We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information.Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that uncertainties in input parameters, which propagate to output uncertainties in the classical sensitivity analysis paradigm, may fail to do so if the transfer functions (or probability distributions) are imperfectly known. We show how, for hierarchical structures, this phenomenon may lead to the non-propagation of uncertainties or information across scales.In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact and on the seismic safety assessment of truss structures, suggesting the feasibility of the framework for important complex systems.The introduction of this paper provides both an overview of the paper and a self-contained mini-tutorial about basic concepts and issues of UQ.

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Masonry infills, commonly found in frame buildings throughout Europe and other parts of the world, have performed poorly in past earthquakes, with infill damage endangering lives, causing disruption and significant monetary losses. To characterize the performance of masonry infills, commonly classified as non-structural elements, an extensive set of experimental test data is collected and examined in this work in order to develop fragility functions for the in plane performance of masonry infills. The collected data stems from testing conducted in Europe, the Middle East and the United States and includes solid and hollow clay brick or concrete block infills, constructed to be in contact within either reinforced concrete or steel framing. The results indicate that infill masonry can exhibit first signs of damage at drifts as low as 0.2% but may not suffer complete failure until drifts as high as 2.0%. Furthermore, it is shown that masonry fragility changes significantly according to the type of infill masonry. Subsequently, a short discussion is provided to highlight the potential use of the infill fragility information within non-linear analysis models of masonry infill. Finally, repair cost estimates for infills in Italy are computed using costing-manuals and are compared with cost estimates obtained through consultation with a number of Italian building contractors, with examination of both the median and dispersion in repair costs. It is anticipated that the results of this work will be particularly useful for advanced performance-based earthquake engineering assessments of buildings with masonry infill, providing new information on the in-plane fragility, repair costs and nonlinear modelling of masonry infills.

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A direct displacement-based design (DBD) procedure for structures that comprise both frames and walls is presented in this paper. Within the new procedure, strength prc+ portions between walls and frames are assigned and are used to establish the design displacement profile before any analysis has taken place. Knowledge of the displacement profile and recommendations for the combination of frame and wall damping compcnents enables representation of the structure as an equivalent single-degree of freedom system. The Direct DBD process is then utilised to set the required strength level which is proportioned to the structure in line with the initial strength assignments. To test the design methodology, two sets of P , 8,-12-, 1 6 and 20-storey reinforced concrete structures are designed. The first set considers frame-wall structures in which the frames are parallel to the walls and the second considers structkes in which link-beams connect from the frames directly onto the ends of the walls. A suite of time-history analyses are conducted to validate the methodology, which is seen to perform excellently.

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