Seismic fragility of reinforced concrete buildings with masonry infills

Overview

Previous studies have proposed different EDPs for fragility assessment of multistory frames; however, such categorized EDPs are not available in the literature for irregular buildings. In addition, there is generally a large uncertainty associated with the estimation of these EDPs, which requires proper consideration.

Major Concerns and Need of the Study

Several documents, such as, HAZUS (2013) and GEM (D' Ayala et al. 2015) provide guidelines for seismic vulnerability assessment of some common building typologies using analytical methods. Another important aspect in seismic vulnerability assessment is the selection of an effective engineering demand parameter (EPP) that correctly interprets the damage associated with the building during earthquakes.

Scope and Objectives of the Study

This question is investigated by assessing the seismic performance of low- and mid-rise masonry infilled RC frames with different infill configurations using nonlinear static and dynamic analyses. Therefore, the sensitivity of EDPs to random input parameters is evaluated for masonry infilled RC frames.

Organization and Outline of the Thesis

In addition, the main findings of this study are summarized in Chapter 8, together with a discussion of the most salient conclusions drawn from the study. Finally, the limitations of the study and the scope of possible future research work are briefly discussed.

Overview

This is followed by an overview of the methods available to assess the seismic performance of selected building typologies. The methods adopted by past researchers in evaluating the sensitivity of the seismic response to uncertain input variables are reviewed in Chapter 5.

Structural Inventory for Seismic Vulnerability Assessment

Finally, the fourth section presents a brief discussion and review of seismic fragility and vulnerability assessment procedures adopted by researchers in the past. This section reviews the seismic behavior and performance of such buildings in past earthquakes.

Identification of damage

Building damage can best be described in terms of its components - structural and non-structural. It is because of the complexity of assessing non-structural damage using conventional methods that their contribution to defining damage states is generally not considered.

Table 2.1 Relation between building damage and performance levels as defined in FEMA 273 (1997)

Damage Probability Matrix (DPM)

Damage Probability Matrix from Expert Opinion

Damage probabilities based on expert opinion was first introduced in ATC 13 (1985) which essentially derived DPM for 78 structures, 40 of which refer to buildings, by asking 58 experts (recognized structural engineers, builders, etc.) estimate the expected percentage of damage that will result in a specific type of structure subjected to a given intensity. Furthermore, it is difficult to extend the ATC 13 methodology to other building types and other regions, as well as to individual building characteristics.

Damage Probability Matrix from Empirical Studies

The ratio (ag/ao) of the maximum PGA of a certain earthquake event to the PGA that characterizes each municipality in the Greek hazard map. The assumption that the buildings not classified into structural types belong to the undamaged structures, together with the fact that the unmeasured buildings are considered undamaged, leads to an underestimation of the probability of damage.

Table 2.6 General format for constructing Damage Probability Matrix (Whitman et al. 1973).

Damage Probability Matrix from Analytical Studies

Seismic Performance Assessment Methods

Capacity Spectrum Method (CSM)
Displacement Coefficient Method (DCM)
N2 method
Nonlinear Dynamic Procedures

Therefore, its strong dependence on the set of selected ground motion records is a major limitation of the method. Again, there are limitations to Bayesian cloud analysis related to the number and selection of ground motion records.

Figure 2.5 Steps in Capacity Spectrum Method (ATC 40 1996): (a) Construction of demand spectrum, and (b) Construction of capacity spectrum

Seismic Fragility and Vulnerability Assessment Methodologies

Expert Judgement Methods
Empirical Methods
Analytical or Mechanical Methods
Hybrid Methods
Seismic Vulnerability Assessment using RVS

Different methods of assessing building vulnerability differ in expenditure and accuracy. Analytical vulnerability curves are further calibrated using the damage database of the buildings in Greece.

Figure 2.8 Diagrammatic representation of the steps involved in seismic vulnerability assessment of buildings.

Summary and Gap Areas in the State-of-the-Art

Furthermore, the importance of each of these building parameters to the sensitivity of the seismic response of the OGS buildings must be recognized before assessing seismic vulnerability. A simplified procedure for the seismic vulnerability and vulnerability assessment of OGS buildings should be developed, which can be easily used by design professionals.

Overview

General
Analytical Idealization of the Generic Buildings
Nonlinear Material Properties for Static Analysis
Nonlinear Material Properties for Dynamic Analysis

Therefore, the shear failure of the piles is not expected and is not considered in this study. 3.3(a) shows a typical stress-strain curve for RC column sections at floors III and IV of the frame.

Figure 3.1 (a) Structural elevation of the considered frame – bare, OGS, and FI, (b) Building floor plan, and detailed sectional properties of (c) columns and (d) beams for the frames

Modal Analysis

Nonlinear Static Pushover Based Methods

General
Input Response Spectrum
Influence of Central Opening Size in Masonry Infill
Influence of Change in Number of Stories
Influence of Change in Number of Bays
Multiple Linear Regression

On the other hand, the effect of Op is found to be negligible in the case of OGS frames compared to the FI frames. The influence of variation in the number of bays (NB) on the lateral load response of RC frames considering 0% and 50% Op is studied by varying NB from one (1B) to six (6B) for both OGS as FI frames.

Figure 3.6 Nonlinear capacity curves for the frames using: (a) FEMA 356 hinges, and (b) fiber hinges

Multiple Stripe Analysis (Nonlinear Dynamic Analyses)

General
Input Ground Motions
Fiber Sensitivity Analysis
Peak Interstorey Drift (ISD) Response
Derivation of Correlation on IM-EDP Pairs
Base Shear vs Roof displacement

3.17(a) by normalizing the ground acceleration with respect to PGA to represent the variation in the energy content of the ground motions. The figure clearly shows that there is a large variation in the dominant frequency of the generated samples.

Table 3.5 Characteristics of ground motions considered for time-history analyses.

Dynamic Amplification Factor

General

Dynamic Amplification Factor for the Frames

Similar to demand variation, DAFs are obtained for the median responses at each level of the intensity measure (PGA). 3.24(b) shows the variation in DAF obtained for the three frames with respect to PGA by a variation in the parameters related to frame capacity.

Figure 3.24 Dynamic Amplification Factors (DAF) obtained for the three frame configurations (Bare frame, OGS frame, and FI frame) with respect to: (a) demand, (c) capacity, and (c) combined response

Application of Dynamic Amplification Factor

PGA series DAF for bare frame DAF for OGS frame DAF for FI frame Demand Capacity Demand Capacity Demand Capacity.

Summary and Conclusion

Comparison of pushover plot obtained from non-linear static analyzes with the median base shift – roof displacement obtained from non-linear dynamic analyzes for the frames shows that the static analyzes mostly give an envelope curve for the lateral load capacity of the frames and can be effectively used for determining the seismic demand. Dynamic amplification factors are calculated for the considered frames, which can be efficiently used to obtain the nonlinear dynamic response from the nonlinear static response.

Overview

Review of Engineering Demand Parameters

Need of the Study

Therefore, a component-level fragility analysis with local demand parameters is performed in this study to estimate the realistic fragility of vertically irregular buildings. Instead, a component-level EDP may be a better alternative for realistic seismic assessment of vertically irregular structures.

Estimation of EDPs for RC Frames with Infill

Previous studies have proposed various VGPs for fragility assessment of multistory frames; however, such categorized VGPs are not available in the literature for irregular buildings. The present study clearly highlights the importance of a component-level VGP in damage assessment of vertically irregular building frames with a focus on open floor storey frames.

Nonlinear Dynamic Analyses

General
Considering Maximum Storey Displacement as the EDP
Considering Maximum Interstorey Drift (ISD) as the EDP
Stiffness Factor

At higher PGA, however, some ground motions cause very high drift demands in the ground floor columns of the FI frames. In contrast, there is practically no difference in the peak displacement at TL and GL in the case of OGS frames for all ground motions.

Figure 4.1 Peak storey displacement demands for Bare vs OGS frames for El Centro (EC), I- I-Burma (IB), Chile (Ch), Kobe (Ko), Kocaeli (Kc), Duzce (Du), and Tabas (Tb) ground motions for 0.3g, 0.5g, 0.7g and 1g

Summary and Conclusion

With increase in PGA, the GL stiffness factor decreases drastically and becomes equivalent to that of the TL stiffness factor. However, in OGS frames, both the TL stiffness factor and the GL stiffness factor follow quite similar trend at all PGA levels.

Overview

Conceptual Background

Need of the Study

It was observed that the sensitivity of the response depends on the collapse mechanism of the system. They observed that the parameters related to masonry infill greatly influence the response sensitivity of masonry-infilled RC frames.

Sensitivity Analysis

General
Uncertain Parameters Considered
Structural Modelling
Ground Motions Considered

The sensitivity analyzes are performed based on the probability distribution of each of the input variables. Three variants of the RC frame typologies (as discussed in Chapter 3) have been considered, namely the bare frame (BF), open ground frame (OGS) and fully infilled (FI) frame.

Table 5.1 Considered uncertain input variables and their statistical characteristics

Sensitivity from Modal Analysis

Sensitivity from Nonlinear Time-History Analyses

General
Sensitivity of Response using Radar Charts
Sensitivity of Response Using Bar Charts
Sensitivity Based on Tornado Diagram Analysis
Comparative Sensitivity for the Three Frames
Sensitivity Based on Sobol’ Index
Sensitivity Based on Lasso Regression
Weightage of Input Uncertainty to Output Sensitivity

It is equally important to understand the sensitivity of the structural response to ground motion variations. Interestingly, the parameters Bc and fck are found to show the greatest sensitivity to the displacement response of the OGS frames.

Figure 5.2 Displacement sensitivity radar charts for uncertain geometric input parameters with their COV for seven ground motions: (a) bare frames, (b) OGS frames, and (c) FI frames

Sensitivity of Other EDPs

Uncertainty in other input variables such as fy, γc, ξ and εm has relatively less influence on the roof displacement, although the weighted uncertainty in some of these variables is very high (e.g. 34% for ξ and 19% for εm).

Summary and Conclusion

2 The response of the frames in which the infill walls are placed uniformly in all floors (FI frame) is most affected by the uncertainty in parameters related to the infill characteristics. 3 The radar maps show that some ground motions, especially those with high input energy, can significantly affect the sensitivity of the frames' response.

Overview

Need of the Study

Baker and Cornell (2008) proposed the use of a combination of numerical integrations and first-order second-moment (FOSM) approaches to integrate both epistemic and aleatoric uncertainty and account for their effects on the output variables. On the other hand, some studies (Fajfar and Dolšek 2012, Choudhury and Kaushik 2018a) have adopted standard dispersion values to be used to determine the probability of exceeding a given limit state.

Uncertainty in Assessment of Vertically Irregular RC Frames

Thus, there is significant uncertainty when considering input parameters in structural modeling and performance assessment of masonry-filled RC buildings. These details regarding the estimation of both types of uncertainties are given in the following paragraphs.

Uncertain Input Parameters in Structural Capacity Evaluation

General

Generation of Data (Sampling)

The difference between the two correlation matrices can be minimized by permutation of the elements of the generated sampling matrix. The norm E is calculated on the basis of the repeated trials for different sizes of the sample Nsim.

Ground Motions Considered

Typically, the analyst requires the use of a fairly large number of ground motion records that are representative of the location of the building or class of buildings being evaluated. To capture ground motion variability, synthetic samples of each ground motion are generated.

Figure 6.1 Comparison between sample values of the selected random input variables before and after optimization of the sample matrix

Choice of IM vs EDP

Probabilistic Performance Evaluation

General

Nonlinear Static Analysis

Nonlinear Response History Analysis

This change in slope marks the failure of masonry infill walls on the ground floor of FI frames, after which the FI frames become flexible. As observed in the pushover analysis, the variation in the EDPs is maximum in the case of FI frames.

Estimation of Uncertainties in EDPs

General
Epistemic Uncertainty
Aleatoric Uncertainty
Total Uncertainties

The maximum uncertainty in the FI frame response considering both TL and GL displacement is approximately equal to 0.6. In case of OGS framework, there is no difference at all in the uncertainty of the two EDPs, i.e. the uncertainty in TL displacement and GL displacement is exactly the same.

Figure 6.4 Epistemic uncertainty in response with respect to PGA at (a) top storey level and (b) ground storey level

Uncertainty for Damage State Definition

It is observed that the median threshold values obtained in the present study for the bare frame are mostly higher than those for the C1M values. The uncertainty values defined in HAZUS are very high for RC-URM category, compared to the uncertainty values obtained in the present study.

Summary and Conclusion

It is noted that the uncertainty values recommended in that study were more or less similar for the bare frame and OGS for any number of stories and these values agree quite well with the uncertainty values obtained in this study for the full damage condition. However, their proposed uncertainty values for FI frames increase significantly as the number of floors increases; and these values are much smaller than the uncertainty values obtained in this study for FI frames for the full damage condition.

Overview

Formulation of Seismic Fragility

Ф represents the standard normal cumulative distribution function, θd is the median (threshold) value of EDP, (e.g. interstory drift, spectral displacement) considered for different damage conditions, and βT is the normalized standard deviation of the natural logarithm of the threshold ( θd). The median and standard deviation of the statistical models can be estimated by different parameter estimation techniques, such as maximum likelihood.

IM vs EDP in Fragility Assessment

A fragility curve can also be constructed by fitting a statistical model to building damage data at different IM values. Such statistical models are generally fitted to the probability of exceedance for a given IM, which is calculated as in Eq. 7.2), where NF is the number of analysis cases where the considered EDP exceeds the limit, and NT is the total number of analysis cases at this IM level.

Damage Dependent Limit States

These damage states are quantified based on the yield and ultimate displacement of the building frames. The transfer displacement (dy) is defined as the displacement during which the initiation of the first plastic hinge in any columns on the ground floor takes place.

Table 7.1 Average interstorey drift (ISD) thresholds (∆ ds ) as specified in HAZUS (2013)

Treatment of Uncertainties in Fragility Estimation

General

Influence of Total Uncertainty

It is clear that at an Sd value of 0.6 (threshold value) the difference {P[βT1] - P[βT2]} is zero at all values of uncertainty as shown in the figure, since this is the median value. The seismic vulnerability can also be estimated for other values of uncertainties based on code recommendations.

Figure 7.2 (a) Effect of total uncertainty (β T ) on construction of fragility curves, (b) Difference in discrete cumulative probabilities of exceedance with respect to total uncertainty for different S d values

Influence of Epistemic and Aleatoric Uncertainties

Seismic fragility for different frame configurations is assessed in the next section, taking into account the obtained values of epistemic and aleatory uncertainties. The seismic fragility of the RC-URM mid-rise frame to low design code level (HAZUS 2013) is also compared with the fragility of two variants of infilled frames (OGS and FI frames) considered in this study (Fig. 7.5).

Figure 7.3 Comparison of seismic fragility estimates considering different sources of uncertainty-epistemic (Ep), aleatoric (Al) and combined (Co) for (a) Bare, (b) OGS, and (c) FI frames

Seismic Fragility Assessment

General
Comparative Seismic Fragility of the Frames
Influence of Central Opening Size in Infill
Influence of Number of Bays and Number of Stories
Influence of Analysis Type
Influence of EDPs

It is noted that the seismic vulnerability of the three frames is very different from each other. On the other hand, the seismic vulnerability of FI frames with any Op is higher than that of the bare frame for mild, moderate and extreme damage conditions.