VULNERABILITY MAPS FOR RC MOMENT FRAMES FOR MEXICO CITY S METROPOLITAN AREA UNDER A M S =8.1 EARTHQUAKE SCENARIO ABSTRACT

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1 Proceedings of the th U.S. National Conference on Earthquake Engineering April -,, San Francisco, California, USA Paper No. VULNERABILITY MAPS FOR RC MOMENT FRAMES FOR MEXICO CITY S METROPOLITAN AREA UNDER A M S =. EARTHQUAKE SCENARIO Arturo Tena-Colunga, Eber A. Godínez-Domínguez and Luis E. Pérez-Rocha ABSTRACT This paper presents vulnerability maps for reinforced concrete moment frames (RCMFs) in Mexico City s Metropolitan Area for a M s =. earthquake scenario assessing peak nonlinear dynamic responses using the concept of displacement ductility demand spectra (DDDS). The considered earthquake scenario is an equivalent scenario to the M s =. September, Michoacán Earthquake that severely affected Mexico City. These vulnerability maps were compared with the geographic area of severe structural damage and collapses mapped during the earthquake. Based on the results of this study, it is believed that this procedure can be used with confidence to locate zones of high demands for different structural systems and earthquake scenarios, being therefore potentially useful for urban planning of cities located in zones of high seismic risk. Introduction The seismic evaluation of existing structures is an issue of paramount importance in earthquake engineering. The evaluation of existing structures is not only important to assess the vulnerability of specific structures, but also to complement strategic plans directed to mitigate the seismic hazard in the built environment of a given region based on integral vulnerability studies. This paper summarizes an integral study where vulnerability maps for reinforced concrete moment frames (RCMFs) in Mexico City s Metropolitan Area were defined for a M s =. earthquake scenario assessing peak nonlinear dynamic responses using the concept of displacement ductility demand spectra (DDDS) presented in Tena-Colunga (). The considered earthquake scenario is an equivalent scenario to the M s =. September, Michoacán Earthquake that severely affected Mexico City. The methodology used in this study, as well as a summary of previous vulnerability studies conducted for this region are addressed in following sections. Professor, Departamento de Materiales, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo, Col. Reynosa Tamaulipas, Mexico City, MEXICO. PhD Student, Departamento de Materiales, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo, Col. Reynosa Tamaulipas, Mexico City, MEXICO. Researcher, Instituto de Investigaciones Eléctricas, Reforma, Col. Palmira, Cuernavaca, MEXICO.

2 Previous Vulnerability Studies For Mexico City s Metropolitan Area Mexico City was severely affected during the earthquake, among other reasons, because of important amplifications in the ground motions due to site effects, particularly in the lake-bed region, were very soft soil deposits (clay) of different depths exist. The lack of a reasonable seismic instrumentation in Mexico City at the time of the earthquake (only instruments: in firm soils, in the lakebed region, and one in transition soils) allowed only a limited understanding on how site effects affected the existing built environment at the times, as it was difficult to correlate the observed damage with the recorded ground motions. From the lakebed instrumentation, only SCT station was located in a zone where heavy damage and collapses were observed. The other five stations were located in places were no severe structural damage was observed. In fact, there were no instruments located in the zone where most collapses were observed during the earthquake: Roma and Condesa districts, as well as downtown area. Given that the characteristics of the built environment and soil deposits near SCT site were very similar to those found in Roma and Condesa districts, it was difficult to explain why there were much more collapses in these last two districts than near SCT. Therefore, it was clear that a densification of the instrumentation in Mexico City was much needed to understand better why this happened during the earthquake (in addition to many other valuable uses, as to improve the seismic zonation of the city for design purposes, etc). The most important densification of the instrumentation in Mexico City s Metropolitan Area occurred between and, when more than instruments were installed, about of them in the free field (Figure ). Most of the instruments were located in the lakebed zone where most severe damage and collapses were observed during the, and earthquakes. The first important moderate earthquake recorded by this network was the April, earthquake (M s =.), a benchmark event that allowed us to understand better site effects in Mexico City s valley. As the network continued to have good performances recording earthquakes of M> to help understand the dynamics of this region, and the studies of the recorded ground motions provided consistent results, then, the interest on vulnerability maps for Mexico City s Metropolitan Area to assess the performance of the built environment triggered. Perhaps the first study with this orientation is the one presented by Gómez-Bernal et al. (), where they showed Arias Intensity tensors and ductility demands contours (incomplete) for some areas of Mexico City s Metropolitan Area for elastic-perfectly-plastic systems for a period range between.s to.s. They used for their study the recorded ground motions at stations for the April, earthquake (M s =.), scaling them to the earthquake based upon a simple but arbitrary factor (f) based on the Arias intensity. Pérez-Rocha () presented hazard maps based upon average pseudo acceleration spectral ordinates (S a /g) for systems with effective structural periods T=±.s and T=±.s for four different earthquake scenarios that may affect Mexico City s Metropolitan Area: (a) a M s =. subduction earthquake from the coasts of Michoacán State, a similar scenario to the September earthquake, (b) a M s =. subduction earthquake from the coasts of Guerrero State, a similar scenario to the July, earthquake, (c) a M s =. subduction earthquake from the coasts of Guerrero State, the worst scenario expected by seismologists from the Guerrero Gap and, (d) a M s =. normal faulting earthquake occurred km from Mexico City.

3 Latitude Figure. Strong motion array in Mexico City s Metropolitan Area available since. Figure. Boundaries defined for firm soil sites (green line) and transition soil sites (red line for T=.s, blue line for T=s). Reinoso and Ordaz () presented a study where spectral amplification ratios for acceleration for dominant periods T=.s, T=s, T=s and T=s are shown for the same region using a similar procedure than the one outlined in Pérez-Rocha (). Huerta and Reinoso () presented maps for the elastic input energy (E I ) for the April, earthquake (M s =.) for systems with effective structural periods T=s, T=s, T=s and T=s. They also presented maps for the Normalized Hysteretic Energy (NE H ) for elasticperfectly-plastic systems with µ= for the same earthquake scenario and structural periods. Finally, maps for the elastic input energy (E I ) for systems with an effective structural period T=s were presented for the following additional earthquakes: (a) September, subduction earthquake (M=.), (b) September, subduction earthquake (M=.) and, (c) June, normal faulting earthquake (M=.). Therefore, previous studies have concentrated primarily on average elastic demand parameters to assess the vulnerability of Mexico City s Metropolitan Area (Gómez-Bernal et al., Pérez-Rocha, Reinoso and Ordaz, Huerta and Reinoso ). The only studies that considered inelastic response parameters (for elastic-perfectly-plastic systems) are those presented by Gómez-Bernal et al. () and the work presented by Huerta and Reinoso (). This paper briefly summarizes a study where vulnerability maps for reinforced concrete moment frames (RCMFs) in Mexico City s Metropolitan Area are defined for a M s =. earthquake scenario assessing peak nonlinear dynamic responses using the concept of displacement ductility demand spectra (DDDS). RCMFs are studied as most of the medium-rise buildings that were severely damaged or collapsed during the September, earthquake

4 had this structural system, as it can be observed from Tables and. This study constitutes a step forward from previous vulnerability studies as: (a) degrading characteristics of RC structures are considered using the Takeda model and, (b) minimum strength requirements for RC structures related to the versions of Mexico s Federal District Code (RCDF) that were effective before the earthquake are assessed. Table. Damage inventory of RC structures and bearing walls from the September, earthquake in Mexico City (adapted from Fundación ICA, ). STRUCTURAL SYSTEM NUMBER OF STORIES to to to to or more Total of Structures Damaged Structures % Bearing Walls,,,. RCMFs made of waffle flat,. slabs RCMFs,,,. RC frames & walls. Total of Structures,,,,. Damaged Structures % Table. damage and collapse inventory of buildings for the September, earthquake in Mexico City (adapted from Instituto de Ingeniería, ). STRUCTURAL SYSTEM Reinforced Concrete Moment Frames (RCMFs) Steel Moment Frames (SMFs) RCMFs made of Waffle Flat Slabs Masonry Bearing Walls Other Systems Total DAMAGE YEAR OF CONSTRUCTION NUMBER OF STORIES < - > - - > TOTAL Methodology Used The methodology used in this study is described in detail in Godínez-Domínguez () and schematically summarized in Figure. This methodology takes advantage of previous research conducted by Pérez-Rocha () to estimate ground motions for the site for a given earthquake scenario based upon empirical data, and the vulnerability of the structural system is assessed by using the concept of displacement ductility demand spectrum (DDDS) as presented and discussed in detail elsewhere (Tena-Colunga ). A DDDS relates peak displacement ductility demands (and other important response quantities, i.e., displacements) with structural periods of nonlinear SDOF systems with a given yield strength. In order to compute a DDDS for a given building inventory located in a region of interest from a vulnerability assessment viewpoint, the following information is needed:

5 . Acceleration records for the sites of interest.. Estimates of natural periods (frequencies) of response for subject structures.. Estimates for the lateral load capacities for the building inventory of interest.. A suitable hysteretic model for the structural system of interest. Ground Motion Assessment As mentioned before, Mexico City had only stations available at the time the September, earthquake stroke the city. In order to estimate the intensity of the ground motions in Mexico City s Metropolitan Area for an earthquake scenario similar to the M s =., September earthquake, a methodology to define additional artificial acceleration records related to this earthquake scenario was required, as briefly described in following sections. Fourier Amplitude Spectra (FAS) for Firm Soil Sites Motion This study used a method where the records of small (M s <) or moderate (<M s <) earthquakes are used to simulate the motions produced by greater earthquakes, as described in detail elsewhere (Pérez-Rocha, Godínez-Domínguez ). The relative amplifications of the ground motions can be described quantitatively by means of empirical transfer functions (ETF). For any arbitrary site, Fourier Amplitude Spectra (FAS) for the site is specified by means of the product between the ETF for the site and the FAS in firm soil for a postulated earthquake. For the free-field stations of the Strong Motion Array available in Mexico City since (Figure ), Pérez-Rocha () obtained statistical measurements from several earthquakes to describe the observed dynamic amplifications in the ETF. He calculated average ETF (two horizontal components) and coefficients of variation which are relatively small (between. to.). The intention of this was to construct a database of ETF that would allow developing a spatial interpolation model (using Bayes method) with the purpose of having reasonable estimations for ETF for uninstrumented sites within Mexico City s Metropolitan Area. Generation of Artificial Acceleration Records The procedure used for obtaining synthetic acceleration records considers the use of the updated average ETF obtained by Pérez-Rocha (until ) and the average FAS corresponding to firm soils. For this study, the average FAS obtained for CU station is taken as the average FAS for firm soils. During the scaling process of the seismic source, the recorded ground motions for the stations for the April, earthquake (M=.) were used as Green s functions. Synthetic records (two horizontal components) for the sites were obtained with a specialized program developed by Pérez-Rocha. The general procedure to obtain the synthetic records is summarized elsewhere (Godínez-Domínguez ). The final stages of the procedure used to obtain an artificial accelerograms after scaling the seismic source is illustrated in Figure. FAS S and SA S corresponding to the Green s function are depicted with red ink. Target scaled FAS STE and Sa STE are depicted with yellow ink. The generated artificial acceleration record and their corresponding FAS AR and Sa AR are depicted with blue ink. As observed in this figure, the generated artificial record matches well the target FAS STE and Sa STE for this site.

6 Methodology Characterization of the structural system Characterization of seismic risk for the site Acel m/s Assessment of the lateral load capacity and selection of the hysteretic behavior Estimates of dynamic properties Soil Profile Type Topographic and geologic factors Seismic source and path effects Tiempo (Seg) Displacement ductility demand spectra Estimates of dynamic properties Acceleration records for the site Amplitud Sa Periodo T (Seg) Ambient vibration tests Forced vibration tests Analytical methods Simplified formulas Frecuencia f (Hertz) Assessment of the lateral load capacity and selection of the hysteretic behavior Figure. Final steps of the procedure used to compute artificial acceleration records. Limit analysis Pushover analysis Code estimates considering the year of construction Figure. Methodology used for the vulnerability assessment of structures using DDDS. Characterization of the Structural System Since most of the RCMF buildings that experienced severe damage or collapse were medium-rise buildings between and stories built before (Table ), from a global vulnerability viewpoint, it was necessary to estimate the approximate dynamic properties, the lateral strength required by building codes of the times and to define a suitable hysteretic model for RCMFs, as described below. Estimates of Natural Periods The expressions proposed by Murià and González () to estimate fundamental periods of vibration of RCMF buildings located in Mexico City s Metropolitan area were used in this study (T=.N for firm soils, T=.N for soft soils, where N=number of stories). These expressions were obtained from measurements of dynamic properties of existing buildings in Mexico City s Metropolitan Area. Fundamental periods of vibration for RCMFs buildings from to stories in height were estimated using these expressions, taking into account the damage survey reported by the Institute of Engineering of UNAM in (Table ). Estimates of Lateral Load Capacities Lateral load capacities for existing RCMFs buildings in Mexico City s Metropolitan Area were crudely estimated according to the minimum nominal strength required by the building codes that were effective before the September, earthquake, this is, RCDF-,

7 RCDF-, RCDF- and RCDF-. The seismic coefficient c for the elastic design spectra for the building codes of reference are reported in Table. For RCDF- and RCDF- codes, B category stands for buildings with non-structural walls properly linked to the structural system and B category for buildings where non-structural elements are properly separated from the structural system ( Fundación ICA, ). From to, RCDF norms used a constant value for the seismic coefficient, independent from the building s period, but dependent on the soil profile type (Table ); in addition, allowable stresses were used for the design of structures. The first regulation in Mexico to define elastic design spectra as known today and to use ultimate strength design criteria was RCDF- code. Response modification factors Q and strength reduction factors Q were first introduced in RCDF-, and Q= and Q= were allowed for the design of RCMF buildings. It is worth noting that RCDF- established that c/q a. Table. Seismic coefficient c=v/w for the elastic design spectra for different versions of Mexico s Federal District Building Code, for the RCMF buildings under study. FIRM SOILS (SOIL PROFILE TYPE I) Number of Stories Period (s) RCDF- RCDF- (B) RCDF- (B) RCDF- (B) RCDF- (B) RCDF- < Transition Soils (Soil Profile Type II) Number of Stories Period (s) RCDF- RCDF- (B) RCDF- (B) RCDF- (B) RCDF- (B) RCDF- < Soft Soils (Soil Profile Type III) Number of Stories Period (s) RCDF- RCDF- (B) RCDF- (B) RCDF- (B) RCDF- (B) RCDF- < Overstrenght sources associated to these structural systems were also crudely considered with an overstrength factor R =. In the new RCDF- seismic provisions an overstrength factor R= is proposed for building structures with natural periods greater than. seconds. Selected Hysteretic Model A variation of Takeda model as presented by Otani was used to model the hysteretic behavior of RCMFs (Godínez-Domínguez ). Vulnerability Maps for RCMF Buildings in Mexico City for a M s =. Earthquake DDDS were computed for each building category and code (RCDF-, RCDF-, RCDF- and RCDF-) for all the acceleration records and soil profile types, considering nominal strength and overstrength sources for a period range <T<s. From these DDDS,

8 vulnerability maps based on contours of equal displacement ductility demands and nonlinear displacements were defined for the RCDF version and the natural structural period of interest. The fundamental structural periods of interest were T=.s, T=s, T=.s and T=s, corresponding to RCMF buildings from to stories in height, were most of the severe damage or collapses were observed during the earthquake (Table ). As explained in detail in Godínez-Domínguez (), a total of vulnerability maps were constructed, for ductility demands and for nonlinear displacements. Given the lack of instrumentation for firm soils (hill zone) and transition soils sites in the east of Mexico City s Metropolitan Area (Figure ), the average DDDS obtained for firm soils and transition soils (T=.s and T=s) were used in these borders to force the curves to follow these limits, as depicted in Figure. Some of the most interesting results are depicted in Figure, where the vulnerability maps based on contours of equal ductility demands (µ) for RCMF structures considering overstrength sources for each code version of utmost interest [RCDF-, RCDF- (B), RCDF- (B) and RCDF- (Q=)], and the strongest ground component are compared among them for the structural period of interest T=s. Vulnerability maps for B type structures are presented for RCDF- and RCDF- and for Q= for RCDF- as they are the most representative code category from the existing building inventory of the times. A color scale for µ values is depicted in each map. Elastic response is depicted with white (from to ), whereas important damage could be associated to µ>. Because of the nonductile detailing of the times, severe damage could be associated to µ> and collapses to µ>. The resulting vulnerability maps are directly compared with the geographic area of heavy structural damage and collapses mapped during the earthquake, as the thick blue contour line depicts the zones where damage was observed during the September, earthquake and the thick green contour line depicts the zones were the most severe damage and structural collapses were observed. It can be observed from Figure that for RCMF structures about - stories in height (T=s), ductility demands µ could be expected for the minimum standards of RCDF- code, but since there were not many RCMF structures of such characteristics available in the city, this fortunately did not happen. Only structures with severe damage could be associated to this category, analyzing the data of Table. Most medium-rise RCMF structures (standard frames and RC frames composed with waffle flat-slabs) were built according to RCDF-, RCDF- and RCDF- codes, so these maps are the most interesting to observe to correlate with the heavy damage reported in Table and depicted in the zones with thick green and blue line contours in the maps presented in Figure. It is observed that ductility demands µ are found within the blue and green contours for RCDF-, RCDF- and RCDF- codes, so important and severe structural damage, as well as structural collapses, should be expected for such building categories. This fact correlates well with the data presented in Table for RCMFs and RCMFs made of waffle flat slabs. From the evolution viewpoint of RCDF codes to protect RCMFs of T=s against strong earthquakes within Mexico City s Metropolitan Area, one can conclude that RCDF- considerably reduced the hazard with respect to the previous RCDF- code. However, RCDF- and RCDF- increased the vulnerability of such structures. There are similarities in the

9 ductility demand contours of RCDF- and RCDF- codes, but the main difference is that RCDF- code had improved provisions for the seismic detailing of RCMF structures with respect to previous codes. This fact may explain why fewer structures of this category built according to RCDF- collapsed or were severely damaged compared with those reported for previous code versions (- category, Table ) a) RCDF b) RCDF- (B) a) RCDF- (B) d) RCDF- (Q=) Figure. Vulnerability maps based on contours of equal ductility demands (µ) for RCMF structures with T=.s for a M s =. earthquake scenario, considering overstrength sources and the action of strongest ground components. Concluding Remarks It can be concluded that the vulnerability maps based on contours of equal ductility demands presented for RCMF structures under a postulated M s =. earthquake scenario similar

10 to the September, earthquake presented in this study had a good correlation with the reported and observed damage from a general vulnerability assessment viewpoint. Therefore, it is believed that the procedure outlined in this study can be used with confidence to locate zones of high demands for different structural systems and earthquake scenarios, being therefore potentially useful for urban planning of cities located in zones of high seismic risk. As it was discussed earlier, in addition to the well-know downtown area where most of the structural damage and collapses have been observed during the, and earthquakes, the highest ductility demand contours in Mexico City s Metropolitan Area are usually found within: a) Texcoco lakebed zone nearby Mexico City s International Airport and neighboring Nezahualcoyotl City, b) Xochimilco lakebed zone and, c) Chalco-Tláhuac lakebed zone. These zones, particularly Xochimilco and Tláhuac, were also recognized before as having a high amplification (Reinoso and Ordaz ) and a high energy input (Huerta and Reinoso ). However, as the density of the instrumentation in these zones is scarce, the magnitude and extension of such contours should be carefully examined before making strong conclusions on this regard. Nevertheless, as the density of population and structures in those areas has considerably increased since the earthquake, a warning call should be made for Nezahualcoyotl City, Tláhuac, Chalco and Xochimilco districts (Reinoso and Ordaz in already made a warning call for the new urbanized zones at Xochimilco lakebed). References Fundación ICA,. Experiencias derivadas de los sismos de septiembre de, primera edición, Limusa, México (in Spanish). Godínez-Domínguez, E. A.,. Evaluación de la vulnerabilidad sísmica de estructuras existentes en el Distrito Federal. El caso específico del sismo del de septiembre de, MSc. Thesis, Posgrado en Ingeniería Estructural, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana Azcapotzalco, May (in Spanish). Gómez-Bernal, A., Juárez, H., and Iglesias, J.,. Intensidades y demandas de ductilidad de sismos recientes en la ciudad de México, Revista de Ingeniería Sísmica, SMIS,, - (in Spanish). Huerta, B. and Reinoso, E.,. Espectros de energía de movimientos fuertes registrados en México, Revista de Ingeniería Sísmica, SMIS,, - (in Spanish). Instituto de Ingeniería, UNAM,. La UNAM ante los sismos del de septiembre de, Informe Preliminar, México, October (in Spanish). Murià, D. and González, R.,. Propiedades dinámicas de edificios de la ciudad de México, Revista de Ingeniería Sísmica, SMIS,, - (in Spanish). Pérez-Rocha, L. E.,. Respuesta sísmica estructural: efectos de sitio e interacción suelo-estructura (aplicaciones al valle de México), Ph.D. Thesis, División de Estudios de Posgrado de la Facultad de Ingeniería, Universidad Nacional Autónoma de México (in Spanish). Reinoso, E. and Ordaz, M.,. Spectral rations for Mexico City from free-field recordings, Earthquake Spectra, (), -. Tena-Colunga, A.,. International seismic zone tabulation proposed by the UBC code: Observations for Mexico, Earthquake Spectra, (), -. Tena-Colunga, A.,. Displacement ductility demand spectra for the seismic evaluation of structures, Engineering Structures, (), -.