Seismic Reliability Analysis of Structural Systems

Modified subset simulation method for reliability analysis of structural systems

This paper studies the effects of spatially varying ground motions on the responses of a bridge frame located on a canyon site. Compared to the spatial ground motions on a uniform flat site, which is the usual assumptions in the analysis of spatial ground motion variation effects on structures, the spatial ground motions at different locations on surface of a canyon site have different intensities owing to local site amplifications, besides the loss of coherency and phase difference. In the proposed approach, the spatial ground motions are modelled in two steps. Firstly, the base rock motions are assumed to have the same intensity and are modelled with a filtered Tajimi-Kanai power spectral density function and an empirical spatial ground motion coherency loss function. Then, power spectral density function of ground motion on surface of the canyon site is derived by considering the site amplification effect based on the one dimensional seismic wave propagation theory. Dynamic, quasi-static and total responses of the model structure to various cases of spatially varying ground motions are estimated. For comparison, responses to uniform ground motion, to spatial ground motions without considering local site effects, to spatial ground motions without considering coherency loss or phase shift are also calculated. Discussions on the ground motion spatial variation and local soil site amplification effects on structural responses are made. In particular, the effects of neglecting the site amplifications in the analysis as adopted in most studies of spatial ground motion effect on structural responses are highlighted.

The present paper focuses on reliability analysis of structural systems under ground motion acceleration taking into account the inherent random nature of the excitation as well as epistemic uncertainties affecting the definition of its spectrum. Specifically, seismic excitation is modelled as a zero-mean stationary Gaussian random process fully characterized by an imprecise power spectral density (PSD) function i.e. with interval parameters. The ranges of such interval parameters are determined by analysing a large set of accelerograms recorded on rigid soil deposits. To discard outliers, the Chauvenet’s Criterion is applied iteratively. The proposed imprecise PSD function may be viewed as representative of the actual accelerograms recorded on rigid soil deposits. Reliability assessment is carried out by incorporating the imprecise PSD function of ground motion acceleration into the formulation of the classical first-passage problem using Vanmarcke’s failure criterion. Due to imprecision of the excitation, the reliability function and the fractile of order p of the selected extreme value response process turn out to have an interval nature. Thus, the aim of reliability analysis is the evaluation of the bounds of such functions which define the range of structural performance. Numerical results show that neglecting imprecision of the PSD may lead to significant overestimation of the safety level.

System and measurement uncertainties play a key role in finding the reliability of complex and safety-critical structural systems such as buildings and bridges. Current mainstream techniques in structural reliability analysis use an iterative first-order reliability method that performs an indirect uncertainty evaluation by finding the most probable failure point. However, such an approach could lead to high computational time due to slower convergence, and in some cases, poor convergence that leads to unreliable results. In order to address the shortcomings, this paper applies a new high-order moment propagation technique (that was initially developed for the measurement uncertainty analysis) to structural reliability analysis problems aiming to obtain results that are simultaneously accurate and computational efficient. The proposed approach was implemented on a three-story elastic frame structure, and the presented results prove that the application of a technique from the field of measurement uncertainly can indeed be applied to complex problems in the structural reliability analysis in order to reduce the trade-off between accuracy and computational efficiency.

Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method

The evaluation of the seismic hazard for a given site is to estimate the seismic ground motion at the surface. This is the result of the combination of the action of the seismic source, which generates seismic waves, the propagation of these waves between the source and the site, and site local conditions. The aim of this work is to evaluate the sensitivity of dynamic response of extended structures to spatial variable ground motions (SVGM). All factors of spatial variability of ground motion are considered, especially local site effect. In this paper, a method is presented to simulate spatially varying earthquake ground motions. The scheme for generating spatially varying ground motions is established for spatial locations on the ground surface with varying site conditions. In this proposed method, two steps are necessary. Firstly, the base rock motions are assumed to have the same intensity and are modelled with a filtered Tajimi-Kanai power spectral density function. An empirical coherency loss model is used to define spatial variable seismic ground motions at the base rock. In the second step, power spectral density function of ground motion on surface is derived by considering site amplification effect based on the one dimensional seismic wave propagation theory. Several dynamics analysis of a curved viaduct to various cases of spatially varying seismic ground motions are performed. For comparison, responses to uniform ground motion, to spatial ground motions without considering local site effect, to spatial ground motions with considering coherency loss, phase delay and local site effects are also calculated. The results showed that the generated seismic signals are strongly conditioned by the local site effect. In the same sense, the dynamic response of the viaduct is very sensitive of the variation of local geological conditions of the site. The effect of neglecting local site effect in dynamic analysis gives rise to a significant underestimation of the seismic demand of the structure.

Performance-based design and seismic reliability analysis using designed experiments and neural networks

Dominant mechanisms in stochastic plastic frames

This paper outlines an improved simulation method for a time-dependent reliability analysis of structural systems subjected to stochastic loads. Strengths of structural elements are assumed to degrade with time proportionally during the life cycle of the structural system, and stochastic load events are modeled as Poisson processes. The structural failure probabilities are estimated through the life cycle simulation, in which the directional simulation method is applied just to sample random load variables to execute each life cycle simulation efficiently. Numerical examples are presented and results are compared with those obtained by the crude Monte Carlo simulation to show the effectiveness of the proposed method. It is shown that the proposed method is effective for the assessment of the time-dependent failure probability of structural systems.

Performance-based seismic design (PBSD) is considered by many to be the next generation of design philosophy that focuses on the system performance of a structure during earthquake loading. For steel and concrete structures, this design philosophy is being used by a select group of practitioners. However, application to wood-frame buildings is still in the research stages; several approaches for PBSD are proposed with rehabilitation concepts available in ASCE 41. Currently, most of the PBSD methods for wood-frame buildings require designers to utilize a level of approach that is far more detailed than current design approaches. This increases the cost of any engineering for the design of wood-frame buildings. Therefore, in this study, a simplified design approach is developed that allows a designer to employ the PBSD methodology without complex analysis. Different from most existing PBSD procedures, this prescriptive approach was developed based on a significant number of numerical simulations using a sim...

Performance-based optimum seismic design of cable tray system

Reliability analysis of nonlinear structural systems using response surface method

A new performance-based seismic design procedure for eccentrically braced frames (EBF) based on pre-selected yield mechanism and target drift is proposed in this paper. The design base shear is derived from a modified energy balance equation. A new seismic lateral force distribution based on nonlinear dynamic behavior is also presented. Two EBF (3-story and 10-story), which were used in a recent related study where they were designed by following current design practice and IBC 2000 provisions, were re-designed by the proposed performance-based design methodology by using the same basic design spectral values as used for the code designed frames. The proposed design procedure was validated by extensive non-linear dynamic analyses for a number of ground motion records. Comparisons are made between the responses of the code designed frames with the ones designed by the proposed method. The results confirm the validity of the proposed method for the study EBF in terms of meeting all the performance design objectives, such as target drifts, and intended yield mechanism, in other words, yielding occurring in a controlled manner in pre-selected elements. Thus, yielding was confined to the shear links only, and plastic hinging in the columns was eliminated except some occurring at the column bases, which was expected. This resulted in superior performance of the frames designed by the proposed method over that of the code designed frames. The total weight of steel used in the frames designed by the two approaches was the same. No attempt was made to compare the costs because of many factors that may affect them.

Studies on the theory of structural system reliability includes identifi- cation of main the failure modes and calculation of inclusive failure probabilities for the structural system. The efficient and accurate identification of failure modes in structural systems is difficult and represents a key focus for research in sys- tem reliability. The fundamental theory of the branch and bound algorithm for stage critical strength is reviewed in this paper. Some deficiencies in this method are highlighted. Corresponding approaches to overcome these deficiencies are pro- posed. Calculated system reliability solutions to the classical model, a truss with 10 elements, indicate that the improvement measures proposed in this paper increase the efficiency of recognising the main failure modes of the structural system, and are readily validated. The outcomes of this type of benchmark analysis suggest that the proposed methodology may be capable of representing a suitable basis for the structural system reliability analysis of complex truss-like structures, includ- ing transmission towers. Using the proposed approach, the principal failure modes and system reliability of a transmission tower are calculated. Based on practical engineering considerations, effective methods to improve this structural system re- liability are proposed.

This study presents an in-depth examination of recent progress in damping technologies tailored for structural systems under seismic loading.It evaluates a broad spectrum of damping approaches-including friction-based systems, hysteresis models, eddy current dampers, inertial devices, and advanced material solutionsfor their efficiency in reducing vibrations and dissipating seismic energy.Key innovations such as the Variable Damping Inertial Eddy Current Damper (VD-IECD), notched bilinear hysteretic models, and nanostructure-enhanced CFRP composites have shown notable effectiveness in simultaneously controlling structural displacement and acceleration.The review also highlights emerging solutions like self-cantering rocking elements, high-damping offshore mooring systems, and honeycomb structural configurations designed for vibration suppression.Furthermore, topics such as nonlinear damping behaviour, wave motion in cable-supported systems, and stochastic-based sensitivity analysis are explored to improve accuracy in seismic performance prediction.By synthesizing current developments and identifying future research directions, this paper emphasizes the importance of advanced damping mechanisms in achieving earthquake-resilient infrastructure.Takewaki (2009) advocated for a sensitivity-based approach in damping system design, enabling engineers to systematically evaluate the influence of various damping parameters on structural performance.His methodology facilitates performance-based seismic design by identifying optimal damping configurations tailored to probabilistic ground motion characteristics.Zhang and Makris (2001) studied the dynamic response of free-standing rocking blocks subjected to seismic excitations.Their analytical approach provided criteria for overturning and stability, highlighting the effectiveness of rocking as a self-centering mechanism.Their work supported the use of rocking systems in modern prefabricated and modular structures for enhanced seismic resilience.Giaralis and Petrini (2017) explored the emerging use of mechanical metamaterials for seismic protection.These materials, engineered with tailored microstructures, offer enhanced damping capabilities through mechanisms such as negative stiffness and frequency bandgaps.Their review emphasized how integrating materials science with structural engineering can create highly effective, space-efficient vibration solutions.2021) reviewed the application of honeycomb structures for vibration reduction under dynamic loads such as earthquakes.Their study demonstrated that honeycomb cores with optimized geometry not only reduce weight but also enhance damping and load distribution, making them suitable for aerospace and civil engineering applications where both performance and efficiency are critical. Rahman et al. (Li and Lam (2014) carried out a comparative study on outrigger damping systems, particularly in tall buildings.Their results showed that combining controlled rocking bases with damped outriggers significantly improved lateral stiffness and energy dissipation, reducing overall drift and base shear, and enhancing building stability during strong ground motions.2019) examined the use of micro-perforated plates (MPP) for structural vibration control in low-frequency ranges.They explained how the interaction between air and solid boundaries within the micro-perforations introduces additional viscous damping.Their findings suggest that MPPs can serve dual purposes in sound and vibration control, particularly in industrial and aerospace structures. Zhang et al. ( Lu et al. (2021)proposed a stochastic sensitivity-based framework for evaluating damping performance in non-stationary seismic environments.Their methodology allowed for quantifying how damping parameters affect time-varying spectral characteristics, facilitating more robust design strategies for damping devices in complex structural systems.2020) demonstrated through experimental work and molecular simulations that a hybrid structure of graphene oxide and carbon nanotubes enhances both the damping and mechanical properties of CFRP composites.This advancement enables the development of multifunctional materials that resist vibration and maintain structural integrity under seismic conditions.2019) presented a method for identifying damping coefficients in real steel buildings using actual seismic data.Their process, validated through shake table experiments and numerical models, is particularly suited to first-mode dominant low-rise structures and contributes to more accurate dynamic modeling in structural design. Zhou et al. ( Diotallevi et al. (Kim and Kim (2010) investigated the integration of damping devices into performance-based seismic designs for reinforced concrete and steel buildings.Their analysis highlighted how proper device selection and placement can significantly reduce inter-story drift and improve energy dissipation, promoting safer and more resilient structural systems.