Bridges are structures of both great socio-economic importance and vulnerable to earthquakes. Seismic base isolation is usually an effective way to protect bridges from major earthquakes. The hysteretic properties of isolation systems govern the seismic performance of bridges. However, these properties vary under the effect of several factors, including temperature. Current codes take into account the variation of these properties by means of a bounding analysis approach. The effects of factors, such as temperature, are thus combined with those of the earthquake, regardless of their probability of simultaneous occurrence. This is not consistent with the reliability approach used for other load combinations, based on a target reliability index, excluding earthquake. For the Canadian code CAN/CSA-S6: 19, an annual target reliability index of 3.75 is adopted for most bridge structures and during its lifetime. The bounding analysis method does not allow a target reliability index to be defined and would lead to an underestimation of the variation in hysteretic characteristics and consequently to a non-optimal design of the bridge and of the seismic isolation system.
The main objective of this thesis is to estimate the seismic reliability of base-isolated bridges in Canada, by means of a probabilistic approach, taking into account, in particular, the variability of the hysteretic properties of lead rubber bearing isolation system with temperature, seismic hazard and including the effect of other random variables (RVs).
First, a probabilistic methodology based on the Monte-Carlo method for estimating the reliability of base-isolated bridges is detailed and applied to a typical reinforced concrete bridge with two spans with seismic isolation system (SIS). Two limit states are considered: (1) failure by bending of the bridge pier and (2) failure by exceeding the displacement capacity of the seismic isolator. The main considered RVs are: the seismic hazard, the temperature, the dimensions of the pile and the mechanical properties of the materials. A continuous function, of the seismic hazard as function of the period of the structure, including epistemic uncertainty is developed. In addition, a method of transforming the ambient temperature into the effective temperature of the seismic isolation system, by means of the Laplace transform is developed. The probabilistic distributions of these RVs are modeled based on a review of the literature and on the available data. The preliminary results reveal that the overall reliability of the bridge is equal to the reliability of the limit state (2). In addition, the results reveal that the seismic reliability of the limit state (2) depends more on the seismic hazard of the studied site than on the effect of the low temperature at the same site.
Second, a study that aims to estimate the seismic reliability, associated to no damage state, of a simple typical two span lifeline base-isolated bridge designed for seven localities in Quebec is presented. Two limit states are considered for possible damage: the flexure at pier-base and the displacement within the SIS. The main problem random variables (RVs) considered are: seismic hazard, temperature, pier base dimensions and material mechanical properties. The probabilistic distributions of these RVs are modelled according to available literature and data. Two models of the uncertainties on seismic hazard are considered: 1) normal distribution of the epistemic uncertainty; 2) lognormal distribution of the total uncertainty. Using seismic hazard model 1, preliminary results reveal that in spite of the large temperature and seismic hazard variabilities between the seven sites in Quebec, the global reliability indices are almost uniform, around B=3.45+0.02 (for flexure, Bm=3.59+0.07 and for SIS displacement, BD=3.48+0.04).
Third, a study is being carried out to estimate the variation in the seismic reliability of a typical two-span reinforced concrete bridge, with seismic isolation system, located on a seismic Site Class C in Montreal. Epistemic uncertainties (EUs), considered as RVs, associated with the modeling and the modal spectral seismic analysis method, with the heating of the lead core of the seismic isolation system and with the temperature versus the properties of the SIS are identified and their statistical distributions parameters, with their margins of variation, are estimated. The effects of the variation of the probabilistic distribution parameters associated with these EUs on the reliability of the bridge are also presented. The temperature, the bidirectional horizontal seismic hazard and the main parameters affecting the resistance of the components of the bridge are also modeled as RVs. The same limit states and the same probabilistic method used in the previous study cases are adopted. Results show that including the effects of these EUs, the estimated overall reliability index varies between 3.36 and 3.62, compared to an estimated overall reliability index of 3.49 obtained without including these EUs. By including the epistemic uncertainty associated with the method of analysis of the seismic response of the bridge, the reliability index of the limit state of bending behavior at the pier-base varies between 3.52 and 3.76 (versus 3.56 obtained without including the above EUs). Also, including the epistemic uncertainty associated with the lead core heating effect, the SIS displacement limit state reliability index varies between 3.31, for an extreme effect, and 3.49 for a more representative effect (against 3.51 obtained without including the EUs above).
Finally, the proposed methodology can be used to estimate the reliability of existing bridges, especially in the context of rehabilitation of bridge structures with seismic isolation systems. In addition, estimating the reliability of base isolated bridges using a reliability-based methodology will also provide legislative authorities, responsible for establishing codes and standards, the basis for revising the current standardization. Note that variation models linking aging and other influencing parameters to characteristics of the structural model and /or loading are required. Moreover, an effort of optimisation and improvement is necessary in order to consider the effective application of the methodology on complex bridges.
| Date | 14 Feb 2022 |
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| Original language | French |
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| Awarding Institution | - École de technologie supérieure
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| Supervisor | Lotfi Guizani (Supervisor) & Marie-José Nollet (Co-supervisor) |
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