Incremental Dynamic Analysis Method Research Articles

An efficient method for incorporating modeling uncertainties into collapse fragility of steel structures

Deterioration parameters that are commonly used to simulate nonlinear behavior of steel components were mainly calibrated based on the results from experiments on steel beams. Recently, the state of knowledge for deterioration behavior of steel columns has been improved by experimental and analytical studies on the wide-flange steel columns. These deteriorating characteristics are introduced as regression relationships in which the associated uncertainties are represented by the coefficient of variation (COV). Accounting for these uncertainties in estimating collapse fragility curves through the incremental dynamic analysis (IDA) and simulation-based reliability methods is impractical due to the large amount of required computational effort. In this study, two main goals are pursued. The first goal is comprehensive evaluation of the main, interaction, and quadratic effects of the modeling random variables on the collapse capacity of steel structures. The second goal is to propose an efficient approach to create response surface (RS), which in combination with the Monte Carlo (MC) sampling method will be used to incorporate modeling uncertainties into the collapse fragility. This efficiency will be achieved by employing screening design techniques to reduce the amount of analysis required to create a quadratic RS and also endurance time (ET) analysis as an efficient alternative nonlinear dynamic analysis method with less computational time to estimate the structural responses. In order to develop a reliable probabilistic model, the Bayesian model inference approach is applied to account for the uncertainties in the created model. The proposed procedure is performed with both IDA and ET methods on a prototype 5-story steel frame. Results indicate that collapse capacity is highly influenced by the strength modeling variables of beam as well as the ultimate rotation capacity of column components. In addition, ET method by a considerable reduction in the computational costs provides comparable responses with IDA in a probabilistic framework.

Comparative assessment of seismic collapse risk for non-ductile and ductile bridges: a case study in China

Risk assessment plays an important role in quantifying earthquake loss and has been widely used in the field of seismic engineering. However, current studies of the risk assessment rarely consider the different failure modes of piers (i.e., flexure failure, flexure-shear failure and shear failure), which will lead to an excessive estimation for the seismic performance and collapse safety of the reinforced concrete girder bridges. This paper focuses on studying the seismic behavior of bridges considering different failure modes and comparing the seismic collapse risk of the bridges with and without ductile detailing. The numerical analysis is performed in an open source finite element (FE) software framework, Open Sees. Nonlinear shear springs are introduced into the FE models of reinforced concrete (RC) columns to accommodate the shear and flexural-shear effect of the bridges. The accuracy of the FE models is validated by using the existing results of static cyclic-loading experiments. Case studies are conducted for two categories of the girder bridges, which are designed based on new and old seismic design criteria in China, respectively. The collapse fragility curves are developed by using the incremental dynamic analysis method, which considers the uncertainties of the ground-motion characteristics and the structural material parameters. Based on the seismic hazard curve of a designated region, a comparative assessment of the seismic collapse risk is performed regarding mean annual collapse rate for the non-ductile and ductile bridges. The main results of the paper are: (1) The FE model with the nonlinear shear spring provides an acceptably accurate solution for simulating the initial stiffness, shear failure point, strength degradation slope and residual shear strength of the RC columns; (2) The structural collapse safety is shown to be related not only to the collapse probability of the bridges but also to the occurring probability of the ground motion intensity exceeding a given threshold; (3) The mean annual collapse rate of the ductile girder bridges is significantly smaller than that of the non-ductile girder bridges. The results can be used as a reference to implement specific policies for appraising and mitigating the seismic risk of existing RC bridges.

Seismic fragility evaluation of a diagrid structure based on energy method

Diagrid structural systems have been brought into attention among architectures and engineers during recent years due to high structural efficiency and aesthetic potentials. Therefore, seismic behavior of diagrid structural systems under near and far-field earthquakes is investigated in this paper based on energy approach concepts in order to achieve a better understanding of their seismic behavior and the advantages of utilizing energy methods. For this aim, a 50-story building is modeled with a finite element method and its behavior is investigated through the Incremental Dynamic Analysis (IDA) method. Maximum story drifts, and plastic strain energy are studied as the engineering demand parameters (EDP). In addition, a fragility assessment method of the structure is presented with the aid of plastic strain energy and is compared to the fragility curves of maximum story drifts. This paper illustrates that the energy method can be applied to calculate the probability of the structure to exceed four performance levels including elastic, LS, CP and global instability. The results indicate that the fragility of the structure in far-field earthquakes is more than near-field ones in both maximum story drift and energy methods. Moreover, the fragility curves resulted from the energy method in LS and Instability levels have acceptable correspondence with the curves from the maximum story drift method, while the energy approach presents more conservative results in the CP level. It is demonstrated that the plastic strain energy can be considered as an appropriate parameter as EDP in the fragility evaluation of structures.

Seismic fragility assessment of equipment and support structure in a unit of a petrochemical plant

Petrochemical plants and industrial facilities have shown high vulnerability during the past earthquakes like Kobe (Japan, 1995), Izmit (Turkey, 1999), Gujarat (India, 2001), Tokachi-Oki (Japan, 2003) and other earthquakes. As more than 50% of the petrochemical and refineries in Iran are located on hazardous areas, it is absolutely essential to allocate a great deal of attention to such places. Apart from economic impacts, damage to such facilities may have considerable effects on peoples’ lives. Therefore, it is extremely vital to try to prevent natural disasters from damaging these highly regarded sites. For this reason, this research aims to investigate the seismic fragility of equipment and support structure in a unit that is located in Shiraz-Iran. In so doing, their impact on the overall vulnerability of petrochemical plant will be evaluated. As one of the common methods for this aim seismic risk assessment should be done, and IDA (incremental dynamic analysis) method_a probability method_is utilized. Seismic risk assessment in petrochemical plants plays a key role in making decisions for risk management strategies such as retrofit, etc. For this purpose, seismic risk assessment of equipment and support structure as a section of a petrochemical plant are evaluated. To fulfil the main goal of the research, in this project fragility curves are used to explain the seismic vulnerability of structure. In this method, failure modes are selected based on damages caused by past earthquakes. Shear failure of bolts have been considered as a failure mode of equipment and inter story drift ratio have been considered as failure mode of support structure. Peak ground acceleration is chosen as an earthquake intensity measure. In order to develop seismic fragility curves, created models are subjected to 40 ground motion records, each scaled to multiple levels of intensity to perform incremental dynamic analysis using Seismostruct software. Numerical results represent the significant influence of essential and hazardous equipment on the seismic fragility of the under-study unit of petrochemical plant. Final results show that the equipment that is located on fifth story is the most vulnerable component of the unit.

The effects of mainshock-aftershock in successive earthquakes on the response of RC moment-resisting frames considering the influence of the vertical seismic component

The sequential earthquakes and the vertical component of earthquakes can cause extensive damages to structures. In this study, by applying the incremental dynamic collapse analysis, considering the stability, final curvature and interstory drift, as performance criteria for the intact and damaged structures under the mainshock, the fragility curves are studied. The analyses have been performed for two reinforced concrete moment-resisting frames (RC-MRFs) of 6- and 10-story buildings by considering two scenarios of the horizontal component and the simultaneous effects of the horizontal and vertical components of the earthquakes for two structural conditions with and without damage. The provided fragility curves indicate the probability of the collapse of the structures due to the intensities of the earthquakes and the response of the structures, as well as the exceedance probability of the maximum interstory drifts of the damaged structures under the impact of aftershocks from first damage state (DS1) and second damage state (DS2) in terms of earthquakes intensities. In the DS1, the structure under the mainshock reaches a maximum interstory drift of 0.5%, and in the DS2; it reaches a maximum interstory drift of 0.8%. The results obtained using the incremental dynamic analysis (IDA) method indicate that the damages caused by the previous events and considering the vertical component of the earthquake have significant influences on the interstory drift related to the collapse of the structure. Considering the vertical and horizontal components of the earthquake, as well as the seismic sequence reduces the maximum interstory drift corresponding to the collapse of the structure. By applying the regression analysis some practical equations were submitted to be employed in similar cases as a guideline.

Seismic fragility analysis of nuclear power plant structure under far-field ground motions

This manuscript presents a fragility assessment to evaluate the effects of far-field earthquakes on the damage of the AP1000 nuclear island building (NIB), by using Incremental Dynamic Analysis (IDA) and Multiple Stripes Analysis (MSA) methods. Five categories of performance levels (PL), four limit states (LS) and the relative intensity measure (IM) having a high relation with the ground motion are defined to calculate the fragility of the AP1000 NIB under 15 earthquake sequences. A comparison of the results shows that the probabilities of minor damage, severe damage, and collapse damage for concrete are much higher than the reinforcement bar, which indicates that the fragility of concrete dominates the damage probability of the NIB. The fragility curves of the auxiliary building (AB) and shield building (SB) obtained by IDA and MSA are consistent with each other, but the distinction is mainly on the peak values or increasing ratio. Additionally, the probabilities of minor damage, moderate damage, severe damage and collapse damage of AB are less than the cases of SB. Lastly, the results also indicate that fragility curves are efficiently assessed and essential for risk assessments of the NIB.

Seismic fragility curves of steel structure industrial building using IDA method

Recent natural disaster events have caused damage to structures and led to loss of lives. Steel structure industrial building is one of the important structures that needs to be examined as these structures can have huge impact on the surrounding areas. Therefore, this study presents the fragility curves and performance curves of steel structure industrial building under earthquake loading. The structure consisted of beam, column, and bracing were modelled using three dimensional finite element modelling. The fragility curves were obtained for the structure, and the performance curves were developed based on lateral load, which was affected by the geometry of the building. Three records of far-field ground motion and three records of local ground motion were used for incremental dynamic analysis (IDA). The five levels of performance stated by FEMA-273, namely, operational phase (OP), immediate occupancy (IO), damage control (DC), life safety (LS), and collapse prevention (CP) were used as main guidelines to evaluate the structural performance. Results showed that, probability damage for operational phase, OP started at 0.19g and 5% of the structure analysed are expected to have immediate occupancy IO, indicating minor cracks to the structure at 0.4g PGA. Moreover, the performance response of the structure to the earthquake was obtained from the study.

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.

Performance of Concrete Gravity Dams with Height 50m and 75m based on Incremental Dynamic Analysis

This paper discusses the performance of concrete gravity dam with a height of 50m and 75m is studied by using the incremental dynamic analysis (IDA). The IDA curves were develop based on seven ground motions which fulfil the criteria of i) the distance of near field is less than 15km, (ii) the earthquake magnitude is greater than 5.5 and (iii) the PGA is equal to or greater than 0.15g. Seven of ground motions were converted to response spectrum and scaled according to the characteristic of the soil type for development of elastic response spectrum. Referring to Eurocode 8, elastic response spectrum was developed based on soil type B. By using IDA method, the limit states of the dam which are yielding and ultimate state are identified based on the cracking schemes. The displacement of yielding state for 50m height of dam is 14.60mm and 23.18mm for 75m height of dam. Meanwhile, the ultimate state is 23.18mm and 52.05mm for 50m and 75m height of dam respectively. The results show a greater damage occurred on higher dam and allow us to study the performance of dam with various height under seismic loadings.

Seismic fragility analysis of two-story ultra-high ductile cementitious composites frame without steel reinforcement

This article numerically studies the seismic vulnerability of the frame structure made of ultra-high ductile cementitious composites without longitudinal and transverse reinforcement. A non-linear finite element model is established with the help of Open System for Earthquake Engineering Simulation and calibrated by shaking table test results on an ultra-high ductile cementitious composite-RC frame whose seismic vulnerable parts were replaced by ultra-high ductile cementitious composites without steel reinforcement. Subsequently, an analysis on the structural seismic vulnerability is performed on pure ultra-high ductile cementitious composite frame structure based on the incremental dynamic analysis method. Finally, a seismic vulnerability matrix of the ultra-high ductile cementitious composite frame under various structural limit states is obtained from seismic fragility curves. Under the major earthquake of magnitude 7.5, the probability of ultra-high ductile cementitious composite frame structure under basically intact, slight damage, moderate damage, serious damage, and collapse is 14.2%, 48.1%, 31.7%, 5.3%, and 0.7%, respectively. The achieved results also demonstrate that the ultra-high ductile cementitious composite frame can satisfy the objectivity of “No collapsed under major earthquake” at least for major earthquakes of magnitude 8. It is demonstrated that the ultra-high ductile cementitious composite frame satisfies three-level performance objectivity stipulated in GB 50011-2010 and, thus, preliminarily verifying the feasibility for constructing structures just using high-performance concrete.

Seismic fragility analysis of bridge piers using methods of moment

In this paper, an efficient method is proposed for constructing the seismic fragility curves of bridge piers, in which the dynamical reliability assessment is developed from methods of moment. The main procedure for constructing seismic fragility curves consists of four steps. First, the non-stationary seismic acceleration process samples are simulated by the random function-spectrum representation model (RFSRM) with one elementary random variable at a given PGA value. Second, the first four moments (i.e., mean value, standard deviation, skewness and kurtosis) of extreme structural response are then evaluated from the extremum of each nonlinear time-history seismic response based on RFSRM. Third, the failure probability is then estimated by the fourth-moment reliability index, which is derived from an explicit fourth-moment transformation. Finally, the seismic fragility curves can be constructed by repeating the three steps and considering different PGA values and damage levels (i.e., slight, moderate, extensive, and complete). The efficiency and accuracy of the proposed methodology are demonstrated by a numerical example for constructing the fragility curves of a high-speed railway bridge pier in which the direct incremental dynamic analysis (IDA) method based on Monte Carlo simulations are employed for comparison.

Evaluation of deformation-based seismic performance of RECC frames based on IDA method

Engineered Cementitious Composites (ECC) is a typical High Performance Fiber Reinforced Cement-based Composite (HPFRCC), which possesses the characteristics of ultra-high tensile ductility and energy dissipation capacity. One of the potential applications of ECC is to replace conventional concrete in the seismic resistant structures. However, to date, the investigation on seismic performance of ECC at the structural level is still limited. This paper aims at evaluating the seismic performance of RECC frame on the basis of Performance-based Seismic Design (PBSD) concept and discussing the feasibility and practicability of applying ECC in structures for improving the seismic performance. The non-linear behavior of ECC material was simulated especially considering the strain hardening behavior in tension. By using the Incremental Dynamic Analysis (IDA) method, three types of frames, consisting of a normal RC frame, a RECC frame and an RECC/RC composite frame, were analyzed to evaluate the structural dynamic behavior of the frames. Comparative studies on the deformation limit states at five levels of seismic performance for these three different types of frames validated that RECC frames have superior deformation capacity comparing to traditional RC frames under high intensity earthquake. Comparison results also indicated that rationally applying ECC in key region of the structures can not only improve the seismic performance and deformation capacity of structures but also control the construction cost.

Fragility analysis of reticulated domes subjected to multiple earthquakes

In this paper, single-layer and double-layer reticulated domes were taken as two typical research objects. Through the dynamic time history analysis of reticulated domes in full process domain, log-linear regression was performed with a large number of example results to compare the degrees of correlation and efficiency about 11 common ground motion intensity measures, and PGA was selected as the most applicable one for fragility analysis of reticulated domes with aftershock influence. Then, considering that main shock usually caused structural damage, with incremental dynamic analysis method, fragility analysis of reticulated domes under multiple earthquakes was conducted from two aspects as follows. One part was main shock-aftershock sequence fragility analysis of intact structures. The other part was aftershock fragility analysis of damaged structures with four different damage levels caused by main shocks. Based on the fragility curves, the aftershock influence on fragility of reticulated domes and the aftershock collapse probability of damaged reticulated domes with four different damage levels caused by main shocks were investigated. It was found that when the damage level reached severe damage under main shocks, the aftershock collapse probability of reticulated domes would increase significantly. The results expanded the application scope of traditional fragility analysis in seismic engineering and realized the prediction and evaluation of seismic performance of reticulated domes under aftershocks.

The Influence of Material Hysteretic Property on Seismic Collapse-Resistant Capacity of RC Frame Structure

To study the influence of hysteretic behavior of material on the seismic collapse-resistant capacity of reinforced concrete frame structure, a 5-story plane frame was selected as the research object, the incremental dynamic analysis method was used to analyze the collapse vulnerability of the structure. According to the collapse probability curve, the seismic collapse-resistant capacity of the RC frame structure with different hysteresis parameters was quantitatively evaluated. The research shows that the concrete strength grade has the most significant influence on the seismic collapse- resistant capacity. Reducing the concrete strength degradation or increasing the strain hardening rate of the steel can slightly improve the seismic collapse-resistant capacity ability; The concrete hysteresis pinch and the steel hysteresis energy consumption has no effect on the seismic collapse-resistant capacity of the structure. The seismic collapse-resistant capacity of the structure is negatively correlated with the strength grade of the steel bar, but its impact is not obvious.

Developing a modified IDA-based methodology for investigation of influencing factors on seismic collapse risk of steel intermediate moment resisting frames

Incremental dynamic analysis (IDA) widely uses for the collapse risk assessment procedures of buildings. In this study, an IDA-based collapse risk assessment methodology is proposed, which employs a novel approach for detecting the near-collapse (NC) limit state. The proposed approach uses the modal pushover analysis results to calculate the maximum inter-story drift ratio of the structure. This value, which is used as the upper-bound limit in the IDA process, depends on the structural characteristics and global seismic responses of the structure. In this paper, steel mid-rise intermediate moment resisting frames (IMRFs) have selected as case studies, and their collapse risk parameters are evaluated by the suggested methodology. The composite action of a concrete floor slab and steel beams, and the interaction between the infill walls and the frames could change the collapse mechanism of the structure. In this study, the influences of the metal deck floor and autoclaved aerated concrete (AAC) masonry infill walls with uniform distribution are investigated on the seismic collapse risk of the IMRFs using the proposed methodology. The results demonstrate that the suggested modified IDA method can accurately discover the near-collapse limit state. Also, this method leads to much fewer steps and lower calculation costs rather than the current IDA method. Moreover, the results show that the concrete slab and the AAC infill walls can change the collapse parameters of the structure and should be considered in the analytical modeling and the collapse assessment process of the steel mid-rise intermediate moment resisting frames.

Seismic performance factors of RC frames with infilled walls based on APOA and IDA

Seismic performance factors are important parts of performance-based seismic design, and values of seismic performance factors are directly related to structural safety and economy. Six typical RC structures in high intensity region are designed according to the current Chinese Codes, and finite element models are built on OpenSees platform. The objectivity and accuracy of modeling methods are verified by existing experimental results. Values and rules of seismic performance factors are revealed by adaptive pushover analysis (APOA) and incremental dynamic analysis (IDA). Through comparison with values of design codes, values of the system overstrength factor, the ductility reduction factor, the response modification factor and the deflection amplification factor in this paper is reasonable, and this study provides theoretical reference for Chinese Codes. Analytical methods have important effect on seismic performance factors. Comparing with the IDA method, the APOA method underestimates seismic performance factors. Structural height has significant influence on seismic performance factors. Overstrength factor increases with increase of structural height but ductility reduction factor, response modification factor and deflection amplification factor decrease. Infilled walls increase seismic performance factors of RC frame with infilled walls. The effect of infilled walls on seismic performance factors decreases gradually with increase of structural height.

Assessing Seismic Collapse Safety and Retrofitting Low-Ductility RC Frame Structures on the Basis of the Acceptable Collapse Safety Margin in China

The relationship between the average annual collapse probability and collapse safety margin of structures is identified to evaluate structural collapse performance quantitatively. A method is then proposed to determine the acceptable collapse margin ratio (CMR) with a certain annual collapse probability. Two methods, namely adopting steel braces and enlarging column cross sections, are used to retrofit a four-story, low-ductility reinforced concrete (RC) frame structure. On the basis of the acceptable CMR, the seismic collapse resistance of the structure is assessed before and after strengthening. Furthermore, a four-story RC frame structure, which is designed in conformity to the minimum design criteria of the building code, is constructed. The incremental dynamic analysis method is used in consideration of collapse uncertainties. Results show that when the acceptable annual collapse probability is equal to 1.24 × 10−4, which is calculated using the collapse probability at maximum considered earthquake (5%, as proposed in CECS 392), the collapse safety margin of the four structures does not satisfy the seismic collapse resistance requirements with large collapse uncertainty. The structures that are retrofitted and designed in conformity to the code can satisfy the collapse safety margin requirements when the acceptable annual collapse probability is increased to 2 × 10−4. The comparison of the two retrofitting schemes used to improve the seismic collapse resistance of the structure indicates that the steel brace-retrofitting method is better than increasing the column section. This work is an important reference for the reinforcement of the seismic resistance of structures and for corresponding research on collapse resistance.

Seismic performance of the frame-skin structure based on 3D scanning technology

The research in this paper is based on a reinforcement project. The structure is covered by a skinned copper plate supported by the internal steel frame. The skin portion is mapped by 3D scanning technology and UAV (Unmanned Aerial Vehicle) photography. In this process, the skin portion is converted into point cloud data. On this basis, these data are converted into a surface for finite element simulation, which is combined with the internal steel frame to form an integral model. Based on the model, the seismic performance analysis of the structure was carried out by using the incremental dynamic analysis method. The results show that the design scheme of the internal steel frame satisfies the requirements of the seismic performance of the whole structure by the evaluation index of inter-layer displacement. The modeling method proposed in this paper can be used for the verification of existing structural reinforcement and transformation, based on which the bearing capacity and safety of the structure are evaluated.

Research on Seismic Vulnerability of Continuous Beam Bridges Based on Incremental Dynamic Analysis Method

The seismic vulnerability of highway continuous girder bridges is analyzed to provide theoretical basis for the study of multi-stage fortification and seismic design of such bridges. Based on the concept of performance seismic design, five performance levels of structures are determined, and the displacement ductility ratio of piers is taken as the performance quantitative index to calculate the damage limit values of bridges in different limit states. On this basis, IDA analysis method is used to calculate 20 subjects. Based on the reliability theory, logarithmic regression fitting analysis is carried out to obtain the seismic vulnerability curve. The theoretical vulnerability curve is indicated that the bridge has good comprehensive seismic performance. Under 0.3 g ground motion, the probability of minor damage, moderate damage and serious damage are 57.9%, 44.7% and 3.6% respectively. The comprehensive seismic performance of bridges and the probability of exceeding the damage status at all levels are reflected in the results, the guiding significance to analysis of the seismic performance of the entire traffic and the formulation of emergency rescue plans.

Seismic Risk Probability Assessment of Frame Structures Based on Incremental Dynamic Analysis

To assess the seismic risk probability of frameworks in different seismic fortification intensity zones in China, three fortification intensity framework models-specifically, 6 (0.05 g), 7 (0.1 g), and 8 (0.2 g)-were established as the research objects. The incremental dynamic analysis method was used to conduct a structure seismic fragility assessment, in which the fragility curves as well as the damage probabilities under certain peak ground accelerations were obtained. The risk probabilities of all the seismic damage levels of the frameworks in the next 50 years were calculated using the Monte Carlo method based on a study of the seismic hazard of different fortification intensity zones. The results indicate that, in the next 50 years, the risk probabilities of fortification intensity framework models 6, 7, and 8 exceeding “serious damage” were 1.92, 4.25, and 8.28%, respectively. Additionally, the risk probabilities of the models having a damage degree of “collapse” were 0.14, 0.43, and 1.07%, respectively. Based on the risk probability of the structure, the risk level is classified. This study forms the basis for the comprehensive evaluation of building seismic damage risk and can be used as a reference for the development of building seismic disaster prevention countermeasures.