Conclusiones Respuesta a la pregunta de investigación
Anexo 6 EP2 – Preguntas para sesión de reflexión final
This proposed generalized cross-building EDP reconstruction model is also demonstrated on simulation data. The model calibration procedure described in Equation (5-17) is applied to reconstruct PSDR and PFA median for a collection of seismic building responses generated using NRHA for concrete moment frame buildings subjected to the 1994 Northridge earthquake at 152 sites (Figure 5.18). OpenSees [42] models were used for five different concrete moment frame
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buildings with 2, 4, 8, 12, and 20 stories, respectively. Model details can be found in [100]. The two horizontal ground motion acceleration histories are applied to the 2D model and the resultant maximum absolute responses from the two orthogonal directions, PSDR and PFA, along building height profile are shown in Figure 5.19a and Figure 5.19b versus rupture distance. Comparing to Figure 5.5 (recorded building response data subjected to the same 1994 Northridge earthquake event), similar attenuation trend patterns over rupture distance are observed for both EDPs across different height of buildings.
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(a) (b)
Figure 5.19 (a) PSDR and (b) PFA subjected to the 1994 Northridge earthquake from concrete moment frame model
Table 5.5 Calibrated Adopted Model Parameter for Simulation Dataset of the Northridge earthquake
Adopted EDP
Prediction Model C1 C2 C3 Peak Story Drift
Ratio 1.326 -1.5626 1.5457 Peak Floor
Acceleration 0.6968 0.2784 0.4775
The same procedure used to develop Equation (5-17) is applied to retrieve model parameters for reconstructing PSDR and PFA median using the simulation dataset summarized in Table 5.5. Comparing to Table 5.4 of the same model parameters using recorded dataset from 26 historical earthquake events, considerable changes are observed for both EDPs, indicating that the model sensitivity is relatively high between different datasets. It should also be mentioned that the simulation data comes from a single event such that the earthquake source term is no longer effective. In addition, the building material and types are limited to concrete moment frames. The
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observed-to-prediction ratio is shown in Figure 5.20 and compared to Figure 5.12, where mean ratio for PSDR and PFA is at 1.003 and 0.997 also suggesting unbiased property of the model. As observed in Figure 5.20a, prediction performance of PSDR is among the best as it is bounded by 0.63 and 1.32. On the other hand, there are 1.3% and 5.8% of the entire PFA dataset with over 2 and less than 0.5 observed-to-predicted ratio and majority of which are within 10km rupture distance (Figure 5.20b). Figure 5.21 shows that the observed-to-prediction ratio over rupture distance, building height, magnitude and ASCE-7 empirical period for PFA to visualize specific bias towards each used feature. It can be observed that the high dispersion in observed-to- prediction ratio exists for lower rupture distance, lower building height and empirical period. Similar trend is also observed in the result of recorded dataset in previous section. The result suggests that the proposed model does not fully capture near-epicenter PFA patterns of the buildings, which are subjected to the highest seismic forces and response in the nonlinear range. Force related seismic responses from buildings are expected to be restrained due to yielding at critical components (beam-column joints between first and second floor level for this particular dataset) while deformation related seismic responses, PSDR, are expected to increase as contribution from plastic deformation increases significantly. The lower predictive performance of the PFA model may be caused by greater amount of data focusing at higher rupture distance range in this simulation dataset as opposed to the recorded dataset that shifts the model focus at the linear seismic demand range. This finding indicates that data-driven model performance is highly dependent on appropriate selection of dataset.
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(a) (b)
Figure 5.20 Observed-to-prediction ratio versus rupture distance of (a) PSDR and (b) PFA from concrete moment frame models subjected to the 1994 Northridge earthquake
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(c) (d)
Figure 5.21 Total residual versus (a) rupture distance, (b) building height, (c) magnitude and (d) ASCE-7 empirical period for PSDR of the simulation dataset of the 1994
Northridge earthquake 5.7 Summary
An empirical data-driven model to estimate the median of two critical seismic building responses, PSDR and PFA, is presented. Two versions of the model are included in this study. One follows the design of GMPE and applies a mix-effect model to calibrate model parameters and is referred to as the generalized cross-building EDP reconstruction model. An alternative model, that adopts the predicted median of ground motion intensity and spectra acceleration from a current GMPE to represent event characteristics, intensity attenuation, and site characteristics, is referred to as the adopted generalized cross-building EDP reconstruction model. Both versions contain a building term that incorporates cross-building features, building height, and ASCE-7 empirical period, which includes fundamental building properties into model consideration. A recorded dataset containing building seismic response histories collected from 196 buildings subjected to 26 historical earthquakes within California since 1984 are used to validate the proposed model. In addition, a simulation dataset containing NRHA building seismic responses from 5 representative
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concrete moment frame buildings subjected to the 1994 Northridge earthquake is also used to examine the validity of the model for different datasets. The major contribution of the proposed model is that it is the first, generalized empirical data-driven model in the strucutral and earthquake engineering field that considers both cross-event and -building features. In addition, the recorded dataset used in this study is among the largest real-world set of recordings in terms of building seismic responses. The proposed model can be used to estimate median damage related EDPs in a rapid manner after a seismic event to provide vital information for community response and recovery. It can also be used as in probabilistic seismic risk assessment for buildings to provide a median EDP estimation which incorporates additional uncertainties from event, site, and path phenomena.
The two versions of the proposed generalized EDP reconstruction model are different in the consideration of moment scaling, distance function, and site amplification terms. While the regular version is designed based on earlier GMPE models with a relatively simple layout, the adopted version directly uses these terms from modern GMPE which has been carefully calibrated in prior studies and includes a fairly complex formulation. The building term for both versions remains the same. The observed/predicted ratios indicate that the regular version is biased for both EDPs and has more outliers compared to the adopted version, which is perfectly unbiased, most likely due to the prior calibration effort from researchers contributing to the development of GMPEs. Although the adopted version is recommended based on model performance over the recorded dataset, the need for a separate, independent approach to reconstruct EDP median values remains an interesting topic to investigate.
In order to fully reconstruct the EDPs, the total residuals, subtracting the predicted median using the proposed model from actual EDPs, are further evaluated by decoupling event and site
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residuals to generate record residuals, which are predicted using the kriging interpolation method developed by Sun et. al. in [28]. Results show that the generalized cross-building EDP reconstruction model, together with decoupling procedures, removes trends corresponding to sites with more than 10km inter-site distance. The kriging interpolation procedure is applied to reconstruct the total residuals using the Alum Rock earthquake. Comparing results from models with and without kriging interpolation demonstrates that the kriging interpolation procedure reduces variance of the observed/predicted ratio to improve reconstruction performance. However, it should be noted that this is not guaranteed for all event cases due to lack of recorded data within an event resulting less representative correlation patterns being captured in the kriging interpolation. A Monte Carlo simulation procedure is proposed to generate synthetic data as an alternative to retrieve more reliable correlation patterns.
A simulation dataset from 5 representative concrete moment frame buildings subjected to ground motions recorded in the Northridge earthquake is used to demonstrate the adaptability of the proposed model for a different dataset. The adopted generalized cross-building EDP reconstruction model is observed to perform the best for PSDR among all datasets but the worst for PFA. The large discrepancy shown in the simulation dataset suggests that the prediction performance of the model is highly dependent on appropriate selection of dataset.
There are several limitations in this proposed generalized model which can be improved through the following aspects. First, the recorded dataset is processed based on the assumption that torsional responses from buildings are negligible, which can be improved by investigating peripheral channels at available floors to correct channel data from unavailable floors. Second, the current empirical period feature is retrieved based on ASCE-7 estimation and is systematically biased towards empirically stiffer buildings compared to actual building responses period. Future
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studies could focus on investigating each considered building according to their strucutral type and apply system identification methods to retrieve their actual building response period from measured data. In addition, the retrieval of VS30 in this current model is through 1-nearest neighbor
approach based on a provided map from USGS with resolution at 250m. Due to the high variation observed in VS30, it would be more reliable to retrieve VS30 at each considered site using their
exact site geology and survey data. The residual decoupling and interpolation procedure could also be improved by applying Bayesian approach to retrieve within-event and site residuals given the small size of current dataset rather than sample mean, which will be demonstrated in next chapter.
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