Formulation of Seismic Fragilities for a Wood-Frame Building Based on Visually Determined Damage Indexes

The study of earthquake engineering has made significant strides over the last one-half century with scientists developing methods to better understand the basis and mechanisms of earthquakes and engineers working to mitigate economic loss and fatalities. A paradigm known as performance-based seismic design (PBSD) not only provides life safety to building occupants, but seeks to control structural and nonstructural damage in buildings and other structures. The development of fragility curves based on the well-known Park-Ang damage index is examined herein. This type of formulation can provide the information needed to assess the seismic vulnerability of a structure. Existing shake table test data from the NEESWood Project’s test of a 223?m2 (1,800 sq ft) two-story house was combined with a participant survey to calibrate a damage model. The result was the development of damage fragilities based exclusively on nonlinear time history analysis. Then, the proposed numerical damage model was applied and fragility curves were developed for a six-story light-frame wood condominium building. The results appear logical based on observations of system-level shake table tests over the last decade, and thus the method shows promise provided significant torsion is not present in the system.     

Bridge Damage and Repair Costs from Hurricane Katrina

Hurricane Katrina caused significant damage to the transportation system in the Gulf Coast region. The overall cost to repair or replace the bridges damaged during the hurricane is estimated at over $1 billion. This paper describes the observed damage patterns to bridges, including damage attributed to storm surge, wind, impact from debris, scour, and water inundation, as well as examples of repair measures used to quickly restore functionality to the bridges and transportation system. Using the data from the 44 bridges that were damaged, relationships between storm surge elevation, damage level, and repair costs are developed. The analysis reveals that, in general, regions with higher storm surge had more damage, although there were several instances where this was not the case, primarily due to damage resulting from debris impact. It is also shown that a highly nonlinear relationship exists between the normalized repair cost and the damage state. The paper concludes with a brief discussion on the efficacy of using typical seismic design details for mitigating the effects of hurricane loads, and potential design considerations for bridge structures in vulnerable coastal regions.     

Bayesian Probabilistic Inference for Nonparametric Damage Detection of Structures

This paper presents a Bayesian hypothesis testing-based probabilistic assessment method for nonparametric damage detection of building structures, considering the uncertainties in both experimental results and model prediction. A dynamic fuzzy wavelet neural network method is employed as a nonparametric system identification model to predict the structural responses for damage evaluation. A Bayes factor evaluation metric is derived based on Bayes’ theorem and Gaussian distribution assumption of the difference between the experimental data and model prediction. The metric provides quantitative measure for assessing the accuracy of system identification and the state of global health of structures. The probability density function of the Bayes factor is constructed using the statistics of the difference of response quantities and Monte Carlo simulation technique to address the uncertainties in both experimental data and model prediction. The methodology is investigated with five damage scenarios of a four-story benchmark building. Numerical results demonstrate that the proposed methodology provides an effective approach for quantifying the damage confidence in the structural condition assessment.     

Probabilistic Performance-Based Procedure to Evaluate Pile Foundations at Sites with Liquefaction-Induced Lateral Displacement

Liquefaction-induced ground deformation has caused major damage to bridge and wharf structures in past earthquakes. Large lateral ground displacements may induce significant forces in the foundation and superstructure, which may lead to severe damage or even collapse. A performance-based earthquake engineering (PBEE) approach can provide an objective assessment of the likely seismic performance, so that agencies can evaluate bridge or wharf structures, compare retrofit strategies, and rank them within their overall system. In this paper, a probabilistic PBEE design procedure that incorporates findings from recent research on this problem is presented. The proposed approach can provide answers in terms that are meaningful to owners, such as expected repair costs and downtimes. The methodology is validated through its application to a well-documented case history. Results show that the proposed approach provides a good estimate of the seismic performance of pile-supported structures at sites with liquefaction-induced lateral displacement.     

Inelastic Damage Analysis of Reinforced Concrete Bridge Columns Based on Degraded Monotonic Energy

This paper summarizes the prediction of seismic damage of two existing bridges. The objective is to apply a damage index definition for reinforced concrete bridge columns under cyclic loading to existing bridge columns that might experience real seismic loading in the future, and to evaluate the ability of the damage index in describing the damage progression of the bridge columns during real seismic loading. Two existing bridges were selected from the Greater Vancouver Area in Canada. The first bridge, the Garneau Flyover, was designed in 1985 to ATC-6-1981 and is expected to have sufficient resistance to lateral earthquake loading. The second bridge, the Clydesdale Street Underpass, was designed long before ATC-6-1981 and is expected to show little or no lateral earthquake resistance. The damage index is applied to each of these structures, with columns modeled using the CANNY nonlinear structural analysis program. Shear and bond slip deformations were considered by making a simple modification to the column flexural properties. A series of nonlinear dynamic analyses were performed using records from the 1971 San Fernando, 1978 Miyaki-Oki (Japan), 1989 Loma Prieta, and 1999 Taiwan earthquakes fitted to the Vancouver firm ground spectrum. The calculated damage index provides a simple numerical indicator of the damage during an earthquake, easily computed from the results of a nonlinear dynamic analysis.     

Wavelet-Based Approach for Structural Damage Detection

A wavelet-based approach is proposed for structural damage detection and health monitoring. Characteristics of representative vibration signals under the wavelet transformation are examined. The methodology is then applied to simulation data generated from a simple structural model subjected to a harmonic excitation. The model consists of multiple breakable springs, some of which may suffer irreversible damage when the response exceeds a threshold value or the number of cycles of motion is accumulated beyond their fatigue life. In cases of either abrupt or accumulative damages, occurrence of damage and the moment when it occurs can be clearly determined in the details of the wavelet decomposition of these data. Similar results are observed for the real acceleration data of the seismic response recorded on the roof of a building during the 1971 San Fernando earthquake. Effects of noise intensity and damage severity are investigated and presented by a detectability map. Results show the great promise of the wavelet approach for damage detection and structural health monitoring.     

Damage Detection and Damage Detectability— Analysis and Experiments

A technique to identify structural damage in real time using limited instrumentation is presented. Contrast maximization is used to find the excitation forces that create maximum differences in the response of the damaged structure and the analytical response of the undamaged structure. The optimal excitations for the damage structure are then matched against a database of optimal excitations to locate the damage. To increase the reliability of the approach under modeling and measurement errors, the contrast maximization approach is combined with an approach based on changes in frequency signature. The detectability of any particular damage with the proposed technique depends on the ratio of the magnitude of damage and the magnitude of errors in the measurements, as well as on how much the damage influences the measurements. A damage detectability prediction measure, that incorporates these effects, is developed. The technique is first tested numerically on a 36 degree-of-freedom space truss. To simulate experimental conditions, an extensive study is carried out in the presence of noise. A similar truss is then built and the finite-element method (FEM) model of the structure is corrected using experimental data. The technique is applied to locate the damage in several members. The experimental results indicate that this technique can robustly identify the damaged member with limited measurements and real-time computation. The effectiveness of the damage detection measure is also demonstrated.     

Simplified Method to Include Cumulative Damage in the Seismic Response of Single-Degree-of-Freedom Systems

In this paper a consistent method including damage criteria in the seismic response of single-degree-of-freedom systems is proposed. The method allows the determination of suitably modified strength or displacement inelastic spectra through the introduction of an equivalent damage factor pdam that accounts for earthquake damage potential; analogously capacity spectra could be obtained. Three types of damage indices are considered (Park and Ang index DP&A, energy index DE, and low-cycle fatigue index DF) and derivation of pdam is pursued for all these cases. Moreover approximate simplified expressions in the function of Cosenza and Manfredi seismological ID index, which accounts for cyclic damage potential of an earthquake, are also proposed. In this way damage capacity spectra are obtained to improve the seismic assessment of existing structures including damage effect.     

Impact of Great December 26, 2004 Sumatra Earthquake and Tsunami on Structures in Port Blair

This paper reports on the effects of the great Sumatra earthquake and tsunami of December 26, 2004, in and around Port Blair, the capital city of the Andaman and Nicobar Islands, India. The earthquake shaking and subsequent tsunami caused substantial damage to structures that include buildings, harbors, overhead water tanks, seaport control towers, and so on. Other important structures, for example, dams, bridges, hangars, and so on, also suffered minor damage without disrupting their functioning. Reinforced concrete structures on the islands were the worst performers, while traditionally constructed timber and masonry structures performed well in response to ground shaking. The mandatory Indian Standards were not complied within the design of many recent structures on the islands located in the most severe seismic zone in India.     

Urban Damage Estimation Using Statistical Processing of Satellite Images

Remotely sensed satellite imagery of an earthquake-affected region can significantly assist in estimating the severity of infrastructure damage. Modern high-resolution satellite systems have been launched to provide users optical imagery with submeter accuracy, which enable the possibility of sensing damage for individual structures by means of pre- and postevent imagery. Recognizing these advancements, herein, we focus our study on the region of Bam, Iran, which was devastated by a moment magnitude Mw = 6.6 earthquake on December 26, 2003, causing approximately 43,200 lives lost. The recognition of urban structures within the Bam region is obtained by performing morphological filtering and intensity thresholding, which is further optimized through a statistical procedure. By overlaying the recognized structures with the pre- and postevent images, three object-based change detection methods are presented. The performance of change indices resulting from the three change detection methods is evaluated by means of a histogram-based classification approach. Damage estimation results are presented using easily interpretable maps, wherein individual structures are rendered with colors representing the severity of damage.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Highway Bridges with One Single-Column Bent

In performance-based seismic design, general and practical seismic demand models of structures are essential. This paper proposes a general methodology to construct probabilistic demand models for reinforced concrete (RC) highway bridges with one single-column bent. The developed probabilistic models consider the dependence of the seismic demands on the ground motion characteristics and the prevailing uncertainties, including uncertainties in the structural properties, statistical uncertainties, and model errors. Probabilistic models for seismic deformation, shear, and bivariate deformation-shear demands are developed by adding correction terms to deterministic demand models currently used in practice. The correction terms remove the bias and improve the accuracy of the deterministic models, complement the deterministic models with ground motion intensity measures that are critical for determining the seismic demands, and preserve the simplicity of the deterministic models to facilitate the practical application of the proposed probabilistic models. The demand data used for developing the models are obtained from 60 representative configurations of finite-element models of RC bridges with one single-column bent subjected to a large number of representative seismic ground motions. The ground motions include near-field and ordinary records, and the soil amplification due to different soil characteristics is considered. A Bayesian updating approach and an all possible subset model selection are used to assess the unknown model parameters and select the correction terms. Combined with previously developed capacity models, the proposed seismic demand models can be used to estimate the seismic fragility of RC bridges with one single-column bent. Seismic fragility is defined as the conditional probability that the demand quantity of interest attains or exceeds a specified capacity level for given values of the earthquake intensity measures. As an application, the univariate deformation and shear fragilities and the bivariate deformation-shear fragility are assessed for an example bridge.     

Optimization and Multihazard Structural Design

There is a growing interest in the development of procedures for the design of structures exposed to multiple hazards. The goal is to achieve safer and/or more economical designs than would be the case if the structures were analyzed independently for each hazard and an envelope of the demands induced by each of the hazards were used for member sizing. We describe an optimization approach to multihazard design that achieves the greatest possible economy while satisfying specified safety-related and other constraints. We then present an application to illustrate our approach.     

Damage Detection in Composite Materials Using Identification Techniques

The present paper describes an approach for damage detection in composite structures that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from a mathematical model of the original structure, where such a model is typically a finite‐element representation of the structure. In the present work dealing with composite materials, two distinct analytical models, one using two‐dimensional (2D) elements in conjunction with the classical lamination theory and another using three‐dimensional (3D) elements were considered. The output error approach of system identification was employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. The proposed method is an extension of the stiffness‐reduction approach for damage detection to realistic structures. Numerical simulation of measurements of static deflections, strains, and vibration modes were used in the identification procedure. The methodology was implemented for representative composite structures. Principal shortcomings in the proposed approach and possible methods to circumvent these problems are discussed in the paper.     

Observations of Structural Damage Caused by Hurricane Katrina on the Mississippi Gulf Coast

The loads associated with Hurricane Katrina led to the destruction or severe damage of approximately 130,000 homes and over 200 deaths in the state of Mississippi. This paper discusses the results of a field inspection of structural damage along the state’s Gulf Coast area caused by this hurricane. It was found that reinforced concrete, steel frame, and heavy timber structures generally performed well, with minimal structural damage. Precast concrete, light frame wood, and bridge structures generally performed poorly. Nonstructural components of all building types, in particular facades and interior partitions subjected to storm surge, were typically destroyed. For various structures, the primary cause of failure was found to be insufficient connection strength. A comparison of Katrina’s storm surge and wind loads is made to those specified in current design standards. It was found that Katrina’s forces exceeded those specified in design standards in many parts of the state.     

Deficiency Analysis of Coastal Buildings toward Storm Damage Reduction

Engineering services provided by one of the writers to property owners, insurance companies, attorneys, and others have resulted in a compilation of case studies, based on more than 1,000 site inspections, suitable to generate a database regarding various aspects of building performance. The scope of those services typically included identifying the cause and origin of damage to residential and commercial structures, as well as an estimation of the magnitude of damage sustained by those structures. The majority of those damaged structures was located in proximity to a coastal region and experienced recent exposure to a storm or other weather event. Compilation of data from those case studies allowed identification and ranking of the occurrence of chronic building problems. It has become apparent that building-related deficiencies often exist as a common feature in similar structures. Some of those recurring deficiencies could be eliminated with alternate building design, better construction practices, or proper routine maintenance procedures. Where applicable, proposed remedial solutions are presented for specific building deficiencies or problems identified.     

Improved Damage Localization and Quantification Using Subset Selection

Because a structure’s modal parameters (natural frequencies and mode shapes) are affected by structural damage, finite- element model updating techniques are often applied to locate and quantify structural damage. However, the dynamic behavior of a structure can only be observed in a narrow knowledge space, which usually causes nonuniqueness and ill-posedness in the damage detection problem formulation. Thus, advanced optimization techniques are a necessary tool for solving such a complex inverse problem. Furthermore, a preselection process of the most significant damage parameters is helpful to improve the efficiency of the damage detection procedure. A new approach, which combines a parameter subset selection process with the application of damage functions is proposed herein to accomplish this task. Starting with a simple 1D beam, this paper first demonstrates several essential concepts related to the proposed model updating approach. A more advanced example considering a 2D model is then considered. To determine the capabilities of this approach for more complex structures, a trust region-based optimization method is adopted to solve the corresponding nonlinear minimization problem. The objective is to provide an improved robust solution to this challenging problem.     

Load Vectors for Damage Localization

A technique to localize damage in structures that can be treated as linear in the pre- and postdamage states is presented. Central to the approach is the computation of a set of vectors, designated as damage locating vectors (DLVs) that have the property of inducing stress fields whose magnitude is zero in the damaged elements (small in the presence of truncations and approximations). The DLVs are associated with sensor coordinates and are computed systematically as the null space of the change in measured flexibility. The localization approach based on the use of DLVs is not structure type dependent and can be applied to single or multiple element damage scenarios. Knowledge about the system is restricted to that needed for a static analysis in the undamaged state, namely, the undamaged topology and, if the structure is indeterminate, the relative stiffness characteristics. Numerical simulations carried out with realistic levels of noise and modeling error illustrate the robustness of the technique.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. I: Methodology and Input Motion

Based on observed damage patterns from previous earthquakes and a rich history of analytical studies, asynchronous input motion has been identified as a major source of unfavorable response for long-span structures, such as bridges. This study is aimed at quantifying the effect of geometric incoherence and wave arrival delay on complex straight and curved bridges using state-of-the-art methodologies and tools. Using fully parametrized computer codes combining expert geotechnical and earthquake structural engineering knowledge, suites of asynchronous accelerograms are produced for use in inelastic dynamic analysis of the bridge model. Two multi-degree-of-freedom analytical models are analyzed using 2,000 unique synthetic accelerograms with results showing significant response amplification due to asynchronous input motion, demonstrating the importance of considering asynchronous seismic input in complex, irregular bridge design. The paper, Part 1 of a two-paper investigation, presents the development of the input motion sets and the modeling and analysis approach employed, concluding with sample results. Detailed results and implications on seismic assessment are presented in the companion paper: Effect of Asynchronous Motion on Complex Bridges. Part II: Results and Implications on Assessment.     

Terrestrial Laser Scanning-Based Structural Damage Assessment

Terrestrial laser scanning (TLS) provides a rapid, remote sensing technique to model 3D objects. Previous work applying TLS to structural analysis has demonstrated its effectiveness in capturing simple beam deflections and modeling existing structures. This paper extends TLS to the application of damage detection and volumetric change analysis for a full-scale structural test specimen. Importantly, it provides a framework necessary for such applications, in combination with an analysis approach that does not require tedious development of complex surfaces. Intuitive slicing analysis methods are presented, which can be automated for rapid generation of results. In comparison with conventional photographic and surface analysis methods, the proposed approach proved consistent. Furthermore, the TLS data provided additional insight into geometric change not apparent using conventional methods. As with any digital record, a key benefit to the proposed approach is the resulting virtual test specimen, which is available for posttest analysis long after the original specimen is demolished. Uncertainties that can be introduced from large TLS data sets, mixed pixels and parallax in the TLS analysis are also discussed.