CALIBRATION UNDER UNCERTAINTY FOR FINITE ELEMENT MODELS OF MASONRY MONUMENTS
Open Access
- Author:
- Atamturktur, Huriye Sezer
- Graduate Program:
- Civil Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- July 06, 2009
- Committee Members:
- Thomas E Boothby, Dissertation Advisor/Co-Advisor
Thomas E Boothby, Committee Chair/Co-Chair
Jeffrey A Laman, Committee Chair/Co-Chair
Martin Wesley Trethewey, Committee Member
Andrew Scanlon, Committee Member
Francois Hemez, Committee Member - Keywords:
- Sensitivity Analysis
Uncertainty Quantification
Verification and Validation
Nondestructive Testing
Modal Analysis
Gothic Cathedrals
Bayesian Inference
Markov Chain Monte Carlo
Vaulted Structures - Abstract:
- Historical unreinforced masonry buildings often include features such as load bearing unreinforced masonry vaults, and their supporting framework of piers, fill, buttresses, and walls. The masonry vaults of such buildings are among the most vulnerable structural components and certainly among the most challenging to analyze. The versatility of finite element (FE) analyses in incorporating various constitutive laws, as well as practically all geometric configurations, has resulted in the widespread use of FE method for the analysis of complex unreinforced masonry structures over the last three decades. However, an FE model is only as accurate as its input parameters, and there are two fundamental challenges while defining FE model input parameters: (1) material properties and (2) support conditions. The difficulties in defining these two aspects of the FE model arise from the lack of knowledge in the common engineering understanding of masonry behaviour. As a result, engineers are unable to define these FE model input parameters with certainty, and inevitably uncertainties are introduced to the FE model. As the complexity of the building increases, as is the case for historical unreinforced masonry buildings, the errors and uncertainties in the analysis also increase. In the presence of high and numerous uncertainties originating from multiple sources, deterministic approaches in which parameters are defined as constant values assumed to be known with certainty cannot be implemented reliably. Probabilistic methods, however, provide a rigorous and rational means in treating the uncertainty present in the FE analysis of historical unreinforced masonry buildings. The way in which uncertainty in historical unreinforced masonry construction is treated is one of the novel and main contributions of this dissertation. While building FE models, sometimes it is advantageous to model only a smaller portion of a larger structure. This substructure modelling approach not only reduces the computational time of FE analysis but also reduces required preliminary work for the model development. In this dissertation, substructure FE models of vaulted sections of two Gothic churches are calibrated using a Bayesian statistics-based procedure against physical evidence collected through experimental modal analysis. During calibration both the FE calculations and experimental measurements are treated probabilistically. The probabilistic nature of the FE calculations stems from the fact that several FE model parameters which are determined to introduce significant analysis uncertainty, are treated probabilistically. The probabilistic nature of experimental measurements stems from the fact that a large number of repeated experiments are compiled in order to determine experimental uncertainty. The fact that uncertainty in both numerical calculations and experimental measurements are accounted for is one of the novelties of this dissertation. The modal parameters measured on the vault are statistically compared to the predictions of the FE model during calibration. According to the automated Bayesian statistics based calibration procedure, the posterior distributions for the appropriately selected calibration parameters, such as modulus of elasticity of the vault material, and support spring constants of the vaults, are obtained. This stochastic procedure is applied to the substructure FE models of the choir vaults of the National Cathedral, Washington, DC. and to the nave vaults of Beverley Minster, Beverley, UK.