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Life-Cycle of Structures and Infrastructure Systems – Biondini & Frangopol (Eds)
© 2023 The Author(s), ISBN 978-1-003-32302-0
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A framework for digital twinning of masonry arch bridges
I.B. Muhit
School of Civil Engineering, University of Leeds, Leeds, UK
School of Computing, Engineering & Digital Technologies, Teesside University, Middlesbrough, UK
D. Kawabe
Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan
D. Loverdos & B. Liu
School of Civil Engineering, University of Leeds, Leeds, UK
Y. Yukihiro & C-W. Kim
Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan
V. Sarhosis
School of Civil Engineering, University of Leeds, Leeds, UK
ABSTRACT: As the significant number of European bridge stock comprises more than 100
years old masonry arch bridges, restrictions to the operation of these bridges or their closure due
to increased traffic load can result in network disruptions with subsequent economic losses.
Apparently, most of these bridges are carrying loads above those envisaged by their original
designs. This paper presents the development of a framework for the digital twinning of masonry
arch bridges to enhance their management and provide informed decisions for their repair and
maintenance schemes. As a case study, a full-scale masonry arch bridge with a 3.0m span is con-
sidered here. The framework starts with the development of a 3D geometry using an innovative
photogrammetry approach, which accurately captured the overall geometry and local irregular-
ities of the masonry bridge. Afterwards, dynamic characteristics i.e., natural frequency and modal
shape of the masonry arch bridge can be obtained from ambient vibration tests by instrumenting
the bridge with accelerometers. A Bayesian approach is then implemented to identify structural
modal properties under different time windows as a comparison for further assessments. Data
from the developed 3D geometry (via photogrammetry) and modal properties are combined to
develop a high-fidelity numerical model for structural analysis. This numerical model can be con-
tinuously calibrated using monitoring data from the testing of the masonry arch bridges under
service loadings. The framework presented in this study has the potential to conduct an autono-
mous condition-based assessment of ageing masonry arch bridges, characterised by advanced
real-time monitoring, and data-informed decisions to understand damage accumulation.
1 INTRODUCTION
Although the introduction of new and modern construction materials such as steel, reinforced
and prestressed concrete has reduced the further development of masonry arch bridge construc-
tion, there are still thousands remaining stone and brick masonry arch bridges around Europe,
most of which were built between the second half of the 19
th
century and the first decades of the
20
th
century. For instance, only in the UK, there are about 40,000 masonry arch bridges in daily
use on highways, railways and canals, representing an estimated 40–50% of the total bridge stock
(Page 1993). Most of these bridges are still in service despite the current traffic loads are much
higher than those assumed in the original design, which was carried out on the base of empirical
criteria or simple design rules (Brencich & Morbiducci 2007). Moreover, masonry arch bridges are
deteriorating over time after being subjected to a prolonged exposure to traffic loads, large vibra-
tions, foundation settlements, environmental conditions and extreme natural events.
DOI: 10.1201/9781003323020-99
817
The management and assessment of ageing masonry structures constitute a major challenge
across the public infrastructure. Network Rail (UK) acknowledged that the assessment methods
currently used by the industry are antiquated and/or over-simplistic (Network Rail 2011). For
example, for the assessment of masonry arch bridges, the Military Engineering Experimental
Establishment (MEXE) method is still in use; which dates back to the 1940s, has a very limited
predictive capability, and offers little scope for future enhancement (Sarhosis et al. 2016).
Over the last three decades, significant efforts have been devoted to the development of
numerical models to represent the complex geometry and non-linearity behaviour of masonry
bridges subjected to external loads and extreme events e.g. floodings, subsidence and earth-
quakes. Such models range from considering masonry as a continuum (macro-models) to the
more detailed ones that consider masonry as an assemblage of units separated by mortar
joints (meso-models). The precise quantification of the masonry structure is further compli-
cated by the higher degree of spatial variability of the masonry material properties compared
to other construction materials, such as steel or concrete. Variations of material properties
can be incorporated into the finite element analysis (FEA) combined with Monte-Carlo simu-
lation (Muhit et al. 2022, Sarhosis et al. 2020).
Furthermore, a vital aspect when modelling masonry structures based on the meso-scale mod-
elling approach is the accuracy in which the geometry of the masonry structure is transferred in
the numerical model. So far, the geometry of masonry bridges is captured with traditional tech-
niques (e.g. visual inspection and manual surveying methods) which are labour intensive and
error prone. In the last ten years, advances in laser scanning and photogrammetry have started
to drastically change the building industry since such techniques are able to capture rapidly and
remotely digital records of objects and features in a point cloud format. In particular, there are
cost-effective works in transitioning from point clouds obtained from images and/or terrestrial
laser scanning to structural analysis models (Loverdos & Sarhosis 2022, 2023a, 2023b).
On the other hand, considerable research efforts have also been devoted to replacing trad-
itional maintenance plans based on periodic visual inspections with more efficient structural
health monitoring (SHM) plans. In general, SHM relates the implementation of long-term
monitoring systems and damage identification algorithms to conduct condition-based mainten-
ance. Damage identification is organised on a scale of increasing complexity, including (i) Detec-
tion, (ii) Localization, (iii) Classification, (iv) Extension, and (v) Prognosis. In this context,
damage identification algorithms are generally classified as unsupervised or supervised tech-
niques (Giglioni et al. 2021). The implementation of unsupervised techniques is relatively
simple, since damage inference is conducted by simply processing monitoring data. Neverthe-
less, their ability to achieve damage identification levels beyond detection (Level I) is consider-
ably limited. Conversely, supervised learning techniques exploit both monitoring data and
engineering knowledge through structural simulation models. While the implementation of such
techniques is challenging due to the epistemic uncertainties typically involved in any structural
model, their ability to relate the structural performance to the intrinsic health condition makes
it possible to detect, localise, quantify and predict the evolution of damage. It is thus essential to
count on reliable structural models to effectively develop condition-based maintenance plans.
Therefore, it is evident that the traditional way of assessing masonry arch bridges becomes
obsolete with the rapid changes in traffic loading and natural material degradation; hence, man-
agement practices will have to evolve to reduce the impact of novel threats. This paper presents
the development of a framework for the digital twinning of masonry arch bridges to enhance
their management and provide informed decisions for their repair and maintenance schemes.
2 MASONRY ARCH BRIDGE DIGITAL TWIN FRAMEWORK
The principal motivation of the proposed framework is to develop and establish
a methodology for autonomous condition-based assessment of ageing masonry arch bridges,
characterised by advanced photogrammetry and/or laser-scanning, real-time monitoring,
probabilistic damage identification and data-informed decisions for repair and maintenance
schemes. The first step of the workflow is to develop an initial geometric digital twin of masonry
818
arch bridges from digital images followed by the development of high-fidelity numerical models
capable of reproducing the main damage mechanisms and accounting for the inherent variabil-
ity of the material properties. Then, automated Operational Modal Analysis (OMA) using
ambient vibration data can be accomplished in order to develop a computational digital twin
model through surrogate modelling. Continuous model calibration using Bayesian model selec-
tion and parameter inference methods are necessary to localise and quantify the damage of the
masonry arch bridge. As a case study, a full-scale masonry arch bridge constructed in the
George Earle testing laboratory of the University of Leeds is considered here. The bridge has
been constructed as part of the EPSRC project, Exploiting the resilience of masonry arch bridge
infrastructure: a 3D multi-level modelling framework (EP/T001348/1).
2.1 Advanced photogrammetry/ laser-scanning
The workflow of documentation, inspection, and assessment of existing structures can be
improved by the use of modern technologies such as laser-scanning and photogrammetry. Ter-
restrial laser-scanning (TLS) uses specialised equipment which able to emit multiple laser-
beams to measure the distance of random points in space and acquire their XYZ coordinates,
and possibly colour. The recorded points form a point cloud (Point Cloud Data, PCD), that
provides an accurate representation of an object or space. Multiple records can be combined
to extend the coverage to regions not visible from a single capture point. Photogrammetry, on
the other hand, refers to the process followed to obtain realistic information about an object
or area from image data (i.e. distance, colour, etc.). It can be used to produce similar results
to TLS by following a different approach. A sequence of images is used to generate a PCD of
the captured object and can be achieved by identifying the location of a common point
between multiple images through triangulation. Due to the nature of photogrammetry, it is
more approachable, than laser-scanning, since it does not require specialised equipment.
Regarding structural assessment, the PCD can also be used to generate numerical models for
structural analysis (Kassotakis & Sarhosis 2021). Other applications of photogrammetry/laser-
scanning include the generation of orthorectified imagery of structures. Ortho-images may be
used for reliable measurements on a single plane (i.e. XY, XZ, YZ). Combined with recent
advances in computer vision can offer a further understanding of the asset. Applications of
image processing allow the automatic feature detection of masonry elements. Especially when
combined with artificial intelligence to provide more reliable results (Loverdos & Sarhosis
2022). That even makes the generation of discrete models of masonry structures viable (Lover-
dos et al. 2021), albeit limited to 2D-plane. The integration of detected features, to the PCD or
reality mesh directly, is also possible (Kalfarisi et al. 2020) which assists with the aspect of visu-
alisation and can be a powerful tool for automation of the visual inspection of existing masonry
structures. Lastly, a combination of the methods and technologies mentioned above is the pre-
cursor of future developments regarding the generation of digital-twin models, of existing
masonry structures from visual-data. Those techniques can be utilised to generate semi-
automatically a complete digital replica of a structure, visualise changes to the structural form,
assess the current state, and evaluate the future behaviour of the structure.
The case study considered here is a 3.0 m span masonry arch bridge constructed in the labora-
tory and using sophisticated photogrammetry techniques a 3D model of the structure was gener-
ated. Initially, 1218 pictures of the structure were captured, with a minimum of 50% overlap.
Sample images used to generate the PCD are shown in Figure 1. These images were recorded using
a smartphone with a 64-megapixel camera and a maximum resolution of 9248 x 6944 (POCO F2
Pro). The images were captured from the surrounding of the structure, at different heights and dis-
tances (Figure 2). Photogrammetry software such as the Context-Capture from Bentley was used
to generate the dense point-cloud and reality-mesh. Four control points were assigned manually, to
improve the alignment and scale the structure to the real dimensions. The control points were
assigned to multiple images, at the 4 main corners of the structure near the bottom (upper side of
the concrete floor). The control points were necessary to connect the multiple alignments produced.
Finally, the reality mesh was coloured, textured, and smoothed (Figure 3).
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2.2 Stochastic computational model and numerical analysis
The imported 3-D geometry can be used to develop a high-fidelity stochastic numerical model
of the masonry arch bridge. This numerical model can be a finite element model (FEM) or
discrete element model (DEM) depending on the requirements. Stochastic spatial numerical
modelling, which considers the variability of material properties within a given structural
system, often better represents the real scenario; nevertheless, it involves different levels of
complexity in terms of model development, probabilistic information of crucial material
Figure 1. Sample images for the generation of the sparce point-cloud.
Figure 2. Camera locations and sparce point-cloud (tie-points).
Figure 3. Textured reality-mesh of the dense point-cloud.
820
parameters, computational cost, etc. For a simplistic case a deterministic model can be con-
sidered, where various material properties are each assumed to have a single de-fined value
(mean value) throughout the structure. However, since inconsistency in the quality of work-
manship, curing processes, and masonry materials may result in spatial variability even in the
same structure, it is vital to consider the spatial and temporal variability of material strengths
to estimate the capacity of the masonry arch bridge. In this way, the mesoscale modelling
approach can be combined with the Monte-Carlo simulation (MCS) technique. The rationale
for this choice is that not only does mesoscale allows separate descriptions of masonry units
and mortar joints, but also it permits the consideration of the unit-to-unit variability in the
spatial stochastic analyses. In this case, it is necessary to quantify and restrict the number of
random variables to only those parameters on which the masonry arch bridge response under
service loading is sensitive. Random variables or uncertainty parameters can be categorised as
statistically independent, spatially variable, and/or spatially dependent.
2.3 Operational modal analysis and digital twin
The computational model developed in the previous stage (initial numerical model) may involve
considerable sources of uncertainty that should be minimised before constructing the digital
twin. Hence certain parameters of the numerical model should be calibrated using structural
health monitoring data. One way could be utilising the modal properties determined by an ini-
tial ambient vibration test (AVT). Vibration-based structural health monitoring technique ori-
ginated in the 1990s and is now being used extensively. Its fundamental principle is to assess the
state of a structure by detecting changes in its dynamic properties, such as natural frequencies,
mode shapes, and modal damping ratios, before and after damage occurs. More specifically, the
natural frequency (or the natural period of vibration) of a structure is regarded to be only asso-
ciated with the mass and stiffness of the structure. For a large-scale structure, i.e., a bridge, the
damage-induced loss in the mass of the structure is negligible. However, these damages, includ-
ing the local buckling and cracks, can result in stiffness reduction, which can further lead to
changes in the natural frequencies of the structure (Huynh et al. 2005).
The process of AVT consists of two main steps. The first is the detection of the vibration
response of the structure. In principle, structural vibration should be excited by external loads
and captured by, i.e. accelerometers. In the laboratory condition, the vibration of model struc-
tures could be excited by impact-load or other forced vibration excitation techniques. For the
real large-scale structure, the usage of forced vibration excitation techniques (e.g. shakers) as
excitation is usually impractical. In these cases, measuring structural response triggered by
environmental excitations or ground microtremors (i.e. traffic loads, wind, etc.) could be an
option. The number of sensors and the location of each sensor should be designed based on
the geometry, dynamic response characteristics, and boundary conditions of the structure. So
far, several methodologies have been proposed for optimising the placement of sensors (Gao
et al. 2005). After the dynamic response is captured, extraction of the dynamic properties
from the measurements and identification of damage indicators is the second step. It is worth
noting that pre-processing of the raw data may be required to attenuate the influence of envir-
onmental noise on the detected signal, such as baseline correlation and low-pass filtering.
The masonry arch bridge considered in this paper as a case study was instrumented with
four tri-axial accelerometers on top of the two spandrel walls of the full-scale masonry arch
bridge model as shown in Figure 4. Three of the accelerometers were mounted on the south-
face of the spandrel wall above the quarter span, crown and three-quarters of the arch barrel,
and one on the middle of the north wall, allowing the torsional mode of the bridge to be deter-
mined. It’s worth noting that the setup of these accelerometers is not definitive and can be
arranged in different patterns, if needed. AVTs were conducted before and during each phase
of loading applications to capture frequency variations of the masonry arch bridge which
facilitated the identification of the damage to the bridge resulting from load applications. For
each vibration test, impact loads were applied manually using a rubber hammer as the excita-
tion. Ten impacts were carried out with an interval of 5 seconds between each impact.
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Therefore, each measurement took around 1 minute. In addition, the sampling frequency was
set to be equal to 200 Hz in order to accurately capture the dynamic response of the bridge.
The modal features of the structure can be identified through operational modal analysis
(OMA), and the uncertainties in the numerical modelling shall be reduced through model
updating, minimising the differences between the experimental and the numerical modal signa-
tures. On this basis, potential damage scenarios and failure patterns of the masonry arch
bridge can be simulated from this stochastic computational model followed by sensitivity ana-
lysis for parametrisation. The simulated damage mechanisms then be used to train a set of
computationally efficient surrogate models, which will act as black-box functions mapping the
considered damage-sensitive parameters and the modal features of the structure (Garcia-
Macias & Ubertini, 2022). In particular, the surrogate modelling approach can combine adap-
tive sparse polynomial chaos expansion (PCE) and Kriging meta-modelling to provide local/
global modelling capabilities with maximum flexibility. These surrogate models will act as
Digital Twins of the structure under investigation, being possible to conduct quasi-real-time
damage identification. To do so, automated OMA techniques can be developed to continu-
ously extract the modal features of the bridge from periodically recorded ambient vibrations.
2.4 Bayesian model update and damage identification
Damage identification is organised in a scale of increasing complexity, including Level I -
Detection, Level II - Localization, Level III - Classification, Level IV - Extension, and Level
V - Prognosis. The time series of modal signatures can be processed through statistical pattern
recognition and in case an anomaly is detected (Level I), the damage identification algorithm
should be activated. This algorithm can involve a Bayesian model selection approach, through
Transitional Markov Chains (TMC) to identify which damage mechanism has been activated.
A major limitation of traditional Bayesian model updating regards the difficulties related to
the presence of ill-conditioning in the inverse model calibration. Although the definition of
prior probability distribution functions to certain parameters may limit this aspect, ill-
conditioning can be hardly eliminated, and the appearance of misidentifications may arise.
This may compromise the efficiency of the subsequent detailed inspection or rehabilitation
intervention. To alleviate this issue, an innovative approach, post-event photogrammetry
(captured from laboratory tests after the damage occurred) can be used to constrain the opti-
misation problem, thus minimising the ill-conditioning in the calibration. To achieve so,
simple local metrics based on image processing are under development to constrain (0 –
unconstrained, 1- fully constrained) certain model parameters that do not clearly experience
damage, while imposing no constraints on model parameters that may have experienced
Figure 4. Accelerometer instrumentation for ambient vibration test on the masonry arch bridge (note:
backll is not shown here for simplicity).
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damage. Once the Bayesian model selection completes, the probability distributions of the
model parameters will be used to localise and quantify the damage The general workflow of
the digital twin development based on photogrammetry, MCS and SHM techniques are
sketched in Figure 5.
3 CONCLUSIONS
This paper presents an overview and workflow of the framework for digital twinning of
masonry arch bridges which will automate the SHM of masonry arch bridges from a physical
bridge to the prediction of damage by digital twin. This concept is well-positioned to promote
world-class state-of-the-art research and a significant academic and scientific impact is envis-
aged through the utilisation of innovative algorithms, high-quality monitoring techniques and
novel numerical methods.
This proposed framework involves the systematic development of the 3D geometry of the
masonry arch bridge from digital images, i.e. using photogrammetry. Unit block and mortar
joint recognition can be achieved by using an image processing algorithm based on an
improvement of the marked controlled watershed algorithm. The result will be an automatic-
ally segmented point cloud with each individual masonry unit isolated and in a format suitable
to be inputted into structural analysis models, if necessary. The geometrical accuracy of the
algorithm can be assessed based on its ability to map geometric irregularities by verification
against measurements from total stations.
The processed 3D computational modelling geometry can then be used to develop a high-
fidelity stochastic numerical modelling of masonry arch bridges. A suitable FEM or DEM can
be considered where spatial variability of material strengths are considered and the modelling
approach is combined with the Monte-Carlo simulation technique to evaluate the probabilis-
tic response of the bridge.
To improve the computational model and minimise the sources of uncertainty, the devel-
oped model should be calibrated using the modal properties determined by an ambient vibra-
tion test. The modal features of the structure could be identified through operational modal
analysis, and the uncertainties in the FEM/DEM can be reduced through model updating,
minimising the differences between the experimental and the numerical modal signatures.
Then a digital twin can be developed from surrogate modelling which combines adaptive
sparse polynomial chaos expansion and Kriging meta-modelling to provide local/global
Figure 5. Workow of masonry arch bridge digital twin development.
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modelling capabilities. These digital twins can be further calibrated or enhanced through
Bayesian model updates when any anomaly is detected from the automated operational
modal analysis.
This concept is still in its infancy and several components of it need further studies to
enhance clarity and obtain reliable information. The framework proposed and the work
reported in this paper is part of a broader project, which is in progress. The developed frame-
work would inform dynamic characteristics such as parametric resonance, eigenfrequencies,
dynamic amplification factor, and periodic motions attributed to the interaction between
vehicle and masonry arch bridge. The fundamental idea is to establish a relationship and form
a ‘bridge’ between existing knowledge/practice and advanced automation techniques.
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