Seismic response of corroded r.c. structures - Abece

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 SimioniDepartment of Architectural Construction, University IUAV, Venezia, Italy

Luisa Berto & Renato VitalianiDepartment of Structural and Transportation Engineering, University of Padova, Padua, Italy

ABSTRACT: An accurate diagnosis of r.c. structures requires the investigation of their progressive degradationover time. As a matter of fact, the increasing damage resulting from the environmental attacks that the structuremay suffer during its service life, affects not only the load bearing capacity, but also the failure mechanism, leadingto a more brittle behavior. The loss of ductility strongly influences the structural response to external loads espe-cially 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 seismicresponse of r.c. structures are presented. Some case studies are analyzed under a moderate corrosive attack andthe 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 overtime implies the reduction of the load bearing capacityand, in some cases, also the shift of the failure mecha-nism from the ductile to the fragile type. Consequently,the evaluation of the structural performance and of thelifetime is time-dependent and the estimation of thedeterioration level becomes a main issue in safetyassessment, especially in seismic areas where the duc-tility characteristics of the structure play a primaryrole. Actually, the response to external excitationsdepends on the real level of structural damage.

In particular, the location of the structure in veryaggressive environments, such as tidal or industrialscenarios, facilitates the occurrence of degradationprocesses. Nevertheless, poor quality materials (e.g.low concrete characteristics) as well as not controlledtechniques (e.g. absence of detailing practices) mayaccelerate these phenomena, leading to a significantreduction of the structural performance, even after arelatively short service time.

One of the major causes of degradation is thecorrosion of reinforcement, generally associated tocarbonation and chloride attack, which leads to thevariation of the mechanical properties of steel andconcrete over time.

Experimental tests on corroded r.c. members haveevidenced not only the reduction of the load carryingcapacity with increasing levels of corrosion, but alsothe variation of the failure mechanism from the duc-tile to the fragile type, with noteworthy implications

on the seismic behaviour. Moreover, local damageinduced by corrosion may alter the mechanisms of loaddistribution considered in the initial design.

An interesting investigation is provided by Çagatay(2005). In some of the r.c. buildings collapsed duringthe Izmit earthquake (Turkey, August 17th 1999), seasand was found inside the concrete mix and signif-icant reinforcement corrosion due to the penetrationof chlorides was observed. It was concluded that thepresence of sea sand may result in structural failure ina period of 10–20 years even under static loads.

Therefore, the correct diagnosis of r.c. structures,in particular when performing their seismic assess-ment, requires a preventive evaluation of the damagestate induced by corrosion, resulting from the specificenvironmental conditions, as well as by other causesof degradation.

In this study, the effects of reinforcement corro-sion on the seismic response of r.c. structures areinvestigated. Some case studies are analyzed under amoderate corrosive attack and the outcomes are dis-cussed in terms of capacity curves and compared withthe European Code provisions.

2 CORROSION EFFECTS ON STRUCTURALBEHAVIOUR

The following aspects are involved when assessing themain effects of reinforcement corrosion:

– Steel section reduction (localized in the case of pit-ting corrosion, commonly associated to chlorides

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penetration, or uniformly distributed, usually whencarbonation occurs), resulting in the reduction ofresistance and load bearing capacity.

– Variation of the mechanical properties of the rein-forcing bars, in terms of reduction of steel ultimateelongation (ductility loss) and in some cases thetendency to the reduction of yield and ultimatestrengths with increasing corrosion (Almusallam2001). It is worth noting that the ductility lossmay produce some significant effects on structuralbehaviour, such as a decrease of the redistributioncapacity of bending moments.

– Formation of corrosion products (i.e. iron oxides)along the steel bar surface, causing the increase ofthe tensile stresses in the concrete surrounding therebars, which may exceed the tensile strength. Themain consequences are cover cracking with possi-ble delamination of the outer concrete layers, andthe reduction of steel-concrete bond even leadingto total loss of anchorage. It is interesting to notethat under moderate corrosive attacks steel-concretebond is generally not significantly affected (e.g.Rodriguez et al. 1994).

3 MODELLING APPROACH

When modelling the response of a corroded structureand its progressive degradation, sophisticated non lin-ear FE models may be adopted, able to account forthe coupling effects of mechanical and environmen-tal damage (e.g. Saetta et al. 1999, Coronelli et al.2004). In the framework of distributed plasticity, alsofiber models accounting for rebars slippage have beenrecently proposed (e.g. Spacone et al. 2000). As analternative, the concentrated plasticity approach maybe assumed, with the advantage of a reduced compu-tational effort respect to the previously cited detailedformulations. By following this approach the effects ofthe material degradation may be considered by modi-fying the constitutive relationships of the plastic hingesas a function of the corrosion level. The definition ofsuch laws may be achieved in two ways: by performingdetailed analyses of the critical zones of the structurewith proper damage laws (micro level approach) or byattributing proper moment-curvature relationships tothe plastic zones (macro level approach).

In this paper, the concentrated plasticity model andthe macro level approach are adopted and pushoveranalyses 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 theoreti-cal as well as experimental expressions available inliterature are used.

Finally, since a moderate corrosive attack is con-sidered, in this preliminary phase of the research, theeffect of steel corrosion on bond is neglected and thehypothesis of the conservation of plane sections isassumed.

3.1 Steel section reduction

The depth of the corrosive attack penetration Px isevaluated with the following expression:

where Icorr = average corrosion rate; t = ‘propagationtime’ that is the time after corrosion started, i.e. afterthe aggressive front reached the bar. In this study,it is assumed Icorr = 1 µA/cm2, corresponding to amoderate corrosion level (Rodriguez et al. 1994).

For the evaluation of the ‘initiation time’, that isthe period of time necessary until the aggressive agentreaches the reinforcing bar, the diffusive model devel-oped by Saetta et al. (1999) is adopted. The followingset of differential equations governs the diffusion andtransport processes of aggressive species within theconcrete matrix:

where c = diffusive species concentration; h = relativehumidity; w = free water content; T = temperature;R = degree of chemical reaction (ratio between theactual and the reference concentration of the pollu-tant). For the definition of all the symbols see Saettaet al. (1999). Under the hypothesis of a medium-lowconcrete quality and a cover of 20 mm, the model forcarbonation phenomenon provides an initiation timeof about 10 years.

Given Px from the (1) the residual section of thecorroded bar is:

where φt = residual diameter at time t; φ0 = nominaldiameter; α = coefficient depending on the type ofattack, ranging from 2 for distributed corrosion until10 for pitting.

For small rebar diameters (e.g. stirrups), localizedcorrosion may produce section reductions up to 50%in less than 20 years since the chlorides reach the bar.

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In this study the maximum loss of steel area is assumedequal to 20% for the stirrups, given that a distributedcorrosion type is supposed.

3.2 Steel mechanical characteristics

Experimental laboratory tests (Rodriguez et al. 2001)have shown a significant reduction of rebars ductil-ity and consequently of the maximum elongation until30% and 50% for loss of transversal area of 15% and28% respectively.

By a linear interpolation of these results, the per-centage reduction of the ultimate deformation for theconsidered case studies has been calculated. In thiswork, variations of the ultimate and yield strengthsare neglected, because of their negligible values andthe objective difficulty to identify a uniform tendencyin the available experimental results.

4 APPLICATIONS

The proposed methodology is applied to two case stud-ies: a two-storey, two-span structure (Figure 1) whoseregularity in plan and in elevation allows analysing atypical frame with a 2D model; and a 3D, four-storeybuilding. For both cases the seismic response is inves-tigated in sound conditions and at the end of the servicelife (50 years). In particular some pushover analysesare carried out considering gravitational and seismicloads and a uniform distribution of the lateral forces(proportional to the storeys masses).

4.1 Case Study 1

Two different scenarios are considered: corrosionaffecting the columns at the ground floor and corro-sion 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 corrosionscenarios are herein provided.

From (1) a corrosion penetration depth of 0.57 mmis obtained, and the corresponding reduced diametersfor longitudinal and transversal bars are calculatedfrom (3). A loss of 21% is estimated for steel ultimatedeformation, assuming an average corrosion degree of9% for the longitudinal bars.

These results are used in the calculation of themoment-curvature relationships of the corroded sec-tions and consequently the moment-rotation laws ofplastic hinges are evaluated. As shown in Figure 2(b),the comparison between the capacity curves of thesound and the corroded frame evidences the ten-dency to the reduction of the resistance in presenceof corrosion and a relevant loss of ductility.

According to the European Standard the ratios ρbetween the demand and the capacity in terms of

Figure 1. Case Study 1: Front view (units in cm).

plastic rotations (for ductile failure mechanisms) andin terms of shear (for brittle failure mechanisms) areevaluated. In particular, the rotation capacity is calcu-lated adopting the relationship suggested by Eurocode8 – part 3 (2005). Obviously, the failure for theconsidered verification is achieved when ρ becomesequal to 1, which means the demand becomes equal tothe member capacity and the corresponding limit stateis achieved.

As it commonly occurs in existing r.c. buildingswithout seismic details, the governing failure mech-anism can be ascribed to shear collapse, as evidencedby the diagrams of shear ratios ρ: sh-sound andsh-corr, respectively for sound and corrosion scenarios(Figure 2(a)). Assuming that such a failure can be pre-vented, the analyses are continued until the occurrenceof ductile mechanism.

In sound conditions the shear failure occurs in cor-respondence to a roof horizontal displacement of about0.04 m (“B.F._sound” triangular mark), while the duc-tile 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 agreementbetween the numerical prediction and the Code limitvalue for the sound condition, while for the corrodedone the Code limit becomes unsafe. Therefore, a mod-ification should be introduced in the Code expressionof the rotation capacity to obtain a reliable predictionof 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 affectingthe columns of the ground floor is considered, with thesame environmental conditions of Case Study 1. Thecomparison with the sound scenario is shown in termsof capacity curves (Figure 3).As evidenced, also in thiscase the governing failure mechanism is a brittle one(see the B.F. marks) and a reduction of resistance andductility for the corroded case occurs. It is interesting

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Figure 2. Case Study 1: (a) Rotation and shear ratios vs.displacement; (b) Capacity curves for sound and corrodedpattern.

Figure 3. Case Study 2: Capacity curves (sound and cor-roded scenarios).

to note that such reductions are less relevant than inCase Study 1 as a consequence of the collapse mecha-nism that is closer to a global one, with a larger energydissipation confirmed by the formation of a consid-erable number of plastic hinges in both columns andbeams (Figure 4).

5 CONCLUSIONS

The growth of interest in the scientific community onmodelling corroding structures is confirmed by thewide literature production of the last years (e.g. Fib

Figure 4. Case Study 2: Hinges formation (corroded sce-nario).

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 num-ber of parameters is required, becoming an importantphase of the analysis.

In this paper, an investigation of the degradationeffects on the seismic behaviour of r.c. structuresis presented. The comparison between the obtainedresults and the European Code provisions suggeststhe opportunity to modify the code expression of therotation capacity accounting for the effects of corro-sion attacks. Further research is necessary for a moreaccurate calibration of the moment-rotation relation-ships of the corroded hinges in order to account forcover cracking and rebars slippage, which may occurin case of particularly aggressive attack. The futureresearch will also investigate the possibility to followa combined approach, in which detailed analyses of thecritical zones performed at a “micro” level allow thedefinition of proper moment-rotation relationships forthe plastic hinges as a function of the corrosion level.

ACKNOWLEDGEMENTS

The second case study is investigated in the frameworkof the ReLUIS research project launched by the ItalianDepartment of Civil Protection.

REFERENCES

Almusallam, A. A. 2001. Effect of degree of corrosion onthe properties of reinforcing steel bars. Constr. and Build.Mat. 15: 361–368.

Çagatay, I.H. 2005. Experimental evaluation of buildingsdamaged in recent earthquakes in Turkey. Eng. FailureAn. 12: 440–452.

Coronelli, D. & Gambarova, P. 2004. Structural assessment ofcorroded reinforced concrete beams: modeling guidelines.J. of Struct. Eng. 130(8): 1214–1224.

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fib 2000. Bond of reinforcement in concrete. State-of-Art Rep., Bulletin No. 10. International Federation forStructural Concrete. Switzerland.

Rodriguez, J., Ortega, L.M. & Casal, J. 1994. Corrosion ofreinforcing bars and service life of reinforced concretestructures: corrosion and bond deterioration. Int. Conf.Concrete across Borders. Odense, Denmark.

Rodriguez, J. & Andrade C. 2001. Contecvet – A validatedusers manual for assessing the residual service life ofconcrete structures. Geocisa, Madrid.

Saetta, A., Scotta, R. & Vitaliani, R. 1999. CoupledEnvironmental-Mechanical Damage Model of RC Struc-tures. J. of Eng. Mech. (125)8: 930–940.

Spacone, E. & Limkatanyu, S. 2000. Responses of Rein-forced Concrete Members Including Bond-Slip Effects,ACI Struct. J. 97(6): 831–839.

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