Seismic Reliability Research Articles

Seismic reliability analysis of energy-dissipation structures by combining probability density evolution method and explicit time-domain method

Hysteretic dampers such as buckling restrained braces (BRBs) have been widely used for improving the performance of civil structures exposed to seismic hazard. In this study, a hybrid approach, which combines the probability density evolution method (PDEM) and the explicit time-domain method (ETDM), is proposed for system reliability analysis of energy-dissipation structures with hysteretic dampers under seismic excitations. The PDEM can capture the probability density function (PDF) of system limit-state function for a structure by constructing a virtual random process associated with the limit state. The system failure probability of the structure can be directly evaluated through the integration of the PDF of system limit-state function over the failure domain. However, hundreds of deterministic nonlinear time-history analyses corresponding to the selected representative points need to be conducted in the solution procedure of PDEM, leading to high computational cost when applied to large-scale energy-dissipation structures. To enhance the efficiency of PDEM, the ETDM with dimension-reduced iteration scheme is incorporated into PDEM to conduct the required nonlinear time-history analyses with high efficiency, in which only a small number of degrees of freedom associated with the hysteretic dampers are considered in the iteration process. A real engineering building with 32 BRBs is investigated to illustrate the accuracy and efficiency of the proposed method and its feasibility to practical structures.

Seismic reliability assessment of RC tunnel-form structures with geometric irregularities using a combined system approach

Tunnel-form structures represent a new type of structural systems with enhanced earthquake resistance and considerably reduced construction times, if compared to conventional reinforced concrete frames and dual systems. Due to the limited information about the seismic performance of tunnel-form buildings in the presence of vertical and horizontal irregularities, seismic design standards generally prevent such irregularities and therefore impose significant architectural limitations. To address this issue, a liability assessment is here conducted on irregular 5- and 10-storey tunnel-form buildings subjected to 12 different earthquakes, representing a design spectrum. The structural response of these buildings is obtained under both Design Basis Earthquake (DBE) and Maximum Considered Earthquake (MCE) hazard levels by using time-history and nonlinear static (pushover) analyses. The reliability of the buildings is then assessed by using a novel combined system approach, in which the structural effects of walls and coupling beams at each storey are modeled as series and parallel sub-systems. The results of this study show that, despite the geometric irregularities, all the structural elements could satisfy the Immediate Occupancy (IO) performance level under both DBE and MCE scenarios with over 95% reliability. Therefore, enforcing the regularity for tunnel-form structures in current seismic design guidelines appears to be too conservative; the results of this study can then prove useful for a more efficient design of irregular tunnel-form structures in seismic regions.

Random Seismic Response Analysis of Long-Span Steel-Concrete Composite Structure

Considering the randomness of seismic input and the nonlinear characteristic of long-span structures, the probability density evolution method is used to study the dynamic response of the long-span steel-concrete composite structure under random earthquake. Three-dimensional structural model is established in the finite element software SAP2000, and then the displacements between layers and the response rule of vertical displacements of truss roof of the composite structure are obtained. The results show that under the input of three-dimensional earthquake, the vertical displacement of the grid roof of the isolated long-span steel-concrete composite structure is an order of magnitude larger than the horizontal direction of each layer. The probability density evolution method can offer comprehensive probability information of nodal displacements, and provide a reasonable way for the seismic reliability analysis of long-span isolated structures.

Seismic Reliability Investigation of Bearing Capacity of Foundations Based on Limit Analysis and Limit Equilibrium Methods

In this paper, by considering the upper-bound limit analysis method in calculating the seismic bearing capacity of foundations, the comparison between a limit equilibrium method such as Hansen and limit analysis method in terms of reliability is investigated. Limit equilibrium has been the oldest method for performing bearing capacity of foundations. However, it seems that theoretical equations proposed by the majority of old limit equilibrium methods to calculate the bearing capacity of foundations (such as Hansen) do not consider the effects of inertial forces of the earthquake in the soil mass. These methods only take into account the horizontal load applied to the foundation and disregard the earthquake forces applied to the soil. By comparing the results of this study, it can be inferred that the reliability of the Hansen approach is very close to the limit analysis method that ignores the impact of horizontal earthquake forces applied to rigid soil blocks. Since the upper-bound limit analysis takes into account the seismic effect of inertial forces in an earthquake, its results may be considered more accurate than Hansen. This study shows that in both granular and cohesive soils in high seismicity-prone areas, usage of a more realistic method as the limit analysis is more reasonable. Considering the facility of RBD by Hansen method using EXCEL spreadsheet in comparison to the seismic reliability-based design using MATLAB programming following the upper-bound limit analysis method, graphs that offer coefficients for obtaining the equivalent value of target reliability in the limit analysis by using the Hansen formulation are presented. Additionally, this study shows that the horizontal seismic coefficient (kh) is an impressive parameter that affects the differences between the two mentioned approaches.

The Application of Computer Simulation Technology in Seismic Reliability Random Vibration Analysis of Shear Wall Structures

In recent years, the computer simulation technology has been widely studied, among which the seismic reliability theory of the structure and the seismic performance evaluation of the structure is widely concerned. The seismic reliability analysis of structures is of great significance to the seismic performance evaluation, design and decision of structures. Taking earthquake action as a random process and using random vibration theory to study the probabilistic characteristics is an important development of structural seismic theory. In the more than half a century since Housner first used stochastic processes in 1947, the random vibration theory has been applied and developed rapidly in engineering seismic analysis, and has increasingly become a more advanced and reasonable seismic analysis tool.

The Method of Improving the Seismic Reliability of Building Structure Based on Kriging Optimization Theory

The development of social economy accelerates the process of urbanization and makes the population denser. Once the earthquake happens, it will cause serious harm to people. The building constructed by traditional methods cannot meet the seismic requirements. Based on Kriging optimization theory, this paper studies the method of improving the seismic reliability of building structure, introduces the principle of the method, and establishes the seismic model of building structure. Compared with the traditional methods, it can be found that the optimized seismic method can effectively improve the seismic capacity of the building structure, provide a better guarantee for the safety of citizens’ property and life, and has a very good use value.

Identification and Model Update of the Dynamic Properties of the San Silvestro Belfry in L’Aquila and Estimation of Bell’s Dynamic Actions

The authors investigated the dynamic behaviour of the San Silvestro belfry in L’Aquila (Italy). The 2009 earthquake in L’Aquila caused severe damages to the entire masonry complex. Extensive rehabilitation works, ended in 2019, repaired the structure and enhanced its seismic safety. In this paper, the authors discuss three aspects typical of masonry towers by interpreting the outcomes of Operational Modal Analysis carried out on December 2019: the interactions between the tower and the masonry complex, the dynamic effects of the bell, and the seismic reliability assessment of the tower. Specifically, the experimental mode shapes drive the estimation of an equivalent cross-section, whose principal axes of inertia match with the directions of oscillation of the mode shapes, and the parameters of an equivalent cantilevered beam roughly representative of the tower dynamics. In a second step, a two-degrees-of-freedom analytical model simulates the dynamic coupling between the tower and the more massive bell. The response of the system to a set of seven strong-motion earthquakes yields the assessment of the bell effects over the seismic performance of the masonry tower.

Seismic reliability of reinforced concrete bridges subject to environmental deterioration and strengthened with FRCM composites

Ensuring adequate seismic reliability levels for existing infrastructure components is a key issue for owners in earthquake-prone countries. In particular, bridges may suffer relevant damage in case of a seismic event, and this issue can be magnified due to deterioration phenomena induced by environmental agents, like CO2 emissions or chlorides. Among the available techniques, seismic retrofitting can be pursued through the use of composite materials. For a proper bridge management policy, infrastructure owners need to know at which time instant scheduling restoration interventions on bridges, and such issues have to be fixed with a reliability-based metric. The present study numerically investigates the effectiveness of the use of fabric reinforced cementitious matrix (FRCM) systems in the seismic retrofitting of an existing multi-span simply supported (MSSS) reinforced concrete (RC) bridge subject to aging. Fragility curves are first derived on the basis of refined non-linear time-history analyses performed on the “as built” configuration. Fragilities are further computed for different combinations of deterioration scenarios and seismic retrofitting schemes with increasing number of FRCM layers. Time-variant seismic reliability profiles are thus assessed, and reliability gains achievable at different time instants with the implementation of the FRCM retrofitting scenarios are quantified in order to provide useful information for the infrastructure owner decision-making.

Seismic resilience analysis of a retrofit-required bridge considering moment-based system reliability

For a bridge, its columns or piers, which are the main seismically resistant members of the bridge, are generally retrofitted to improve seismic performance. However, retrofitting may cause unexpected damage to the non-retrofitted components/members. Therefore, a corresponding retrofitting of these components/members should be considered as part of any retrofitting method to eliminate unexpected damage. This work is to develop an estimating procedure of the seismic reliability of the system for a bridge considering the seismic reliability of each specified component/member. Additionally, the damage state of bridge for the system reliability analysis is built based on the engineering judgement. For the convenience of the calculation, the seven-point estimation method and the Nataf transformation method are combined to calculate the first four moment values of a specified limit state function in the moment-based system reliability analysis. For determining the retrofitting strategy, this work also presents a method for calculating the relationship between the resilience in functionality and seismic intensity that is achieved using a particular retrofitting method. Moreover, the system reliability and recovery time of each damaged component/member are considered in a resilience analysis. Finally, a bridge is selected as an example to demonstrate the application of this work.

The seismic reliability analysis of moment resisting frames with bolted end-plate connection

This paper presents an algorithm to determine the reliability index of moment-resisting steel frames with bolted end-plate connections, by considering the effect of the uncertainties of capacity and seismic demand. To reflect the probabilistic response of structures, the horizontal and vertical distance of the bolt from edge of end-plate, the pretension force and the ultimate strength of the bolts, yield strength and the elastic modulus of plates for beam and column, which are the main parameters of construction errors in bolted end-plate connection, considered as a random variables for the moment-rotation behavior of connections. All the components of the connections have been regarded as random parameters. Then, the probabilistic moment-rotation curve of connections was determined by means of the Latin Hypercube sampling method. Afterward, by conducting a nonlinear dynamic analysis in the 2-dimensional 5, 10, and 15 stories frames and considering the idealized random behavior of the connections as well as the random effect of different records of the earthquake, the results obtained with the aid of Monte Carlo sampling technique. Finally, the appropriate probability density function (PDF) fitted to the results, which this figure for reliability index and probability of failure for the limit state function is 1.62 and 0.052 respectively and also the mean value state is 1.85 and 0.033. This procedure has been named as the Simplified Response Surface Method (SRSM). Results show the structural reliability index is acceptable at the performance level of Life Safety, yet it exceeded this level only by a small amount.

Reliability analysis and multi-level response modification factors for buckling restrained braced frames

This study aims to assess the seismic performance of buckling restrained braced frames (BRBFs) using a probabilistic approach and develop multi-level response modification factors for performance-based design of these systems. Unlike traditional seismic design methods, the proposed response modification factors can take into account the seismic conditions of the site as well as the target design performance level. An engineering damage parameter method (EDP-Based) is adopted for reliability analysis of 4, 8 and 12 storey BRBFs using systems of parallel and serial components. In general, the results demonstrate the high seismic reliability of BRBFs for high levels of earthquake intensity. Considering the axial strain of the brace core as the local damage index, it is shown that the studied models remain in performance levels higher than life safety under the design hazard level (return period of 475 years). The upper bond response modification factor for the life safety and collapse prevention performance levels is estimated to be around 8.4 and 10.0 with the corresponding intensities of 0.68 and 0.85, respectively. Based on the outcomes of this study, in general, using a response modification factor between 4 and 8 for seismic design of BRBFs would guaranty their adequate performance under both the design basis and maximum considered earthquake levels.

Fragility and risk assessment of freestanding building contents

SummaryMultistorey buildings often have a valuable inventory consisting of objects that their possible damage during an earthquake will cause unacceptable losses. The paper presents a novel, fully performance‐based seismic reliability and risk assessment framework for freestanding structural components and contents that can be modelled as rocking rigid blocks. The seismic response of building contents depends on several parameters such as the geometry of the object, the dynamic characteristics of the building and the storey that the object is located. The demand at the storey level is first obtained, and then the response of the contents is calculated using the storey acceleration response history. The demand of the structure is obtained with the aid of a modified version of the Incremental Dynamic Analysis method and subsequently the fragility curves of the rocking building contents are derived for every storey of interest. Different options for fragility assessment are discussed, and the underlying details of the problem are investigated. A simplified approach, where the fragility of the freestanding components and the structure are derived separately, is also presented. The method combines existing fragility curves and thus is suitable for quickly assessing the reliability of a building's inventory, offering sufficient risk estimates.

Reliability Assessment of Reinforced Concrete Buildings Using Field Data in Tehran

Abstract Reinforced Concrete (RC) structures are a prevalent type of structure. In each year a lot of RC buildings are constructed and there is a large investment on RC buildings. Dual systems (containing RC shear walls and moment resisting frame) and moment resisting frame systems are the most common type of RC buildings in Iran. Earthquake can cause severe damages to RC buildings and it is important to identify which structural system has better performance under seismic excitation. Some researchers have studied seismic reliability of the bridges structures using field data. However, real field data are not used to analyze the reliability of RC buildings. In this study the reliability analysis is used to evaluate the performance of each structural system. The probability distribution of the concrete and steel bars strength are gathered by nun-destructive tests and bar tensile tests. The mentioned tests are done in 110 RC buildings in Tehran. A series of time history analysis are done to determine the probability of failure. Monte Carlo sampling is used for reliability analysis. The reliability of two prevalent RC structural systems are compared under different earthquake records. It is found that the dual system can have a better performance under seismic excitation and it can reduce damages in the earthquake.

Seismic reliability analysis of water distribution networks on the basis of the probability density evolution method

In this study, a new approach for assessing the seismic functional reliability of water distribution networks is presented on the basis of the probability density evolution method. The original contribution of this paper is to build a new framework for the reliability analysis of water distribution networks on the basis of the physical mechanism of water distribution networks subjected to earthquakes. Firstly, a finite element model is established to capture the seismic response of the entire buried pipe networks. Then the nodal head of water distribution networks is derived through hydraulic analysis of water distribution networks with leakages. Secondly, owing to the randomness of ground motions, the probability density functions of the nodal heads of water distribution networks are obtained on the basis of the probability density evolution method. Thirdly, the seismic functional reliability of water distribution networks is evaluated considering the demand heads of nodes. When the nodal head is larger than the predetermined water head, the node is reliable while when the nodal head is smaller than the predetermined water head, the node is not reliable. Two examples, namely, a virtual and an actual water distribution networks, are examined in detail to investigate the feasibility of the proposed method. Results show that the proposed method effectively evaluates the seismic functional reliability of water distribution networks.

Seismic reliability analysis of structures based on cumulative damage failure mechanism

Non-stationary random seismic response and reliability of multi-degree of freedom hysteretic structure system are studied based on the cumulative damage failure mechanism. First, dynamic Eqs. of multi-degree of freedom hysteretic structure system under earthquake action are established. Secondly, the random seismic response of a multi-degree freedom hysteretic structure system is investigated by the combination of virtual excitation and precise integration. Finally, according to the damage state level of structural, the different damage state probability of high-rise frame structure is calculated based on the boundary value of the cumulative damage index in the seismic intensity earthquake area. The results show that under the same earthquake intensity and the same floor quality and stiffness, the lower the floor is, the greater the damage probability of the building structure is; if the structural floor stiffness changes abruptly, the weak layer will be formed, and the cumulative damage probability will be the largest, and the reliability index will be relatively small. Meanwhile, with the increase of fortification intensity, the reliability of three-level structure fortification is also significantly reduced. This method can solve the problem of non-stationary random seismic response and reliability of high-rise buildings, and it has high efficiency and practicability. It is instructive for structural performance design and estimating the age of the structure.

Концепции по обоснованию проектных решений сооружений атомных станций с учетом особых динамических воздействий

В настоящей работе изложены основные концепции по расчёту сооружений атомных станций на особые динамические природные и техногенные воздействия и обоснованию их проектных решений.
 В общем объёме задач по обоснованию проектных решений сооружений атомных станций особое место отводится разработке методов расчёта сооружений при особых динамических воздействиях. В частности, повышенные требования предъявляются к сейсмостойкости и надёжности энергетических объектов и устанавливаемому на них оборудованию как при нормальном режиме эксплуатации, так и при особых динамических воздействиях.
 Исследование проблемы взаимодействия сооружения с основанием с учётом геологического строения строительной площадки и конструктивных особенностей сооружения даёт возможность перейти к более обоснованным расчётным моделям.
 Приведены основные актуальные направления расчёта сооружений на особые динамические воздействия. Рассмотрена специфика оценки прочности и надёжности основания, строительных конструкций сооружения, оборудования атомных станций при указанных воздействиях.
 В работе изложены и систематизированы основные концепции по определению расчётных сейсмических воздействий на свободной поверхности площадки строительства атомных станций, современные методы моделирования и расчётов сооружений атомных станций, требования к определению техногенных воздействий от летающих тел и взрывов, методы расчётов защитных конструкций сооружений. Продемонстрирована практическое использование новых высокопрочных материалов, в том числе сталефибробетона, в качестве важного стратегического этапа совершенствования оптимизации компоновочных решений сооружений атомных станций. Приведена оценка эффективности применения сталефибробетона вместо обычного бетона.

Exploration on Damage Mechanism and Equivalent Damage Model of High Arch Dams under Earthquakes

Damage identification technology of high arch dams has been well developed under strong earthquakes. However, the failure mechanism of high arch dams at different locations remains unclear. For this purpose, a series of deterministic dynamic analyses for a 3D 289-m-high arch dam based on concrete damaged plasticity constitutive model are performed. The failure mechanism at different locations of high arch dams under earthquakes is studied systematically. According to the sensitivity of different indicators to different damaged positions, an effective sensor placement scheme is proposed to assess the seismic reliability in practical engineering. Furthermore, a new effective equivalent damage model based on prior information is proposed, which can improve the efficiency of damage identification, as well as solving the problem that the real damage is concealed by homogenizing the damage in a pre-set region. The results provide suggestions and theoretical basis for sensor placement in actual monitoring of high arch dams; and the equivalent damage model provides a new solution to balance the efficiency and accuracy of damage identification.

Seismic reliability and limit state risk evaluation of plain concrete arch bridges

Masonry arch bridges are vital infrastructures in the system of railway transportation. In Iran's railway network, there is a large number of masonry arch bridges built 80 years before. These structures have been designed just for gravity loads, not for earthquake excitations. Thus, their seismic assessment is critical. Probabilistic performance-based earthquake engineering (PBEE) is preferred to other seismic response assessment methods, since the randomness and uncertainty in structural resistance, as well as seismic excitation, is involved in this method. The PBEE procedure assesses the seismic performance of structures concerning decision variables of downtime, fatalities, and monetary losses. The decision variables involve the evaluation of the limit state risk. For this purpose, 22 far-field earthquake records are employed for incremental dynamic analysis (IDA) of two railway arch bridges located at km 23 and 24 of the old railway of Tehran-Qom, respectively. Using the results of IDA, the capacities of performance levels, the mean annual frequency of exceeding the performance limits and levels of confidence of meeting seismic performance objectives, fragility curves, damage state probabilities, mean rate of a certain limit state per year, deaggregation of annual rate of limit states, and probability of reaching limit states over different life spans are obtained.

Reinforce-Optimization of regional network seismic based on connectivity reliability

Road traffic is an important access for emergency service and disaster relief after the earthquake. In this paper, a reinforce-optimization model for road network seismic is established in combination with the analysis results of the seismic reliability of road segment and the importance of road segment. The model is aimed at the lowest cost of reinforcement and optimization, ensuring the aseismic reliability of the road segment and the system to reach the lowest limited value after the reinforcement and optimization, and the highest reliability of the system is mainly considered after the reinforcement and optimization. The orthogonal enumeration method is used to solve the scheme which satisfies the model condition, and a design method for seismic reinforcement and optimization of road network is given. Finally, it confirms the feasibility of this method with an example.

Seismic reliability and loss assessment of RC frame structures with traditional and innovative masonry infills

This paper presents a performance-based earthquake engineering framework aimed at the assessment of fragility, reliability and expected annual loss (EAL) of reinforced concrete (RC) frames with traditional infills (TI) and innovative infills with sliding joints (SJ). The main concern is first related to the modification of seismic reliability levels achievable for structural and non-structural limit states by code conforming RC structures when explicitly considering the influence of masonry infills and the quantification of the gain associated with the eventual use of sliding-joint infills (SJI). Further, expected annual losses within the service life are evaluated and compared for the considered structural typologies. The framework is based on the determination of fragility via incremental dynamic analysis (IDA) in order to consider statistical response to input variability. The analyses are carried out on a reference multi-storey multi-bay 2D structure modeled in OpenSEES using a fiber-section approach. Specific structural and non-structural limit states are individuated for the TI and SJI frame structures. Seismic reliability is evaluated by integrating site hazard and structural fragilities resulting for each limit state. Expected annual loss assessment is performed by directly using period dependent hazard curves to determine annual rates of failures associated with limit states. Results show that similar probabilities of exceedance and loss rates are obtained by traditional infill and sliding-joint infill structures at life safety and collapse limit states. On the contrary significant convenience in using SJI is observed for operational and damage limit states in terms of reduced probability of occurrence and EAL.