benchmarking works.

Life-cycle failure probability analysis of deteriorated RC bridges under multiple hazards of earthquakes and strong winds

Engineering structures may be exposed to one or more extreme hazards during their life-cycles.Current structural design specifications usually treat multiple hazards separately in designing structures and there is a limited probabilistic basis on extreme load combinations.Additionally,the performance of engineering structures will be deteriorated by the aggressive environments during their service periods,such as chloride attack,concrete carbonation,and wind-induced fatigue.This study presents a probabilistic methodology to assess the time-dependent failure probability of RC bridges with chloride-induced corrosion under the multiple hazards of earthquakes and strong winds.The loss of cross-section area of reinforcements and the reduction in strength of reinforcing steel and concrete cover induced by the chloride attack are considered.Moreover,the Poisson model is employed to obtain the occurrence probabilities of the individual and concurrent earthquake and strong wind events.The convolution integral is used to determine the joint probability distribution of combined load effects under simultaneous earthquakes and strong winds.Numerical results indicate that the structural failure probability under multiple hazards increases significantly during the bridge′s life-cycle due to the chloride corrosion effect.The contribution of each hazard event on the total structural failure probability varies with time.Thus,neglecting the combined influences of multiple hazards and chloride-induced corrosion may bring erroneous predictions in failure probability estimates of RC bridges.

Methodology for estimating probability of dynamical system's failure for concrete gravity dam

Methodology for the reliability analysis of hydraulic gravity dam is the key technology in current hydropower construction.Reliability analysis for the dynamical dam safety should be divided into two phases:failure mode identification and the calculation of the failure probability.Both of them are studied based on the mathematical statistics and structure reliability theory considering two kinds of uncertainty characters(earthquake variability and material randomness).Firstly,failure mode identification method is established based on the dynamical limit state system and verified through example of Koyna Dam so that the statistical law of progressive failure process in dam body are revealed; Secondly,for the calculation of the failure probability,mathematical model and formula are established according to the characteristics of gravity dam,which include three levels,that is element failure,path failure and system failure.A case study is presented to show the practical application of theoretical method and results of these methods.

Deterministic and probabilistic analysis of great-depth braced excavations:A 32 m excavation case study in Paris

The Fort d’Issy-Vanves-Clamart(FIVC)braced excavation in France is analyzed to provide insights into the geotechnical serviceability assessment of excavations at great depth within deterministic and probabilistic frameworks.The FIVC excavation is excavated at 32 m below the ground surface in Parisian sedimentary basin and a plane-strain finite element analysis is implemented to examine the wall deflections and ground surface settlements.A stochastic finite element method based on the polynomial chaos Kriging metamodel(MSFEM)is then proposed for the probabilistic analyses.Comparisons with field measurements and former studies are carried out.Several academic cases are then conducted to investigate the great-depth excavation stability regarding the maximum horizontal wall deflection and maximum ground surface settlement.The results indicate that the proposed MSFEM is effective for probabilistic analyses and can provide useful insights for the excavation design and construction.A sensitivity analysis for seven considered random parameters is then implemented.The soil friction angle at the excavation bottom layer is the most significant one for design.The soil-wall interaction effects on the excavation stability are also given.

Failure probability analysis of coal crushing induced by uncertainty of influential parameters under condition of in-situ reservoir

The uncertainties of some key influence factors on coal crushing,such as rock strength,pore pressure and magnitude and orientation of three principal stresses,can lead to the uncertainty of coal crushing and make it very difficult to predict coal crushing under the condition of in-situ reservoir.To account for the uncertainty involved in coal crushing,a deterministic prediction model of coal crushing under the condition of in-situ reservoir was established based on Hoek-Brown criterion.Through this model,key influence factors on coal crushing were selected as random variables and the corresponding probability density functions were determined by combining experiment data and Latin Hypercube method.Then,to analyze the uncertainty of coal crushing,the firstorder second-moment method and the presented model were combined to address the failure probability involved in coal crushing analysis.Using the presented method,the failure probabilities of coal crushing were analyzed for WS5-5 well in Ningwu basin,China,and the relations between failure probability and the influence factors were furthermore discussed.The results show that the failure probabilities of WS5-5 CBM well vary from 0.6 to 1.0; moreover,for the coal seam section at depth of 784.3-785 m,the failure probabilities are equal to 1,which fit well with experiment results; the failure probability of coal crushing presents nonlinear growth relationships with the increase of principal stress difference and the decrease of uniaxial compressive strength.

Numerical method of slope failure probability based on Bishop model

Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.

A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

Genetic Algorithm Optimization Model for Determining the Probability of Failure on Demand of the Safety Instrumented System

A more accurate determination for the Probability of Failure on Demand(PFD)of the Safety Instrumented System(SIS)contributes to more SIS realiability,thereby ensuring more safety and lower cost.IEC 61508 and ISA TR.84.02 provide the PFD detemination formulas.However,these formulas suffer from an uncertaity issue due to the inclusion of uncertainty sources,which,including high redundant systems architectures,cannot be assessed,have perfect proof test assumption,and are neglegted in partial stroke testing(PST)of impact on the system PFD.On the other hand,determining the values of PFD variables to achieve the target risk reduction involves daunting efforts and consumes time.This paper proposes a new approach for system PFD determination and PFD variables optimization that contributes to reduce the uncertainty problem.A higher redundant system can be assessed by generalizing the PFD formula into KooN architecture without neglecting the diagnostic coverage factor(DC)and common cause failures(CCF).In order to simulate the proof test effectiveness,the Proof Test Coverage(PTC)factor has been incorporated into the formula.Additionally,the system PFD value has been improved by incorporating PST for the final control element into the formula.The new developed formula is modelled using the Genetic Algorithm(GA)artificial technique.The GA model saves time and effort to examine system PFD and estimate near optimal values for PFD variables.The proposed model has been applicated on SIS design for crude oil test separator using MATLAB.The comparison between the proposed model and PFD formulas provided by IEC 61508 and ISA TR.84.02 showed that the proposed GA model can assess any system structure and simulate industrial reality.Furthermore,the cost and associated implementation testing activities are reduced.

Processing for Zero-Failure Data of the Products

In this paper, an estimation method for reliability parameter in the case of zero-failuare data-synthetic estimation method is given. For zero-failure data of double-parameter exponential distribution, a hierarchical Bayesian estimation of the failure probability is presented. After failure information is introduced, hierarchical Bayesian estimation and synthetic estimation of the failure probability, as well as synthetic estimation of reliability are given. Calculation and analysis are performed regarding practical problems in case that life distribution of an engine obeys double-parameter exponential distribution.

Strength Reliability Analysis of Stiffened Cylindrical Shells Considering Failure Correlation

The stiffened cylindrical shell is commonly used for the pressure hull of submersibles and the legs of offshore platforms. There are various failure modes because of uncertainty with the structural size and material properties, uncertainty of the calculation model and machining errors. Correlations among failure modes must be considered with the structural reliability of stiffened cylindrical shells. However, the traditional method cannot consider the correlations effectively. The aim of this study is to present a method of reliability analysis for stiffened cylindrical shells which considers the correlations among failure modes. Firstly, the joint failure probability calculation formula of two related failure modes is derived through use of the 2D joint probability density function. Secondly, the full probability formula of the tandem structural system is given with consideration to the correlations among failure modes. At last, the accuracy of the system reliability calculation is verified through use of the Monte Carlo simulation. Result of the analysis shows the failure probability of stiffened cylindrical shells can be gained through adding the failure probability of each mode.

A probe into“mining technique in the condition of floor failure”for coal seam above longwall goafs

Targeting at the coal seam with useful value discarded above goafs,attempted to explore the feasibility of'mining technique in the condition of floor failure' from theoretical point of view,and predicted.It indicated that mining technique in the condition of floor failure used above Longwall Goafs in Baijiazhuang Mining is totally feasible.At law,the deformation of the floor in the mining technique by means of probability-integral method.And it is discov- ered that deformed basin can emerge in the footwall of No.6 coal seam and its maximum subsidence was possibly 1 633 mm or so and its maximum positive curvature is 61.74/10^(-3). At last,it therefore suggests appropriate ground pressure control measures as strengthening observation of ground pressure and adopting false slope for exploitation and strengthening support for reasonable push and slide based on the adverse ground pressure behaviors possibly occurring in the mining technique.This serves to gather data and lay sturdy founda- tion for further probe into the mining technique,and offers theoretical and technical grounds for concrete implementation of the mining technique.

Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.

GENERAL FAILURE PROBABILITY SIMULATION AND APPLICATION FOR MULTI-MODE

A general failure probability simulation and deviation evaluation methods were presented for fuzzy safety state and fuzzy failure state. And the corresponding number integral method was simultaneously established. As the distribution of state variable and the membership of the state variable to the fuzzy safety set were normal, the general failure probability of the single failure mode had precise analytic solution, which was used to verify the precision of the presented methods. The results show that the evaluation of the simulation method convergences to the analytic solution with the number increase of the sampling. The above methods for the single failure mode was extended to the multi-mode by the expansion and probability principles. The presented methods were applied to the engineering problem. For the number of significant mode is not too many, the high precision solution can be given by the presented number simulation and number integral methods, which is illustrated by the engineering examples. In addition, the application scope of the methods was discussed.

Application of Importance Sampling Method in Sliding Failure Simulation of Caisson Breakwaters

It is assumed that the storm wave takes place once a year during the design period, and Nhistories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.

Reconstruction of Probability Density Function for Gamma Distribution

The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.

硫化氢环境下老旧管道失效概率评价方法研究

老旧管道在服役过程中存在着失效风险,而影响老旧管道失效的因素有很多,在众多影响因素中硫化氢对管道产生的腐蚀损伤较严重。为解决受腐蚀损伤的老旧管道安全评估问题,文章建立了一种在硫化氢环境下老旧管道失效概率评价方法。以在硫化氢环境中使用了约20年的老旧集气管道为研究对象,采用蒙特卡洛法模拟管道服役过程中的动态压力和腐蚀损伤引起的剩余强度的变化,计算了单一腐蚀因素引起管道失效的概率,并通过正态分布概率给出管道使用的安全范围。研究结果表明:投运20年以上的含硫老旧管道在氢致开裂实验与应力腐蚀开裂实验中,均未发生开裂。根据模型计算得出,老旧管道依旧可以安全服役,但服役6年后失效概率超过0.5,需要进行整修工作,服役27年后,管道内腐蚀严重,剩余强度降到3.82 MPa,需要更换管道。通过模拟得到了失效概率与腐蚀缺陷和服役时间的关系,为老旧集气管道再服役提供理论依据和参考价值。

基于F-J-M法的桥梁温度与地震作用效应组合研究

目前铁路桥梁设计逐渐由容许应力法向极限状态法转变,而《铁路桥涵设计规范(极限状态法)》(Q/CR 9300—2018)并未提及地震作用与温度等可变作用的联合作用,给高寒高烈度区桥梁结构抗震设计带来了较大困难。为了推进桥梁以更经济的抗力方式抵御外荷载作用,通过目标可靠度指标确定其最优地震设计状况荷载组合分项系数,从而对现行桥梁设计规范抗震设计进行优化。建立了高寒地区某桥温度作用效应概率模型,使用Ferry Borges荷载组合理论探究地震和环境温度作用的效应分布特征,并基于JC法和多灾害荷载系数设计法(MH-LRFD)建立地震、温度作用荷载系数的表达式。依托某桥梁工程实例分别探究了地震、温度以及两者共同作用下的桥梁的失效概率。研究结果表明:环境温度引起的桥梁温度内力响应、主要构件材料特性变异均能显著影响桥梁的失效概率;对于高寒大温差地区,现行规范忽略环境温度效应将显著低估桥梁在地震作用下的失效概率。本文提出的F-J-M(Ferry Borges+JC+MH-LRFD)方法计算地震、温度作用组合系数,可为高寒地区桥梁抗震设计提供必要理论依据。

鹤壁九矿工作面开采对副井井筒采动影响分析

煤矿副井是地下开采活动的重要通道,肩负着矿井的人员提升、物料运输和通风等重要功能,在井筒保护煤柱开采中对井筒稳定性的研究至关重要。以鹤壁九矿新副井保护煤柱内工作面开采为研究对象,利用概率积分法计算井筒移动变形规律,并以此为基础,通过Drucker-Prager准则对井筒全段岩层的破坏情况进行判定,以此来评价开采方案对新副井的采动影响,可为煤矿的生产规划提供依据,为类似条件矿井井筒保护煤柱开采提供理论指导。