Evaluation of Earthquake-Induced Risks in Modern, Code-Conforming Reinforced Concrete Moment Frames

The main objective of this study is to employ performance assessment procedure to evaluate earthquakeinduced risks in modern, code-conforming Reinforced Concrete (RC) moment frames in terms of collapse risk and possible financial losses. In order to accomplish this goal, a set of 15 archetype RC moment frames is evaluated in this study. The buildings are different regarding height and structural system ductility. The archetypes are assumed to be located in three zones with different levels of seismicity. The findings of the collapse assessment procedure indicate that the constraint of ASCE 7-05 for the lower limit of design base shear has the most significant impact and the ductility has the least influence on collapse risk. Also, it has been found that buildings located in the low seismicity zone have significantly lower levels of losses. Sensitivity analysis is employed to study the variations of earthquake consequences due to the variations in the design decisions.


INTRODUCTION
The reliance of current seismic design provisions on the empirical and judgmental axis will put a question on the ability of these codes in providing approximately uniform risk against earthquake among all the conforming buildings.This study applies the Performance-Based Earthquake Engineering (PBEE) methodology through the nonlinear dynamic time history analysis to assess the seismic performance of a set of 15 reinforced concrete moment framearche types.The set of archetypes are designed to be in accordance with the requirements of ASCE 7-05 (ASCE, 2005) and ACI 318-05, (2005).In this study, taking advantage of the collapse assessment methodology proposed by Haselton and Gregory, (2007) and Liel and Deierlein (2008) and the FEMA P-58 (FEMA, 2012) recommended loss evaluation process, we focus on expanding the previous findings to the buildings located in different seismic zones and having distinct levels of structural ductility to examine to which extent the modern loading and design provisions are successful in achieving an approximately uniform seismic risk.
With the purpose of clarifying how the variations in height, ductility and seismicity would affect the seismic risk in modern code-conforming RC moment frames, the set of representative archetypes is selected to include 4-, 8-and 12-story buildings with the lateralresisting structural system consists of ordinary, intermediate and special perimeter moment frames.The buildings are sited in regions with three different levels of seismic hazard including low, moderate and high seismicity.The differences between the outcomes of the collapse assessment and loss prediction processes among the set of the set of archetypes are investigated through the use of sensitivity analysis.

MATERIALS AND METHODS
Site selection and seismic hazard: The selected archetypes are located in Los Angeles, Las Vegas and Austin at which the ASCE-recommended Maximum Considered Earth quake (MCE) level 1-second spectral acceleration corresponds to the values of 0.912, 0.363 and 0.078 g, respectively.Site-specific seismic hazard parameters are extracted from the USGS hazard maps (USGS, 2012) for ASCE 7-05. Figure 1 compares the uniform hazard MCE spectra of ASCE 7-05 for the mentioned sites.
In order to perform Incremental Dynamic Analysis (IDA) (Vamvatsikos and Cornell, 2002), 22 pairs of far field ground motion records, which has been recommended by FEMA P-695 (FEMA and ATC, 2009), is employed.The intensity measure for representing the intensity parameter and scaling the ground motions is selected to be the spectral acceleration at the first mode period with 5% coefficient of damping.In order to account for the important effect of spectral shape on the collapse 394 Fig. 1: Uniform hazard seismic design spectra for the selected sites assessment results, outcomes of the collapse assessment procedure are modified using the method suggested by Haselton and Gregory (2007).

Archetypes design and specifications:
In order to provide a robust base to investigate the differences that variations in design parameters of code-conforming RC buildings might induce in seismic risk, the set of archetypes is selected to represent the important parameters that variation among them is permitted in codified seismic provisions and these variations might impact the seismic performance of conforming structures.These variations include key design parameters such as height which is chosen to vary from 4 to 12 stories, ductility of the structural system which reflects in the three types of moment frames including special, intermediate and ordinary frames and finally the seismicity of the site in which the archetype are located and is represented by the three sites described in materials and methods section.The governing design criteria lies between the ASCE 7-05 loading provisions and ACI 318-05 design necessities for special, intermediate and ordinary RC frames.The lateral-force resisting structural system has the bay span of 6-m width.Story heights are 4 m in the first story and 3.3 m in all other above stories.
Structural nonlinear modeling and analysis: All of the archetypes are modeled through a two-dimensional model of the lateral-force resisting system using the OpenSEES (2012) platform.The gravity frames are not included directly in the models.However, the adverse P ∆ effects resulting from the additional tributary mass on the gravity frames are involved by applying these additional gravity loads on a leaning column.Nonlinear modeling in this study has two different aspects.A fiber-type model is used for modeling beams and columns in lower levels of intensity at which cracking and tension-stiffening effects are important and the fiber model is known to be more accurate than the plastic hinge model in capturing these effects.Beside the fiber model, because of the ability of the plastic hinge models in incorporating deterioration resulted from rebar buckling and concrete crushing, a lumped plasticity model is employed to simulate the nonlinear behavior of structures at high levels of intensity which finally leads to the collapse of structure.Collapse in this study is defined as the point of dynamic instability at which a minor increase in intensity will result in an infinite increase in response, which is defined here as the maximum of Interstory Drift Ratio (IDR).The nonlinear plastic hinge model for beams and columns employs a trilinear backbone curve and hysteretic rules introduced by Ibara et al. (2005) to simulate the nonlinear and hysteretic behaviors of the structural elements.The design and modeling uncertainties are incorporated by modifying the total dispersion of collapse fragilities regarding the method proposed by Haselton and Gregory (2007) and an assumed value of 0.45 for these types of variation.Haselton and Gregory (2007) showed that design and modeling uncertainties have a significant effect on the collapse assessment outcomes.

RESULTS AND DISCUSSION
Collapse assessment findings: The results of collapse assessment can be summarized in 4 major measures including one ductility-related measure namely maximum Interstory Drift Ratio IDR at collapse and three performance-related measures recognized as the collapse margin ratio defined as the ratio of the median of collapse spectral acceleration to the spectral acceleration with 2% probability of exceedance in 50 years, the probability of collapse conditioned on occurring the 2% in 50-year ground motion P C Sa obtained from the collapse fragility curve and the mean annual frequency of collapse λ which is the result of integration of collapse fragility function together with the site-specific hazard curve.Sensitivity analysis shows that variations in the design parameters causes the collapse margin ratio to range from 1.14 to 3.21, the probability of collapse to vary between 2 and 41% and the mean annual frequency of collapse to lie across 1.9×10 -4 and 20×10 -4 .

Trends between height and collapse performance:
Figure 2 shows how the collapse margin ratio, for the whole set of frames, changes as the building height changes.The margin against collapse has a completely different trend for buildings located in the high and moderate seismicity regions (Los Angeles and Las  Vegas) in comparison with the buildings located in the low seismicity region (Austin).For the buildings located in the sites with high and moderate seismic hazard, the collapse margin decreases as the building height increases.This reduction in collapse safety is primarily the result of the more significant P ∆ effects in the taller frames.
Although a similar trend is expected for the frames located in Austin, the constraint imposed by ASCE 7-05 for the lower limit of the design base shear coefficient (equation 12.8-5) makes the design base shear for the 8-and 12-story frames much more conservative and leads to the substantial improvement in the collapse performance of the taller buildings in Austin.The conservatism imposed by the equation 12.8-5 of ASCE 7-05 increases as the height of the buildings increases and thus leads to the better collapse performance for the taller buildings in Austin.

Trends between ductility and collapse performance:
Figure 3 compares the collapse fragility curves for the 4, 8-and 12-story special, intermediate and ordinary frames located in Austin.The horizontal axis is normalized by the 2% in 50-year ground motion.As illustrated in Fig. 3, the collapse fragility curves for all types of frames with the same height are approximately equal.One notable observation is the better collapse performance of the 4-story ordinary frame in comparison with the special and intermediate 4-story frames.This better collapse performance of the 4-story ordinary frame is the result of the higher design base shear coefficient of this frame and the low seismic hazard of Austin.The low seismic demands in Austin lead to the structural members (beams, columns) of considerably low stiffness which, despite the higher element-level ductility in special and intermediate frames, results in the intensified P ∆ effects in the columns and decreases the system-level ductility of all 3 types of frames.Additionally, the low seismic forces in the 4-story frames located in Austin considerably reduces the effects of the ACI 318 special seismic provisions such as the strong-column weak-beam ratio and the joint shear panel requirements and, as a result, virtually there would be no differences between the design outcomes of the 4-story special, intermediate and ordinary frames in Austin.As the height of the frames increases, these special seismic provisions become more effective and consequently the performance of the special and intermediate frames improves.
Trends between earthquake hazard and collapse performance: Figure 4 shows how median of the IDR at collapse, for the special frames located in the three considered zones, changes as the height increases.As the seismic hazard decreases, the reduction in the Fig. 4: Trends between the height and median of IDR at collapse for all of the special frames stiffness of the structural members of frames leads to the intensified destabilizing P ∆ effects for the frames located in Austin and, as a result, the IDR at collapse decreases as the seismic hazard reduces.This reduction in the ductility might result in the misleading conclusion that the collapse performance of frames declines as the seismic hazard decreases.Figure 5, which compares the collapse fragility curves of 4-, 8and 12-story special frames, shows that this conclusion is not generally true.The better collapse performance of the 8-and 12-story special frames located in Austin, as it is discussed in section 6.1, is the result of the constraint imposed by the equation 12.8-5 of ASCE 7-05.Specifically, the approximately negligible additional conservatism imposed by this equation on the 4-story frame located in Austin has caused this frame to have a collapse fragility curve nearly identical to that the frame located in Los Angeles.However, the significant conservatism levels for the 8and 12-story frames in Austin, which is the result of the restriction imposed by equation 12.8-5, has resulted in the better collapse performance in comparison with the similar frames located in the two other cities.The similarity between the collapse fragility curves of the frames located in Los Angeles and Las Vegas, despite the substantial differences in the return periods of design spectral accelerations, shows that this type of variation has virtually no impact on the collapse risk of the frames located in zones with different seismic hazard.However, this conclusion is based on a limited set of representative archetypes and, in order to generalize these conclusions, a large set of archetypes located in different seismic zones must be examined.

Financial consequences of earthquake:
In this section, we further examine the seismic-induced risks by employing metrics for assessing the financial losses.

CONCLUSION
In this study, we employed the performance-based earthquake engineering framework to evaluate the seismic-induced risks in modern, code-conforming RC moment frames which their design procedure stands among the constraints of ASCE 7-05 and ACI 318-05.The set of representative archetypes are selected so that the effects of variations in height, ductility and seismicity on the seismic risks can be examined.The assessment procedure is divided into two sections; in the first section the collapse performance of the archetypes and effects of the variations in the design parameters on collapse assessment outcomes is studied and in the second section monetary consequences of earthquake is compared for the set of structures.
Findings of the collapse assessment show that the margin against collapse lies between 1.2 and 2.4 with an average of 1.7 and the mean annual frequency of collapse varies from 3.5 10 to 20 10 with the mean value of 7.3 10 .Among the investigated design parameters, the collapse risk is mostly influenced by the minimum design base shear constraint of ASCE 7-05.Applying this constraint leads to the better collapse performance of the 8-and 12story buildings in Austin than the 4-story frame because of the more conservative design base shear of the 8-and 12-sroty frames.For the frames located in Los Angeles and Las Vegas, in which the equation 12.8-5 of ASCE 7-05 does not affect the design base shear, collapse risk is relatively consistent over height with the taller frames being slightly more vulnerable to collapse because of the intensified P ∆ effects in the taller frames.
Comparing the collapse risk for the ordinary, intermediate and special frames, we found that the collapse risk does not significantly changes as the ductility of frames changes.Also, outcomes of the collapse assessment procedure shows that frames located in zones with different levels of seismic hazard have relatively similar collapse risks unless the constraint of the equation 12.8-5 of ASCE 7-05 makes the design base shear for 8-and 12-story frames located in the zone with low seismic hazard significantly conservative and thus, enhances the collapse performance of these frames.
By conducting damage assessment procedure for the whole set of archetypes, this study shows that, expected annual losses due to earthquake occurrence varies significantly with the seismic hazard and buildings located in the zone with low seismic hazard have considerably lower losses.
Outcomes of the collapse assessment procedure of this study shows to which extent are the modern seismic requirements successful in providing uniform safety among the conforming structures with different configurations.Furthermore, findings of the loss assessment procedure can provide authorities, stakeholders and insurance companies with metrics to assess the financial risks associated with earthquake and contribute them in making decisions that lead to the minimization of adverse consequences of earthquake.

Fig. 5 :
Fig. 5: Normalized collapse fragility curves for the special (a) 4-story frames, (b) 8-story frames and (c) 12-story frames located in Los Angeles, Las Vegas and Austin

Table 1 :
Loss assessment assumptions and findings Design and framing

Table 2 :
Most damaging spectral acceleration and collapse mechanism for the buildings Archetype properties - -