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1 INTRODUCTION
1.1 State of the Art
The oldest existing arch bridges were designed
based on experience. Later graphical methods for the
static were available and approximation formulas
based on the arch thrust line to design major geome-
trical parameters such as span, arch shape and arch
thickness at the apex and the abutments were devel-
oped. These simplifying estimations can also now be
useful to perform the bearing capacity of existing
arch bridges on the basis of their geometrical para-
meters. Especially for old arch bridges which were
designed for different loads at their design and con-
struction date, these methods can be used as an first
estimation for the current bearing capacity or the fu-
ture use of these buildings. The recalculation of
these buildings under the valid load approach
enables the assessment of the bearing capacity and
the suitability for an usage under nowadays valid
load. Any necessary upgrading which considers the
conservation of the existing structures both pre-
serves the appearance of the arch bridges and saves
costs. For the estimation of the bearing capacity as a
result of a static recalculation, the knowledge of the
construction and the material properties is required.
If bridges are designed nowadays, e.g. made from
reinforced concrete, steel or wood, these parameters
are well known, In case of existing arch bridges
made from stone, brick or rammed concrete, the ma-
terial properties often cannot be identified, because
too many factors which have an influence on the
bearing capacity.
The assessment of existing bridge structures can
be used as a helpful method for the responsible or-
ganisations, e.g. road or railway maintenance com-
panies, and the proper governments. In terms of the
life cycle concept, the increasing axle loads, load re-
strictions, inspections, monitoring, maintenance
measurements or even a replacement of the struc-
tures have to be considered. A conventional ap-
proach for the recalculation of arch bridges, the elas-
ticity theory can provide results which differ
significantly from the actual bearing capacity. Hori-
zontal abutment displacements and weaknesses in
the arch reduce the load. The involvement of the
Optimized Monitoring Concepts for Arch Bridges
A. Krawtschuk, A. Strauss & K. Bergmeister
Institute for Structural Engineering, BOKU University Vienna, Austria
R. Wendner
Department of Civil and Environmental Eng., NW University Evanston, IL, USA
ABSTRAC
T:
Arch bridges made from nature stone nowadays are the oldest structures which are still in use
on road and railway lines. With an average age of more than hundred years, these structures often are seen as
historical important buildings. Most of them had been constructed during the great building period of roads
and railways from the 1840ies to 1900. Lots of the considered nature stone bridges are constructed as circle or
three center curve, some of them also in a parabolic form or catenaries or cycloide. The height of the apex
cover varies in a large range. If masonry was appropriated, usually sand, chalkstone or clay bricks were used.
For most bridges no observations of the material parameter are available, as a result the stone and the mortar
strengths are unknown. Under the usage of the German railway company, there are more than 8000 arch
bridges yet, although at local roads there is an additional unknown number of them. In Austria, the railway
network, especially along the southern railway line has around 1000 arch bridges in usage. In whole Europe,
the stock of masonry railway bridges is estimated with around 70.000. In the course of route expansion plans
in the past especially arch bridges have been replaced by new steel or reinforced concrete structures. Consid-
erations of preservation, the budgetary situation of the rail and road operators, as well as a sustainable, re-
source efficient usage of resources and existing infrastructure are motivations to maintain and – if necessary –
toughen up existing arch bridges. Therefore, the issues of sustainability, durability and serviceability become
more important.
Keywords: arch bridge, sustainability, durability, serviceability, monitoring, modelling
Bridge Maintenance, Safety, Management, Resilience and Sustainability – Biondini & Frangopol (Eds)
© 2012 Taylor & Francis Group, London, ISBN 978-0-415-62124-3
879
wing walls and the interaction with the surrounding
soil influence the capacity significantly. Therefore
the issue of structure-soil-interaction as depicted in
Figure 1 is particularly essential for arch bridges,
however, calculations on the basis of existing studies
cannot be performed correctly. These interactions
can be summarized as follows:
Figure 1: Structure – Soil – Interaction in accordance to UIC
Code 778-3 (2011)
(a) traffic load is distributed laterally over the depth,
the distribution is dependent on the shear strength
and stiffness of the backfill
(b) dead load of the backfill acts as a destabilizing
force on the arch on the side loaded by the traffic
load
(c) horizontal components on the loaded side of the
arch as a result of the shear strength, stiffness, dead
load of the backfill material and the traffic load
(d) stabilizing effect of the dead load of the backfill
on the unloaded side of the arch
(e) horizontal components on the unloaded side of
the arch as a result of the shear strength, stiffness,
dead load of the backfill material and the traffic load
Practical considerations have shown that stone
arches in combination with an appropriate structural
state can have considerable reserves in their bearing
capacity. Therefore they often reach the standards
which are recommended nowadays. If the age of the
structure is taken as a safety indicator, existing arch
bridges show the convenience and the robustness of
arch structures. Current tools of structural design are
quite manifold and take account both geometrically
and physically non-linear structural properties. Nev-
ertheless, because the structural behaviour of natural
stone masonry is quite complex due to various influ-
ence factors, it has not been possible to set up an ap-
propriate model for masonry which considers all de-
cisive effects up to now. The codes for proofing the
bearing capacity and the serviceability only allow an
overhead assessment of the resistance values. Thus
there is a noticeable gap between the possibilities of
mechanical modelling and the available safety
proofs.
Current finite element programs serve a quite
good approximation for modelling the material be-
haviour, as a result different models are imple-
mented in these programs. In the calculation models,
the spatial dimension of the arch structures is simpli-
fied to a cross section of one meter. The most impor-
tant point for a correct modelling is to identify the
relevant meter-stripe and to describe the loadings
correctly, particularly single loads in the transversal
direction of the arch.
The well-known graphical methods with thrust
line have been followed by analytical methods, par-
ticularly since the development of computational
calculations. By means of elasticity and plasticity
theory, the models were enhanced, although there is
still no satisfactory solution approach for the issue of
the discontinuous joint. Since a few years, some FE-
Programs can bear with discontinuous joints, but
these models require an enormous calculation effort.
Additionally, there is the possibility that these mod-
els give completely wrong results, as a result of un-
known boundary conditions.
2 MONITORING BASED MODELLING
Generally monitoring systems can be used for the
assessment of structures, for specifying changes
from an initial state to an actual state or for the de-
tection of expected and critical processes as Strauss
et al. (2009a) and Wendner et al. (2010) have
pointed out. For setting up a monitoring system it is
required to have information of the expected struc-
tural behaviour, which can be achieved from (a) ex-
perience, (b) analytical approach (c) numerical mod-
elling and simulation. Nowadays numerical
simulations are state of the art and they are not only
the base of design, but also a fundamental element
of the assessment of monitoring data. International
and national standards as e.g. in Austria
RVS 13.03.11 call for numerical and analytical
models in order to maintenance and inspection strat-
egies, for interpretation and measurement of data.
Type and coverage of the required models (geome-
trical, physical, linear or non-linear, 2D or 3D) for
the monitoring observations depends on the com-
plexity of the structure and its members as Zilch et
al. (2009) mentioned. In addition, there are a few re-
quirements, which have to be fulfilled by each mod-
el: (a) the real structure has to be simulated by the
model according to the problem type, (b) deteriora-
tion processes and other time-dependent processes
have to be simulated, if the remaining life time is
concerned, (c) the setup of the model must allow the
incorporation of monitoring data (e.g. by simulation
of the observed problem), (d) efficient model updat-
ing of the model parameter, boundary conditions and
system stiffness information, (e) the final aim of
each model is the time-dependent assessment of the
880
serviceability, bearing capacity and durability (con-
sidering the Serviceability Limit State SLS, Ultimate
Limit State ULS and Durability Limit State DLS in
accordance to EN 1990) according to the codes and
specifications and the structural requirements. Ade-
quate specifications for modelling (e.g. linear vs.
non-linear and 2D-modelling vs. 3D-modelling) can
be achieved from the observation requirements and
the aims of the monitoring processes as Strauss et al.
(2009b), Hoffmann (2008) and Zilch et al.(2009)
have worked out. It has to be considered in setting
up the model, how obtained data can become part of
the model, which aims (a) to calibrate and optimise
the model and (b) to make predictions of a struc-
ture’s future bearing capacity and the remaining life-
time. These models can base on influence line con-
cepts and correlation coefficient concepts, which
permit the input of monitoring data into numerical
analysis models.
3 MODEL SETUP
In Figure 2 the scheme of the model setup for a
structural model is depicted. The model itself is
based on the description of the structural quantities,
material properties and the boundary conditions.
These structural information is influenced by two
types of factors, firstly the given information (exter-
nal) from codes, material and statics and secondly
results from performed tests on the structure. These
parameters are described in more detail below. The
model reproduces the structural response by the se-
lected simulation, furthermore the simulation is up-
dated by monitoring data. The loads which are put
on the structure result from the dead load, the traffic
loads and a proof loading which shall be put on se-
lected structures. From the updated model and the
measured monitoring data, there can be calculated a
model correction factor, which allows to compare
the data from the calibrated model to the measured
ones.
Figure 2: Scheme of model updating by monitoring data and
structural characteristics
4 MATERIAL
The bearing capacity of arch bridges contains lots of
uncertainties. In addition to displacement of the ab-
utments and the occurrence of cracks, the parameters
of the used material considerably influence the con-
dition of the structure. Arch bridges can be made of
different materials, natural stone, masonry or com-
pressed concrete, as discussed below. In case of nat-
ural stones or masonry, the strength of the material
can vary in a large range. The strengths of historical
bricks are much less than from bricks which are used
nowadays, as described by Zimmermann & Strauss
(2011). Another point which has to be considered is,
that the mortar characteristics often are unknown
and can vary, too. If the mortar becomes incoherent
ore the joints have not been filled up completely, the
bearing capacity can behave unpredictable. Mortar
strength is an important point to ensure the safety of
the structure. Moreover, the material parameters of
the back filling often differ from those of the exter-
nal masonry, but in most of the cases there is no in-
formation of the used material
5 CODES
The first regulations for loads on railway bridges in
Austria were set up in 1870. As a result of the pro-
gressing development of the used materials and the
increasing loads, these specifications have been
modulated often as described in Simandl (2011). In
Figure 3 there is given an overview of the design
axle load limits from 1870 up to now. The regula-
tions came from the Austrian Department of Rail-
way Affairs, from the German State Railway while
WWII, from the Austrian Department of Traffic Af-
fairs after WWII, from the Austrian Standard Insti-
tute and the last specification is a result of EC 1-2.
130 130
200
250 250 250 250 250 250 250 250
303 303
0
100
200
300
max. axial load limits [kN]
Figure 3: Development of the design axial loads for railway
bridges in Austria from 1870 up to now
881
6 TEST METHODS
6.1 Non-destructive testing
By means of non-destructive testing methods lots
of information in respect to arch brigdes can be
achieved, e.g. the shape of the abutment, thickness
of the arch, constitution and dead load of the back-
fill. A few examples for non-destructive testing me-
thods whose application is intended are listed below
in accordance with Proske &van Gelder (2009)
• Georadar: This type of measurements is a
non-destructive method for get information
about the material properties, structural de-
tails and soil. The monitoring system is
aimed to control the accuracy and the appli-
cation of various measurement parameters
(frequency, distance, etc.)
• 3D-Laserscanning is a non-destructive testing
method for define structures geometrically
and physically. By applying this procedure
an admissable accuracy of damage detection
is aimed by recorded frequencies and moni-
toring of the distances.
• Infrared Thermography
• Sonar methods
• Conductivity measurement
• Endoscopy
6.2 Destructive testing
In addition to the geometrical definitions for per-
forming calculations it is essential to get specified
information of the material parameter. These materi-
al properties can be achieved by material testing me-
thods on test specimens. Examples are listed below.
• Drill cores: can be performed in norm or in
small size, required samples are standardised
f.i. in DIN EN 13791:2008
• Flat Jack: identification of the stress-strain
curve and of masonry compressive strength
7 CASE STUDY AUSTRIAN NORTHERN
RAILWAY LINE
Section heading shall appear on the left, be fully
capitalised and bold, and there shall be one line
space above section headings. Section text shall ap-
pear in the line directly below a section heading.
The use of subheadings shall be avoided. One line
space should appear between paragraphs of a sec-
tion. The Baltic-Adriatic axis (BAA) from Gdansk
(PL) to Bologna (I) is one of the most important
North-South transversal of Europe which connects
upcoming regions of three new EU Member States
(Poland, Czech Republic, Slovakia) with economical
centres and agglomerations in Austria and Italy. In
addition, it offers a connection to a few other prior-
ity axes of the trans-European transport network
(TEN-V) and enables the relocation of transportation
of cargo from road to railway lines as an important
component of reaching the international climate
aims. The Austrian Northern Railway Line as part of
the BAA is a double tracked main railway line,
which has been electrified fully in the year 1978.
The Northern Railway Line is a direct connection
from Austria to the Czech Republic and was built in
the 19th century as Kaiser Ferdinands Nordbahn
from Vienna to Krakow (finished 1856). The rail-
way line leaves Vienna at railway station Praterstern
in the direction to Moravia. As described the line is
part one of the most important European railway
lines with international train service to Prague, Kra-
kow, Warszawa, Berlin and Hamburg. The Austrian
part of the Northern Railway Line contains several
arch bridge structures. For instance, some of them
are analysed below.
7.1 Linear and nonlinear models
As described above, the Austrian Northern Railway
Line is one of the most important European railway
lines (BAA). One of the considered arch bridge
structures is located in a distance of ca. 80km from
Vienna, the static system is a three-span natural
stone arch bridge, see Figure 4. The modelling of the
bridge was set up with the program SOFISTIK, Fig-
ure 5 shows a part of the geometric model of arch
bridge „Bernhardsthal km 75.702“. The chief arch
spans amount to 11.40m and the arch rise 3.80m.
The lateral arches on either side span amount 2.70m
and the arch rise 1.40m. The used coordinate sys-
tems are both a Cartesian global and some local sys-
tems. The model consists of 17634 elements and
18788 nodes. In advance the material model is the
Standard EC 2 (1992) Concrete Structures with
country code 43 (Austria, reinforced concrete and
prestressed with unbonded tendons). The first consi-
dered load case was set up in accordance to the load
model UIC 71 from EC 1-2.
Figure 4: Arch bridge “Bernhardsthal“
882
Figure 5: Modeling of the arch bridge “Bernhardsthal
km 75.702“ in SOFISTIK
7.2 Proof loading with unit loads
In the first modelling and simulation steps by means
of the static software SOFiSTiK a unit load P was
put on the system. The altogether 36 unit loads (P to
P36) were applied on defined nodes at four prede-
fined load axes 1 to 4, see Figure 6. In the longitudi-
nal dimension of the axes 9 load positions were de-
fined as it is shown in Figure 6. The corresponding
monitoring points M1 to M8 in which the vertical
displacements uz at one of the front surfaces of the
considered arch bridge shall be measured are de-
picted in Figure 7. Additionally the exact coordi-
nates of the mentioned monitoring points are listed
in Table 1.
Axis 2
Axis 3
Axis 4
Axis 1
P1-P9
P10-P18
P19-P27
P28-P36
Figure 6: Definition of the axes and load positions at arch
bridge object “Bernhardsthal km 75.702“
M1 M2
M3 M4 M5
M6
M7 M8
Figure 7: Configuration of the monitoring points M1-M8 at the
considered arch bridge
Table 1. Load case position from the 8 load cases
Monitoring-
Points
Position
x y z
M1 0,000 -12,923 -6,407
M2 0,000 -9,350 -5,880
M3 0,000 -6,479 -7,385
M4 0,000 -4,519 -7,623
M5 0,000 0,000 -8,450
M6 0,000 4,681 -7,632
M7 0,000 8,593 -6,444
M8 0,000 11,675 -5,730
Exemplarily the calculated vertical displacements uz
from the performed analysis in SOFiSTiK are de-
picted in the figures below (Figure 8 to Figure 10).
Figure 8 shows the plot of the influence areas with
the corresponding unit loads P1 to P36, measured in
monitoring point M1 according to Figure 7. It can be
seen that the displacements in monitoring point M1
are highly influenced by the unit loads in the range
of the first both load axes 1 and 2 and up to point 2
of the longitudinal stationing along the bridge
(Figure 8). Applied unit loads on the back axes 3 and
4 do not have any noticeable influence on the dis-
placement in M1. Figure 9 shows the influence of
the load positions on the vertical displacements in
monitoring point M3. It is obvious that unit loads on
the axes 1 to 3 with longitudinal stationing of 1 to 5
influence the displacements. The non-decisive areas
can be determined quite good here, too. For monitor-
ing point M3 the area between longitudinal station-
ing 7 to 9 and axes 1 to 4 does not influence the
measurement. In Figure 10 the influence of the ap-
plied unit loads on the displacement at monitoring
point M5, which is placed in the middle of the arch
span. In this case an equally influence in both direc-
tions of the arch bridge can be identified. Unit loads
on the load axes 1 to 3 and with a longitudinal sta-
tioning of 3 to 6 mainly influence the identified dis-
placement at M5. Unit loads above this area do not
influence the detected displacement significantly and
therefore can be neglected. Due to modelling in
SOFiSTiK and the discussed analysis an optimisa-
tion of the montitoring system can be conducted.
This aims to reduce of the monitoring points and the
associated equipment to an adequate number. On the
one hand the volume of the recorded data shall be
optimised, and on the other hand the monetary effort
should be minimised due to budgetary restrictions,
however the monitoring system should provide reli-
able data.
883
Axis1
Axis2
Axis3
Axis4
0,0
0,2
0,4
0,6
0,8
1,0
123456789
no
influence
mean
influence
high
influence
Longitudinal Station of the Bridge
rel. Displacement uz
Figure 8: 3D-Influence areas of load positions P1 to P36 ac-
cording to monitoring point M1
Axis1
Axis2
Axis3
Axis4
0,0
0,2
0,4
0,6
0,8
1,0
123456789
rel. Displacement uz
high
influence
mean
influence
no
influence
Longitudinal Station of the Bridge
Figure 9: 3D Influence areas of load positions P1 to P36 ac-
cording to monitoring point M3
Axis1
Axis2
Axis3
Axis4
0,0
0,2
0,4
0,6
0,8
1,0
123456789
rel. Displacement u
z
high
influence
no
influence
no
influence
mean
influence
mean
influence
Longitudinal Station of the Bridge
Figure 10: Influence areas of load positions P1 to P36 accord-
ing to monitoring point M5
8 CONCLUSIONS
The existing arch bridges in Austria and in Europe
respectively often have an age of hundred or more
years and have been put under preservation order.
As a result of this and of budgetary restrictions, arch
bridges have to be maintained, toughed up during
their lifetime and in addition they must be assessed
considering new load scenarios according to the
codes. The recalculation of these structures is quite
difficulty, due to the lack of initial plans and ade-
quate data of material parameters. The interaction
between the single components of arch bridges (soil,
masonry, backfill) is afflicted to many uncertainties.
Thus from the point of view both of the responsible
official corporations and of pure research, it is ne-
cessary to design well operating concepts for esti-
mating the load bearing behaviour of existing arch
bridges. Intention of research incorporate measured
data into modelling for update the models in terms
of the various unknown influence parameters and to
be able to make an efficient assessment of the bear-
ing capacity of existing arch bridges.
ACKNOWLEDGEMENT
The research concepts presented in this contribution
are funded by the research projects ILATAS and
NANUB. Further the cooperation with the Institute
of Mountain Risk Engineering, BOKU University, is
gratefully acknowledged
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