Bayesian estimation of maximum drift ratio from combined visual and measurable damage indicators: Rc bridge pier case study

Abstract

Damage assessment of a structure following a damaging event plays a critical role in evaluating its safety. This decision-making process becomes particularly critical in the context of aftershock sequences. Even ductile reinforced concrete (RC) structures that successfully survive the mainshock may have sustained significant damage that compromises their ability to withstand subsequent events. The numerous real-life examples of buildings collapsing during aftershocks highlight the consequences of improper damage assessment. It is well established that the maximum deformations experienced during a damaging event are directly related to the extent of damage sustained by the structure. Exhibited maximum displacements, alter the stiffness and strength, both of which govern the structure's overall response capacity and its ability to resist future seismic demands. Following a damaging event, often experienced teams conduct initial inspection based on visual damage indicators. This first evaluation can also be referred to as a rapid assessment technique. After the rapid assessment, structures that are deemed unsafe for continued use require a more detailed engineering evaluation to decide whether they should be repaired or demolished. In such cases, the structural properties are thoroughly investigated through visual and measurable damage indicators. Visual damage indicators include observed cracks, spalling, and reinforcement damages in structural members. In addition, measurable damage can be more comprehensively evaluated through parameters such as residual displacement, period shift, stiffness change and cumulative energy dissipation. There are numerous damage indicators as well as damage assessment techniques available in the literature. Although many techniques have been proposed, there is a very limited number of studies that combine multiple damage assessment techniques for a more comprehensive evaluation. In this thesis, the objective is to perform structural damage assessment by integrating both visual and measurable damage indicators. A probabilistic framework is adopted in which visual damage indicators are jointly considered with residual drift ratio and period elongation to estimate the maximum drift ratio exhibited by the structure. Within this framework, the major uncertainties affecting the system are explicitly incorporated, namely material uncertainty and ground motion excitation uncertainty. As a case study, a ductile RC bridge model designed and constructed according to the California Department of Transportation (Caltrans) guidelines is selected. The bridge model had been tested on a shaking table, and the results were reported along with photographs taken at the end of each ground motion excitation in 2015. These experimental results are then used for the validation of the key components of the numerical model utilized in this thesis. The numerical modelling is carried out using the Open System for Earthquake Engineering Simulation (OpenSees) version 3.7.0, and nonlinear time history analyses are conducted as a part of the simulations. In the model, a fiber section approach is adopted in combination with a with a distributed plasticity model using a plastic hinge integration scheme. The tested model is assumed to represent a ductile structure to be assessed for the level of damage after a damaging earthquake. It is assumed that the maximum drift demand during the earthquake was unknown, and was to be inferred based on the identifiable damage indicators. Considering the probabilistic approach adopted in this study, both material properties and the ground motion excitation are introduced into the system as uncertain parameters. This is very often the case in post-earthquake damage assessment since detailed material properties and the ground motion at the site of the damaged structure is typically unavailable. Monte Carlo simulations are employed to propagate the related uncertainties through the analyses. From the resulting data, a Bayesian inference method is applied, and four distinct cases of conditional probability distributions of maximum displacement, are evaluated. The first case considers conditioning only on visual damage indicators. The second probability distribution is conditioned on visual damage combined with residual drift, the third on visual damage combined with period elongation, and the fourth considers all parameters together. Furthermore, the relative contributions of material uncertainty and ground motion uncertainty are examined to identify which source governs the damage assessment results. It is observed that the estimated probability distribution of the maximum drift ratio improves when it is conditioned on the visual damage indicators. The mode of the distribution systematically increases. When measurable damage indicators are subsequently incorporated alongside the visual damage indicator, a further improvement in the maximum drift ratio estimation is observed. Here, residual drift and the period elongation are jointly referred to as measurable indicators. Comparing the two measurable indicator cases, conditioning on visual damage combined with residual drift yields a 161% increase in the median compared to the prior estimation, whereas conditioning on visual damage combined with period elongation results in a 124% increase in the median. Based on these results, it can be concluded that residual drift has a greater effect on damage assessment as compared to period elongation. The primary objective of this study is to demonstrate that the most accurate estimation of the maximum drift ratio is achieved when both the visual damage indicators, residual drift ratio and the period elongation are considered together. Comparing the median values of the distribution, the maximum drift is 1.21% in the prior probability, whereas when all indicators are considered together, it increases to 3.41%, corresponding to nearly a 181% improvement in the estimation. Regarding the uncertainty analysis, separate simulations were conducted for material and ground motion uncertainties following the same procedure. Ground motion uncertainty is found to be the most influential parameter in the analysis. The findings of this study, demonstrated on a bridge pier system using a probabilistic approach, show that post-earthquake damage assessment can be performed more accurately by combining the visual damage indicators with measurable indicators, namely residual drift ratio and period elongation, compared to assessments based on a single indicator.