Parametric uncertainties in reliability analysis of bridge structures

Probability-based reliability methods have placed an increased emphasis on realistic simulation of structural behavior in bridge engineering. Uncertainty is present in every aspect of structural analysis. Aleatory uncertainties in the loading and load-carrying capacities, and epistemic uncertainties in mathematical idealization of bridge systems are the major contributors to uncertain structural response. However, the range of possible response and resistance of bridge components can be predicted in probabilistic means.The objective of this study is to develop efficient reliability analysis methods for bridge components using existing concepts of probability, structural reliability and finite element analysis. A finite element reliability procedure is proposed to evaluate the probability of failure while accounting for both aleatory and epistemic uncertainties in bridge girders subjected to live loads as well as columns to extreme seismic loadings. OpenSees, the Open System for Earthquake Engineering Simulation, an object-oriented open source framework for finite element analysis, is used to implement in the proposed methodology.For this probabilistic analysis approach, a gradient based first order reliability method (FORM) that provides importance measures of uncertain parameters is used instead of approximate integral solutions such as Monte-Carlo simulations. The uncertain parameters are treated as random variables with continuous probability density functions. The random variables are ranked to determine which parameters have the most influence on the structural response to applied loadings.Force-based elements whose integration points coincide with critical locations are ideal for moving load simulations of bridge girders. Moving vehicle loads are taken into account as the part of the element, rather than nodal, equilibrium equations and it is straightforward to link section forces to a constitutive model rather than relying on rigid body equilibrium. However, FORM requires explicit formulations for the derivative of the structural response to be obtained with respect to each uncertain parameter. For sensitivity formulations in force-based finite elements, the direct differentiation method (DDM) is adopted in the framework for evaluating the function and its gradient at the same precision. The numerical examples verify DDM response sensitivity equations are correct and reliability analysis setup is prepared for continuous reinforced concrete bridge girders.As a unique contribution to the reliability assessments of bridge girders, the interaction of moment and shear is considered on both the demand and resisting sides of the limit state function. A new material model based on Modified Compression Field Theory (MCFT) is implemented in OpenSees to represent moment-shear interaction. For performance limits placed on girder members, the moment-shear capacity is defined using a multi-line closed curve adapted from the AASHTO design code implementation of MCFT.To contribute safety measurements of bridge girders, the framework runs fully probabilistic reliability analyses while treating aleatory and epistemic uncertainties simultaneously. Sensitivity formulations for new implementations in the proposed methodology is another important contribution to reliability analysis of bridge components with force-based elements. The numerical examples indicate the moment-shear interaction is significantly high in most probable failure modes of bridge girders. The limit state definitions in the proposed methodology is recommended to use instead of uncoupled shear and moment capacity that can lead to non-conservative estimates of reliability. The importance measures highlights the axle loads and distribution factors have significant influence on the most probable failure mode.Another important source of uncertainty in bridge systems is due to modeling approaches of column members subjected to extreme load cases such as seismic. The methodology provides an approach for the reliability analysis of bridge columns using the formulated response sensitivity of force-based elements. One force-based element represents bridge columns under lateral loading to avoid discretization uncertainty of meshing displacement-based elements. However, the choice of an integration method in the state determination of force-based finite elements has a significant influence on the computed element response.Recent advances in the literature regularize the strain-softening response of force-based frame elements by either modifying the constitutive parameters or scaling selected integration weights. While the former case maintains numerical accuracy for strain-hardening behavior, the regularization requires a tight coupling of the element constitutive properties and the numerical integration method. In the latter case, objectivity is maintained for strain-softening problems however, there is a lack of convergence for strain-hardening response. To resolve the dichotomy between strain-hardening and strain-softening solutions, a numerically consistent regularization technique is developed for force-based frame elements using interpolatory quadrature with two integration points of prescribed characteristic lengths at the element ends.To assess the modeling uncertainty associated with integration methods in force-based elements, analytical sensitivity of one-dimensional interpolatory quadrature is developed via direct differentiation of the locations and weights of integration points. Using the analytical sensitivity formulations, the additional integration parameters in the new regularization technique are considered as epistemic uncertainty in reliability analysis of bridge columns. The numerical examples quantify the epistemic uncertainty of selecting a force-based integration method as well as permitting integration points and weights to be treated as random variables in a probabilistic structural analysis.