ADVANCED NON-LINEAR NUMERICAL SIMULATION TOOLS FOR IN-SERVICE AND RETROFITTING ASSESSMENT OF STONE MASONRY RAILWAY ARCH
BRIDGES – EXPERIMENTAL CALIBRATION AND VALIDATION
Rúben Filipe Pereira da Silva 2022
Dissertation submitted to the Faculty of Engineering of the University of Porto in fulfilment of the requirements for the degree of Doctor in Civil Engineering
Supervisor: Prof. António José Coêlho Dias Arêde (Associate Professor, FEUP) Co-supervisor: Prof. Cristina Margarida Rodrigues Costa (Adjunct professor, IP Tomar)
Co-supervisor: Prof. Daniel Vitorino de Castro Oliveira (Associate Professor, U. Minho)
Perseverança...
Cais, mas levantas-te!
Teimosia de criança.
Um sonho...
Um horizonte inalcançável.
Firme no rumo, certo e inabalável, De pedra e cal.
E o que parecia impossível, é possível afinal!
Abstract
ABSTRACT
Currently, in several railway networks all over the world, there is a significant number of masonry arch bridges still in operation. According to data provided by International Union of Railways (UIC), the majority of railway bridges are either masonry arched or culverts and 70% of the total number of bridges are aged between 100 and 150 years. According to the master plan of the European Union for the system of transport, railways are planned to have a crucial role in the expansion of the safe transport of passengers and goods, contributing to a more sustainable and environment-friendly transport network.
In that scenario, the increase in high-speed and mixed traffic implies an increase in the load capacity of the bridges, given the increase in load demands and the introduction of dynamic effects resulting from speeds’ increase.
The longevity, robustness and low operating costs that are associated with stone masonry arch bridges allow them to be considered a good example of sustainability. Many masonry bridges remain in service for hundreds of years quite often without the need for significant repair or reinforcement interventions, while still meeting current safety criteria and, in some cases, even exceeding the design requirements of modern structures. Despite their resilience, masonry arch bridges are deteriorating over time mainly due to damages induced by prolonged exposure to traffic loads, large vibrations, foundation settlements and aggressive environmental conditions. Therefore, there is an increasing need of defining efficient condition assessment strategies aiming to extend the life cycle of these old structures meeting safety and serviceability requirements.
This type of structure is generally characterised by its high durability and structural complexity, the latter mainly due to the heterogeneity of its constituent materials. In railways, masonry arch bridges are normally constituted by regular stone blocks with thin mortar joints and the infill material found in these bridges is stronger than common granular materials present in roadway bridges, consisting of a low cement content mixture of irregular stones, winding up as a mortared material. Therefore, it is essential to perform laboratory tests in samples taken from the bridges and in-situ experimental tests for material characterisation, in order to evaluate realistic material characteristics and to have properly calibrated numerical models. Through simplification of the numerical models, such as the case of continuous models, the need for an adequate calibration becomes even more evident, to have an equivalent composite material with properties similar to the combination of its various components: stone blocks, mortar and interfaces between them.
Therefore, in the present study, numerical simulation tools suitable for the structural analysis of stone masonry arch bridges were developed based on the finite element method (FEM) and continuous models, considering equivalent isotropic homogeneous materials, aiming at the in-service assessment of the bridges. These material models are calibrated with broad experimental data and using a methodology to calibrate and validate the material parameters, through numerical simulation of laboratory and in-situ tests. These simplified models are essential to perform realistic non-linear dynamic vehicle-bridge interaction analysis, with long load histories, reducing the computational cost of a full-scale model.
Using the same numerical methodologies, two nonlinear modelling strategies were adopted to simulate the damage state condition in bridges. One strategy aims at a global representation of damage using FEM continuous homogeneous models, meaning a strength reduction of the materials, while another aims at a localized damage simulation where the FEM model includes a dedicated contact model. This
discrete crack modelling is adopted in an existing FE bridge model and a simplified equivalent straight geometry of the crack is proposed followed by calibration and validation. These strategies were applied to a single-span railway bridge, in different damage scenarios, to test its applicability for in-service assessment of bridges under static and dynamic railway traffic loading. The proposed numerical strategies revealed potential to represent localized damages in masonry bridges, particularly longitudinal cracks in different opening conditions. By combining the potentialities of a continuous homogeneous model with a discrete crack modelling, a better representation of localized damage is achieved, in particular the transversal movement of the arch and spandrel walls.
The proposed numerical methodologies and calibrated strategies are applied to a multi-span bridge model, for its experimental validation under in-service freight trains. The bridge is globally in a good condition considering its age; nevertheless, there is one relevant structural damage observed in some arches consisting on the existence of longitudinal cracking that follows the interface between the stones in the first and second rows of the arches’ intrados beneath the spandrel walls. The validation of the dynamic behaviour of the bridge was based on advanced non-linear vehicle-bridge dynamic interaction models, including the measured track irregularities. Both, the bridge and the vehicle FE models were previously calibrated based on dedicated dynamic tests. The simulation of the dynamic behaviour of the train-bridge system is performed for realistic scenarios of freight traffic considering speeds between 40 and 140 km/h, some of them likely to be implemented in the near future due to the high demand for freight traffic on the bridge. The results show a global trend of increasing accelerations for all arches due to the increase of speeds, but no resonance phenomenon, nor speeds, ultimately responsible for higher amplifications of the arches’ dynamic responses were identified.
Finally, a strengthening technique was simulated in the bridge model, and the results show that it can effectively reduce the deformations in the longitudinal crack interfaces for the freight train passages.
The proposed calibrated numerical tools for the structural analysis of stone masonry arch bridges, proved to present a robust and efficient strategy procedure to evaluate structural safety, bridge-vehicle stability and strengthening solutions, under in-service railway traffic loading.
KEYWORDS:stone masonry railway bridges, FE numerical modelling, experimental characterization, constitutive material parameters, non-linear dynamic analysis, train-bridge interaction; strengthening and retrofitting assessment
Abstract
RESUMO
Atualmente, em diversas redes ferroviárias em todo o mundo, existe um número significativo de pontes em arco de alvenaria ainda em serviço. De acordo com os dados fornecidos pela UIC, a maioria do total de pontes ferroviárias é em alvenaria e 70% do número total de pontes têm entre 100 e 150 anos. De acordo com o plano diretor da União Europeia para o sistema de transportes, prevê-se que a ferrovia tenha um papel crítico na expansão do transporte seguro de passageiros e mercadorias, contribuindo para uma rede de transportes mais sustentável e amiga do ambiente. Nesse cenário, o aumento do tráfego de alta velocidade e misto implica um aumento da capacidade de carga nas pontes, dado o aumento das necessidades de carga transportada e a introdução de efeitos dinâmicos decorrentes do aumento da velocidade.
A longevidade, robustez e baixos custos operacionais associados às pontes em arco de alvenaria de pedra permitem que sejam consideradas um bom exemplo de sustentabilidade. Muitas pontes de alvenaria permanecem em serviço por mais de uma centena de anos sem a necessidade de reparações significativas ou intervenções de reforço, mantendo os critérios de segurança atuais e, em alguns casos, até superando os requisitos de projeto de estruturas modernas. Apesar da sua resiliência, as pontes em arco de alvenaria vão se deteriorando ao longo do tempo, principalmente devido aos danos induzidos pela exposição prolongada a cargas dinâmicas de tráfego, grandes vibrações, assentamentos de fundações e condições ambientais agressivas. Portanto, há uma necessidade crescente de definir estratégias eficientes de avaliação estrutural visando estender o ciclo de vida destas estruturas centenárias.
Este tipo de estruturas é geralmente caracterizado pela sua elevada durabilidade e complexidade estrutural, esta última principalmente pela heterogeneidade dos seus materiais constituintes. No meio ferroviário, as pontes em arco de alvenaria são normalmente constituídas por blocos regulares de pedra com juntas de argamassa de reduzida espessura e o material de enchimento encontrado nestas pontes é mais resistente que os materiais granulares comuns que se encontram nas pontes rodoviárias, e consiste numa mistura de baixo teor de cimento com pedras irregulares, formando um material similar a um betão magro. Assim, é essencial a caracterização dos materiais da ponte através da realização de ensaios laboratoriais em amostras extraídas das pontes e ensaios experimentais in-situ, de forma a dispor de modelos numéricos devidamente calibrados. Através da simplificação dos modelos numéricos, como é o caso dos modelos contínuos, torna-se ainda mais evidente a necessidade de uma adequada estratégia de calibração dos materiais que formam o material compósito equivalente à alvenaria, com propriedades semelhantes à combinação dos seus diversos componentes: blocos de pedra, argamassa e interfaces.
Neste trabalho são apresentadas ferramentas de simulação numérica adequadas para a análise estrutural de pontes em arco de alvenaria de pedra, desenvolvidas com base no método dos elementos finitos, considerando materiais homogéneos e isotrópicos equivalentes, visando a avaliação destas pontes para cargas de serviço. Os modelos numéricos são calibrados com resultados experimentais e usando uma metodologia para a calibração e validação dos parâmetros adotados para os materiais, através da simulação numérica de ensaios laboratoriais e ensaios in-situ. Esses modelos, com um certo grau de simplificação, são essenciais para se realizarem análises dinâmicas não-lineares com interação veículo- ponte com longas histórias de carga, reduzindo assim o tempo computacional.
Usando as mesmas metodologias numéricas, duas estratégias de modelação não-linear são estudadas para simular a condição de dano neste tipo de pontes. Uma estratégia visa a representação global dos danos usando modelos homogéneos e contínuos equivalentes, representando por exemplo uma redução
da resistência dos materiais, enquanto outra estratégia visa a simulação de danos localizados num modelo de elementos finitos e inclui a definição de um modelo de contato. Na segunda estratégia, fendas longitudinais no arco são simuladas no modelo numérico da ponte seguindo uma geometria simplificada, e de seguida procede-se à sua calibração e validação. Estas estratégias foram aplicadas a uma ponte ferroviária de apenas um vão, com diferentes cenários de danos, para testar a sua aplicabilidade para a avaliação estrutural de pontes, em análises estáticas e dinâmicas sob tráfego ferroviário. As estratégias propostas revelaram potencial para representar um dano localizado em pontes de alvenaria, particularmente fendas longitudinais com diferentes condições de abertura. Ao combinar as potencialidades de um modelo homogéneo e contínuo com uma modelação discreta de fendas, obtém- se uma melhor representação dos danos localizados, em particular as deformações transversais do arco e dos muros-tímpano.
As estratégias e metodologias desenvolvidas ao longo deste trabalho foram aplicadas ao estudo de uma ponte ferroviária de vários vãos, para a validação experimental do modelo numérico usando um comboio de mercadorias. A ponte encontra-se globalmente em bom estado tendo em conta a sua idade, no entanto, existe um dano estrutural relevante observado em alguns arcos que consiste na fissuração longitudinal que segue a interface entre as pedras da primeira e segunda fiada do intradorso dos arcos. A validação do comportamento dinâmico da ponte foi baseada em modelos avançados dinâmicos não-lineares considerando a interação veículo-ponte e incluindo as irregularidades da via. Os modelos de elementos finitos da ponte e do vagão de mercadorias usado nas análises foram previamente calibrados com base em ensaios dinâmicos. A simulação do comportamento dinâmico do sistema comboio-ponte foi realizada para cenários realistas de tráfego e considerando velocidades entre 40 e 140 km/h, alguns deles que podem vir a ser implementados num futuro próximo devido à expansão do tráfego de mercadorias.
Os resultados mostram uma tendência global de aumento das acelerações para todos os arcos com o aumento das velocidades, mas não foram identificados fenómenos de ressonância, nem velocidades eventualmente responsáveis por maiores amplificações das respostas dinâmicas nos arcos.
Por fim, uma solução de reforço foi simulada no modelo da ponte, e os resultados mostram que essa solução pode efetivamente eliminar as deformações transversais nas fendas longitudinais existentes na ponte. As estratégias numéricas desenvolvidas e calibradas para a análise estrutural de pontes em arco de alvenaria de pedra, provaram ser um processo robusto e eficiente para a avaliação da segurança estrutural das pontes, da estabilidade comboio-ponte e de soluções de reforço, sob cargas ferroviárias de serviço.
PALAVRAS-CHAVE: pontes ferroviárias em alvenaria de pedra, modelação numérica, método dos elementos finitos, caracterização experimental, parâmetros constitutivos dos materiais, análises dinâmicas não-lineares, interação comboio-ponte, avaliação de reparação e reforço
Acknowledgements
ACKNOWLEDGEMENTS
Many individuals and institutions contributed to this academic achievement, without their valuable contributions, constant support and encouragement this thesis would not have been possible. Therefore, I take this opportunity to express my deep gratitude to all of them:
To my supervisor, Prof. António Arêde, for all the efforts in providing me with the necessary resources to develop this thesis, in particular his willingness to support all the experimental campaigns of this work. His enthusiasm and scientific knowledge of structural engineering and particularly masonry structures were essential to the success of this work. I would also like to thank him, not only for all the guidance and insightful thoughts provided during this period but also for the friendship established between us;
To my co-supervisor, Prof. Cristina Costa, for all the constant support throughout this thesis, and her willingness to help me, at any day and hour. Her positivism and vast knowledge about masonry bridges and numerical modelling were key to unlock many challenges and problems that arose during the numerical tools tasks. The friendship that grew between us will never be forgotten;
To my co-supervisor, Prof. Daniel Oliveira, for all the support and availability throughout this thesis.
His readiness in answering all my questions and his teachings were also important for the success of this thesis;
To Prof. Diogo Ribeiro, for his dedication to help me, and whom I sincerely thank for his meaningful collaboration in some of the scientific papers that resulted from this work. His vast knowledge about the dynamic behaviour of railways structures resulted in valuable teachings that help me to succeed in the strategy adopted for the bridges’ dynamic analysis. From this collaboration, the friendship that already existed grew up, and will always be kept in the future;
To Prof. António Topa Gomes, for his teachings and assistance in the execution of Ménard Pressuremeter tests in the bridges;
To Cássio Bragança for his availability and knowledge shared regarding the optimization iterative methodology;
To the Portuguese Foundation for Science and Technology (FCT), for the funding of this work through the iRail programme scholarship PD/BD/127812/2016;
To LESE, the Structural and Seismic Engineering Laboratory research group of CONSTRUCT - Institute of R&D in Structures and Construction, for providing me with all the equipment and human resources for the experimental campaigns. In particular to Nuno Pinto, Valdemar Luís and Guilherme Nogueira for their indispensable assistance during the preparation and execution of the experimental tests;
To IP – Infraestruturas de Portugal, for giving me the opportunity and conditions to carry out all the experimental tests in the bridges. In particular to Engineers Ana Isabel Silva, Hugo Patrício, Pedro Campos and Nuno Lopes for their collaboration in the experimental tests and for the precious help on providing information about the bridges;
To Navigator company, in particular to Dr. João Prina and Dr. Amilcar Ferreira, as well as Dr. Germán Fonseca from Takargo company, for the authorization and collaboration on the experimental tests of the freight wagon;
To all my friends and colleagues at FEUP: André Furtado, Sérgio Pereira, Aires Colaço, Cláudio Horas, Ana Ramos, Alexandre Pinto, Ana Gomes, João Pacheco, Cássio Gaspar, Rodrigo Moreira, Andreia Meixedo, Pedro Montenegro, Aralyia Mosleh, Pedro Jorge, José Melo and Rui Silva for providing me support, companionship and good moments;
To my friends Jorge Gadelho and Mário Moreno, for always being present, for the encouragement, for all the good moments and laughs;
À Katy por todo o seu amor, e apoio incondicional e toda a energia positiva que me deu e que foram fundamentais para o sucesso deste trabalho. À Sophia, a minha maior motivação e a razão dos melhores momentos que guardo desta etapa;
À minha irmã, Marta, por todo o seu apoio e por estar sempre presente em todos os momentos da minha vida. Aos meus pais Raúl e Conceição, pelo amor incondicional, pelo apoio e pelo exemplo que são para mim. A vossa dedicação em me possibilitar todas as condições para perseguir os meus sonhos foram também essenciais para a realização e conclusão desta tese;
Table of Contents
TABLE OF CONTENTS
1. INTRODUCTION ... 1
1.1.CONTEXT ... 1
1.2.MOTIVATION ... 2
1.3.OBJECTIVES ... 4
1.4.THESIS OUTLINE ... 5
1.5.PUBLISHED CONTRIBUTIONS ... 7
2. OVERVIEW ON RAILWAY STONE MASONRY ARCH BRIDGES ... 9
2.1.BRIEF INTRODUCTION ... 9
2.2.STRUCTURAL COMPONENTS AND MATERIALS ... 10
2.3.CONSTRUCTION DETAILS ... 12
2.4.LOADS ... 18
2.5.EXISTING RAILWAY BRIDGES’ STOCK ... 22
2.6.FUTURE ... 25
2.7.FINAL CONSIDERATIONS ... 27
3. LITERATURE REVIEW ON STRUCTURAL BEHAVIOUR AND ASSESSMENT METHODS ... 29
3.1.BRIEF INTRODUCTION ... 29
3.2.BRIDGES’ STRUCTURAL BEHAVIOUR ... 30
3.2.1 Materials’ behaviour ... 30
3.2.2 Global behaviour ... 33
3.2.3 Identification of failure modes ... 34
3.2.4 Damages overview ... 38
3.2.5 Main strengthening techniques ... 44
3.3.STRUCTURAL ASSESSMENT METHODOLOGIES ... 48
3.3.1 Simplified methods ... 49
3.3.2 Limit analysis ... 49
3.3.4 Numerical methods ... 51
3.4.MASONRY AS A HOMOGENEOUS MATERIAL... 54
3.4.1 Models for masonry and infill based on plasticity theory ... 55
3.4.2 Models for masonry based on damage models ... 58
3.5.IN-SERVICE ASSESSMENT ... 59
3.5.1 Static analysis ... 60
3.5.2 Dynamic methodologies ... 60
3.5.3 Calibration and validation ... 63
3.6.FINAL CONSIDERATIONS ... 64
4. CHARACTERIZATION OF STONE MASONRY ARCH BRIDGES’ MATERIALS: EXPERIMENTAL TESTS AND NUMERICAL SIMULATIONS ... 65
4.1.BRIEF INTRODUCTION ... 65
4.2. EXPERIMENTAL CHARACTERIZATION ... 67
4.2.1. Experimental campaigns ... 67
4.2.2. Material characterization... 68
4.2.2.1 Laboratory tests on stone and masonry joint samples ... 68
4.2.2.2 In-situ flat-jack tests ... 72
4.2.2.3 In-situ pressuremeter tests technique ... 76
4.2.3. Global behaviour ... 80
4.3.NUMERICAL SIMULATION OF THE EXPERIMENTAL MATERIAL TESTING ... 83
4.3.1 Simulation of masonry joints’ shear tests ... 83
4.3.2 Pressuremeter test simulation ... 87
4.3.3 Flat-jack simulation ... 89
4.4.FINAL CONSIDERATIONS... 99
5. NUMERICAL METHODOLOGIES FOR THE ANALYSIS BEHAVIOUR OF BRIDGES WITH DAMAGE UNDER RAILWAY LOADING ... 101
5.1.BRIEF INTRODUCTION ... 101
5.2.DAMAGE SIMULATION IN MASONRY RAILWAY BRIDGES ... 102
5.2.1 Methodology ... 102
5.2.2. Damage simulation with global models ... 103
5.2.3 Damage simulation with discrete cracks ... 103
5.3.CASE STUDY ... 108
5.3.1 Brief description ... 108
5.3.2 FE bridge model ... 109
5.3.3 Free-vibration test ... 110
5.3.4 Material scenarios ... 112
5.4LINEAR RESPONSE OF THE BRIDGE MODEL UNDER RAILWAY LOADING ... 114
5.4.1 Load model ... 114
5.4.2 Dynamic linear analysis under service loading ... 115
5.5.NON-LINEAR ANALYSIS OF THE BRIDGE UNDER RAILWAY LOADING ... 118
5.5.1 Continuous Model ... 118
5.5.1.1 Dynamic analysis with moving loads ... 118
5.5.1.2 Incremental static analysis ... 119
5.5.2 Models with contact elements... 122
5.5.2.1 Longitudinal crack modelling calibration: real and equivalent straight geometries ... 122
5.6FINAL CONSIDERATIONS ... 128
6. DEFINITION AND CALIBRATION OF A FREIGHT VEHICLE MODEL BASED ON DYNAMIC TESTS ... 131
6.1.BRIEF INTRODUCTION ... 131
6.2.THE FREIGHT TRAIN ... 132
6.2.1 The Sgnss wagon ... 132
6.3.DYNAMIC TESTS ... 135
6.3.1 Overview ... 135
6.3.2 Loading configurations ... 135
Table of Contents
6.3.4 Modal identification ... 138
6.4NUMERICAL MODELLING ... 140
6.4.1 Description ... 140
6.4.2 Modal parameters ... 142
6.5CALIBRATION ... 144
6.5.1 Sensitivity analysis ... 144
6.5.2 Optimization ... 145
6.5.3 Correlation analysis ... 151
6.6FINAL CONSIDERATIONS ... 153
7. EXPERIMENTAL CALIBRATION AND VALIDATION OF A NON-LINEAR TRAIN- TRACK-BRIDGE DYNAMIC MODEL ... 155
7.1.BRIEF INTRODUCTION ... 155
7.2DURRÃES RAILWAY BRIDGE ... 156
7.2.1 Description ... 156
7.2.2 Experimental testing ... 158
7.2.2.1 Ambient vibration tests ... 158
7.2.2.2 Static loading tests ... 161
7.2.2.3 Dynamic tests under railway traffic ... 164
7.3FENUMERICAL MODELS ... 165
7.3.1 Bridge ... 165
7.3.2 Train ... 170
7.3.3 Train-bridge Interaction ... 172
7.3.4 Track irregularities ... 174
7.4VALIDATION ... 174
7.4.1 Static analyses ... 174
7.4.2 Dynamic analysis ... 176
7.5SIMULATIONS FOR DIFFERENT SPEED SCENARIOS... 179
7.5.1 Scenarios ... 179
7.5.2 Bridge response ... 180
7.5.3 Train response ... 182
7.6FINAL CONSIDERATIONS ... 183
8. NUMERICAL SIMULATION OF A STRENGTHENING TECHNIQUE IN A STONE MASONRY RAILWAY BRIDGE ... 185
8.1.BRIEF INTRODUCTION ... 185
8.2ADOPTED STRENGTHENING TECHNIQUE ... 185
8.2.1 Solution description and numerical simulation ... 185
8.2.2 Infill pressure evaluation ... 187
8.3SENSITIVITY ANALYSIS ... 188
8.3.1 Infill state condition ... 188
8.3.2 Tie rods diameter ... 189
8.4BRIDGE RESPONSE... 192
8.4.1 Longitudinal crack displacements ... 192
8.4.2 Vertical displacements and accelerations ... 195
8.5FINAL CONSIDERATIONS ... 196
9. CONCLUSIONS ... 197
9.1.GENERAL CONCLUSIONS ... 197
9.2.FUTURE DEVELOPMENTS ... 203
REFERENCES ... 205
Table of Contents
List of Figures
Figure 1.1 – Masonry arch bridge construction periods. ... 1 Figure 1.2 – Thesis organization flowchart. ... 7 Figure 2.1 – Masonry arch railway bridge: a) main elements (Adapted from UIC code 778–3R) and b) typical cross-section. ... 10 Figure 2.2 – Cross-section of collapsed masonry stone bridges: a) roadway bridge over Vouga river and b) railway bridge (León & Espejo, 2007)... 12 Figure 2.3 – European main railways old map (end of 19th century) (Atlas Classique, Librerie Colin, Paris, 1894). ... 12 Figure 2.4 – Construction of the original Solkan railway bridge (in 1905) (http://www.tol-muzej.si/) and b) Viaduct de la Crueize at the end of construction (in 1883) (https://gallica.bnf.fr/ark:/12148/btv1b12001437/f1.item). ... 13 Figure 2.5 – Graphical construction for the laying out of the thrust line proposed by Méry (1840). ... 15 Figure 2.6 – Construction of Leça bridge in Leixões railway line: a) Cross-section from the design project (1929); b) construction views (Gazeta Ferroviária - 1112)... 16 Figure 2.7 – Construction of Poço de Santiago bridge in Portuguese Vouga railway line (in Gazeta Ferroviária, 1914). ... 17 Figure 2.8 – Côa bridge: a) in 1948 (Reitor Pinto) and b) nowadays; Tâmega bridge: c) in 1947 (http://monumentosdesaparecidos.blogspot.com) and d) nowadays. ... 18 Figure 2.9 – Historical train load models: a) Italian code standard (issued in 1906); b) German code standard (issued in 1925); c) Portuguese code standard (issued in 1929). ... 19 Figure 2.10 – Load models in EN1991-2: a) LM 71; b) SW/0 and SW/2 (CEN, 2003). ... 20 Figure 2.11 – Trains nowadays in the Portuguese railway networks: a) Diesel locomotive series 6000 and b) MU series 4000. ... 21 Figure 2.12 – Railway bridge distribution a) age and b) span of the main arch (Adapted from SB, 2007).
... 22 Figure 2.13 – Railway bridge distribution by material type in a) France, b) Italy, c) Spain and d) UK, (adapted from SB). ... 23 Figure 2.14 – Portuguese railway bridges stock: a) by material and b) by function (masonry bridges) (Source: IP). ... 24 Figure 2.15 – Portuguese granite stone masonry railway bridge examples: a) Culvert in Vouga line), b) Underpass in Trofa Line, c) Pala viaduct in Douro Line and d) Areosa bridge in Minho line. ... 24 Figure 2.16 – Main railways in Europe: a) High-speed network (goddessworks.me/europe-map- rail/41295) and b) Freight network (webrails.tv). ... 25
Figure 2.17 – Main implementations by Ferrovia 2020
(http://www.infraestruturasdeportugal.pt/ferrovia-2020-0): a) electrification of lines and b) Projected new railway connection between Sines seaport and Spain border. ... 26 Figure 2.18 – Viaduct of Flandres in Beira-Baixa line: a) before renovation (2012); b) after track renovation and electrification (2021). ... 26 Figure 3.1 – Failure modes in masonry (Lourenço & Rots, 1997)... 30 Figure 3.2 – a) Tensile and b) compressive behaviour of stone-like materials (Lourenço, 1998). ... 31 Figure 3.3 – Shear test in mortared joints: a) Evolution for different normal stresses and b) Mohr- Coulomb envelope (Costa, 2009). ... 31 Figure 3.4 – Shear test in dry joints: a) Evolution for different normal compression values and b) Mohr- Coulomb envelope (Costa, 2009). ... 32
Figure 3.5 – Typical stress-strain diagrams for compression tests: a) monotonic and b) cyclic (Vasconcelos & Lourenço, 2009). ... 32 Figure 3.6 – Scheme of loads transmission: a) longitudinal direction, b) transversal direction (adapted from Costa, 2007). ... 34 Figure 3.7 – Development of a collapse mechanism in the arch (adapted from Martín (2017)). ... 35 Figure 3.8 – Failure mechanisms of four (a) and five (b) hinges in the arch (adapted from Costa, 2007).
... 36 Figure 3.9 – 3 hinges “snap-through” (Wang & Harvey, 1995). ... 36 Figure 3.10 – a) Prestwood bridge during load test b) collapse mechanism (Page, 1987). ... 37 Figure 3.11 – Arch failure modes from laboratory experiments: a) Varró et al. (2021) b) Zhao et al.
(2020). ... 37 Figure 3.12 – Effect of wing, spandrel walls and fill on the load-carrying capacity (Royles & Hendry, 1991). ... 38 Figure 3.13 – Longitudinal cracking in the arch intrados of Melos bridge in Vouga line (presently closed). ... 39 Figure 3.14 – Longitudinal cracking in the arch intrados of Areosa bridge in Minho line: a) frame detachment; b) detail of the crack. ... 40 Figure 3.15 – Detachment and vertical displacement of stones in the arch: a) general aspect; b) measurement. ... 40 Figure 3.16 – Spandrel wall damages: a) bulging, b) sliding and c) rotation (Ozaeta García-Catalán, 2006). ... 41 Figure 3.17 – Longitudinal cracking: a) between voussoirs and the arch barrel, b) between arch voussoirs and spandrel walls and c) due to rotation of the spandrel walls. ... 41 Figure 3.18 – Damages on wing walls (Ozaeta García-Catalán, 2006). ... 42 Figure 3.19 – Wing walls’ damages: a) vertical cracking at the joint between wing wall and bridge spandrel wall, and b) diagonal cracking in the wing wall. ... 42 Figure 3.20 – Collapse of the Trigno river bridge (Italy) (Zampieri et al., 2017). ... 42 Figure 3.21 – Example of growth vegetation: a) in wing walls and b) in spandrel walls. ... 43 Figure 3.22 – Stains and black films in spandrel and piers of: a) Quebradas bridge (Douro line), and b) Coval bridge (Beira Alta line). ... 43 Figure 3.23 – Examples of dissolution of salts: a) carbonate crusts and efflorescences in Noemi bridge (Beira-Alta line); b) formation of stalactites in Pala bridge (Douro line). ... 44 Figure 3.24 – Repairing works between 2008-2010 in Cize-Bolozon viaduct: a) concrete beam below parapet and b) installation of impermeable membranes in the deck (Marion, 2016). ... 45 Figure 3.25 – Schematic representation of Areosa and Canharda bridges’ structural reinforcement a) crossed tie rods (Martins, 2001) and b) Transverse ties connecting spandrels (Martins, 2006)... 46 Figure 3.26 – Anchoring: a) radial drilling; b) Archtec system CINTEC (2022). ... 47 Figure 3.27 – Piers strengthening: a) pre-stressed concrete beams in Tamega bridge b) concrete cap in Coval bridge. ... 48 Figure 3.28 – a) The model of soil pressure used in Archie-M (Obvis, 2007) and b) representation of backfill elements in LimitState Ring (LimitState, 2016). ... 50 Figure 3.29 – The three principal modelling strategies of masonry (adapted from Bakeer (2009)). .... 51 Figure 3.30 – Modelling of masonry arch bridges: a) continuous model (Conde et al., 2017), b) mesoscale model (Minga et al., 2018), c) discrete model (Lemos, 2001). ... 53 Figure 3.31 – Homogenization process scheme (Lourenço et al., 2010). ... 55
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Figure 3.33 – Drucker-Prager model in Ansys: a) classic version; b) extended version; c) concrete
version (adapted from Ansys). ... 57
Figure 3.34 – Sbeta material model: a) the biaxial failure envelope and b) the equivalent uniaxial stress- strain relationship (Jendele et al., 2001). ... 58
Figure 3.35 – Yield surfaces for the damaged model: a) uniaxial tensile, b) uniaxial compression (Faria, 1994). ... 59
Figure 3.36 – Different dynamic methodologies for evaluating the effects due to railway traffic: a) moving loads (Goicolea et al., 2008) and b) train-bridge interaction (Ribeiro, 2012). ... 61
Figure 4.1 – Case study bridges: a) Durrães; b) PK124. ... 67
Figure 4.2 – Locations of in-situ testing in: a) Durrães and b) PK124 bridges. ... 68
Figure 4.3 – Examples from samples extracted from: a) Durrães bridge b) PK124 bridge. ... 68
Figure 4.4 – a) Uniaxial compression test and b) indirect tensile testing and c) Young Modulus Uniaxial compressive strength testing. ... 69
Figure 4.5 – a) Equipment for shear and compression tests on the joints, b) shear box b) one sample after a shear test. ... 70
Figure 4.6 – Shear tests in stone-to-stone samples of: a) Durrães and b) PK124. ... 71
Figure 4.7 – Compressive cyclic tests in stone-to-stone joints’ samples in different weathered conditions of: a) Durrães and b) PK124. ... 71
Figure 4.8 – Mohr-Coulomb failure envelope for samples tests: a) Durrães and b) PK124. ... 72
Figure 4.9 – Phases in a single flat-jack test: a) fixation of the gauge points, b) slot and c) inserted flat jack and pressure is applied. ... 73
Figure 4.10 – Flat-jack tests: a) site view in the pier P14 of Durrães bridge (FJ2); b) site view in the abutment of PK124 bridge (FJ3); c) tests’ layout. ... 74
Figure 4.11 – Flat-jack test curves: a), b), c) and d) Durrães bridge and e), f), g) and h) PK124 bridge. ... 75
Figure 4.12 – Typical curve of a Ménard pressuremeter test (Adapted from (Mair, 1987)). ... 77
Figure 4.13 – Ménard Pressuremeter (G type) (fabricated by APAGEO): a) equipment, b) probe and its components and c) working scheme (APAGEO). ... 77
Figure 4.14 – Ménard pressuremeter test: a) drilling, b) borehole c) probe insertion and d) readings. 78 Figure 4.15 – Experimental pressiometric curves for Durrães bridge: a) P1, b) P2, c) P3 and d) P4 tests and for PK124 bridge: e) P5 and f) P6 tests. ... 79
Figure 4.16 – Type of equipment used in dynamic tests: a) accelerometers; b) cDAQ and c) laptop. . 81
Figure 4.17 – PK124 bridge dynamic test excitation system. ... 82
Figure 4.18 – Post-processing phase: a) output-only technique: EFDD method (Durrães bridge) b) input- output technique: transfer functions (PK124 bridge). ... 82
Figure 4.19 – Shear test numerical model: a) solid blocks with an interface and b) deformed mesh after loading. ... 84
Figure 4.20 – Shear stress vs. tangential displacement model: a) Coulomb friction model and b) Combined cohesive and Coulomb friction model. ... 85
Figure 4.21 – Numerical simulation and experimental test results of the tangential behaviour of split joint samples: with different ks values for a) Durrães bridge and b) PK124 bridge; and with a mean ks value for c) Durrães bridge and d) PK124 bridge. ... 86
Figure 4.22 – Numerical simulation of the bonded joint samples of Durrães bridge: a) comparison with the experimental shear test results; b) for other levels of normal stress. ... 87
Figure 4.23 – 2D axisymmetric FEM model (dimensions in metres). ... 88
Figure 4.24 – Numerical simulation of pressuremeter tests: a) Durrães bridge and b) PK124 bridge. . 89
Figure 4.25 – FJ2 model (Pier P14 of Durrães bridge): a) general view; b) flat-jack insertion zones. . 91 Figure 4.26 – FJ3 model (abutment of PK124 bridge): a) general view; b) flat-jack insertion zones... 91 Figure 4.27 – Drucker-Prager concrete model: a) biaxial behaviour with Rankine tension cut-off, b) exponential hardening and softening in compression and c) exponential softening in tension. ... 92 Figure 4.28 – Spearman correlation matrix: a) Durrães pier model and b) PK124 abutment model. ... 93 Figure 4.29 – Non-linear model calibration strategy. ... 94 Figure 4.30 – Objective function variation: a) FJ2 model and b) FJ3 model. ... 95 Figure 4.31 – Relative errors for the non-linear response parameters before and after calibration: a) FJ2 model and b) FJ3 model. ... 96 Figure 4.32 – Durrães flat-jack test (FJ2) numerical results: a) with optimal values from run 1 and b) with optimal values from run 2... 97 Figure 4.33 – Minimum principal stresses (in kPa) in Pier P14 of Durrães bridge, for two load cases: a) elevation and b) vertical cross-section views. ... 97 Figure 4.34 – PK124 flat-jack test (FJ3) numerical results: a) with optimal values from run 1 and b) with optimal values from run 2. ... 98 Figure 4.35 – Minimum principal stresses (in kPa) in the masonry wall of the abutment of PK124 bridge:
a) elevation and b) section views. ... 99 Figure 5.1 – Flowchart of non-linear modelling strategies for in-service assessment... 103 Figure 5.2 – Example of contact joint numerical representation: a) real geometry; b) equivalent straight;
c) normal pressure and induced displacements. ... 104 Figure 5.3 – Results of contact numerical example: a) shear and b) and normal force - displacement plots in real geometry; and c) normal force - displacement plots in equivalent fictitious straight geometry.
... 105 Figure 5.4 – Determination of the equivalent stiffness for an equivalent fictitious straight joint: a) schematic representation of forces’ transfer; b) springs’ parameters and contact lengths. ... 106 Figure 5.5 – CZM model: a) interface behaviour in the normal direction; b) resultant forces in X direction vs. joint opening distance, for the real and equivalent straight joint geometries (without and with CZM).
... 107 Figure 5.6 – Leça railway bridge - downstream view: a) in the past (picture by Emilio Biel) and b) presently. ... 108 Figure 5.7. Original design drawings of Leça bridge (units in mm): a) lateral view and b) transversal cross section view. ... 108 Figure 5.8 – FE numerical model of Leça bridge: a) perspective, b) transverse cross-section. ... 109 Figure 5.9 – Numerical model of Leça bridge: a) general perspective of the included contact elements;
longitudinal contact elements in b) the real geometry and c) the fictitious straight geometry of a potential crack along the arch development. ... 110 Figure 5.10 – Leça bridge free-vibration test: a) test setup, b) accelerometers and c) data acquisition system. ... 110 Figure 5.11 – Experimental modal identification of Leça bridge using the EFDD method. ... 111 Figure 5.12 – Experimental vibration modes, in a perspective view of the Leça bridge, frequencies and damping ratios. ... 111 Figure 5.13 – Takargo freight train load scheme. ... 114 Figure 5.14 – Leça bridge model scenario A - Stress level in the bridge under dead load: (a) maximum principal stresses (in kPa) and (b) minimum principal stresses (in kPa). ... 115 Figure 5.15 – Vertical displacements in the arch at mid-span (influence line) for an 80km/h train passage
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Figure 5.16 – Linear dynamic response of Leça bridge model in terms of dynamic amplification factors of: a) maximum tensile stresses in the arch at mid-span; b) minimum compressive stresses in the infill;
c) vertical displacements in the arch at mid-span; d) transversal displacements in the arch at mid-span;
and in terms of e) vertical and f) transversal accelerations in the top of spandrels. ... 117 Figure 5.17 – Leça bridge model response with scenario B. Vertical displacement in the arch at mid- span for train speed a) 50 km/h and b) 80km/h (linear and non-linear dynamic results are shown). .. 118 Figure 5.18 – Plastic strains due to train passage at 50 km/h: a) maximum principal (tension) and b) minimum principal (compression) strain distributions. ... 119 Figure 5.19 – Stress level in the bridge deformed configuration for the final loading step (10P): (a) maximum principal stresses (in kPa) and (b) minimum principal stresses (in kPa). ... 120 Figure 5.20 – Plastic strains in the bridge deformed configuration for the final loading step (10P): a) maximum principal strains (in ‰) and b) minimum principal strains (in ‰) ... 121 Figure 5.21 – Stress level for the final loading step (10P) in a cross-section through the infill material:
a) maximum principal (tension) stresses (in kPa) and (b) minimum principal (compression) stresses (in kPa). ... 121 Figure 5.22 – Loading scenarios for longitudinal crack modelling calibration: a) concentrated vertical load; b) concentrated transversal load. ... 122 Figure 5.23 – Comparison between real and equivalent straight crack modelling simulations under increasing vertical loading: vertical displacement in the arch crown... 123 Figure 5.24 – Comparison between real and equivalent straight crack modelling simulations under increasing vertical loading: a) vertical relative movements between contacts; b) Gap distance in the contact elements. ... 123 Figure 5.25 – Shear stress in the transversal contact elements of real geometry crack modelling simulations under increasing vertical load multipliers: a) arch crown; b) arch ¼ span. ... 124 Figure 5.26 – Comparison between real and equivalent straight crack modelling simulations under transversal loading: a) Transversal displacement in the spandrel wall; b) Gap distance in the contact elements... 125 Figure 5.27 – Leça bridge model with contacts (A-ct) – response at arch crown: a) vertical displacements and b) transversal displacements. ... 126 Figure 5.28 – Leça bridge model with contacts (B-ct) – response at arch crown: a) vertical displacements and b) transversal displacements. ... 127 Figure 5.29 – Gap distance in the contact elements in the arch crown for train passage at 80km/h.
Comparison between real and simplified straight crack modelling (both from static and dynamic responses). ... 127 Figure 5.30 – Gap distance in the contact elements along the arch span due to self-weight and train passages at 30, 50, 80 and 120km/h. ... 128 Figure 6.1 – Freight train locomotive EURO 4000 with Sgnss type wagon: a) general overview;
b) loading scheme (distances in meters and loads in kN). ... 132 Figure 6.2 – Sgnss wagon: a) layout for containers, b) layout for timber transportation. ... 133 Figure 6.3 – Sgnss wagon: lateral view and plan of the platform (dimensions in mm). ... 133 Figure 6.4 – Y21 bogie: a) overview and main elements, b) primary suspension detail, c) cross-section in the transverse direction (adapted from (Pagaimo et al., 2020)). ... 135 Figure 6.5 – Dynamic tests of Sgnss wagon: a) loaded configuration, b) detail of the central stowage, c) unloaded configuration. ... 136 Figure 6.6 – Dynamic tests of Sgnss wagon: measurement setup. ... 137 Figure 6.7 – Dynamic tests of Sgnss wagon: DAQ and accelerometers on the platform and bogies. 137
Figure 6.8 – EFDD method - average normalized singular values of the spectral matrices: a) unloaded
configuration, b) loaded configuration. ... 138
Figure 6.9 – Experimental modal parameters: a) unloaded configuration, b) loaded configuration. .. 140
Figure 6.10 – FE numerical model of the Sgnss vehicle including a detail of the bogie. ... 141
Figure 6.11 – Numerical modal parameters before calibration. ... 143
Figure 6.12 – Spearman correlation matrix: a) unloaded configuration, b) loaded configuration. ... 145
Figure 6.13 – Model calibration strategy. ... 146
Figure 6.14 – Values of the optimal parameters for the optimization runs GA1–GA4 for the unloaded vehicle numerical model: a) stiffness parameters, b) additional mass parameters and steel elastic modulus. ... 148
Figure 6.15 – Residue of the objective function throughout the optimization process for the unloaded vehicle numerical model. ... 149
Figure 6.16 – Values of the optimal parameters for the optimization runs GA1–GA4 for the loaded vehicle numerical model. ... 150
Figure 6.17 – Residue of the objective function throughout the optimization process for the loaded vehicle numerical model. ... 150
Figure 6.18 – Variation of the optimal values of numerical parameter K1: a) unloaded vehicle; b) loaded vehicle. ... 151
Figure 6.19 – Errors between experimental and numerical modal responses, before and after calibration: a) natural frequencies, b) MAC. ... 152
Figure 6.20 – Comparison between the experimental and numerical (after updating) modal parameters for: a) unloaded configuration, b) loaded configuration. ... 153
Figure 7.1 – Durrães railway bridge: a) overview; b) railway track... 156
Figure 7.2 – Durrães bridge design drawings: a) overall elevation; b) pier elevation; c) arches’ details. ... 157
Figure 7.3 – Durrães railway bridge: details of the lateral longitudinal cracks on the intrados of arch A15. ... 158
Figure 7.4 – Experimental setups of the ambient vibration tests: a) global test; b) local test. ... 159
Figure 7.5 – Ambient vibration test: average normalized singular values of the spectral density matrices of all test setups. ... 159
Figure 7.6 – Experimental modal configurations. ... 160
Figure 7.7 – Static load tests: experimental setup: a) plan layout of arch intrados; b) pier elevation view. ... 161
Figure 7.8 – Static load tests: a) position 1.1; b) position 1.2; c) position 2.1; d) position 2.2. ... 162
Figure 7.9 – Static load test results: a-b) vertical displacement measured in 1/3 span of arches A11 and A15; c-d) vertical stresses measured in the flat-jacks located in the piers P11 and P14. ... 163
Figure 7.10 – Static load tests results – relative transversal displacements on arches: a) A11; b) A15. ... 164
Figure 7.11 – Dynamic test: a) setup measurement points in arches and piers (distances in meters); b) accelerometer on the deck; c) accelerometer on the pier. ... 164
Figure 7.12 – Dynamic test: a-b) vertical acceleration in positions A2 and A5; c-d) longitudinal acceleration in positions A8 and A9. ... 165
Figure 7.13 – 3D global numerical model of Durrães bridge. ... 166
Figure 7.14 – Comparison between some of the numerical and experimental global modal parameters of Durrães bridge. ... 167
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Figure 7.15 – 3D local numerical model of Durrães bridge: a) arch A15 and adopted contact model; b) location of contact/target elements on both spandrel walls interfaces; c) location of contact/target elements on other interfaces. ... 168 Figure 7.16 – Contact model behaviour: a) normal direction; b) tangential direction. ... 169 Figure 7.17 – Comparison between the numerical and experimental local vertical modal parameters of Durrães bridge. ... 170 Figure 7.18 – Takargo freight train: a) general view; b) loading scheme (dimensions in meters and static loads in kN); c) train dynamic signature. ... 171 Figure 7.19 – Train-bridge interaction model: a) overview; b) detail of the wheel-rail contact and c) contact/target pair scheme. ... 173 Figure 7.20 – Irregularities’ profile on the Durrães bridge: a) longitudinal levelling b) auto-spectra amplitude. ... 174 Figure 7.21 – Loading cases for the static numerical analysis. ... 175 Figure 7.22 – Experimental and numerical static vertical displacements: a) load test 1 (positions 1.1 and 1.2); b) load test 2 (positions 2.1 and 2.2). ... 175 Figure 7.23 – Stress variation on the bridge piers under permanent and live loads: a) pier P11; b) pier P14. ... 176 Figure 7.24 – Experimental and numerical crack opening values on the spandrel wall interfaces of arch A15: a) in the same side of transducer L1; b) in the side of transducer L3. ... 176 Figure 7.25 – Dynamic responses for the passage of the freight train at 60 km/h at mid-span of the arches in the vertical direction: a) accelerations time series, b) PSD amplitude, c) train dynamic signature. 177 Figure 7.26 – Dynamic responses for the passage of the freight train at 60 km/h at half-height of piers in the longitudinal direction: a) acceleration time series, b) PSD amplitude, c) train dynamic signature.
... 178 Figure 7.27 – Plastic strain level in terms of principal maximum strains (in ‰) for the freight train passage at 60km/h: a) arch A9; b) arch A15. ... 179 Figure 7.28 – Maximum vertical dynamic response of several arches of Durrães bridge for the passage of the freight train for speeds between 40 km/h and 140 km/h in terms of: a) displacements; b) accelerations. ... 180 Figure 7.29 – Vertical displacements in Durrães bridge in linear and non-linear dynamic analysis: a) arch A11 and b) arch A15. ... 181 Figure 7.30 – Crack opening values at the interface between spandrel wall and arch A15, due to the freight train passages at 60, 80, 100, 120 and 140 km/h. ... 182 Figure 7.31 – Influence of the track irregularities in the vertical accelerations in the wagon: a) vehicle platform and b) bogie. ... 182 Figure 7.32 – Maximum vertical accelerations at different points of the wagon’s platform for the: a) first wagon, b) intermediate wagon, c) last wagon. ... 183 Figure 8.1 – Adopted anchor scheme for the arch strengthening: a) solution A and b) solution S. .... 186 Figure 8.2 – Strengthening model of arch A15 in Durrães sub-models: a) solution A; b) solution S. 187 Figure 8.3 – Lateral pressure in the faces of the spandrel wall caused by the infill: a) due to self-weight;
b) due to live load c) due to self-weight and live load. ... 187 Figure 8.4 – Lateral pressure vs theoretical pressure in the faces of the spandrel wall caused by the infill due to self-weight; ... 188 Figure 8.5 – Transversal displacements in the contact interface in arch A15, due to static loading, for different infill material scenarios: a) alignment 1 and b) alignment 2. ... 189
Figure 8.6 – Transversal displacements in the contact interface in arch A15, after strengthening, for different tie rods’ diameters: a) solution A and b) solution S. ... 190 Figure 8.7 – Axial force in the tie rods for different tie rods’ diameters: for strengthening solution A; b) for strengthening solution S. ... 190 Figure 8.8 – Response parameters for strengthening solution A, after pre-stressing: a) transversal displacements in the contact interface in arch A15 and b) axial force in the tie rods. ... 191 Figure 8.9 – Response parameters for strengthening solution S, after pre-stressing: a) transversal displacements in the contact interface in arch A15 and b) axial force in the tie rods. ... 191 Figure 8.10 – Transversal displacements in the cracks with passive tie rods (with ϕ=32mm): a) longitudinal crack alignment 1; b) longitudinal crack alignment 2. ... 192 Figure 8.11 – Axial force in the passive tie rods (with ϕ=32mm): a) for strengthening solution A; b) for strengthening solution S. ... 193 Figure 8.12 – Transversal displacements in the cracks after prestressing of tie rods (with ϕ=32mm): a) longitudinal crack alignment 1; b) longitudinal crack alignment 2. ... 193 Figure 8.13 – Axial force in the tie rods (with ϕ=32mm): a) for strengthening solution A; b) for strengthening solution S. ... 194 Figure 8.14 – Transversal displacements in the cracks after prestressing of tie rods (with ϕ=17.5mm): a) longitudinal crack alignment 1; b) longitudinal crack alignment 2. ... 194 Figure 8.15 – Axial force in the tie rods (with ϕ=17.5mm): a) for strengthening solution A; b) for strengthening solution S. ... 195 Figure 8.16 – Vertical response at 1/3 span in arch A15: a) vertical displacements and b) vertical accelerations. ... 196
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List of Tables
Table 2.1 – Historical design rules for the arch thickness from different authors (s: thickness of the arch crown; S: span; R: radius; α: skewback angle) (adapated from De Santis and De Felice (2014)). ... 14 Table 2.2 – Historical empirical rules for the thickness of the pier top from different authors (s: thickness of the arch crown; S: span; P: thickness of the pier top section) (adapated from De Santis and De Felice (2014)). ... 15 Table 2.3 – Total and axle loads for the most representative trains operating in Portuguese railway lines.
... 20 Table 2.4 – Railway line categories (IP). ... 21 Table 2.5 – Terminology used by IP for railway bridges: ... 23 Table 2.6 – State-of-art by material (Data from IP) ... 23 Table 3.1 – Failure modes in arch masonry bridges. ... 35 Table 3.2 – Frequency of railway masonry arch bridge damages, adapted from (Orbán, 2004). ... 39 Table 3.3 – Repair techniques for masonry arch bridges adapted from (Orbán, 2004). ... 45 Table 3.4 – Advantages and disadvantages of using simplified, limit analysis and numerical methodologies for structural assessment of masonry bridges (adapted from Sarhosis et al., 2016). .... 48 Table 3.5 – Comparison between continuous and discrete modelling for masonry arch bridges (adapted from (Sarhosis et al., 2016). ... 54 Table 4.1 – Physical and mechanical parameters of granite stone blocks (average values). ... 69 Table 4.2 – Physical and mechanical parameters of masonry joints. ... 72 Table 4.3 – Estimated values of in-situ installed stress and masonry deformability... 76 Table 4.4 – Average values of GM e EM for each pressuremeter test. ... 80 Table 4.5 – Non-linear material properties for the stone-to-stone contacts. ... 85 Table 4.6 – Exponential hardening and softening model input parameters. ... 92 Table 4.7 – Numerical parameters values used in the calibration process. ... 93 Table 4.8 – Flat-jack numerical models’ optimal values. ... 96 Table 5.1 – Experimental vs Numerical vibration modes of Leça bridge. ... 112 Table 5.2 – Elastic parameters of the Leça bridge materials. ... 113 Table 5.3 – Contact elements’ parameters. ... 113 Table 5.4 – Drucker-Prager concrete model parameters. ... 113 Table 5.5 – Experimental vs Numerical vibration modes of Leça bridge: Different material scenarios ... 114 Table 6.1 – Geometrical characteristics of the main elements of the wagon platform. ... 134 Table 6.2 – Main parameters of the numerical model of Sgnss wagon. ... 142 Table 7.1 – Experimental frequencies and damping coefficients identified for Durrães bridge. ... 160 Table 7.2 – Elastic and mass parameters of the FE model of Durrães bridge. ... 167 Table 7.3 – Contact elements’ parameters. ... 169 Table 7.4 – Drucker-Prager (D-P) model parameters. ... 170 Table 7.5 – Main parameters of the numerical model of Sgnss vehicle (loaded configuration). ... 172 Table 7.6 – Key options set for the contact-pair model. ... 173 Table 8.1 – Technical details of the threaded bars (DYWIDAG-Systems, 2022). ... 186
Introduction
I NTRODUCTION 1.
1.1.CONTEXT
Masonry arch bridges have lasted several generations until present times and are still a very important part of the infrastructure systems. Throughout history, masonry bridges were being built in different typologies, using different materials and techniques, being the construction related to different civilizational periods as illustrated in Figure 1.1.
(Trajano bridge in Chaves) (Ucanha bridge) (Soure bridge) (Ovil viaduct)
Roman period Medieval period Modern period
(3rd BC – 5th AD century) (5th – 16th century) (16th – 20th century) (19th - 20th century)
Roman roads Medieval trade routes Road network Rail network
Figure 1.1 – Masonry arch bridge construction periods.
The beginning of the history of masonry arch bridges takes place with the Roman civilization. The arch was first used as the main structural element for bridge construction, applying the arch concept learned from the Etruscans. The architectural advantage of this system lies in the fact that the arch transfers the entire weight of the existing bridge body onto the piers operating essentially under compression. The ancient Romans had a good understanding of forces, geometry and material properties and this allowed them to create arch spans significantly large with the ability to support heavy loads due to the high
compressive strength of stones. The masonry bridges built by the ancient Romans were fundamental for its expansion through new territories allowing faster communication and the transportation of water and goods to the cities. Its legacy is still present in many countries and many examples can be found also in Portugal.
The fall of the Roman Empire also represented the end of the construction of large bridges throughout Europe for a very long time (ECCE, 2014). This type of bridge is very expensive and requires a lot of specialized labour and many years to construct. For these reasons the great masonry bridges built during the medieval and renascence periods were mostly financed by the church. These bridges present particular traces from this period: the semi-circular arch was substituted by the ogive arch, the existence of symbols engraved in stones, and some religious motifs, like stone crosses on the deck.
In the modern period, with the development of the transportation infrastructure systems, audacious solutions for the masonry bridges’ construction were adopted, with larger spans, lower rises and higher piers, exploring the limits of the simpler technology brought by the Romans. In the railway system, the adopted solutions consisted mainly of multiple semi-circular arches (like the roman arch) with identical spans, supported by higher and thinner piers, and featuring transition frames between the piers and the arch. This construction period is coincident with the construction of the railway network across Europe, with its beginning in the 19th century and subsequent expansion in the 20th century.
Once the expansion of the railway networks in Europe has stabilized, the construction of masonry arch bridges practically disappeared. Thereafter, masonry has been replaced by reinforced concrete structures and new modern techniques such as precast structures. This inevitably led to the loss of specialized workmanship, knowledge and construction techniques, which also contribute to the decline of stone masonry arch bridges’ construction.
However, the large number of stone masonry bridges still in operation nowadays in the railway network, justifies the need to study this type of bridges, which is deemed essential to ensure this past knowledge is not lost but further deepened in light of current modern techniques, such as the use of computational models and experimental tools.
1.2.MOTIVATION
The longevity, robustness and low operating costs that are associated with stone masonry arch bridges allow them to be considered a good example of sustainability. By contrast, many metallic and concrete bridges built in the last century required considerable expenses in maintenance and repair or even replacement during the first 30 to 40 years of service (McKibbins et al., 2006). According to Jackson (2004) masonry arch bridges require the lowest maintenance costs of all bridge types.
In recent years, the assessment of the state of conservation of bridges has received particular attention from the railway managing entities. In addition to being a vital part of the transportation infrastructure, masonry bridges have countless cultural and heritage values, by their historical and architectural background, which were transmitted us by past generations, and in most cases in excellent service conditions. Moreover, the safety and efficiency of railway networks require the establishment of suitable safety criteria and management plans for the bridges which account for the constant pressure for expansion and capacity increase while addressing economy and sustainability issues.
Introduction
A large number of existing and in operation masonry arch bridges within the rail network across Europe is evidenced in the European research project “Sustainable Bridges - Assessment for Future Traffic Demands and Longer Lives” (Bell, 2004). This project aimed to assess the structural state of existing railway bridges in view of the requirements foreseen for the year 2020 and to find solutions to adapt them in case they do not meet those requirements. In this scenario, the increase in high-speed and mixed traffic implies an increase in the load capacity of the bridges, given the increase in higher load demands and the introduction of dynamic effects resulting from the high-speed train passages.
The study of stone arch bridges was also addressed in the research project “Improving Assessment, Optimisation of Maintenance and Development of Database for Masonry Arch Bridges” (Orbán, 2004) developed by the International Union of Railways (UIC). Other working groups, such as the Construction Industry Research and Information Association (CIRIA), have also contributed to a better organization of data available on this subject (McKibbins et al., 2006). Several studies of experimental and numerical nature have been presented worldwide, particularly in the nine editions of the International Conference on arch bridges over the two past decades. The last edition was held in 2019 in Porto, Portugal, and the goal is to maintain an international forum addressed to members of the arch bridge structures’ community, seeking for exchange and diffusion of related knowledge. More recently, Europe’s Rail Joint Undertaking an European partnership on rail research and innovation (EU-Rail, 2022), also focuses its main goals on the study of solutions for repair and upgrading existing railway bridges and methodologies that significantly improve operational performance in terms of maintenance and cost-efficiency.
In recent years, rail freight traffic has experienced a significant increase in the total amount of transported goods, since railway operators have employed more efficient strategies, which include, for example, increasing the axle load, length and speed of trains, making this type of transport more competitive (ECA, 2016). Moreover, the European Union has increased its multi-annual budget to achieve more efficient and sustainable transportation systems, mainly rail transportation. In the 2014- 2020 framework programme, most of the rail investments stem from the Cohesion Fund, which represents more than a quarter (27.1 % in 2019) of all cohesion policy investments in the transport sector.
For the subsequent programme period (2021-2027), this support tends to increase, aiming for a more connected Europe by enhancing mobility.
In this framework, the representativeness of this type of bridge in the railway network infrastructure and the growing need for expansion, higher capacity and new requirements for people and freight mobility are issues of major importance, which justify a better understanding of the structural behaviour and assessment methodologies of masonry bridges. This endeavour is further supported considering that numerical modelling strategies allow evaluating the structural response of masonry bridges with realistic service and limit loading conditions, settlements, material and structural composition, thus contributing to help in the assessment of the bridge structural condition and in the implementation of suitable management plans for this type of bridge.
However, more than the adoption of a numerical model, the main difficulties that arise are concerned with the characterization of the constituent materials, since masonry is a heterogeneous and orthotropic material. Therefore, by simplifying the numerical models, such as the adoption of equivalent continuous models, more relevance needs to be given to material calibration in order to have an equivalent composite material with properties similar to the combination of its various components: stone blocks, mortar and interfaces in between them. Furthermore, due to their age, the characterization of these
bridges’ conservation state is essential to allow assessing their real structural behaviour and identifying the exploitation limits for future rail networks.
1.3.OBJECTIVES
In the framework set in the previous section, this work aims to contribute for a better understanding of the structural behaviour of stone masonry arch bridges, including its material characterization in a weathered and damaged condition. This is expected to provide valuable means to help on defining adequate and calibrated constitutive models to be used in numerical simulations of the bridges’ structural behaviour.
Thus, this study aims at establishing a set of numerical simulation tools suitable for the structural analysis of stone masonry arch bridges under railway traffic loading for their in-service assessment.
Such tools, based on existing numerical techniques calibrated with experimental data, can be adapted to support the effective implementation of operational plans appropriate for this type of bridge for safety assessment purposes and for the design of strengthening interventions. The numerical methodologies are based on the finite element method (FEM) with continuous models, simplified by considering equivalent isotropic homogeneous materials, and developed in Ansys software (ANSYS, 2017). These simplified models are essential to perform realistic non-linear dynamic vehicle-bridge interaction analysis, with long load histories, since they allow reducing the computational cost of a full-scale and complete structural model analysis.
Another major effort will be put on choosing techniques for retrofitting and strengthening in-service stone masonry bridges, fostering interventions reduced to the least possible, respecting and preserving at the most the original construction and structural behaviour, using compatible materials with reversible techniques.
The study focuses on a particular type of masonry arch bridge, namely granite stone arch bridges, which is a very representative typology present in the Portuguese railway network. For the railway traffic loading, a freight train is adopted which is representative of the most demanding loading in the Minho railway line where the case study bridges of this work are located. Particularly for the freight trains, their effects on the bridges can be more severe than those caused by passenger trains, since, although having lower speeds, they have significantly higher axle loads.
The following milestones are to be achieved with this research work:
- Identification of representative stone masonry arch bridge cases in the Portuguese railway network, including the survey of the frequent damages observed in this type of bridges;
- Results obtained from experimental campaigns in bridge case studies, aiming for global and material characterization;
- Definition and calibration of input material properties for both masonry and infill materials, based on the simulation of the material experimental behaviour, observed in laboratory and in- situ testing, using homogeneous equivalent materials;
- Proposal of non-linear modelling strategies resorting to FEM continuous homogeneous models for global damage representation while combining the potentialities of FEM with discrete crack modelling to simulate localized existing cracks;
