THE SIMULATION OF CORROSION DEGRADATION OF CONCRETE SPECIMEN IN STATIONARY HEAT AND MOISTURE CONDITIONS

S t r e s z c z e n i e W tej pracy skupiono się na prognozowaniu uszkodzeń w próbkach betonowych w wyniku korozji chlorkowej prętów zbrojeniowych. W obliczeniach uwzględniono czas wypełnienia otuliny, jak również czas potrzebny na doszczelnienie produktów korozji w warstwie przejściowej. W obliczeniach zastosowano podejście zakładające powstawanie korozyjnych odkształceń dystorsyjnych spowodowanych przyrostem masy produktów korozji zależnych od natężenia prądu korozyjnego. K e y w o r d s : Concrete cover splitting; Corrosion of reinforced concrete; Mass transport; Theory of plasticity. 4/2017 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 107 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T The Si les ian Univers i ty of Technology No. 4/2017 F . R e c h a , T . J a ś n i o k , T . K r y k o w s k i tal significance for the description of physicochemical processes occurring in the concrete cover [6, 7, 8, 9]. Mechanical interactions of corrosion products in the concrete cover are initiated by corrosion products, after filling up pores in the interfacial transition zone. Time necessary for filling tightly the structure of pores was analyzed, among other things, in the papers [10, 11, 12]. In [10, 12, 13], problems of damage evolution in concrete cover caused by the volumetric increase of corrosion products were analyzed. In [14, 15], the description of effects of the damage theory, including distortional strains that are the result of the volumetric increase of corrosion products, was used. The process of embedding corrosion products in the structure of pores was assumed to be described by diffusion equations [1, 16]. It was also accepted that the corrosion products could be transferred from the interfacial transition layer deeper into cement paste surrounding the rebar [16]. This paper concentrates on forecasting the evolution of damage in concrete specimens, which is the result of the performed experimental analysis. The experimental research presume adding chlorides into concrete mix during the formation phase of concrete specimens. We analyzed results that can be obtained in the laboratory conditions (constant relative humidity in concrete pores, constant temperature and chloride ions concentration in the rebar’s surface). The damage mechanism of concrete cover was analyzed, and the time of filling transition zone was considered as time required to tighten corrosion products in the interfacial transition zone. This issue was described with reference to the approach based on the concept similar to the well-known idea of damage mechanics, namely the degradation parameter [17]. The purpose of this paper is to answer the question related to time necessary for damage evolution in concrete specimens under conditions of uniform corrosion in the reinforcement and excluded impact of rheology. 2. EVOLUTION OF EQUIVALENT CHANGE IN VOLUME OF CORROSION PRODUCTS The structure of steel-concrete interfacial transition zone has a crucial impact on evaluation and description of concrete cover fracturing. Concrete in the vicinity of reinforcing bars has slightly different structure by the reason of solid phase effect on hydration process of cement. This layer known as the interfacial transition zone, has a thickness of about 50–100 μm. It is composed of an electric double layer of thickness about 1–2 μm, a layer of cement paste with increased porosity, and a layer of large crystals [6, 18]. In the moment of activating the process of corrosion, corrosion products start to accumulate in the interfacial transition zone. After filling the structure of pores, those products affect mechanically the concrete cover. It is very important to define what part of corrosion products directly contribute to damage of the concrete cover. In the initial stage, the process of creation of corrosion products is not accompanied by the increased stress in concrete cover. The corrosion products are located on the corrosion pit surface and fill empty space in pores in the interfacial transition layer. Along with the increased pressure exerted on concrete cover by the corrosion products, some of them can be transported from the high porosity ITZ layer. Then, they are transferred into deeper layers of concrete, characterized with smaller porosity. While analyzing the mechanisms of corrosion products formation and transfer in the ITZ layer, four variables were found to have an influence on the function of the rate of change of effective volume V eff. These variables are the production rate of corrosion products V R, the rate of corrosion cavity creation V Fe2+, the rate of corrosion product loss as the result of transfer into ITZ layer V por , and the rate of change in corrosion products volume V tran as the result of transfer from high porosity ITZ layer deeper into the concrete cover layer. The transport of corrosion products from the ITZ layer deep into concrete cover is the result of increased pressure exerted by these products on pores of concrete structure. The aforementioned dependence can be formally written [16] using the following equation: The first two values in the equation (1), the rate of changes V R and V Fe2+ can be defined as functions of corrosion current intensity I, [14]. The determination of next two values V por and V tran is complex and complicated in the theoretical description. However, it can be assumed [17] that those values can be defined as functions of changes V R and V Fe2+ and a certain additional variable which was called the damage parameter of the equivalent volume β = β (τ) ⟨0.1⟩ by the analogy to the mechanics of damage The value V ekw that exists in equations (1) and (2) can 108 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 4/2017 tran por ekw tran por Fe R eff V V V V V V V V − − = − − − = + 2 , (1) ( ) ekw Fe R tran por V V V V V β β = − = + + 2 , (2) THE SIMULATION OF CORROSION DEGRADATION OF CONCRETE SPECIMEN IN STATIONARY HEAT AND MOISTURE CONDITIONS be determined according to the Faraday’s law and a linear relationship between the amount of ferrous ions transferred to the pore solution and the volume of corrosion products. Taking into account the equation (2) in (1), we can express a relationship between the rate of change of effective volume and the rate of change of equivalent volume in a way that is close to the approach adopted in the continuum damage mechanics [17] where ρFe2+ is the density of ferrous ions, α and – parameters, which in the literature are accepted in dependence of composition of corrosion products [13], [14]. The β parameter determines the intensity of developing corrosion impact on the structure of the concrete cover. This parameter describes three phases of corrosion products impact on the structure of concrete cover. The initial precedes filling of empty pore spaces in the ITZ layer. This phase takes place in the time τ τ0 , where τ0 is assumed as time necessary to fill the space of pores without producing the mechanical effects in the concrete cover, β = 1. The second phase takes place in the imaginary range of time τ0 τ τu , 0 β = β (τ) 1 . In this stage, we can observe the progressive increase of pressure exerted by corrosion products on the walls of pores. The time τu corresponds to the level of tightness of corrosion products, which blocks the diffusion of these products from the ITZ layer into surrounding concrete. It is treated as the imaginary time of the second phase of the degradation process. The formation of a tight layer of corrosion products is an equivalent of accepting the evolution of volume change in concrete cover in accordance with the equation (3) V eff= V ekw. This phase of concrete cover degradation is the third and the last stage of the process of concrete cover degradation. This stage is observed when τ τu and β parameter is zero. The exemplary linear function of degradation β that is applied in this paper, can be expressed in the form of the following expression [17]: The value τ0 can be determined from the Faraday’s law as the time necessary to fill pores in the ITZ layer. The time τu is the parameter that must be determined experimentally. 3. THE COMPUTATIONAL MODEL The analysis of fracture was made using ATENA system. The elastic-plastic-brittle model of concrete implemented in this system uses the Rankine surface for fracturing description: where fti is tensile strength in the material direction i. In other situations, the fracture of concrete is defined by Menetrey-Williams failure surface where ξ , ρ, θ – are Heigh-Vestergard coordinates, fc – material resistance to compression, ft – material resistance to tension, e – a parameter defining a shape of the failure surface. Kinetics of the electrode process was described using the function of corrosion current density obtained on the basis of a few years of empirical research [10], where icorr is the density of corrosion current (μA/cm2) , Cfc – the concentration of free chlorides on the rebar surface (kg/m3) , T – the temperature on the rebar surface (K), Rc,res – electrical resistance of concrete (Ω), t – time of exposition (year) . Electrical resistance of concrete in the form of empirical relationship of relative humidity φ (1), [19] was also included in that equation: C I V I L E N G I N E E R I N G ce 4/2017 A R C H I T E C T U R E C I V I L E N G I N E E R I N G E N V I R O N M E N T 109 ( )( ) ( ) ( ) I k V V V V V