PROBABILISTIC PERFORMANCE ASSESSMENT
FOR MASONRY STRUCTURES OF SCHOOL
BUILDINGS IN EL SALVADOR
Luis Ernesto Mixco Durán
MEE17713

Supervisor:

Shunsuke SUGANOABSTRACTThis study focuses in the Probabilistic Performance Assessment for Masonry Structures of School
Buildings in El Salvador, through analytical fragility functions and its application to seismic risk
analysis, following the Performance-based Earthquake Engineering (PBEE) methodology developed by
PEER Center. Three combinations of two-story masonry buildings with openings (A: Mixed, B:
Reinforced Concrete Masonry Infill and C: Confined Masonry Walls) were taken as target structures,
based on configurations commonly found in the school’s portfolio of the country. Updated results of a
Probabilistic Seismic Hazard Assessment and soil amplification effects of El Salvador, were used.
Similarly, both the variation of seismic demand response as the deformation capacities of each structure,
have been taken into account. Three performance levels, known as Immediate Occupancy (IO), Life
Safety (LS) and Collapse Prevention (CP) limit states, were deemed, on which the Seismic Demand andDamage Fragility Functions were built, along with the calculation of the Failure Probabilities in termsof Mean Annual Frequencies (MAFs) of each combination. Results indicate that for IO and LS limit
states, the Combination B has the highest structural reliability (best seismic performance) for bothintensity measures [PGA and Sa (T1, 5%)], due to its low failure probabilities obtained concerning theother combinations. For the CP limit state, the combination C provides the greater structural reliability
for both intensity measures. Nevertheless, none of the combinations managed to meet the acceptable
MAFs at the less frequent seismic hazard levels of 475 and 975 years of return period.
Keywords: Confined Masonry, Masonry Infill, Limit States, Fragility Function, Failure Probability.
1. INTRODUCTION
In the last two centuries, El Salvador has suffered the onslaught of earthquakes from the two main
seismic sources that affect the country, shallow upper-crustal earthquakes due to geological local faults
activation (1965 and 1986 events), and offshore earthquakes due to subduction processes (2001 events).
These kinds of earthquakes have exposed the high seismic vulnerability of existing buildings along thecountry, especially those that belong to the education sector. Several types of structures are found in theschool portfolio, where masonry structures are predominant, and until now very few studies exist thatdeal more closely with their seismic risk in an integral manner. The principal objective of this study isto perform a Probabilistic Safety Assessment of three popular configurations (combinations) of school
masonry buildings focusing in three limit states associated to a shear failure mechanism and determine
which of them has more reliability against different design earthquakes hazard levels. A secondary
objective is to focus in the Conditional Failure Probability for specific acceleration ground motion
through the derivation of Seismic Demand and Damage Fragility Curves for the three combinations andmake comparison between them, considering the variation in both, the seismic demand response anddeformation capacities, with a strict management of its aleatory and epistemic uncertainties.


Ministry of Environment and Natural Resources, El Salvador.
Professor Emeritus, Hiroshima University, and Visiting Research Fellow, IISEE, BRI, Japan.

12. METHODOLOGY
The methodology used in this study is based on the analytical steps of the innovative Performance-Based
Earthquake Engineering (PBEE) developed by Pacific Earthquake Engineering Research (PEER)
Center. Generally, this starts from the definition of the target building, the determination of the nonlinear properties of its constituent structural elements and its grouping into an advanced computationalmodel. Then the results obtained from a probabilistic seismic hazard model, at the site of interest, areused to collect ground motions that will be applied to the structure. The response of the structure to theseseismic demands is obtained with a probabilistic seismic demand analysis, based on a nonlinear dynamic
analysis. To assess the ability of the structure to support such seismic actions, a probabilistic seismic
capacity analysis is carried out, based on reviewing real test data and comparing with empirical model
reflected in the nonlinear static pushover analysis results. Finally, the seismic reliability analysis of thestructure against the exceedance of limit states is obtained.
3. SELECTION OF TARGET BUILDINGIn Figure 2, a typical façade of target
building in direction X is observed. This
corresponds to a prototype structurecommonly used for school buildings in El
Salvador. Therefore, three types of systems
were selected as target buildings. These arebased on three combinations (named as A,
B, and C) of two-story masonry buildings,
Figure 1. Typical façade of the target building.
where openings (windows and doors) arefound in their longest direction. The combination A was defined in its 1st level of RC masonry infill(MI) walls and the 2nd story of Confined Masonry (CM) walls, the combination B has in its 1st and 2ndstory RC MI walls and the combination C has in its 1st and 2nd story CM walls. During the constructionof the computational model of each building, it was obtained that the eigenvalue first mode period of
the combination A, B, and C, were 0.174 sec., 0.179 sec., and 0.124 sec., respectively.
4. NONLINEAR PROPERTIES OF MI AND CM WALLS
Three computational 3D models for each structural combination
were built. The STERA3D V9.6 software (Saito T. 2004) wasused to perform the non-linear analysis, which provides somebuilt-in hysteresis models and represents internal stressdeformation with non-linear springs. For the MI panels, theanalytical model from (Mostafaei & Kabeyasawa, 2004) wasused. This model is based on a degrading trilinear backbone
curve similar to that shown in Figure 3, where restoring forcesand deformation capacities of Cracking (τcr, Rcr), Maximum(τmax, Rmax) and Ultimate (τu, Ru) States of the walls, comes to Figure 2. Backbone curve of MI andlight. It is important to highlight, the need to use more detailed CM walls with a Shear Failure Mode.
expressions that involve factors that influence the in-planestructural capacity of MI walls, based on experimental data instead of using an analytical approach. For
this reason, during this study, Dr. Sugano was developing equations for each characteristic point using
real experimental data and considering a Masonry Infill wall (RC columns + infill panel) as one element.
Thus, this would give a chance (for future works) to obtain more precise values of the MI non-linear
behavior. For the CM walls in the combination C, a similar shape of the backbone curve in Figure 3 wasused, where the value of each characteristic point is obtained from Sugano, S. 2018 empirical equations.

25. PROBABILISTIC SEISMIC HAZARD ASSESSMENT (PSHA)
The PSHA focuses on characterizing the seismic threat at the site where the structure is located, by
estimating the MAF of exceeding a specified ground motion intensity measure (IM), either PGA or Sa(T₁, 5%). As a product of this analysis, both uniform hazard spectra (UHS) and seismic hazard curves,
are obtained. Furthermore, this analysis helps to select a set of ground motions that jointly represent thesite hazard through four earthquake design levels (or hazard levels): 72, 250, 475 and 975 years of return
period. Figure 3 shows the approximation of seismic hazard curve for PGA and its equation in terms of
MAF. This approximation was made using the acceleration values (from the PSHA) for the four hazard
levels on soft soil site conditions. Figure 4 shows the response spectra of selected 40 ground motions
which satisfy (as much as possible) the results from the seismic hazard disaggregation for a specificperiod. This figure also shows a scaling technique based on the matching of the response spectra with
the UHS for a hazard level (e.g., 475 years), over a range of periods, which include the natural periodsof structural combinations, to minimize the dispersion in the nonlinear dynamic response.

Figure 3. Linear function and its equation ofseismic hazard curve for PGA and four design
earthquakes levels applied for all threecombinations.

Figure 4. 40 ground motions response spectra
matched to the UHS for 475 years of return
period (solid red line) over a range of periods of
0.12-0.18 sec (vertical dashed lines).

6. DAMAGE AND LIMIT STATES OR PERFORMANCE LEVELSIn this study, the Maximum Interstory
Table 1. Limit States for MI and CM walls database.
Drift Ratio (IDRmax) has been chosen as
RC MASONRY INFILL WALLS
the engineering demand parameter (EDP)
Authors
IO
LS
CP
Data
to measure the structural demandµ = 0.211%µ = 0.616%µ = 1.054%
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response. This measure can be related Cardone et
σ
COV
σ
COV
σ
COV
walls
al. (2015)
0.09 0.42
0.30 0.49
0.31 0.30
with the quantification of the in-planeµ = 0.219%µ = 0.81%µ = 1.588%
damage due to earthquake loading in both52
Sugano S.
σ
COV
σ
COV
σ
COV
CM and MI walls, using drift thresholds
walls(2018)
0.18 0.81 0.54 0.66
0.96 0.61
called Limit states or Performance
CONFINED MASONRY WALLS
Levels. In this study, three limit states,
118
Ruiz et al.
µ = 0.09%µ = 0.31%µ = 0.5%
known as Immediate Occupancy (IO),
walls(2009)µ = 0.081%µ = 0.535%µ = 0.927%
Life Safety (LS), and Collapse Prevention
171
Sugano S.
σ
COV
σ
COV
σ
COV
(CP) were deemed by a Shear failurewalls(2018)
0.01 0.88 0.48 0.90
0.64 0.69
mechanism. Table 1 shows the values ofthe limit states obtained from MI and CM walls experimental databases gathered by different authors,
together with their statistical measures, such as the median value (µ), standard deviation (σ) and thecoefficient of variance (COV). These databases were used and compared between them, to derive themost adequate conditional (fragility curves) and unconditional (MAFs) failure probabilities of eachstructural combination, on the basis, of which database provides less conservative values.

37. PROBABILISTIC SEISMIC DEMAND ANALYSIS (PSDA)
The PSDA focuses on evaluating the statistics of the dynamic responses of a structure and being able toderive seismic demand fragility curves. This can be achieved with the use of the Incremental Dynamic
Analysis (IDA), which is based on a series of nonlinear dynamic analysis under a multiplied scaled suiteof ground motion records (Vamvatsikos, D. 2002). Thus, the classified 40 ground motions mentioned
above, will be used to subject the structures under this procedure. Likewise, this process allows toregistering (for certain hazard levels of interest) the Record to Record Variability (RTR). Figure 5 shows
the IDA results obtained for each structural combination and each IM, either PGA or Sa (T 1,5%),reaching in total 5,765 analyses. Also, in this figure, a linear power relation between the 50 th percentile
EDPs and IM [𝐸𝐷𝑃 =a(IM)b] and its associated uncertainty (RTR=βD|IM) for each combination, is shown.

Figure 5. IDA results of each structural combination and each IM, with their equations and uncertainties.
8. PROBABILISTIC SEISMIC CAPACITY ANALYSIS (PSCA)
The PSCA relates the EDPs with damage measures (DMs) connected to the real structural deformation
capacity that an element could have. Thus, the seismic damage fragility functions can be obtained. It is
important to emphasize that the only way to assess the median capacity (mc) and random uncertainties(βcr) is to compare empirical models with real experimental data, for each limit state, making use of thedatabases shown in Table 1. Figure 6, shows an example of the procedure carried out for the combination
C and its Life Safety limit state, associated with the deformation at maximum strength (Rmax) from its
backbone curve. First, the experimental over calculated capacity ratio (Rexp/Rcalc) is computed.
Second, the statistics of these ratios are found through fitting them to a lognormal distribution, obtaining
the aleatory uncertainty (βcr). Finally, the median capacity will be derived by multiplying the 50 th
percentile of the ratios to the deterministic capacities (mcd) obtained from a static pushover analysis.

Figure 6. Procedure to determine the median capacity and structural capacity uncertainty.

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9. SEISMIC DAMAGE FRAGILITY FUNCTIONS (CONDITIONAL PROBABILITY)
The seismic fragility functions or also known as fragility curves represent the failure probability ofstructural element exceeding a limit state conditioned to a specific earthquake ground motion. Assumingthat the seismic response of structures follows a lognormal distribution, these fragility curves can beobtained through two approaches. The first related only to consider the seismic demand response
uncertainties (RTR=βD|IM), and the second one, with the introduction of both seismic demand andseismic structural capacity uncertainties (βC). The latter includes both the randomness in the material
properties, geometric characteristics (βCr) and the epistemic uncertainties (βCU) in the modeling, design
requirements and test data. These epistemic uncertainties were treated under a quality approach using
predefined values suggested by FEMA P695, where a value of 0.28 was determined. Eq. (1) shows theformulation of the seismic damage fragility function and Figure 7 shows the results of this concept toeach limit state (displaying its respective mc and βC) for each combination and using both IM, i.e. PGA
or Sa (T1, 5%), highlighting the existing sensitivity when using different IM in the fragility analysis.
1b
 ln m EDP  ln a  x b  m CC      ln x  ln m C a 
F RC im  x   1   2222
  C   D | IM   D | IM   C 
2
 1  D2 |IM   Cr2   CU




b



















(1)

where, Ф [·] is the standard normal probability distribution, 𝑥 is any value of a ground motion (im),from PSDA (see Figure 5): 𝐸𝐷𝑃 is the median EDP drift value (a and b, are regression parameters)and (βD|IM) is the seismic demand uncertainty, from PSCA (see Figure 6): (mc) is the median capacity,(βcr) is the seismic capacity aleatory uncertainty and (βcu) is the seismic capacity epistemic uncertainty.

mc = 0.687% (MI)mc = 0.312% (CM)βC-Comb A-B = 0.638
βC-Comb C = 0.658

mc = 0.235% (MI)mc = 0.096% (CM)βC-Comb A-B = 0.545
βC-Comb C = 0.498

mc = 0.931% (MI)mc = 0.651% (CM)βC-Comb A-B = 0.384
βC-Comb C = 0.447

Figure 7. Seismic Damage Fragility Functions for three combinations and both IM (PGA, Sa (T 1,5%).

10. SEISMIC RELIABILITY ANALYSIS (SRA-UNCONDITIONAL PROBABILITY)
The SRA is based on MAF computation of exceeding a limit state of a structural element, where on thisoccasion it would not be conditioned to a specific value of ground motion, but on a whole intensity
domain, covering all possible earthquakes that can occur in a particular area and to which the structure
can be exposed. Considering again the seismic demand and structural capacity uncertainties, theunconditional failure probability can be computed by convolving the seismic damage fragility curvewith the slope of the seismic hazard curve, as expressed in Eq. (2):m  DM C    D  C    FRC x  d IM  x  k 0   c 
x
 a 

1b

1 k 2
2exp 2  D2 | IM   Cr2   CU

2 b








(2)

where, from PSHA: k0 and k are regression parameters, as shown in Figure 3 for PGA. It should be
mentioned, that this was also done for the Sa (T1, 5%). The other parameters were explained in Eq. (1).

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Table 2 shows the results of failure probability of three structural combinations, highlighting whether
or not they meet a desired acceptance criteria associated with the MAF of an Earthquake Design Levels.
Similarly, it is shown which of the combinations presents more structural reliability, based on higher
return periods to exceed a specific limit state.
Table 2. Unconditional failure probability for 3 combinations and both (IM) [PGA or Sa (T 1, 5%)].

11. CONCLUSIONS
The investigation resulted in the following main conclusions: When the aleatory and epistemic uncertainties of both seismic demand and structural capacity are
not taken into account, the real fragility of the structure can be overestimated.
 According to Seismic Damage Fragility Curves, for the Immediate Occupancy (IO) and Life Safety(LS) limit states, the combination C presents the higher fragility than the others. However, inCollapse Prevention (CP) limit state, less fragility is observed.
 For IO and LS limit states, the Combination B has the highest structural reliability for PGA andCombination C has the lowest seismic performance in both (IM). For CP limit state, theCombination C has the highest structural reliability for both (IM) None of the combinations managed to meet the acceptable MAFs at the less frequent seismic
hazard levels of 475 and 975 years of Return Period (RP), in any limit states.
ACKNOWLEDGEMENTS
I would like to express my sincere thanks to my thesis supervisor, Dr. Sugano S., for his tireless efforts
to provide me with the information, knowledge, and support necessary to complete my work. I would
also like to appreciate the valuable help from Dr. Azuhata, Mr. Inukai and Dr. Suwada for their active
participation as advisers, who were able to provide constructive criticism to my master thesis work.
REFERENCES
Cardone, D., and Perrone, G., 2015, Earthquakes and Structures, Vol. 9, No. 1, 257-279.
FEMA P695, 2009, Washington, D.C.
Lu, D.G., Yu, X.H., and Jia, M.M., 2012, Harbin Institute of Technology, Harbin, 150090, China.
Mostafaei, H., and Kabeyasawa, T., 2004, Bull. Earthq. Res. Inst., Earthquake Spectra 24, 701–723.
Ruiz-García, J., and Negrete, M., 2009, J. Earthq. Eng., 13, 520-539.
Saito, T., 2004, Structural Response Analysis 3D (STERA 3D v.9.6 in 2018), Technical Manual, Japan.
Sugano, S., 2018, Lecture notes on Masonry Structures II, IISEE/BRI (2017-2018).
Vamvatsikos, D., and Cornell, C.A., 2002, Earthq. Engineering & Structural Dynamics, 31, 491–514.

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