Michele Barbato

FINITE ELEMENT STRUCTURAL RESPONSE SENSITIVITY AND RELIABILITY ANALYSES USING SMOOTH VERSUS NON-SMOOTH MATERIAL CONSTITUTIVE MODELS

This paper focuses on the effects upon the design point search of gradient discontinuities caused by non-smoothness of material constitutive models in the context of finite element reliability analysis. The response computation algorithm for the Menegotto-Pinto smooth material constitutive model is extended to response sensitivity analysis using the Direct Differentiation Method. Response sensitivity and reliability analysis results are compared for a structural system modelled using smooth and non-smooth material constitutive laws, respectively. Both material and discrete loading sensitivity parameters are considered. Structural reliability analyses are performed using the First-Order Reliability Method. Implications of using smooth versus non-smooth material constitutive models in finite element response, response sensitivity and reliability analyses are discussed. A sufficient condition on the smoothness of uni-axial material constitutive models for obtaining continuous finite element response sensitivities is stated and proved for the quasi-static case. The issue of continuity/discontinuity of response sensitivities for the dynamic case is discussed within the application examples.

Influence of Model Parameter Uncertainty on Seismic Transverse Response and Vulnerability of Steel-Concrete Composite Bridges with Dual Load Path

This paper uses a fully probabilistic approach to investigate the seismic response of multispan continuous bridges with dissipative piers and a steel-concrete composite (SCC) deck, the motion of which is transversally restrained at the abutments. This bridge typology is characterized by complex dual load path behavior in the transverse direction, with multiple failure modes involving both the deck and the piers. Proper assessment of the seismic vulnerability of these structural systems must rigorously take into account all pertinent sources of uncertainty, including uncertainties in both the seismic input (record-to-record variability) and the properties defining the structural model (model parameters). Model parameter uncertainty affects not only the structural capacity, but also the seismic response of a structural system. However, most of the procedures for seismic vulnerability assessment focus on the variability of the response resulting solely from seismic input uncertainty. These procedures either neglect model parameter uncertainty effects or incorporate these effects only in a simplified way. A computationally expensive but rigorous procedure is introduced in this work to include the effects of model parameter uncertainty on the seismic response and vulnerability assessment of SCC bridges with dual load path. Monte Carlo simulation with Latin hypercube sampling, in conjunction with probabilistic moment-curvature analysis, is used to build probabilistic finite-element models of the bridges under study. Extended incremental dynamic analysis is used to propagate all pertinent sources of uncertainty to the seismic demand. The proposed pro- cedure is then applied to the assessment of three benchmark bridges exhibiting different seismic behavior and dominant failure modes. Comparison of the response variability induced by seismic input uncertainty and the response variability induced by model parameter un- certainty highlights the importance of accounting for the latter when evaluating the safety of the typology of bridges considered in this study. DOI: 10.1061/(ASCE)ST.1943-541X.0000456.

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.

New analytical solution of the first-passage reliability problem for linear oscillators

AbstractThe classical first-passage reliability problem for linear elastic single-degree-of-freedom (SDOF) oscillators subjected to stationary and nonstationary Gaussian excitations is explored. Several analytical approximations are available in the literature for this problem: the Poisson, classical Vanmarcke, and modified Vanmarcke approximations. These analytical approximations are widely used because of their simplicity and their lower computational cost compared with simulation techniques. However, little is known about their accuracy in estimating the time-variant first-passage failure probability (FPFP) for varying oscillator properties, failure thresholds, and types of loading. In this paper, a new analytical approximation of the FPFP for linear SDOF systems is proposed by modifying the classical Vanmarcke hazard function. This new approximation is verified by comparing its failure probability estimates with the results obtained using existing analytical approximations and the importance sampling ...

Structural Reliability Applications of Nonstationary Spectral Characteristics

This paper presents new closed-form analytical approximations to the first-passage problem in structural reliability by using the exact closed-form solutions for the spectral characteristics of nonstationary random processes. The first-passage problem applied to a structural system possibly with random parameters and subjected to stochastic loading consists of computing the probability of a response quantity exceeding a deterministic threshold in a given exposure time. This paper also investigates, on the basis of benchmark problems, the absolute and relative accuracy of analytical approximations of the time-variant failure probability, such as Poisson, classical Vanmarcke, and modified Vanmarcke approximations, in the case of nonstationary random vibration. The classical and modified Vanmarcke approximations are expressed as time integrals of the closed forms of the corresponding hazard functions. These closed forms refer to linear elastic systems subjected to stationary and nonstationary base excitation...

Finite element response sensitivity analysis of continuous steel-concrete composite girders

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. This paper focuses on a procedure for response sensitivity analysis using state-of-the-art finite elements for composite beams with deformable shear connection. Monotonic and cyclic loading cases are considered. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the Direct Differentiation Method (DDM); its analytical derivation and computer implementation are validated through Forward Finite Difference (FFD) analysis. Sensitivity analysis results are used to gain insight into the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of continuous composite beams, which are commonly used in bridge construction.

Performance-Based Comparison of Different Storm Mitigation Techniques for Residential Buildings

AbstractIn recent years, severe hurricanes have caused enormous economic losses for society and placed tremendous burden on the insurance industry. As the number of residential buildings in hurricane prone regions continues to rise, hurricane hazard mitigation is of paramount importance for residential buildings. Although different retrofit measures are available to mitigate hurricane damage and to reduce the associated social and economic losses, choosing the most cost-effective ones is still an engineering challenge. This paper uses the performance-based hurricane engineering (PBHE) framework with multilayer Monte Carlo Simulation (MCS) for the loss analysis of residential buildings subject to hurricane hazard. A highly efficient modified version of the multilayer MCS technique based on copula is proposed for the faster re-evaluation of hurricane risk when different hurricane hazard mitigation strategies are considered for the same building. This technique is combined with cost-benefit analysis to provi...

Efficient Approach for the Reliability-Based Design of Linear Damping Devices for Seismic Protection of Buildings

AbstractThis paper presents an efficient reliability-based methodology for the seismic design of viscous/viscoelastic dissipative devices in independent and/or coupled buildings. The proposed methodology is consistent with modern performance-based earthquake engineering frameworks and explicitly considers the uncertainties affecting the seismic input and the model parameters, as well as the correlation between multiple limit states. The proposed methodology casts the problem of the dampers’ design for a target performance objective in the form of a reliability-based optimization problem with a probabilistic constraint. The general approach proposed in this study is specialized to stochastic seismic excitations and performance levels for which the structural behavior can be assumed as linear elastic. Under these conditions, the optimization problem is solved efficiently by taking advantage of existing analytical techniques for estimating the system reliability. This analytical design solution is an approxi...

Establishing Common Nomenclature, Characterizing the Problem, and Identifying Future Opportunities in Multihazard Design

Strong interest in extending the service life of critical infrastructure, compounded by the severity of damages during major disasters, such as Hurricane Katrina in 2005 (FEMA 2006) and the Tohoku earthquake in 2011 (NILIM and BRI 2011), has triggered a growing interest in design concepts that account for cascading effects and the interaction of multiple hazards. Traditionally, design is focused on the effects of various kinds of individual single hazards. In today’s structural design practice, the impacts of various single hazards are translated into equivalent forces. Modern design codes account for concurrence and combinations of multiple hazards by suggesting load combinations and load factors intended to include uncertainties and significance of different hazards. A structural system that is designed to resist maximum load effects is expected to survive the damaging effects of multiple hazards. In recent years, other concepts such as displacement-based design and performance-based design were developed for hazards such as earthquakes. However, current design philosophies fail to consider the complex and intertwined effects of multiple hazards at system-wide and societal levels. Some of the shortcomings of the current design philosophies in reflecting the complex nature of multiple hazards can be identified as follows: • The effects of many hazards cannot be meaningfully translated into “equivalent forces”; for instance, the damage caused by a fire is better represented bymaterial decay than by thermal forces; • Successions of hazards impacting a structure are not explicitly included; for example, earthquakes can have a different impact on structures that suffer from corrosion damage compared with pristine structures (Burke and Bruneau 2016; Shiraki et al. 2007); similarly, scour has a great impact on the seismic fragility of reinforced concrete bridges (Wang et al. 2014); • Magnifying effects of hazards acting together are typically ignored; in the case of the catastrophic collapse of the World Trade Center towers, the impact due to the airplane crash shattered the fire protection coatings, which exposed the load carrying elements to extreme heat effects (FEMA 2002); • Analyses are commonly performed on models of intact structures; during the 2011 Tohoku earthquake, several structures that had been damaged by the mainshock suffered further damage in aftershocks (Li et al. 2014); and • Systemand society-level consequences of multiple hazards are not explicitly included; current design philosophies tend to focus on individual components of a system in isolation (e.g., bridges in a transportation system); to minimize the adverse social and economic impacts of multiple hazards, a holistic approach is necessary to account for different scenarios that may impair system function; for example, an earthquake that causes a landslide that blocks access to a hospital could have a catastrophic system-level impact once supplies dwindle that would be similar to that of the earthquake causing structural damage to the hospital directly. In designing for the effects of multiple hazards, several other deficiencies may be present in current design practice. The concept of superposition of different hazards cannot always accurately predict the risk of damage. The effects of multiple hazards, acting concurrently or over time, can significantly increase the damaging impact of individual hazards. Therefore, an explicit multihazard design is necessary to achieve robustness and resiliency (as further defined later) at a large scale. Multihazard design requires an in-depth understanding of the nature of various hazards and their interactions. It must also include the effects that the hazards have on one another and on the behavior of structures or physical components of a system. Design for multihazard mitigation is a multifaceted and complex challenge that may prohibit the development of a unified approach.

Reliability-Based Dynamic Load Allowance for Capacity Rating of Prestressed Concrete Girder Bridges

The current highway bridge design in the United States follows the AASHTO-LRFD specifications, which prescribe a dynamic load allowance, IM, of 0.33 for the dynamic effect of truck/tandem loading. Studies have shown that the IM value prescribed by the LRFD code may underestimate this dynamic effect under poor road surface conditions (RSCs). One reason for this underestimation is that the IM value employed in the AASHTO specifications was obtained from the statistical properties of the IM relative to average RSC, as defined by the ISO 1995 standards. In addition, the IM, which is a random variable with certain statistical properties, was modeled as a deterministic constant in the code calibration process. In this paper, the reliability indexes of a selected group of prestressed concrete girder bridges, designed following the AASHTO-LRFD code, are calculated by modeling the IM explicitly as a random variable for different RSCs. It is found that although the calculated bridge reliability indexes are usually above the target reliability index value of 3.5 under above-average RSCs, they can be significantly below the target value of 3.5 when the RSCs are below average. Following the load rating procedure proposed by the AASHTO load and resistance factor rating (LRFR) manual, it is also found that the code-employed IM value may overestimate the rating factors when RSCs are below average. Based on these results, appropriate IM values are suggested for different RSCs to achieve a consistent target reliability index and a reliable load rating. The results presented in this paper are particularly valuable for the rating of existing prestressed concrete girder bridges, for which the actual RSCs can be directly evaluated. The RSCs must be properly taken into account to accurately estimate the actual safety of the considered bridge.