Global damage indexes for the seismic performance assessement of RC structures

The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and global damage in civil engineering structures using the finite element method and a continuum damage model, is presented. The method is adequate for the computation of the limit load in reinforced concrete (RC) structures and for the prediction of the failure mechanisms. Details of the applied damage model are given together with a description of the finite element implementation and the procedure for computing the global damage parameters. Examples of applications of the methodology to the nonlinear analysis of a range of RC structures, are presented.

Current Science, 2019

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, limitations and directions of future research on damage assessment of structures. Based on the extensive literature review, the authors have critically analysed the pros and cons of the available methods. However, time-dependent damage assessment, damage estimation for various structural and non-structural components using different materials, variation of damage for different configurations of structures, and deterioration 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. Keywords: Bridges and buildings, damage index, loss assessment, seismicity. DAMAGE to structures is mainly caused by different environmental factors and ageing. Over the years various methods have been used for damage assessment. In this article, an overview of damage assessment is provided. In 1921, Griffith 1 had introduced fracture mechanics for brittle materials, but practically it has been mostly applied to metallic materials. Kaplan 2 had implemented fracture mechanics for concrete. However, several researchers have shown interest in this approach and excavated this area with proficiency. Damage assessment of a building could be easily done with several damage indices (DIs). DI of the structure could be determined either by balancing, demand and capacity of the structure, or by degradation of some structural property 3. In Lee and Fenves plastic damage model, DI was estimated from nonlinear regression of experimental column test data, concentrating on local tensile damage variables such as drift ratio and moment 4. Another DI was proposed based on cumulative member ductility considering limiting rotation capacity for steel, reinforced concrete (RC) columns, composite beams and composite steel-concrete connection sub-assemblies 5. Damage probability matrices are useful for decisive criteria for strengthening strategies and repairing buildings; Monte Carlo simulation with building strength parameters and ground motions are the variables for it 6. DI has been determined from the pushover curve containing initial and final stiffness 7. Damage could be assessed from the relationship between modal parameters-based GDI and local stiffness degradation along with the ageing effect on structures 8. Further, seismic vulnerability of damaged and undamaged RC bare frames, RC buildings with infill wall considering in-plane behaviour, and combined in-plane and out-of-plane nonlinear behaviour examined under main seismic shock as well as aftershock events 9. A damage curve was derived with the decrease of bending stiffness at the fractured section and DI estimated by strain responses of steel beams for pre-and post-earthquakes 10. Structural damage was presented by flexibility matrices with changes of modal parameters (modal damping, frequency and mode shapes) 11. However, irrespective of structure type and material, the ratio between initial resistance and reduced resistance capacity was calculated as general DI 12. Plastic damage of concrete with thermodynamics laws depending on continuum damage mechanics theory was applied on fibre RC beam column simulated in ABAQUS 13. Global damage index (GDI) of RC structure was estimated considering pseudo plastic hinges 14. Seismic damage of RC members for shear-flexure interaction in inelastic range was analysed, which showed a sound relationship between finite element model and experimental results 15. A structural DI was calculated with curvature and stiffness 16. Inclusion of correlative term 'stiffness' in the Park-Ang DI in Bayesi-an framework was introduced 17. Influence of different durations of aftershock was measured in terms of degradation of strength and stiffness of a structure termed as damage ratio 18. Structural damage was accurately detected using modified Cornwell indicator with genetic algorithm 19. DI also depends on hysteretic energy dissipated by a structural member and a drift ratio of 76 RC

2011

Nonlinear dynamic characteristics are appropriate indices to evaluate seismic behavior of damaged structures precisely. These characteristics reflect the effects of material properties, distribution of cracks and plastic hinges, construction quality and infill panels. Nonlinear characteristics may be extracted by some field tests like forced and/or ambient vibration methods. Recently a new damage index, based on nonlinear fundamental period of damaged structures, was represented by the authors to evaluate damage rate of reinforced concrete (RC) buildings after each moderate and/or severe earthquakes. This paper explains the procedure of finding the new period-based damage index and verifies the represented pattern of this damage index through some experimental data. This verification helps to trust and validate a pattern which estimates damage rates of RC buildings without modeling. As the proposed damage index is not depend on modeling, it could be more accurate than others, if it be calibrated using real data; because the modeling procedures which is depend on many known and unknown factors, could affect the results of analyses.

Canadian Journal of Civil Engineering, 2007

A procedure is presented for assessment of the performance of reinforced concrete bridge columns. Fourteen circular reinforced concrete bridge columns were tested under a constant axial load and a cyclically reversed horizontal load. A computer program, named RCAHEST (reinforced concrete analysis in higher evaluation system technology), was used to analyze these reinforced concrete structures. A damage index based on the predicted hysteretic behavior of a reinforced concrete bridge column was used. Damage indices aim to provide a means of quantifying numerically the performance level of reinforced concrete bridge columns under earthquake loading. The proposed numerical method for the performance assessment of reinforced concrete bridge columns was verified by comparison with the experimental results. Key words: assessment procedure, reinforced concrete bridge columns, damage index, hysteretic behavior, performance level.

International Journal of Civil Engineering, 2006

By identifying the damage index of a structure, in addition to a correct understanding from real behavior of the structure, the required criterion for strengthening would be given. Researchers have given many relations for determination of damage index but such relations have been based upon laboratory methods which challenge their usage in a broad term. In this paper two new methods are given for calculation of damage index. Surveying the first crack limit and total structure failure is based upon the formation of plastic joints in the first column and basic floor columns. To give a qualitative simple and functional damage index, the functional method was given in the form of a qualitative method with statistical analysis and collection of different views. Using this method is very simple and meantime offers suitable accuracy. With a numerical study on three models it was made clear that the difference of new method with amended method of Papadopolos in approximate 3%. This shows t...

1st Annual International Conference on Architecture and Civil Engineering (ACE 2013), 2013

Many reinforced concrete (RC) buildings around the world designed and built based on old codes may sustain certain level of damage or even collapse when subjected to earthquakes, as has been evident in recent earthquakes. Decision on strengthening versus demolition can be made based on evaluation of potential damage the building might suffer as a result of earthquake. In this study, the issues of identification, location and quantification of the damage imparted to a tested 3-storey RC frame designed based only for gravity loads are investigated and compared with those from experiment. After calibration, series of different seismic levels based on current seismic codes are applied to the frame and corresponding damage levels and failure mechanisms are obtained. The results demonstrate the potential of using damage index to quantitatively identify and locate the probable damage distribution in the building at a statistically expected earthquake.

Engineering Structures, 2001

This paper proposes a repairability index for damage assessment in reinforced concrete structural members. The procedure discussed in this paper differs from the standard methods in two aspects: the structural and damage analyses are coupled and it is based on the concepts of fracture and continuum damage mechanics. The relationship between the repairability index and the wellknown Park and Ang index is shown in some particular cases.

International Journal of Civil Engineering

This paper deals with both global and local versions of an energetic analytical model to quantify the damage caused to reinforced concrete (RC) structures under monotonic, cyclic, or fatigue loading. The proposed model closely represents the damage to structures, and presents a damage index (DI) formulation for the RC members. The model is based on the cumulative energy absorbed by the structure. The data required to apply the model can be obtained either from numerical simulation or from experimental test. A computer program has been developed to simulate numerically the response of RC members under cyclic loading. In the program, the non-linear behavior of the materials and the structure involved are taken into account. The proposed numerical simulation model was verified by comparison with practical tests undertaken by other researchers on over 20 full-scale RC columns. The comparison demonstrates that the model provides a realistic estimation of the damage of the RC structural members. The comparison between values of the

2013

Many vital reinforced concrete (RC) buildings experience moderate or severe earthquakes in their lifetime because they are located in hazardous areas. However, their importance cause to be evaluated by different types of damage functions. In these procedures, structures are usually modelled. These models neither correctly display the effects of the cracks that emerge and plastic hinges nor precisely consider the effects of asymmetric confi guration and infi ll panels. Furthermore, the actual nonlinear dynamic behaviour of existing buildings could be evaluated by assessing nonlinear dynamic characteristics such as the fundamental period. These dynamic characteristics, which are obtained by some fi eld tests such as forced and/ or ambient vibration methods, comprise the aforementioned effects. This paper offers a damage index (pattern) for seismic damage assessment of RC buildings based on the variation of the nonlinear fundamental period, which is obtained by fi eld tests. Finally, the seismic situation of existing RC buildings that have experienced an earthquake is precisely and expeditiously assessed by this new damage index.

2014

... obtained from dynamic characteristics of frames. Performance point represents the point with maximum lateral displacement of equivalent SDOF system, produced for seismic demand. ... Fig. 5. Evolution of the objective damage index of the case studied ...

IRJET, 2020

The main objective of this study is, evaluation damage index of reinforced concrete moment resisting frames by" NONLINEAR STATIC PROCEDURE" nonlinear static analysis includes the capacity spectrum method (CSM) that uses the intersection of the capacity (pushover) curve and a reduced response spectrum to estimate maximum displacement in terms of damage of building. Nonlinear static procedure is simple and practical method for static damage index. For this purpose, first some functions are derived to estimate damage to the structure using pushover analysis and then designed procedure is proposed. In this study damage function is estimated by using correlation between park-Ang. damage index (NLDD) and nonlinear static damage index (NLSD) which is based on the pushover analysis. For this purpose dynamic and static damage analysis are performed on several concrete frames subjected to various earthquake acceleration records. So the detail explanation is found in this study.

Bulletin of Earthquake Engineering, 2015

Few empirical seismic vulnerability curves exist for non-engineered reinforced concrete buildings in developing countries, and this is particularly true for the South Asian countries. This category of buildings is widespread and is highly vulnerable, since the buildings suffer from serious problems due to poor design and construction and are prone to collapse in moderate earthquakes. In this paper, building damage data from the Kashmir earthquake (2005), Pakistan are utilized to develop empirical vulnerability curves for the non-engineered reinforced concrete structures in the region. In order to develop empirical vulnerability curves, a damage probability matrix was defined and its elements corresponding to damage ratio of different damage states are used to evaluate the mean damage ratio. The developed curve show abrupt damage accumulation at relatively small values of peak ground acceleration. The findings of mean damage ratio as a function of peak ground acceleration are compared with the most relevant existing empirical and judgmental vulnerability curves to show the severity of damage in non-engineered reinforced concrete structures of that region and to validate for use in risk assessment studies.

International Journal of Engineering, 2021

In this study, multiple objectives on earthquake damage assessment procedures have been investigated. The Unified performance-based design (UPBD) method has been used to design the Reinforced Concrete (RC) frame shear wall building. First, the Damage index (DI) of the building has been estimated by using Park and Ang method. It has been found that this method is highly time-consuming. Hence, it is not found suitable for large scale investigation. Therefore, a new approach has been suggested to reduce the computational time and efforts in the case of complex structures in evaluating the global damage index (GDI). In this present study, the most three influencing parameters of the building have been considered to find the GDI. It has also been observed that the most damage occurs on the ground storey of the building. The suggested method efficiently calculates a reliable GDI that can assess building damage from small to large scale buildings.

Engineering Structures, 2012

The aspects of a robust and practical damage-based deterministic seismic design approach for reinforced concrete (RC) buildings have been discussed. The proposed performance-based design approach can be used for different structural systems by using fundamentals of reinforced concrete behavior and practical analyses. Several aspects of the proposed design approach need to be tuned including the selection of the damage measure and its quantification for a required performance level. Ductility damage index is a suitable damage measure for performance-based design of RC frame members. Currently, there is no systematic approach for selecting the bounds for a damage index according to the required performance level. The preset values provided in literature are based on engineering judgment and cannot be extended to RC members with all kinds of geometries and detailing. In this article, the correlation of damage level to concrete core and rebar strains is used to establish a procedure for determination of damage index intervals for different performance levels of RC plastic hinges. Then, the developed procedure is illustrated through numerical simulations for square and circular columns. The strain-consistent curvature ductility damage index values are determined for operational, immediate occupancy, life-safety, and collapse prevention performance levels used for seismic design of new columns.

Journal of Building Engineering, 2019

Damage progression indexes are widely used to evaluate the performance of structural elements in buildings and bridges subjected to seismic actions. Although the Park & Ang damage index is currently implemented in several computational tools, the index has not been calibrated for squat and thin reinforced concrete (RC) elements controlled by shear deformations. It has been observed that the equations originally proposed for the Park & Ang damage index are unsuited for these types of structural elements, which are characterized by a failure mode dominated by shear instead of flexural deformations. The index was evaluated in this study for squat, thin and lightly-reinforced concrete walls using experimental data from a program comprising monotonic and reversedcyclic load testing of 25 RC squat cantilever walls. The experimental program included walls, with and without openings, having height-to-length ratios equal to 0.5, 1.0 and 2.0. Full-scale wall thickness and clear height were 100 mm and 2.4 m, respectively. The specimens were built using three different types of concrete (normal-weight, lightweight and self-consolidating) with nominal compressive strength of 15 MPa. A novel formulation for the parameter β included in the Park & Ang damage index was proposed in this study using key variables of the wall specimens such as web reinforcement ratio and cumulative ductility. Comparison between the computed damage index and crack pattern evolution observed in wall specimens at different damage states demonstrated the ability of the model to numerically assess the damage of the wall specimens. Hence, this new formulation proposed for parameter β leads to a better estimation of damage for this particular type of elements when applying the broadly used Park & Ang damage index.