E. Tubaldi

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.

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 ...

A parametric study on the axial behaviour of elastomeric isolators in multi-span bridges subjected to horizontal seismic excitations

Abstract This paper investigates the potential tensile loads and buckling effects on rubber-steel laminated bearings on bridges. These isolation bearings are typically used to support the deck on the piers and the abutments and reduce the effects of seismic loads and thermal effects on bridges. When positive means of fixing of the bearings to the deck and substructures are provided using bolts, the isolators are exposed to the possibility of tensile loads that may not meet the code limits. The uplift potential is increased when the bearings are placed eccentrically with respect to the pier axis such as in multi-span simply supported bridge decks. This particular isolator configuration may also result in excessive compressive loads, leading to bearing buckling or in the attainment of other unfavourable limit states for the bearings. In this paper, an extended computer-aided study is conducted on typical isolated bridge systems with multi-span simply-supported deck spans, showing that elastomeric bearings might undergo tensile stresses or exhibit buckling effects under certain design situations. It is shown that these unfavourable conditions can be avoided with the rational design of the bearing properties and in particular of the shape factor, which is the geometrical parameter controlling the axial bearing stiffness and capacity for a given shear stiffness. Alternatively, the unfavourable conditions could be reduced by reducing the flexural stiffness of the continuity slab.

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...

Effect of the damper property variability on the seismic reliability of linear systems equipped with viscous dampers

Abstract Viscous dampers are dissipation devices widely employed for seismic structural control. To date, the performance of systems equipped with viscous dampers has been extensively analysed only by employing deterministic approaches. However, these approaches neglect the response dispersion due to the uncertainties in the input as well as the variability of the system properties. Some recent works have highlighted the important role of these seismic input uncertainties in the seismic performance of linear and nonlinear viscous dampers. This study analyses the effect of the variability of damper properties on the probabilistic system response and risk. In particular, the paper aims at evaluating the impact of the tolerance allowed in devices’ quality control and production tests in terms of variation of the exceedance probabilities of the Engineering Demand Parameters (EDPs) which are most relevant for the seismic performance. A preliminary study is carried out to relate the variability of the constitutive damper characteristics to the tolerance limit allowed in tests and to evaluate the consequences on the device’s dissipation properties. In the subsequent part of the study, the sensitivity of the dynamic response is analysed by harmonic analysis. Finally, the seismic response sensitivity is studied by evaluating the influence of the allowed variability of the constitutive damper characteristics on the response hazard curves, providing the exceedance probability per year of EDPs. A set of linear elastic systems with different dynamic properties, equipped with linear and nonlinear dampers, are considered in the analyses, and subset simulation is employed together with the Markov Chain Monte Carlo method to achieve a confident estimate of small exceedance probabilities.

Reliability-based optimal design of nonlinear viscous dampers for the seismic protection of structural systems

Viscous dampers are widely employed for enhancing the seismic performance of structural systems, and their design is often carried out using simplified approaches to account for the uncertainty in the seismic input. This paper introduces a novel and rigorous approach that allows to explicitly consider the variability of the intensity and characteristics of the seismic input in designing the optimal viscous constant and velocity exponent of the dampers based on performance-based criteria. The optimal solution permits controlling the probability of structural failure, while minimizing the damper cost, related to the sum of the damper forces. The solution to the optimization problem is efficiently sought via the constrained optimization by linear approximation (COBYLA) method, while Subset simulation together with auxiliary response method are employed for the performance assessment at each iteration of the optimization process. A 3-storey steel moment-resisting building frame is considered to illustrate the application of the proposed design methodology and to evaluate and compare the performances that can be achieved with different damper nonlinearity levels. Comparisons are also made with the results obtained by applying simplifying approaches, often employed in design practice, as those aiming to minimize the sum of the viscous damping constant and/or considering a single hazard level for the performance assessment.

Reliability-Based Methodology for the Optimal Design of Viscous Dampers

Energy dissipation devices are widely utilized to improve the response of structures subjected to dynamic loadings (e.g. earthquakes, winds). In particular, viscous dampers are hydraulic devices widely employed in structural engineering that dissipate the kinetic energy by producing a damping force against the motion. Despite the uncertainty present in the loads (seismic input) and in the structural models, simplified approaches for the design of the damper properties often neglect the response dispersion due to these uncertainties, or treat them in a simplified way by focusing on the mean response only. In this study, a novel reliability-based methodology for the optimal design of nonlinear viscous dampers is proposed. The methodology involves a reliability analysis nested in an outer optimization loop, which seeks the minimization of an optimal function related to the damper cost subjected to the reliability constraint on the structural performance. In particular, subset simulation is used in the inner loop, while the optimization problem is solved via the COBYLA algorithm. The application of the Subset Simulation and of the proposed design approach is illustrated by considering a realistic case study consisting of a three-storey building equipped with nonlinear viscous dampers, for different levels of the damper nonlinearity.

Stochastic Seismic Analysis and Comparison of Alternative External Dissipative Systems

This paper deals with the seismic retrofit of existing frames by means of external passive dissipative systems. Available in different configurations, these systems allow high flexibility in controlling the structural behaviour and are characterized by some feasibility advantages with respect to dissipative devices installed within existing frames. In particular, this study analyzes and compares the performances of two external solutions using linear viscous dampers. The first is based on the coupling of the building with an external fixed-based steel braced frame by means of dampers placed horizontally at the floor levels. The second is an innovative one, based on coupling the building with a “dissipative tower,” which is a steel braced frame hinged at the foundation level, and activating the dampers through its rocking motion. The effectiveness of the two solutions is evaluated and compared by considering a benchmark existing reinforced concrete building, employing a stochastic dynamic approach, under the assumption of linear elastic behaviour for the seismic performance evaluation. This allows efficiently estimating the statistics of many response parameters of interest for the performance assessment and thus carrying out extensive parametric analyses for different properties of the external systems. The study results provide useful information regarding the design and the relative efficiency of the proposed retrofit solutions.

Seismic Response Analysis of Continuous Multispan Bridges with Partial Isolation

Partially isolated bridges are a particular class of bridges in which isolation bearings are placed only between the piers top and the deck whereas seismic stoppers restrain the transverse motion of the deck at the abutments. This paper proposes an analytical formulation for the seismic analysis of these bridges, modelled as beams with intermediate viscoelastic restraints whose properties describe the pier-isolator behaviour. Different techniques are developed for solving the seismic problem. The first technique employs the complex mode superposition method and provides an exact benchmark solution to the problem at hand. The two other simplified techniques are based on an approximation of the displacement field and are useful for preliminary assessment and design purposes. A realistic bridge is considered as case study and its seismic response under a set of ground motion records is analyzed. First, the complex mode superposition method is applied to study the characteristic features of the dynamic and seismic response of the system. A parametric analysis is carried out to evaluate the influence of support stiffness and damping on the seismic performance. Then, a comparison is made between the exact solution and the approximate solutions in order to evaluate the accuracy and suitability of the simplified analysis techniques for evaluating the seismic response of partially isolated bridges.

Reliability-based design of fluid viscous damper for seismic protection of building frames

Viscous dampers are energy dissipation devices widely employed to control the structural response of mechanical and civil systems subjected to dynamic loadings. In particular, such dampers have been extensively applied in earthquake engineering to enhance the seismic performance of new and existing building frames. Although simplified methodologies for the preliminary design of the optimal damper properties are well established, they are often based on deterministic or semiprobabilistic approaches neglecting the response dispersion due to the uncertainties inherent to the seismic input and the system model. This paper proposes a reliability-based methodology for the optimal design of viscous dampers in structural systems subjected to the uncertain seismic input. The methodology is capable of controlling the probability of exceeding limit states related to the structural failure, while limiting the damper forces. Thus, it provides a useful mean to identify the optimal damper properties based on performance-based criteria.