Definition Of Limit States Research Articles

An advanced assessment framework for seismic resilience of railway continuous girder bridge with multiple spans considering 72h golden rescue requirements

Given the common sense that people in danger could survive with high probability in the golden rescue time of 72 h after earthquakes, railway bridges that are important transportation hubs and the lifelines for earthquake relief have been required to satisfy the necessities of safe passage and fast traffic for emergency response personnel in this critical period. To ensure the post-earthquake temporary functionality of the railway bridges to a sufficient safety level in golden rescue scenario, an advanced resilience assessment framework, including seismic resilience determinations for individual bridge components based on residual responses with respect to the plastic capacities originated from performance limit state definitions, definitions of three recovery levels considering repair efficiency for different recovery phases, and the series-parallel and parallel-serial system resilience models developed in temporal and spatial domains, was established. A commonly constructed irregular railway multi-span continuous girder bridge was chosen to verify the practicability of the aforementioned framework. The finite-element model of the illustrative bridge was developed taking abutment-girder interaction effects and nonlinear seismic behaviors of girder into account. Average spectral acceleration was taken as the intensity measure (IM) to consider the response variations originated from higher modes and natural period extension during earthquakes, and the site-matched and IM-based scaled ground records were adopted in the multiple stripe analysis to obtain instantaneous peak and residual seismic responses. Based on the framework, post-event resilience characteristics of bridge components were discussed, four recovery strategies were proposed for bridge system, and the seismic resilience of the illustrated bridge was assessed at system level. The research shows that the response contribution of fundamental dominant mode is only 64.37 %, indicating the dynamic response contributions from higher modes are considerable and the case bridge can show a strong irregularity during seismic events. Obvious nonlinear seismic behaviors occur to the superstructure where material strain in girder critical sections can increase to 0.00422 during earthquakes, which illustrates the inaccuracy of girder modeling only taking elastic behavior into consideration. Also, the prestress loss after earthquakes can reach 31.14 % and attention should be paid to the prestress recovery in subsequent repair works. Most components can satisfy the easy recovery resilience level, and the resilience is closely related to ground intensities and repair-waiting time; earthquake-induced functionality reduction can be 46.57 %, and resilience can increase by 25.35 % if the waiting time is shortened by 5 h. System resilience is influenced by the similar factors with component and varies in cases of different repair sequences due to the accumulation effect of repair-waiting time for various subsystems.

Data-Driven Damage State Assessment of RC Shear Walls with Experimental Validation

This paper introduces a probability-based damage state evaluation methodology for shear walls deriving from a data-driven calculation. A previously proposed damage quantification index, formulated in the time domain, which is capable of tracking damage progression based on the availability of structural monitoring data, is adopted here for the quantification of structural hysteresis damages. The probability of the structure lying in a specific damage state is determined on the basis of the derived damage index and the limit state definitions, yielding valuable information for postearthquake decisions. In this study, a database of the hysteretic behavior of 1,000 shear walls, considering different structural parameters, is generated utilizing OpenSees. Four limit states of seismic performance are defined based on material properties and in relation to the simulated stress and strain data. Accordingly, the exceeding probabilities of damage can be estimated by fitting statistical models to the damage index values grouped in terms of the axial load ratio. Followingly, an informative mapping, between the monitoring-derived damage index and postearthquake damage levels, is established considering structural uncertainty. Illustrative examples, including two shear walls subjected to cyclic loading and a seven-story shear wall slice subjected to a shaking table test, are investigated to show the capability and feasibility of the proposed performance evaluation method on damage state evaluation.

Definition of limit state of flexible pipe material in coiled tubing technology

Currently, the use of coiled tubing technologies has become widespread in drilling and oil production. The flexible pipes (FP) used in this technology undergo a complex of several impacts that accelerate the process of damage accumulation and thereby cause an accelerated process of seats of destruction formation, which often leads to accidents. Statistics show that the main reason for the destruction of the FP is the fatigue of the material loading and basically it is a cyclic bending according to the repeating stress cycle scheme. This loading scheme has a feature that is associated with the fact that tensile loads occur mainly in the convex zone of the pipe and compressive loads in the concave zone. Since the physical and mechanical properties of steels under stretch and compression are different, the process of damage and destruction accumulation during cyclic stretch and cyclic compression will have a different character. Information about the patterns of changes in the properties of the FP material allows to estimate the period of reaching the limit state and, thereby, prevent accidental destruction. In this regard, fatigue tests were carried out with a step-by-step measurement of magnetic characteristics that are structurally sensitive to the accumulation of fatigue damage. The determination of the stress amplitude for the FP fragment was determined by preliminary calculation in the ABAQUS PC. The test results showed that during cyclic stretch of the samples, the magnetic characteristics for assessing the limit state in the FP material were not informative. Notably in samples loaded with cyclic compression, the results of magnetic characteristics measuring (the resulting intensity and the gradient of the intensity of the constant magnetic field) showed sensitivity to the onset of the limit state. Based on the conducted studies, it is proposed to control the limit state of FP in the concave zone, where compressive loads mainly occur. These measurements allow us to estimate the value of the residual life of the FP material and to put this object out of operation in a timely manner, preventing accidental destruction.

Reliability-based seismic performance of masonry arch bridges

Seismic structural assessment of masonry arch bridges is essential due to their cultural, economic and strategic importance and vulnerability. A realistic and rigorous structural assessment is necessary in order to protect the bridges and use resources carefully. At this time, there are no standardised or widely accepted assessment procedures, and the performance criteria for masonry arch bridges are not available. This study presents an overarching reliability-based seismic assessment methodology based on analytical modelling, laboratory testing and probabilistic assessment. It investigates the performance criteria concept and proposes performance limit states. The methodology is applied to a historical masonry arch bridge in Turkey. To consider rigorously the uncertainties in material properties and seismic input, probabilistic nonlinear analyses are conducted using a detailed 3D finite element model. The results are combined with the proposed limit state definitions to generate the capacity and demand distributions. Both distributions are used in Monte Carlo simulation and First-Order Reliability Method (FORM) to estimate the probability of exceedance and reliability indexes for each limit state. The proposed probabilistic assessment methodology will be a useful approach to obtaining more reliable information about masonry arch bridges' expected seismic performance and for better-informed decision-making, especially when designing intervention actions and post-earthquake scenarios.

Shedding Light on the Effect of Uncertainties in the Seismic Fragility Analysis of Existing Concrete Dams

The seismic risk assessment of existing concrete gravity dams is of primary importance for our society because of the fundamental role of these infrastructures in the sustainability of a country. The seismic risk assessment of dams is a challenging task due to the lack of case histories, such as gravity dams’ seismic collapses, which hinders the definition of limit states, thus making the application of any conventional safety assessment approach difficult. Numerical models are then fundamental to predict the seismic behaviour of the complex dam-soil-reservoir interacting system, even though uncertainties strongly affect the results. These uncertainties, mainly related to mechanical parameters and variability of the seismic motion, are among the reasons that, so far, prevented the performance-based earthquake engineering approach from being applied to concrete dams. This paper discusses the main issues behind the application of the performance-based earthquake engineering to existing concrete dams, with particular emphasis on the fragility analysis. After a critical review of the most relevant studies on this topic, the analysis of an Italian concrete gravity dam is presented to show the effect of epistemic uncertainties on the calculation of seismic fragility curves. Finally, practical conclusions are derived to guide professionals to the reduction of epistemic uncertainties, and to the definition of reliable numerical models.

Stochastic load effect characterization of floating wind turbine support structures

Achieving substantial reductions in Levelized Cost of Energy (LCOE) of floating wind turbines (FWTs) requires robust reliability assessment that accounts for inherent design uncertainties. A key aspect of such reliability assessment is the definition of limit states. In this regard, load effects need to be evaluated accurately. This paper presents a computational framework for evaluating load effects on FWT support structures. The computed load effect is subsequently characterized. A high fidelity finite element model of the National Renewable Energy Laboratory (NREL) 5MW reference turbine mounted on the OC3-Hywind spar buoy was developed and validated for this purpose. The loads from fully coupled time domain aero-hydro-servo-elastic simulations are transferred for detailed finite element (FE) load effect computation in Abaqus. Matlab® and Python are used as the computational tools for automating the whole analysis from start to finish. The initial part of this study addresses the amount of run-in-time to be excluded from response statistics. Based on convergence studies carried out, recommendations are made for run-in-time to be excluded from response statistics. The maximum von Mises stress in the tower as a measure of yielding is the load effect investigated in this study.

Limit state design and methodologies in ice class rules for ships and standards for Arctic offshore structures

Sea ice poses hazards to ships and offshore structures which create challenges for designers. Designers have to take into account the ice actions resulting from the various ice conditions, interactions and operational scenarios which may occur during the lifetime of structures. In this paper the methodologies used in ship and offshore structure standards, such as the Finnish Swedish Ice Class Rules, International Association of Classification Societies Polar Class rules and ISO 19906, are considered with respect to Limit State Design principles and design air temperature definitions. The paper presents an overview of the design approach used in these standards and especially the criteria for the structural limit used. Case study examples based on ship measurements in the Baltic, as well as design air temperature data from the Russian Arctic, are used to highlight the different approaches and their implementation. The analysis shows clearly that explicit design ice action and structural limit are required for the rational basis in the future development of Limit State definitions in standards accounting for ice actions.

Seismic response of reinforced concrete frames at different damage levels

Performance-based seismic engineering is focused on the definition of limit states to represent different levels of damage, which can be described by material strains, drifts, displacements or even changes in dissipating properties and stiffness of the structure. This study presents a research plan to evaluate the behavior of reinforced concrete (RC) moment resistant frames at different performance levels established by the ASCE 41-06 seismic rehabilitation code. Sixteen RC plane moment frames with different span-to-depth ratios and three 3D RC frames were analyzed to evaluate their seismic behavior at different damage levels established by the ASCE 41-06. For each span-to-depth ratio, four different beam longitudinal reinforcement steel ratios were used that varied from 0.85 to 2.5% for the 2D frames. Nonlinear time history analyses of the frames were performed using scaled ground motions. The impact of different span-to-depth and reinforcement ratios on the damage levels was evaluated. Material strains, rotations and seismic hysteretic energy changes at different damage levels were studied.

Limit state equations for circular cross sections subjected to combined loading

Quick information about the capacity of any cross section for combined loading is very useful information at the early stages of engineering design. These combined loads can be pressure, axial force, bending moment and torsion, depending on application of cross section. Interaction formula based on limit loads is a very useful equation to estimate the capacity of any cross section for a combination of loads. For hollow circular cross section the complexity of interaction formulae depends on definition of limit state and type of loads. Interaction formulae for circular cross section with different limit state assumptions are easily available in literature for pressure, axial force and bending moment. This paper proposes interaction formulae for circular cross section with additional term of torsional moment at elastic limit load.

Probabilistic Performance Analysis of Existing Buildings under Earthquake Loading

A probabilistic methodology is proposed for the seismic performance analysis of existing buildings using global metrics to determine if the behavior conforms to a given limit state. The referred performance metrics are the mean annual frequency of the limit state, the corresponding expected loss associated to the repair of the building, and the corresponding number and type of mechanisms that occur. The consideration of these assessment parameters to control building performance widens the scope of the limit state definitions proposed in current codes. Therefore, current limit state descriptions were updated to establish adequate risk- and cost-related limit state definitions using the Eurocode 8 Part 3 proposals as a basis for discussion. The description of the proposed procedure is detailed and addresses its applicability for different limit states and its ability to include the uncertainty in the limit state capacities. An application involving the performance analysis of a reinforced concrete structure for several limit states is also presented and discussed.

Performance limits for structural walls: An analytical perspective

Recently proposed changes to modeling and acceptance criteria in seismic regulations for both flexure and shear dominated reinforced concrete structural walls suggest that a comprehensive examination is required for improved limit state definitions and their corresponding values. This study utilizes nonlinear finite element analysis to investigate the deformation measures defined in terms of plastic rotations and local concrete and steel strains at the extreme fiber of rectangular structural walls. Response of finite elements models were calculated by pushover analysis. We compare requirements in ASCE/SEI 41, Eurocode 8 (EC8-3) and the Turkish Seismic Code (TSC-07). It is concluded that the performance limits must be refined by introducing additional parameters. ASCE/SEI 41 limits are observed to be the most accurate yielding conservative results at all levels except low axial load levels. It is shown that neither EC8-3 nor TSC-07 specifies consistent deformation limits. TSC-07 suggests unconservative limits at all performance levels, and it appears to fall short of capturing the variation reflected in the calculated values. Likewise EC8-3 seems to fail to represent the variation in plastic rotation in contrast to several parameters employed in the calculation. More accurate plastic rotation limits are proposed.

Maintenance procedures and definition of limit states for exterior wood coatings

Maintenance procedures of different wood coating systems were studied in field exposure trials with coated balcony constructions. Maintenance coatings were applied on one half of each of the balcony parts after 18 months and assessed after 24 months of total exposure time. It was found that the opaque white coating systems were the most durable ones reaching long intervals of required maintenance. For systems with lower durability on the maintained surfaces further degradation of the coatings was prevented. Different characteristics were observed for film forming and non film forming semi-transparent varnishes. Definitions of a series of limit states for coating systems on wood were suggested including esthetical limits and three levels of durability limits. Film forming coatings can reach two durability limits, i.e. the maintenance interval and the renovation interval. For non film forming coatings there is only one limit state of coating durability where maintenance is needed. The third durability limit is related to the coated substrate, i.e. the wood component, by the onset of decay in wood.

Fragility-based assessment of typical mid-rise and low-rise RC buildings in Turkey

This paper focuses on the seismic fragility assessment of typical low-rise and mid-rise reinforced concrete (RC) buildings in Turkey by considering Düzce Damage database, which was compiled after the two devastating earthquakes in 1999 that affected the Marmara region. A set of fragility curves is developed by making use of the building characteristics in the database. The generated fragility curve set is referred as “reference” since it forms the basis of a parametric study. Then the influence of sampling techniques, sample size, type of hysteresis model and limit state definitions on the fragility curves is investigated. The results revealed that the uncertainty in capacity and degradation characteristics have a significant influence whereas the other investigated parameters do not seem to have an important role on the final fragility functions. In the last part of the study, the damage observed in Düzce buildings after 1999 earthquakes is estimated by using the generated fragility curves for low-rise and mid-rise RC frame buildings. Estimated damage distributions seem to be comparable with the actual damage data.

ReliabIlity analysis of containment building subjected to earthquake load using response surface method

The seismic safety of reinforced concrete containment building can be evaluated by probabilistic analysis considering randomness of earthquake, which is more rational than deterministic analysis. In the safety assessment of earthquake-resistant structures by the deterministic theory, it is not easy to consider the effects of random variables but the reliability theory and random vibration theory are useful to assess the seismic safety with considering random effects. The reliability assessment of reinforced concrete containment building subjected to earthquake load includes the structural analysis considering random variables such as load, resistance and analysis method, the definition of limit states and the reliability analysis. The reliability analysis procedure requires much time and labor and also needs to get the high confidence in results. In this study, random vibration analysis of containment building is performed with random variables as earthquake load, concrete compressive strength, modal damping ratio. The seismic responses of critical elements of structure are approximated at the most probable failure point by the response surface method. The response surface method helps to figure out the quantitative characteristics of structural response variability. And the limit state is defined as the failure surface of concrete under multi-axial stress, finally the limit state probability of failure can be obtained simply by first-order second moment method. The reliability analysis for the multiaxial strength limit state and the uniaxial strength limit state is performed and the results are compared with each other. This study concludes that the multiaxial failure criterion is a likely limit state to predict concrete failure strength under combined state of stresses and the reliability analysis results are compatible with the fact that the maximum compressive strength of concrete under biaxial compression state increases.

The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure

Starting from the premise that vulnerability curves are an indispensable ingredient of earthquake loss assessment, this paper focuses on establishing the relative effect of strong-motion variability and random structural parameters on the ensuing vulnerability curves. Moreover, the effect of the selection of statistical models used to present simulation results is studied. A three story ordinary moment resisting reinforced concrete frame, previously shake-table tested, is used as a basis for the fragility analysis. The analytical environment and the structural model are verified through comparison with shaking-table test results. The selection of ground motion sets, definition of limit states, statistical manipulation of simulation results, and the effect of material variability are investigated. No approximations are used to reduce the sample size or minimize the analytical effort, in order that attention is focused on the parameters under investigation. Notwithstanding the limited scope of the study, the results presented indicate that the effect of randomness in material response parameters is far less significant than the effect of strong-motion characteristics. Therefore, the importance of scrupulous selection and scaling of strong-motion and use of appropriate limit states and statistical models is emphasized.