The assessment and design of masonry vaulted structures in seismic regions presents challenges to the designer. Typical form-finding methods for compression-only shells may not directly consider horizontal loading, leading to uncertainty regarding structural performance during earthquake events. In the case of new design, this can result in inefficient structures and material overuse, while historic structures may be condemned or damaged through inappropriate interventions. Direct consideration of the static horizontal force capacity - the threshold at which hinge formation triggers dynamic, rocking-like mechanisms in the vault - would allay these concerns, and is primarily a product of the structural geometry. Recent work by the authors has presented a methodology for form-finding compression-only shells under combined vertical and horizontal loading, which is based on the theories of Limit Analysis and Membrane Equilibrium Analysis. However, this method relies on the constrained optimisation of a concave stress potential, which can result in computational challenges. Solutions may be further complicated in the case of vaults containing either cracking damage or intentional geometric discontinuities, such as cross vaults. This paper outlines the key challenges in refinement and implementation of the new form-finding methodology and presents two potential computational solutions, utilising non-convex optimisation and machine learning methods.

Masonry arch bridges are often between 100-150 years old and have complex histories of damage. Uncertainties regarding their condition and behaviour can present asset management challenges, potentially leading to operational restrictions that may or may not be warranted. This can be compounded when the extent, severity, and cause of deformations are difficult to judge. The challenge is particularly onerous for skewed arch bridges, which can behave highly three-dimensionally. Point cloud-based analysis offers a means to interrogate long-term structural deformation and can be coupled with theories of masonry behaviour to interpret kinematic mechanisms behind these movements. Building on previous work by some of the authors, this paper utilises exploratory point cloud-based assessment to study two typical skewed arch bridges. Specifically, the methodology enables distributed structural deformations to be mapped relative to best-fit shapes representing likely construction geometry, and for kinematic mechanisms to be overlaid on these maps. In this way, potential magnitudes of support movements behind the observed deformations may be gauged. The two case studies highlight the complex threedimensional behaviour of skewed masonry bridges and provide experimental evidence of concentrated support deformations at their obtuse corners, aligned with their square span direction. This is consistent with the hypothesis that large thrusts may initially follow the square span direction before being redistributed as local deformation of these corners occurs and that, consequently, assumptions of rigid boundary conditions for skewed arch bridges are unrealistic.

Purely compressed shells are often elegant and highly efficient structural forms, but this leanness may create risk if they are subjected to unexpected patterns and magnitudes of loading, such as may arise due to seismic events. In the same way that historic masonry structures were designed to sustain loads by activating purely compressive force paths, a modern metamaterial can be designed for specific purposes following the same logic. Conventional analysis methods for compression-only shells and vaults, often developed for masonry structures, have tended not to model combined vertical and horizontal loads directly. This has created a significant challenge for engineers assessing historic vaults or designing new shells. To address this gap, this paper presents an enhanced method based on membrane equilibrium analysis (MEA) and the static theorem of limit analysis. This approach is the first application of MEA to directly consider vertical and horizontal body forces acting on a compression-only shell through a parametric formulation of an Airy stress function. The method is applied to a case study of a sail vault subjected to vertical and horizontal loads. Moreover, it is demonstrated how this approach can be used to define iso-resistant shapes that offer more sustainable design options while preserving structural capacity.

Masonry arch bridges are common, especially in the UK and Europe, but interpretation of their structural behaviour can be challenging and is often complicated by histories of damage over their long working lives. Assessing the performance of repair works at these bridges is vital, to provide confidence in their continued use. This paper presents novel applications of fibre-optic sensing and videogrammetry to measure and visualise the three-dimensional, dynamic structural response of a skewed masonry arch railway bridge in unprecedented detail. In particular, fibre-optic strain rosettes are used to map the distributions of principal strains, and hence force flow, throughout the arch, while videogrammetry reveals a secondary load path in the form of transverse arch bending. Monitoring results are then combined with simplified analytical models of this transverse bending, to study the effectiveness of intervention works aimed at restoring structural connectivity between the arch and its spandrel walls.

Masonry bridges are common in many countries and their maintenance is a critical task, to preserve not only architectural heritage but also the embodied carbon invested in their construction. Sensing technologies can offer vital information to engineers responsible for these structures. In this paper, a multi-sensing approach is used to study the behaviour of a skewed, three-span masonry rail bridge in the UK, focusing on its deformation history and the movements at four transverse fractures that extend the full width of the bridge. Specific technologies include laser scan analysis, videogrammetry, and Fibre-Bragg gratings (FBGs) to monitor the multi-dimensional bridge response, which at the transverse cracks is of particular concern to engineers. Based on these data, the distributed nature of the structural behaviour of the bridge is discussed. The results demonstrate that complex masonry bridge degradation can be quantified and tracked, providing crucial insights for bridge maintenance and structural interpretation.

Masonry arch bridges are numerous across European transportation networks. Many are ageing structures, with service lives of 100–150 years to date, and exhibit historic damage and repairs, leading to uncertainty regarding structural behaviour. For skewed bridges particularly, this can be complicated and three-dimensional, and detailed experimental data describing behaviour are rare. In 2018–2019, the authors deployed Fibre Bragg Grating (FBG) strain monitoring at a recently repaired, skewed masonry rail bridge in the UK. Following an on-site trial, the FBG monitoring system was substantially upgraded in 2020 to enable long-term, autonomous, remote sensing. This new system is introduced, including processes to automate data classification based on the date and time of measurements, and train class/operator, direction, and speed. This system has recorded the bridge responses to thousands of trains. Data analysis is presented, focusing particularly on seasonal and long-term variation of behaviour. Findings include the impact of ambient temperature; an inverse relationship is observed. Decreasing temperature causes thermal contraction of the masonry, allowing cracks to open and increasing the potential for bridge movements. After decoupling such effects, residual long-term changes may correspond to damage. Therefore, this system can provide valuable asset management information on the early onset of bridge deterioration.

This paper presents an application of Membrane Equilibrium Analysis (MEA) to a historic masonry arch railway bridge in Leeds, United Kingdom. This case study structure is representative of the many masonry arch bridges present on UK and European railway transport networks. It has been chosen because, since 2016, it has been the subject of a detailed Structural Health Monitoring (SHM) campaign, making it an ideal candidate against which to test analytic models. Typically, asset engineers will be responsible for maintaining a large stock of these structures and will lack the time to perform thorough computational analyses. Therefore, simplified approaches, such as MEA, which can offer insight into structural behaviour, have the potential to be highly valuable. This study represents the first step in applying MEA to masonry arch railway bridges.

Skewed masonry arch railway bridges are common, yet their structural behaviour under typical working loads, along with gradual changes in behaviour due to degradation, can be difficult to determine. This paper aims to address this problem through detailed monitoring of a damaged, skewed masonry arch railway bridge in the UK, which was recently repaired. A comprehensive Structural Health Monitoring system was installed, including an array of fibre-optic Fibre Bragg Grating (FBG) sensors to provide distributed sensing data across a large portion of the bridge. This FBG monitoring data is used, in this paper, to investigate the typical dynamic structural response of the skewed bridge in detail, and to quantify the sensitivity of this response to a range of variables. It is observed that the dynamic bridge response is sensitive to the time of day, which is a proxy for passenger loading, to the train speed, and to temperature. It is also observed that the sensitivity of the response to these variables can be local, in that the response can differ throughout the bridge and be affected by existing local damage. Identifying these trends is important to distinguish additional damage from other effects. The results are also used to evaluate some typical assumptions regarding bridge behaviour, which may be of interest to asset engineers working with skewed masonry arch bridges.

Skewed masonry arch bridges present a challenge to asset owners because their structural response under traffic loads can be hard to predict.This can be further complicated by damage such as spandrel wall separation cracks, which are common for this type of structure.For skewed masonry bridges in particular, the effect of damage on the load distribution, and therefore on the effective load carrying capacity, is not well understood.This paper presents results from a field investigation of a typical skewed masonry arch railway bridge.Both the current response to train loading and the current geometry, which has likely been affected by long-term deformations resulting from historic loading and damage, are considered.The objectives of the study are to (a) describe and quantify the current structural response, and to (b) investigate long-term deformations over the skewed bridge's history.The current dynamic response is captured using a distributed network of fibre-optic Fibre Bragg Gratings, arranged in a novel triangular rosette implementation so that detailed time histories of principal strain directions and magnitudes can be mapped across the arch as trains travel overhead.Meanwhile, potential long-term deformation is evaluated through postprocessing of detailed laser scan data and comparison of this point cloud against assumed reference geometries to infer potential movements and mechanisms which could explain these.The methodologies described here allow for possible connections to be investigated between the current behaviour and either long-term mechanisms of deformation or recent intervention work, and for the feasibility of these connections to be commented on. Notation ϵ a,b,cMeasured strains within an FBG rosette θ a,b,cOrientation angles of rosette strains ϕ Orientation angle of local rosette coordinate system ϵ x,yNormal strains within local rosette coordinate system ϵ xy Shear strain within local rosette coordinate system ϵ 1,2Principal strains within an FBG rosette

Linear-elastic finite-element analysis is sometimes used to assess masonry arch bridges under service loads, despite the limitations of this method. Specifically, linear-elastic analysis can be sensitive to material properties, geometry, and support settlements, while also allowing the development of tensile stresses that may be unrealistic for masonry structures. However, even though linear-elastic methods remain appealing for their simplicity, it is rare to evaluate their output against experimental data. In this paper, detailed strain and displacement monitoring data for a masonry arch viaduct are used to evaluate a series of independently developed linear-elastic simulations of this structure. Although uncertainties in input parameters mean the magnitude of modeling results cannot be presumed accurate, the simulated response pattern was found to agree reasonably well with monitoring data in regions of low damage. However, more damaged regions produced a markedly different local response. Comparisons between the simulations revealed useful conclusions regarding common modeling assumptions, namely the importance of modeling backing material, spandrels, and foundation stiffness, to capture their influence on the arch response.

An extensive monitoring installation of a skewed masonry arch railway bridge is presented, where a range of technologies were used to measure the strain and displacement response of the bridge under train loading. Fibre-Bragg Gratings, videogrammetry, vibrating wire strain gauges, crack sensors utilizing potentiometers, and a laser distometer are employed. The objective of the study is to evaluate techniques for measuring the behavior of masonry arch bridges in order to facilitate future monitoring decisions by asset owners. Characteristics and practicalities of each technique are compared, as well as specific monitoring data. While the monitoring data from most methods agrees reasonably well, disagreements do exist due to error or measurement limitations, and the implications of this disagreement for asset owners are discussed. In general, the work also exemplifies the potential of structural health monitoring technologies to provide insight into the dynamic behaviour of masonry arched structures, and in particular heritage structures which may have a complicated history of damage, the progression of which is of interest to their owners.

Skewed masonry arch bridges form an important part of the rail and road infrastructure networks in the UK, as well as other European countries. However, the precise flow of forces in these structures is not well understood, which can pose a problem when it comes to assessment and maintenance. The skewed masonry arch railway bridge considered in this study has suffered significant historic damage, which led to a pronounced response under live loads and prompted extensive repair work. Subsequently, a network of fibre-optic Fibre Bragg Grating sensors was installed on the arch barrel of the repaired bridge. In this paper, the monitoring method is outlined, and the detailed measurement of the dynamic response under train loading is presented. Results quantify both the principal directions of strain and the strain magnitude in a skewed arch barrel during the passage of a train. Thus, the monitoring data provide rare insight into the structural response of skewed masonry arch bridges.

The masonry viaduct at Marsh Lane is an important part of the railway network near Leeds, UK, dating from the 1860s. However, deterioration has resulted in notable deflections under train loads, which have concerned asset managers. Coupled with uncertainty regarding the true structural behaviour under serviceability conditions, this has led to detailed monitoring of the viaduct. This paper summarises the main conclusions of the monitoring installation before focusing on the evaluation of computational modelling of the viaduct, through comparison of modelling and monitoring results. In the monitoring scheme, fibreoptic cables containing Fibre-Bragg Gratings allowed measurement of dynamic in-plane barrel strains while digital image correlation captured displacements using commercial video cameras. The results illuminated a complicated three-dimensional dynamic response under train loading and highlighted the importance of interaction between adjacent spans. Separately, rail loading of the viaduct was simulated with a series of finite element models, each with increasing levels of complexity, to establish the relative stiffness contributions of various structural components. These models were then compared to detailed measurements from the real viaduct so that their validity could be evaluated. This approach revealed the impact of some common modelling assumptions and permitted assessment of nonlinear contributions to structural behaviour. Sam H. Cocking, Sinan Acikgoz and Matthew J. DeJong