Influence of ground motion duration on ductility demands of reinforced concrete structures
This article investigates the level of influence that strong motion duration may have on the inelastic demand of reinforced concrete structures. Sets of short-duration spectrally equivalent records are generated using as target the response spectrum of an actual long-duration record. The sets of short-duration records are applied to carefully calibrated numerical models of the structures along with the target long-duration records. The input motions are applied in an incremental dynamic analysis fashion, so that the duration effect at different levels of inelastic demand can be investigated. It was found that long-duration records tend to impose larger inelastic demands. However, such influence is difficult to quantify, as it was found to depend on the dynamic properties of the structure, the strength, and stiffness degrading characteristics, the approach used to generate the numerical model and the seismic scenario (target spectrum). While for some scenarios, the dominance of the long record was evident; in other scenarios, the set of short records clearly imposed larger demands than the long record. The detrimental effect of large strong motion durations was mainly observed in relatively rigid structures and poorly detailed flexible structures. The modeling approach was found to play an important role in the perceived effect of duration, with the lumped plasticity multilinear hysteretic models suggesting that the demands from the long records can be up to twice the inferred from distributed plasticity fiber models.
KeywordsGround motion duration Incremental dynamic analysis Reinforce concrete structures Nonlinear modeling
In structural design and assessment, the preferred representation of seismic hazard continues to be based on the elastic response spectrum. Even when dynamic time-history analyses are required, the acceleration time histories used are usually required to be compatible with a prescribed design spectrum. One option to comply with this requirement is to use spectrally matched records. The criteria for developing these time histories is provided in design codes and guides like the 2015 NEHRP Recommended Seismic Provisions (BSSC 2015) and the Appendix F of the US Nuclear Regulatory Commission RG-1.208 (US-NRC 2007). While most of the criteria in these documents are devoted to quantifying the required level of matching, limitations on strong motion duration are no explicitly established (e.g., NEHRP, for conventional structures) or are rather vague (e.g., RG-1.208, for nuclear facilities). Prescriptions regarding duration on the US-NRC RG-1.208, for example, are limited to check that the spectrum-compatible series have durations consistent with characteristic values for the magnitude and distance of the events controlling the design spectrum. This absence of duration regulations is likely due to earlier research works on this topic finding correlation between duration and cumulative damage metrics but no with peak deformations, which are the base of the seismic acceptance criteria (Chandramohan 2016). For a comprehensive review of earlier works, see Hancock and Bommer (2006). Nevertheless, more recent studies that made use of more realistic structural models (i.e., models that account for cyclic strength/stiffness degradation and p-delta effects) have found positive correlations between duration of the strong motion excitation and peak deformations. Montejo and Kowalsky (2008) found that duration influences mainly the peak inelastic demand of short-period structures with stiffness and strength degradation and subjected to relatively large level of inelastic demand. Chandramohan (2016) examined the collapse capacity of a modern steel moment frame and a reinforced concrete bridge pier using sets of spectrally equivalent short- and long-duration records. When using the long-duration set, the median collapse capacities were found to be 29% and 17% lower for the frame and pier, respectively. Barbosa et al. (2017) investigated the effect of duration on steel moment resisting frames of 3, 9, and 20 stories. They observed that the effect of duration on peak deformation becomes palpable for scenarios, where the lateral demand surpasses interstory drift ratios of ~ 4%. Molazadeh and Saffari (2018) investigated the effect of duration on single degree of freedom systems with different hysteretic behaviors and periods of vibration, and they found that duration has a substantial effect in short-period pinching-degrading models. Bravo-Haro and Elghazouli (2018) performed nonlinear analyses on 50 numerical models of steel moment frames using a suite of 77 spectrally equivalent pairs of short and long records as input. As the previous studies, they noticed that the effect of duration is larger for structures that exhibit cyclic degradation and becomes more pronounced at increasing levels of lateral demand. A typical reduction of about 20% in the collapse capacity was observed, with up to 40% for buildings with significant cyclic deterioration.
Evaluate the influence of strong motion duration on the seismic response of structures with different dynamic properties and degradation parameters For this purpose, numerical models are developed for an RC bridge column and for an RC squat wall. Both models are calibrated using large-scale experimental data, and then, the parameters affecting the cyclic deterioration characteristics are altered to obtain a second pair of models’ representatives of poor detailed structures.
Identify the influence of duration at different levels of inelastic demand To accomplish this, the seismic input is applied to the numerical models in an Incremental Dynamic Analysis (IDA, Vamvatsikos and Cornell 2002), where a set of ground motions is scaled to different intensity levels, so that predefined structural performance levels can be studied.
Asses if the modeling approach employed to simulate the response of the structure impacts the observed duration influence Two modeling approaches are engaged to assess the impact of the modeling strategy on the observed duration influence. One approach is based on distributed plasticity using unidirectional fibers and the other lumps the inelastic action to the hinge, which is modeled using Modified Ibarra-Medina-Krawinkler Deterioration Models (Ibarra et al. 2005; Lignos and Krawinkler 2012).
Development of the structural models
The structures analyzed are maintained simple in geometry, that is, their dynamic response is mainly dominated by their fundamental mode. This allow us to focus on the deterioration characteristics (i.e., cyclic strength and stiffness deterioration) and p-delta effects at large inelastic demands that have been identified as the mechanisms by which duration may influence structural response (Chandramohan et al. 2017). Two different types of structures are analyzed: a single column bridge bent and a squat reinforced concrete wall. These two types of structures were selected to have two fundamentally different scenarios in terms of the dynamic behavior and lateral deformation mechanisms. While the bridge column represents a long period and ductile structure dominated by flexural deformations, the squat wall is rather rigid and dominated by shear deformations. Nevertheless, a drawback is that both cases exhibit a low degree of redundancy which also affect the structure ductility capacity. All the structural models in this research were developed within the OpenSees software framework system (McKenna et al. 2000).
RC bridge column models (ductile, original column)
For the column, two modeling approaches are engaged, one based on distributed plasticity using unidirectional fibers and the other lumping the inelastic action at the hinge. Having the same structure modeled using two significantly different methodologies allows us to identify if the duration effect is influenced by the approach used to model the structure. Both models were calibrated using experimental data from a series of large-scale shake table tests. Once calibrated, the degradation parameters in the models are varied to analyze the effect of duration on different deterioration scenarios.
Lumped plasticity model
In the lumped plasticity modeling approach, the column is modeled using a linear elastic element connected to a zero-length element at the base that represents a rotational spring, where the inelastic deformations are concentrated (Fig. 2—right). The “ModIMKPeakOriented” material available in OpenSees is used to define the behavior of the hinge; in the sake brevity, we will refer to this model as the IMK model. This material implements the Modified Ibarra–Medina–Krawinkler Deterioration Model with Peak-Oriented Hysteretic Response (Ibarra et al. 2005; Lignos and Krawinkler 2012). The input required to define this material is comprised of the parameters required to define the backbone curve and additional parameters to account for the cyclic deterioration of strength and stiffness. This approach provides an efficient way of modeling and controlling plastic hinge formation. However, a drawback to concentrated plasticity models is that axial force–moment interaction and axial force–stiffness interaction are separate from the element behavior. Further information and details on the development of the numerical models are available in De Jesus-Vega (2018).
RC bridge column models with reduced ductility capacity and strength
RC squat wall model (well detailed, original squat wall)
As current fiber-based approaches have not reached the required maturity to capture shear deformations in a robust manner, the squat wall is modeled using the lumped plasticity approach only. Similar to the bridge column, the model parameters are calibrated using experimental data and the degradation parameters are then varied to analyze the effect of duration on different structural deterioration scenarios.
RC squat wall model with reduced displacement capacity
The numerical models previously described will be used to assess the influence of strong motion duration on inelastic response. To accomplish this, sets of 20 short strong motion duration acceleration time series are generated with records made spectrally equivalent to a target long-duration record. By spectrally equivalent, we mean that the short records are modified, so that their 5% damping pseudo-acceleration response spectrum match the response spectrum of the long-duration record used as target in each set.
Database of long-duration records
Target long-duration records
Set of long-duration records
CAV (g s)
HUALANE S/N 4564
Sets of short-duration spectrally equivalent records
Duration effects on the inelastic response of RC bridge columns
Figure 15 shows the results obtained for EQ69 (SD5-75 = 70.6 s) and its corresponding set of 20 short-duration spectrally equivalent records (average SD5-75 = 9.6 s) for the fiber model of the ductile column. It is seen that the long-duration record seems to impose larger peak inelastic demands for ductility levels below 5; after this point, the differences are reduced. For the average peak ductility demand (average from both directions), the differences between both IDA curves are less significant. Nevertheless, when the same model is subject to the EQ96 scenario (SD5-75 = 61.9 s), it is seen that the short records (average SD5-75 = 9.3 s) consistently impose larger inelastic demands (Fig. 16). When the same pair of set records are applied to the reduced ductility column (Figs. 17 for EQ69 and 18 for EQ96), the results follow the same trend: for the EQ69 case, the long record imposed the larger demands, and for EQ96, the short records do. However, in the EQ69 scenario, the control of the long record is more consistent than for the ductile column, covering all the range of ductilities studied and increasing as the inelastic demand increases. Similar results were obtained for the IMK model and are not shown here in the sake of brevity.
Duration effects on the inelastic response of RC shear walls
Conclusions and final remarks
Despite the overwhelming number of analyses performed and the simplicity of the structural models evaluated, a direct measure of the level of influence of strong motion duration on the inelastic demand of reinforced concrete structures is not possible due to the scatter on the results and the dependency on other factors. Overall, it was found that long-duration records tend to impose larger inelastic demands (Figs. 22, 23). However, such influence is difficult to quantify, as it was found to depend on the dynamic properties of the structure, the strength and stiffness degrading characteristics, and the approach used to generate the numerical model and the seismic scenario (target spectrum). While for some scenarios, the dominance of the long record was evident, there were some cases, where the set of short records clearly imposed larger demands than the target long record (e.g., see Fig. 18).
Comparing the lateral demand ratios obtained for the column and wall models, it is apparent that duration seem to have a more harmful effect in the squat wall model than in the bridge column model. That is, the effect of large strong motion duration seems to be more detrimental in relatively rigid structures.
Comparing the ratios obtained for the “well” versus the “poorly” detailed column, it is seen that duration have a larger detrimental effect on the “poorly” detailed column. However, for the wall cases, there are no major differences between the ratios obtained for the “well” and the “poor” detailed wall. It can be said that the duration effect would be augmented on poorly detailed structures if the structure is relatively flexible. However, in the case, where the structure is relatively rigid, and with an inherent reduced displacement capacity, the influence of the degradation parameters in the effect of duration seems negligible.
The results obtained also show that the largest duration effect occurs at intermediate levels of lateral demand. As the lateral demand increases at levels associated with severe damage, the duration effect is reduced. An exception is noted when the reduced ductility column is modeled using the IMK approach, where some isolated large ratios appear at large levels of inelastic demand. However, this is likely due to limitations of the lumped plasticity model.
The modeling approach may play an important role in the perceived effect of duration with the lumped plasticity multilinear hysteretic model, suggesting that the demands from the long records can be up to twice the inferred from the fiber models. This, despite the fact that all models were calibrated using the same sets of experimental results.
This work was performed under awards NRC-HQ-84-14-G-0057 and NRC-HQ-60-17-G-0033 from the US Nuclear Regulatory Commission. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the view of the US Nuclear Regulatory Commission.
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