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Heritage masonry structures require detailed monitoring during nearby underground construction, to address the concerns of building owners and mitigate uncertainties relating to the soil–structure system. This paper discusses innovative displacement and strain monitoring of a listed masonry church undergoing ground movements due to nearby tunnelling in London Clay. In addition to conventional surveying and tilt monitoring, laser scan displacement monitoring and fibre optic strain sensing was conducted. Prior to construction, point clouds of the structure were used to map pre-existing geometric distortions in the structure. During construction, detailed monitoring of displacements and strains was conducted across the building facades and the tower. The same techniques were also used to monitor the painted dome of the church where conventional displacement monitoring was not feasible. With a focus on the new engineering insight provided by the innovative monitoring techniques, the impact of the underground construction activities on the church is discussed in this paper. The proposed sensing techniques provide new data on the influence of pre-existing damage and tunnel advance on soil–structure interaction.

Tunnelling and deep excavation activities cause ground movements. Monitoring the influence of these ground movements on nearby surface assets is a major component of urban underground construction projects. Such projects often require large-scale and comprehensive monitoring of nearby buildings to track displacements and identify structural damage. Masonry assets are particularly vulnerable to ground movements due to the low tensile strength of the material; these structures may experience unsightly cracking and structural stability issues. Current monitoring practice for these buildings is labour intensive and cannot fully characterise the response of the assets due to the limited number of measurement points. This paper presents a non-contact monitoring solution using terrestrial laser scan (TLS) data, which develops a modified non-rigid iterative closest point (N-ICP) algorithm. This algorithm optimises the displacement fields by establishing point to point correspondences that penalise non-smooth deformations and deviations from landmarks (i.e. feature points where displacements are known). The algorithm outputs rich 3D displacement fields that can be used in established assessment and decision-making procedures. To demonstrate this algorithm's ability to estimate 3D displacement fields from point clouds, several synthetic datasets are processed in this study. The results demonstrate the algorithm's potential for recovering underlying deformations with the help of landmarks and optimisation weightings.

Dynamic amplification of loads in masonry archrailway bridgesis not well understood. There is a scarcity of experimental data and previous numerical studies have only addressed a few specific bridge geometries. Despite this, guidance documents provide empirical and unvalidated formulae to calculate dynamic amplification for masonry arch railway bridges. To improve our fundamental understanding of the problem, determine appropriate modelling strategies and evaluate the reliability of guidance documents, simple 2D and 3D models are explored in this paper. The 2D approach idealises key bridge components (pier, arch, fill and backing elements) with straight Timoshenko beams, springs andlumped masses. It uses an analyticaldynamic stiffnessformulation, which is computationally efficient and well-suited to explore a range of bridge models. The higher fidelity 3D modelling approach uses shell and solid finite elements and is used to evaluate the limitations of 2D models. In both approaches, linear-elasticmaterial behaviouris assumed and train loads are idealised as moving vertical loads distributed over an effective area. The modelling results indicate a complex relationship between train speed and dynamic amplification that depends critically on bridge geometry and axle spacing. In general, the multi-span bridge configurations experienced higher dynamic amplification over operational train speeds. The results also higlight deficiencies in existing code provisions and demonstrates how efficient numerical models may replace these provisions.

Motivated by the rocking motion of non-rigid structures during earthquakes, this paper investigates the rocking behaviour of laterally flexible oscillators. Previous studies in this area utilised ad hoc assumptions to consider transitions between different motion phases at impact. Some models explored direct transitions between two rocking phases assuming that elastic translational velocities remain the same, while others assumed the dissipation of all vertical momentum after a rocking phase, leading to a full contact phase upon impact. In this paper, an improved impact model is proposed, where consistent mechanical principles are used to determine the phase transition criteria. The model departs from the principle that the spring and damper elements of the oscillator cannot transfer horizontal impulses over infinitesimally small durations. Alongside other mechanical constraints, this principle yields a series of momentum equations, which are solved to determine the post-impact velocities when transiting from one rocking phase to another. Through these equations, it is shown that a transition to full contact implies a specific locus of the vertical impulse from the support medium. Analytical and numerical investigations are then conducted to comparatively evaluate the new impact model. It is demonstrated that the new impact model yields equivalent results to established rigid rocking impact models for effectively rigid structures and resolves long-standing issues associated with excessive energy dissipation observed in previous models. Time histories of free rocking motion and stability analyses under pulse excitations are used to illustrate and generalise the findings for a range of geometries.

© 2020 Baran Bozyigit, et al.The aim of this study is to investigate free vibration characteristics of arch-frames which consist of two columns and an arch. Firstly, an exact formulation of the problem is presented using the Dynamic Stiffness Method (DSM). The end forces and displacements of column elements are obtained analytically using Timoshenko beam theory (TBT). These are then combined with the end forces and displacements of the semi-circular arch, which is modeled with exact curved beam elements that consider axial and shear deformations and rotational inertia. By employing standard assembly and bisection based root finding procedures, exact free vibration analysis of the whole vibrating system is carried out. Then, in an effort to simplify the formulations, an approach based on approximating the arch as assembly of linear straight beam segments is presented. The calculated natural frequencies using DSM for both exact and approximate results are then tabulated for comparison purposes. The mode shapes are also compared. The results show that the proposed model simplification is effective and produces accurate mode frequency and shape estimations.

Fibre-optic sensing technologies provide the opportunity to measure detailed structural response in real time over long durations. This paper describes a first-of-its-kind application of Fibre Bragg Grating (FBG) measurement to monitor the impact of tunnelling works on two Grade-I listed buildings in London, UK. After describing the principles behind the strain sensing technology, laboratory tests are discussed. These tests are used to calibrate strain sensors and validate the newly developed temperature compensation technique. The arrangement of sensors and their installation on the buildings is then presented. Fibre-optic temperature and strain measurements from the ensuing three-year monitoring period are compared with other independent measurements. It is demonstrated that the system enabled direct real-time monitoring of both the short- and long-term impact of tunnelling on the historic assets in a reliable manner.

Controlling building displacements induced by tunnelling is a major issue in densely urbanised areas, particularly for listed heritage structures. Major tunnelling projects provide opportunities to assess the ability of advanced numerical models to address this issue, in conjunction with the large amount of monitoring data that are gathered during the works. This paper considers the case of two Grade-I listed buildings (St. Mary Abchurch and Mansion House) affected by the Bank Station Capacity Upgrade in London (UK) where complex excavation works were conducted to improve the existing underground infrastructure. Both conventional and innovative monitoring was carried out to control the effect of tunnel construction on these buildings. Following the works, three-dimensional finite element analyses were conducted by adopting a semi-coupled modelling approach. In these analyses, the pre-existing damage in the buildings prior to tunnelling has been considered by adjusting the properties of embedded solids that are used to idealise the structure. The analyses also considered salient aspects that are often neglected in routine risk-assessment procedures, such as the excavation modelling sequence covering both pilot tunnelling and enlargement, the skew building-tunnel alignment, and the effect of closely spaced tunnel excavations on surface ground deformations. The results highlight the challenges associated with idealising historic structures with semi-coupled models; nevertheless, they encourage the integrated use of innovative monitoring systems and advanced numerical modelling as a tool to control the process of tunnel excavation in complex urban environments.

Detailed site investigation and monitoring data gathered during underground construction projects creates an opportunity to evaluate and improve the techniques used to model the influence of tunnelling on existing buildings. This paper discusses the application of the semi-coupled modelling technique to two historic buildings affected by the construction of new tunnels for the Bank Station Capacity Upgrade in London, UK. Using the semi-coupled modelling approach, the buildings were idealised as equivalent elastic anisotropic solids, while high fidelity models were used to model nonlinear behaviour of the soil and tunnel excavation process. These analyses highlight the flattening of displacement profiles, and the important influence of tunnel advance on skew facades. However, comparison of modelling results to levelling data, highlight some limitations of using equivalent solid models to represent masonry buildings.

This paper proposes simple numerical models that simulate the influence of tunneling-induced ground movements on masonry buildings founded on shallow strip footings. The focus is on develop...

For rigid rocking models, energy dissipation relies solely on impact. Consequently, the position of the impulse acting on the rocking body determines the magnitude of energy loss and strongly influences the subsequent dynamic response. This paper evaluates the corresponding influence of the location of the vertical impulse on the dynamic behaviour of flexible rocking oscillators. The dynamic behaviour of a rocking flexible oscillator is explored in this study with an impact model that parametrically considers the position of impulse. The influence of the position of impulse on the expected energy loss during impact, and on the overturning stability of the flexible rocking oscillator are then examined. It is shown that the energy loss at impact reduces and the potential for overturning instability increases, for impulses located at increasing distances from the future rocking corner.

Due to urban tunnelling activities, bridges may be subjected to excavation-induced ground movements that can affect their serviceability. The Tideway Tunnel being constructed in London involves multiple under-crossings of bridges along the River Thames. The monitoring data collected will provide an opportunity for the application and validation of numerical methods for tunnel-bridge interaction. Although field monitoring data are not yet available for publication, the response of the Grosvenor Bridge at Battersea to tunnelling-induced displacements is examined in this work with numerical models. In particular, a simple approach for the preliminary assessment of tunnelling impact on framed structures on shallow foundations is presented; the adopted two-stage finite element model uses integral forms of Mindlin’s solutions to calculate the soil stiffness matrix, while structural members including the piers, arches, deck and spandrel columns are modelled as beam elements in the superstructure stiffness matrix. Preliminary results provide useful insights into the response of arch bridges to tunnelling-induced ground movements at different levels of model complexity.

© 2020 European Association for Structural Dynamics. All rights reserved.This paper is concerned with the dynamic response analysis of single and multi-span beams under moving point loads. The Dynamic Stiffness Method (DSM) is used to calculate the mode frequencies and shapes of single, two and four-span Bernoulli-Euler beams. The exact mode shapes obtained from dynamic stiffness formulations are used to derive generalized mass, stiffness and force terms for normal modes using Galerkin 's method. This enables efficient and accurate calculation of the time-history response of the investigated structures. This is demonstrated by comparing the results from this study with advanced finite element simulations of the same problem from the literature. The results validate the accuracy of this approach and demonstrate how this technique can be used to model dynamic amplification of bridges under the influence of moving loads.

Masonry arch bridges constitute over half of the European bridge stock. The dynamic response of these bridges to traffic loads is influenced by their free vibration properties, i.e. their natural vibration frequencies and mode shapes. However, these properties have not been systematically examined to date. This paper utilises the dynamic stiffness method (DSM) to obtain an improved fundamental understanding of the free vibration properties of idealised single and multi-span arch bridges. In this approach, the piers and arches are modelled as an assembly of linear Timoshenko beam segments, the backing and infill are represented with axial struts and the underlying soil with concentrated spring elements. These idealisations enable rapid but accurate calculations of in-plane free vibration properties. To demonstrate this, the proposed procedure is applied to a simply-supported arch structure, a small-scale single-span arch bridge model and a multi-span arch bridge, where published experimental data is available. Then, free vibration analyses of representative single and multi-span arch bridges are performed. The results obtained from DSM analyses agree with detailed 3D finite element models and reveal the critical influence of backing elements and the interactions between adjacent spans on free vibration properties. Lastly, a range of arch bridge geometries are examined to reveal the shortcomings of existing provisions for modal frequency estimation in codes of guidance.

© 2018 New Zealand Society for Earthquake Engineering. All rights reserved. Rocking action at the foundation-structure interface has long been proposed to isolate structures from strong ground motion. In this paper, the fundamental concept of rocking isolation is examined in depth to guide further design efforts. This is achieved by first deriving an analytical model of a flexible structure freely rocking on rigid ground. Decomposing the coupled equations of motion of the model into their modal components provides new information on the mechanics of rocking isolation. After identifying the salient parameters needed to quantify rocking isolation, equations to predict the lateral accelerations, base shear and overturning moments arising during rocking are provided. The analytical model and the simplified equations are then validated using some of the earliest experiments on rocking structures, which were completed in New Zealand. These validations clarify poorly understood phenomena concerning rocking isolation, such as how rocking and vibrations of the structure couple, how this influences the excitation mechanisms of the structure, resulting in seismic shear forces and overturning moments larger than those required for uplift. The findings provide an analytical basis for designing efficient rocking systems that successfully limit force demands.

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., This work forms part of a PhD, which is funded through an EPSRC Doctoral Training Partnership (grant reference number EP/M506485/1). Data collection was made possible by the Cambridge Centre for Smart Infrastructure and Construction, through additional EPSRC funding (grant reference number EP/L010917/1).

Assessment of masonry railway arch bridges are typically conducted using static loads. To account for the increase in structural response due to the dynamic application of loads, amplification factors are prescribed by the codes. These amplification factors have been derived from extensive large-scale laboratory testing on model concrete and steel bridges, carried out in the 1970s. Analytical solutions to the dynamic response of an undamped simply supported beam to moving loads demonstrate general agreement with these tests, and form the basis of the formulae used to determine dynamic amplification factors. This paper investigates the suitability of applying the dynamic amplification formulae to masonry arches. In particular, the critical role of determinant length and the chosen vibration mode and frequency is considered. To achieve this, the dynamic response of a damped two-hinged circular arch due to a moving point load is evaluated using Galerkin’s method. Solutions are compared to classical solutions and finite element analysis results for an instrumented single span arch, to highlight the limitations of codified formulae.

Vision based displacement monitoring techniques are increasingly used to monitor dynamic displacements in operational bridges. These techniques are particularly well-suited to remotely monitor masonry bridges, which possess textured surfaces that enable effective tracking of sub-mm displacements simultaneously at many locations of the bridge. However, end users need to be aware of potential measurement errors which can impact their measurements. This paper discusses two sources of errors which are particularly relevant for monitoring displacements in masonry bridges with the 2D DIC technique: scaling errors and out of plane movement induced errors. The former category of errors occur due to incorrect scaling of tracking results in pixel units to displacements in metric units. In this paper, a new calibration method is proposed to minimise these errors. The method uses the naturally existing parallel lines in the masonry texture to identify two vanishing points in the image. These vanishing points and the known world coordinates of an identified feature in the image are then used to determine the relative rotation of the image and object planes and the correct scaling factors for different displacement points. The second source of error relates to the limitation of 2D DIC to measure only planar displacements. When out of plane movements occur in the object plane, these are registered incorrectly as in-plane movements. Using a pinhole camera model, the impact of out of plane movements on measurement accuracy are quantified. The results provide insight into how out of plane errors may be minimised or removed in order to achieve a higher measurement accuracy. The findings are explained with the application of the aforementioned techniques to the monitoring of a masonry viaduct.

Summary This paper presents a new analytical model for describing the large rocking response of an elastic multi-mass structure resting on ideally rigid ground. Using the experimental results from a rocking steel column, the ability of the proposed analytical model to estimate the rocking and translational acceleration response under free vibration, pulse and earthquake excitations is evaluated. It is observed that the classical treatment of impact may result in an unrealistically large transfer of energy to vibrations. Therefore a new Dirac-delta type impact model that spreads the effects of impact over time and space is proposed. The use of a Dirac-delta model and accurate restitution factors play a pivotal role in prediction of rocking and acceleration responses. In order to characterize the nonlinear response better, a modal analysis of the linearized system is proposed. With this approach, the vibration mode frequencies and shapes during rocking action were determined. A comparison of analytical and experimental modal estimations suggests good agreement. The results emphasize that the vibration characteristics of several vibration modes are affected by rocking action, and these modes may be excited at impact. Copyright © 2016 John Wiley & Sons, Ltd.

This article presents the results of free vibration and earthquake excitation tests to investigate the dynamic behavior of freely rocking flexible structures with different geometric and vibration characteristics. The primary objective of these tests was to identify the complex interaction of elasticity and rocking and discuss its salient effects on the rocking and vibration mode frequencies, shapes and excitation mechanisms. The variability of response is discussed, including critical investigation of the repeatability of the tests. It was found that the variability in energy dissipation and energy transfer to vibrations at impact may lead to significantly different responses to almost identical excitations.

Dynamic displacement measurements provide useful information for the assessment of masonry rail bridges, which constitute a significant part of the bridge stock in the United Kingdom and Europe. Commercial 2D digital image correlation (DIC) techniques are well suited for this purpose. These systems provide precise noncontact displacement measurements simultaneously at many locations of the bridge with an easily configured camera set-up. However, various sources of errors can affect the resolution, repeatability, and accuracy of DIC field measurements. Typically, these errors are application specific and are not automatically corrected by commercial software. To address this limitation, this paper presents a survey of relevant DIC errors and discusses methods to minimise the influence of these errors during equipment set-up and data processing. A case study application of DIC for multipoint displacement measurement of a masonry viaduct in Leeds is then described, where potential errors due to lighting changes, image texture, and camera movements are minimised with an appropriate set-up. Pixel-metric scaling errors are kept to a minimum with the use of a calibration method, which utilises vanishing points in the image. However, comparisons of DIC relative displacement measurements to complementary strain measurements from the bridge demonstrate that other errors may have significant influence on the DIC measurement accuracy. Therefore, the influence of measurement errors due to lens radial distortion and out-of-plane movements is quantified theoretically with pinhole camera and division distortion models. A method to correct for errors due to potential out-of-plane movements is then proposed.

Predicting the displacement and force response of flexible rocking structures to ground motion is important for their assessment and design. Insofar as practical, it is desirable to use simple mechanical models to make these predictions. However, the complex coupling between rocking and vibration makes accurate predictions with simple models difficult. In this paper, the use of semi-coupled equivalent models to approximate the dynamic response of multi-mass structures rocking on rigid ground is evaluated. These equivalent models feature a two-degree of freedom coupled rocking oscillator to describe the interaction of rocking and the first mode of vibration, and uncoupled linear elastic oscillators to describe higher mode vibration response. To evaluate these equivalent models, the modal components of the dynamic response of multi-mass structures are first determined. These components highlight the critical influence of the excitation of vibration modes at impact. Then, further investigations are carried out by comparing equivalent model simulations to recent shake table tests and multi-mass analytical model simulations. These comparisons reveal that the equivalent models can capture the rocking response accurately for a realistic range of displacements, if a new ground acceleration scaling term is adopted. However, the uncoupled linear elastic oscillators do not consider excitation at impact and consequently, the equivalent models do not capture the acceleration response adequately. Therefore, on the basis of the analytically identified modal components, a further modification that improves the equivalent model acceleration predictions is proposed and validated.

The rocking response of structures subjected to strong ground motions is a problem of ‘several scales’. While small structures are sensitive to acceleration pulses acting successively, large structures are more significantly affected by coherent low frequency components of ground motion. As a result, the rocking response of large structures is more stable and orderly, allowing effective isolation from the ground without imminent danger of overturning. This paper aims to characterize and predict the maximum rocking response of large and flexible structures to earthquakes using an idealized structural model. To achieve this, the maximum rocking demand caused by different earthquake records was evaluated using several ground motion intensity measures. Pulse-type records which typically have high peak ground velocity and lower frequency content caused large rocking amplitudes, whereas non-pulse type records caused random rocking motion confined to small rocking amplitudes. Coherent velocity pulses were therefore identified as the primary cause of significant rocking motion. Using a suite of pulse-type ground motions, it was observed that idealized wavelets fitted to velocity pulses can adequately describe the rocking response of large structures. Further, a parametric analysis demonstrates that pulse shape parameters affect the maximum rocking response significantly. Based on these two findings, a probabilistic analysis method is proposed for estimating the maximum rocking demand to pulse-type earthquakes. The dimensionless demand maps, produced using these methods, have predictive power in the near-field provided that pulse period and amplitude can be estimated a priori. Use of this method within a probabilistic seismic demand analysis framework is briefly discussed.

Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified 'equivalent' oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. © 2012 John Wiley & Sons, Ltd.