Masonry arch bridges have been around for centuries and are, in the Netherlands, mostly located in historical city centres. As the axle loads of vehicles passing these bridges have increased over the years, the need to re-evaluate the structural safety of these bridges has increases. To do so, different techniques have been developed. However, assumptions had to be made due to limited computational power and lack of knowledge regarding the actual behaviour of masonry. Over the years, the computational power has increased, making it possible to perform more advanced analysis and describe the behaviour of complex materials. Despite this increase, a conservative approach is still used to determine the safety of masonry arch bridges. When it is not sure whether the bridge is safe enough, the bridge is immediately strengthened or a weight restriction is applied, without calculations of the bridges actual capacity. As these interventions could be costly or cause issues with the supply of goods to the city, it is needed to find a better approach and understanding of the actual behaviour of masonry arch bridges. Therefore this study addresses the following research question:
What is the role of constitutive models on simulating the structural behaviour of masonry arch bridges?
In order to formulate an answer to the question, the behaviour of masonry, masonry arch bridges and soils have been investigated first. The investigation shows which function each part of a masonry arch bridge fulfils and which failure modes are expected to occur. When a masonry arch bridge is loaded, the backfill spreads the load and transfers this to the masonry arch. Due to this load, the arch will deform. This deformation is, however, restricted by the backfill. This interaction between the backfill and the masonry arch makes the behaviour of these types of structures a complex structural-geotechnical problem.
For masonry arch bridges, the most common failure mode is the formation of a four hinge mechanism, therefore this study focusses on modelling the behaviour of the masonry arch. Alongside the behaviour of the materials, the development in numerical tools is investigated as well. Doing so, it can be determined what assumptions have been made in the past and what the shortcomings of the approaches are. With the combined knowledge, it is possible to select different material models that can be used for masonry arch bridges. Three different models were created, two macro models and a micro model. The two macro models are both total-strain based models, where one is described by an isotropic - and one with an anisotropic material model, the so called “Total strain crack” and “Engineering masonry” model, respectively. The macro models consider the masonry as a continuum, whereas the micro model distinguishes between units and joints.
To validate the numerical models, test results are needed. As the study focuses on modelling the masonry arch, the different models are first compared to the results of a test on just a masonry arch. The chosen test was performed at the University of Minho in Portugal; a masonry arch was created and, in a displacement control manner, loaded until failure. Prior to performing the tests, the materials were first tested and their properties accurately reported, which is very useful when making a numerical model. After creating and comparing the results of the models and tests, it was found that the Engineering masonry and micro model show a similar shape of the force-displacement curve, while the isotropic “total strain crack” model does not. The engineering masonry and micro model are able to show the brittle failure of the arch, which was also obtained with the tests. However, this failure occurred when only two hinges were formed, where, in the test, a four hinge mechanism was formed. The numerical results do show that cracks are starting to form, however, this does not mean that it also is a hinge. Besides that, the test results show that there is still some redistribution of forces after the peak load. This is not possible when four hinges are already formed. It is expected that the, by the researchers defined, hinges are not actually hinges, but, are the points where cracks start to form. Despite this difference in hinge formation, the resulting force-displacement curves of the models are very close to those of the tests, therefore it can be stated that the used models are suitable to represent the behaviour of masonry arches.
After validating the effectiveness of the masonry material models, the modelling of the problem was extended by adding backfill. Again test results were needed to determine whether the models are also suitable to simulate the extended problem. This test was performed at the University of Salford in the United Kingdom and has been used by Wittenveen+Bos to validate other numerical programs in the past. The bridge was tested in a specially designed chamber, in such a way that plain strain conditions hold, and the load was applied at quarter span in a displacement controlled manner. The results were obtained by loading the arch beyond the peak load, with the applied force being reduced while the displacement continued to increase, which was, according to the research, when a four hinge mechanism was formed.
A negative consequence of plain strain conditions is that the engineering masonry material model was not available to be used, therefore only the “total strain crack” model and the micro model were compared. The initial results of the numerical model resulted in local failure of the soil just below the point load, which did not occur in reality. In order to eliminate this local failure, a small area below the load had to be given linear elastic properties. Although this local failure now doesn’t happen, the results still show that plastic strains develop in the backfill, as well as cracks in the masonry arch. A parametric study was conducted to determine the sensitivity of the models to small changes in material properties. This study showed that the models are most sensitive to changes in soil properties, specifically the internal friction angle. For the micro model, it even appeared that only changes in the soil properties affect the behaviour of the structure, meaning that the sliding failure in the backfill is the governing failure mechanism. In the isotropic “total strain crack” model, a lower tensile strength caused the behaviour of the structure to change drastically. It is found that this is due to Poisson’s ratio and the isotropic nature of the material model. The compressive stresses cause small lateral strains which, due to Poisson’s ratio, cause longitudinal strains. Due to the isotropic nature of the material model, a low tensile strength is assigned in this longitudinal direction, causing the arch to form an unrealistic crack or failure pattern. While in reality the tensile strength in this longitudinal direction, the brick tensile strength, is larger compared to the assigned the brick-mortar bond strength.
Eventually, it could be concluded that it is possible to model the behaviour of masonry arch bridges with great detail. However, in this study the behaviour of the backfill governed the behaviour of the structure, making it difficult to state which modelling approach should be used for the masonry arch. What can be said, is that a micro modelling approach is currently preferred. The study shows that this model is capable of mimicking the behaviour of just a masonry arch, and is less sensitive to changes is masonry properties when backfill is added compared to the isotropic “total strain crack” material model. The anisotropic “engineering masonry” model would be a good alternative, but cannot be used in plain strain conditions, yet. Further research is needed to investigate other modelling options, as a three-dimensional model. However, to fully understand the behaviour, more tests are needed. These tests should not only be focussed on the behaviour of the arch, but also on the behaviour of the backfill; and these material properties should be tested and reported extensively.