Draft – Do not distribute
Chapter 13
Recent advances in the seismic analysis and
design of RC bridges in Slovenia
Tatjana Isaković and Matej Fischinger
Abstract An overview of the research related to the seismic analysis and design
of RC bridges, recently performed at UL FGG is made. Four main topics are
addressed: 1) Pushover based analysis of bridges; several recommendations
related to the use of different pushover methods are overviewed and criteria which
define the applicability of single-mode methods are proposed; 2) Modelling of RC
bridge columns; three types of frequently used macro-models are discussed on the
example of typical bridge columns; 3) Estimation of the shear strength and shear
strengthening of typical RC hollow box bridge columns with substandard
construction details; three methods for estimation of the shear strength are
compared; the method, proposed at UCSD was found the most appropriate in the
investigated case; the concrete jacket and CFRP strips successfully prevented the
shear failure of the strengthened column; 4) Seismic isolation of RC bridges using
new semi-active device – magnetically controlled elastomer (MCE); the efficiency
of the smart MCE bearings in partially isolated bridges, subjected to earthquakes
weaker than the design earthquake, is discussed and demonstrated.
Keywords: RC bridges, numerical models, nonlinear analysis, seismic strengthening, shear
strength, seismic isolation, semi-active isolation
13.1
Introduction
Several topics related to the research of the seismic analysis and design of
reinforced concrete (RC) bridges, performed at the University of Ljubljana,
Faculty of Civil Engineering (UL FGG) are overviewed. They are: 1) Pushover
based analysis of bridges, 2) Modelling of RC bridge columns, 3) Estimation of
the shear strength and shear strengthening of typical RC hollow box bridge
columns using different types of jacketing, 4) Seismic isolation of RC bridges
using new semi-active device – magnetically controlled elastomer.
The inelastic response history analysis has been used for the research purposes
for several decades. However, it is still too complex to be used in the design
practice. To simplify the nonlinear seismic analysis, several nonlinear static, or socalled, pushover methods have been developed. They recently became quite
popular analysis tool. However, due to the limited understanding of their
limitations, these methods are frequently used indiscriminately. Their
indiscriminate use is particularly typical for bridges. The principles, rules and
T. Isaković
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, 1000 Ljubljana,
Slovenia
e-mail: tisak@ikpir.fgg.uni-lj.si
2
procedures which were originally developed for buildings have often been simply
extrapolated to bridges, neglecting the major differences between these structural
systems and their seismic response. In Section 2 basic specifics in the application
of the pushover methods for the analysis of bridges are briefly summarized, and
criteria defining the applicability of the N2 method, which is included into
Eurocode standards, are introduced.
To perform the nonlinear analysis, adequate numerical models are needed.
Some experiences obtained at UL FGG in modelling RC bridge columns are
summarized in Section 3.
To establish an appropriate numerical model the adequate data about the
capacity of columns are needed. While the quantities defining the flexural
response are usually well defined, the shear response of columns is much more
difficult to predict. The knowledge related to this problem is still incomplete. This
is e.g. indicated by quite large differences in the results of different methods
proposed for the estimation of the shear strength and stiffness of RC columns.
This problem is analyzed on the example of columns of a typical existing viaduct,
which includes several construction deficiencies. Several methods for estimation
of the shear strength are compared and evaluated by means of the experimental
results (see Section 4).
There are numerous existing bridges, which were designed before the modern
principles of the seismic engineering were established. From the nowadays point
of view, they include many substandard construction details which demand
adequate strengthening and retrofit. One of such examples is analyzed in Section
4. Different retrofitting techniques, including concrete and FRP jacketing are
analyzed on the example of a typical viaduct, built in 1970’ies.
One of the possibilities for the seismic protection of new bridges as well as for
the strengthening of existing structures is the seismic isolation. In the last part of
Chapter (Section 5) a new semi-active seismic isolation device, magnetically
controlled elastomer (MCE) is briefly introduced and the possibilities for its use in
bridges are overviewed.
13.2
Simplified nonlinear analysis of bridges
To simplify the inelastic analysis, and to make it more convenient for everyday
design, several simplified nonlinear analysis methods have been developed. They
are so called pushover methods. There are several methods of this type available.
The simplest methods are so called single-mode pushover methods. One of the
main assumptions of these methods is that the response of a structure is governed
mostly by one predominant mode. The typical representative of this group is the
N2 method [1], which is included in the Eurocode standards [2], [3]. The specifics
in the application of this method for the analysis of bridges are described in
Section 2.1.
It is typical for long bridges (with the total length of 500 m and longer) that the
response can be considerably influenced by higher modes of vibration. In those
cases, the single-mode methods are less accurate, and multi-mode pushover
3
methods can be used instead. Some of the conclusions related to their applicability
for the analysis of bridges are shortly overviewed in Section 2.2.
13.2.1 The N2 method – Single-mode pushover methods
The N2 method was originally developed for the analysis of buildings. Therefore
it should be modified when it is used for the analysis of bridges, since their
structural system is considerably different than that of buildings (particularly in
their transverse direction). In this Section the appropriate modifications are
proposed and summarized. Further details can be found in [4] - [6].
The proposed modifications of the N2 method for the analysis of bridges are:
1) The distribution of lateral forces along the superstructure;
2) The choice of the point where the displacements are monitored to obtain the
force-displacement relationship;
3) Idealization of the force-displacement curve, and calculation of yielding
force and yielding displacement.
1) The distribution of the “inertial” forces (lateral load) should be assumed
before the nonlinear static analysis is performed. Some of the distributions
appropriate for bridges are summarized in Fig. 13.1. Note that two extreme cases
of the constraints above the abutments are addressed. In the Annex H of standard
Eurocode 8/2 (EC8/2) two possible distributions are proposed: a) distribution
proportional to the 1st mode of the bridge in the elastic range, b) uniform
distribution (see Figs. 13.1(1)a and 13.1(1)b). The first distribution can be defined
based on a modal analysis with some of the standard programs for elastic modal
analysis.
In the previous research [5] - [6] it was found that the parabolic distribution
(Fig. 13.1(1)c) is appropriate for bridges that are pinned at the abutments. This
distribution is simpler to define than that proportional to the first mode. In many
cases, the results of the N2 method and the inelastic response history analysis
correspond better when the uniform distribution is replaced by the parabolic one.
(1)
(2)
L
L
X
m1
F1
...
mi
i
m1
Fi  mi   i
F1
Fn
Fi
1
mn
n
proportional to the
1st mode
a) proporcionalna
1. nihajni
obliki
...
mi
Fi  mi   i
Fn
Fi
1
mn
i
n
proportional to trenutni
the instant
1 st mode
a) proporcionalna
1. nihajni
obliki
1stnihajna
mode oblika
i – 1.
 – trenutna
i
instant
1. nihajna
oblika
1st mode
uniform
b) enakomerna
b) enakomerna
uniform
i = 1
i = 1
parabolic
c) parabolična
i  
4 2 4
x  x
L
L2
Fig. 13.1 Distributions of the lateral load, appropriate for bridges that are: 1) pinned at the
abutments, 2) with roller supports at the abutments
4
Table 13.1 Advantages and limitations of the presented elements
Type of
Element
Advantages
Limitations
BeamColumn
Element with
Lumped
Plasticity
Simple model with small number of
elements (often one per column)
Non-linearity defined based on the
hysteretic rule with clear physical
meaning
Easy to control
Cannot be used for the analysis of
coupled bi-directional response
Unable to estimate stresses and
strains
Fibre
Element
Able to estimate strains and stresses
Can be used for the analysis of bidirectional response
Relatively complex analysis
Several iterations are necessary to
establish the appropriate model
Control of results is more complex
MVL
Element
Relatively simple
Non-linearity defined based on the
hysteretic rule with clear physical
meanings
Able to estimate strains and stresses
Can be used for analysis of bidirectional response
In general, several elements per
column are necessary to obtain
acceptable estimation of the
response
Appropriate number of elements
should be defined iteratively
OL S15
33.3
S16
34.0
S17
34.0
S18
34.0
S19
34.0
S20
34.0
S21
34.0
S22
34.0
S23
S24
34.0
34.0
591.4 m
S25
34.0
S26
37.7
S27
37.7
Fig. 13.13 Typical existing viaduct with substandard construction details
S28
37.7
S29
34.0
S30
OD
37.7 33.3
5
References
1. Fajfar P (2000) A nonlinear analysis method for performance-based seismic design.
Earthquake Spectra 16:573-592.
2. CEN (2004) Eurocode 8: Design of structures for earthquake resistance. Part 1: General
rules, seismic action and rules for buildings. EN 1998-1, Euro Commit for Stand, Brussels,
December 2004
3. Kanaan A.E., Powell G.H. (1973) A general purpose computer program for dynamic
analysis of planar structures, , Report UBC/EERC-73/6, Univ. of California, Berkeley.
4. McKenna F, Fenves GL (2007) Open system for earthquake engineering simulation, Pacific
Earthquake Engineering Research Center, Berkeley, California, http://opensees.berkeley.edu
5. Prakash V., Powell G.H., Filippou F.C. (1993) DRAIN-3DX: Base program users guide,
Department of Civil Engineering, University of California, Berkeley, USA.
6. Vulcano A., Bertero V.V., Caloti V. (1989) Analytical modelling of R/C structural walls,
Proceedings of the 9th WCEE, Tokyo-Kyoto, Maruzen, Vol. 6, pp. 41-46.
7. Fischinger M., Vidic T., Fajfar P. (1992) Non-linear seismic analysis of structural walls
using the multiple-vertical-line-element model, Non-linear Seismic Analysis and Design of
Reinforced Concrete Buildings, Elsevier, Bled, Slovenia, pp.191-202.
Keywords:
Bridges, RC bridges, nonlinear analysis, simplified nonlinear analysis, static nonlinear analysis,
pushover methods, single mode pushover methods, multi mode pushover methods, applicability
of pushover methods, N2 method, MPA, IRSA, RC columns, numerical model, nonlinear
response history analysis, flexural response, macro models, beam-column elements with lumped
plasticity, fiber element, multiple vertical line element, MVLEM, Takeda hysteretic rules,
seismic strengthening, concrete jacketing, CFRP, CFRP strips, shear strength, shear
strengthening, existing bridges, substandard construction details, experiment, hollow box
columns, Eurocode 8, EC8/2, EC8/3, EC2, Eurocode 2, UCSD method, shear failure, buckling of
the longitudinal bars, seismic isolation, rubber bearings, elastomeric bearings, semi-active
isolation, magnetically controlled elastomers, MCE, MCE bearings, partial isolation, weak
earthquakes