Local Damage Index Research Articles

Multidimensional Seismic Fragility Study of Intake Towers Based on Incremental Dynamic Analysis

Assessing the fragility of intake towers using a single damage index does not allow for accurate evaluation of the potential for structural damage under seismic conditions. In this study, based on the probabilistic seismic demand analysis method, the effects of ground motion intensity on maximum displacement, local damage index, and global damage index are considered, and the seismic fragility of an intake tower structure is analyzed. First, 10 natural ground motion records were selected from the ground motion database (PEER) and 2 artificial seismic waves were synthesized. These seismic waves were amplitude-modulated for incremental dynamic analysis (IDA). The trends of the IDA curves were analyzed to divide the performance levels of the intake tower structure. Furthermore, a two-dimensional fragility curve for the intake tower structure was plotted in this study. The maximum displacement in the direction of parallel flow and the damage index were taken into account in the two-dimensional fragility curve. The results show that, under the designed seismic acceleration, the two-dimensional fragility curve for the intake tower structure was lower than the one-dimensional curve. This indicates that the seismic design based on the one-dimensional performance index was unstable. This provides a theoretical reference for seismic optimization design and the strengthening of intake towers. Therefore, it is recommended to use multidimensional fragility analysis to study the seismic performance of intake tower structures in seismic design.

Enhanced high-resolution structural crack detection using hybrid interacting Particle-Kalman filter

Monitoring the health of large-scale infrastructure with the required precision necessitates high-dimensional support models and extensive instrumentation. However, in a model-based structural health monitoring (SHM) framework, the ability to localize damage is constrained by the discretization of the model. To enhance the resolution of discretization, dense instrumentation is essential to address the inherent challenges in solving the inverse problem. Yet, increasing dimensionality can introduce detection delays, a critical concern in SHM. Additionally, addressing uncertainties stemming from the model, measurements, or external factors is crucial for reliable real-world SHM. This study focuses on localized damages, such as cracks, where detection precision is paramount. To tackle these challenges, this study proposes an innovative hybrid interacting Particle-Kalman filter (h-IPKF)-based SHM approach that surpasses model discretization limitations for detection resolution. This approach employs two distinct indices for crack localization: global (GDI) and local (LDI) damage indices. GDI identifies the affected element using a coarsely discretized predictor model, while LDI precisely pinpoints the crack location within the element. This paper represents the crack as a massless rotational spring with deteriorated stiffness (γ) and parameterizes it using GDI, LDI, and γ. Subsequently, the h-IPKF framework is employed to estimate the crack parameters, capable of handling both continuous and discrete random variables, which is advantageous for addressing discrete variables like GDI. Extensive numerical and real validation tests on beam structures were conducted to assess the algorithm’s sensitivity to noise and damage severity, demonstrating its efficiency, promptness, and precision in detecting cracks within structures.

Combined Global Seismic Damage for 3D RC Buildings Using Recorded Floor-Displacement Data

ABSTRACT A novel method is proposed for predicting the combined global damage index through newly developed formulae utilizing recorded floor-displacement data, local and global capacity-based parameters for 3D RC buildings. Multilinear regression analysis is performed to develop the new formulae for predicting the global damage index obtained from modified Park and Ang-type 3D local damage indices. Further, explicit expressions for the global damage coefficients of the new formulae are developed as a function of structural properties and soil type for wider applicability of the formulae. The computed global damage indices are found to represent the damage states of RC buildings satisfactorily.

Probabilistic Assessment of Global Damage Index for Steel Moment-Resisting Frames Based on Local Responses

ABSTRACT A new scenario-based method is proposed to determine the performance range of structural systems. The advantage of this method is using inter-storey drift as a damage index, while exploiting local damage indices of the main structural members without the need for detailed analytical models and computationally expensive non-linear dynamic analyses. A new damage function is proposed by linking the local (plastic hinge rotations) and global (inter-storey drifts) damage levels. The accuracy of the proposed function is evaluated and compared with the indices in ASCE41–06, ATC-13, and HAZUS for a set of steel moment-resisting frames subjected to earthquakes of varying intensities.

Seismic performance of RC bent columns: Experimental, numerical and life-cycle cost analysis

Reinforced concrete (RC) bent structures are widely used in single-story industrial buildings, with a considerable portion of them located in high-intensity seismic areas. Therefore, it is significant to study the seismic performance of the RC bent column while keeping construction costs in mind. To evaluate the seismic performance of the RC bent column from an economic perspective, pseudo-static tests combined with construction cost analysis were first carried out on three RC bent columns designed according to different versions of Chinese codes. A numerical simulation method based on the extended finite element method (XFEM) for the RC bent column was then established and verified. Subsequently, the relationship between the local damage index related to the apparent damage characteristics and the overall damage index was established by conducting numerical analysis on RC bent columns with different design parameters. Based on the established relationship between the local and overall damage indexes, a calculation method for the residual bearing capacity based on apparent damage was developed. The results show that, when compared to the constructional requirements in the Chinese code for seismic design of industrial and civil buildings published in 1978 (TJ11–78), the constructional requirements in the Chinese code for seismic design of buildings published in 1989 (GBJ11–89) can effectively reduce the stress concentration at the column bottom and delay the formation of the plastic hinge with minimal cost increase, while the constructional requirements in the Chinese code for seismic design of buildings published in 2016 (GB50011–2010) can further effectively reduce the damage to the upper column. Besides, the constructional requirements in GBJ11–89 and GB50011–2010 can improve the energy dissipation and maximum bearing capacity of the RC bent column while decrease the cost/ductility coefficient by more than 5.0 %. The proposed calculation method can effectively predict the residual bearing capacity of earthquake-damaged RC bent columns by comparing the calculation results to the test results.

Impact of asymmetrical corrosion of piers on seismic fragility of ageing irregular concrete bridges

This article investigates the seismic fragility of ageing irregular multi-span reinforced concrete (RC) bridges. Different irregularity sources are considered, including: (i) substructure stiffness irregularity arising from the unequal-height piers, (ii) substructure stiffness irregularity arising from the spatially variable (asymmetrical) corrosion damage of piers and (iii) irregular distribution of effective tributary masses on piers of varying heights. To this end, a three-dimensional nonlinear finite element model is developed for multi-span RC bridges and verified against a large-scale shake table test results of a two-span concrete bridge specimen available in the literature. Nonlinear pushover, incremental dynamic and seismic fragility analyses are performed on three groups of two-span RC bridges with different configurations. Moreover, a time-dependent dimensionless local damage index is employed to evaluate the failure sequence and collapse probability of selected bridge layouts. The analysis results of the three studied irregularity sources show the considerable significance of spatially variable corrosion of bridge piers and substructure irregularity on the failure sequence of piers and seismic fragility of multi-span RC bridges. Furthermore, analysis outcomes show that uneven corrosion of piers triggers an unbalanced distribution of seismic ductility demands and irregular seismic response of equal-height multi-span RC bridges.

Seismic performance upgrade of substandard RC buildings with different structural systems using advanced retrofit techniques

There has been ongoing deliberation to arrive at promising retrofit strategies for pre-seismic code reinforced concrete (RC) structures. Against this backdrop, the research reported in this study puts forth solutions by focusing on advanced retrofit approaches for improving the seismic performance of substandard RC buildings with structural systems common to medium seismicity regions. High-performance reinforced concrete (HPRC) jacket application and self-centering energy dissipative (SCED) braces are the contemporary retrofit alternatives prioritized in this study to upgrade RC structural systems deficient in stiffness, strength and/or ductility. While these retrofit techniques were previously investigated at the member level, this study focuses on implementing thin-HPRC jacket applications, innovative outrigger-belt truss SCED bracing systems, and hybrid approaches on three-dimensional (3D) fiber-based numerical models representing substandard RC structures with different heights. Inelastic pushover analyses and multi-record dynamic response simulations are conducted to assess the retrofit alternatives by monitoring several local damage indices (LDIs) and the related global damage measure (GDM). The study confirms the effectiveness of retrofit measures for a moment-resisting frame building (MRF) deficient in lateral capacity and a high-rise shear wall (SW) building with insufficient global ductility. The presented systematic methodology accounts for the redistribution of seismic demands after retrofitting critical elements and enables selecting effective seismic retrofit solutions, namely SCED bracing system for MRF structure and hybrid retrofit for the high-rise SW building, using probabilistic seismic performance assessment along with cost and practical considerations.

Engineering demand parameters for the definition of the collapse limit state for code-conforming reinforced concrete buildings

This article discusses the main Engineering Demand Parameters (EDPs) found in the literature to define collapse of newly constructed reinforced concrete buildings. Currently, the definition of building collapse is still under debate, as different building codes and authors define them with different EDPs and even different values of the same EDPs.The EDPs can be defined locally (chord rotation, Local Damage Index, etc.) or globally (Inter-Story Drift Ratio, Roof Drift Ratio, Global Damage Index, etc.). A modified Global Damage Index that considers damage in both structural and non-structural elements is proposed in this paper The study compares the outcomes of some of these EDPs when applied to two case study moment-resisting reinforced concrete frames designed and analyzed in the framework of the RINTC — Reluis Project funded by the Italian Civil Protection Department (Ricci et al., 2018). One is a 6-story buildings (in Naples) the other a 9-story building (in L’Aquila). Nonlinear static and multiple-stripe dynamic analyses were carried out on 3D models with concentrated hinges. In addition to the above mentioned EDPs this study proposes and tests a new economic EDP that assumes that collapse is reached when the repair costs become larger than the reconstruction costs. Complete validation of the proposed economic EDP requires additional testing on code-conforming and, most importantly, on non-conforming older buildings, where brittle failures become an important issue.

A new endurance time analysis method for damage evaluation of high arch dams under the oblique incidence of mainshock-aftershock seismic sequences by wavelet decomposition

Pulse and oblique incidence features that may be generated by near-fault seismic sequences are neglected in current earthquake-resistant design codes for arch dams. To solve the shortcomings of endurance time analysis method which cannot consider near-fault pulse-like ground motions, this paper attempted to develop a new endurance time analysis method by wavelet decomposition to assess the differences in damage mechanisms of arch dams under the cross-stream and stream oblique incidences of near-fault seismic sequences. This study decomposed a typical near-fault earthquake into high-frequency and low-frequency ground motion through wavelet decomposition, which is used to perform several nonlinear dynamic analyses under different seismic intensities and seismic sequence incidence angles. On the basis of dynamic calculations, the local and global damage indices of the dam were presented, with a focus on the comparison of the damage distribution and damage volume ratios of arch dams under the action of single and sequence earthquakes and by analysing the damage mechanisms of arch dams under two diagonal incidence conditions at different peak accelerations. Then, the effects of different frequency components of ground motions on dam damage indices were compared, and finally, additional damage to the dam after the mainshock damage was quantified for various aftershocks. The proposed novel prediction model was used to estimate aftershock damage by considering mainshock damage. The numerical results indicate that the dam damage development is highly complex during original mainshock cross-stream and stream oblique incidences. This finding differs from dam damage that spread from the downstream face to the upstream face during the vertical incidence. The dam damage degree is smaller for the original mainshock stream oblique incidence than for the original mainshock cross-stream oblique incidence. The original aftershock induces stronger damage requirements on the damaged dam during the mainshock than during the high-frequency aftershock. Original and high-frequency seismic sequences with cross-stream and stream oblique incidences do not contribute to variations in dam damage patterns during aftershocks. Therefore, the influence of near-fault pulse impacts and the oblique incidence angle of seismic sequences need to be considered comprehensively in the seismic calculations and reinforcement studies of arch dams.

Damage detection in bridges under moving loads based on subspace projection residuals

This paper proposes a data-driven method using subspace projection residual of the responses to identify the damage locations in bridges subjected to moving loads. In this method, a moving window with a certain length determined by the sampling frequency and the fundamental frequency of the measured responses is used to cut out the acceleration responses of the bridge subjected to a moving vehicle. The characteristic subspaces of the windowed signals are subsequently extracted to calculate the local damage index using the subspace projection residual. When the window moves to the damage location, the orthogonality between the active subspace of the damaged state and the null subspace of the healthy state is invalid, which leads to a relatively large projection residual that can be used to localize the damage. To improve the reliability of the proposed approach, a one-side upper confidence limit is introduced. A simply supported beam bridge subjected to a moving mass is simulated to verify the effectiveness of the proposed method. Numerical results indicate that the proposed approach can accurately localize the single and multiple damages, even when the responses are smeared with a significant noise. Experimental tests conducted on a steel beam bridge model also demonstrate the performance and accuracy of the proposed approach. The results demonstrate that the proposed method can localize the damage even with a small number of sensors, indicating the method has a good and promising performance for practical engineering applications.

A combined global-local approach for delamination assessment of composites using vibrational frequencies and FBGs

In this paper, a combined global-local strategy was developed for structural health monitoring (SHM) of fiber reinforced polymer (FRP) composites to assess the internal delamination damage, which has combined vibrational frequency shifts as the global index and the fiber Bragg grating (FBG) wavelength shifts as the local index. The delamination detection was carried out in two steps. The first step was based on the global damage index, which is the changes in multiple modes of frequencies measured by a non-contact scanning laser Doppler vibrometer (SLDV) system. Machine learning (ML) algorithms including support vector machine (SVM) and extreme learning machine (ELM) algorithms were used to initially predict the delamination interface, location, and size through frequency shifts. Numerical and experimental verification results show that SVM has a higher prediction accuracy than ELM when only a small number of samples exist, and the classification of SVM is better than its regression function to be used in the prediction of discrete delamination interfaces. To verify the damaged area predicted by frequency changes and further update the delamination edges with better accuracy, the second step has taken the changes in the wavelength of multiple FBG sensors as the local damage index. Multistage loads were applied at equidistant positions of the FRP specimens to induce deformations and the wavelength shifts in FBGs were used to determine the boundary of delamination. The results showed that delamination in FRP composites can be assessed more precisely using the global-local two-step SHM strategy, which can compensate for the shortcomings of only using vibration-based or FBG-based monitoring techniques. Besides, the SVM algorithm showed excellent predictive performance in both steps and had great potential in delamination damage monitoring.

Multi-level performance-based design optimisation of steel frames with nonlinear viscous dampers

This paper presents a practical multi-level performance-based optimisation method of nonlinear viscous dampers (NVDs) for seismic retrofit of existing substandard steel frames. A Maxwell model is adopted to simulate the behaviour of the combined damper-supporting brace system, with a fractional power-law force–velocity relationship for the NVDs, while a distributed-plasticity fibre-based section approach is used to model the beam-column members thus incorporating the nonlinearity of the parent steel frame in the design process. The optimum height-wise distribution of the damping coefficients of NVDs satisfying given performance requirements is identified via a uniform damage distribution (UDD) design philosophy. The efficiency of the proposed multi-level performance-based design optimisation is illustrated through nonlinear time-history analysis of 3-, 7- and 12-storey steel frames under both artificial and natural spectrum-compatible earthquakes. Sensitivity analysis is performed to investigate the effects of initial height-wise damping distribution, convergence factor and uncertainty in design ground-motion prediction on the optimisation strategy. The efficiency of the final optimum design solution is also investigated by using drift-based, velocity-based, and energy-based UDD approaches to identify the most efficient performance index parameter for optimisation purposes. It is found that regardless of the selected performance parameter, the optimum damping distribution identified by the proposed methodology leads to frames exhibiting lower maximum inter-storey drift, local damage (maximum plastic rotation) and global damage index compared to an equal-cost uniform damping distribution. However, using drift-based UDD approach generally results in a better seismic performance. It is shown that the proposed UDD optimisation method can be efficiently used to satisfy multiple performance objectives at different intensity levels of the earthquake excitation, in line with performance-based design recommendations of current seismic codes. The proposed method is easy to implement for practical design purposes and represents a simple yet efficient tool for optimum seismic retrofit of steel frames with NVDs.

Numerical investigation of the influence of cross-sectional shape and corrosion damage on failure mechanisms of RC bridge piers under earthquake loading

The study presented in this paper describes the coupled influence of corrosion and cross-sectional shape on failure mechanism of reinforced concrete (RC) bridge piers subject to static and dynamic earthquake loading. To this end, two RC columns varied in cross-sectional shape and corrosion degree are considered. An advanced nonlinear finite element model, which accounts for the impact of corrosion on inelastic buckling and low-cycle fatigue degradation of reinforcing bars is employed. The proposed numerical models are then subjected to a series of monotonic pushover and incremental dynamic analyses. Using the analyses results, the failure mechanisms of the columns are compared at both material and component levels. Furthermore, using an existing model in the literature for uncorroded columns, a dimensionless corrosion dependent local damage index is developed to assess the seismic performance of the examined corroded RC columns. The proposed new damage index is validated against the nonlinear analyses results. It is concluded that the combined influence of corrosion damage and cross-sectional shape result in multiple failure mechanisms in corroded RC columns.

Reliability analysis and multi-level response modification factors for buckling restrained braced frames

This study aims to assess the seismic performance of buckling restrained braced frames (BRBFs) using a probabilistic approach and develop multi-level response modification factors for performance-based design of these systems. Unlike traditional seismic design methods, the proposed response modification factors can take into account the seismic conditions of the site as well as the target design performance level. An engineering damage parameter method (EDP-Based) is adopted for reliability analysis of 4, 8 and 12 storey BRBFs using systems of parallel and serial components. In general, the results demonstrate the high seismic reliability of BRBFs for high levels of earthquake intensity. Considering the axial strain of the brace core as the local damage index, it is shown that the studied models remain in performance levels higher than life safety under the design hazard level (return period of 475 years). The upper bond response modification factor for the life safety and collapse prevention performance levels is estimated to be around 8.4 and 10.0 with the corresponding intensities of 0.68 and 0.85, respectively. Based on the outcomes of this study, in general, using a response modification factor between 4 and 8 for seismic design of BRBFs would guaranty their adequate performance under both the design basis and maximum considered earthquake levels.

Damage Assessment of Reinforced Concrete-Framed Building Considering Multiple Demand Parameters in Indian Codal Provisions

This paper investigated multi-objective seismic damage assessment procedure. Primarily, it estimates damage index (DI) of reinforced concrete-framed residential buildings situated in seismic zone V as per IS-1893-2016 (0.36 g) in India. Three-dimensional DI has been estimated for a four-storey building by Park–Ang method. With the increase in the storey number, calculation of Park–Ang DI becomes tedious and more time-consuming procedure; therefore, this method is not suitable for large-scale damage investigation. To avoid the complexity, a simplified method has been proposed to estimate global damage index (GDI) of buildings easily. For this purpose, a four-storey residential building having plan aspect ratio 0.5, 0.75 and 1 has been analysed. In this study, the most influential parameters such as inter-storey drift, joint rotation and peak roof displacement have been combined to estimate GDI of structures directly. Based on this study, it has been observed that 0.893 times ground-storey DI (i.e. local DI) estimates similar Park–Ang GDI for a four-storey building. In this study, it has been observed that ground floor experiences maximum damage and top floor experiences least damage for all cases. The proposed approach effectively estimates reliable GDI that is useful for small- to large-scale damage assessment of buildings.

Nonlinear dynamic analysis and damage evaluation of hydraulic arched tunnels under mainshock–aftershock ground motion sequences

The significant life engineering failure and financial toll caused by mainshock–aftershock (MSAS) ground motion sequences have highlighted the importance of focusing on aftershocks. The current seismic design of hydraulic arched tunnels generally involves a dynamic analysis that assumes that a single seismic excitation or multiple single seismic excitations are applied. However, this assumption may underestimate the seismic response of hydraulic arched tunnels. The focus of this study is to evaluate the effect of both the mainshock excitation-induced nonlinear response and the MSAS excitation-induced nonlinear response of hydraulic arched tunnels. For this purpose, a numerical model is built in the commercial software ABAQUS, and it considers the fluid-structure-rock interaction system. Twenty-one as-recorded MSAS ground motion sequences are selected, and the seismic wave input method is verified before a nonlinear dynamic analysis is conducted. According to the damage patterns of tunnels under Wenchuan seismic excitation, the lining local damage index (LLDI) and the lining global damage index (LGDI) are established to assess the effect of single mainshock excitations and MSAS excitations on hydraulic arched tunnels. The results reveal that MSAS excitations can cause relatively severe cumulative damage and have a negative impact on the nonlinear dynamic response of the hydraulic arched tunnel compared to single mainshock excitations. Moreover, the aftershocks not only lead to an increase in the LGDI of the hydraulic arched tunnel at the end of the MSAS excitations but also enhance the LLDI of the arch section and sidewall section. In contrast, the aftershocks induce no significant change in the LLDI of the bottom section of the hydraulic arched tunnel. Thus, MSAS excitations should be considered in the seismic design of hydraulic arched tunnels.

Condition assessment of RC beams using artificial neural networks

In this study, an imaged-based methodology for condition assessment of Reinforced Concrete (RC) road bridge components is presented. The study is divided into experiments on RC rectangular beams and scaled (1:12) T-beams, validation of numerical models for T-beams and training of corresponding artificial neural networks (ANNs). In the experimental work, Digital Image Correlation (DIC) was used as a virtual sensor for data extraction. Rectangular RC beams of size 1800 mm × 150 mm × 200 mm and scaled (1:12) RC T-beams were tested under four-point flexural loading on a 100-ton dynamic testing machine. The experimental stress-strain curves obtained from the compression test on prism specimens at 28 days were used as input data for material model parameters in finite element model (FEM) software SAP2000. To assess the condition of structural components, a local damage index (LDI) was developed. Validation of FEM results with experimental results enables derivation of moment-curvature backbone curve for full-scale bridge girders, which enables further quantification of damage and residual moment capacity of full-scale bridges designed by Ministry of Road Transport and Highways (MoRTH). The correlation between the experiments, simulation and ANN predictions was found to be very satisfactory.

The second-order output spectrum-based method for fault localization in ring type structures

In this paper, the application of properties of the second-order output spectrum (SOOS) for nonlinear fault localization in ring type structures is studied. A more general ring type multiple-degree-of-freedom model, which regards nonlinear faults (bolt loosening or fatigue crack) and inherent material or boundary nonlinearities as nonlinear restoring forces, is utilized to describe the nonlinear behavior of ring type structures. Through harmonic excitation analysis and a novel local tuning approach, properties of the SOOS of nonlinear ring type structures are analyzed and clearly demonstrated with examples. Based on these properties, a novel SOOS-based method with a local damage index is proposed for nonlinear fault localization. The effectiveness and feasibility of this novel method are validated with multiple bolt loosening fault localization on a satellite-like structure in experiments and are further illustrated through comparisons with several existing methods.

Bridge condition monitoring under moving loads using two sensor measurements

A novel damage detection approach using only two sensors to detect the damage in beam bridges subjected to a moving vehicle is proposed in this article. In this approach, a moving mass is considered representing a vehicle moving across the bridge, and structural vibration responses at two locations are measured from a pair of sensors. A moving window is defined with a certain length determined by the sampling frequency and the fundamental frequency of the measured responses. The windowed pair time series extracted from these two measured responses are used to calculate the cross-correlation, which is used to define the local damage index. A simply supported beam bridge subjected to a moving mass is simulated to demonstrate the effectiveness and accuracy of the proposed approach. Numerical results indicate that the proposed approach can accurately identify the single and multiple damages using both displacement and acceleration responses, even when the responses are smeared with a significant noise. This indicates a good robustness to the noise effect. Experimental verifications on a laboratory beam bridge model demonstrate that the proposed approach can successfully identify the damage location using different selections of sensor pairs. Both the numerical and experimental results demonstrate that the new damage index is a good candidate for structural damage detection with very limited measurement information.

New proposed drift limit states for box-type structural systems considering local and global damage indices

The maximum displacement responses under the seismic motions are usually considered as an indicator for damage evaluation. It is obvious that appropriate selection of drifts corresponding to various damage levels plays an important role in safety and economy of a design project. Despite the extensive use of the box-type structural system in mass construction and housing industry, there is no special design requirement for this structural system. Due to three-dimensional behavior and interaction of intersecting walls and slabs, it is expected that this system presents different seismic performance in comparison to the conventional shear wall buildings. This study evaluates the overall and story failure mechanism as well as global and local damage indices in this structural system. Maximum allowable drift ratios of 0.45%, 0.65%, and 0.8% are suggested for the immediate occupancy, life safety, and collapse prevention levels, respectively. Moreover, a damage index based on the maximum relative inter-story drifts is proposed to assess the failure in the height domain. According to the assessments, the story and global failure occurring due to considerable damages in main load bearing elements reveals high importance of local damage indices in box-type structural system. Based on the results, it is concluded that the proposed maximum values for drifts in different standards and codes are not reliable. Considering the shear-control behavior and depending on the expected performance levels, the proposed local damage indices are considered as accurate control indicators for box-type structural system.