Consequence-based structural design approach for black swan events

The metaphor of black swan refers to unpredictable events like 9/11, the Indian Ocean tsunami, or the Oklahoma City Federal Building bombing, that cause catastrophic consequences for structural system safety. The likelihood of occurrence for such unforeseen events cannot be estimated from the observed data or prognosticated by experts. The absence of event and likelihood information renders futile the application of usual risk-based methods for design. Therefore, a shift from the probabilistic approach to consequence-based structural design is necessary for coping with the unexpected demands. This is accomplished through the conceptual development of a system capacity oriented design approach, where structural members are designed for variable reliabilities based upon their contribution to causing adverse system consequences. Information about general structural integrity encoded in the stiffness matrix is applied, using member consequence factors ranging from 0 to 1, for determining a member’s contribution towards system response. The structural system is designed using member consequence factors as additional partial factors on the resistance side of the design equations. The consequence-based scheme does not need a triggering hazard event (or its likelihood) and is an apt structural design approach for black swan events.     

VULNERABILITY OF SYSTEMS

A system is vulnerable if any damage from any source produces consequences that are disproportionately large in comparison with that damage. Conversely a system is not robust if it cannot withstand arbitrary damage. Reliability theory is not sufficient for robust safety. In this paper, we propose a contribution to a general theory of vulnerability that is a theory of form and connectivity. The purpose is to identify weak links. This preliminary theory can be applied to a wide range of systems including structures, water pipe works, traffic flows and organisations and is potentially of use for safety management and to reduce the risk of overlooking vulnerable failure scenarios.     

Vulnerability of buildings to windstorms and insurance loss estimation

Windstorms cause enormous loss to life and property worldwide. Insurance companies use risk assessment models to assess the financial risk to their insurance exposure due to windstorms. The estimation of the intensity of hazard and the vulnerability of buildings to windstorms are important parts of a windstorm risk assessment model. The vulnerability functions (or curves) are, in general, based on analyses of loss data from insurance companies. The loss data available from insurance companies following a natural disaster is generally comprised of losses representative of a wide variety of buildings, often lacking information on building-specific characteristics such as height and material. Analysis of such data may not go beyond the development of an aggregate (or generic) vulnerability curve for a combined portfolio giving no idea of the vulnerability of individual building types represented by this curve. The paper discusses the vulnerability of buildings to windstorms and the development of vulnerability functions for windstorm loss estimation. A methodology is presented for the disaggregation of a generic vulnerability curve into several curves representing individual building types. The methodology provides a convenient way of translating known vulnerabilities for a region to those for another region by combining them with actuarial data and building inventory information of the region. The methodology is applied for the disaggregation of generic vulnerability curves for the Caribbean Island of Puerto Rico. The hurricane hazards and the consequent property losses in the region are also discussed.     

On the assessment of robustness

A framework for assessing robustness is proposed, taking basis in decision analysis theory. Robustness is assessed by computing both direct risk, which is associated with the direct consequences of potential damages to the system, and indirect risk, which corresponds to the increased risk of a damaged system. Indirect risk can be interpreted as risk from consequences disproportionate to the cause of the damage, and so the robustness of a system is indicated by the contribution of these indirect risks to total risk. A framework is presented for measuring robustness in this way, and implications for system modelling and acceptable levels of robustness are discussed. Numerical studies of idealized structural systems are performed using this framework, to demonstrate the use of the proposed robustness index and provide insight into system properties affecting robustness. Considered exposures include the design live load and an extraordinary exposure representing a fire or explosion that causes the loss of one or more system components. The results indicate that properties affecting system reliability, such as number of components or the stochastic properties of the load, also affect robustness. Perhaps more interestingly, it is seen that properties such as failure consequences and time to repair a damaged system also affect this measure of robustness. The assessment framework is applied here to study damage tolerance, but the procedure can be applied as well to other aspects of robustness such as tolerance to human error in design or construction.     

柱突然时效导致的多层建筑连续坍塌(1)——简化评估框架

对柱突然失效导致的多层建筑连续坍塌评估提出了新的简化框架。所提框架对于评估结构的鲁棒性提供了实际手段,重要的是,新的简化方法对于影响鲁棒性的因素进行了量化。新方法的主要特点是能够提供非线性结构响应的简化和具体模型。所提出的评估框架主要有三个阶段,包括确定非线性静态响应、采用新简化方法的动态评估以及延性评估。所提框架概念清楚,方法多样,结构鲁棒性的指标合理,所建议的鲁棒性的度量标准对柱突然失效的建筑结构非常适用。本文的姊妹篇论文,对采用新方法评估钢框架组合多层建筑的连续坍塌进行了详细地论述,得到了这类结构有关内在鲁棒性和满足当前设计规定的重要结论。     

Vulnerability of bank filtration systems to climate change

Bank filtration (BF) is a well established and proven natural water treatment technology, where surface water is infiltrated to an aquifer through river or lake banks. Improvement of water quality is achieved by a series of chemical, biological and physical processes during subsurface passage. This paper aims at identifying climate sensitive factors affecting bank filtration performance and assesses their relevance based on hypothetical ‘drought’ and ‘flood’ climate scenarios. The climate sensitive factors influencing water quantity and quality also have influence on substance removal parameters such as redox conditions and travel time. Droughts are found to promote anaerobic conditions during bank filtration passage, while flood events can drastically shorten travel time and cause breakthrough of pathogens, metals, suspended solids, DOC and organic micropollutants. The study revealed that only BF systems comprising an oxic to anoxic redox sequence ensure maximum removal efficiency. The storage capacity of the banks and availability of two source waters renders BF for drinking water supply less vulnerable than surface water or groundwater abstraction alone. Overall, BF is vulnerable to climate change although anthropogenic impacts are at least as important.     

Vulnerability of road networks

Current evaluations of the vulnerability of a road network tend to focus on the probability of damage and the change of traffic demand. The forecasting of low-probability but high-consequence events is a major difficulty. In this paper, a new theory, using a systems-thinking approach, for examining the vulnerability of the form of the network is presented. Our purpose is not to simulate traffic flow but to identify high-consequence scenarios that may arise from vulnerable weaknesses in the form of the network. Such scenarios are independent of models of traffic demand or the source of the damage and can subsequently be combined with specific demands to assess risk. A hierarchical model with clusters of road circuits formed at various levels of granularity of a road network is developed for use in a search process. Only free uncongested flow is considered. A search algorithm for finding vulnerable failure scenarios is described. A vulnerability index is proposed as a measure of the disproportionateness of the consequences of a series of events within a failure scenario in relation to the damage causing those events. The theory is illustrated with two examples.     

The risk of vulnerable failure

There is, as yet, no generally accepted theory of structural robustness or of its corollary, structural vulnerability. The theory of structural vulnerability developed at the University of Bristol is a theory of form that seeks to identify failure scenarios where small damage can lead to disproportionate consequences. In this paper the previously reported theory is combined with a standard response analysis to produce a measure of structural risk which includes the chance of a vulnerable loss of functionality. A simple example of a pin jointed structure is presented.     

Progressive collapse of multi-storey buildings due to sudden column loss — Part I: Simplified assessment framework

This paper proposes a novel simplified framework for progressive collapse assessment of multi-storey buildings, considering sudden column loss as a design scenario. The proposed framework offers a practical means for assessing structural robustness at various levels of structural idealisation, and importantly it takes the debate on the factors influencing robustness away from the generalities towards the quantifiable. A major feature of the new approach is its ability to accommodate simplified as well as detailed models of the nonlinear structural response, with the additional benefit of allowing incremental assessment over successive levels of structural idealisation. Three main stages are utilised in the proposed assessment framework, including the determination of the nonlinear static response, dynamic assessment using a novel simplified approach, and ductility assessment. The conceptual clarity of the proposed framework sheds considerable light on the adequacy of commonly advocated measures and indicators of structural robustness, culminating in the proposal of a single rational measure of robustness that is applicable to building structures subject to sudden column loss. The companion paper details the application of the new approach to progressive collapse assessment of real steel-framed composite multi-storey buildings, making in the process important conclusions on the inherent robustness of such structures and the adequacy of current design provisions.     

Dynamic failure of structural joint systems

Transportation structures rely heavily on the use of structural jointing based on fixing systems such as bolting or welding. Experimental work in this paper offers some insight into the differences between the static and dynamic failure of some joint configurations made using these methods. The main emphasis of this paper is on the examination of a simple dynamic failure of a spot welded lap joint in thin sheet materials that are used extensively in vehicle construction. A comparison is made with similar bolted type lap joints.     

竖向几何不规则性对钢架鲁棒性及其非比例倒塌影响的评估

建筑物由于其结构系统遭受初始局部破坏后发生的非比例倒塌,往往被认定为建筑物局部失效或整体失效。不同结构体系的建筑物能否更好地应对非比例倒塌事件,要依赖其延性和冗余度;建筑物的抵抗力为多参数函数,其中可能包括其规则性。对不规则钢架在遭遇假设的初始破坏(依次移除柱子,直到全部移除)下的反应进行大量的参数研究。按照欧洲和希腊规范,设计15个钢架作为1组。从形态学上讲,钢架的竖向几何不规则性,在抵抗非比例倒塌上是很有效的。最后,给出了钢架的极限状态分析,弹性极限及其各自的鲁棒性测量结果。比较表明,应对钢架的竖向几何不规则性给予特别关注。     

A simplified method for collapse capacity assessment of moment-resisting frame and shear wall structural systems

A simplified methodology for predicting the median and dispersion of collapse capacity of moment-resisting frame and shear wall structural systems subjected to seismic excitations is proposed. The method is based on nonlinear static (pushover) analysis. Simple mathematical models denoted as “generic structures” are utilized to model moment-resisting frames and shear walls. After examining a wide range of structural parameters of the generic structures, a comprehensive database of collapse fragilities and pushover curves (using ASCE 7-05 lateral load pattern) are generated. Based on the obtained pushover curves, closed-form equations for estimation of median and dispersion of building collapse fragility curves are developed using multivariate regression analysis. Comparing the estimates of the median collapse capacity calculated from the closed-form equations with the actual collapse capacities determined from nonlinear response-history analysis indicates that the simplified methodology is reliable. The effectiveness of this methodology for predicting the median collapse capacity of frame and wall structures is further demonstrated with two case studies of structural systems designed based on current seismic provisions.     

Linkage-shredding genetic algorithm for reliability assessment of structural systems

The identification of the probabilistically dominant failure modes of complex structures and the estimation of their reliability can be reduced to the solution of an optimization problem in the standardized normal space of the variables that control the random loads applied on the structure and the random strengths of its members. Hence, the ability of genetic algorithms to identify local and global optima makes them especially suitable for solving structural reliability problems. To reduce the known inefficiencies of traditional genetic algorithms, this paper proposes the use of a hybrid genetic search algorithm that is capable of efficiently identifying the dominant failure modes of a structural system and estimating their reliability index values.The proposed algorithm combines the benefits and the efficiency of the linkage learning process of the gene expression messy genetic algorithm (GEMGA) to the ability of the shredding genetic operator to explore new significant search domains. By reducing the dimensionality of the problem through linkage learning, the number of generations needed to reach convergence is greatly reduced. To further ameliorate the GA search’s efficiency, the Shredding operator is used to estimate the value of the reliability index in a given search direction by building and updating a fitness value matrix based on an evolutionary learning process. This will drastically reduce the number of structural analyses that are usually required during the reliability assessment of structural systems. Furthermore, an exploitation process is implemented during the search for the local optima to obtain accurate reliability indexes and quantify the contributions of various variables to the structural failure modes identified during the search process. Thus, the proposed algorithm provides detailed information about a structure’s failure modes that would be helpful for optimizing the design and improving the structure’s safety against local and global failures. Examples are provided to demonstrate the high efficiency and accuracy of the proposed hybrid genetic algorithm.     

An energy-based partial pushdown analysis procedure for assessment of disproportionate collapse potential

A disproportionate (or progressive) collapse is triggered by localized structural damage that propagates throughout a large portion of a structural system. The current guidelines issued by the US Department of Defense use the alternative path method to assess the vulnerability of a structural system to disproportionate collapse. In this method, the capability of a structure to sustain local damage is evaluated by notionally removing primary load-bearing elements and checking whether the local damage can be absorbed. The assessment can be performed using linear or nonlinear static structural models or a nonlinear dynamic model. Although nonlinear dynamic analysis gives the most accurate results, it is computationally intensive and requires considerable skill to implement properly. In this paper, the vulnerability of three steel frames to disproportionate collapse is assessed using an energy-based nonlinear static pushdown analysis. The predictions are sufficiently close to the results of a nonlinear dynamic time history analysis that the method would be useful for disproportionate collapse-resistant design of buildings with regular steel framing systems.     

Application of neural networks for the structural health monitoring in curtain-wall systems

In a curtain-wall system, the main and the most possible cause of failures, is the total or partial destruction of its connections with the bearing structure. The present paper deals with the respective health monitoring problem and proposes an Artificial Neural Network (ANN) in order to identify possible imperfections in a typical curtain-wall system. Several Finite Element (FE) models of the curtain-wall system were developed and a parametric analysis was carried out dealing with the loss of rigidity in the aforementioned connections. During the numerical investigations, datasets containing the deflections of the columns of the curtain-wall structure were computed. The obtained results were used to create the Patterns Database, which, in turn, was used as the input for the training of the ANNs. Due to the relatively small number of training patterns, the regularization technique was also employed in order to improve the network generalization. The number of sensors and their optimal placement for appropriate network training were investigated. A wide variety of network architectures was studied and their influence on the network training was analyzed. The obtained results showed that ANNs can be an efficient method for the identification and localization of imperfections in curtain-wall systems.     

Evaluation of wind load integration in disproportionate collapse analysis of steel moment frames for column loss

The design of steel structures, in most cases, depends majorly on the level of wind loads which are prescribed by codes and regulations and are used in the structural analysis due to the fact that steel structures being light and ductile systems are strongly affected from a slight difference in the values of wind loading. During the last decades, disproportionate collapse analysis has become of major interest mainly due to the increasing number of failures occurring in that pattern. Commonly accepted guidelines and methods of analysis have been produced, the most dominating of which being the Department of Defense Facilities criteria or DoD. In the DoD, as well as in other criteria, the event of a column loss is suggested as the modeling scenario which has to be sustained by a structural system in order to be robust. However, all the guidelines so far have disconnected the column loss analysis from wind loads and have only performed it for gravity loading. This paper presents the dynamic time history disproportionate collapse analysis of steel frames, including various levels of wind loading. Interesting aspects are discussed through the parametric analysis of five different numerical examples of moment resisting frames.     

A design-oriented model for the collapse resistance of composite floors subjected to column loss

A design-oriented model is proposed for computing the load-resisting capacity of composite steel-concrete floors subjected to interior column loss. The model is based on the premise that floor collapse is resisted through the development of membrane action in the slab elements and catenary forces in the steel beams. A number of simplifying assumptions are made in the model pertaining to the deformed shape of the system, development of failure-resisting mechanisms, and overall system behavior. The proposed model is incremental in nature and tracks the evolution of damage in a floor system loaded up to failure. The model is shown to be able to capture the effect of influential variables on collapse resistance. Key limitations on the model are highlighted and discussed.     

Progressive collapse design of seismic steel frames using structural optimization

This paper uses structural optimization techniques to cost-effectively design seismic steel moment frames with enhanced resistance to progressive collapse, which is triggered by the sudden removal of critical columns. The potential for progressive collapse is assessed using the alternate path method with each of the three analysis procedures (i.e., linear static, nonlinear static, and nonlinear dynamic), as provided in the United States Department of Defense United Facilities Criteria (UFC) Design of Buildings to Resist Progressive Collapse. As a numerical example, member sizes of a two-dimensional, nine-story, three-bay regular steel immediate moment frame are optimally determined such that the total steel weight is minimized while the design satisfies both AISC seismic provisions and UFC progressive collapse requirements. Optimization results for the example frame reveal that the traditional minimum weight seismic design, which does not explicitly consider progressive collapse, fails to meet the UFC alternate path criteria associated with any analysis procedure. Progressive collapse design optimization using the linear static procedure produces the most conservative and consequently heaviest design against progressive collapse. In contrast, the more accurate nonlinear static and dynamic procedures lead to more economical designs with UFC-acceptable resistance to progressive collapse, at the expenses of considerable modeling and computing efforts.     

Disproportionate collapse performance of partially restrained steel frames with bolted T-stub connections

Current design and regulatory documents require the assessment of certain buildings with regard to their vulnerability to disproportionate collapse through notional load-bearing element removal followed by an alternative path analysis. While several recent studies have examined the robustness of steel building frames with fully moment-resistant connections and their ability to sustain local damage to load-bearing elements, only limited research is available regarding the robustness of steel frames with partially restrained (PR) connections. This paper investigates the performance of steel frames with partially restrained connections fabricated from bolted T-stubs following damage to load-bearing columns. A macro-model of a bolted T-stub connection for use in nonlinear analysis is presented, verified through experimental data, and incorporated in a nonlinear finite element model to evaluate the performance of PR frames. Two prequalified T-stub connections are considered, one of which is intended to develop the full moment capacity of the beam. The evaluation is conducted for various floor plans of typical office buildings. The analysis indicates that the frames with strong T-stub connections can resist collapse in damage scenarios involving notional removal of one first-story column, while the robustness of the frames with weak T-stub connections is questionable.