PhD Oral Exam - Avirup Sarkar, Civil Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

This thesis introduces a two-dimensional spectral finite element formulation designed for the dynamic analysis of concrete gravity dams. While the Finite Element Method (FEM) remains a widely used tool for dynamic structural analysis, its application to large structures demands substantial computational resources and time. Consequently, alternative computationally efficient modeling techniques, collectively known as "Spectral Finite Element Methods" (SFEMs), have been developed over recent decades.

In this study, Time Domain-based SFEM (TDSFEM) has been chosen for dynamic time history analysis of a concrete gravity dam due to its perceived advantages over Frequency Domain-based SFEM (FDSFEM), particularly in handling irregular geometries and finite domains. Sensitivity analysis and convergence studies were conducted using 4-noded and 9-noded elements. Notably, the dam's foundation was modeled using two-dimensional infinite elements in both FEM and TDSFEM analyses. The computational times for the analysis using TDSFEM and conventional FEM were compared, underscoring TDSFEM's computational efficiency in dynamic analysis.

Results indicated the higher computational efficiency of TDSFEM over FEM when higher order elements were utilized. Modal analysis and time history analysis results suggested that employing higher order elements in TDSFEM could serve as a practical alternative to conventional FEM, offering significant savings in computational time while maintaining reasonable accuracy for dynamic analysis of large structures such as concrete gravity dams.

The study also focused on damage detection based on modal parameters. The efficiency of modal parameters in detection of damage and localization of damage was investigated. Damage indices were defined for three modal parameters- modal displacement, modal curvature and modal strain energy for localization of damage. It was observed that strain energy is an efficient and consistent indicator of damage location among the modal parameters studied.

TDSFEM has also been used to model the behavior of FRP reinforced concrete deep beams and their failure modes. The results have been compared with experimental investigations previously conducted at the Structural Engineering Laboratory of Concordia University. The benefit of using TDSFEM in terms of saving in computation time is also demonstrated.

Another application of TDSFEM showcased in this thesis is the modeling of deterioration of large concrete structures like concrete gravity dams like alkali aggregate reactions (AAR). While several AAR modeling techniques based on chemical reactions are available in literature, this thesis presents a simplified thermo-mechanical approach to model the deterioration caused by AAR on concrete gravity dams.

Overall, it can be concluded that the Time Domain based spectral finite element method (TDSFEM) can be used as a viable alternative solution technique for the analysis of large structures like concrete gravity dams to gain significant savings in time of computation. This procedure can also be effectively used for other structural analysis procedures where a large number of iterations or high computational time is required. In this regard, the measured data can be used complimentary to numerical techniques like modal strain energy-based damage indices to detect the presence of and possible locations of damage. Again, the TDSFEM procedure will lead to numerical efficiency in this regard which is highly beneficial for large structures. The simplified modeling of material deterioration effects seen in large concrete structures like AAR using TDSFEM showcased in this thesis is beneficial for an estimate of the stage of these effects on a structure.