nonlinear analysis of load-bearing capacity of reinforced concrete ...

June 5 th – June 8 th , Telč, Czech Republic
NONLINEAR ANALYSIS OF LOAD-BEARING CAPACITY OF REINFORCED
CONCRETE BRIDGE
M. Šomodíková 1 , D. Lehký 2
Summary: The aim of the paper is to describe possibilities of utilization of nonlinear
fully probabilistic approach to reliability assessment of load-bearing capacity of existing
bridges. Information about current state of bridges is very important for load-bearing capacity
analysis using deterministic as well as fully probabilistic approach. In connection
with durability limit states of reinforced concrete structures, the influence of carbonation
and the corrosion of reinforcement on load-bearing capacity and the structural reliability
are also discussed.
1 Introduction
Keywords: load-bearing capacity, reliability, degradation, corrosion
Quality of information about current state of existing bridges is essential for load-bearing capacity assessment.
The information can be obtained from basic or detailed inspection of structure. Currently, load-bearing
capacity assessment is usually performed by deterministic calculation. However, for more detailed information
about level of structures reliability, a stochastic approach with consideration of the input parameters as
random variables should be used. The load-bearing capacity of reinforced concrete bridges is dependent not
only on random properties of used materials, but especially on their condition. The load-bearing capacity
is significantly reduced due to degradation of the structure. This can be mainly caused by carbonation of
concrete and corrosion of reinforcement.
2 Load-bearing capacity
In Czech Republic, load-bearing capacity assessment of new and existing bridges is currently performed
according to ČSN 73 6222 ”Zatížitelnost mostů pozemních komunikací” [1]. The standard defines essential
types of load-bearing capacities as well as methods for their assessment. Load-bearing capacity can
be divided into three categories: normal (V n ), reservation (V r ) and exceptional (V e ). As described above,
information about current state of existing structures is very important aspect for load-bearing capacity assessment.
Depending on the quality of information from inspection of structure, load-bearing capacity can
be assessed as follows:
• Using detailed static calculation – this approach is used, when detailed inspection of the bridge was
performed; geometry of individual parts of the structure, reinforcement and properties of used materials
are known. Load-bearing capacity is then assessed according to current standards and standards valid
at the time of realization of the structure become only informative;
1 Ing. Martina Šomodíková, Brno University of Technology, Faculty of Civil Engineering, Institute of Structucal Mechanics,
Veveří 95, 602 00 Brno, email: somodikova.m@fce.vutbr.cz
2 Ing. David Lehký, Ph.D., Brno University of Technology, Faculty of Civil Engineering, Institute of Structucal Mechanics, Veveří
95, 602 00 Brno, email: lehky.d@fce.vutbr.cz
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XIII th Bilateral Czech/German Symposium
• Using combined static calculation – in the case that only geometric parameters of structure are known,
combined static calculation is used. According to standards valid at the time of realization of the structure,
probable reinforcement is designed and load-bearing capacity is assessed with using of current
standards;
• Using specific regulations.
3 Deterministic and stochastic analysis, degradation
Currently, deterministic analysis is performed for assessment of load-bearing capacity of most bridges.
Variability of input parameters is incorporated to the calculation using safety factors. Although information
values of individual load-bearing capacities is obtained, this method do not indicate actual reliability of the
structure. For this reason fully probabilistic approach can be used as an alternative for reliability assessment.
The level of structural reliability can be quantified by the failure probability p f or reliability index β.
Important difference between stochastic and deterministic analysis of load-bearing capacity is definition
of input parameters (material properties, location of reinforcement, etc.). Stochastic approach considers them
as random variables based on the mathematical model of probability distributions. These can be obtained
for example from recommendations of Joint Committee on Structural Safety (see JCSS Probabilistic Model
Code [2]). Load-bearing capacity is then assessed with respect to target reliability level.
Very important aspect for load-bearing capacity assessment using deterministic as well as fully probabilistic
approach is the current state of structures. Increasing age of structure leads to degradation of used
materials hence load-bearing capacity and reliability of structures become significantly reduced. Degradation
and loss of durability have a significant role for planning reconstruction or demolition of structures,
thus they have economical consequences. It is therefore important to develop methods for controlling other
types of limit states (in addition to traditional ultimate limit state and serviceability state). In the case of
reinforced concrete structures the depassivation of reinforcing steel can be included as the limit state. This
phenomenon is caused by carbonation of surrounding concrete. Protective (passivation) layer on the surface
of reinforcement is disrupted and corrosion of reinforcement is initiated.
4 Analyzed structure
Analyzed structure was the arch bridge over the Morava river near Veselí nad Moravou. The bridge was
built in 1940 (see Fig. 1). Detailed inspection of the bridge was carried out so that the detailed static calculation
was used for load-bearing capacity assessment. The geometry of individual parts of the structure as well
as type and position of reinforcement was obtained by the inspection (classic cut probes and radiographic
inspection was used for reinforcement detection).
The numerical model of the structure was created using ATENA 2D software [3] (see Fig. 2), which was
developed especially for 2-dimensional and 3-dimensional nonlinear analysis of concrete and reinforced concrete
structures using finite element method (FEM). Stochastic reliability analysis was then performed using
FReET software [4]. Because nonlinear FEM analysis was time-consuming only 32 simulations of Latin
Hypercube Sampling method were performed to calculate random response of analyzed bridge. Reliability
index according to Cornell [5] was determinated as the main parameter of reliability. Comparison of obtained
response and defined load was used for individual load-bearing capacity assessment (see Tab. 1) with respect
to target value of reliability index β = 3.8, which is defined in standards.
Sensitivity analysis and parametric study of influence of decreasing amount of reinforcement due to
corrosion on load-bearing capacity was also performed. Time dependent area of reinforcement was modeled
using mathematical models of corrosion and concrete carbonation (see [6]). Dependence of reliability index
β on values of normal load-bearing capacity V n in time is shown in Fig. 3. Decrease of load-bearing capacity
with respect to degradation of used materials is obvious.
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June 5 th – June 8 th , Telč, Czech Republic
Figure 1: View on the analyzed bridge in the direction from Veselí nad Moravou toward Bzenec
Figure 2: Numerical model in ATENA software
5 Conclusion
The aim of this paper was to describe utilization of stochastic approach for load-bearing capacity assessment
of bridges. This is usually assessed using deterministic approach without detailed consideration
of variability of input parameters. Depending on the quality of information from inspection of structure the
detailed static calculation was performed for individual load-bearing capacities assessment of the arch bridge
over the Morava river. Fully probabilistic approach with consideration of input values as random variables
was used. The efficacy of stochastic analysis was proved and detailed information about level of structure
reliability was obtained. With respect to the age of existing bridges, the significance of degradation of used
materials on the value of normal load-bearing capacity was also discussed and the influence of decreasing
amount of reinforcement due to corrosion on normal load-bearing capacity was shown.
Table 1: Computed values of individual load-bearing capacities and corresponding safety indices
Load-bearing capacity Computed Value Safety index
Normal (V n ) V n = 34 tons β = 3.821
Reservation (V r ) V r = 120 tons β = 3.832
Exceptional (V e ) V e = 183 tons β = 3.806
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XIII th Bilateral Czech/German Symposium
Figure 3: Normal load-bearing capacity with respect of reinforcement corrosion
6 Acknowledgment
This contribution was financially supported by Research project No.
Agency of Czech Republic (TACR).
TA01011019 of Technological
References
[1] Úřad pro technickou normalizaci, metrologii a státní zkušebnictví. ČSN 73 6222 ”Zatížitelnost mostů
pozemních komunikací. Praha (2009), http://www.normy.biz/.
[2] Joint Committee on Structural Safety. Probabilistic Model Code, Part 3: Material Properties, (2000),
http://www.jcss.byg.dtu.dk.
[3] Červenka, V., Jendele, L. & Červenka, J. ATENA Program documentation, Part 1: Theory, Červenka
Conslting, Prague (2010), http://www.cervenka.cz.
[4] Novák, D., Vořechovský, M., Rusina, R., et al. FReET Program Documentation, Part 2: FReET M/A
User Manual, Červenka Consulting, Prague (2005), http://www.freet.cz.
[5] Teplý, B. & Novák, D. Spolehlivost stavebních konstrukcí: teorie, numerické metody, navrhování, software:
skriptum FAST VUT, Učební texty vysokých škol (Vysoké učení technické v Brně. Stavební
fakulta), CERM, Brno (2004)
[6] Teplý, B., Chromá, M., Vořechovská, D., et al. FReET-D Deterioration Module Program Documentation,
Part 1: Theory, Červenka Consulting, Prague (2006), http://www.freet.cz.
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