Design and sensitivity analysis using the probability-safety-factor method. An application to retaining walls

This paper presents a new method for designing engineering works that makes the classical approach, based on safety factors, and the modern, probability-based, approach compatible, and includes a sensitivity analysis. The method consists of a sequence of classical designs, based on given safety factors, that (a) minimize cost or optimize an alternative objective function, (b) calculate the different failure mode probabilities or their upper bounds, and (c) update the safety factors to satisfy both the safety factors and the failure probability requirements. The process is repeated until convergence. As a result, an automatic design of the engineering work, the safety factors and the corresponding probabilities of failure for all failure modes are obtained. A double safety check is used and the correspondence between safety factors and probabilities of failure for the different modes are easily understood. An advantage of this approach is that the optimization procedure and the reliability calculations are decoupled. In addition, a sensitivity analysis is performed using a method that consists of transforming the data parameters into artificial variables and using the dual associated problem. The method is illustrated by its application to a retaining wall design.     

高地应力下白鹤滩地下洞室群含错动带岩体破坏模式及机制研究

 在建的白鹤滩地下洞室群规模巨大,具有“高边墙、大跨度、高地应力、复杂地质条件”的特点,在高应力开挖卸荷过程中,遭遇到延展性强且力学性质差的多条大型错动带的影响,使得含错动带岩体遭遇到不同程度的变形破坏问题。结合地质、施工、监测、测试及数值分析等资料,首先从错动带产状、成因和自身特点等方面对错动带的工程特性进行详细论述,然后对因错动带导致工程岩体结构变形失效或破坏的实例进行归纳总结,从结构控制因素上将含错动带岩体的破坏模式划分为塑性挤出型拉伸破坏、结构应力型塌方/掉块和剪切滑移型破坏3种类型;其次,研究分析各类含错动带岩体的破坏特征与机制,包括时空演化过程、形态特征、破坏规模等,初步揭示3种破坏模式对应的力学机制;最后,给出典型的含错动带岩体破坏模式分析预测和支护探讨实例,从而为白鹤滩地下厂房施工过程中含错动带岩体不稳定性问题的预测和调控提供借鉴。上述研究成果对于高应力条件下类似的地下洞室群含错动带岩体的稳定性研究具有重要的参考价值和指导意义。     

钢筋混凝土梁式构件抗爆分析的改进等效单自由度方法

爆炸荷载作用下钢筋混凝土梁式构件可能会出现多种破坏模式，主要有弯曲破坏、直剪破坏和弯剪联合破坏等。现有结构构件抗爆分析方法主要考虑爆炸荷载下结构构件的弯曲破坏，对直剪破坏和弯剪联合破坏研究较少，尤其缺少快速准确的抗爆分析方法。基于等效单自由度模型理论，改进了钢筋混凝土梁抗爆分析的直剪单自由度方法，提出了直剪、弯剪联合破坏的判定准则，给出了两种破坏模式下钢筋混凝土梁动态响应的计算方法。进一步考虑爆炸荷载作用下钢筋混凝土梁的弯曲破坏、直剪破坏和弯剪联合破坏，提出钢筋混凝土梁式构件抗爆分析的改进等效单自由度方法，并给出了其分析步骤。该方法可以直接评估爆炸荷载下钢筋混凝土梁式构件的破坏模式，并计算其动态响应。通过有限元软件LS-DYNA数值模拟了不同爆炸工况下钢筋混凝土梁式构件的动态响应和破坏模式，与改进的等效单自由度方法的计算结果进行了对比，验证了提出的改进等效单自由度分析方法的正确性。     

GFRP空心板静载试验研究及分析

通过玻璃纤维增强复合材料 (GFRP)拉挤空心板的静载试验 ,研究了其受力性能、变形、应力分布和破坏特征 ,并与有限元数值模拟的结果进行了对比。根据试验和分析结果 ,针对FRP材料各向异性、拉压不同的特点 ,提出了按受力状态划分截面取加权平均来计算等效截面刚度的简化方法。还根据板中应变分布与发展的特点 ,对构件的局部屈曲和强度破坏两种破坏机理进行了分析 ,为FRP空心板的设计与应用提供了依据。     

基于滑块平衡法顶部加箍碎石桩承载力计算方法

针对工程实践中出现的顶部加箍碎石桩复合地基形式,分析了其破坏模式。引入滑块平衡法,考虑土体自重效应和加箍段桩侧摩阻力影响,分别基于计算深基础承载力的Meyerhof法和Terzaghi法,建立了顶部加箍碎石桩在深层鼓胀破坏模式下的两种计算模型,并利用随机优化算法搜索临界滑裂面及其所对应的极限承载力。通过与实验结果以及与既有方法的对比分析发现：本计算方法更符合工程实际,而且就承载力而言,顶部加箍碎石桩的最优加箍深度约为4倍桩体直径。     

A PDEM-based perspective to engineering reliability: From structures to lifeline networks

Research of reliability of engineering structures has experienced a developing history for more than 90 years. However, the problem of how to resolve the global reliability of structural systems still remains open, especially the problem of the combinatorial explosion and the challenge of correlation between failure modes. Benefiting from the research of probability density evolution theory in recent years, the physics-based system reliability researches open a new way for bypassing this dilemma. The present paper introduces the theoretical foundation of probability density evolution method in view of a broad background, whereby a probability density evolution equation for probability dissipative system is deduced. In conjunction of physical equations and structural failure criteria, a general engineering reliability analysis frame is then presented. For illustrative purposes, several cases are studied which prove the value of the proposed engineering reliability analysis method.     

Dominant failure modes in stochastic structural systems

In an analysis of redundant structural systems in which either or both loading systems and/or member resistances are stochastic variables, all modes of failure are potentially of significance in the calculation of structural reliability. In practice, however, many modes do not contribute very much, and a problem has been to identify those modes which are stochastically dominant.In this paper a general, iterative procedure called the Truncates Enumeration Method [TEM] to determine the most stochastically dominant modes is derived from successive systematic curtailment of the results which would be obtained by complete enumeration. In this way, it is shown that the procedure presented has the capability to produce all dominant modes to within the accuracy of the criteria used for curtailment. The method is similar to that proposed by Murotsu et al.It is also shown that the incremental load method (ILM), proposed by Moses et al., has certain features common to TEM, that both techniques are essentially incremental in nature and that both methods produced the same mode failure probability statement, each using quite distinct procedures. It is finally argued that the methods are not restricted merely to the materials behaviour properties studied thus far by their proponents.     

大型洞室群围岩破坏模式的动态识别与调控

 在归纳地下工程围岩破坏模式分类、分析方法和控制措施等方面研究成果的基础上,建立大型地下洞室群围岩破坏模式的分类方法。该分类方法充分考虑大型洞室群大尺寸、大高宽比和多洞室相互作用等特点,依据控制因素、破坏机制、发生条件3个层次归纳出18种典型的围岩破坏模式,给出每种破坏模式的主要稳定性分析方法和针对性控制措施等方面的建议。并进一步根据大型洞室群分步开挖过程中不断更新的工程地质条件和围岩性状,提出围岩破坏模式的动态识别、复核与调控方法。该方法已成功应用于锦屏二级水电站地下厂房洞室群的开挖过程中围岩破坏模式识别和实时工程措施(开挖和支护)调控,实现施工过程中围岩局部不稳定性问题的识别、预测与动态调控。实践表明,该方法实用、科学和系统,可有效地指导大型地下洞室群施工过程中的开挖与支护设计动态优化,避免局部不稳定性问题的发生。     

考虑多失效模式相关的岩质边坡体系可靠度分析

 岩质边坡稳定的可靠度分析中包含多个相关的失效模式,传统的岩质边坡体系可靠度分析方法不能有效地考虑多失效模式相关的体系可靠度问题。为此,提出考虑多失效模式相关的岩质边坡平面滑动的体系可靠度分析方法。建立考虑多失效模式相关的岩质边坡平面滑动体系可靠度分析的概率故障树模型。采用b分布描述岩质边坡稳定分析中张裂缝的位置、岩体的黏聚力和内摩擦角。张裂缝中充水深度用截尾指数分布来描述。采用自适应重要抽样方法计算岩质边坡平面滑动的体系可靠度,并进行随机变量分布参数的敏感性分析。算例结果表明,概率故障树模型能够有效地分析岩质边坡多失效模式相关的体系可靠度问题,如果不考虑失效模式间的相关性对边坡体系可靠度的影响,岩质边坡的体系可靠度将会被低估。岩质边坡2个块体之间不发生相互作用的可能性明显地比2个块体之间发生相互作用的可能性要高。建议在进行岩质边坡体系可靠度分析时将张裂缝中充水深度系数取为区间[0.0,1.0]内的截尾指数分布。此外,变量的均值敏感性因子和标准差敏感性因子都表明,张裂缝中充水深度和张裂缝位置对边坡的体系可靠度影响最大,因此设置良好的边坡排水系统以及进行详细的地质勘测工作是提高边坡稳定性的有效措施。变量的均值和标准差敏感性因子之间是高度相关的,它们都可以用来识别最敏感的随机变量。     

Event oriented analysis of series structural systems

The event oriented analysis of technical objects is in general accomplished by representing them as complete or incomplete systems and subsystems of events. It is argued in the article how the compound engineering systems of events can be partitioned by inclusion-exclusion expansion into individual and common cause modes. The event analysis is based on the random variable model and employs the results of operational modes and effect analysis, of the reliability analysis and of the uncertainty analysis. The system redundancy and robustness are considered as uncertainties, due to the fact that really a number of events are possible, expressed by the entropy concept in probability theory, conditioned by operational and failure modes, respectively. Relative and average uncertainty measures are introduced to facilitate uncertainty interpretations in engineering problems. It is investigated how the sensitivity analysis of reliability measures can be applied to the assessments of system uncertainties. Numerical examples presented in the article illustrate the application of event oriented system analysis to series structural systems with common cause failures. Additionally, system performance presentation and optimization with constraints, as well as potential improvements in system analysis, design and maintenance are investigated.     

A multi-level structural assessment strategy for reinforced concrete bridge deck slabs

This paper proposes a multi-level assessment strategy for reinforced concrete bridge deck slabs. The strategy is based on the principle of successively improved evaluation in structural assessment. It provides a structured approach to the use of simplified as well as advanced non-linear analysis methods. Such advanced methods have proven to possess great possibilities of achieving better understanding of the structural response and of revealing higher load-carrying capacity of existing structures. The proposed methods were used for the analysis of previously tested two-way slabs subjected to bending failure and a cantilever slab subjected to a shear type of failure, in both cases loaded with concentrated loads. As expected, the results show that more advanced methods yield an improved understanding of the structural response and are capable of demonstrating higher, yet conservative, predictions of the load-carrying capacity. Nevertheless, the proposed strategy clearly provides the engineering community a framework for using successively improved structural analysis methods for enhanced assessment in a straightforward manner.     

SRC框架结构失效模式识别与优化

控制结构的失效模式,使结构由于非理想的失效模式向理想的失效模式转化,对提高结构的抗震性能,降低地震时人员伤亡和财产损失,具有重要意义。本文以结构失效模式的识别和优化为研究目标,通过基于OpenSees平台对型钢混凝土结构进行IDA分析,搜索出结构的控制地震波,并获得该地震波作用下的失效模式,并采取一些工程手段对其优化。     

A two-dimensional limit equilibrium computer code for analysis of complex toppling slope failures

Evaluation of blocky or layered rock slopes against toppling failures has remained of great concern for engineers in various rock mechanics projects.Several step-by-step analytical solutions have been developed for analyzing these types of slope failures.However,manual application of these analytical solutions for real case studies can be time-consuming,complicated,and in certain cases even impossible.This study will first examine existing methods for toppling failure analyses that are reviewed,modified and generalized to consider the effects of a wide range of external and dead loads on slope stability.Next,based on the generalized presented formulae,a Windows form computer code is programmed using Visual C#for analysis of common types of toppling failures.Input parameters,including slope geometry,joint sets parameters,rock and soil properties,ground water level,dynamic loads,support anchor loads as well as magnitudes and forms of external forces,are first loaded into the code.The input data are then saved and used to graphically draw the slope model.This is followed by automatic identification of the toppling failure mode and a deterministic analysis of the slope stability against this failure mode.The results are presented using a graphical approach.The developed code allows probabilistic introduction of the input parameters via probability distribution functions(PDFs)and thus a probabilistic analysis of the toppling failure modes using Monte-Carlo simulation technique.This allows calculation of the probability of slope failure.Finally,several published case studies and typical examples are analyzed with the developed code.The outcomes are compared with those of the main references to assess the performance and robustness of the developed computer code.The comparisons demonstrate good agreement between the results.     

Structural reliability techniques applied to plume impingement loading of the Space Station Freedom photovoltaic array

A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design due to the examined failure modes is minute. Significantly, this paper details a structural reliability analysis of a complex aerospace structure for which little statistical information is available.     

Selected Problems of Collapse Behaviour Analysis of Structural Members Built from Strain-Hardening Material

In this work the results of the collapse behaviour analysis of thin-walled, trapezoidal box-section beams subject to pure bending are presented. The analysis emphasizes two problems: the strain-hardening effect in the structural material and different modes of stress distribution at yield lines, inducing different plastic moment capacities at those lines. The problem is solved by means of the energy method, based upon the plastic mechanism approach, applied for thin-walled structures. Two theoretical models of plastic mechanisms of failure are discussed.     

Vibration of general triangular composite plates with elastically restrained edges

Triangular fibre reinforced composite plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration behaviour of anisotropic triangular plates with edges elastically restrained against rotation and translation. The approach developed is based on the Rayleigh–Ritz method and the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for single layer composite plates with different fibre orientations and combinations of boundary conditions. For some plates, mode shapes of free vibration are also shown. Selected new transverse vibration mode shapes are presented to illustrate the effects of boundary constraints, aspect ratio and fibre orientation.The method can be applied to a wide range of elastic restraint conditions, any aspect ratio and for higher modes. The effect of the fibre orientation on the natural frequencies for plates with these restraint conditions are also considered.     

单层球壳模型结构振动台试验研究

通过对单层球壳结构模型的振动台试验,分析了结构在地震作用下的破坏模式。为使模型呈现不同的倒塌模式,设计了3个缩尺比为1/10的试验模型：模型1与模型3以期发生承载力破坏倒塌模式;模型2设置6个薄弱区,以期发生动力失稳。采用多次加载方案,水平向输入地震波,逐级提高峰值加速度,完成振动台试验。采用基线调整法对原始试验数据进行校正;采用有限元软件ANSYS中的大质量法对试验模型进行考虑双非线性的多点输入时程分析,获得结构动力响应;采用自编程序对模型结构进行有限元塑性分析。结果表明：试验模型的倒塌模式与试验预期结果吻合良好,验证了振动台试验的完备性;有限元分析结果与实测结果吻合较好,验证了数值计算方法的正确性。     

方钢管混凝土分叉柱与钢梁连接节点的抗震性能研究

通过4个1/2比例的钢管混凝土分叉柱与钢梁连接节点的拟静力试验,对其滞回性能、刚度退化、延性性能、耗能能力以及破坏特征进行了研究与分析,并与纤维杆元模型模拟的结果进行了比较。结果表明:节点在梁端塑性铰破坏模式下钢管混凝土树状节点的抗震性能较好;在局部焊接破坏模式下延性较低,抗震性能相对较差;钢管分叉柱长宽比较大时,设置纵向隔板能更好地保证节点区域的稳定性。     

Ein ungewöhnliches Stabilitä verursacht Schadensfall

An uncommon stability problem causes failure. When bolted two‐plane connections of box shaped compression members in trusses are designed, it is obvious that the boltability must be observed. If however, in doing so, the classic design principle of constructing truss nodes as compact as possible is falling into oblivion this may have serious consequences, as a recently occurred failure of a truss girder shows. The uncommon stability phenomenon that caused this failure is here presented to the structural engineering community in order to help avoiding similar failures in the future. The eigenmodes and eigenvalues obtained from a linear FEM stability analysis are discussed. Supplementary nonlinear FEM analyses (so called GMNIA analyses) show when compared to the acting loading that the failure was inevitable. Some lessons and recommendations how to avoid the uncommon stability failure are presented. As a concluding remark, the paper is seen within the greater context of “forensic engineering” as an instrument to improve the safety of our structures.