Tailor Made Concrete Structures Walraven & Stoelhorst (eds) 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8 Seismic response of corroded r.c. structures Anna Saetta & Paola Simioni Department of Architectural Construction, University IUAV, Venezia, Italy Luisa Berto & Renato Vitaliani Department of Structural and Transportation Engineering, University of Padova, Padua, Italy ABSTRACT: An accurate diagnosis of r.c. structures requires the investigation of their progressive degradation over time. As a matter of fact, the increasing damage resulting from the environmental attacks that the structure may suffer during its service life, affects not only the load bearing capacity, but also the failure mechanism, leading to a more brittle behavior. The loss of ductility strongly influences the structural response to external loads especially in seismic conditions and an effective non linear model able to account for these aspects is strongly required. In this paper, the preliminary results of an investigation concerning the effects of steel corrosion on the seismic response of r.c. structures are presented. Some case studies are analyzed under a moderate corrosive attack and the outcomes are discussed in terms of capacity curves and compared with the provisions of the European Code. 1 INTRODUCTION The progressive deterioration of r.c. structures over time implies the reduction of the load bearing capacity and, in some cases, also the shift of the failure mechanism from the ductile to the fragile type. Consequently, the evaluation of the structural performance and of the lifetime is time-dependent and the estimation of the deterioration level becomes a main issue in safety assessment, especially in seismic areas where the ductility characteristics of the structure play a primary role. Actually, the response to external excitations depends on the real level of structural damage. In particular, the location of the structure in very aggressive environments, such as tidal or industrial scenarios, facilitates the occurrence of degradation processes. Nevertheless, poor quality materials (e.g. low concrete characteristics) as well as not controlled techniques (e.g. absence of detailing practices) may accelerate these phenomena, leading to a significant reduction of the structural performance, even after a relatively short service time. One of the major causes of degradation is the corrosion of reinforcement, generally associated to carbonation and chloride attack, which leads to the variation of the mechanical properties of steel and concrete over time. Experimental tests on corroded r.c. members have evidenced not only the reduction of the load carrying capacity with increasing levels of corrosion, but also the variation of the failure mechanism from the ductile to the fragile type, with noteworthy implications on the seismic behaviour. Moreover, local damage induced by corrosion may alter the mechanisms of load distribution considered in the initial design. An interesting investigation is provided by Çaǧatay (2005). In some of the r.c. buildings collapsed during the Izmit earthquake (Turkey, August 17th 1999), sea sand was found inside the concrete mix and significant reinforcement corrosion due to the penetration of chlorides was observed. It was concluded that the presence of sea sand may result in structural failure in a period of 10 20 years even under static loads. Therefore, the correct diagnosis of r.c. structures, in particular when performing their seismic assessment, requires a preventive evaluation of the damage state induced by corrosion, resulting from the specific environmental conditions, as well as by other causes of degradation. In this study, the effects of reinforcement corrosion on the seismic response of r.c. structures are investigated. Some case studies are analyzed under a moderate corrosive attack and the outcomes are discussed in terms of capacity curves and compared with the European Code provisions. 2 CORROSION EFFECTS ON STRUCTURAL BEHAVIOUR The following aspects are involved when assessing the main effects of reinforcement corrosion: Steel section reduction (localized in the case of pitting corrosion, commonly associated to chlorides 1031
penetration, or uniformly distributed, usually when carbonation occurs), resulting in the reduction of resistance and load bearing capacity. Variation of the mechanical properties of the reinforcing bars, in terms of reduction of steel ultimate elongation (ductility loss) and in some cases the tendency to the reduction of yield and ultimate strengths with increasing corrosion (Almusallam 2001). It is worth noting that the ductility loss may produce some significant effects on structural behaviour, such as a decrease of the redistribution capacity of bending moments. Formation of corrosion products (i.e. iron oxides) along the steel bar surface, causing the increase of the tensile stresses in the concrete surrounding the rebars, which may exceed the tensile strength. The main consequences are cover cracking with possible delamination of the outer concrete layers, and the reduction of steel-concrete bond even leading to total loss of anchorage. It is interesting to note that under moderate corrosive attacks steel-concrete bond is generally not significantly affected (e.g. Rodriguez et al. 1994). 3 MODELLING APPROACH When modelling the response of a corroded structure and its progressive degradation, sophisticated non linear FE models may be adopted, able to account for the coupling effects of mechanical and environmental damage (e.g. Saetta et al. 1999, Coronelli et al. 2004). In the framework of distributed plasticity, also fiber models accounting for rebars slippage have been recently proposed (e.g. Spacone et al. 2000). As an alternative, the concentrated plasticity approach may be assumed, with the advantage of a reduced computational effort respect to the previously cited detailed formulations. By following this approach the effects of the material degradation may be considered by modifying the constitutive relationships of the plastic hinges as a function of the corrosion level. The definition of such laws may be achieved in two ways: by performing detailed analyses of the critical zones of the structure with proper damage laws (micro level approach) or by attributing proper moment-curvature relationships to the plastic zones (macro level approach). In this paper, the concentrated plasticity model and the macro level approach are adopted and pushover analyses of some case studies are performed. The corrosion effects are considered as follows: 1. reduction of rebars and stirrups section; 2. reduction of steel ultimate deformation. In order to evaluate these effects, some theoretical as well as experimental expressions available in literature are used. Finally, since a moderate corrosive attack is considered, in this preliminary phase of the research, the effect of steel corrosion on bond is neglected and the hypothesis of the conservation of plane sections is assumed. 3.1 Steel section reduction The depth of the corrosive attack penetration P x is evaluated with the following expression: where I corr = average corrosion rate; t = propagation time that is the time after corrosion started, i.e. after the aggressive front reached the bar. In this study, it is assumed I corr = 1 µa/cm 2, corresponding to a moderate corrosion level (Rodriguez et al. 1994). For the evaluation of the initiation time, that is the period of time necessary until the aggressive agent reaches the reinforcing bar, the diffusive model developed by Saetta et al. (1999) is adopted. The following set of differential equations governs the diffusion and transport processes of aggressive species within the concrete matrix: where c = diffusive species concentration; h = relative humidity; w = free water content; T = temperature; R = degree of chemical reaction (ratio between the actual and the reference concentration of the pollutant). For the definition of all the symbols see Saetta et al. (1999). Under the hypothesis of a medium-low concrete quality and a cover of 20 mm, the model for carbonation phenomenon provides an initiation time of about 10 years. Given P x from the (1) the residual section of the corroded bar is: where φ t = residual diameter at time t; φ 0 = nominal diameter; α = coefficient depending on the type of attack, ranging from 2 for distributed corrosion until 10 for pitting. For small rebar diameters (e.g. stirrups), localized corrosion may produce section reductions up to 50% in less than 20 years since the chlorides reach the bar. 1032
In this study the maximum loss of steel area is assumed equal to 20% for the stirrups, given that a distributed corrosion type is supposed. 3.2 Steel mechanical characteristics Experimental laboratory tests (Rodriguez et al. 2001) have shown a significant reduction of rebars ductility and consequently of the maximum elongation until 30% and 50% for loss of transversal area of 15% and 28% respectively. By a linear interpolation of these results, the percentage reduction of the ultimate deformation for the considered case studies has been calculated. In this work, variations of the ultimate and yield strengths are neglected, because of their negligible values and the objective difficulty to identify a uniform tendency in the available experimental results. 4 APPLICATIONS The proposed methodology is applied to two case studies: a two-storey, two-span structure (Figure 1) whose regularity in plan and in elevation allows analysing a typical frame with a 2D model; and a 3D, four-storey building. For both cases the seismic response is investigated in sound conditions and at the end of the service life (50 years). In particular some pushover analyses are carried out considering gravitational and seismic loads and a uniform distribution of the lateral forces (proportional to the storeys masses). 4.1 Case Study 1 Two different scenarios are considered: corrosion affecting the columns at the ground floor and corrosion concentrated of the basis of the lateral columns (1.32 m from the ground). For the sake of brevity, only the results regarding the first of the two corrosion scenarios are herein provided. From (1) a corrosion penetration depth of 0.57 mm is obtained, and the corresponding reduced diameters for longitudinal and transversal bars are calculated from (3). A loss of 21% is estimated for steel ultimate deformation, assuming an average corrosion degree of 9% for the longitudinal bars. These results are used in the calculation of the moment-curvature relationships of the corroded sections and consequently the moment-rotation laws of plastic hinges are evaluated. As shown in Figure 2(b), the comparison between the capacity curves of the sound and the corroded frame evidences the tendency to the reduction of the resistance in presence of corrosion and a relevant loss of ductility. According to the European Standard the ratios ρ between the demand and the capacity in terms of Figure 1. Case Study 1: Front view (units in cm). plastic rotations (for ductile failure mechanisms) and in terms of shear (for brittle failure mechanisms) are evaluated. In particular, the rotation capacity is calculated adopting the relationship suggested by Eurocode 8 part 3 (2005). Obviously, the failure for the considered verification is achieved when ρ becomes equal to 1, which means the demand becomes equal to the member capacity and the corresponding limit state is achieved. As it commonly occurs in existing r.c. buildings without seismic details, the governing failure mechanism can be ascribed to shear collapse, as evidenced by the diagrams of shear ratios ρ: sh-sound and sh-corr, respectively for sound and corrosion scenarios (Figure 2(a)). Assuming that such a failure can be prevented, the analyses are continued until the occurrence of ductile mechanism. In sound conditions the shear failure occurs in correspondence to a roof horizontal displacement of about 0.04 m ( B.F._sound triangular mark), while the ductile failure occurs much later (0.22 m displacement). In presence of corrosion, both failures are anticipated. It is worth noting that there is a good agreement between the numerical prediction and the Code limit value for the sound condition, while for the corroded one the Code limit becomes unsafe. Therefore, a modification should be introduced in the Code expression of the rotation capacity to obtain a reliable prediction of the seismic behaviour of existing r.c. buildings. 4.2 Case Study 2 The building was designed basing on outdated codes, under vertical loads only. A corrosive attack affecting the columns of the ground floor is considered, with the same environmental conditions of Case Study 1. The comparison with the sound scenario is shown in terms of capacity curves (Figure 3). As evidenced, also in this case the governing failure mechanism is a brittle one (see the B.F. marks) and a reduction of resistance and ductility for the corroded case occurs. It is interesting 1033
Case Study 2: Hinges formation (corroded sce- Figure 4. nario). Figure 2. Case Study 1: (a) Rotation and shear ratios vs. displacement; (b) Capacity curves for sound and corroded pattern. 2000). Nevertheless, the problem is still an open issue, especially in case detailed analyses were performed. In fact, in such investigation the calibration of a number of parameters is required, becoming an important phase of the analysis. In this paper, an investigation of the degradation effects on the seismic behaviour of r.c. structures is presented. The comparison between the obtained results and the European Code provisions suggests the opportunity to modify the code expression of the rotation capacity accounting for the effects of corrosion attacks. Further research is necessary for a more accurate calibration of the moment-rotation relationships of the corroded hinges in order to account for cover cracking and rebars slippage, which may occur in case of particularly aggressive attack. The future research will also investigate the possibility to follow a combined approach, in which detailed analyses of the critical zones performed at a micro level allow the definition of proper moment-rotation relationships for the plastic hinges as a function of the corrosion level. Figure 3. Case Study 2: Capacity curves (sound and corroded scenarios). to note that such reductions are less relevant than in Case Study 1 as a consequence of the collapse mechanism that is closer to a global one, with a larger energy dissipation confirmed by the formation of a considerable number of plastic hinges in both columns and beams (Figure 4). 5 CONCLUSIONS The growth of interest in the scientific community on modelling corroding structures is confirmed by the wide literature production of the last years (e.g. Fib ACKNOWLEDGEMENTS The second case study is investigated in the framework of the ReLUIS research project launched by the Italian Department of Civil Protection. REFERENCES Almusallam, A. A. 2001. Effect of degree of corrosion on the properties of reinforcing steel bars. Constr. and Build. Mat. 15: 361 368. Çağatay, I.H. 2005. Experimental evaluation of buildings damaged in recent earthquakes in Turkey. Eng. Failure An. 12: 440 452. Coronelli, D. & Gambarova, P. 2004. Structural assessment of corroded reinforced concrete beams: modeling guidelines. J. of Struct. Eng. 130(8): 1214 1224. 1034
fib 2000. Bond of reinforcement in concrete. State-of- Art Rep., Bulletin No. 10. International Federation for Structural Concrete. Switzerland. Rodriguez, J., Ortega, L.M. & Casal, J. 1994. Corrosion of reinforcing bars and service life of reinforced concrete structures: corrosion and bond deterioration. Int. Conf. Concrete across Borders. Odense, Denmark. Rodriguez, J. & Andrade C. 2001. Contecvet A validated users manual for assessing the residual service life of concrete structures. Geocisa, Madrid. Saetta, A., Scotta, R. & Vitaliani, R. 1999. Coupled Environmental-Mechanical Damage Model of RC Structures. J. of Eng. Mech. (125)8: 930 940. Spacone, E. & Limkatanyu, S. 2000. Responses of Reinforced Concrete Members Including Bond-Slip Effects, ACI Struct. J. 97(6): 831 839. 1035