Due to the developments of computer science and technology in recent years, computer models and numerical simulations for large and complicated structures can be done. Among the vast information and results obtained from the analysis and simulations, the damage performance is of great importance since this damage might cause enormous losses for society and humanity, notably in cases of severe damage occurring. One of the most effective tools to handle the results about the damage performance of the structure is the damage index (DI) together with the damage states, which are used to correlate the damage indices with the damage that occurred in the actual structures. Numbers of damage indices proposed and developed rely on the fact that the damage causes noticeable changes in the structural and dynamic properties of the structural components or the whole structure. Therefore, this study presents a comprehensive review of the damage assessment of Reinforced Concrete (RC) structures. It presents step by step the development of the damage indices that are most widely used to estimate the performance of structural components in the structure and subsequently assess the damage degree of such these structures either based on the structural properties or dynamic properties of the structure. Also, several damage states have been introduced to estimate the performance level of the structure. Finally, case studies, methodologies, and applications on the damage assessment of RC structures are reviewed and presented.

Microcracks are initiated in the reinforced concrete elements due to shrinkage, hydration, etc., even if they have not been subjected to an external load. Subsequently, these microcracks propagated and led to macrocracks formulation during the structure life cycle due to various types of external loads and various types of structural shortcomings such as cracking, buckling, yielding of steel reinforcement, crushing of concrete. Structural damage and collapse might occur due to various types of external loads and, according to different structural faults, which might cause enormous losses for society and humanity, see

The structural damage can be defined as the degradation degree, which represents the structure capacity resisting and withstand further loadings since the failure of the structures might cause considerable losses. Therefore, performing the damage assessment and determining the structural damage degree became the main challenge for structural analysts. As a subsequent step for the damage assessment, the structural analysts can estimate the maximum loading capacity and the structure’s remaining capacity before reaching the failure limit. Accordingly, the structure safety can be assessed. Many researchers have studied the damage and safety performance of different RC structures from various perspectives [

The damage progression index has been widely used to investigate the performance of structural elements and assess the degree of damage for the structure. In seismic regions, damage indices have a fundamental role in decision-making about retrofit and maintenance [

Damage index at the structural level has been defined according to the main characteristic associated with the structure. The classification of the damage index has been done in four groups based on resistance demands (in the linear and nonlinear stages), ductility requirements, energy dissipation, and finally, the reduction of stiffness. It has been suggested by Krawinkler et al. [

The damage index based on mathematical functions, which depend accordingly on many structural parameters that determine the structural damage, has ranged from 0 to 1. Zero indicates that there is no damage in the structure and the structural behavior remains in the elastic stage. In contrast, the unit value of the damage index represents the failure state or collapse of the structure [

Significant and considerable efforts have been presented to describe the damage level of specific structures through damage indices which can assess and quantify the damage degree. For instance, Powell et al. [

Two different methodologies have been proposed and introduced to provide a reliable prediction for the damaged structure state. The first approach is based on the structural response and the change in the structural properties when the structure is subjected to a particular loading condition. In the case of reinforced concrete, several structural response parameters can numerically represent the degree of structural damage, including structure’s drift, displacement, strain, plastic dissipated energy, or a combination of these [

Kappos [

The following sections introduce the alternative methods for implementing these approaches and the formulae of different damage indices. Section 2 presents the damage assessment based on structural properties, where Section 3 presents the damage assessment based on modal analysis, Appendix 1.

The classification of damage indices based on structure properties has been introduced by several researchers [

The local damage indices have been divided and classified as follows:

Cumulative damage index in case of cyclic loading.

Non-cumulative damage index if no-cyclic loading exists.

These sets of damage indices depend on the number of loading and unloading cycles. It has been generally concluded that the degree of the damage for a structural element is not only dependent on the maximum displacement recorded under the earthquake effect but also on the number of load cycles and hysteretic energy absorbed [

Banon et al. [

Here

Miner [_{F}, and it has been expressed as follows:

Here

Plastic dissipated energy is considered one of several structural response parameters, which can numerically reflect the damage degree of the structure. Therefore, it has been used to define energy-based damage indices. The energy dissipated by the structure is supposed to be less than or equal to a threshold value before the structure reaches the collapse limit. Gosain et al. [

where

Hwang et al. [_{D,} and this damage index has been presented as follows:

Here

The stated damage indices in the previous sections have been developed and expressed based on the deformation or the energy dissipated individually depending on the structure response. However, the displacement index or displacement ductility index cannot give a reliable description for damage performance and the dynamic response of structures [

Here

where:

_{0} less than or equals to 0.2),

Cosenza et al. [

Kunnath et al. [

Here

According to the basic concept and original definition of the damage index, the damage index values range from 0 to 1.0. Therefore, the value of the damage index is supposed to be equal to 1.0 at the maximum deformation limit

Here

Another modification has been presented for the Park–Ang damage index regarding the elastic response. However, the value of the damage index is supposed to be zero in the elastic response indicating no damage occurred; the value of the original formula of the Park–Ang damage index or its modifications seems to be more than zero. To overcome this drawback, Bozorgnia et al.{[

Here μ refers to the displacement ductility ratio

Kunnath and the National Institute of Standards and Technology (US) have investigated the Park–Ang damage index and its association with the different values of displacement and the energy dissipated. This investigation resulted in some discoveries; one of these findings has been stated that at different deformation values, the same energy dissipated leads to different values of damage index and damage level. Based on these findings, Wang et al. [

Here

However, the structural members most likely would be subjected to three-dimensional loading during the seismic events,

Here

Here _{2,i}, θ_{3,i}) corresponding to the plastic hinge area’s axial load level. Both

Damage indices, mainly dependent on degradation in structure stiffness, have been widely explored [

Here

The damage in the structures is mainly occurred due to the plastic deformation, not the total deformation. Consequently, the inter-story drift damage index has been modified and presented in another formulation by subtracting the part related to elastic displacement from the maximum displacement and the plastic drift damage index

Here

In the set of the non-cumulative damage indices, another formula for the damage index called displacement ductility-based damage index based on the ductility of the member had been developed and introduced. Since the ductility tends to the structure ability towards plastic deformation without complete failure and degradation of structural strength, therefore it has been used as an indication of the structural damage, and ductility damage index has been widely used in seismic analysis to evaluate the seismic damage and the capacity of structures [

Here

It has been generally concluded that the structural element’s damage level depends on the maximum deformation and mainly depends on the number of load cycles and the energy dissipated [

Here

In the nonlinear analysis of structures subjected to static horizontal load, it is necessary to consider damage index, which incorporates stiffness degradation. Relying on this fact, Skærbæk et al. [

Here

According to the stiffness degradation, a new formula for the damage index has been proposed and presented [

Here

This section introduces the global damage indices used to assess the damage for the whole damaged structure. The global damage indices are most likely quantified by weighting the local indices of the different elements of a specific structure. The global damage indices have been classified as follows:

Strength-based global damage indices.

Weighted average global damage indices.

Powell et al. [

where

By adopting the same previous concept, Roufaiel et al. [

where

The most prevalent global damage indices that use the energy absorbed at different locations are the weighting function developed and presented by weighting and summing the local damage indices of the individual elements [

Here

where

However, severely damaged members might limit its overall stability; this has not been reflected in the averaging effect of the previous equation. Therefore, Bracci et al. [

Higher values of parameter b are used when more emphasis on the most severely damaged member is required.

Moreover, Amziane et al. [

Natural frequencies, damping ratios, modal participation factor, and mode shapes represent the most common modal properties obtained from the analytical solution of time histories, which can indicate the damage performance of the structures and have been used to calculate story damage index [

Based on the fact that modal damage assessment can be performed based on changes in these dynamic properties, Dipasquale et al. [

where

Since the structures suffering softening when damage increases and after a specific step, structures suffering severe softening and become irreparable. Therefore, several damage indices have been proposed to account for this softening and accounting for the fundamental period variation [

Here

The period degradation might be considered as an indication of the stiffness degradation. According to this concept, Hori et al. [

Here

As common knowledge, structure deterioration creates an increase in damping, especially in nonlinear material such as concrete, where damping enhancement is related to concrete cracking and yielding steel reinforcement. Therefore, the normalized damping ratio changes and then serves as a damage indicator [

where

Moreover, Wang et al. [

The damage states are usually used to estimate the structural damage level, and this has been done according to the values of the damage indices determined for the structure, as mentioned in published literature. Also, these damage states are used to correlate the damage indices with the damage that occurred in the actual structures. Therefore, the damage states have been classified according to the damage indices values. The damage index is a normalized quantity where the value of this quantity ranges from zero and 1.0. Zero value of the damage index represents the undamaged structure and mean that the structural behavior still in the elastic stage and did not suffer any damage, while the unit value of the damage index refers to the failure of the structure, and this means a part of the whole of the structure is collapsed. The damage states also can be classified according to the cost required for repairing the structure due to the occurred damage. Priestley [

Generally, the available damage states have been defined based on damage factors, engineering judgment, or experimental calibration. One of the limitations of the available damage states that most of these damage states have not been defined or classified according to the structural response parameters and have not considered the differences in the structure lateral load resisting system and nonstructural elements damage. Here are some of the damage states mentioned in the literature. One of the damage state definitions was related to Park–Ang damage indices [

D_{PA} |
Damage state | Comment |
---|---|---|

0 | No damage | – |

0~0.2 | Minor damage (MID) | Repairable |

0.2~0.4 | Moderate damage (MOD) | – |

0.4~1.0 | Strong damage (SD) | Almost unrepairable (repair cost is very high) |

>1.0 | Collapse damage (CD) | Total loss of the structure |

Also, Kunnath [

Damage levels | Damage index |
---|---|

No damage | 0~0.10 |

Light damage (MID) | 0.10~0.24 |

Moderate damage (MOD) | 0.25~0.4 |

Strong damage (SD) | 0.40~1.0 |

Collapse damage (CD) | >1.0 |

The degree of the damage can also be evaluated through the damage index by comparing the specific structural response parameters induced by the seismic event with the structural deformation capacity. However, the ductility demand and amount of dissipated hysteretic energy are effective parameters of the nonlinear response; they do not provide information on the degree of damage by themselves. Therefore, the structural available deformation capacity must be known to get a reliable estimation of the damage level of the structure. Ladjinovic et al. [

Damage state | Damage index | State of the structure |
---|---|---|

Minor damage (MID) | 0~0.2 | Serviceable |

Moderate damage (MO) | 0.2~0.5 | Repairable |

Severe damage (SD) | 0.5~1.0 | Irreparable |

Collapse damage (CD) | >1.0 | Total loss of the structure |

Since the story drift is considered one of the most influential and earliest tools to evaluate and assess structural damage, in many building codes [

Performance level | Damage state | Damage index (Drift) (%) |
---|---|---|

Immediate occupancy | No damage | <0.2 |

Damage Control (DC) | Minor Damage (MID) | <0.5 |

Life Safety (LS) | Moderate Damage (MOD) | <1.5 |

Collapse Prevention (CP) | Severe Damage (SD) | <2.5 |

Collapse | Collapse | >2.5 |

Cho et al. [

Zhang et al. [

Here

Zhai et al. [

where _{t 0.1}_{t 0.9}

Massumi et al. [

Based on this study, the developed damage index has been presented as follows:

where

Moreover, the deformation has been expressed as follows:

Here

The proposed damage pattern in this study also represented in a new format as follows:

The value of δ_{critical} indicates the initial elastic period; based on some references; the experimental elastic period can be replaced by the analytical elastic period in this newly developed damage formula since it slightly affected the results. Therefore, this new approach has great importance for structures whose initial elastic periods not available or cannot be determined experimentally.

Carrillo et al. [

The values of β calculated using the previous formula of

where

where

Moreover, much work has been performed to investigate and identify the seismic response of several RC structures subjected to near-fault ground motions [

Guo et al. [

The first term in the previous equations refers to the damage that occurred due to mainshock

Here

where

In this study, an overview of available damage assessment methods through damage indices is presented. Their formulation, features, limitations, and progressive development of these indices have also been introduced. According to this review, it can be concluded that:

These damage indices are considered an effective tool to quantify the degree of structural components’ damage or the overall structural damage.

Damage indices can practically be used in the evaluation of damage induced due to seismic events.

In this context, it should be mentioned that researchers widely use the well-known Park–Ang damage index to assess the damage because of its high accuracy and simplicity in application.

Park–Ang damage index is initially proposed for slender sections (slender beam and columns) where the flexural deformations dominated. However, it is rarely calibrated for shell structures or for the element in which shear deformation dominated instead of flexural deformations such as RC walls.