th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China AN ASSESSMENT OF DAMAGE POTENTIAL AND OF BUILDING PERFORMANCE DEMANDS FOR ROMANIAN VRANCEA EARTHQUAKES 1 I.-G. Craifaleanu and D. Lungu 1 2 Associate Professor, Dept. of Reinforced Concrete Structures, Technical University of Civil Engineering & National Institute for Building Research, Bucharest, Romania Email: iolanda@incerc2004.ro, i.craifaleanu@gmail.com 2 Professor, Dept. of Reinforced Concrete Structures, Technical University of Civil Engineering & National Institute for Historical Monuments, Bucharest. Romania ABSTRACT : Damage spectra, based on the Park-Ang damage index, DM, were generated, for Vrancea events with moment magnitude larger than 6.0. Strength demand spectra were also computed, in order to assess the strength capacity required to limit the damage index to a specified (target) value. The resulted strength demands were then mapped, for several values of DM.µ u, and of structural period. Some applications of the approach, from the structural engineering point of view, were shown. KEYWORDS: damage index, Vrancea earthquakes, damage spectra, maps of strength demands 1. INTRODUCTION Damage indices can provide valuable information in evaluating the building damage potential of ground motions. A more recently used approach is the mapping of damage spectra ordinates (Bozorgnia and Bertero, 2001). This has proved to give useful information in assessing the spatial distribution of damage for a given earthquake and for buildings with specified strength and stiffness characteristics. One of the most widely used indices is the Park-Ang damage index (Park and Ang, 1985). The index is defined by the following relationship: DM = where umax uu EH Fy u max EH +β uu Fy u y (1.1) = maximum deformation demand during the ground motion = ultimate deformation capacity of the system under monotonically increasing lateral deformation = hysteretic energy = yield strength = constant depending on structural characteristics. As one can observe from Eqn. 1.1, DM takes into account both the damage due to the maximum deformation attained during the ground motion and the damage due to repeated cycles of inelastic deformation. According to experimental results and field observations in earthquakes, can be taken as equal to 0.15 (Cosenza et al., 1992; Fajfar, 1992). The conventional interpretation of DM values is the following: DM = 0.4 is considered as the upper limit of repairable damage; values between 0.4 and 1.0 characterize non-repairable damage, while values larger than 1.0 correspond to failure (Teran-Gilmore, 1996). th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China The Park-Ang damage index has some drawbacks that have been pointed out in the literature (Bozorgnia and Bertero 2001). For instance, for elastic response, when EH is 0 and the damage should be zero, the value of DM is greater than zero Moreover, the index does not provide correct results for a system subjected to monotonic deformation. However, DM it is still largely used for different applications due to its simplicity and its experimental validation. By writing the expressions of displacement ductility, , ductility under monotonically increasing lateral deformation, u, and equivalent ductility (Mahin and Bertero, 1981), E : µ = u max u y (1.2) µu = u u u y (1.3) µ E = 1 + E H (F y u y ) (1.4) it results from Eqn. 1.1 that DM can be expressed as a function of the three ductilities above: DM = µ −1 µ +β E µu µu (1.5) or DM ⋅ µu = µ + β (µ E − 1) (1.6) The use of the product DM.µ u instead of DM was considered as more convenient for the present study, as it separates on the right-hand side of Eqn. 1.6 the values corresponding to alternate loading. Therefore, throughout the paper, damage is expressed by using DM.µ u. The interpretation of results is made by considering relevant values of u. 25 µE 20 15 DM .µu R µ=10 µ 10 µE 5 µ µE DM .µu µ R µ=5 DM .µu R µ=2.5 0 0 0.5 1 1.5 2 2.5 3 T (s) Figure 1. Comparison between the variations of , E and DM.µ u. INCERC, March 4, 1977, NS component Figure 1 (Craifaleanu, 1998) shows spectra of the product DM.µ u and of the ductilities and E, for the NS component of the ground motion recorded at INCERC during the earthquake of March 4, 1977. Spectra were determined for an elastic-perfectly plastic system with a damping ratio of 5%. The parameter of the curves in Fig. 1 is the strength modification factor, R , expressed by R µ = Fel ,max F y (1.7) where Fel, max is the maximum strength demand for the considered ground motion, if the system would behave elastically. th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China As one can observe from Fig. 1, the values of DM.µ u are always situated between those of , while for inelastic response, DM.µ u > 1. response, 0 DM.µ u and E. For elastic 2. DAMAGE SPECTRA Damage spectra were calculated for several ground motions recorded during the strong earthquakes of March 4, 1977 (moment magnitude Mw = 7.5, focal depth h = 109 km) and August 30, 1986 (Mw = 7.1, h = 133 km). Records provided by 35 seismic stations were used. Of these stations, 34 were located in Romania (24 in the INCERC network, 10 in the NIEP network (Seismic Database 2001)) and one was located in the Republic of Moldova (station Chisinau, IGG network). Only the horizontal components of ground motions were taken into account in the study. The total number of analyzed seismic records was 72, including the two horizontal components of the INCERC Bucharest single record of March 4, 1977. The spectra were determined by considering a bilinear, elastic-perfectly plastic hysteretic behavior of the SDOF systems, and a damping ratio of 5%. The above hypotheses were used throughout the entire study presented in this paper. As a parameter of spectral curves, the yield strength coefficient Cy, was chosen. The coefficient Cy can be expressed as C y = Fy G (2.1) where G is the weight of the SDOF system and Fy has the same signification as in Eqn. 1.1. The coefficient Cy is a simple measure of the yield strength of the system and can be quite easily related to the code-specified base shear coefficient Cs. By denoting the overstrength factor as ROV, the following expression can be written (Craifaleanu, 2005): C y = C s R OV (2.2) For illustration, spectra of the product DM.µ u are shown in Fig. 2 (Craifaleanu 2001) for the NS component of the March 4, 1977 INCERC record and for different values of Cy. 10 ξ=5% March 4, 1977 INCERC NS component 9 8 C y =0.05 DM .µu 7 6 5 C y =0.10 4 C y =0.20 3 C y =0.30 2 C y =0.40 C y =0.50 C y =0.60 1 Elastic response 0 0 0.5 1 1.5 2 2.5 3 T (s) Figure 2. Spectra of the product DM.µ u, computed for different values of the yield strength coefficient, Cy. March 4, 1977, INCERC Bucharest, NS component As it can be observed from Fig. 2, at short periods, for Cy values lower than 0.2 (which corresponds to the PGA, in g’s, for this record), the values of DM.µ u are very large. They tend to infinity as SDOF system period and Cy th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China tend to zero. With the increase of yield strength, the values of DM.µ u decrease, reaching values below unity for elastic response. A comparison between the DM.µ u spectra of several ground motions recorded in Bucharest during the previously mentioned seismic events (Fig. 3) reveals large differences between their damage potential. The largest values of DM.µ u were obtained, as expected, for the records of 1977. Larger values were also obtained for the 1986 earthquake, at the stations EREN, Otopeni and Magurele, situated in the peripheral, sparsely built area of the city. 20 BUCHAREST March 4, 1977 - 2 records August 30, 1986 - 22 records C y =0.10 ξ=5% 18 16 14 DM.µu 12 10 8 INCERC 1977, NS INCERC 1977, EW EREN 1986, NS Otopeni 1986, EW 6 Magurele 1986, NS 4 2 Elastic response 0 0 0.5 1 1.5 2 2.5 3 T (s) Figure 3. Comparison of DM.µ u values for the two horizontal components of the INCERC Bucharest record of March 4, 1977 and for 22 Bucharest records of the August 30, 1986 earthquake. Cy = 0.10 3. STRENGTH DEMAND SPECTRA FOR TARGET VALUES OF DAMAGE INDEX An alternate approach in the study of damage indices is to determine the yield strength that would ensure that for buildings with certain characteristics, damage for the considered seismic motion is limited to a desired (target) level, DM. For the case of DM.µ u spectra, this requires that the values of µ u are specified. 0.7 March 4, 1977 INCERC NS component 0.6 0.5 DM .µ u =1 Cy 0.4 DM .µ u =2 0.3 DM .µ u =4 0.2 DM .µ u =6 0.1 0 0 0.5 1 1.5 2 2.5 3 T (s) Figure 4. Spectra of Cy for different values of DM.µ u. March 4, 1977, INCERC, NS component For the purpose of the present study, strength demand spectra for a set of relevant values of DM.µ u were determined for all 72 ground motions analyzed. Figure 4 shows the strength demand spectrum of the north-south component of the INCERC March 4, 1977 record, computed for four values of DM.µ u., among which the value 1, corresponding to the upper limit of elastic behavior. One can notice on this diagram the evolution of the shape of the curves with the increase of th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China DM.µ u, and the progressive attenuation of the “fingerprint” of the predominant period of the ground motion. 4. DISTRIBUTION OF YIELD STRENGTH DEMANDS FOR TARGET VALUES OF DM.µU Maps were generated for two values of structure period T = 0.5 s and T = 1.0 s and for three values of the product DM.µ u, i.e. 2, 4 and 6. By mapping the Cy ordinates for the 35 seismic stations considered, the maps in Figs. 5 and 7 were obtained. a) DM.µ u = 2 b) DM.µ u = 4 c) DM.µ u = 6 Figure 5. Spatial distribution of yield strength demands (Cy) for the Vrancea earthquake of August 30, 1986. Structure period T = 0.5 s a) DM.µ u = 2 b) DM.µ u = 4 c) DM.µ u = 6 Figure 6. Three-dimensional representation of the interpolation surfaces in Fig. 5 To provide a more intuitive image of the spatial distribution of strength demands and of their variation with the target damage level, Figs. 6 and 8 show three-dimensional views of the interpolation surfaces in Figs. 5 and 7. One of the most distinct features of the maps is the orientation of contours along a northeast-southwest direction. This feature, which was previously observed also on maps generated for other parameters, such as the peak ground acceleration or the spectral acceleration (Craifaleanu et al., 2006; Lungu and Craifaleanu, 2007), corresponds to the results of previous studies concerning the predominant direction of propagation of seismic waves for the August 30, 1986 seismic event. The Cy ordinates calculated for T = 0.5 s are larger than the values corresponding to T = 1.0 s, as a consequence of the spectral contents of the analyzed records. The spatial variation of Cy is more marked for T = 0.5 s than for T = 1.0 s. th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China The most evident consequences of increasing DM.µ u are the narrowing of the range of variation of the Cy ordinates and the general decrease of their values, i.e. the flattening of the interpolation surfaces. a) DM.µ u = 2 b) DM.µ u = 4 c) DM.µ u = 6 Figure 7. Spatial distribution of yield strength demands (Cy) for the Vrancea earthquake of August 30, 1986. Structure period T = 1.0 s a) DM.µ u = 2 b) DM.µ u = 4 c) DM.µ u = 6 Figure 8. Three-dimensional representation of the interpolation surfaces in Fig. 7 The detailed spatial distribution of yield strength demands for the city of Bucharest is shown in Figures 9 and 10, for the same values of DM.µ u and of the structure period mentioned above. As it can be observed on all maps, the larger the accepted value of DM.µ u, the smaller the strength capacity requirements. Also the strength capacity requirements for T = 1.0 s are less significant, compared with those corresponding to T = 0.5 s. As for the spatial distribution of the ordinates, the largest Cy values occur in the three stations located in the sparsely built zones around the city, i.e. in stations Otopeni, Magurele and EREN, as it was already shown in the previous section of the paper. However, as DM.µ u increases, the spatial distribution of Cy ordinates becomes more and more uniform. In order exemplify the interpretation of the above maps, a value of µ u = 6 is assumed. For the values considered for DM.µ u, it results in DM = 0.33, 0.67 and 1.00. It can then be observed that, in the central area of the city, a damage level corresponding to DM = 0.33 (in the range of repairable damage) could be obtained by providing the building an overall yield strength equal to 12–17% of the building weight, for T = 0.5s (Fig. 9 a), and equal to 7–9% of the building weight, for T = 1.0s (Fig. 10 a). For DM = 0.67, the same values were 8–10% (Fig. 9 b) th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China and b 5–6%, respectively (Fig. 10 b), while for DM = 1.00, values of 7–8% (Fig. 9 c) and 4–5% (Fig. 10 c) were found. a) DM.µ u = 2 b) DM.µ u = 4 c) DM.µ u = 6 Figure 9. Spatial distribution of yield strength demands (Cy) in Bucharest, for the Vrancea earthquake of August 30, 1986. Structure period T = 0.5 s a) DM.µ u = 2 b) DM.µ u = 4 c) DM.µ u = 6 Figure 10. Spatial distribution of yield strength demands (Cy) in Bucharest, for the Vrancea earthquake of August 30, 1986. Structure period T = 1.0 s The above results should be correlated with the typology, characteristics and spatial distribution of the building stock in Bucharest. Also, the limitations of the damage index considered and of the SDOF model used in the calculations, as compared to the actual MDOF models, should be taken into account. 5. CONCLUDING REMARKS The paper presented some possible applications of damage indices in estimating the damage potential and the building performance demands of seismic ground motions. Spectra and maps of yield strength demands were generated for records of strong Romanian Vrancea earthquakes, taking into account different values of a target damage index. The study focused particularly on the earthquake of August 30, 1986, the strongest seismic event for which distributed records were available. Despite the relatively small number of stations which provided data, interesting conclusions could be drawn. The mapping of strength demand spectral ordinates showed a spatial distribution pattern which is consistent with that obtained by the authors in previous mapping studies of th The 14 World Conference on Earthquake Engineering October 12-17, 2008, Beijing, China ground motion parameters and of linear/nonlinear spectra. Also, it was shown that, for higher target (acceptable) damage levels, strength demands decrease and, furthermore, their spatial variation attenuates. Hence, in this case, the influence of structural behavior tends to prevail over that of ground motion characteristics. Strength demand spectra, determined for specified (target) values of the damage index, appear to represent a more complex and promising way for assessing seismic demands, as compared with constant ductility spectra. The obtained values need, however, further validation based on experimental and analytical data. ACKNOWLEDGEMENTS This research was sponsored by NATO's Scientific Affairs Division in the framework of the Science for Peace Programme, project SfP-980468. REFERENCES Bozorgnia, Y., Bertero, V. V. (2001). Improved shaking and damage parameters for post-earthquake applications. Proceedings of the SMIP01 Seminar on Utilization of Strong-Motion Data, Los Angeles, California, September 12, 1-22. Cosenza, E., Manfredi, G., Ramasco, R. (1993). The use of damage functionals in earthquake engineering: a comparison between different methods. Earthquake Engineering and Structural Dynamics, 22, 855-868. Craifaleanu, I. G. (2001). 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Ph.D. Thesis. University of California, Berkeley. ___ Seismic Database for Romanian Earthquakes (2001). National Institute for Building Research, INCERC, and National Institute for Earthquake Physics, NIEP. Research founded by the Romanian Ministry of Education and Research.