3D nonlinear modeling and testing of historic stone masonry arch bridges: The case of Justinian's Bridge

Hundreds of historical masonry bridges form a very important part of our cultural heritage in Turkey. Hence, these structures are the living wealth and so they need to be protected and rehabilitated from time to time. Recently, a great of number of surveying, restitution, and restoration projects on historical building are underway to upgrade these heritage structures. However, restoration projects on historical bridges are still somewhat limited when compared to historical buildings. In this respect, an important task has always been to understand the true structural behavior to be able to determine appropriate retrofit/restoration intervention methods for this historical heritage. To address this need and to possibly develop a road map, the present work focuses on evaluating nonlinear structural behavior of stone masonry arch bridges by determining the influence of different constitutive material laws, modeling approaches, and boundary conditions. In order to do that, two methodologies are applied: experimental and the finite element method (FEM). It is shown that the governing collapse mechanism of a multi-span arch bridge could be sufficiently represented by the mechanism of the main (i.e. the longest) span of that bridge. In the current study, two phases of numerical modeling are presented: First modeling work is done on a ¼ scaled single-span stone masonry arch bridge tested to failure in two phases in the laboratory. Secondly, an approximate modeling work is carried out on an existing historical multi-span stone masonry arch bridge. The latter is the Justinian's Bridge or Sangarius Bridge (also known also Historical Beşköprü or Justinianos Bridge in Turkey) from the Byzantine era over the Sakarya River of Turkey. Constructed in the 6th century, the Justinian's Bridge is investigated as a case study within the scope of this thesis. FE model of the Justinian's Bridge is prepared by separate modeling of the arches, spandrel walls, piers, parapets and fill material. The bridge is considered pinned longitudinally and fixed in the base part of the model by the ground. Modal characteristics are evaluated by the modal analysis. Nonlinear structural analyses of the bridge under the prescribed incremental static loading are performed and its collapse/failure mechanism is investigated for assumed three load cases, which are the quarter-span (1/4), third span (1/3), and the middle (1/2) of the bridge. Within the scope of the experimental part of the study, a ¼-scaled model of a selected span of the multi-span arch bridge at Uzunköprü, Edirne, Turkey was constructed and tested in the Materials Laboratory of Civil Engineering Department of Istanbul Technical University (ITU). The bridge specimen was designed to explore the vertical load capacity of the whole structure, i.e. the arch ring, the spandrel walls, and the fill, under restrained (first phase) as well as unrestrained (second phase) cases in the longitudinal direction. The bridge specimen was loaded at quarter span and load was applied in three cycles by providing a constant increments of 30 kN vertical load up to the failure load. Finally, the single-span arch bridge specimen collapsed from the generation of a 4-hinge mechanism in the second phase of the loading. Macro (composite) and simplified micro finite element models (FEM) of the bridge were simulated in order to predict itsnonlinear behavior and collapse mechanismin both restrained and unrestrained boundary conditions. Onset of the collapse mechanism reached, damage distributions were observed during the loading test of the single-span stone masonry arch bridge. In the both modeling approaches, results obtained from three different constitutive material models, which are Multi-Directional Fixed Crack Model with Drucker-Prager plasticity, Multi-Directional Fixed Crack Model without Drucker-Prager plasticity and Total Strain Based Fixed Crack Model available in DIANA software, are compared in order to decide the most realistic material model according to the experimental results. When the nonlinear static analyses (NSAs) of the bridge areperformed, material sensitivity analysis is carried out at each stage, therefore the initial stiffness for the first phase of loading and the stiffness reduction for the second phase of loading are determined in the components such as the stone units, fill material, and mortar joints of the bridge. Upon sensitivity analyses, conclusive results reached are compared with the experimental results. Comparisons were made with deflection values obtained from three control points, which are locations of LVDTs in the experimental study, and a comprehensive numerical evaluation of the tested bridge is made. The results of the analyses show that similar results are obtained for the first model that used the plastic properties of the masonry material, MDFCM with Drucker-Prager and the third model, TSBFCM. Nevertheless, the results obtained in some loading cases for the first model could not corroborate the experimental results are there were some discrepancies between the theoretical and experimental results. Furthermore, the second model, in which the plasticity parameters of the material are not defined, has resulted in improbable results, especially in the first phase of loading. Note that similar discrepancies between the theoretical and experimental results have been obtained in other references published to date as such bridges constitute a highly nonlinear behavior mainly from their material and system properties. The most convenient material model among the three material models has been determined as the 'Total Strain Based Fixed Crack Model (TSBFCM)' as a result of the numerical investigation made on the single-span tested masonry arch bridge. However, quite similar results have been obtained with the macro (composite) and simplified micro models of the bridge. The results obtained from a comprehensive numerical investigation show that the composite modeling approach could give accurate predictions for the hinge mechanism of the bridge while the joint openings could be observed in the collapse mechanism of the bridge by detailed modeling technique. Detailed modeling techniques require a great deal of time and effort, as well as a detailed material knowledge to model accurately the bridge. Therefore, a macro modeling technique could be especially preferred for multi-span masonry bridges having a complex geometry. As a case study and using the information gained in the previous chapters, structural behavior and collapse mechanism of the Justinian's Bridge, which is a multi-span stone masonry arch bridge, are investigated under vertical incremental static loading for three different load cases. These loadins cases are, the quarter (1/4), one-third (1/3), and middle (1/2) of the maximum span of the bridge. The NSA results obtained for lower and upper values of the tensile fracture energy, which is one of the nonlinear parameters of masonry materials, are compared and a more realistic non-linear response has been obtained for an upper value of the tensile fracture energy of the stone material. Numerical results show that the bridge model collapses by a-three hinge mechanism to have occurred at the loaded arch in the upper value of the tensile fracture energy for the selected three load cases. The most critical loading point of the bridge is obtained as the quarter-span. The NSA results have been compared with similar studies in the available literature. The method adopted in the numerical implementation and the results obtained have been confirmed. This thesis consists of seven chapters: In the First Chapter, the importance, objective, and scope of the study are given. The Second Chapter summarizesa comprehensive literature review on structural behavior and collapse mechanism of masonry arch bridges and masonry modeling techniques. The Third Chapter gives a brief introduction related to constitutive material models followed in this research. The testing procedure related to the experimental study carried out in the laboratory, construction of the bridge, material testing, and results of the two-phases loading are explained in detail in the Fourth Chapter. 3D FE models, nonlinear analysis procedures, material sensitivity analyses, nonlinear static analyses results for each numerical implementation and the evaluation carried out in comparison with test results related to the stone masonry pointed arch bridge specimen are given in the Fifth Chapter. In the Sixth Chapter, the Justinian's Bridge, which is a multi-span stone arch bridge in Turkey, is introduced and considered as a case study with its historical background, current situation, geometric and material properties. Using the information gained in the previous chapters, structural behavior and failure mechanisms of the bridge for different load cases are evaluated. In the Seventh Chapter, major results obtained within the scope of this study are outlined and based on the work done here some recommendations are made for the future potential studies regarding this topic.