Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Numerical and Empirical Models for Service Life Assessment of RC Structures in Marine Environment

Numerical and Empirical Models for Service Life Assessment of RC Structures in Marine Environment The service life prediction of reinforced concrete (RC) structures in marine environment is essential in structural repair and health monitoring. In this paper, a numerical model for predicting the service life of reinforced concrete is first developed which considering the time-varying boundary of chloride concentration, critical chloride concentration and density of corrosion current. Based on the model, the effects of water–cement ratio, reinforcement diameter, concrete cover thickness and critical chloride ion concentration on the service life and deterioration duration of RC structures are investigated. The key factors affecting the service life of reinforced concrete structures are determined. More importantly, based on regression analysis, a new simplified empirical model for predicting the service life of RC structures is also developed. It provides a fast assessment tool for practical engineers. Both the numerical model and empirical model validated are suitable for practical engineering applications. The results show that with the increase of water–cement ratio, the service life of reinforced concrete structure decreases exponentially. And with the increase of the thickness of the concrete cover, the service life, deterioration duration, and safety reserve increase linearly. How- ever, the influence of the diameter of the reinforcing bar on the service life can be ignored. Keywords: service life prediction, RC structures, chloride diffusion, critical chloride value, corrosion current density 1 Introduction for marine projects, predicting the service life of the RC Reinforced concrete (RC) structures are widely used in structure in marine environment has become an impor- normal construction projects, such as tall buildings (Fu, tant design task for design engineers. The accurate pre - 2018, 2021) and bridges (Fu, 2015, 2016) offshore bridges, diction enables effective health monitoring and timely subsea tunnels, and harbour projects (Pillai et  al., 2019; retrofitting of marine projects in their service life Xu et al., 2019), and for these types of projects, chloride (Bouteiller et al., 2016; Dhandapani et al., 2018). Even for ingress due to marine environment is one of the main projects under construction, service life prediction can factors causing the corrosion of steel bars (Chang et  al., provide important guidelines for designers. 2020; Marks et  al., 2015). However, serious corrosion of Chloride ingress is particularly problematic to con- steel bars causes the deterioration of structural capac- crete (Nogueira et  al., 2012; Shaikh, 2018). Driven by ity, causing serious challenges to the durability of RC the concentration difference, chloride ions and oxygen structures (Alexander & Beushausen, 2019). Therefore, in the marine environment diffuse into the interior of concrete through its pores. Unfortunately, once the chlo- ride concentration on the steel surface reaches the criti- cal value, the passivation film on the steel surface will be *Correspondence: feng.fu.1@city.ac.uk College of Civil Engineering and Architecture at Guilin University destroyed. Consequently, the steel reinforcement mem- of Technology, Guilin 541004, China bers encased are subject to corrosive damages (Guo et al., Full list of author information is available at the end of the article 2004). This erosion of the steel can cause a reduction in Journal information: ISSN 1976-0485 / eISSN 2234-1315 © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 2 of 12 the RC structures’ ability to resist tensile stresses. Hence, The life cycle performance of reinforced concrete struc - chloride ingress induced reinforcement corrosion is one tures after reinforcement corrosion is rarely concerned of the main factors affecting the durability of concrete in the existing service life models (Pan et al. 2015). Most structures and at present, many scholars have carried out importantly, most of the existing models calculated the extensive research on this issue. Stambaugh et  al. (2018) service life of RC structures by solving complex partial used the critical value of chloride ion concentration on differential equations, which greatly increases the com - the surface of steel bars as the service life assessment putational cost and is difficult to use in practical engi - standard and studied the service life of RC structures neering. Moreover, the chloride concentration at the in marine environments under different circumstances boundary of concrete is time-dependent rather than con- such as the location and the mix ratio (Jung et  al., 2018; stant, which will directly affect the distribution of chlo - Khanzadeh-Moradllo et al., 2015; Mir et al., 2019). How- ride in concrete. ever, they assumed that the chloride ion concentration on Therefore, the focus of this research is to address above the concrete surface was constant and did not consider issues. The main purpose of this research is to establish the time-varying characteristics of the chloride ion con- a practical models for practising engineers, allowing centration on the surface (Huan et  al., 2015; Yang et  al., them to use easily quantifying engineering parameters 2017). Muthulingam et  al., (2014) established a service for predicting the service life of RC structures. Firstly, a life prediction model by considering the influence of complex numerical model to predict the service life of wet-heat–diffusion coupling and the time-varying char - RC structures is established by diffusion-corrosion the - acteristics of the chloride concentration at the boundary. ory. The model verifications show that both the chloride However, the model requires too many input parameters, ion concentration and service life predictions agree well so it is not practical. It can only predict the moment with the measured values. Secondly, based on proposed when the steel bar begins to rust, but it cannot predict model, the influence of factors such as the thickness of when the RC structure will fail, that is, the failure life. the cover, the water–cement ratio, the critical value of Cao et al. (2014) and Zhu et al. (2017; Zhang et al., 2019) chloride ion concentration, and the diameter of the rein- established a mechanical model to predict the service life forcement on the service life of the RC structure are ana- of RC structures. It is based on analysis of the corrosion lysed. Finally, through a two-stage regression simulation mechanism of steel bars considering the thickness of con- of the service life of RC structures under 300 different crete cover (Enright & Frangopol, 1998), the critical value conditions, an empirical model for predicting the service of the chloride concentration (Bastidas-Arteaga et  al., life of RC structures is established. By comparing with 2009; Enright & Frangopol, 1998), and the chloride dif- the numerical simulation results, the empirical model is fusion coefficient (Pack et  al., 2010). Zheng et  al. (2009) in good agreement with the numerical model. The mod - also developed a numerical model to assess the influ - els proposed in this paper provide important theoretical ence of ITZ on the steady-state chloride diffusion. Based support for life assessment of existing projects and opti- on the finite difference method of Crank Nicolson, Song mization of service life design of projects to be built. et  al. (2009) and Petcherdchoo et  al. (2015) studied the effect of retrofitting agents on the service life of RC struc - 2 Theoretical Background tures. Jones et  al. studied the effectiveness of using filler 2.1 Chloride Diffusion Model to repair concrete cracks on prolonging the service life After decades of theoretical and experimental research of RC structures. These studies show that when micro- by many scholars (Hobbs, 1999; Wang et al., 2018, 2019; cracks appear on the surface of concrete, repair agents Zeng, 2007; Zheng et al., 2018), the diffusion of chloride can greatly prolong the service life of RC structures. Fur- ions in concrete in line with Fick’s second law has become thermore, Attari et  al. established a failure probability a widely used. And the governing equation for the diffu model for RC structures. In these studies, when the fail- sion of chloride ions in concrete is expressed as: ure probability reached 10%, the RC structure is consid- ered to have reached the service life, and the cracks in the dc ∂c ∂c ∂c ∂c = D + D , c c (1) RC structure have reached an acceptable limit. dt ∂x ∂x ∂y ∂y Although many service life prediction models for RC where c is chloride ion concentration (mass ratio of chlo- structures have been developed, there are still many chal- ride ion to concrete, %), D is chloride ion diffusion coef - lenges that have not been resolved. For example, most of ficient (m /s), respectively. the existing models only use the critical chloride concen- tration as the basis for predicting service life. However, the critical chloride concentration is only the indication of beginning of steel bar corrosion (Zhao, et  al., 2011b). Presuel F.J.(2016) Huan J. Z.(2015) Oslakovic I. S.(2010) Meira G. .(2007) Tang L. P (2003) LNEC E465 (2007) Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 3 of 12 2.1.1 Chloride Diffusion Coefficient 3.0 It can be seen from Eq.  (1) that the chloride ion diffu - 2.5 sion coefficient is a key parameter that determines the diffusion rate of chloride ions in concrete. The chloride 2.0 ion diffusion coefficient is not only related to the factors 1.5 such as concrete types, pore structure, water–cement 1.0 ratio, hydration degree, etc., but also to the external envi- ronment, such as temperature (Bažant & Najjar, 1972), 0.5 humidity (Muthulingam & Rao, 2014), current time 0.0 (Zeng, 2007). However, to simplify it, in this paper, the chloride ion diffusion coefficient is calculated with only considerations of the effects of water–cement ratio, tem - perature, humidity, and aging. Its expression is (Muthul- Fig. 1 Statistics of surface chloride ion concentration. ingam & Rao, 2014; Chen et al., 2019): −1 2.75 4 m 2 × ϕ D p U 1 1 (1 − h) t p c ref D = · exp − · 1 + · , 2.75 (2) 1.75 R T T (1 − h ) t ϕ 3 − ϕ + n 1 − ϕ ref p p Temperature Curing age Humidity Water - cement ratio Stipanovic Oslakovic et  al. 2010). It can be seen from where U is the activation energy for chloride ion diffu - Fig.  1 that the surface chloride ion concentration ranges sion, t is the average exposure time, R is the gas con- ref from 0.1% to 2.5%. There are many factors that affect the stant, T is the absolute ambient temperature, h is ref chloride ion concentration on the concrete surface, such humidity, h is critical humidity (0.75), D is the diffu - c p as temperature, humidity, cement type, and water-binder sion coefficient of chloride ions in water, n is an empirical ratio. Yang et al. (2019) obtained the regression equation constant (using 14.44 as reference (Du, et al., 2014)), m is of surface chloride ion and time function through regres- the time decay index, and f is the porosity of the cement sion analysis of 372 sets of surface chloride ion concen- slurry, respectively. f can be expressed as (Chen, et  al., tration data. It is worth noting that Eq.  (5) is based on 2021): the test results of ordinary Portland concrete. Therefore, w/c − 0.17α Eq.  (5) is only applicable to ordinary Portland concrete, ϕ = , p (3) but not to special concrete, such as fly ash concrete, slag w/c + 0.32 concrete, etc.: where is the degree of hydration of cement slurry, and 5.3t w w/c is water to cement ratio, respectively. The value of C (t) = × . (5) 1 + 0.7047t c the degree of hydration of cement slurry α in formula (3) can be calculated by: α = 1 − exp (−3.15 × w/c). (4) 2.2 Rebar Corrosion 2.2.1 Critic al Chloride Ion Concentration 2.1.2 Surface Chloride Ion Concentration Chloride ions accumulate on the surface of the steel bars The surface chloride ion concentration on the concrete over the time. When the concentration of chloride ions is another key factor affecting the chloride ion concen - on the surface of the steel bars reaches certain value, the tration inside the concrete. In the numerical solution, steel bar begins to corrode. This value is called the criti - the surface chloride ion concentration is also called the cal chloride ion concentration. The critical chloride ion boundary condition. In the marine environment, chlo- concentration indicators include free chloride ion con- ride ions are transmitted to the surface of offshore engi - centration, total chloride ion concentration, and the ratio neering concrete structures through the flow of the air, of free chloride ion concentration to hydroxide concen- and then diffuse into the concrete through the pores of tration (Cao et al., 2019). In this paper, the total chloride the concrete (Yang, et al., 2017). Fig. 1 shows statistics of ion concentration is used as an index to measure the chloride ion concentration on the surface of marine engi- critical chloride ion concentration. Due to the differences neering concrete structures in different coastal areas by in the measuring methods and the discrete type of con- different scholars (Huan et  al., 2015; Meira et  al., 2007; crete materials, the critical chloride ion concentration Surfacechlorideconcent % Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 4 of 12 0.25% ln 1.08i = 7.89 + 0.7771 ln (1.69c ) − − 0.000116R , corr t c (7) 0.20% where i is the corrosion current density, c is total corr t chloride ion concentration, and R is resistance of the 0.15% concrete cover, respectively. The empirical formula given by Liu et  al. (1998) for Averagevalue=0.10098% 0.10% resistivity of concrete cover is: ln R = 8.03 − 0.549 ln (1 + 1.69c ). c t (8) 0.05% 2.3 Determination of Service Life 0.00% 05 10 15 20 25 30 35 40 45 50 In general, when the chloride ion concentration on the Data index surface of the steel bar reaches the critical chloride ion Fig. 2 Statistics of critical chloride ion concentration. concentration, the marine engineering concrete structure is considered to have reached the service life. The limit state function at this stage can be expressed as: cannot be determined at present. The critical chloride ion concentration currently reported is between 0.079% G (c, t) = C − C(max, t), 1 cri (9) and 0.2% (Zhao, et  al., 2011a). The critical chloride ion where G (c, t) is the limit state function, c is the critical 1 cri concentration from 51 existing literature is collected in chloride ion concentration, and c(max, t) is the maximum this paper. Their statistical distribution is shown in Fig.  2. chloride ion concentration on the steel bar surface at the From Fig. 2, the critical chloride ion concentration distri- ingress time of t, respectively. bution is relatively scattered. Therefore, the mean value It is worth mentioning that when the maximum chlo- of 0.10098% is used in this paper as the critical chloride ride ion concentration on the surface of the steel bar ion concentration. reaches the critical chloride concentration, the offshore engineering concrete structure does not fail, and only the 2.2.2 Corrosion Current Density steel bars begin to rust (Zhao, et  al., 2011a; Zhao et  al., The chloride ion concentration is not constant across the 2016). The radial expansion stress is developed during whole volume of concrete. The chloride ion concentration the corrosion process. When the radial expansion stress near the erosion surface is high, and the chloride ion con- starts to cause damage to the concrete cover, the cover centration away from the erosion surface is low (Pan, et al., will crack and peel, and the structure will fail (Zhao, 2015). Therefore, the chloride ion concentration on the sur - et al., 2011b). In this paper, it is called the structural fail- face near the cover first reaches the critical chloride ion con - ure life. The limit state function can be expressed as: centration, and the passivation film was damaged (Li, et al., 2019). Research in literature (Cao, 2014) shows that there is G (lim, t) = ρ − ρ(lim, t), (10) 2 cr a potential difference between the active area formed after where ρ is the steel rebar erosion rate at failure of the cr the passivation film on the steel bar is damaged and the inert structural concrete (%), it is calculated as: area where the passivation film is not damaged, and a mac - roscopic electrochemical corrosion is formed. At the same 2(δ + δ ) 1 2 ρ = , time, there is also a micro-corrosion current, the total cor- cr (11) rosion current density can be expressed as (Zhu & Zi, 2017): where δ is the depth of rust generated by filling the pores i = i + i , corr mic mac (6) in the transition zone between the steel bar and con- crete at the interface between the corrosion products is where i is the total corrosion current density, i is corr mic 12.5 µm; δ is the depth of rust producing radial pressure, the micro-battery corrosion current density, and i is 2 mac it is worked out based on the theory of thick-walled cyl- the macro-battery corrosion current density, respectively. inders (Xu, et al., 2019b), and can be expressed as: At present, many empirical, theoretical, and numerical models have been established to calculate the corrosion r (r + c) + r c 0 0 current density of steel bars. In this paper, the Probabil- 0 δ = + v · 0.3 + 0.6 · f , 2 c t 2 2 E 2r istic mode of Papakonstantinou et  al. (2013) is adopted, (r + c) − r c 0 0 with the expression: (12) Chlorine concentrationthreshold Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 5 of 12 2π 2π where r is the reinforcement radius (mm), v is the Pois- 0 c ρ ∫ u(θ, t)dθ ∫ u(θ, t)dθ 0 0 ρ(lim, t) = × 100% = × 100% . 2 2 son’s ratio of the concrete cover, E is elastic modulus c ρ · π · r π · r 0 0 of concrete (MPa), and f is tensile strength of concrete t (15) (MPa), respectively. In summary, the flowchart of service life prediction for ρ(lim, t) is the corrosion rate of steel bars at time t (%). RC structures is shown in Fig. 3. According to Faraday’s law, the distribution of corro- sion depth u (θ , t) around steel bars can be expressed as 3 Numerical Model Validation (Alexander & Beushausen, 2019; Chen et al., 2019; Zhang The numerical model proposed in this paper comprises et al., 2019): two stages modelling. The first stage is the diffusion of t chloride ions, and the second stage is the corrosion of u (θ, t) = ∫ 0.0116 · i (θ, t)dt. corr (13) steel bars. Therefore, the model verification in this sec - tion is also divided into two aspects: chloride ion diffu - The mass loss of rebar can be expressed as: sion verification and service life. The parameters used in the simulation are listed in Table  1. In the process of 2π numerical simulation, the finite difference method (FEM) M = ρ ∫ u θ, t dθ, ( ) S s d (14) is adopted to solve the chloride ion diffusion equation 3 (Eq. 1) to obtain the distribution of chloride ion concen- where ρ is the density of the rebar (kg/m ). tration in concrete. Once the chloride concentration on So: Fig. 3 The flowchart of the derivation of the proposed multiphase numeric model. Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 6 of 12 Table 1 Numerical simulation parameters. thickness of the concrete cover is 50  mm and 60  mm, and the water–cement ratio is selected as 0.55. In addi- Symbol Parameter value Mean tion, the concrete is saturated, i.e. the relative humid- U 44.6 [K J/mol] The activation energy for chloride diffu- ity is 1. The average temperature of the environment is sion 293 K. Reinforcement diameter is 10 mm. Fig.  5 shows t 28 [d] Reference time of chloride ingress ref the comparison of the service life of the three models; it R 8.314 [J/K mol] The gas constant can be seen that the differences in the service life pre - h 0.75 [–] The critical humidity dictions of the three models are small, which indicates h 1 Humidity that the numerical model established in this paper has a −10 D The diffusion coefficient of chloride in p 1.07 × 10 [m /s] certain degree of reliability. water m 0.2 The time decay index of chloride diffu- 4 Parametric Analysis Using the New Numerical sion Model ρ 7500 [kg/m ] The density of the rebar Using the proposed numerical model, intensive paramet- T 293 [K] Reference temperature ref rical studies are made, which are show as follows. δ 12.5 µm The depth of rust generated by filling the pores r 8–13 mm The reinforcement radius 0 4.1 Influence of Different Water–Cement Ratios E 30 [GPa] Elastic modulus of concrete c The water–cement ratio for different concrete strength f 1.43 [MPa] Tensile strength of concrete t grades is different. However, different water–cement v 0.2 The Poisson’s ratio of the concrete ratio has great influence on the chloride diffusion coeffi - c 40–70 mm Thickness of reinforced concrete cover cient and the chloride ion concentration on the concrete w/c 0.45, 0.55, 0.65 The water-to-cement ratio surface, especially for the chloride diffusion coefficient (Ishida, et  al., 2009). Therefore, the water–cement ratio has a very important influence on the durability of RC the steel surface reaches the critical chloride concen- structures (Pack et al., 2010). Fig. 6a shows the service life tration, the concrete structure will reach its service life. of RC structures in the marine environment as a func- Secondly, the steel corrosion rate is calculated through tion of water–cement ratio. It can be seen from Fig.  6a Eq. (15). Once the steel corrosion rate reaches the critical that the water–cement ratio has a very important effect steel corrosion rate, the concrete structure will reach its on the service life of the marine engineering concrete failure life. structure. For example, when the water–cement ratio is 0.36, the service life is 46.1  years. However, when the 3.1 Chloride Diffusion Verification water–cement ratio is increased to 0.55, the service life The experimental data of Chalee et  al. (2009) will be is only 6.3 years. Therefore, in marine engineering, using used to compare with the numerical simulation in this a low water–cement ratio can effectively increase the paper. The size of the concrete cube specimen was service life of the structure. Besides, Fig.  6a also shows 200  mm × 200  mm × 200  mm, and the water–cement the relationship between the deterioration duration ratio was 0.45, 0.55, 0.65. And the concrete is immersed and the water–cement ratio. The deterioration dura - in seawater, which indicates that the concrete is satu- tion also decreases exponentially as the water–cement rated. Therefore, relative humidity of the concrete is 1 ratio increases. Moreover, as the water–cement ratio in numerical simulation. In addition, the average value increases, the safety reserve decreases more slowly. The of the external ambient temperature is 293 K. The com - larger the water–cement ratio is, the longer the safety parison between numerical simulation results and test reserve period is, and the safety reserve period varies results is shown in Fig.  4. Obviously, the chloride con- from 5.8  years to 9.8  years. Fig.  6b shows the change of centration curve obtained by numerical simulation is the maximum chloride ion concentration on the surface very close to that obtained by experiment, which indi- of the steel bar with time under different water–cement cates that the chloride diffusion model is reliable. ratios. It can be seen from Fig.  6b that under the same ingress time, as the water–cement ratio increases, the chloride ion concentration gradually decreases. For 3.2 Service Life Verification example, when the water–cement ratio is 0.55, the maxi- The service life prediction model proposed in this mum chloride ion concentration on the surface of the paper is compared with Moraddllo et  al. (2012) and steel bar increased rapidly within 0 to 20 years, and then Aruz et  al. (Petcherdchoo & Chindaprasirt, 2019). The increased slowly. Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 7 of 12 (a) (b) 6 6 W. Chalee'sexperiment W. Chalee's experiment 5 NumericalSimulation NumericalSimulation 3 3 Distance fromsurface (mm) Distance fromsurface (mm) (c) (d) W. Chalee'sexperiment W. Chalee'sexperiment NumericalSimulation 5 Numerical Simulation 2 2 1 1 0 0 020406080100 020406080100 Distance from surface (mm) Distance fromsurface (mm) Fig. 4 Chloride diffusion verification: a w/c = 0.65, time = 2 years. b w/c = 0.65, time = 5 years. c w/c = 0.5, time = 5 years. d w/c = 0.45, time = 5 years. 4.2 Thickness of Concrete Cover The thickness of the concrete cover is an important parameter for structural design. For different environ - ments, the requirements for the thickness of the concrete cover are different in the Code for durability Design of concrete structures. Therefore, it is necessary to study the effect of concrete cover thickness on service life. Fig.  7a shows the values of three indicators of service life, fail- ure life, and safety reserve under different concrete cover thicknesses. It can be seen from Fig.  7a that with the increase of the concrete cover thickness, the service life, deterioration duration and safety reserve all increase. For example, when the thickness of the cover is 40  mm, the service life is only 15.2  years. However, when the thick- ness of the concrete cover increased to 70  mm, the ser- Fig. 5 Service life verification. vice life increased to 55.7 years, which was an increase of - - Cl (%by weight of binder) Cl (%by weight of binder) - Cl (%by weight of binder) Cl (%by weight of binder) Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 8 of 12 (a)(b) Servicelife Service life 0.5% Failurelife Structural crackingtime Safety Safety reserv reservee 0.4% w/c=0.55 Crack w/c=0.50 0.3% w/c=0.45 w/c=0.40 0.2% w/c=0.36 Ccri C=Ccir 0.1% Ccri Ccir 0.0% 0.35 0.40 0.45 0.50 0.55 020406080100 Water-cementratio Exposure time (a) Fig. 6 Eec ff t of water–cement ratio on service life and chloride concentration distribution. a Service life. b Chloride concentration distribution. Fig. 7 Influence of concrete cover thickness on sand corrosion layer depth. a Service life. b Corrosion layer depth. 3.67 times compared to the 40 mm thickness of the con- crete cover. Further research found that with the increase of the thickness of the cover, the range of the change in the safety reserve period was small and had a linear relation- 42.1 ship with the thickness of the concrete cover. However, 37.1 35.9 deterioration duration increases greatly with the increase 32.2 30.7 of the thickness of the concrete cover. Fig.  7b shows the 27.9 25.7 depth of the corrosion of the steel bar when the cover is 21.2 cracked under different thicknesses of the concrete cover. It can be seen from Fig.  7b that the corrosion geomet- ric form of the steel bar with different cover thickness is similar, but the peak of the corrosion depth increases 6.7 6.5 6.4 6.2 with the thickness of the cover and increase. For instance, when the thickness of the concrete cover is 40  mm, the 0.08% 0.1% 0.12% 0.14% depth of rust is 82.3 µm, however, when the thickness of Chloride concentrationthreshold (%) the concrete cover is 70 µm, the depth of rust is 100.4 µm. Fig. 8 Eec ff t of critical chloride ion concentration on service life. Moreover, the corrosion depth curve of the steel bar in this paper is similar to the numerical model of Jinxia (Xia Time(a) Chlorideion concentration(%) Time (a) Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 9 of 12 et al., 2019), and this corrosion curve is similar to the cor- This is mainly because the service life mainly depends rosion mode of the entire steel bar observed through field on the critical chloride concentration and thickness exposure test experiments (Kessler et  al., 2016; Poupard of concrete cover. Additionally, as the diameter of the et al., 2006; Sun et al., 2002). steel bar increases, the deterioration duration and safety reserve both increases, but the upward trend is 4.3 I nfluence of Critical Chloride Ion Concentration also slight. For example, when the rebar diameter is The critical chloride ion concentration is another 16  mm, the deterioration duration and safety reserve important factor affecting the corrosion of steel bars. are 32.7  years and 6.4  years, respectively. And when For different types of steel bars, cement types and ser - the rebar diameter changes to 26  mm, the deteriora- vice environments, the critical chloride ion concentra- tion duration and safety reserve of the RC structure are tion is not same. The critical chloride ion concentration 34.6 years and 8.1 years, respectively. Fig.  9 also shows obtained by many scholars has a very large value (Cao, the corrosion rate of steel bars when the structure fails et al. 2019, Zhang, et al. 2019). Therefore, in this section, under different the rebar diameters. It is worth men - the influence of different critical chloride ion concentra - tioning that as the rebar diameter increases, the cor- tions on the service life of RC structure is studied with a rosion rate of the rebar decreases significantly. For water–cement ratio of 0.4. As shown in Fig. 8, as the criti- example, when the rebar diameter is 16  mm, the cor- cal chloride ion concentration increases, both the service rosion rate of the rebar is 0.382%; however, when the life and the deterioration duration of the RC structure rebar diameter is 26  mm, the rebar corrosion rate is increase. More importantly, it turns out that the critical only 0.241%. chloride ion concentration has a linear relationship with the service life, which is consistent with the results of Muthulingam et al. (2014). For instance, for every 0.01% 5 A Simplified Empirical Model for Service Life increase in the critical chloride ion concentration, the RC Prediction structural service life increases by 2.5 years. According to the discussion in Sect. 4, it can be seen that the rebar diameter has a small effect on the service life of 4.4 E ec ff t of Rebar Diameter the structure. And the thickness of the cover, the water– For different types and functions RC structures, the cement ratio and the critical chloride ion concentration rebar diameter in the RC structure is also different. all have significant impact on the service life of the con - Therefore, it is of great significance to study the impact crete structure. The cover thickness and water–cement of the rebar diameter on the service life of marine RC ratio are important parameters in engineering design. structures. Fig.  9 shows a histogram of the service life, Therefore, in this paper, 300 groups RC structures with failure life, and safety reserve of marine RC structures different water–cement ratios, concrete cover thick - in the range of rebar diameters from 16 to 26  mm. It ness are simulated to predict their service life. These 300 can be seen from Fig.  9 that the influence of the rebar groups of data are divided into two categories: first, the diameter on the service life could be ignored (e.g., the thickness of the cover—40 mm, 45 mm, 50 mm, 55 mm, difference between the maximum and the minimum 60  mm, 70  mm, and the water–cement ratios 0.36, 0.40, service life for different rebar diameter is only 0.5 year). 0.50, and 0.55. Second, the cover thickness is 65 and the water–cement ratio is 0.45 as a control group. A two- stage data fitting and regression analysis method are used to establish an empirical service life prediction model. In 50 0.5% the first stage, the functional representing the relation - ship between the thickness of the cover and the service 40 0.4% life is obtained through regression analysis, as shown in 34.6 34.0 33.3 32.7 32.9 formula (16), where A and B is the undetermined coef- 30 0.3% 26.6 ficient related to water–cement ratio. In the second stage, 26.4 26.3 26.5 26.4 through regression analysis, the relationship between 20 0.2% the undetermined coefficients A and B and the water– cement ratio is obtained, as shown in formula (17): 10 0.1% 8.1 7.6 6.8 6.4 6.7 f (w/c, cd) = A + B × cd, (16) 0 0.0% 16 18 20 22 26 where A and B are fitting parameters; wc is water– Reinforcement diameter(mm) cement ratio; cd is the thickness of concrete cover: Fig. 9 Eec ff t of rebar diameter on service life. Time (a) Corrosion rate of reinforcement(%) Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 10 of 12 (a)(b) 30 Numerical Simulation Numerical Simulation Proposed model Proposed model 0 0 0.35 0.40 0.45 0.500.55 35 40 45 50 55 60 65 70 Water-cement ratio Concrete cover thickness mm Fig. 10 Validation of practical service life prediction model. a Cover thickness = 65 mm. b Water–cement ratio = 0.45. life is 46.1 years. However, when the water–cement 326w/c f (wc, cd) =− 4.0 + exp − + 10.364 ratio is increased to 0.55, the service life is only 6.3 years. 2 137w/c + + exp − + 6.945 × cd. (2) With the increase of the thickness of the concrete 11 8 cover, the service life, failure life, and safety reserve (17) all linear increase. Thickness of corrosion layer with However, in the process of numerical simulation, we different cover thickness is similar, but the peak of assume that the ambient temperature is 293  K and the the corrosion depth increases with the thickness of concrete is saturated. Therefore, the applicable condi - the cover increase. tion of formula (17) is saturated concrete with an ambi- (3) As the critical chloride ion concentration increases, ent temperature of 293 K. both the service life and the deterioration duration Fig.  10 shows the comparison between the service of the RC structure increase. More importantly, it life prediction model proposed in this paper and the turns out that the critical chloride ion concentra- numerical simulation results. It can be found that the tion has a linear relationship with the service life. numerical simulation results are distributed near the (4) The influence of the rebar diameter on the service prediction model curve, which indicates that the pro- life can be ignored. It is worth mentioning that as posed model in this paper is reliable. the rebar diameter increases, the corrosion rate of steel bars decreases significantly. 6 Conclusion (5) Various factors (water–cement ratio, protective In this paper, both numerical and empirical mod- layer thickness, rebar diameter, etc.) have a small els for predicting the service life of RC structures in impact on the safety reserve period. The safety the marine environment are proposed. The proposed reserve period of RC structure is generally less than numerical analysis model not only considers the service 10 years. life of RC structures, but also the deterioration dura- (6) Through regression analysis of 300 sets of simula - tion. Moreover, the effects of water–cement ratio, rebar tion data, the proposed empirical forecasting model diameter, concrete cover thickness and critical chloride has good reliability in the service life prediction of ion concentration on the service life and deterioration RC structures and is suitable for practical engineers. duration of RC structures are comprehensively ana- lysed, and the key factors affecting the service life of RC Acknowledgements structures are determined. The following conclusions The authors appreciate the financial supports from the National Natural can be drawn: Science Foundation of China (No. 51968014, 52078509, 51968013), Guangxi Key Laboratory of New Energy and Building Energy Saving Foundation (No. 19-J-21-4, 19-J-21-8), and Guangxi Universities Scientific Research Project (1) With the increase of water–cement ratio, the ser- (2020KY06029). vice life of RC structure decreases exponentially. When the water–cement ratio is 0.36, the service Service life (a) Service life (a) Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 11 of 12 Authors’ contributions Chalee, W., Jaturapitakkul, C., & Chindaprasirt, P. (2009). Predicting the chloride XC: writing—original draft preparation, data curation, writing, conceptualiza- penetration of fly ash concrete in seawater. Marine Structures, 22(3), tion, methodology, investigation. FF: writing—original draft preparation, 341–353. https:// doi. org/ 10. 1016/j. marst ruc. 2008. 12. 001 writing—reviewing and editing, methodology, investigation. PC: validation, Chang, W., et al. (2020). Durability and aesthetics of architectural concrete software. YM: software, data curation. All authors read and approved the final under chloride attack or carbonation. Materials, 13(4), 839. https:// doi. manuscript.org/ 10. 3390/ ma130 40839 Chen, X., et al. (2019). Meso-numerical simulation of service life prediction for Authors’ information marine structures. Journal of Building Materials, 22(6), 894–900. https:// doi. Xuandong Chen MSc, lecturer, College of Civil Engineering and Architecture, org/ 10. 3969/j. issn. 1007- 9629. 2019. 06. 009 Guilin University of Technology, Guilin 541004, China; China. Guangxi Key Chen, X., et al. (2021). A multi-phase mesoscopic simulation model for the Laboratory of New Energy and Building Energy Saving, Guilin 541004, China; long-term chloride ingress and electrochemical chloride extraction. Guangxi Engineering and Technology Center for Utilization of Industrial Waste Construction and Building Materials, 270, 121826. https:// doi. org/ 10. 1016/j. Residue in Building Materials, Guilin, 541004, China.conbu ildmat. 2020. 121826 Yang Ming, MSc, Engineer, Guangxi Engineering and Technology Center for Dhandapani, Y., et al. (2018). Mechanical properties and durability perfor- Utilization of Industrial Waste Residue in Building Materials, Guilin, 541004, mance of concretes with Limestone calcined clay cement (LC3). Cement China. and Concrete Research, 107(March), 136–151. https:// doi. org/ 10. 1016/j. Feng Fu, PhD Associate Professor, School of Mathematics, Computer Science cemco nres. 2018. 02. 005 and Engineering, City, University of London, London EC1C,0HB U.K. (cor- Du, X., Jin, L., & Ma, G. (2014). A meso-scale numerical method for the simula- responding author). tion of chloride diffusivity in concrete. Finite Elements in Analysis and Ping Chen PhD, Senior Research Fellow, Guangxi Engineering and Technology Design, 85, 87–100. https:// doi. org/ 10. 1016/j. finel. 2014. 03. 002 Center for Utilization of Industrial Waste Residue in Building Materials, Guilin, Enright, M. P., & Frangopol, D. M. (1998). Probabilistic analysis of resistance 541004, China. degradation of reinforced concrete bridge beams under corrosion. Engineering Structures, 20(11), 960–971. https:// doi. org/ 10. 1016/ S0141- Funding0296(97) 00190-9 National Natural Science Foundation of China (No. 51968014, 52078509, Fu, F. (2015). Advanced Modeling Techniques in Structural Design. USA: Wiley. 51968013). Guangxi Key Laboratory of New Energy and Building Energy 978-1-118-82543-3. Saving Foundation (No. 19-J-21-4, 19-J-21-8). Guangxi Universities Scientific Fu, F. (2016). Structural Analysis and Design to Prevent Disproportionate Collapse. Research Project (2020KY06029). USA: CRC Press. 978-1-4987-0680-3. Fu, F. (2018). Design and Analysis of Tall and Complex Structures. UK: Butter- Availability of data and materials worth-Heinemann. 978-0-08-101121-8. All data that support the findings of this study are available from the cor - Fu, F. (2021). Fire Safety Design for Tall Buildings. England: Taylor Francis. responding author upon reasonable request. 978-0-367-44452-5. Guo, H., et al. (2004). Durability of recycled aggregate concrete—A review. Cement and Concrete Composites, 26(2), 97–98. https:// doi. org/ 10. 1016/ Declarations S0958- 9465(03) 00091-X Hobbs, D. W. (1999). Aggregate influence on chloride ion diffusion into con- Competing interests crete. Cement and Concrete Research, 29(12), 1995–1998. https:// doi. org/ The authors declare no competing interests. 10. 1016/ S0008- 8846(99) 00188-X Huan, X. U. E., Zuquan, J. I. N., & Xiaojie, W. (2015). Chloride ion penetration into Author details concrete exposed to marine environment for a long period. The Ocean College of Civil Engineering and Architecture at Guilin University of Tech- Engineering, 33(5), 60–65. https:// doi. org/ 10. 16483/j. issn. 1005- 9865. 2015. nology, Guilin 541004, China. School of Mathematics, Computer Science 05. 008 and Engineering, City, University of London, London EC1C 0HB, UK. Ishida, T., Iqbal, P. O. N., & Anh, H. T. L. (2009). Modeling of chloride diffusivity coupled with non-linear binding capacity in sound and cracked concrete. Received: 21 May 2021 Accepted: 14 January 2022 Cement and Concrete Research, 39(10), 913–923. https:// doi. org/ 10. 1016/j. cemco nres. 2009. 07. 014 Jung, S.-H., et al. (2018). Maintenance for repaired RC column exposed to chlo- ride attack based on probability distribution of service life. International Journal of Concrete Structures and Materials, 12(1), 22. https:// doi. org/ 10. References 1186/ s40069- 018- 0259-2 Alexander, M., & Beushausen, H. (2019). Durability, service life prediction, and Kessler, S., et al. (2016). Eec ff t of freeze–thaw damage on chloride ingress into modelling for reinforced concrete structures—Review and critique. concrete. Materials and Structures, 50(2), 121. https:// doi. org/ 10. 1617/ Cement and Concrete Research, 122, 17–29. https:// doi. org/ 10. 1016/j. s11527- 016- 0984-4 cemco nres. 2019. 04. 018 Khanzadeh Moradllo, M., Shekarchi, M., & Hoseini, M. (2012). Time-dependent Bastidas-Arteaga, E., et al. (2009). Probabilistic lifetime assessment of RC struc- performance of concrete surface coatings in tidal zone of marine envi- tures under coupled corrosion-fatigue deterioration processes. Structural ronment. Construction and Building Materials, 30, 198–205. https:// doi. org/ Safety, 31(1), 84–96. https:// doi. org/ 10. 1016/j. strus afe. 2008. 04. 001 10. 1016/j. conbu ildmat. 2011. 11. 044 Bažant, Z. P., & Najjar, L. J. (1972). Nonlinear water diffusion in nonsaturated Khanzadeh-Moradllo, M., et al. (2015). Eec ff t of wet curing duration on long- concrete. Matériaux Et Constructions, 5(1), 3–20. https:// doi. org/ 10. 1007/ term performance of concrete in tidal zone of marine environment. BF024 79073 International Journal of Concrete Structures and Materials, 9(4), 487–498. Bouteiller, V., Marie-Victoire, E., & Cremona, C. (2016). Mathematical relation of https:// doi. org/ 10. 1007/ s40069- 015- 0118-3 steel thickness loss with time related to reinforced concrete contami- Li, D., Wang, X., & Li, L. (2019). An analytical solution for chloride diffusion in concrete nated by chlorides. Construction and Building Materials, 124, 764–775. with considering binding effect. Ocean Engineering, 191, 106549. https:// doi. https:// doi. org/ 10. 1016/j. conbu ildmat. 2016. 07. 078 org/ 10. 1016/j. ocean eng. 2019. 106549 Cao, C. (2014). 3D simulation of localized steel corrosion in chloride con- Liu, Y., & Weyers, R.E. (1998). Modeling the time-to-corrosion cracking in chloride taminated reinforced concrete. Construction and Building Materials, 72, contaminated reinforced concrete structures. ACI Materials Journal 95(6). 434–443. https:// doi. org/ 10. 1016/j. conbu ildmat. 2014. 09. 030 https:// doi. org/ 10. 14359/ 410. Cao, Y., et al. (2019). Critical chloride content in reinforced concrete—An Marks, M., Glinicki, M. A., & Gibas, K. (2015). Prediction of the chloride resistance of updated review considering Chinese experience. Cement and Concrete concrete modified with high calcium fly ash using machine learning. Materi- Research, 117, 58–68. https:// doi. org/ 10. 1016/j. cemco nres. 2018. 11. 020 als, 8(12), 8714–8727. https:// doi. org/ 10. 3390/ ma812 5483 Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 12 of 12 Meira, G. R., et al. (2007). Chloride penetration into concrete structures in the marine Xu, Q., Shi, D., & Shao, W. (2019). Service life prediction of RC square piles based atmosphere zone—Relationship between deposition of chlorides on the wet on time-varying probability analysis. Construction and Building Materials, 227, candle and chlorides accumulated into concrete. Cement and Concrete Com- 116824. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 116824 posites, 29(9), 667–676. https:// doi. org/ 10. 1016/j. cemco ncomp. 2007. 05. 009 Yang, L., Cai, R., & Yu, B. (2017). Formation mechanism and multi-factor model for Mir, Z. M., et al. (2019). Enhanced predictive modelling of steel corrosion in concrete surface chloride concentration of concrete in marine atmosphere zone. Tumu in submerged zone based on a dynamic activation approach. International Gongcheng Xuebao/china Civil Engineering Journal, 50(12), 46–55. https:// doi. Journal of Concrete Structures and Materials, 13(1), 11. https:// doi. org/ 10. 1186/ org/ 10. 15951/j. tmgcxb. 2017. 12. 006 s40069- 018- 0321-0 Yang, L., Chen, C., & Yu, B. (2019). Multi-factor time-varying model of marine envi- Muthulingam, S., & Rao, B. N. (2014). Non-uniform time-to-corrosion initiation in ronmental action on concrete in splash zone. Journal of the Chinese Ceramic steel reinforced concrete under chloride environment. Corrosion Science, 82, Society, 11(47), 1566–1572. 304–315. https:// doi. org/ 10. 1016/j. corsci. 2014. 01. 023 Zeng, Y. (2007). Modeling of chloride diffusion in hetero-structured concretes by Nogueira, C., Leonel, E., & Coda, H. (2012). Probabilistic failure modelling of rein- finite element method. Cement and Concrete Composites, 29(7), 559–565. forced concrete structures subjected to chloride penetration. International https:// doi. org/ 10. 1016/j. cemco ncomp. 2007. 04. 003 Journal of Advanced Structural Engineering, 4(1), 10. https:// doi. org/ 10. 1186/ Zhang, K., et al. (2019). Analytical model for critical corrosion level of reinforcements 2008- 6695-4- 10 to cause the cracking of concrete cover. Construction and Building Materials, Pack, S. W., et al. (2010). Prediction of time dependent chloride transport in concrete 223, 185–197. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 06. 210 structures exposed to a marine environment. Cement and Concrete Research, Zhao, Y., et al. (2016). Non-uniform distribution of a corrosion layer at a steel/con- 40(2), 302–312. https:// doi. org/ 10. 1016/j. cemco nres. 2009. 09. 023 crete interface described by a Gaussian model. Corrosion Science, 112, 1–12. Pan, Z., Chen, A., & Ruan, X. (2015). Spatial variability of chloride and its influence https:// doi. org/ 10. 1016/j. corsci. 2016. 06. 021 on thickness of concrete cover: A two-dimensional mesoscopic numerical Zhao, Y., Hu, B., et al. (2011a). Non-uniform distribution of rust layer around steel bar research. Engineering Structures, 95, 154–169. https:// doi. org/ 10. 1016/j. engst in concrete. Corrosion Science, 53(12), 4300–4308. https:// doi. org/ 10. 1016/j. ruct. 2015. 03. 061corsci. 2011. 08. 045 Papakonstantinou, K. G., & Shinozuka, M. (2013). Probabilistic model for steel corro- Zhao, Y., Karimi, A. R., et al. (2011b). Comparison of uniform and non-uniform corro- sion in reinforced concrete structures of large dimensions considering crack sion induced damage in reinforced concrete based on a Gaussian description effects. Engineering Structures, 57, 306–326. https:// doi. org/ 10. 1016/j. engst ruct. of the corrosion layer. Corrosion Science, 53(9), 2803–2814. https:// doi. org/ 10. 2013. 06. 0381016/j. corsci. 2011. 05. 017 Petcherdchoo, A. (2015). Repairs by fly ash concrete to extend service life of Zheng, J. J., et al. (2018). A numerical algorithm for evaluating the chloride diffusion chloride-exposed concrete structures considering environmental impacts. coefficient of concrete with crushed aggregates. Construction and Building Construction and Building Materials, 98, 799–809. https:// doi. org/ 10. 1016/j. Materials, 171, 977–983. https:// doi. org/ 10. 1016/j. conbu ildmat. 2018. 03. 184 conbu ildmat. 2015. 08. 120 Zheng, J. J., Wong, H. S., & Buenfeld, N. R. (2009). ‘Assessing the influence of ITZ on Petcherdchoo, A., & Chindaprasirt, P. (2019). Exponentially aging functions coupled the steady-state chloride diffusivity of concrete using a numerical model. with time-dependent chloride transport model for predicting service life of Cement and Concrete Research, 39(9), 805–813. https:// doi. org/ 10. 1016/j. cemco surface-treated concrete in tidal zone. Cement and Concrete Research, 120, nres. 2009. 06. 002 1–12. https:// doi. org/ 10. 1016/j. cemco nres. 2019. 03. 009 Zhu, X., & Zi, G. (2017). A 2D mechano-chemical model for the simulation of Pillai, R. G., et al. (2019). Service life and life cycle assessment of reinforced concrete reinforcement corrosion and concrete damage. Construction and Building systems with limestone calcined clay cement (LC3). Cement and Concrete Materials, 137, 330–344. https:// doi. org/ 10. 1016/j. conbu ildmat. 2017. 01. 103 Research, 118, 111–119. https:// doi. org/ 10. 1016/j. cemco nres. 2018. 11. 019 Poupard, O., et al. (2006). Corrosion damage diagnosis of a reinforced concrete Publisher’s Note beam after 40 years natural exposure in marine environment. Cement and Springer Nature remains neutral with regard to jurisdictional claims in published Concrete Research, 36(3), 504–520. https:// doi. org/ 10. 1016/j. cemco nres. 2005. maps and institutional affiliations. 11. 004 Shaikh, F. U. A. (2018). Eec ff t of cracking on corrosion of steel in concrete. Interna- tional Journal of Concrete Structures and Materials, 12(1), 3. https:// doi. org/ 10. 1186/ s40069- 018- 0234-y Song, H. W., et al. (2009). Service life prediction of repaired concrete structures under chloride environment using finite difference method. Cement and Concrete Composites, 31(2), 120–127. https:// doi. org/ 10. 1016/j. cemco ncomp. 2008. 11. Stambaugh, N. D., Bergman, T. L., & Srubar, W. V. (2018). Numerical service-life modeling of chloride-induced corrosion in recycled-aggregate concrete. Construction and Building Materials, 161, 236–245. https:// doi. org/ 10. 1016/j. conbu ildmat. 2017. 11. 084 Stipanovic Oslakovic, I., Bjegovic, D., & Mikulic, D. (2010). Evaluation of service life design models on concrete structures exposed to marine environment. Materials and Structures/materiaux Et Constructions, 43(10), 1397–1412. https:// doi. org/ 10. 1617/ s11527- 010- 9590-z Sun, W., et al. (2002). Eec ff t of chloride salt, freeze–thaw cycling and externally applied load on the performance of the concrete. Cement and Concrete Research, 32(12), 1859–1864. https:// doi. org/ 10. 1016/ S0008- 8846(02) 00769-X Wang, Y., et al. (2018). Prediction model of long-term chloride diffusion into plain concrete considering the effect of the heterogeneity of materials exposed to marine tidal zone. Construction and Building Materials, 159, 297–315. https:// doi. org/ 10. 1016/j. conbu ildmat. 2017. 10. 083 Wang, Y., Gong, X., & Wu, L. (2019). Prediction model of chloride diffusion in concrete considering the coupling effects of coarse aggregate and steel reinforcement exposed to marine tidal environment. Construction and Building Materials, 216, 40–57. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 04. 221 Xia, J., et al. (2019). Numerical simulation of steel corrosion in chloride contaminated concrete. Construction and Building Materials, 228, 116745. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 116745 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Concrete Structures and Materials Springer Journals

Numerical and Empirical Models for Service Life Assessment of RC Structures in Marine Environment

Download PDF
12 pages

Loading next page...
 
/lp/springer-journals/numerical-and-empirical-models-for-service-life-assessment-of-rc-M1w4dvz0Is

References (57)

Publisher
Springer Journals
Copyright
Copyright © The Author(s) 2022
ISSN
1976-0485
eISSN
2234-1315
DOI
10.1186/s40069-022-00504-0
Publisher site
See Article on Publisher Site

Abstract

The service life prediction of reinforced concrete (RC) structures in marine environment is essential in structural repair and health monitoring. In this paper, a numerical model for predicting the service life of reinforced concrete is first developed which considering the time-varying boundary of chloride concentration, critical chloride concentration and density of corrosion current. Based on the model, the effects of water–cement ratio, reinforcement diameter, concrete cover thickness and critical chloride ion concentration on the service life and deterioration duration of RC structures are investigated. The key factors affecting the service life of reinforced concrete structures are determined. More importantly, based on regression analysis, a new simplified empirical model for predicting the service life of RC structures is also developed. It provides a fast assessment tool for practical engineers. Both the numerical model and empirical model validated are suitable for practical engineering applications. The results show that with the increase of water–cement ratio, the service life of reinforced concrete structure decreases exponentially. And with the increase of the thickness of the concrete cover, the service life, deterioration duration, and safety reserve increase linearly. How- ever, the influence of the diameter of the reinforcing bar on the service life can be ignored. Keywords: service life prediction, RC structures, chloride diffusion, critical chloride value, corrosion current density 1 Introduction for marine projects, predicting the service life of the RC Reinforced concrete (RC) structures are widely used in structure in marine environment has become an impor- normal construction projects, such as tall buildings (Fu, tant design task for design engineers. The accurate pre - 2018, 2021) and bridges (Fu, 2015, 2016) offshore bridges, diction enables effective health monitoring and timely subsea tunnels, and harbour projects (Pillai et  al., 2019; retrofitting of marine projects in their service life Xu et al., 2019), and for these types of projects, chloride (Bouteiller et al., 2016; Dhandapani et al., 2018). Even for ingress due to marine environment is one of the main projects under construction, service life prediction can factors causing the corrosion of steel bars (Chang et  al., provide important guidelines for designers. 2020; Marks et  al., 2015). However, serious corrosion of Chloride ingress is particularly problematic to con- steel bars causes the deterioration of structural capac- crete (Nogueira et  al., 2012; Shaikh, 2018). Driven by ity, causing serious challenges to the durability of RC the concentration difference, chloride ions and oxygen structures (Alexander & Beushausen, 2019). Therefore, in the marine environment diffuse into the interior of concrete through its pores. Unfortunately, once the chlo- ride concentration on the steel surface reaches the criti- cal value, the passivation film on the steel surface will be *Correspondence: feng.fu.1@city.ac.uk College of Civil Engineering and Architecture at Guilin University destroyed. Consequently, the steel reinforcement mem- of Technology, Guilin 541004, China bers encased are subject to corrosive damages (Guo et al., Full list of author information is available at the end of the article 2004). This erosion of the steel can cause a reduction in Journal information: ISSN 1976-0485 / eISSN 2234-1315 © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 2 of 12 the RC structures’ ability to resist tensile stresses. Hence, The life cycle performance of reinforced concrete struc - chloride ingress induced reinforcement corrosion is one tures after reinforcement corrosion is rarely concerned of the main factors affecting the durability of concrete in the existing service life models (Pan et al. 2015). Most structures and at present, many scholars have carried out importantly, most of the existing models calculated the extensive research on this issue. Stambaugh et  al. (2018) service life of RC structures by solving complex partial used the critical value of chloride ion concentration on differential equations, which greatly increases the com - the surface of steel bars as the service life assessment putational cost and is difficult to use in practical engi - standard and studied the service life of RC structures neering. Moreover, the chloride concentration at the in marine environments under different circumstances boundary of concrete is time-dependent rather than con- such as the location and the mix ratio (Jung et  al., 2018; stant, which will directly affect the distribution of chlo - Khanzadeh-Moradllo et al., 2015; Mir et al., 2019). How- ride in concrete. ever, they assumed that the chloride ion concentration on Therefore, the focus of this research is to address above the concrete surface was constant and did not consider issues. The main purpose of this research is to establish the time-varying characteristics of the chloride ion con- a practical models for practising engineers, allowing centration on the surface (Huan et  al., 2015; Yang et  al., them to use easily quantifying engineering parameters 2017). Muthulingam et  al., (2014) established a service for predicting the service life of RC structures. Firstly, a life prediction model by considering the influence of complex numerical model to predict the service life of wet-heat–diffusion coupling and the time-varying char - RC structures is established by diffusion-corrosion the - acteristics of the chloride concentration at the boundary. ory. The model verifications show that both the chloride However, the model requires too many input parameters, ion concentration and service life predictions agree well so it is not practical. It can only predict the moment with the measured values. Secondly, based on proposed when the steel bar begins to rust, but it cannot predict model, the influence of factors such as the thickness of when the RC structure will fail, that is, the failure life. the cover, the water–cement ratio, the critical value of Cao et al. (2014) and Zhu et al. (2017; Zhang et al., 2019) chloride ion concentration, and the diameter of the rein- established a mechanical model to predict the service life forcement on the service life of the RC structure are ana- of RC structures. It is based on analysis of the corrosion lysed. Finally, through a two-stage regression simulation mechanism of steel bars considering the thickness of con- of the service life of RC structures under 300 different crete cover (Enright & Frangopol, 1998), the critical value conditions, an empirical model for predicting the service of the chloride concentration (Bastidas-Arteaga et  al., life of RC structures is established. By comparing with 2009; Enright & Frangopol, 1998), and the chloride dif- the numerical simulation results, the empirical model is fusion coefficient (Pack et  al., 2010). Zheng et  al. (2009) in good agreement with the numerical model. The mod - also developed a numerical model to assess the influ - els proposed in this paper provide important theoretical ence of ITZ on the steady-state chloride diffusion. Based support for life assessment of existing projects and opti- on the finite difference method of Crank Nicolson, Song mization of service life design of projects to be built. et  al. (2009) and Petcherdchoo et  al. (2015) studied the effect of retrofitting agents on the service life of RC struc - 2 Theoretical Background tures. Jones et  al. studied the effectiveness of using filler 2.1 Chloride Diffusion Model to repair concrete cracks on prolonging the service life After decades of theoretical and experimental research of RC structures. These studies show that when micro- by many scholars (Hobbs, 1999; Wang et al., 2018, 2019; cracks appear on the surface of concrete, repair agents Zeng, 2007; Zheng et al., 2018), the diffusion of chloride can greatly prolong the service life of RC structures. Fur- ions in concrete in line with Fick’s second law has become thermore, Attari et  al. established a failure probability a widely used. And the governing equation for the diffu model for RC structures. In these studies, when the fail- sion of chloride ions in concrete is expressed as: ure probability reached 10%, the RC structure is consid- ered to have reached the service life, and the cracks in the dc ∂c ∂c ∂c ∂c = D + D , c c (1) RC structure have reached an acceptable limit. dt ∂x ∂x ∂y ∂y Although many service life prediction models for RC where c is chloride ion concentration (mass ratio of chlo- structures have been developed, there are still many chal- ride ion to concrete, %), D is chloride ion diffusion coef - lenges that have not been resolved. For example, most of ficient (m /s), respectively. the existing models only use the critical chloride concen- tration as the basis for predicting service life. However, the critical chloride concentration is only the indication of beginning of steel bar corrosion (Zhao, et  al., 2011b). Presuel F.J.(2016) Huan J. Z.(2015) Oslakovic I. S.(2010) Meira G. .(2007) Tang L. P (2003) LNEC E465 (2007) Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 3 of 12 2.1.1 Chloride Diffusion Coefficient 3.0 It can be seen from Eq.  (1) that the chloride ion diffu - 2.5 sion coefficient is a key parameter that determines the diffusion rate of chloride ions in concrete. The chloride 2.0 ion diffusion coefficient is not only related to the factors 1.5 such as concrete types, pore structure, water–cement 1.0 ratio, hydration degree, etc., but also to the external envi- ronment, such as temperature (Bažant & Najjar, 1972), 0.5 humidity (Muthulingam & Rao, 2014), current time 0.0 (Zeng, 2007). However, to simplify it, in this paper, the chloride ion diffusion coefficient is calculated with only considerations of the effects of water–cement ratio, tem - perature, humidity, and aging. Its expression is (Muthul- Fig. 1 Statistics of surface chloride ion concentration. ingam & Rao, 2014; Chen et al., 2019): −1 2.75 4 m 2 × ϕ D p U 1 1 (1 − h) t p c ref D = · exp − · 1 + · , 2.75 (2) 1.75 R T T (1 − h ) t ϕ 3 − ϕ + n 1 − ϕ ref p p Temperature Curing age Humidity Water - cement ratio Stipanovic Oslakovic et  al. 2010). It can be seen from where U is the activation energy for chloride ion diffu - Fig.  1 that the surface chloride ion concentration ranges sion, t is the average exposure time, R is the gas con- ref from 0.1% to 2.5%. There are many factors that affect the stant, T is the absolute ambient temperature, h is ref chloride ion concentration on the concrete surface, such humidity, h is critical humidity (0.75), D is the diffu - c p as temperature, humidity, cement type, and water-binder sion coefficient of chloride ions in water, n is an empirical ratio. Yang et al. (2019) obtained the regression equation constant (using 14.44 as reference (Du, et al., 2014)), m is of surface chloride ion and time function through regres- the time decay index, and f is the porosity of the cement sion analysis of 372 sets of surface chloride ion concen- slurry, respectively. f can be expressed as (Chen, et  al., tration data. It is worth noting that Eq.  (5) is based on 2021): the test results of ordinary Portland concrete. Therefore, w/c − 0.17α Eq.  (5) is only applicable to ordinary Portland concrete, ϕ = , p (3) but not to special concrete, such as fly ash concrete, slag w/c + 0.32 concrete, etc.: where is the degree of hydration of cement slurry, and 5.3t w w/c is water to cement ratio, respectively. The value of C (t) = × . (5) 1 + 0.7047t c the degree of hydration of cement slurry α in formula (3) can be calculated by: α = 1 − exp (−3.15 × w/c). (4) 2.2 Rebar Corrosion 2.2.1 Critic al Chloride Ion Concentration 2.1.2 Surface Chloride Ion Concentration Chloride ions accumulate on the surface of the steel bars The surface chloride ion concentration on the concrete over the time. When the concentration of chloride ions is another key factor affecting the chloride ion concen - on the surface of the steel bars reaches certain value, the tration inside the concrete. In the numerical solution, steel bar begins to corrode. This value is called the criti - the surface chloride ion concentration is also called the cal chloride ion concentration. The critical chloride ion boundary condition. In the marine environment, chlo- concentration indicators include free chloride ion con- ride ions are transmitted to the surface of offshore engi - centration, total chloride ion concentration, and the ratio neering concrete structures through the flow of the air, of free chloride ion concentration to hydroxide concen- and then diffuse into the concrete through the pores of tration (Cao et al., 2019). In this paper, the total chloride the concrete (Yang, et al., 2017). Fig. 1 shows statistics of ion concentration is used as an index to measure the chloride ion concentration on the surface of marine engi- critical chloride ion concentration. Due to the differences neering concrete structures in different coastal areas by in the measuring methods and the discrete type of con- different scholars (Huan et  al., 2015; Meira et  al., 2007; crete materials, the critical chloride ion concentration Surfacechlorideconcent % Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 4 of 12 0.25% ln 1.08i = 7.89 + 0.7771 ln (1.69c ) − − 0.000116R , corr t c (7) 0.20% where i is the corrosion current density, c is total corr t chloride ion concentration, and R is resistance of the 0.15% concrete cover, respectively. The empirical formula given by Liu et  al. (1998) for Averagevalue=0.10098% 0.10% resistivity of concrete cover is: ln R = 8.03 − 0.549 ln (1 + 1.69c ). c t (8) 0.05% 2.3 Determination of Service Life 0.00% 05 10 15 20 25 30 35 40 45 50 In general, when the chloride ion concentration on the Data index surface of the steel bar reaches the critical chloride ion Fig. 2 Statistics of critical chloride ion concentration. concentration, the marine engineering concrete structure is considered to have reached the service life. The limit state function at this stage can be expressed as: cannot be determined at present. The critical chloride ion concentration currently reported is between 0.079% G (c, t) = C − C(max, t), 1 cri (9) and 0.2% (Zhao, et  al., 2011a). The critical chloride ion where G (c, t) is the limit state function, c is the critical 1 cri concentration from 51 existing literature is collected in chloride ion concentration, and c(max, t) is the maximum this paper. Their statistical distribution is shown in Fig.  2. chloride ion concentration on the steel bar surface at the From Fig. 2, the critical chloride ion concentration distri- ingress time of t, respectively. bution is relatively scattered. Therefore, the mean value It is worth mentioning that when the maximum chlo- of 0.10098% is used in this paper as the critical chloride ride ion concentration on the surface of the steel bar ion concentration. reaches the critical chloride concentration, the offshore engineering concrete structure does not fail, and only the 2.2.2 Corrosion Current Density steel bars begin to rust (Zhao, et  al., 2011a; Zhao et  al., The chloride ion concentration is not constant across the 2016). The radial expansion stress is developed during whole volume of concrete. The chloride ion concentration the corrosion process. When the radial expansion stress near the erosion surface is high, and the chloride ion con- starts to cause damage to the concrete cover, the cover centration away from the erosion surface is low (Pan, et al., will crack and peel, and the structure will fail (Zhao, 2015). Therefore, the chloride ion concentration on the sur - et al., 2011b). In this paper, it is called the structural fail- face near the cover first reaches the critical chloride ion con - ure life. The limit state function can be expressed as: centration, and the passivation film was damaged (Li, et al., 2019). Research in literature (Cao, 2014) shows that there is G (lim, t) = ρ − ρ(lim, t), (10) 2 cr a potential difference between the active area formed after where ρ is the steel rebar erosion rate at failure of the cr the passivation film on the steel bar is damaged and the inert structural concrete (%), it is calculated as: area where the passivation film is not damaged, and a mac - roscopic electrochemical corrosion is formed. At the same 2(δ + δ ) 1 2 ρ = , time, there is also a micro-corrosion current, the total cor- cr (11) rosion current density can be expressed as (Zhu & Zi, 2017): where δ is the depth of rust generated by filling the pores i = i + i , corr mic mac (6) in the transition zone between the steel bar and con- crete at the interface between the corrosion products is where i is the total corrosion current density, i is corr mic 12.5 µm; δ is the depth of rust producing radial pressure, the micro-battery corrosion current density, and i is 2 mac it is worked out based on the theory of thick-walled cyl- the macro-battery corrosion current density, respectively. inders (Xu, et al., 2019b), and can be expressed as: At present, many empirical, theoretical, and numerical models have been established to calculate the corrosion r (r + c) + r c 0 0 current density of steel bars. In this paper, the Probabil- 0 δ = + v · 0.3 + 0.6 · f , 2 c t 2 2 E 2r istic mode of Papakonstantinou et  al. (2013) is adopted, (r + c) − r c 0 0 with the expression: (12) Chlorine concentrationthreshold Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 5 of 12 2π 2π where r is the reinforcement radius (mm), v is the Pois- 0 c ρ ∫ u(θ, t)dθ ∫ u(θ, t)dθ 0 0 ρ(lim, t) = × 100% = × 100% . 2 2 son’s ratio of the concrete cover, E is elastic modulus c ρ · π · r π · r 0 0 of concrete (MPa), and f is tensile strength of concrete t (15) (MPa), respectively. In summary, the flowchart of service life prediction for ρ(lim, t) is the corrosion rate of steel bars at time t (%). RC structures is shown in Fig. 3. According to Faraday’s law, the distribution of corro- sion depth u (θ , t) around steel bars can be expressed as 3 Numerical Model Validation (Alexander & Beushausen, 2019; Chen et al., 2019; Zhang The numerical model proposed in this paper comprises et al., 2019): two stages modelling. The first stage is the diffusion of t chloride ions, and the second stage is the corrosion of u (θ, t) = ∫ 0.0116 · i (θ, t)dt. corr (13) steel bars. Therefore, the model verification in this sec - tion is also divided into two aspects: chloride ion diffu - The mass loss of rebar can be expressed as: sion verification and service life. The parameters used in the simulation are listed in Table  1. In the process of 2π numerical simulation, the finite difference method (FEM) M = ρ ∫ u θ, t dθ, ( ) S s d (14) is adopted to solve the chloride ion diffusion equation 3 (Eq. 1) to obtain the distribution of chloride ion concen- where ρ is the density of the rebar (kg/m ). tration in concrete. Once the chloride concentration on So: Fig. 3 The flowchart of the derivation of the proposed multiphase numeric model. Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 6 of 12 Table 1 Numerical simulation parameters. thickness of the concrete cover is 50  mm and 60  mm, and the water–cement ratio is selected as 0.55. In addi- Symbol Parameter value Mean tion, the concrete is saturated, i.e. the relative humid- U 44.6 [K J/mol] The activation energy for chloride diffu- ity is 1. The average temperature of the environment is sion 293 K. Reinforcement diameter is 10 mm. Fig.  5 shows t 28 [d] Reference time of chloride ingress ref the comparison of the service life of the three models; it R 8.314 [J/K mol] The gas constant can be seen that the differences in the service life pre - h 0.75 [–] The critical humidity dictions of the three models are small, which indicates h 1 Humidity that the numerical model established in this paper has a −10 D The diffusion coefficient of chloride in p 1.07 × 10 [m /s] certain degree of reliability. water m 0.2 The time decay index of chloride diffu- 4 Parametric Analysis Using the New Numerical sion Model ρ 7500 [kg/m ] The density of the rebar Using the proposed numerical model, intensive paramet- T 293 [K] Reference temperature ref rical studies are made, which are show as follows. δ 12.5 µm The depth of rust generated by filling the pores r 8–13 mm The reinforcement radius 0 4.1 Influence of Different Water–Cement Ratios E 30 [GPa] Elastic modulus of concrete c The water–cement ratio for different concrete strength f 1.43 [MPa] Tensile strength of concrete t grades is different. However, different water–cement v 0.2 The Poisson’s ratio of the concrete ratio has great influence on the chloride diffusion coeffi - c 40–70 mm Thickness of reinforced concrete cover cient and the chloride ion concentration on the concrete w/c 0.45, 0.55, 0.65 The water-to-cement ratio surface, especially for the chloride diffusion coefficient (Ishida, et  al., 2009). Therefore, the water–cement ratio has a very important influence on the durability of RC the steel surface reaches the critical chloride concen- structures (Pack et al., 2010). Fig. 6a shows the service life tration, the concrete structure will reach its service life. of RC structures in the marine environment as a func- Secondly, the steel corrosion rate is calculated through tion of water–cement ratio. It can be seen from Fig.  6a Eq. (15). Once the steel corrosion rate reaches the critical that the water–cement ratio has a very important effect steel corrosion rate, the concrete structure will reach its on the service life of the marine engineering concrete failure life. structure. For example, when the water–cement ratio is 0.36, the service life is 46.1  years. However, when the 3.1 Chloride Diffusion Verification water–cement ratio is increased to 0.55, the service life The experimental data of Chalee et  al. (2009) will be is only 6.3 years. Therefore, in marine engineering, using used to compare with the numerical simulation in this a low water–cement ratio can effectively increase the paper. The size of the concrete cube specimen was service life of the structure. Besides, Fig.  6a also shows 200  mm × 200  mm × 200  mm, and the water–cement the relationship between the deterioration duration ratio was 0.45, 0.55, 0.65. And the concrete is immersed and the water–cement ratio. The deterioration dura - in seawater, which indicates that the concrete is satu- tion also decreases exponentially as the water–cement rated. Therefore, relative humidity of the concrete is 1 ratio increases. Moreover, as the water–cement ratio in numerical simulation. In addition, the average value increases, the safety reserve decreases more slowly. The of the external ambient temperature is 293 K. The com - larger the water–cement ratio is, the longer the safety parison between numerical simulation results and test reserve period is, and the safety reserve period varies results is shown in Fig.  4. Obviously, the chloride con- from 5.8  years to 9.8  years. Fig.  6b shows the change of centration curve obtained by numerical simulation is the maximum chloride ion concentration on the surface very close to that obtained by experiment, which indi- of the steel bar with time under different water–cement cates that the chloride diffusion model is reliable. ratios. It can be seen from Fig.  6b that under the same ingress time, as the water–cement ratio increases, the chloride ion concentration gradually decreases. For 3.2 Service Life Verification example, when the water–cement ratio is 0.55, the maxi- The service life prediction model proposed in this mum chloride ion concentration on the surface of the paper is compared with Moraddllo et  al. (2012) and steel bar increased rapidly within 0 to 20 years, and then Aruz et  al. (Petcherdchoo & Chindaprasirt, 2019). The increased slowly. Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 7 of 12 (a) (b) 6 6 W. Chalee'sexperiment W. Chalee's experiment 5 NumericalSimulation NumericalSimulation 3 3 Distance fromsurface (mm) Distance fromsurface (mm) (c) (d) W. Chalee'sexperiment W. Chalee'sexperiment NumericalSimulation 5 Numerical Simulation 2 2 1 1 0 0 020406080100 020406080100 Distance from surface (mm) Distance fromsurface (mm) Fig. 4 Chloride diffusion verification: a w/c = 0.65, time = 2 years. b w/c = 0.65, time = 5 years. c w/c = 0.5, time = 5 years. d w/c = 0.45, time = 5 years. 4.2 Thickness of Concrete Cover The thickness of the concrete cover is an important parameter for structural design. For different environ - ments, the requirements for the thickness of the concrete cover are different in the Code for durability Design of concrete structures. Therefore, it is necessary to study the effect of concrete cover thickness on service life. Fig.  7a shows the values of three indicators of service life, fail- ure life, and safety reserve under different concrete cover thicknesses. It can be seen from Fig.  7a that with the increase of the concrete cover thickness, the service life, deterioration duration and safety reserve all increase. For example, when the thickness of the cover is 40  mm, the service life is only 15.2  years. However, when the thick- ness of the concrete cover increased to 70  mm, the ser- Fig. 5 Service life verification. vice life increased to 55.7 years, which was an increase of - - Cl (%by weight of binder) Cl (%by weight of binder) - Cl (%by weight of binder) Cl (%by weight of binder) Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 8 of 12 (a)(b) Servicelife Service life 0.5% Failurelife Structural crackingtime Safety Safety reserv reservee 0.4% w/c=0.55 Crack w/c=0.50 0.3% w/c=0.45 w/c=0.40 0.2% w/c=0.36 Ccri C=Ccir 0.1% Ccri Ccir 0.0% 0.35 0.40 0.45 0.50 0.55 020406080100 Water-cementratio Exposure time (a) Fig. 6 Eec ff t of water–cement ratio on service life and chloride concentration distribution. a Service life. b Chloride concentration distribution. Fig. 7 Influence of concrete cover thickness on sand corrosion layer depth. a Service life. b Corrosion layer depth. 3.67 times compared to the 40 mm thickness of the con- crete cover. Further research found that with the increase of the thickness of the cover, the range of the change in the safety reserve period was small and had a linear relation- 42.1 ship with the thickness of the concrete cover. However, 37.1 35.9 deterioration duration increases greatly with the increase 32.2 30.7 of the thickness of the concrete cover. Fig.  7b shows the 27.9 25.7 depth of the corrosion of the steel bar when the cover is 21.2 cracked under different thicknesses of the concrete cover. It can be seen from Fig.  7b that the corrosion geomet- ric form of the steel bar with different cover thickness is similar, but the peak of the corrosion depth increases 6.7 6.5 6.4 6.2 with the thickness of the cover and increase. For instance, when the thickness of the concrete cover is 40  mm, the 0.08% 0.1% 0.12% 0.14% depth of rust is 82.3 µm, however, when the thickness of Chloride concentrationthreshold (%) the concrete cover is 70 µm, the depth of rust is 100.4 µm. Fig. 8 Eec ff t of critical chloride ion concentration on service life. Moreover, the corrosion depth curve of the steel bar in this paper is similar to the numerical model of Jinxia (Xia Time(a) Chlorideion concentration(%) Time (a) Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 9 of 12 et al., 2019), and this corrosion curve is similar to the cor- This is mainly because the service life mainly depends rosion mode of the entire steel bar observed through field on the critical chloride concentration and thickness exposure test experiments (Kessler et  al., 2016; Poupard of concrete cover. Additionally, as the diameter of the et al., 2006; Sun et al., 2002). steel bar increases, the deterioration duration and safety reserve both increases, but the upward trend is 4.3 I nfluence of Critical Chloride Ion Concentration also slight. For example, when the rebar diameter is The critical chloride ion concentration is another 16  mm, the deterioration duration and safety reserve important factor affecting the corrosion of steel bars. are 32.7  years and 6.4  years, respectively. And when For different types of steel bars, cement types and ser - the rebar diameter changes to 26  mm, the deteriora- vice environments, the critical chloride ion concentra- tion duration and safety reserve of the RC structure are tion is not same. The critical chloride ion concentration 34.6 years and 8.1 years, respectively. Fig.  9 also shows obtained by many scholars has a very large value (Cao, the corrosion rate of steel bars when the structure fails et al. 2019, Zhang, et al. 2019). Therefore, in this section, under different the rebar diameters. It is worth men - the influence of different critical chloride ion concentra - tioning that as the rebar diameter increases, the cor- tions on the service life of RC structure is studied with a rosion rate of the rebar decreases significantly. For water–cement ratio of 0.4. As shown in Fig. 8, as the criti- example, when the rebar diameter is 16  mm, the cor- cal chloride ion concentration increases, both the service rosion rate of the rebar is 0.382%; however, when the life and the deterioration duration of the RC structure rebar diameter is 26  mm, the rebar corrosion rate is increase. More importantly, it turns out that the critical only 0.241%. chloride ion concentration has a linear relationship with the service life, which is consistent with the results of Muthulingam et al. (2014). For instance, for every 0.01% 5 A Simplified Empirical Model for Service Life increase in the critical chloride ion concentration, the RC Prediction structural service life increases by 2.5 years. According to the discussion in Sect. 4, it can be seen that the rebar diameter has a small effect on the service life of 4.4 E ec ff t of Rebar Diameter the structure. And the thickness of the cover, the water– For different types and functions RC structures, the cement ratio and the critical chloride ion concentration rebar diameter in the RC structure is also different. all have significant impact on the service life of the con - Therefore, it is of great significance to study the impact crete structure. The cover thickness and water–cement of the rebar diameter on the service life of marine RC ratio are important parameters in engineering design. structures. Fig.  9 shows a histogram of the service life, Therefore, in this paper, 300 groups RC structures with failure life, and safety reserve of marine RC structures different water–cement ratios, concrete cover thick - in the range of rebar diameters from 16 to 26  mm. It ness are simulated to predict their service life. These 300 can be seen from Fig.  9 that the influence of the rebar groups of data are divided into two categories: first, the diameter on the service life could be ignored (e.g., the thickness of the cover—40 mm, 45 mm, 50 mm, 55 mm, difference between the maximum and the minimum 60  mm, 70  mm, and the water–cement ratios 0.36, 0.40, service life for different rebar diameter is only 0.5 year). 0.50, and 0.55. Second, the cover thickness is 65 and the water–cement ratio is 0.45 as a control group. A two- stage data fitting and regression analysis method are used to establish an empirical service life prediction model. In 50 0.5% the first stage, the functional representing the relation - ship between the thickness of the cover and the service 40 0.4% life is obtained through regression analysis, as shown in 34.6 34.0 33.3 32.7 32.9 formula (16), where A and B is the undetermined coef- 30 0.3% 26.6 ficient related to water–cement ratio. In the second stage, 26.4 26.3 26.5 26.4 through regression analysis, the relationship between 20 0.2% the undetermined coefficients A and B and the water– cement ratio is obtained, as shown in formula (17): 10 0.1% 8.1 7.6 6.8 6.4 6.7 f (w/c, cd) = A + B × cd, (16) 0 0.0% 16 18 20 22 26 where A and B are fitting parameters; wc is water– Reinforcement diameter(mm) cement ratio; cd is the thickness of concrete cover: Fig. 9 Eec ff t of rebar diameter on service life. Time (a) Corrosion rate of reinforcement(%) Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 10 of 12 (a)(b) 30 Numerical Simulation Numerical Simulation Proposed model Proposed model 0 0 0.35 0.40 0.45 0.500.55 35 40 45 50 55 60 65 70 Water-cement ratio Concrete cover thickness mm Fig. 10 Validation of practical service life prediction model. a Cover thickness = 65 mm. b Water–cement ratio = 0.45. life is 46.1 years. However, when the water–cement 326w/c f (wc, cd) =− 4.0 + exp − + 10.364 ratio is increased to 0.55, the service life is only 6.3 years. 2 137w/c + + exp − + 6.945 × cd. (2) With the increase of the thickness of the concrete 11 8 cover, the service life, failure life, and safety reserve (17) all linear increase. Thickness of corrosion layer with However, in the process of numerical simulation, we different cover thickness is similar, but the peak of assume that the ambient temperature is 293  K and the the corrosion depth increases with the thickness of concrete is saturated. Therefore, the applicable condi - the cover increase. tion of formula (17) is saturated concrete with an ambi- (3) As the critical chloride ion concentration increases, ent temperature of 293 K. both the service life and the deterioration duration Fig.  10 shows the comparison between the service of the RC structure increase. More importantly, it life prediction model proposed in this paper and the turns out that the critical chloride ion concentra- numerical simulation results. It can be found that the tion has a linear relationship with the service life. numerical simulation results are distributed near the (4) The influence of the rebar diameter on the service prediction model curve, which indicates that the pro- life can be ignored. It is worth mentioning that as posed model in this paper is reliable. the rebar diameter increases, the corrosion rate of steel bars decreases significantly. 6 Conclusion (5) Various factors (water–cement ratio, protective In this paper, both numerical and empirical mod- layer thickness, rebar diameter, etc.) have a small els for predicting the service life of RC structures in impact on the safety reserve period. The safety the marine environment are proposed. The proposed reserve period of RC structure is generally less than numerical analysis model not only considers the service 10 years. life of RC structures, but also the deterioration dura- (6) Through regression analysis of 300 sets of simula - tion. Moreover, the effects of water–cement ratio, rebar tion data, the proposed empirical forecasting model diameter, concrete cover thickness and critical chloride has good reliability in the service life prediction of ion concentration on the service life and deterioration RC structures and is suitable for practical engineers. duration of RC structures are comprehensively ana- lysed, and the key factors affecting the service life of RC Acknowledgements structures are determined. The following conclusions The authors appreciate the financial supports from the National Natural can be drawn: Science Foundation of China (No. 51968014, 52078509, 51968013), Guangxi Key Laboratory of New Energy and Building Energy Saving Foundation (No. 19-J-21-4, 19-J-21-8), and Guangxi Universities Scientific Research Project (1) With the increase of water–cement ratio, the ser- (2020KY06029). vice life of RC structure decreases exponentially. When the water–cement ratio is 0.36, the service Service life (a) Service life (a) Chen  et al. Int J Concr Struct Mater (2022) 16:11 Page 11 of 12 Authors’ contributions Chalee, W., Jaturapitakkul, C., & Chindaprasirt, P. (2009). Predicting the chloride XC: writing—original draft preparation, data curation, writing, conceptualiza- penetration of fly ash concrete in seawater. Marine Structures, 22(3), tion, methodology, investigation. FF: writing—original draft preparation, 341–353. https:// doi. org/ 10. 1016/j. marst ruc. 2008. 12. 001 writing—reviewing and editing, methodology, investigation. PC: validation, Chang, W., et al. (2020). Durability and aesthetics of architectural concrete software. YM: software, data curation. All authors read and approved the final under chloride attack or carbonation. Materials, 13(4), 839. https:// doi. manuscript.org/ 10. 3390/ ma130 40839 Chen, X., et al. (2019). Meso-numerical simulation of service life prediction for Authors’ information marine structures. Journal of Building Materials, 22(6), 894–900. https:// doi. Xuandong Chen MSc, lecturer, College of Civil Engineering and Architecture, org/ 10. 3969/j. issn. 1007- 9629. 2019. 06. 009 Guilin University of Technology, Guilin 541004, China; China. Guangxi Key Chen, X., et al. (2021). A multi-phase mesoscopic simulation model for the Laboratory of New Energy and Building Energy Saving, Guilin 541004, China; long-term chloride ingress and electrochemical chloride extraction. Guangxi Engineering and Technology Center for Utilization of Industrial Waste Construction and Building Materials, 270, 121826. https:// doi. org/ 10. 1016/j. Residue in Building Materials, Guilin, 541004, China.conbu ildmat. 2020. 121826 Yang Ming, MSc, Engineer, Guangxi Engineering and Technology Center for Dhandapani, Y., et al. (2018). Mechanical properties and durability perfor- Utilization of Industrial Waste Residue in Building Materials, Guilin, 541004, mance of concretes with Limestone calcined clay cement (LC3). Cement China. and Concrete Research, 107(March), 136–151. https:// doi. org/ 10. 1016/j. Feng Fu, PhD Associate Professor, School of Mathematics, Computer Science cemco nres. 2018. 02. 005 and Engineering, City, University of London, London EC1C,0HB U.K. (cor- Du, X., Jin, L., & Ma, G. (2014). A meso-scale numerical method for the simula- responding author). tion of chloride diffusivity in concrete. Finite Elements in Analysis and Ping Chen PhD, Senior Research Fellow, Guangxi Engineering and Technology Design, 85, 87–100. https:// doi. org/ 10. 1016/j. finel. 2014. 03. 002 Center for Utilization of Industrial Waste Residue in Building Materials, Guilin, Enright, M. P., & Frangopol, D. M. (1998). Probabilistic analysis of resistance 541004, China. degradation of reinforced concrete bridge beams under corrosion. Engineering Structures, 20(11), 960–971. https:// doi. org/ 10. 1016/ S0141- Funding0296(97) 00190-9 National Natural Science Foundation of China (No. 51968014, 52078509, Fu, F. (2015). Advanced Modeling Techniques in Structural Design. USA: Wiley. 51968013). Guangxi Key Laboratory of New Energy and Building Energy 978-1-118-82543-3. Saving Foundation (No. 19-J-21-4, 19-J-21-8). Guangxi Universities Scientific Fu, F. (2016). Structural Analysis and Design to Prevent Disproportionate Collapse. Research Project (2020KY06029). USA: CRC Press. 978-1-4987-0680-3. Fu, F. (2018). Design and Analysis of Tall and Complex Structures. UK: Butter- Availability of data and materials worth-Heinemann. 978-0-08-101121-8. All data that support the findings of this study are available from the cor - Fu, F. (2021). Fire Safety Design for Tall Buildings. England: Taylor Francis. responding author upon reasonable request. 978-0-367-44452-5. Guo, H., et al. (2004). Durability of recycled aggregate concrete—A review. Cement and Concrete Composites, 26(2), 97–98. https:// doi. org/ 10. 1016/ Declarations S0958- 9465(03) 00091-X Hobbs, D. W. (1999). Aggregate influence on chloride ion diffusion into con- Competing interests crete. Cement and Concrete Research, 29(12), 1995–1998. https:// doi. org/ The authors declare no competing interests. 10. 1016/ S0008- 8846(99) 00188-X Huan, X. U. E., Zuquan, J. I. N., & Xiaojie, W. (2015). Chloride ion penetration into Author details concrete exposed to marine environment for a long period. The Ocean College of Civil Engineering and Architecture at Guilin University of Tech- Engineering, 33(5), 60–65. https:// doi. org/ 10. 16483/j. issn. 1005- 9865. 2015. nology, Guilin 541004, China. School of Mathematics, Computer Science 05. 008 and Engineering, City, University of London, London EC1C 0HB, UK. Ishida, T., Iqbal, P. O. N., & Anh, H. T. L. (2009). Modeling of chloride diffusivity coupled with non-linear binding capacity in sound and cracked concrete. Received: 21 May 2021 Accepted: 14 January 2022 Cement and Concrete Research, 39(10), 913–923. https:// doi. org/ 10. 1016/j. cemco nres. 2009. 07. 014 Jung, S.-H., et al. (2018). Maintenance for repaired RC column exposed to chlo- ride attack based on probability distribution of service life. International Journal of Concrete Structures and Materials, 12(1), 22. https:// doi. org/ 10. References 1186/ s40069- 018- 0259-2 Alexander, M., & Beushausen, H. (2019). Durability, service life prediction, and Kessler, S., et al. (2016). Eec ff t of freeze–thaw damage on chloride ingress into modelling for reinforced concrete structures—Review and critique. concrete. Materials and Structures, 50(2), 121. https:// doi. org/ 10. 1617/ Cement and Concrete Research, 122, 17–29. https:// doi. org/ 10. 1016/j. s11527- 016- 0984-4 cemco nres. 2019. 04. 018 Khanzadeh Moradllo, M., Shekarchi, M., & Hoseini, M. (2012). Time-dependent Bastidas-Arteaga, E., et al. (2009). Probabilistic lifetime assessment of RC struc- performance of concrete surface coatings in tidal zone of marine envi- tures under coupled corrosion-fatigue deterioration processes. Structural ronment. Construction and Building Materials, 30, 198–205. https:// doi. org/ Safety, 31(1), 84–96. https:// doi. org/ 10. 1016/j. strus afe. 2008. 04. 001 10. 1016/j. conbu ildmat. 2011. 11. 044 Bažant, Z. P., & Najjar, L. J. (1972). Nonlinear water diffusion in nonsaturated Khanzadeh-Moradllo, M., et al. (2015). Eec ff t of wet curing duration on long- concrete. Matériaux Et Constructions, 5(1), 3–20. https:// doi. org/ 10. 1007/ term performance of concrete in tidal zone of marine environment. BF024 79073 International Journal of Concrete Structures and Materials, 9(4), 487–498. Bouteiller, V., Marie-Victoire, E., & Cremona, C. (2016). Mathematical relation of https:// doi. org/ 10. 1007/ s40069- 015- 0118-3 steel thickness loss with time related to reinforced concrete contami- Li, D., Wang, X., & Li, L. (2019). An analytical solution for chloride diffusion in concrete nated by chlorides. Construction and Building Materials, 124, 764–775. with considering binding effect. Ocean Engineering, 191, 106549. https:// doi. https:// doi. org/ 10. 1016/j. conbu ildmat. 2016. 07. 078 org/ 10. 1016/j. ocean eng. 2019. 106549 Cao, C. (2014). 3D simulation of localized steel corrosion in chloride con- Liu, Y., & Weyers, R.E. (1998). Modeling the time-to-corrosion cracking in chloride taminated reinforced concrete. Construction and Building Materials, 72, contaminated reinforced concrete structures. ACI Materials Journal 95(6). 434–443. https:// doi. org/ 10. 1016/j. conbu ildmat. 2014. 09. 030 https:// doi. org/ 10. 14359/ 410. Cao, Y., et al. (2019). Critical chloride content in reinforced concrete—An Marks, M., Glinicki, M. A., & Gibas, K. (2015). Prediction of the chloride resistance of updated review considering Chinese experience. Cement and Concrete concrete modified with high calcium fly ash using machine learning. Materi- Research, 117, 58–68. https:// doi. org/ 10. 1016/j. cemco nres. 2018. 11. 020 als, 8(12), 8714–8727. https:// doi. org/ 10. 3390/ ma812 5483 Chen et al. Int J Concr Struct Mater (2022) 16:11 Page 12 of 12 Meira, G. R., et al. (2007). Chloride penetration into concrete structures in the marine Xu, Q., Shi, D., & Shao, W. (2019). Service life prediction of RC square piles based atmosphere zone—Relationship between deposition of chlorides on the wet on time-varying probability analysis. Construction and Building Materials, 227, candle and chlorides accumulated into concrete. Cement and Concrete Com- 116824. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 116824 posites, 29(9), 667–676. https:// doi. org/ 10. 1016/j. cemco ncomp. 2007. 05. 009 Yang, L., Cai, R., & Yu, B. (2017). Formation mechanism and multi-factor model for Mir, Z. M., et al. (2019). Enhanced predictive modelling of steel corrosion in concrete surface chloride concentration of concrete in marine atmosphere zone. Tumu in submerged zone based on a dynamic activation approach. International Gongcheng Xuebao/china Civil Engineering Journal, 50(12), 46–55. https:// doi. Journal of Concrete Structures and Materials, 13(1), 11. https:// doi. org/ 10. 1186/ org/ 10. 15951/j. tmgcxb. 2017. 12. 006 s40069- 018- 0321-0 Yang, L., Chen, C., & Yu, B. (2019). Multi-factor time-varying model of marine envi- Muthulingam, S., & Rao, B. N. (2014). Non-uniform time-to-corrosion initiation in ronmental action on concrete in splash zone. Journal of the Chinese Ceramic steel reinforced concrete under chloride environment. Corrosion Science, 82, Society, 11(47), 1566–1572. 304–315. https:// doi. org/ 10. 1016/j. corsci. 2014. 01. 023 Zeng, Y. (2007). Modeling of chloride diffusion in hetero-structured concretes by Nogueira, C., Leonel, E., & Coda, H. (2012). Probabilistic failure modelling of rein- finite element method. Cement and Concrete Composites, 29(7), 559–565. forced concrete structures subjected to chloride penetration. International https:// doi. org/ 10. 1016/j. cemco ncomp. 2007. 04. 003 Journal of Advanced Structural Engineering, 4(1), 10. https:// doi. org/ 10. 1186/ Zhang, K., et al. (2019). Analytical model for critical corrosion level of reinforcements 2008- 6695-4- 10 to cause the cracking of concrete cover. Construction and Building Materials, Pack, S. W., et al. (2010). Prediction of time dependent chloride transport in concrete 223, 185–197. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 06. 210 structures exposed to a marine environment. Cement and Concrete Research, Zhao, Y., et al. (2016). Non-uniform distribution of a corrosion layer at a steel/con- 40(2), 302–312. https:// doi. org/ 10. 1016/j. cemco nres. 2009. 09. 023 crete interface described by a Gaussian model. Corrosion Science, 112, 1–12. Pan, Z., Chen, A., & Ruan, X. (2015). Spatial variability of chloride and its influence https:// doi. org/ 10. 1016/j. corsci. 2016. 06. 021 on thickness of concrete cover: A two-dimensional mesoscopic numerical Zhao, Y., Hu, B., et al. (2011a). Non-uniform distribution of rust layer around steel bar research. Engineering Structures, 95, 154–169. https:// doi. org/ 10. 1016/j. engst in concrete. Corrosion Science, 53(12), 4300–4308. https:// doi. org/ 10. 1016/j. ruct. 2015. 03. 061corsci. 2011. 08. 045 Papakonstantinou, K. G., & Shinozuka, M. (2013). Probabilistic model for steel corro- Zhao, Y., Karimi, A. R., et al. (2011b). Comparison of uniform and non-uniform corro- sion in reinforced concrete structures of large dimensions considering crack sion induced damage in reinforced concrete based on a Gaussian description effects. Engineering Structures, 57, 306–326. https:// doi. org/ 10. 1016/j. engst ruct. of the corrosion layer. Corrosion Science, 53(9), 2803–2814. https:// doi. org/ 10. 2013. 06. 0381016/j. corsci. 2011. 05. 017 Petcherdchoo, A. (2015). Repairs by fly ash concrete to extend service life of Zheng, J. J., et al. (2018). A numerical algorithm for evaluating the chloride diffusion chloride-exposed concrete structures considering environmental impacts. coefficient of concrete with crushed aggregates. Construction and Building Construction and Building Materials, 98, 799–809. https:// doi. org/ 10. 1016/j. Materials, 171, 977–983. https:// doi. org/ 10. 1016/j. conbu ildmat. 2018. 03. 184 conbu ildmat. 2015. 08. 120 Zheng, J. J., Wong, H. S., & Buenfeld, N. R. (2009). ‘Assessing the influence of ITZ on Petcherdchoo, A., & Chindaprasirt, P. (2019). Exponentially aging functions coupled the steady-state chloride diffusivity of concrete using a numerical model. with time-dependent chloride transport model for predicting service life of Cement and Concrete Research, 39(9), 805–813. https:// doi. org/ 10. 1016/j. cemco surface-treated concrete in tidal zone. Cement and Concrete Research, 120, nres. 2009. 06. 002 1–12. https:// doi. org/ 10. 1016/j. cemco nres. 2019. 03. 009 Zhu, X., & Zi, G. (2017). A 2D mechano-chemical model for the simulation of Pillai, R. G., et al. (2019). Service life and life cycle assessment of reinforced concrete reinforcement corrosion and concrete damage. Construction and Building systems with limestone calcined clay cement (LC3). Cement and Concrete Materials, 137, 330–344. https:// doi. org/ 10. 1016/j. conbu ildmat. 2017. 01. 103 Research, 118, 111–119. https:// doi. org/ 10. 1016/j. cemco nres. 2018. 11. 019 Poupard, O., et al. (2006). Corrosion damage diagnosis of a reinforced concrete Publisher’s Note beam after 40 years natural exposure in marine environment. Cement and Springer Nature remains neutral with regard to jurisdictional claims in published Concrete Research, 36(3), 504–520. https:// doi. org/ 10. 1016/j. cemco nres. 2005. maps and institutional affiliations. 11. 004 Shaikh, F. U. A. (2018). Eec ff t of cracking on corrosion of steel in concrete. Interna- tional Journal of Concrete Structures and Materials, 12(1), 3. https:// doi. org/ 10. 1186/ s40069- 018- 0234-y Song, H. W., et al. (2009). Service life prediction of repaired concrete structures under chloride environment using finite difference method. Cement and Concrete Composites, 31(2), 120–127. https:// doi. org/ 10. 1016/j. cemco ncomp. 2008. 11. Stambaugh, N. D., Bergman, T. L., & Srubar, W. V. (2018). Numerical service-life modeling of chloride-induced corrosion in recycled-aggregate concrete. Construction and Building Materials, 161, 236–245. https:// doi. org/ 10. 1016/j. conbu ildmat. 2017. 11. 084 Stipanovic Oslakovic, I., Bjegovic, D., & Mikulic, D. (2010). Evaluation of service life design models on concrete structures exposed to marine environment. Materials and Structures/materiaux Et Constructions, 43(10), 1397–1412. https:// doi. org/ 10. 1617/ s11527- 010- 9590-z Sun, W., et al. (2002). Eec ff t of chloride salt, freeze–thaw cycling and externally applied load on the performance of the concrete. Cement and Concrete Research, 32(12), 1859–1864. https:// doi. org/ 10. 1016/ S0008- 8846(02) 00769-X Wang, Y., et al. (2018). Prediction model of long-term chloride diffusion into plain concrete considering the effect of the heterogeneity of materials exposed to marine tidal zone. Construction and Building Materials, 159, 297–315. https:// doi. org/ 10. 1016/j. conbu ildmat. 2017. 10. 083 Wang, Y., Gong, X., & Wu, L. (2019). Prediction model of chloride diffusion in concrete considering the coupling effects of coarse aggregate and steel reinforcement exposed to marine tidal environment. Construction and Building Materials, 216, 40–57. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 04. 221 Xia, J., et al. (2019). Numerical simulation of steel corrosion in chloride contaminated concrete. Construction and Building Materials, 228, 116745. https:// doi. org/ 10. 1016/j. conbu ildmat. 2019. 116745

Journal

International Journal of Concrete Structures and Materials – Springer Journals

Published: Dec 1, 2022

Keywords: service life prediction; RC structures; chloride diffusion; critical chloride value; corrosion current density

There are no references for this article.