PSI - Issue 33

Francesco Freddi et al. / Procedia Structural Integrity 33 (2021) 371–384 Author name / Structural Integrity Procedia 00 (2019) 000–000

372 2

due to the corrosion process, heavily affects the serviceability and the durability of the structures rising important safety issues (Bertolini et al., 2013; Bossio et al., 2019; Fernandez et al., 2016; Sun et al., 2020). In fact, due to corrosion, the cross section of the reinforcement bars is progressively reduced, affecting the bearing capacity and the ductility of the structure. Additionally, due to the oxidation process, residual materials are formed, and the volume occupied by the reinforcement increases. Therefore, the swelling of rebar creates pressure buildups on the surrounding concrete which might lead to cracking and spalling phenomenon of the concrete cover. Numerous efforts have been made in the research of the corrosion effects on reinforced concrete structures. Extensive experimental tests have been performed in order to reproduce and investigate the corrosion process (Andrade et al., 1993; Choe et al., 2020; Nguyen et al., 2011; Ouglova et al., 2008; Verma et al., 2014) to cite a few. From the experimental data, analytical models have been developed to describe various aspect of the degradation process. Models for the cracking phenomena due to the volume expansion of the corroded reinforcement bars are presented in (Andrade et al., 1993; Imperatore & Rinaldi, 2019; Lin et al., 2017), whereas in (Imperatore et al., 2017; Ou et al., 2016) relationship between the corrosion state and the degradation of material properties are proposed. The effects of corrosion on reinforced concrete structures have also been investigated via predictive numerical models. In (Ansari et al., 2018; Clarelli et al., 2014; Mai et al., 2016; Sheng & Xia, 2017) models for the metal corrosion are presented and simulations of the cracking phenomena in the concrete cover has been performed in (Lin et al., 2010; Molina et al., 1993; Richard et al., 2010, 2016; Zhang & Su, 2020). A predictive model capable to reproduce the carbonation corrosion cover cracking phenomenon in RC coupled with phase-field approach to brittle fracture is presented. First, the concrete carbonation process is described. A reaction diffusion system of equations is used to describe the penetration and the chemical effects of the air pollutants to the concrete cover (Bonetti et al., 2019, 2021; Giavarini et al., 2008; Isgor & Razaqpur, 2004; Papadakis et al., 1991). As the carbonation front reaches the reinforcement bars, a generalized corrosion process occurs (Isgor & Razaqpur, 2006; Popov, 2015). Oxidation products form and the associated volumetric expansion is used as loading condition in the elasticity problem, where the damage in the concrete cover is described. Here, damage evolution is modelled via the phase-field approach to brittle fracture (Bourdin et al., 2000), where two-field energy functional (displacement and damage) allows to determine the formation and evolution of the cracks within the material. The versatility of the method to replicate a wide variety of failure modes such as asymmetric behavior (Amor et al., 2009; Freddi & Royer-Carfagni, 2010, 2011), shear fracture (Alessi et al., 2020; Lancioni & Royer Carfagni, 2009), cohesive (Freddi & Iurlano, 2017) and ductile (Alessi et al., 2014, 2015; Freddi & Royer Carfagni, 2014, 2016) materials, made it the best candidate to reproduce the cover cracking phenomena in corroded beams. The carbonation and corrosion processes are coupled with the phase-field approach to keep into account the alteration phenomena due to damaging process. After validation against experimental data, numerical simulations are performed to reproduce the cracking process of corroded RC beams.

Nomenclature [i] concentration of the i-th species [mol/mm 3 ] carbonation state of the concrete ( ) concrete porosity as a function of the carbonation state f volume fraction of pores corresponding to the liquid phase � volume fraction of the pores occupied by the film of water ��� diffusion coefficient of the carbon dioxide [mm 2 /day] r n neutralization reaction rate RH relative humidity H Henry constant for the dissolution of CO 2 (g) in water (34.2∙10 universal gas constant (8.2057∙10 4 [mm 3 ∙atm / K∙mol])

-9 [mol/mm 3 ] at 25°C)

R T

absolute temperature [K]

k 2

rate constant of reaction of CO2 and OH- (8.3∙109 [mm3 / mol∙s])

[OH - ] d i ( ) material modulation functions E � eq molar concentration of OH

- at equilibrium (43.2∙10 -9 [mol/mm 3 ] at 25°C)

standard electric potential of the semi-reaction [V]