Nonlinear Response History Analysis Research Articles

Seismic design of concrete structures for damage control

Recent earthquakes have demonstrated that code-conforming modern (i.e. post-1970s) reinforced concrete (RC) buildings can satisfy life safety performance objectives. However, the accumulated earthquake damage in these modern buildings raised concerns about their performance in future events, contributing to widespread demolition and long-term closure of damaged buildings. The economic and environmental impacts associated with the demolition and long-term closure of modern buildings led to societal demands for improved design procedures to limit damage and shorten recovery time after earthquakes. To address societal demands, this study proposes a damage-control-oriented seismic design approach that targets functional recovery by ensuring structural component demands do not exceed the damage-control limit state (DLS) under design-level events. Herein, DLS is defined as the post-earthquake state beyond which the strength and deformation capacity of a structural component is compromised, and its performance in a future event cannot be relied upon without safety-critical repair. This study proposes a methodology to determine component deformation limits for the design of structures for damage control. Using the developed methodology, we propose component rotation limits for RC beams, columns, and walls. The seismic performance and capability of buildings designed using the proposed design approach to satisfy recovery-based performance objectives is demonstrated through nonlinear response history and recovery analyses (using the ATC-138 methodology) of four archetype frame buildings, designed per New Zealand standards to different beam deformation limits. The analyses show that building codes can achieve functional recovery using the proposed component deformation limits without the need for sophisticated recovery analyses.

Protection of Reinforced Concrete Columns from Pounding-Induced Effects in Adjacent Buildings

The pounding damage is one of the most common seismic damages observed after past earthquakes in adjacent reinforced concrete (RC) buildings having insufficient gap in-between. Particularly in highly populated regions, there are numerous adjacent RC buildings, in which pounding can cause severe damage or total collapse. Many previous reconnaissance reports following earthquakes have emphasized severe column damage due to pounding with the slab of adjacent building. In this paper, a retrofitting method is presented to reduce the seismic damage caused by pounding on existing RC structural elements in cases where collision is unavoidable. Pounding effects are investigated by using 4- and 7-story RC buildings with unequal floor elevations. As a retrofitting solution for pounding, steel columns and neoprene rubber pads are placed at the mid-height of the story so that the pounding takes place between the neighboring slab and added steel columns instead of existing RC columns. The mid-column pounding of existing RC buildings with and without retrofitting are numerically investigated. In the numerical model, buildings are connected by link elements to reproduce the pounding in-between. Nonlinear response history analyses are performed using 11 different real ground-motion records. Pounding forces, peak floor accelerations, inter-story drift ratios, story shear force distributions, and plastic hinge distributions are obtained and compared for each of the pounding conditions. The analysis results revealed that the proposed retrofitting method protects the existing RC columns from brittle type of shear failure and reduces the destructive effects of pounding.

Lateral load response and collapse probability of reinforced concrete shear walls retrofitted for repairability

AbstractThis paper demonstrates the efficacy of a new reinforced concrete shear wall seismic retrofit method through a series of nonlinear static and incremental dynamic analyses. Unlike traditional retrofit methods, the method investigated aims to convert conventional walls into self‐centering walls whose behavior is governed by rocking and flexure. The retrofit involves creating a cold joint at the foundation–wall interface, cutting some reinforcing bars to allow rocking, adding external post‐tensioning to enable self‐centering, and externally confining wall toes to prevent concrete crushing. The retrofit was applied to two building archetypes, each with two different shear wall designs. The four walls were retrofitted by varying retrofit parameters (portion of the vertical reinforcement bars cut, and external post‐tensioning amount). Nonlinear static and nonlinear response history analyses were performed using experimentally validated, computationally efficient models that simulate walls with fiber‐based beam–column elements. Incremental dynamic analysis was used to create collapse fragility functions for pre‐ and post‐retrofit walls. The results show that the retrofit is effective when some vertical reinforcement bars are left uncut across the foundation–wall interface. The retrofit is more effective for walls with vertical reinforcement distributed across cross‐section as compared to walls with reinforcement concentrated near boundary elements and for walls with structurally efficient amounts of reinforcement as compared to walls with higher amounts of reinforcement. This is attributed to the larger amount of reinforcement bars cut in walls with concentrated reinforcement layouts or heavy reinforcement amounts, leading to a larger loss of strength, recovery of which requires larger amounts of post‐tensioning.

A comparative study on the seismic performance of long span Engineered Cementitious Composite (ECC) structures

The strain hardening fiber reinforced concrete—generally known as the Engineered Cementitious Composite (ECC)—has rapidly gained the attention of researchers in recent years. However, most of the research on ECC is limited to material and member level, leaving a gap in the understanding of its behavior at the structural scale. Therefore, this study investigates the global seismic response of ECC structures and compares their performance with conventional reinforced concrete (RC) structures. For this purpose, a case study long span building structure (an aircraft hangar having a span length of 40 m) is selected. Under the design-level gravity and lateral loads, its members are separately designed using the conventional RC and ECC. It is observed that for ECC members, the requirement of longitudinal steel is reduced by 30% when compared with the conventional RC members. Similarly, owing to an improved tensile behavior, the ECC members also exhibited a higher shear capacity than RC members, resulting in a significant reduction in the requirement of transverse reinforcement. The detailed inelastic finite element models for both design cases (RC and ECC) were subjected to the pushover analysis and nonlinear response history analysis (NLRHA) to assess their seismic performance. It is observed that (in terms of local and global seismic demands, structural damage, and ductile behavior) the performance of the ECC structure is significantly improved when compared to the conventional RC structure. The comparative cost analysis showed a reduction of 11.9% in the overall material cost of the ECC structure as compared to RC. These results show that ECC can be effectively used at the full structural level as an economic solution to ensure the ductile response and superior seismic performance.

The role of masonry infills on the interstory drift demand of reinforced concrete frames

Most frame buildings, especially those with shear-type moment resistance frames, are affected by masonry infill panels, which change the mechanical properties of whole systems in a big way. In turn, seismic performance varies depending on the infill panel and frame interactions. In conventional structural design practice, such interaction has been overlooked. This study looks at the range of local displacement demands in shear-type frames with and without infill panels. Generic frames are developed by tuning the story stiffness and mass to produce a reasonable period range between 0.2 and 2.0 s. The masonry infill panels are simulated through equivalent diagonal struts. A Bouc–Wen-based hysteretic model is applied to incorporate the post-yielding hysteresis degradations of both columns and masonry panels. The hysteresis loop control parameter values are also given for incorporating masonry infill properties. The correlation analysis between the strength and stiffness of RC frames and masonry infills is supplied as an instrument for calibrating the hysteretic model. In the collection of records, there are a lot of near-fault ground motions, which puts a lot of seismic demands on the buildings. The modification factors via regression analysis are proposed using over 1254 nonlinear response history analyses. This modification factor is figured out by looking at the difference between the mean drift spectrum for a set of generic frames that are both bare and filled. The nonlinear analysis shows that residual drift demands can be reduced in the case of panel effects that exist for masonry-infilled mid-rise RC shear-type frames.

Influence of near‐field ground motions with fling‐step and forward‐directivity characteristics on seismic response of stilted buildings in mountainous area

SummaryNear‐field ground motions with fling‐step and forward‐directivity characteristics contain large‐amplitude pulses in velocity history, causing severe damage to stilted buildings in mountainous areas. In this study, three groups of 20 near‐field ground motions with fling‐step and forward‐directivity characteristics and 10 far‐field ground motions were selected as seismic inputs. Nonlinear response history analysis (NLRHA) was performed on plane finite element models of two seven‐story stilted frame structures, one with steel braces in the stilted story and the other without steel braces in the slope direction. Structural seismic response obtained from NLRHA was discussed in terms of inter‐story drift ratio (IDR) and peak floor acceleration (PFA). In addition, damage to two structures was assessed using the modified Park–Huang damage model. The results show that stilted structures exhibit greater inter‐story ratios and damage index values under near‐field ground motions with fling‐step characteristics and forward‐directivity characteristics than far‐field ground motions, where the stilted story has the highest amplification ratio in both IDR and damage index among floors. Designers should pay sufficient attention to the influence of ground motions with fling‐step and forward‐directivity characteristics on seismic demands and damage to stilted structures. The peak inter‐story ratio and damage index of stilted structures with steel braces were significantly lower than that of stilted structures without braces, proving the validation of setting steel braces on reducing the seismic demands of stilted structures and improving structural seismic safety. Additional NLRHA performed using artificial pulses shows that the seismic response of stilted buildings is related to pulse periods of near‐field ground motions and the greatest seismic demands and damage are obtained when the pulse period is 1.5–1.6 times the fundamental period of the stilted building.

Ductility demands for stiffness-degrading SDOF systems under pulse-like ground motions of the 2023 Pazarcık (Kahramanmaraş) earthquake

This paper investigates the inelastic displacement ratios (IDRs) and displacement ductility demands of a wide range of single-degree-of-freedom (SDOF) systems subjected to pulse-like ground motions (GMs) of the 2023 Pazarcık (Kahramanmaraş) earthquake. A set of twenty-seven GMs characterized as pulse-like are utilized in the study. As-recorded velocity time histories of horizontal components are rotated over 90° at a step of 1° to attain the waveform with the largest peak ground velocity (PGV) over all horizontal orientations. Inelastic displacement ratio and displacement ductility spectra are computed through nonlinear response history analysis (RHA). Local amplifications of both spectra are observed at some periods. The results of this study show that large inelastic displacement and ductility demands are imposed on certain reinforced concrete (RC) structures. Finally, predictive models of the mean inelastic displacement ratio and mean ductility demand spectra (DDS) are developed based on the Gauss–Newton algorithm (GNA). The model provides a strong correlation between the computed and the estimated data, and sufficient convergence criteria. The results of this study collectively emphasize the necessity of integrating pulse-like GMs into future revisions of earthquake codes.

Numerical simulation of the 2010 4-story reinforced concrete structure tested on the E-defense shake table

Due to advancements in computational tools, performing a full nonlinear response history analysis of structures at the system level using detailed numerical simulations of components has become less demanding, even on standard personal computers. However, the modelling approaches need to be calibrated and verified against experimental measurements to ensure the accuracy of the system-level predictions. In this study, an advanced numerical simulation method is used to predict the 3D nonlinear dynamic response of a four-story reinforced concrete building tested at E-Defense shake table. The structure is modelled in the finite element analysis programme DIANA, using a previously developed and validated approach to predict the failure modes of doubly reinforced walls with confined boundary regions. Curved shell elements are used to model the walls and slabs, and the reinforcement is modelled using embedded bar elements. The frame elements are modelled using beam elements with the effect of confinement on the concrete behaviour represented in the material constitutive model. The numerical versus experimental response comparison is conducted at both local and global levels. For local levels, the base shear versus top displacement curves, strain gradients as well as the crack pattern predicted by the numerical model are compared with the test measurements. The inter-story drift response history is considered as the metric for the global level assessment. The effects of different modelling parameters on the accuracy of predictions are also investigated.

Improved response spectrum analysis procedure for an adaptive variable friction pendulum isolated structure considering frictional dependency

The effectiveness of the conventional friction pendulum isolator (FPI) is limited in complex geographical environments and unpredictable earthquake events due to its complex frictional properties and the requirement for a unified setup target. With a view to addressing the aforementioned issues, in conjunction with an adaptive variable friction pendulum isolator (AVFPI), a simple and practical mechanical model is proposed. After applying the mechanical model with a friction-dependent influence model, an improved response spectrum analysis procedure (IRS) is proposed for variable friction pendulum isolation systems. Notably, the proposed procedure allows for the consideration of the effects of variations in velocity, temperature, and pressure on the friction characteristics without the necessity for nonlinear response history analysis (NRHA). The procedure commences with obtaining a numerical model of friction dependency through friction material examinations, then proceeds to verifying the reliability of both the friction dependency and mechanical model through prototype tests of AVFPIs. The following study presents a proposed correction method that depends on random vibration theory to establish a functional relationship between the pseudo-velocity spectrum and the velocity spectrum. Additionally, an association is established between the peak velocity and the generation of frictional heat. Finally, the procedure is evaluated based on the results of an NRHA that takes friction dependence into account through a numerically variable friction pendulum isolation system. The results of the study indicate that the IRS provides a more accurate and secure assessment of the isolator displacement at various temperatures than the response spectrum method, which does not account for the influence of frictional dependency. The failure to consider the influence of friction dependency in high-temperature environments produces an underestimation of isolator slip displacement and a subsequent increase in failure rates. The Polytetrafluoroethylene (PTFE) friction materials that are currently in widespread use exhibit a strong correlation with friction dependence and, as a consequence, cause relatively large displacements at temperatures that are both low and high. The results of this study present an opportunity to expand how response spectrum analysis techniques can be applied to friction pendulum isolation systems.

Seismic performance assessment of post-tensioned CLT shear wall buildings with buckling-restrained axial fuses

Post-tensioned cross-laminated timber (PT-CLT) walls have been demonstrated to be a low-damage seismic force-resisting system (SFRS) due to their self-centering capability. However, there is still a need to examine the seismic performance of such SFRS in high-seismic risk zones. This study evaluates the seismic performance of 6-, 9-, and 12-storey PT-CLT shear wall buildings in Vancouver, Canada, equipped with buckling-restrained axial fuses. The prototype buildings were designed using the displacement-based design method, and the assessment considered the most recent seismic hazard model provided in the 2020 National Building Code of Canada. To conduct nonlinear response history analysis (NLRHA) and incremental dynamic analysis (IDA), numerical models were developed in OpenSeesPy and calibrated based on component- and system-level experimental tests. The NLRHA and IDA results demonstrate that all the studied buildings have adequate collapse margin ratios, with less than a 10% chance of collapsing at the maximum considered earthquakes.

Seismic behaviour of self-centring hybrid steel frames equipped with SMA plates under mainshock–aftershock sequences

This paper focuses on the mechanical behaviour, seismic application in steel frame connections and steel structure of shape memory alloy (SMA) plates. This study commenced by examining the hysteretic response of SMA plates subjected to cyclic tension tests, considering two different loading paths. Subsequently, a self-centring steel frame connection equipped with SMA plates and washers (SC-PW) was examined via quasi-static cyclic loading tests, and comparatively satisfactory self-centring behaviour was observed. However, the degradation of the initial stiffness of the SC-PW due to an initial imperfection was observed. An improvement strategy was proposed to overcome the degradation of the hysteretic behaviour (e.g., initial stiffness) of the SC-PW. Disc springs with a larger stiffness and preloads were introduced to overcome the degradation of the initial stiffness of the SC-PW, and the validation was confirmed via detailed finite element (FE) analyses. To improve the computation efficiency, a simplified FE model was developed to reproduce the hysteretic responses of the connection. Based on the simplified FE model, a six-storey prototype structure, i.e., a self-centring hybrid steel frame (SCHSF), equipped with the improved connection was developed, and the structural dynamic responses were investigated via nonlinear response history analyses, where mainshock–aftershock sequences were considered. The influence of the SMA material properties on the seismic behaviour of the prototype structure was investigated.

The importance of hazard-consistency when estimating seismic residual drifts in steel moment frames

Residual drifts are routinely used to assess the post-earthquake safety of buildings. Despite their importance, studies on the probabilistic assessment of residual drifts in multi-storey buildings with Steel Moment Resisting Frames (SMRF) are far less common than those dealing with their transient peak drift counterpart. More seriously, although residual drift prediction models have been developed with a particular broad ground-motion type or soil condition in mind, all models proposed to date remain oblivious to the central issue of hazard consistency. Hence, missing the causal connection between the seismic hazard level and the ground-motion suite used and potentially compromising the meaningfulness of their results. This oversight is expected to introduce a bias in the estimation of residual drifts but its magnitude has not yet been properly evaluated. In this paper, we evaluate and quantify the significance of these effects. To this end, we use the Conditional Scenario Spectra framework, which provides a set of realistic earthquake spectra with assigned rates of occurrences based on their spectral shape and intensity, thus preserving the critical relationship of hazard consistency. Nonlinear Response History Analyses (NRHA) of 24 deteriorating SMRFs under 816 ground-motion records are performed to construct a database of residual drift demands. These NRHA results are used to examine the residual drift trends and to construct benchmark residual drift hazard curves. An extensive feature selection process employing several Machine Learning (ML) algorithms precedes the development of hybrid data-driven predictive models. Finally, we compare our hazard-consistent predictions with currently available models and quantify the massive under- and over-estimations associated with previously proposed non-hazard-consistent assumptions.

Automated calibration of recorded ground motions for nonlinear response history analysis of isolated bridges

Automated calibration of recorded ground motions for nonlinear response history analysis of isolated bridges

Automated calibration of recorded ground motions for nonlinear response history analysis of isolated bridges

Automated calibration of recorded ground motions for nonlinear response history analysis of isolated bridges

A critical assessment of the design displacements of friction pendulum systems

The equivalent linear static procedure suggested in seismic codes for determining the maximum displacements of seismic isolation systems is evaluated comprehensively for friction pendulum isolators with respect to the benchmark nonlinear response history analysis procedure for a set of radii of curvature and coefficients of friction. A large set of selected and scaled near field ground motions recorded on stiff and soft soils are employed in comparative evaluations. It has been observed that equivalent linear static procedure significantly overestimates the maximum isolator displacements for all practical combinations of radius of curvature and friction coefficient. Overestimation is larger for ground motions on soft soils. Alternatively, a practical description of inelastic displacement spectra is introduced where the hazard is defined in terms of the 1-second spectral acceleration accounting for the seismicity and soil class of the site, and friction pendulum isolation systems are characterized by their radius of curvature and nominal friction coefficient. Employing the proposed design spectra in design and production may lead to significant reductions of the isolator sizes. Moreover, realistic estimation of maximum isolator displacements also leads to realistic estimation of isolator stiffness, as well as the internal design forces of both the isolation system and the superstructure through response spectrum analysis under design spectrum.

Effect of Different Scaling Methods on Seismic Isolator Behavior

This study investigated the maximum displacement, force, and acceleration values occurring at the isolation level in structures with lead rubber bearings using nonlinear response history analyses. Earthquake records used in the dynamic analysis were scaled with four different methods. In order to perform bi-directional analysis, both horizontal components of the earthquake records were applied to the isolation units simultaneously. In the analysis, the loss of strength (deterioration) due to the heating in the lead core due to the cyclical motion has been considered. In addition, in seismic isolated structures, five periods (Tiso=2.5s, 2.75s, 3.0s, 3.25s, and 3.5s) representing the isolation period, and four characteristic strength ratios (Q/W=0.75, 0.90, 0.105 and 0.120) representing the strength of the isolation unit were taken into account. As a result of the study, 10-13% change was observed in the maximum acceleration and displacement values at the isolation level due to different scaling methods. In addition, there was a 3% change in force results, and no significant difference occurred.

Prediction of nonlinear seismic demand of inter-story isolated systems using improved multi-modal pushover analysis procedures

The engineering community requires a simple and engineering-friendly procedure to evaluate the seismic performance of inter-story isolated structures (IIS), considering the widespread application of IIS and the limitations of current static nonlinear analysis procedures. This paper proposes an improved multi-modal pushover analysis procedure (IMMPA) that is compatible with the code design spectrum and can account for the effects of higher mode responses and the strongly nonlinear nature of IIS. Nonlinear response history analysis (NRHA) is unnecessary for a reliable assessment of IIS seismic performance when IMMPA is utilized. The IMMPA involves converting the IIS into a linear non-proportional damping structure to satisfy performance requirements, decoupling it into modal oscillators with the equivalent of the nonlinear structure in the modal coordinates using complex-mode-superposition approaches, adjusting the input response spectrum excitation with its equivalent parameters, and converting the response spectrum excitation into the demand spectrum. The main modal oscillators are identified by the complex modal participation mass ratio; the respective acceleration is used as the weight factor of the lateral pushing force; and the capacity spectrum procedure is employed to determine the performance point. Combining the main modal responses using a complex-mode superposition complete square combination rule (CCQC) produces an effective nonlinear peak response. Finally, the IMMPA procedure is demonstrated using an IIS example and evaluated with NRHA data. The evaluation demonstrated that the IMMPA procedure can overcome conventional pushover limitations and efficiently evaluate IIS seismic requirements.

Quantifying variation in maximum floor accelerations of modular buildings under earthquakes through stochastic nonlinear structural analysis

For earthquake-resistant design of modular buildings, reinforced concrete (RC) cores can be a viable choice as the vertical seismic force resisting system. The maximum floor acceleration determines the maximum inertial force that will be transferred by the connections in the horizontal diaphragm to the RC walls. However, the randomness in the structural properties of RC walls may result in fluctuations in the floor acceleration response. Given the limited number of horizontal inter-module connections in modular buildings, the failure of these connections can have severe consequences. To ensure adequate safety margins in the design of horizontal diaphragm connections, it is essential to account for the variations in maximum floor accelerations. To quantify these variations, a 9-story prototype building with RC walls was examined in this study. Monte Carlo simulations were conducted on sample structures with univariate and bivariate randomness in fc (concrete cylinder compressive strength) and Fy (yield strength of steel rebars) of RC walls. Nonlinear response history analyses were performed for each sample structure using 22 ground motions to account for uncertainty in earthquake excitation. The results demonstrated significant and highly complex variations in the maximum floor accelerations due to the randomness considered. A coefficient of variation (CoV) of 0.13 was determined for the maximum floor acceleration response resulting from the bivariate randomness in fc and Fy. Furthermore, the variations were found to increase as the correlation scale in the spatial variation of fc increased. Based on the findings, it is proposed to apply an increase ratio of 1.2 to the maximum floor acceleration to account for the randomness of RC wall properties to ensure adequate safety margins in the design of horizontal diaphragm connections.

A framework for nonlinear peak response evaluation from linear response spectra of base-isolated structures using the bilinear hysteretic model

This paper proposes a simple computational framework that can account for both properties of the base-isolated structure using the bilinear hysteretic model and reliably evaluate the nonlinear peak response without nonlinear response history analysis. The proposed computational framework requires the construction of new non-proportional damping models that match the base-isolated structure to accurately decompose the nonlinear multi-degree-of-freedom structure into multiple single-degree oscillators with intrinsic frequencies and damping ratios by equivalent linearization and complex-mode superposition methods. Each oscillator is excited by a response spectrum matching its own damping ratio, and this procedure is iteratively computed until the displacement error of the isolation layer achieves a preset value. Simultaneously, the peak nonlinear response of interest is calculated using the complex-mode-superposition complete square combination rule. The effect of peak response on nonlinear parameters is analyzed using a typical numerical example, and the relative error values for the applicable range are presented. Parametric research demonstrates that the new non-proportional damping matrix accurately reflects the modal characteristics of the base-isolated structure and prevents Rayleigh damping from suppressing the first-order modal characteristics. The particular example evaluation shows that the computational framework can effectively evaluate the nonlinear peak response of the BIS, with the isolation layer displacement error controlled within +5 %, the bottom shear force error within +20 %, and the top acceleration error between −10 % and +25 %.

Scaling of earthquake ground motions for tri-directional nonlinear response history analyses of reinforced concrete rectangular bridge piers

In performance-based earthquake design (PBED), both the capacity of the structure and the demand from earthquake ground shaking are required to establish the desired performance levels. A range of possible demands can be estimated through nonlinear response history analyses (NRHA), which requires a suite of earthquake ground motions appropriately scaled to the target earthquake intensity for which the structure's performance is to be evaluated. The scaling is usually done for a particular earthquake intensity measure (IM) to get the associated dispersion in the engineering demand parameter (EDP). Several scaling strategies are available for uni-directional (Uni-NRHA) and bi-directional nonlinear response history analyses (Bi-NRHA). However, for tri-directional nonlinear response history analysis (Tri-NRHA), one literature suggests using the same scale factor (SF) for the vertical component, which is estimated for the Bi-NRHA. Therefore, in this study, three well-known scaling strategies, which are usually used for Uni-NRHA, are employed with 16 different methods for application in Tri-NRHA of a reinforced concrete (RC) single-column bridge pier modelled as a single-mass three-degree-of-freedom (3DoF) system. The absolute maximum drift is taken as the EDP, and a total of 1920 Tri-NRHA of the pier are performed using two suites of 20 far-fault and 20 near-fault ground motions, which are scaled to three levels of target earthquake intensity. The sufficiency and efficiency of all the scaling methods are checked statistically under all three target intensities. The study reports the effects of (i) vertical components in calculating the SF, (ii) earthquake intensity and structural nonlinearity, and (iii) far-fault and near-fault ground motion characteristics on the dispersion of the EDP. Out of 16 scaling methods, one is found to be acceptably efficient than the others for application in Tri-NRHA under both far-fault and near-fault ground motions at all target intensities.