Local Damage Index Research Articles

Overview of Damage Assessment of Structures

Different available analytical and experimental metho-dologies of local and global damage index (LDI and GDI) determination for bridges and buildings along with their mathematical expression are reviewed in this article. In the literature, impact of seismic loading and material deterioration due to ageing effects is the main focus to study the performance. Case studies for assessment of bridges and buildings are appended here to understand variation of damage index (DI) for various levels of seismicity. The utility of the proposed methods has been discussed in this case study. This article also includes progressive development, limita-tions and directions of future research on damage assessment of structures. Based on the extensive liter-ature review, the authors have critically analysed the pros and cons of the available methods. However, time-dependent damage assessment, damage estima-tion for various structural and non-structural compo-nents using different materials, variation of damage for different configurations of structures, and deterio-ration of roads and bridges are the probable future scope for research. In future, damage-based design considering multiple response parameters along with uncertain load characteristics such as seismic load, wind load, blast load, floods and accidental load could be considered to select allowable damage of structures that would help to understand and ensure the time-dependent safety, progressive phases of collapse and serviceability with high reliability satisfying smart structural requirements.

Seismic fragility assessment of optimally designed steel moment frames

This study is devoted to seismic performance assessment of optimally designed steel moment frames (SMFs) in the framework of performance-based design (PBD). The methodology presented in this work includes three phases. The first phase involves the optimization of SMFs by employing an efficient metaheuristic algorithm to meet the PBD requirements according to FEMA-350 code. Subsequently, the overall damage index (ODI) is calculated for the obtained optimal SMFs based on the Park-Ang local damage index (DIPA). In the second phase, incremental dynamic analysis (IDA) is conducted for the optimally designed SMFs and their fragility curves are derived and their collapse margin ratios (CMRs) are determined based on FEMA-P695. In the last phase, the fragility curves of the optimal SMFs are generated for different damage levels ranging from slight damage to collapse state and a new damage measure termed as damage margin ratio (DMR) is introduced to assess the damage-resistance capacity of the SMFs at the different damage levels. In order to illustrate the efficiency of the proposed methodology, three numerical examples of 3-, 6-, and 12-story SMFs are presented and the total cost of optimal SMFs, including initial and seismic damage costs, are determined. The numerical results demonstrate that the SMF with the best total cost has the best CMR, DMR, and degree of repairability.

Development of BP-based seismic behavior optimization of RC and steel frame structures

The present study develops and numerically verifies a new methodology for the seismic behavior enhancement of reinforced concrete (RC) and steel frames incorporating BP (Back Propagation) algorithm and performance-based estimation. The proposed optimization flow allows automatic correction of the assumed damage weighting coefficients of the components with a series of prepared local and global damage indices defined as required. On the basis of the revised coefficients, modification of the sectional dimensions and corresponding reinforcement ratio of a six-story RC frame is carried out. The exceeding probability of each limit state and the Mean Annual Frequency (MAF) are reduced, leading to a better safety margin of the RC structure. And the mechanical model of a user defined element of self-centering energy dissipation brace (SCEDB) is experimentally confirmed. Meanwhile, the installation strategy against the normal continuous arrangement of the SCEDBs in a nine-story benchmark steel frame is proposed as well. As a result, the story drift ratio and local damage of the steel frame are effectively decreased. The BP-based optimization results demonstrate that the seismic performance of the two structures has been improved without any cost increase, resulting in an effective structural optimization method.

RETRACTED ARTICLE: Estimation of Load-Induced Damage and Repair Cost in Post-Tensioned Concrete Rocking Walls

Post-tensioned concrete rocking walls might be used to avoid severe seismic damage at the base of structural walls, decrease residual drift, and lessen post-earthquake repair costs. The prediction of load-induced damage to the rocking wall resulting from seismic loading can provide an extremely valuable tool to evaluate the status and safety of structural concrete walls following earthquakes. In this study, the behavior and the damage state of monolithic, self-centering, rocking walls, as a new type of concrete rocking wall, are investigated. The nonlinear mechanical behavior of the wall is first modeled numerically, and subsequently the mechanical parameters from the numerical simulation are used to generate the local damage index. The results from the damage index model are compared with the full-scale test results, confirming the viability of the numerically based damage index method for estimating the seismically induced damage in concrete walls. Moreover, the estimated damage can be utilized as a qualitative and quantitative scale to assess the status of the wall following seismic loading events. Finally, an equation is proposed to estimate the repair cost based on the predicted damage state for the studied structural system.

Damage demand assessment of mainshock-damaged concrete gravity dams subjected to aftershocks

In China, the current seismic codes specify a single earthquake event as the design seismic load for concrete gravity dams. However, a large mainshock usually triggers numerous aftershocks in a short period. This paper assesses the effects of aftershocks on concrete gravity dam–reservoir–foundation systems and provides a quantitative description of the damage demands prior to and following the aftershocks. For this purpose, a set of 20 as-recorded mainshock–aftershock seismic sequences is considered in this study. The correlation between the ground motion characteristics of the as-recorded mainshocks and those of the aftershocks is examined. In order to identify the influence of the ground motion characteristics of aftershocks on the damage demands of the mainshock-damaged dams, the nonlinear behavior of the concrete gravity dams that are subjected to single seismic events and typical as-recorded seismic sequences is compared in terms of the structural damage, displacement response, and damage dissipated energy. A series of nonlinear dynamic analyses is performed to quantify the influence of aftershocks, which are selected by using different methods, on the damage demands of concrete gravity dam–reservoir–foundation systems in terms of the local and global damage indices. The results show that the aftershocks lead to an increase in the damage demands of the dam at the end of the seismic sequence when the concrete gravity dam is already damaged during the first individual seismic event and has not been repaired. In addition, the results also reveal that the repeated seismic sequences tend to underestimate the level of damage demands.

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.

Cyclic Crack Monitoring of a Reinforced Concrete Column under Simulated Pseudo-Dynamic Loading Using Piezoceramic-Based Smart Aggregates

Structural health monitoring is an important aspect of maintenance for bridge columns in areas of high seismic activity. In this project, recently developed piezoceramic-based transducers, known as smart aggregates (SA), were utilized to perform structural health monitoring of a reinforced concrete (RC) bridge column subjected to pseudo-dynamic loading. The SA-based approach has been previously verified for static and dynamic loading but never for pseudo-dynamic loading. Based on the developed SAs, an active-sensing approach was developed to perform real-time health status evaluation of the RC column during the loading procedure. The existence of cracks attenuated the stress wave transmission energy during the loading procedure and reduced the amplitudes of the signal received by SA sensors. To detect the crack evolution and evaluate the damage severity, a wavelet packet-based structural damage index was developed. Experimental results verified the effectiveness of the SAs in structural health monitoring of the RC column under pseudo-dynamic loading. In addition to monitoring the general severity of the damage, the local structural damage indices show potential to report the cyclic crack open-close phenomenon subjected to the pseudo-dynamic loading.

Increasing Seismic Energy Dissipation of Steel Moment Frames Using Reduced Web Section (RWS) Connection

Connections of steel moment frames are vulnerable to brittle failure. Providing a perforation near the beam-ends is suggested as a potential method to improve seismic behavior of these structures. This article presents a numerical study on the energy dissipation of steel moment connections with perforated beam. Models with elongated circular openings of different dimensions and location are analyzed and compared based on the global and local damage indices, predicted failure time and dissipated energy. Results show that an RWS connection with a proper opening size can develop reasonable inelastic deformations and provide an acceptable seismic improvement to moment-resisting frames.

A general definition of integrated strong motion duration and its effect on seismic demands of concrete gravity dams

Various duration definitions have been proposed to describe the effective strong motion duration based on a single component of ground motions. However, multi-component accelerograms are usually selected as the seismic excitations to evaluate the seismic performance of important infrastructures. Duration definitions able to consider the duration contributions from all components of ground motions are still lacking. In this paper, a general integrated duration definition for multi-component seismic excitations is proposed based on the existing concept of strong motion duration. According to the proposed definition, integrated bracketed duration, integrated uniform duration, and integrated significant duration are presented to measure durations for multi-component ground motions. Twenty as-recorded accelerograms with a broad range of durations are considered to investigate the correlation between integrated and single component durations. A series of nonlinear dynamic analyses are performed to quantify the influence of different integrated ground motion durations on several seismic demands (i.e. peak displacement, damage dissipation energy, and local damage index) of concrete gravity dam-reservoir-foundation systems. In addition, the results also reveal the effects of vertical seismic excitations on the seismic response of concrete gravity dams and emphasize the necessity to consider vertical motions in seismic performance assessment of such infrastructures.

Damage and fatigue quantification of RC structures

Different versions of a damage index (DI) along with a formulation to find the number of cycles at failure due to fatigue, applicable to reinforced concrete (RC) structures are presented. These are based on an energetic analysis method and applicable to both global and local levels. The required data can be found either from the numerical simulation of structures or from the experimental tests. A computer program has been developed to simulate numerically the nonlinear behavior of RC columns under cyclic loading. The proposed DI gives a regular distribution of structural damages up to failure and is validated by the results of the tests carried out on RC columns subjected to cyclic loading. In general, the local and global damage indices give approximately similar results, while each of them has its own advantages. The advantage of the implicit version of DI is that, it allows the comparison of the results with those of the monotonic loading case, while the explicit version makes it possible to estimate the number of loading cycles at failure due to fatigue, and the advantage of the simplified version is that; the monotonic loading data is not needed for the cyclic loading case.

Local Damage Indices of Frames Consisting of Composite Beams and RC Columns

The study is to propose the local damage indices of composite frame structures consisting of high-strength concrete columns confined by continuous compound spiral ties and steel beams (CCSTRCS), the local damage indices would lay a foundation for the study of the overall damage indices for composite CCSTRCS frame. The Mehanny damage model has been modified to predict the local damage behavior of composite CCSTRCS frames, it enlarges the scope of application for the composite structures compared with the previous work. The proposed model is validated by comparing with the present references. The study results suggest the different components corresponding to the extent of the damage and its damage index.

Seismic analyses of a RCC building under mainshock–aftershock seismic sequences

A large mainshock may trigger numerous aftershocks within a short period, and nuclear power plant (NPP) structures have the probability to be exposed to mainshock–aftershock seismic sequences. However, the researchers focused on seismic analyses of reinforced concrete containment (RCC) buildings under only mainshocks. The aim of this paper is to thoroughly investigate the dynamic responses of a RCC building under mainshock–aftershock seismic sequences. For that purpose, 10 as-recorded mainshock–aftershock seismic sequences with two horizontal components are considered in this study, and a typical three-dimensional RCC model subjected to the selected as-recorded seismic sequences is established. Peak ground accelerations (PGAs) of mainshocks equal to 0.3g (safe shutdown earthquake load-SSE load) are considered in this paper. The results indicate that aftershocks have a significant effect on the responses of the RCC in terms of maximum top accelerations, maximum top displacements and accumulated damage. Furthermore, in order to preserve the RCC from large damage under repeated earthquakes, local damage and global damage indices are suggested as limitations under only mainshocks.

Damage analysis of multi-ribbed wall structures under monotonic lateral loads

Multi-ribbed Wall Structures (MRWS) have been developed in recent years and has been increasingly used in China. However, there is no effective way to quantitatively assess the damage of MRWS subjected to lateral load yet. In this paper, a macro-damage model of MRWS is developed based on the damage theory. First, two types of elements, including fiber rigid frame and bar elements, are introduced to take into account material damage, and local damage index (LDI) is proposed for each type of the elements. Unlike traditional frame element, the innovative fiber rigid frame element can be applied for both axial force and biaxial bending and provides more accurate results. Second, a global damage index (GDI) of structure is derived using the energy theory. Third, the model is implemented in an in-house damage analysis program named MRCS-D, which is further used to experimentally study a MRWS subjected to a combined lateral and vertical loading. There is a good correlation between the numerical and test results. It is shown that the GDI developed in this paper can be effectively used to quantitatively evaluate the damage state and describe the damage progress of the MRWS.

Correlation between strong motion durations and damage measures of concrete gravity dams

Strong motion duration affects the cumulative damage of structures significantly. There are more than 30 different definitions of strong motion duration. This study describes numerically, the interdependency between several different definitions of strong motion duration and structural accumulated damage indices, and the aim is to determine the definitions of strong motion duration that exhibit the strongest influence on structural damages. For this purpose, 20 as-recorded accelerograms with a wide range of durations, which are modified to match a 5% damped target spectrum, are considered in this study, and several different definitions of strong motion duration, such as significant duration, bracketed duration and uniform duration are proposed for measuring these durations. On the other hand, nonlinear seismic analyses of concrete gravity dams subjected to earthquake motions with different strong motion durations are conducted according to the Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior. Peak displacement, local damage index, global damage index and damage energy dissipation are established for characterizing the influence of strong motion duration on the dynamic response of concrete gravity dams. The degree of the interrelationship between strong motion durations and damage measures is provided by correlation coefficients. Comparison of the correlation between the different durations of the ground motion and different damage measures reveals that strong motion durations calculated from different definitions have no significant influence on damage measure based on the peak displacement response of the dam, but are positively correlated to the accumulated damage measures such as the local damage index, global damage index and damage energy dissipation for events with similar response spectrum.

Numerical calibration of damage indices

In this study a numerical calibration procedure is proposed; while its application in some of the most widely accepted damage indices (DIs) used for quantifying the extent of damage in reinforced concrete structures is presented. In particular, without loss of generality of the applicability of the proposed procedure, the Park and Ang local damage index, its modified variant presented by Kunnath, Reinhorn and Lobo; the Chung, Meyer and Shinozuka local damage index; along with the maximum and final softening damage indices proposed by DiPasquale and Çakmak, are calibrated on the basis of the width of crack openings. The estimation of the crack width is performed by means of detailed modelling with hexahedral finite elements for the concrete and rod elements for the steel reinforcement; while due to the computing demands the databank of values for the damage indices under investigation is defined based on coarse models with beam–column elements. These two steps of the proposed procedure are based on the incremental dynamic analysis. Next, the statistical characteristics of the DIs are computed by means of horizontal statistics in conjunction with the maximum likelihood function method and an optimization algorithm.

Seismic Response Characteristics of Subway Station Structure

The dynamic Davidenkov model is used to model dynamic characteristics of soils, and plastic-damage model is used to model dynamic characteristics of station structure concrete. So that, considering the influence of soil-station structure interaction for 2D finite element analysis, the dynamic interaction of soil-station structure is modeled. The damage characteristics and energy response of station structure under seismic motion is analyzed. The result shows that damping energy and hysteretic energy are monotone increasing under ground motion, and the seismic characteristic has significant effect on the energy response of subway station structure. Furthermore, concentration effect of hysteretic energy of subway station structure is measured by hysteretic energy density. It is found that the hysteretic energy is the most centralized in the column, so the dynamic response of the columns is the maximum. Furthermore, the nonlinear damage evolution law of station structure is analyzed. The law of local and global damage index is consistent essentially, and the damage index is increased by the effect of accumulative deformation.

Local and microscopic damage indices applicable to RC structures and concretes subjected to cyclic loading

Local and microscopic damage indices applicable to RC structures and concretes subjected to cyclic loading

Effects of near-fault and far-fault ground motions on nonlinear dynamic response and seismic damage of concrete gravity dams

As the forward directivity and fling effect characteristics of the near-fault ground motions, seismic response of structures in the near field of a rupturing fault can be significantly different from those observed in the far field. The unique characteristics of the near-fault ground motions can cause considerable damage during an earthquake. This paper presents results of a study aimed at evaluating the near-fault and far-fault ground motion effects on nonlinear dynamic response and seismic damage of concrete gravity dams including dam-reservoir-foundation interaction. For this purpose, 10 as-recorded earthquake records which display ground motions with an apparent velocity pulse are selected to represent the near-fault ground motion characteristics. The earthquake ground motions recorded at the same site from other events that the epicenter far away from the site are employed as the far-fault ground motions. The Koyna gravity dam, which is selected as a numerical application, is subjected to a set of as-recorded near-fault and far-fault strong ground motion records. The Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is employed in nonlinear analysis. Nonlinear dynamic response and seismic damage analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. Both local and global damage indices are established as the response parameters. The results obtained from the analyses of the dam subjected to each fault effect are compared with each other. It is seen from the analysis results that the near-fault ground motions, which have significant influence on the dynamic response of dam–reservoir–foundation systems, have the potential to cause more severe damage to the dam body than far-fault ground motions.

Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences

A large mainshock may trigger numerous aftershocks within a short period, and large aftershocks have the potential to cause additional cumulative damage to structures. This paper investigates the effects and potential of aftershocks on the accumulated damage of concrete gravity dams. For that purpose, 30 as-recorded mainshock–aftershock seismic sequences are considered in this study, and a typical two-dimensional gravity dam model subjected to the selected as-recorded seismic sequences is modeled. A Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is selected for the concrete material. This model is used to evaluate the nonlinear dynamic response and the seismic damage process of Koyna dam under mainshock–aftershock seismic sequences. According to the characteristics of the cracking damage development, the local and global damage indices are both established to study the influence of strong aftershocks on the cumulative damage of concrete gravity dams. From the results of this investigation, it is found that the as-recorded sequences of ground motions have a significant effect on the accumulated damage and on the design of concrete gravity dams.

The effects of strong motion duration on the dynamic response and accumulated damage of concrete gravity dams

Strong motion duration is one of the challenging characteristics of ground motion, which affects the cumulative damage of structures significantly. Many researchers have conducted investigations related to the effects of strong motion duration on the response of building structures. However, the corresponding studies of concrete gravity dams are limited. In this paper, the effects of strong motion duration on the accumulated damage of concrete gravity dams are investigated. A Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is selected for the concrete material. This model is used to evaluate the nonlinear dynamic response and seismic damage process of Koyna dam during 1976 Koyna earthquake. Subsequently, the damage analyses of Koyna dam subjected to earthquake motions with different strong motion durations are performed. 20 as-recorded accelerograms, which are modified to match a 5% damped target spectrum, are considered in this study. Strong motion durations are obtained based on the definition of significant duration. According to the characteristics of the cracking damage development, both local and global damage indices are established as the response parameters. The results show that strong motion duration is positively correlated to the accumulated damage for events with similar response spectrum, and has significant influence on the cumulative damage of the dam. Longer duration will lead to greater accumulation damage to which aseismic design of the dam should be given attention.