Global Probabilistic Seismic Capacity Analysis Of Reinforced Concrete Frame Structures

At the beginning of the twenty-first century, Pacific Earthquake Engineering Research Center (PEER) proposed a probabilistic decision-making framework for Performance-Based Earthquake Engineering (PBEE). At the same time, Mid-American Earthquake Engineering (MAE) proposed another probabilistic decision-making framework for Consequence-Based Earthquake Engineering (CBEE). Actually, the two frameworks both are based on seismic risk analysis, threrfore, the probabilistic decision-making framework of Risk-Based Earthquake Engineering is put forward in this thesis. Earthquake motion, seismic demand and seismic capacity as well as their relationships are central concerned problems in PBEE, CBEE and RBEE. Because of the randomness of seismic activity, the random process characteristics of earthquake motions and stochastic parameters of engineering structures, the seismic capacities of structures are random in nature. The subject which studies the probabilistic relationships between seismic capacity and seismic demand of structures is called as Probabilistic Seismic Capacity Analysis (PSCA).PSCA is the foundation of seismic reliability analysis, seismic vulnerability analysis and seismic risk analysis of engineering structures. Meanwhile, it is an important part of probabilistic performance-based seismic design and assessment by using full probability method. Moreover, the results of PSCA can also provide scientific support for earthquake loss evaluation and earthquake disaster mitigation decision-making. Since the global seismic capacity of structures can describe the seismic performance of structures from the macroscope viepoint, it is very important to study the theory and methodologies of global PSCA for key civil engineering structures and infrastructure systems.In this thesis, an improved point estimation method (PEM) based on Nataf transformation is put forward to compute the statisticalal momens of complex stochastic functions, The proposed method is compared with crude Monte Carlo simulation method, numerical integration method and mean-value first order second moment (MVFOSM) by an detailed numerical example. Then the four stochastic analysis methods are then combined with pushover analysis (POA) method, which is named"random POA"to compute the statisticalal moments of the stochastic seismic capacity of structures. The inter-story drift angle (ISDA) is taken as the capacity parameter and the computation results of random POA method are compared with that by using two finite element reliability method based on MVFOSM and FORM. After constructing the global probabilistic seismic capacity models (PSCM) of R.C. frame structures, the global seismic capacity fragility and hazard are studied more deeply and systematically considering the seismic hazard of the site. The main conclusions are summarized as follows:(1) The modified point estimation method probopsed by this thesis can improve the accuracy of Zhao-Ono method. Among the four methods to compute the statisticalal moments of a complex random function, the efficiency of the mean-value first order second moment (MVFOSM) method is the best, however, its accuracy is worse, especially in the condition of high nonlinearity of the random function. Numerical integraton method has the same accuracy as the point estimation method, and its efficiency is higher than the latter.(2) Random pushover analysis (RPOA) method combines statisticalal moments analysis of random functions with pushover analysis. Because there are a lot of mathematics problems in implicit functions in structural analysis, this idea that combines finite Element analysis with mathematics method is so revealing for structural analysis.(2) RPOA method and finite element reliability analysis (FERA) method can all be applied to compute the statisticalal moments of random functions. Combining statisticalal moments analysis of random functions with conventional pushover analysis, RPOA can overcome the difficulties of implicit performance functions in global capacity statisticalal analysis of structures. FERA method couples the approximate analytical methods in structural reliability theory with finite element analysis (FEA) and finite element response sensitivity analysis (FERSA) efficiently, therefore, it is a kind of stochastic finite element methods in ature. It can be used to more finely simulate the various uncerainties in structural model.(3) There are some differences in the results of global probabilistic seismic capacity model based on statistical moments analysis and finite element reliability analysis. The former is built upon the"common"assumption that the global capacity of structures satisfies the log-normal model, which is based on a lot of experimental data. However, when the"individual"result that based on reliability analysis also is regressed by log-normal model on the basis of"common"assumptions, then the diversities would surely exist. Although the"individual"sample can reflect the"common"aspect of the population, it still would manifest its more specific characteristics.(4) The probabilistic seismic capacity model of structures can only consider the randomness in structure itself, while the vulnerability model of seismic capacity of structures can further include the variations in earthquake motion's parameters. Obviously, the latter is the generalization of the former.(5) Based on probabilistic seismic capacity fragility analysis of sructures, the hazard analysis of seismic capacity of structures further considers the hazard of the site, so the seismic capacity hazard analysis is the generalization of the probabilistic seismic capacity analysis.