Citation: Campos, E., T. Azuhata, Y. Otsuka (2022), Seismic Evaluation of reinforced concrete buildings inSan Salvador, El Salvador; considering the latest seismic hazard analysis, Synopsis of IISEE-GRIPS
Master’s Thesis.

SEISMIC EVALUATION OF REINFORCED
CONCRETE BUILDINGS IN SAN SALVADOR, EL
SALVADOR; CONSIDERING THE LATEST SEISMIC
HAZARD ANALYSIS
Eugenia Campos 1
MEE21711

Supervisor:Tatsuya AZUHATA2, Yuri OTSUKA3
ABSTRACTThis investigation focuses on the seismic evaluation of low-midrise reinforced concrete buildings in SanSalvador, considering the inelastic demand defined by the current seismic design code (NTDS-94).
Moreover, the latest Probabilistic Seismic Hazard Assessment (PSHA) for the country, which will be
the base for the new seismic code, was used. The implemented methodology was the Probabilistic Based
Earthquake Engineering (PBEE) framework, which involves a holistic overview of the performance
integrating hazard, structural, and damage analysis. Four simplified framed structures treated as a single
degree of freedom systems were studied, two are based on El Salvador seismic standard, and the othersare based on Japanese seismic provisions. The above with the intention to compare the influence of thehazard definition and the required capacity specified in each building code on the building's performance.
Two approaches were employed to give a solution to the PBEE basic formulation; numerical integration
and approximate analytical solution. We calculated the probabilities of limit state exceedance in 50 years
in terms of inter-story drift ratios. Based on the results, the probabilities of exceeding the design limit
drift imposed by El Salvador's seismic code of 0.015 rad are more than 5% for both Salvadoran SDOF
systems (6-story and 10-story buildings) calculated using both approaches. We observed that ElSalvador models have higher probabilities of exceeding safety limits than Japanese models. Hence, theinfluence of the seismic hazard curve and the seismic demand, which in the case of El Salvador depends
on the response reduction factor R, was evident. The approximate solution derived more conservative
results in the performance of the building models studied.
Keywords: PBEE, Reinforced Concrete building, Failure probability.
1. INTRODUCTIONEl Salvador is located in Central America in a zone of high seismicity. The capital city San Salvador
lately presents a tendency to develop vertical urbanization zones, for residential and commercialbuildings, due to the lack of space for new horizontal constructions. Reinforced concrete predominates
as a structural system preferred for mid-rise and high-rise buildings. In the 1986 earthquake, thisconstruction system exhibited a deficient performance, causing the total collapse of many facilities, andseveral more were left badly damaged. The latest seismic code has not been updated since 1994. El
Salvador's Ministry of Environment and Natural Resources (MARN) is developing technical materials
1Engineers and architects, specialized services (INGENYARSE), El Salvador.
Department of Structural Engineering, Building Research Institute.
3
International Institute of Seismology and Earthquake Engineering, Building Research Institute.
2

1that will be the primary inputs and guidance in creating the new seismic design code, including a more
complete PSHA. The current seismic code focuses on life safety, leaving in a second perspective thedamage control on the structure and the time and cost of rehabilitation. In other countries, however, theperformance-based design approach is progressively being adopted. Recently, a second-generation andbroader methodology has been developed by the Pacific Earthquake Research Institute (PEER). Thismethodology establishes the estimation of building performance from a thorough probabilistic overview.
The results can be expressed in more tangible parameters (e.g., downtime, monetary losses, casualties,reparation cost) for the governmental authorities, stakeholders, and proprietaries of structures. From thisperspective, it is a valuable tool for risk analysis and structural reliability assessment. Considering theabove, the performance of San Salvador reinforced concrete buildings designed by the current seismiccode against future earthquakes, which can be predicted by the most recent PSHA is still uncertain. ThePBEE probabilistic-based method is a convenient alternative to evaluate the safety of structures, basedon different limit states in a nondeterministic form. The current research addresses a probabilistic
performance assessment for reinforced concrete buildings in San Salvador, following the provisions in
the current seismic code. Moreover, we explicitly consider the seismic hazard defined by the latest
PSHA.
2. METHODOLOGY
2.1. PEER Performance-Based Earthquake Engineering Methodology
The Pacific Earthquake Engineering Research Center has established a new and more robust
methodology of performance-based earthquake engineering, which is based on four stages: 1) Hazard
Analysis, 2) Structural Analysis, 3) Damage Analysis, and 4) Loss Analysis; each of them involves adifferent key parameter such as Intensity Measure (IM), Engineering Demand Parameter (EDP),Damage Measure (DM) and Decision variable (DV), and inherent uncertainties associated. The
methodology can be described by Eq. (1), based on the integration of probabilities related to the stages
mentioned above using the total probability theorem.
𝜆(𝐷𝑉) = ∭ 𝐺⟨𝐷𝑉|𝐷𝑀⟩|𝑑𝐺⟨𝐷𝑀|𝐸𝐷𝑃⟩|𝑑𝐺⟨𝐸𝐷𝑃|𝐼𝑀⟩|𝑑𝜆(𝐼𝑀)(1)Where 𝜆(𝐷𝑉) is the mean annual frequencies of exceedance (MAF) for DV, 𝜆(𝐼𝑀) represents the meanannual frequencies of exceedance (MAF) for IM, and 𝑑𝐺⟨𝐴|𝐵⟩ means conditional probabilities for thecomponents IM, EDP, DM, and DV, which can be represented by a complementary cumulative
distribution function (CCDF).
The IM selected was Peak Ground Acceleration (PGA), the EDP inter-story drift ratio (IDR)
and the DM was also selected in terms of design limits of IDR. The last stage, Decision variable is notconsidered in this research. Whit the above, Eq. (1) can be reduced as follows.
𝜆(𝐷𝑀) = ∫ 𝐺⟨𝐷𝑀|𝐼𝐷𝑅⟩|𝑑𝐺⟨𝐼𝐷𝑅|𝑃𝐺𝐴⟩|𝑑𝜆(𝑃𝐺𝐴)(2)

2.2. Analytical approximation by Cornell formulation
Eq. (2) could be solved by the analytical approximation of three components: hazard, demand, andcapacity. First, we assumed the approximation of the seismic hazard curve with Eq. (3).
𝜆(𝑃𝐺𝐴) = k 0 (𝑃𝐺𝐴)−𝑘(3)Where 𝑘0 and 𝑘 are coefficients from a regression analysis of the seismic hazard curve in̅̅̅̅̅ can be predicted
logarithmic scale. Then, the demand defined in terms of the mean 𝐼𝐷𝑅
approximately by Eq. (4), which comes from the mean curve of a set of responses in the levelsof PGA of interest.

2̅̅̅̅̅ = 𝑎(𝑃𝐺𝐴)𝑏𝐼𝐷𝑅

(4)

Where 𝑎 and 𝑏 are constants from regression analysis for the mean curve. Finally, the annual probabilityof performance level not being met or 𝜆(𝐷𝑀) could also be expressed as follows.
1 𝑘2

𝑃𝑓 = 𝜆(𝐷𝑀) = 𝜆(𝑃𝐺𝐴𝐷𝑀 ) exp [2 𝑏2 (𝛽(2𝐼𝐷𝑅|𝑃𝐺𝐴) + 𝛽𝐶2 )](5)

1𝐷𝑀𝑃𝐺𝐴𝐷𝑀 𝑏=(𝑎 )(6)Where 𝛽(𝐼𝐷𝑅|𝑃𝐺𝐴) represent the dispersion of IDR, calculated as a standard deviation. and 𝛽𝑐 is thedispersion of the capacity ratios. The above expressions are found in multiple references. First proposedby (Cornell, 1996), and a similar approach is stated as an analytical formulation of seismic demandhazard in (Lu et al., 2012).
3. DATAFor the First step, hazard analysis, approximated seismic hazard curves for El Salvador and Japan werederived. The first one is based on the Seismic Hazard Map for PGA (g) of El Salvador; for a return
period of 475 years, taken from the latest PSHA from (Mixco, 2021). For Japan, the seismic hazard
curve approximation was taken from (NAGAE et al., 2006) and is based on (Architectural Institute ofJapan, 2015). Both are compared in Figure 1(a).
We use Incremental Dynamic Analysis (IDA) (Vamvatsikos & Cornell, 2002) for thestructural analysis phase. Four Model buildings were considered, a pair of six-story and ten-story
facilities simplified as a single degree of freedom systems (SDOF) defined by El Salvador's seismiccode and Japanese provisions. Specifically, the yielding strength coefficient 𝑐𝑦 was taken from theinelastic response spectrum of El Salvador, and for Japanese models, a constant value of 0.3 wasconsidered. Takeda model was adopted (Takeda, 1970) to evaluate the nonlinear properties; the tri-linear
capacity curves are shown in Figure 1(b).
Figure 1. (a) Approximation of seismic hazard curves of El Salvador, Japan, and real hazard curve of El
Salvador (MAF= Mean annual rate of exceedance). (b) SDOF model representation and Capacity curves.
Figure 2 shows the response spectrum of the selected waves for the analysis, corresponding to40 Inland earthquakes recorded in site class D, with magnitudes from 6.5 to 6.9Mw and source-to-site
distances from 13 to 40km (Medina & Krawinkler, 2004). In the damage analysis stage, we defined theultimate deformation capacity fragility curve to evaluate safety limit states based on the research of(NAGAE et al., 2006), and (Architectural Institute of Japan, 2015) experimental results of calculated toultimate deformation ratios. The median of the ratios was 1.41, and the equivalent dispersion 0.39.

3Figure 2. Acceleration response spectrumof the selected 40 Inland earthquakes
scaled at 𝑃𝐺𝐴 = 1𝑔.

4. RESULTS AND DISCUSSION
Incremental dynamic analysis was performed tocharacterize the responses in different seismic intensity
levels. The range of PGA applied varies from 0.1g to
1.5g. For each building, 600 points conformed the IDAcurves. We applied counted statistics to the results to getthe 16th, 50th and 84th percentile (see Figure 3(a)), thenwe made a comparison between the medians of allmodels (see Figure 3(b)) as well as the equivalentdispersion (Figure 3(c)).
A lower slope was identified in the mediancurves for Salvadoran building models, which meanshigher story drifts are achieved for the same level ofPGA. This pattern is related to the structure's capacity.
In the case of El Salvador, it mainly depends on theresponse reduction factor (R). Additionally, theequivalent dispersions were higher for Salvadoranmodels, disregarding the buildings' height.
Four safety limit drifts were studied, 0.01,0.015, 0.02, and 0.03rad; the second one corresponds tothe design limit drift indicated in the seismic code of El
Salvador. Following the first approach, numericalintegration, we calculated the hazard curve of IDR(figure 4 (a)). We then derived the mean annual rate ofexceedance of the above limit drifts (figure 4(b)).
Comparing the hazard curves of IDR, we observe thatthe displacement demand will be more significant for El
Salvador building models. Additionally, as the slope ofdescending in Japan's curve is steeper, the mean annual
exceedance rate decays more rapidly in higher drifts,
contrary to El Salvador's 6-story and 10-story models.
The return period, which is the inverse of the MAF of Figure 3. (a) 16th, 50th, and 84th
the established limit drifts, is lower for the SDOF percentiles of seismic responses for El
system of El Salvador, implying that the limit drifts will Salvador 6-story building. (b) Mediancomparison.
(c)
Equivalent
be exceeded more frequently. Additionally, we applied curve
dispersioncomparison.
the approximate procedure, obtaining the relationship ofPGA and mean IDR from the results of IDA as shownin Figure 5(a), and with Eq. (5), we calculate the mean annual rate of exceedance of the safety limit
drifts (Figure 5(b)).

4








Figure 4. (a) Hazard curve of IDR for all buildings (b) Annual failure probability and return periods
given limit states of 0.01, 0.015, 0.02, and 0.03, calculated with numerical integration.



Figure 5. (a) Regression analysis on IDA results (b) Annual failure probability and return periods given
for limit states of 0.01, 0.015, 0.02, and 0.03, calculated using Cornell formulation.
For a better representation, we transformed the MAF into probabilities of exceedance safety
limit drifts in 50 years, assuming a poison process (Figure 6). Higher POE were obtained for El Salvador
systems compared to those from Japan using both calculation approaches. From the results, andconsidering El Salvador's design allowable drift, the probabilities of the studied country-based structures
not meeting this requirement are high (more than 5%). Nevertheless, considering the limit state definedby a drift of 0.03 rad, which could represent the onset of collapse, the probabilities are below 2%, except
for the response of the 6-story building based on Cornell formulation. Comparing both methods, higher
POE were found with the approximate solution, varying from 1.2 to 4.5 times the numerical integration
results.





Figure 6. (a) probabilities of exceedance IDR in 50 years calculated using numerical integration (b)probabilities of exceedance IDR in 50 years calculated using Cornell formulation.

55. CONCLUSIONS
We used the latest study of seismic hazard in El Salvador and the current seismic code to define thebuilding models' capacity for evaluating the performance of El Salvador buildings in a probabilistic
approach. Moreover, Japanese building models were used considering the seismic hazard of Japan andthe capacity specified in the codes to compare the seismic responses.
The probability of exceedance limit states was higher for El Salvador buildings considering
the 40 Inland waves using both calculation approaches, numerical integration, and analytical solution.
The capacity of El Salvador buildings is directly related to the response modification factor R,
which made the seismic coefficient small compared to Japan. Reconsideration in the definition of thisfactor is needed in the future seismic code to have more reliable buildings.
The results obtained using the approximate solution proposed by Cornell are moreconservative. Nevertheless, this method is more practical and still reliable.
In this study, we applied the incremental dynamic analysis outcome to the Cornell method,
specifically to obtain the mean IDR and the uncertainties. Another simplified approach, such as thecapacity spectrum method, could be studied to reduce the calculation time and effort.
ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my advisors and supervisors, Dr. Otsuka Y. andDr. Azuhata T., for their continuous guidance and support throughout this research.
REFERENCES

Architectural Institute of Japan, A. (2015). Recommendations for Loads on Buildings.
Lu, D.-G., Yu, X., & Jia, M. (2012, July). Analytical Formulations of Fragility Functions withApplications to Probabilistic Seismic Risk Analysis. Proceedings of the 15th World
Conference on Earthquake Engineering.
Ministry of Public Works (MOP). (1994). Norma técnica para Diseño por sismo [Technicalstandard for seismic Design].
Mixco, L. (2021). Dissemination of technical data for updating the national standard fordesign and construction in El Salvador, MARN. In MARN.
NAGAE, T., SUITA, K., & NAKASHIMA, M. (2006). Performance Assessment for
Reinforced Concrete Buildings with Soft First Stories. Annuals of Disaster Prevention
Research Institute, Kyoto University.
Takeda, T. (1970). Reinforced Concrete response to simulated earthquakes. Journal of theStructural Division, 96, 2557–2573.
Vamvatsikos, D., & Allin Cornell, C. (2002). Incremental dynamic analysis. Earthquake
Engineering and Structural Dynamics, 31(3), 491–514.

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