2. In-service performance of Adriatic Reinforced Concrete Arch Bridges

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1 Service Life Modelling of Reinforced Concrete Bridges Marija KUŠTER MEng CE, Research Assistant Faculty of Civil Engineering - University of Zagreb, Croatia marijak@grad.hr Marija Kuster, born 1982, received her civil engineering degree from the Univ. Of Zagreb. Her main areas of research are bridge durability and aesthetics. Joško OŽBOLT PhD, CE Professor Institute of Construction Materials - University of Stuttgart, Germany Faculty of Civil Engineering - University of Rijeka, Croatia joozbolt@iwb.uni-stuttgart.de Jure RADIĆ PhD, CE Professor and Head of Bridge Division - University of Zagreb; General Manager Institute IGH; Zagreb, Croatia jradic@grad.hr Summary The paper provides a brief overview of degradation of the large reinforced concrete arch bridges on Adriatic coast which is the result of influence of the combination of very aggressive exposure conditions and inadequate attention to durability issues. As chloride-induced corrosion is the major cause of deterioration of these bridges, deterioration prediction models during corrosion process on structural members is essential for efficient bridge management. In this purpose coupled 3D chemo-hygro-thermo mechanical model for transient analysis of corrosion processes before and after depassivation of steel reinforcement in concrete is being developed. The application of the model is illustrated on numerical examples, which results are in good agreement with the available experimental observations. Keywords: Reinforced Concrete Bridges, Maritime Environment, Damage, Chloride Induced Corrosion, Modelling, Finite elements. 1. Introduction Chloride-induced corrosion of steel bars in reinforced concrete is one of the major causes of deterioration of reinforced concrete structures, especially those exposed to de-icing salts and aggressive maritime environment condition, such as large Adriatic arch bridges. Corrosion causes reduction of steel cross-section area and damage of concrete cover due to expansion of corrosion product. Moreover, with advanced corrosion ductility of reinforcement, due to the pitting effect, and bond properties can be significantly reduced. A reliable numerical model, which can realistically simulate effects of reinforcement corrosion in concrete, enables to predict service life of new or already damaged structure. Moreover, by employing such a model, it is possible to formulate simple engineering models & design rules in order to increase the durability of structure and reduce its maintenance costs. In this purpose 3D numerical chemo-hygro-thermo-mechanical model is currently being developed to realistically simulate corrosion process, before and after depassivation of steel, and its consequences for the structural safety. 2. In-service performance of Adriatic Reinforced Concrete Arch Bridges The first generation of large Adriatic reinforced concrete arch bridges (Šibenik Bridge, Pag Bridge and Krk Bridge) suffered greatly over four decades of service, due to combination of very aggressive exposure conditions and inadequate attention to durability issues. The dangerous influences of marine environment on durability of the bridges are: (i) relatively high salinity of the Adriatic Sea (approximately 3.5%); (ii) local marine environment with the very frequent changes of very strong southern and northern winds which are blowing and carrying sea spray during several winter months and posing it on the structure; (iii) the winter drops of temperature below freezing point which varies from 1 to 15 times.

2 Fig. 1: The first generation of Adriatic large reinforced concrete arches: Šibenik Bridge (left), Pag Bridge (right) and Krk Bridge (bottom). The first generation of large Adriatic reinforced concrete arch bridges, built in the 196 s and 197 s, were ground breaking engineering structures, both in terms of length (with spans ranging from 193 m to 39 m) and construction technique (first reinforced arch in the world erected entirelyby cantilever method), and much effort was put into assuring stability. However, the durability design was generally considered as that of secondary importance since the threat of chloride attack on reinforced concrete structures was not highly regarded risk at the time of their design and construction, as it is today. Thus, several failures in conceptual design and errors and negligence on site have been done [1]: (i) not sufficiently large concrete cover (designed of only 2.5 cm on the Krk bridge, but executed even thinner); (ii) poor structural solution of superstructure supports designed as stiff framed connections between columns and longitudinal girders or as halfjoints which were greatly deformed and cracked, probably because of concrete shrinkage and temperature change; (iii) inadequate drainage system substantially has contributed to structural deterioration. All this factors accelerated the corrosion process, which through the expansion of corrosion product around the reinforcement bar led to new damages manifested in the form of cracking and spalling of concrete cover. Therefore, it is not surprising that repair works on the Pag Bridge and the Krk Bridge started already after a decade of their services. During major reconstruction of the Pag bridge ( ) the original precast concrete superstructure was dismantled and replaced by a completely new structure in steel, while the columns were repaired by encasing in steel and concrete [2]. The repair works on the Krk Bridge have started several years after its completion and still presents major challenge to engineers since they are not only expensive, but technically demanding tasks and very difficult to perform [3]. The designs of the second generation of Adriatic reinforced concrete arch bridges (Maslenica, Skradin and Cetina), took into account the experience from the in-service performance of older arch bridges. However, beginning stage of chloride-induced corrosion has been noticed on few structural members of those bridges during the main visual inspections. Fig. 2: The second generation of Adriatic large reinforcement concrete arches: Maslenica Bridge (left), Krka Bridge (middle) and Cetina Bridge (right).

3 3. 3D transient model for steel corrosion in concrete As chloride-induced corrosion is the major cause of deterioration of cracked RC bridge elements exposed to sea water and/or de-icing salt, deterioration prediction models during corrosion process on structural members is essential for efficient bridge management. To estimate reduction of the reinforcement cross-section and to predict the volume increase of the corrosion product it is necessary to calculate the corrosion rate what requires modelling of the following physical, electrochemical and mechanical processes: (i) transport of capillary water, heat, oxygen and chloride through the concrete cover; (ii) immobilization of chloride in the concrete; (iii) cathodic and anodic polarization, (iv) transport of OH - ions through electrolyte in concrete pores, (v) distribution of electrical potential and current density, (vi) transport of corrosion products in concrete and cracks and (vii) damage of concrete due to mechanical and non-mechanical actions [5]. In the model the corrosion effects, such as the corrosion products expansion or the reinforcement cross-section reduction, have an effect on the mechanical response of concrete structures. On the other hand, the mechanical properties, such as strength or fracture energy, also influence the corrosion process [1]. 3.1 Initional stage of corrosion Based on the assumption that transport processes take place in aged concrete, transport of capillary water is described in terms of volume fraction of pore water in concrete by Richard s equation [4], where capillary water diffusion coefficient is described as a strongly non-linear function of moisture content [5]. Transport of chloride ions through a non-saturated concrete occurs as a result of convection, diffusion and physically and chemically binding by cement hydration product [4], where the effective chloride diffusion coefficient is treated as a function of moisture content and concrete temperature. Assuming that oxygen does not participate in any chemical reaction before depassivation of steel, transport of oxygen through concrete is considered as oxygen diffusion, where the effective oxygen diffusion coefficient dependents on porosity of hardened cement paste and pore relative humidity and oxygen convection as a consequence of capillary suction and moisture diffusion [4]. The equation which describes temperature distribution in continuum is based on the constitutive law for heat flow and conservation of energy, where the heat capacity and thermal conductivity are assumed as constant concrete parameters [6]. 3.2 Propagation stage of corrosion The active corrosion of steel will start when the surface film of ferric oxide is broken or depassivated by reaching the critical concentration of chloride ions in concrete near steel surface. The non-mechanical processes relevant for the propagation stage of steel corrosion in concrete are: (i) mass sinks of oxygen at steel surface due to cathodic and anodic reaction, (ii) the flow of electric current through pore solution and (iii) the cathodic and anodic potential equations [7]. The model was implemented into the 3D finite element code. More detailed discussion about the mathematical formulations of the processes before and after the depassivation of reinforcement bar and their implementation into a 3D finite element code can be found in reference [6, 7]. 3.3 Mechanical part of the model The model is formulated in the framework of continuum mechanics following basic principles of irreversible thermodynamics. The mechanical part of the model is based on the micro-plane model for concrete with relaxed kinematic constraint. In the finite element analysis cracks are treated in a weak discontinuity, i.e. so called smeared crack approach is employed. To assure the objectivity of the results with respect to the size of the finite elements, the crack band method is used [8]. In the mechanical part of the model the total strain tensor is decomposed as mechanical strain, thermal strain, hygro strain (swelling-shrinking) and strain due to expansion of corrosion product. The macroscopic strain vector is decomposed into micro-plane strain components - normal (volumetric and deviatoric) and shear. The stress increments at the micro-plane level are calculated from the in advance defined uniaxial micro-plane constitutive laws (volumetric, deviatoric and shear directions) and from the corresponding, in advance known, micro-plane strain increments [9].

4 3.4 Interaction between mechanical and non-mechanical part of the model The main difficulty in the formulation of the model is to quantify relevant parameters, which control processes before and after depassivation of reinforcement. It is especially demanding to formulate the influence of damage of concrete (cracking) on its transport properties and corrosion as well as to model the influence of corrosion on degradation of mechanical properties of concrete structures. In the first trial it is assumed that porosity, diffusivity coefficient of capillary water and diffusivity coefficient of oxygen depend on damage (crack width) of concrete. The crack width is calculated from the mechanical part of the model using micro-plane model for concrete [9] according to: w c = ε 1 h, where ε 1 is the maximal principal strain and h is the element width. The numerical analysis is incremental. In each time or load step partial differential equations of non-mechanical and mechanical part of the model (equation of equilibrium) are solved simultaneously. When solving non-mechanical part of the problem, mechanical parameters are constant, equal to those of the previous time step, and conversely (Fig. 3). Fig. 3: Model algorithm. 4. Numerical examples 4.1 Damage induced depassivation of reinforcement The aim of first numerical example is to demonstrate the influence of cracks in concrete on transport processes and on depassivation time [6]. Simply supported reinforced concrete slab was first damaged by external load and subsequently exposed to aggressive influence of seawater at the bottom side (Fig. 4) Chloride attack Fig. 4: Geometry of investigated reinforced concrete slab with concrete cover of 3 mm (left) and FE discretization and distribution of cracks with red zones as maximal principal strains in the slab (right)

5 Fig. 5: Distribution of free and bond chlorides after 1 hour, 1 day, 1 year and 1 years (left) and distribution of free chlorides at the level of reinforcement, left and right of the crack (right). The distribution of free and bounded chloride, in time sequences between 1 hour and 1 years, is shown in Fig. 5 (left). The analysis predicts depassivation time of reinforcement (concentration of free chloride: 7. kg/m 3 of pore water) in the cracked zone immediately after the crack formation. On the contrary to this, for the un-cracked part of the slab depassivation time is not reached even after 1 years. Comparing the distribution of the chlorides at different times (Fig. 5, right), it can be seen that the free chlorides penetrate in the region between the cracks (horizontal direction). Therefore, there is a slight decrease of their concentration in the crack, i.e. with increase of time chlorides tend to be smeared-out into the horizontal direction. A similar result was observed in experiments [1]. 4.2 Corrosion rate in cracked and un-cracked concrete In second numerical example processes after depasivation of reinforcement are analysed [7]. The study is performed for a concrete beam, cracked under axial tensile loading and exposed to splash zone. The aim of the study was to demonstrate the influence of concrete quality, water saturation and cracks in concrete on corrosion current density of a macro cell (Fig. 6). The 3D distributions of oxygen, electric potential and corrosion current density on both sides of the vertical section of the beam through the steel reinforcement bar, for un-cracked and cracked concrete (w/c =.4, S= 45%) after 1 minutes of corrosion process are shown in Fig. 7. The distribution of electric potential and current density indicates the pitting corrosion in the anodecathode transition zone, which is especially dangerous because of rapid reduction of the reinforcement cross-section area and strong degradation of ductility. Maximal consumption of oxygen is predicted in the transition zone between anode and cathode (Fig. 8). The oxygen distribution in cracked and un-cracked concrete is very similar. The only difference is noticed in the vertical row of elements representing crack. There is almost no consumption of oxygen because of a continuous oxygen supply in the crack. The consumption of oxygen is much faster in a good quality concrete (w/c=,4) than in poor quality concrete (w/c=,7), since water and oxygen diffusivities increase with increase of the water to Fig. 6: Geometry (all in mm), mechanical and non-mechanical loading, boundary conditions and finite element discretization.

6 Fig. 7: 3D distribution of oxygen (left), electric potential (middle) and current density (right) for good quality concrete at saturation of 45% after 1 minutes of corrosion process for: a) un-cracked and b) cracked concrete. C o [kg/m 3 ] Co [kg/m 3 ] Distance [mm] Time [minutes] Uncracked Uncracked concrete, concrete, w/c=.4 w/c=.4 Oxygen Oxygen conc. conc. Saturation (%) Time (minutes) Co [kg/m 3 ] Co [kg/m 3 ] Distance [mm] Time [minutes] Uncracked Cracked concrete, concrete, w/c=.7w/c=.4 Oxygen Oxygen conc. conc. Saturation (%) Time (minutes) Fig. 8: Oxygen concentration at the level of reinforcement in un-cracked (left) and cracked (right) good quality concrete. Co [kg/m 3 ] Time [minutes] Uncracked concrete, w/c=.4 Oxygen conc Saturation (%) Time [minutes] Co [kg/m 3 ] Uncracked concrete, w/c=.7 Oxygen conc. Saturation (%) Fig. 9: Oxygen concentration as function of time for different water saturation in transition anode-cathode zone for un-cracked, good (left) and poor (right) quality concrete. i [A/m 2 ] Saturation [%] Current density Uncracked concrete w/c =.4 Cracked concrete w/c =.4 Uncracked concrete w/c =.7 Cracked concrete w/c =.7 i [A/m 2 ] Current density Uncracked concrete, w/c =.4 Lopez & Gonzales (1992) Saturation [%] Fig. 1: Relation between saturation and current density measured at the anode-cathode transition zone: for all calculated cases (left) and comparison with experiments (right). cement ratio (Fig. 9). Furthermore, the consumption of oxygen increases with increase of water saturation up to critical saturation. In the good quality concrete the critical water saturation, at which the concentration of oxygen at cathodic site reaches a small positive value and simulation is

7 still stable, is approximately 7%. Similar results can be observed for poor quality concrete; however, the oxygen consumption is much slower and the critical water saturation is 85%. In all analysed cases the highest corrosion rate is obtained in the anode-cathode transition zone. The corrosion rate is higher in poor than in good quality concrete and crack does not have significant influence on the maximal current density (Fig. 1, left). Numerical results of current density for uncracked, good quality concrete are in good agreement with the experimental results [1] (Fig. 1, right). The used mathematical models for corrosion kinetics and transport of ions simulate the process of reinforcement corrosion in unsaturated concrete for water saturation in the range from 35% up to the critical value (depending on concrete properties) in which corrosion is controlled by both, reactive and transport process. The diffusion-controlled corrosion of steel in concrete takes place in the range of water saturation greater than the critical saturation (not considered in the present work). In such a case the reduction of oxygen is faster than its supply. It is known that corrosion current density of,5 A/m 2 to 1, A/m 2 is equivalent to the reduction of reinforcement diameter for approximately,1 to 2, mm/year, respectively [11,12]. These limits are approximately valid for concrete in the splash zone. The corrosion current densities predicted in the numerical simulations are within the above limits. This confirms that the prediction is realistic and that the splash zone is one of the most critical areas for corrosion of steel in concrete. 5. Conclusions Review of in-service performance of Adriatic arch bridges clearly indicates chloride-induced corrosion as the major cause of deterioration of reinforced concrete structures in maritime environment. Repair of those bridges resulted in relatively high direct and indirect costs. Therefore, to predict durability of new or already damaged reinforced concrete structure it is important to have a numerical tool, which is able to realistically simulate corrosion processes and the consequences for the structural safety. In this purpose coupled 3D chemo-hygro-thermo-mechanical model for transient analysis of corrosion processes before and after depassivation of steel reinforcement in concrete is developed and implemented into 3D FE code. The numerical results are in good agreement with the available experimental observations, what leads to the conclusion that the model is able to realistically predict corrosion of reinforcement. Damage of concrete significantly reduces depassivation time of reinforcement bar, however, within assumed conditions crack does not remarkably influences corrosion rate. Corrosion rate is much higher in poor than in good quality concrete. The maximal values of corrosion rate, achieved at critical water saturation, are within the limits for concrete in splash zone, as one of the most critical areas for corrosion of steel in concrete. As a further extension of the model the transport of corrosion products through concrete pores and cracks should be modelled in order to determinate damage of concrete cover due to expansion of corrosion product. 6. References [1] RADIĆ J., BLEIZIFFER J. and KUŠTER M., Trends and Developments in Bridge and Asset Management, Proceedings of the 11th International Conference on Inspection, Appraisal, Repairs and Maintenance of Structures, Murude Celikag (ed.), Singapore: CI- Premier Pte Ltd, 43-53, 27 [2] ŠAVOR Z., MUJKANOVIĆ N., HRELJA G. and BLEIZIFFER J., Recontruction of the Pag Bridge, Long Arch Bridges, Radić, J. and Chen, B. (ed.), Zagreb: SECON HDGK, , 28 [3] BESLAĆ J., TKALČIĆ D., ŠTEMBERGA K., Difficulties and Successes in the Maintenance of Krk Bridge Long Arch Bridges, Radić, J. and Chen, B. (ed.), Zagreb: SECON HDGK,197-25, 28 [4] BEAR J. and BACHMAT Y., Introduction to Modelling of Transport Phenomena in Porous

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