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Risk-based Framework for Optimal Calibration of Building Seismic Design Provisions through Minimization of Lifecycle Cost

Saeed Hosseini Varzandeh | 2023

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 56747 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mahsuli, Mojtaba
  7. Abstract:
  8. This dissertation proposes a probabilistic framework for optimal calibration of design provisions based on the minimization of lifecycle cost (LCC) and its uncertainty. Subsequently, this framework is utilized to determine the optimal robust design base shear coefficient of building structures, and propose a methodology for codifying it while preserving the current structure of the base shear equation. In the first part of the proposed methodology, various structures are designed with different seismic base shears. Then, at each site, their LCC comprising the construction costs and seismic losses is calculated. Various types of seismic loss considered in this study include the direct economic loss due to the repair cost of structural and nonstructural components and contents, indirect economic loss due to downtime, direct and indirect social loss due to injuries and fatalities and the ensuing life quality reduction, and environmental loss due to carbon and energy emissions. The risk measure minimized in this study is the expected LCC, which is a convex function of the design base shear. The results indicate that the expected LCC is nearly flat within a wide range around its minimum. Therefore, this study proposes selecting a point within this range that minimizes the variance of LCC as the optimal robust design base shear coefficient. This coefficient not only leads to a design with the minimum expected LCC, but also has the least uncertainty within the minimum expected LCC range, reducing the likelihood of catastrophic damages and enhancing life safety. In the second part of the proposed methodology, an equation is presented to compute the optimal robust design base shear coefficient with the objective of preserving the current code structure. The equation is the product of a reference spectral acceleration, the optimal site class factor, and the optimal importance factor, divided by the optimal response modification factor. A new definition for these coefficients is presented based on the minimization of LCC. To this end, the optimal response modification factor for each combination of site, structural system, and building height is calculated by dividing the reference spectral acceleration by the optimal design base shear coefficient for residential buildings located on Site Class B per ASCE 7-16. It is shown that selecting a 2475-year return period for the reference spectral acceleration yields the least spatial variation in the optimal response modification factor for intermediate reinforced concrete moment frames. The optimal site class factor is computed by dividing the optimal design base shear coefficient for a residential building on the desired site class by the corresponding value for a similar building on Site class B. To simplify, first, using a Gaussian mixture model, the resulting optimal site class factors are clustered by zones and subsequently, a relationship between the optimal site class factor and the reference spectral acceleration is presented using Bayesian regression in each zone. Next, the optimal importance factor is calculated by dividing the optimal design base shear coefficient for a building with the desired importance level by the corresponding value for a similar residential building. This coefficient is presented as a function of the ratio of the total seismic losses of the building with the desired importance level to the seismic losses of the residential building. Finally, the proposed framework is implemented on four and eight-story intermediate and special reinforced concrete moment frame buildings at 5706 sites across 14 countries in Western Asia, considering five site classes per ASCE 7-16 and various importance levels. The results of the proposed method are compared with those obtained through Standard No. 2800 of Iran and ASCE 7-16 provisions. For this purpose, 70 moment frame structures with various levels of ductility, height, plan, typing, span length, roof type, and design base shear coefficient are designed. The construction costs of these buildings are calculated based on the cost index, and seismic losses are computed using the FEMA P-58 approach, which entails four steps: hazard analysis, response analysis, damage analysis, and loss analysis. The hazard analysis is conducted using reliability methods, and the response analysis is carried out using incremental dynamic analysis on nonlinear three-dimensional models of each structure. Damage analysis is conducted using fragility curves for structural and non-structural components, and loss analysis is performed using consequence functions that are localized within the scope of this study. In particular, the consequence functions, which have been developed for specific regions, such as those in FEMA P-58 for California, are transferred to the desired regions using a set of relative indicators between the two regions. Finally, the effects of plan, typing, span length, and roof type on the results are evaluated.
    The results reveal that direct adoption of ASCE 7 without calibration in Western Asian codes leads to building designs whose LCC is not minimum whereas the proposed framework provides a solution for the optimal calibration of provisions while preserving their structure. It is also observed that the 50-year collapse probability of structures designed with the proposed optimal robust base shear coefficients is, on average, 0.09%, which is significantly lower than the 1% target collapse probability in 50 years according to ASCE 7. The optimal robust design base shear coefficient in this study is, on average, 1.6 and 2.2 times the current values presented by Standard No. 2800 for residential and very important buildings, respectively. This increase results in merely a 1.76% and 3.56% average increase in the construction cost of residential and very important buildings, respectively. However, the mean and variance of LCC are reduced by 5.1% and 22% for residential buildings and 2.5% and 39% for very important buildings, respectively. Such substantial reductions mean that large costs and catastrophic losses are significantly less likely when the proposed approach is practiced. Using the proposed framework, limits and preferences on the use of any structural system under various conditions can be determined. For example, the use of moment frame systems must be avoided for very important buildings on Site Classes D and E. Furthermore, it is observed that collapse probabilities of special and intermediate moment frames designed with identical base shear coefficients do not significantly differ. However, the proposed optimal design base shear coefficient for special moment frames is, on average, about 30% less than that for intermediate moment frames because the allowable elastic drift ratio for special moment frames is smaller, increasing stiffness and reducing deformation-induced damages. This study also demonstrates that the plan, typing, span length, and roof type have a negligible impact compared to seismicity, site class, height, lateral force resisting system, and importance level on the seismic performance, LCC, and optimal design base shear coefficient. Therefore, the results obtained from a common configuration can be generalized to all configurations.
  9. Keywords:
  10. Life Cycle Cost (LCC) ; Code Calibration ; Robustness ; Optimization ; Seismic Risk Index ; Base Shear ; Probabilistic Seismic Structures Vulnerability ; Risk-Based Seismic Design Decision Making

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