Mesoscopic chloride ion diffusion model of marine concrete subjected to freeze-thaw cycles

Construction and Building Materials 125 (2016) 337–351

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Mesoscopic chloride ion diffusion model of marine concrete subjected to freeze-thaw cycles Ben Li a, Jize Mao a,⇑, Toyoharu Nawa b, Zongmin Liu a a b

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China Sustainable Eco-Material Laboratory, Faculty of Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan

h i g h l i g h t s
A new model was obtained for diffusion of chloride subjected to freeze-thaw cycles.
Freeze-thaw stress was proposed to reflect the influence of freeze-thaw cycles.
The concentration gradient was used for evaluating the influence of chloride concentrations.

a r t i c l e

i n f o

Article history: Received 12 March 2016 Received in revised form 8 August 2016 Accepted 13 August 2016

Keywords: Marine concrete Mesoscopic diffusion modelling Freeze-thaw cycles Chlorides

a b s t r a c t This paper presents a new mesoscopic transport model for describing the diffusion of chloride in cementbased materials simultaneously subjected to freeze-thaw (FT) conditions and incorporated with chloride ions (Ch-I). The model uses the concept of freeze-thaw stress (FT-S) to reflect the effect of freezing and thawing cycles on the transport of ionic concentrations in porous materials and the concentration gradient of chloride for calculating the effect of different concentrations of chloride ions. In addition to determining the effect of FT-S, the model also considers the interactional effects between environmental exchanges, namely the effects of different temperatures, Cl concentrations (10.5 g/L, 21.0 g/L and 42.0 g/L), and pore size distributions. The mesoscopic model is validated using experimental data obtained from coupling tests of chloride corrosion and freeze-thaw cycles. Compared with the typical Fick’s results, advantageous agreement between the calculated and measured chloride concentration profiles is demonstrated. The new mesoscopic diffusion model can help compensate for the lack of research on the effect of freeze-thaw cycles on chloride diffusion. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The corrosion of reinforcing steel in concrete is a worldwide problem that affects the durability of a large number of reinforced concrete structures. The major causes of reinforcement corrosion are chloride ion contamination and temperature differences in the concrete, as both lead to depassivation of the embedded steel [1]. Durability and service-life evaluations are often significant and complicated in the application and programming of reinforced concrete structures in harsh environmental conditions. To prevent the corrosion of concrete structures due to freeze-thaw conditions, chloride ions or coupling actions, one must restrict the diffusion of species from the environment into concrete by using highly impenetrable concrete or fibre reinforced polymer/plastic (FRP) composite structures [2]. This restriction requires quantitative ⇑ Corresponding author. E-mail address: [email protected] (J. Mao). http://dx.doi.org/10.1016/j.conbuildmat.2016.08.052 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.

information about the factors affecting the rates of diffusion of chloride ions in concrete. As several interacting processes are always involved, the development of a theoretical mechanism is essential to enable an accurate prediction of chloride levels at various depths throughout the service life of concrete structures [3–8]. To understand the mechanism of chloride diffusion into concrete, a large number of theoretical models have been developed based on laboratory and field tests using experimental methods [9–13]. However, most of these efforts have been primarily concerned with the causes and mechanisms of chloride diffusion, and few studies have focused on the effect of chloride corrosion due to other factors, such as freeze-thaw cycles, loading, and carbonation [14]. In practical engineering, particularly for marine concrete structures, two or more actions usually combine to deteriorate the properties of concrete. When marine concrete structures are attacked by chloride ions derived from seawater, the frost deterioration of concrete becomes increasingly severe. Chloride ions

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List of notation rh rn r0 r tðrÞ Prh tðrh Þ

is the average harmful pore size is the maximum pore size is the feature pore size is the experimental pore size is the pore distribution is the porosity of harmful pore structures is the harmful pore distribution srh is the tortuosity of harmful pore structure V rh is the volume of harmful pore structures V r0 is the volume of feature pore structures h is the geometric height of pores f ðr h Þ is the normal random function for determining the random pore structures ½Aw is the amount of water g1 is the hydration influence parameters on the porosity of concrete g2 is the water/cement (w/c) influence parameters on the porosity of concrete N is the number of freeze-thaw cycles K FTS is the freeze-thaw acceleration coefficient rijFN is the freeze-thaw stress tensor is the concrete elastic modulus (constant and isotropic) C ijkl deFijN is the mesoscopic strain of freeze-thaw cycles d is the infinitesimal variation r is the Laplace operator N is the harmful pore size of concrete subjected to the N r Fh
ij cycle r ih and rhj are the mesoscopic strain tensor bases of harmful pores is the acceleration coefficient of chloride K ChI

ingress into concrete, causing concentration changes inside the concrete and reducing the frost resistance of marine concrete. Chloride ions facilitate damage and defects through cracking or scaling during freeze-thaw cycles. Chloride ions and freeze-thaw cycles influence each other, which accelerates the damage of concrete structures and shortens their service life. Therefore, it is important to study the behaviour of concrete under these simultaneous actions to accurately estimate the service life of concrete structures. Many studies have investigated chloride ion diffusion in concrete over the past decade [15–17] but few studies have examined the simultaneous actions of chloride ion diffusion and freeze-thaw cycles. Chindaprasirt [18] investigated the effect of chloride ions on the frost resistance of steel concrete, declaring that the mechanical properties and frost resistance of steel concrete decreased in chloride ion solutions. Sun et al. [19] emphasized that the dynamic modulus of concrete decreased more significantly under freezing conditions in salt solutions than in water. Niu et al. [20] suggested that weight loss and splitting tensile strength loss of concrete were more significant in salt solutions than in water. It should be noted that most recent studies on the effect of chloride ions on frost resistance [21–23] also considered the macroscopic properties of freeze-thaw cycles affecting chloride ions based on various experiments. However, the interaction between different ion concentrations was not taken into account. In addition, typical macro-erosion models were unable to reveal the mechanism underlying the effects of freeze-thaw cycles on chloride ion diffusion and did not incorporate the effect of pore structures on the transport of various chloride ions in concrete. In this paper, a new mesoscopic transport model describing the diffusion of chloride ions in cement-based materials subjected to different freeze-thaw cycles is presented. To reflect the effect of freeze-thaw cycles on the transport of chloride ions, the mesoscopic model uses the concept of freeze-thaw stress (FT-S) based

c0 and cN are chloride ion contents subjected to different freezethaw cycles ci is the boundary condition of chloride ion concentrations mn C mn is the ion concentration tensor 0 and C N X mn is ion concentration density tensor Ka is the initial coupling effect coefficient tensor is the eulerian coordinate tensor ka fKg is the coupling effect tensor R is the correlation coefficient between freeze-thaw and chlorides K FTS is the weighted average of FT-S acceleration coefficient K ChI is the weighted average of Ch-I acceleration coefficient jKj is the value of fKg Da is the diffusion parameter of the material x is the diffusion depth cf is the free chloride concentrations in concrete ct is the total chloride concentrations in concrete is the combined chloride concentration cb Dm is the mesoscopic diffusion parameter a is the time effect coefficient t simulation is the calculation time ~ N is the number of test cycles N is the average annual cycle in Bohai a^ is the volume percentage ðTypeÞ T size is the value of the cumulative amount of mercury injection of various types of pore structures ðAllÞ T size is the value of the cumulative amount of mercury injection of all pore structures

on the pore size variation and consider the coupling coefficient between different concentrations of chloride ions and number of freeze-thaw cycles. To verify the model comparisons between the chloride concentrations predicted based on the present mesoscopic model and the typical results obtained under Fick’s law, coupled chloride and freeze-thaw tests were performed.

2. Theoretical analysis 2.1. Feature pore size and harmful pore distribution density Chloride transport can occur in concrete through several mechanisms, including diffusion, absorption, migration, pressureinduced flow, environmental coupling-induced flow, and wick action [24]. Diffusion is the primary mechanism of chloride transport in concrete in a chloride environment. As previously noted, Fick’s law of diffusion is widely used to evaluate the behaviour of chloride transport in the pore structure of concrete. If environmental changes alter the chloride concentrations in the pore structures of concrete, the coupling of environmental factors can enhance chloride diffusion in pores. Hence, the chloride diffusion coefficient in pore structures of concrete is a key parameter that determines the durability of marine concrete structures as it characterizes the velocity of chloride diffusion into concrete subjected to the marine environment. Chloride diffusion in cement-based materials is largely controlled by the pore structure. Thus, understanding the pore structure of cement-based materials is crucial to the development of mechanistic models. The porosity, pore size, and pore size distribution are believed to be the main factors that affect the diffusion of chlorides in cement-based materials. A typical pore size distribution for hardened cement encompasses a large range, extending from approximately 15 mm to 0.5 nm or less in

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diameter from the capillary pores to the gel pores of C-S-H [25]. However, the water or pore solution in the gel pores of C-S-H does not occur in the liquid state but in the solid state; therefore, these gel pores are not treated as significant pore structures for analysing the transport of chlorides in concrete. This finding suggests that the concept of feature pore size, which has an important effect on the transport of chloride ions, must be taken into account when developing an appropriate diffusion model. Capillary or mesoscopic scale action is the main focus of this paper. The concept of feature pore size r 0 was proposed to determine whether capillary pores affect chloride diffusion. Pore sizes greater than the feature pore size were defined as harmful, as these pores play an important role in the transport of chloride ions. The harmful pore size is determined as follows [26]:

Z rh ¼

rn

Z r  tðrÞdr

r0

tðrÞdr

ð1Þ

1

r0

where rh represents the average harmful pore size (pores larger than r 0 ), r n is the maximum pore size, tðrÞ represents the pore distribution, r is the experimental pore size, which is determined by the pore size distribution (MIP test), and r 0 is the feature pore size, which can be determined according to the saturation degree and critical pore size. Consider chloride diffusion in a cement-based material that consists of a microscopically inhomogeneous porous matrix filled with a homogeneous pore solution. The inhomogeneous or random harmful pore size distribution can affect the transport of chloride ions. A distribution density of harmful pore sizes was established according to the self-consistent theory and the normal distribution for defining and calculating the inhomogeneity effect of harmful pore sizes for chloride. The harmful pore distribution density was determined as follows: r0 V rh

1 ðV r 0 þ V rh Þ

Z V r0 ¼

r0

0

ZZZ

Hh ¼ 

ð2aÞ

 ½Aw 

½Aw  ¼ g1  g2 ;

According to diffusion theory, the application of Fick’s second law requires a single environment or condition. This ideal condition assumption leads to some errors in the design and evaluation of marine concrete. In multi-stress environments, long-term and periodical loads have different effects on accelerating chloride diffusion. Gerard [27] coupled chloride diffusion with freeze-thaw conditions and found that the diffusion parameters increased 1.5- to 7-fold. Samaha [28] analysed the electric flux of circular concrete under a horizontal load, and the results showed that when the stress level exceeded 75% of the ultimate stress, the electric flux increased by 10–20%. Under the rapid effect of temperature, parts of the liquid pore solution were frozen to ice. The increase in volume caused by ice formation was confined by the porous material, but the rest of the pore solution flowed away to larger pores according to Darcy’s law, and the harmful pore size increased due to the damage caused by the freeze-thaw cycles. Hence, the transport of chloride ions was accelerated by the freeze-thaw cycles. In the current study, the effect of freeze-thaw cycles on chlorides due to changes in pore sizes was defined as freeze-thaw stress (FT-S) because of the generalized mechanical significance for determining the acceleration of freeze-thaw cycles on chloride ions. The freeze-thaw stress (FT-S) can be derived based on microscopic elastic-plastic mechanics and the changes of pore structures. In addition, the acceleration coefficient can be determined based on the changes in FT-S under different freezethaw cycles:

K FT-S

2 Z ¼1þ4

g1 ¼

P0 1 P rh

Z

tðrÞdr; V rh ¼

1

N 0

Z

Pr n Prh ¼ Prn

2.2. Estimation of freeze-thaw stress (FT-S) and concentration gradient of chloride (Ch-I)

rijFN ¼

0

N

  3 d 43 p  rijFN rih  rhj   dN5 ij i j 4 p  r r  r F0 h h 3

C ijkl deFijN r ih  r hj dN

ð7Þ FN

N  rh
ij0 Þrih  rhj deFijN ¼ rdu_ FijN ¼ rdðr Fh
ij

H ;

g2 ¼ w=c

ð2bÞ

ð6Þ

ð8Þ

where N is the number of freeze-thaw cycles, K FT-S is the freezethaw acceleration coefficient and the value of it equals to 1 at

rijFN is the freeze-thaw stress tensor, C ijkl is the concrete elastic modulus (constant and isotropic), deFijN is the mesoscopic strain of

0 N,

tðrÞdr

ð3Þ

r0

freeze-thaw cycles due to the changes of pore size, d is the infinitesN is the harmful pore imal variation, r is the Hamilton Operation, r Fh
ij

16 Pr Prh tðr h Þdr  ½f ðrh Þ  45 h Vh

ð1  tðr h Þ2 Þð10  3tðr h ÞÞ   sr h 2  tðr h Þ

2 1 2 f ðr h Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi eðrh r0 Þ =1:155r0 ; 1:155pr20

ð4Þ Z

sr h ¼

rn

Ph dr

ð5Þ

rh

where Prh is the porosity of harmful pore structures (= the amount of capillary pore in concrete or paste), Hh is the density of harmful pore, tðr h Þ is the harmful pore distribution, srh is the tortuosity of harmful pore structure, V rh is the volume of harmful pore structures and V r0 is the volume of feature pore structures, h is the geometric height of pores (pore structures are cylinders in this paper), f ðrh Þ is the normal random function for determining the random pore structures, g1 and g2 respectively are the hydration (or the amount of cement) and water/cement (w/c) influence parameters on the porosity of concrete, ½Aw is the amount of water which equals to the original pore volume and H is the hydration degree of concrete.

size of concrete subjected to the N cycle, rih and rhj are the mesoscopic strain tensor bases of harmful pores. The dynamic force of chloride ion diffusion in concrete was determined by the differences between the external and internal concentrations of chloride ions according to Darcy’s law and Fick’s law [29]. Due to different environments concentrations can provide different diffusion dynamic of chloride ions, the concentration gradient of chloride has a significant effect on the transport of chloride ions into concrete. In this study, acceleration on diffusion of differences in concentration can be calculated through a concentration gradient ratio. The effect of the concentration gradient was determined as follows:

2 K Ch-I ¼ 1 þ 4

Z

cN

c0

  3 d cNi  xNj C mn N  X mn   dci 5  X c0i  x0j C mn mn 0

ð9Þ

where K Ch-I is the acceleration coefficient of chloride and the initial value of it is 1, c0 and cN are chloride ion contents subjected to different freeze-thaw cycles, ci is the boundary condition of chloride and C mn is the ion concentration tensor, ion concentrations, C mn 0 N

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X mn is ion concentration density tensor, and cNi  xNj is the concentration coefficient subjected to different freeze-thaw cycles. Finally, the two kinds of influences between the freeze-thaw cycles and chloride contents were combined for determining the interaction and coupling influence. The coupling coefficient can be established as follows [30,31]:

fKg ¼ R  fK FT-S  K Ch-I gK a  ka   Pn  l K lChI  K ChI l¼1 K FTS  K FTS R ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P  2 Pn  l n l l¼1 K FTS  K FTS l¼1 K FTS  K FTS Z jKj ¼ R 

Z cN mn p  rijFN rih  rhj C N  X mn dN  dci K a ka mn ij i j 4 C  X p  r r  r mn c 0 0 F0 h h 3

N 4 3

0

ð10Þ ð11aÞ

ð11bÞ

where K a is the initial coupling effect coefficient tensor, ka is the eulerian coordinate tensor, fKg is the coupling effect tensor, R is the correlation coefficient between freeze-thaw and chlorides, K FT-S and K Ch-I is the weighted average of FT-S and Ch-I acceleration coefficient and jKj is the value of fKg. 2.3. Mesoscopic diffusion mechanism In the framework of Fick’s first law, the diffusion flux was derived as follows:

@cf Da @ 2 cf ¼ b @x2 @t 1 þ @c @c

ð12Þ

f

where Da is the diffusion parameter of the cement material, x is the diffusion depth, cf is the free chloride concentrations and cb is binding chloride concentrations with concrete. Due to the influence of random harmful pore structure on the diffusion parameter [32,33], the mesoscopic diffusion parameter based on the density of characteristic pore structure is obtained as:

Dm ¼ Da  Hh

ð13Þ

where Dm is the mesoscopic diffusion parameter. The mesoscopic diffusion of chloride ions on the influence of pore structures can be determined coupling Fick’s second law and the mesoscopic diffusion parameter:

 a @cf jKj  Da  Hh t 0 @ 2 cf ¼ b @t t @x2 1 þ @c @c

ð14Þ

f

R t0 Then, let @t 0 ¼ ta @t and t0 ¼ 0 t a dt. Eq. (14) can then be changed as follows: h i RRR Þ2 Þð103tðr h ÞÞ  srh  ta0 P tðr h Þdr  f ðr h Þ  16 P ð1tðrh2 V rh rh tðrh Þ 45 rh @cf jKj  Da  ¼ @cb 0 @t 1 þ @c f

@ 2 cf  @x2

ð15Þ

Hence, the theoretical solution diffusion formal based on the changes of pore structure can be determined as:

cf ¼ c0 þ ðcs  c0 Þ             x  1  erf vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i   RRR u 2 Þð103tðr ÞÞ ð1 t ðr Þ  aþ1  16P h h u jKjD  P t ðr Þdr f ðr Þ  s t rh 0  h 45 r h 2tðrh Þ  t a V r h rh h   2 @c   1þ @cb f

where a is the time effect coefficient.

ð16Þ

3. Experimental and numerical details 3.1. Experimental materials 3.1.1. Raw materials and mix proportions Raw materials, including local ordinary Portland cement of grade P.O 42.5, a polycarboxylic series water-reducing agent, local river sand with a fineness modulus of 2.3, and water, were used throughout the study. Local limestone was used as a coarse aggregate, with sizes ranging from 5 mm to 25 mm. Tables 1 and 2 show the mechanical and chemical properties of ordinary Portland cement. The physical properties of the river sand and coarse aggregates are presented in Table 3. In this experiment, the water-tocement ratio (w/c) was 0.36, and the mixing proportion of concrete is shown in Table 4.

3.1.2. Specimen casting The concrete specimens were prepared is in accordance with Chinese standard JTGE30-2005 [34]. The dimensions of the concrete specimens were 100 mm  100 mm  100 mm and 100 mm  100 mm  400 mm, and the specimens were demoulded after 24 h. Each sample was placed in saturated limewater to cure at room temperature (i.e., 20 ± 2 °C) for 28 days according to GB/T 50081-2002 [35]. The specimens’ surfaces were repaired by using the same cement mortars and sealed on one side for chloride testing.

3.1.3. NaCl concentrations The concentrations determined by the rapid chloride ion test were divided into three levels, i.e., 10.5 g/L, 21.0 g/L and 42.0 g/L, according to the actual NaCl concentration of ocean salinity in Bohai Bay. Simultaneously, the samples were periodically taken out to measure the chloride content at different depths of concrete according to GB/T 50082-2009 [36]. Table 1 Mechanical properties of Portland cement (MPa). Flexural strength (MPa)

Compressive strength (MPa)

Fineness

Setting time (h:m)

3 days

28 days

3 days

28 days

1.8

4.8

6.8

21.3

55.8

Initial setting 1:03

Final setting 2:40

Table 2 Chemical properties of Portland cement (%). Chemical component

Weight (%)

Chemical component

Weight (%)

SiO2 Al2O3 Fe2O3 CaO MgO Mno

21.50% 4.50% 3% 65.70% 1.30% 0.14%

TiO2 Na2O K2O SO3 P205 Cl

0.23% 0.33% 0.39% 2% 0.27% 0.01%

Table 3 Physical properties of aggregates. Physical properties

Fine aggregate

Coarse aggregate

Type Size (mm) Apparent density (kg/m3) 24-h water absorption (%) Fineness modulus

Natural sand 0.16–2.5 2540 3.06 2.37

Crushed stone 5–20.5 2590 2.17 ——

Table 4 Mixing proportions of concrete (kg/m3). W/C

Cement

Water

Sand

Stone

Admixture

Air-entraining agent

0.36

458

165

707

1060

2.016

0.0916

B. Li et al. / Construction and Building Materials 125 (2016) 337–351

3.2. Experimental and numerical calculated methods The experimentation presented in this paper aimed to modify the mesoscopic computational model of chloride ion diffusion subjected to different freeze-thaw cycles and provide calculation parameters, and finally conducts better understanding of the mechanism of chloride ion diffusion under the influences of temperature. Fig. 1(a) provides a flowchart of the

341

experimental procedures and analysis methods used in this study and Fig. 1(b) shows the flowchart of simulation calculation method. 3.2.1. Freeze and thaw cycle tests Tests of concrete exposed to freeze-thaw cycles in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions were carried out in accordance with GB/T 50082-2009. The temperatures of the concrete samples

Fig. 1. (a) Flowchart of the experimental procedures and analysis methods (b) flowchart of the simulation calculation method.

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ranged from 18 ± 2 °C to 10 ± 5 °C. The rate of temperature change was 12–15 °C/h, and the duration of each freeze-thaw cycle was 2 ± 0.5 h to 3.5 ± 0.5 h. 3.2.2. Determination of Cl concentrations The chloride contents at different depths within the concrete specimens were measured by the ion selective electrode method using a CLCont-U experimental detector. At room temperature, i.e., from 20–25 °C, the concrete sections of different depths were triturated into powder and dissolved in distilled water for rapid measurement testing. 3.2.3. Mechanical properties The compressive strength and dynamic elastic modulus of concrete were measured according to GB/T 50081-2002 and GB/T 50082-2009. For different contents of chloride ions, 54 cubic specimens (100  100  100 mm) and 72 prismatic specimens (100  100  400 mm) were used to determine the dynamic elastic modulus. 3.2.4. Mercury intrusion porosimetry (MIP) Mercury intrusion porosimetry is the most common method for studying the pore properties (e.g., pore size distribution, pore radius and porosity) of ceramics, stones, clays, and cement-based materials. This method is relatively straightforward and generally yields reproducible pore size distributions. Important parameters such as pore size distribution, porosity and theoretical pore diameter can be deduced from these distributions.

Table 5 Simulation time on transport of chlorides (Days). Test cycles

0

50

100

150

200

250

300

Time (t)/Days

0

317

635

950

1260

1590

1900

Fig. 1(b) provides a flowchart of the simulation calculation method used in this study. The natural environmental data and meteorological data of Bohai Bay such as the salt concentration, ambient temperatures, meteorological conditions, and the MIP results were input to the first module. The initial data were then transferred to the input module. In this module, the data were classified and treated as a pointer storage module to invoke at any time. The data in the storage module were transferred and fed to the calculation and analysis module. Then, the input data in the storage module were was selected and distributed into the various calculation modules. After the comprehensive calculation module, the calculation results of chloride ion diffusion subjected to different freeze-thaw cycles were output and stored in excel files for comparing with experimental results. In summary, a calculation system based on its numerical performance and available computers and computing software (Matlab) was established.

3.2.5. Numerical calculation method (Matlab) To examine the validity of the mesoscopic diffusion model and describe the ingress of chloride into concrete, we measured the chloride content in concrete at different depths using numerical software (Matlab) and compared the simulated results to the experimental results. As can be understood in the above research [15–29], the free concentration of chloride ions is commonly used to calculate the transmission concentration of chloride ion in the concrete which is based on the relationship between total chloride ions and binding chloride ions. In this paper, the concentrations for the binding and free transmission chloride ions in the simulation calculation for ion diffusion which could be determined as follows [37]:

cf ¼ 2:07  c0:55 t 11:8ct cb ¼ 1þ4:0c t

ð17Þ

ct ¼ 10:5 g=L; 21:0 g=L and 42:0 g=L where ct is the total (the initial concentration of environment). To assess the accelerating effect of freeze-thaw cycles on chloride transport, 300 cycles of freeze-thaw tests were conducted. In order to simulate the authentic engineering environment for calculating the degree of diffusion in concrete, decades of meteorological data and freeze-thaw cycles of the Bohai Bay have been count. Based on the comparing with the real statistics freeze-thaw cycles, the laboratory freeze-thaw cycles can be transformed into a realistic environment cycles for simulation calculation. The calculation time step could be determined based on meteorological data for Bohai [38] as follows and the results pertaining to the calculation time are shown in Table 5:

t simulation =day ¼

~ N ~ ð1:11:3Þ  365 N=year

ð18Þ

~ is the number of test cycles, where t simulation is the calculation time, N and N is the average annual cycle in Bohai Bay based on meteorological data.

Fig. 2. (a) Compressive strength of concrete in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions at different freeze-thaw cycles (b) dynamic elastic modulus of concrete in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions at different freeze-thaw cycles.

B. Li et al. / Construction and Building Materials 125 (2016) 337–351

343

Fig. 3. (a) Surface damage of concrete in 10.5 g/L NaCl conditions (b) surface damage of concrete in 21.0 g/L NaCl conditions (c) surface damage of concrete in 42.0 g/L NaCl conditions.

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4. Test results and discussion 4.1. Macro-property test results 4.1.1. Mechanical property test results Mechanical properties were investigated by analysing the compressive strength (Fig. 2(a)) and dynamic elastic modulus (Fig. 2 (b)) obtained under different freeze-thaw cycles. The results indicate that with an increasing number of freeze-thaw cycles, the

compressive strength and dynamic elastic modulus of concrete for different NaCl contents decreased by 45.91%–59.84% and by 22.99%–39.26%, respectively. With increasing NaCl content, changes in the macro-mechanical characteristics were not significant in the 10.5 g/L and 21.0 g/L NaCl solutions, but a significant difference was observed in the 42.0 g/L solution. Hence, increasing NaCl concentrations can significantly reduce the mechanical properties of concrete subjected to freeze-thaw cycles. 4.1.2. Surface damage As shown in Fig. 3(a) –(c), the surface scaling of concrete varied substantially with the coupling conditions of NaCl and freeze-thaw cycles. After 50 freeze-thaw cycles, the surface of the concrete became uneven, macro-cracks appeared, and some NaCl crystallization occurred. After 150 freeze-thaw cycles, the coarse aggregates of concrete became exposed and parts of the concrete protective layer were spalled. The coarse aggregates of concrete were exposed, and the mortar peeled off due to freeze-thaw cycles in the 42.0 g/L NaCl solution. Higher NaCl concentrations yielded greater surface damage to the concrete during the freeze-thaw cycling.

Fig. 4. Weight loss of concrete in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions at different freeze-thaw cycles.

4.1.3. Weight loss Fig. 4 shows the weight loss rate of the experimental specimens. As shown, the weight loss rate of concrete in the 10.5 g/L NaCl solution was lower than that in the other two solutions. The weight loss rates of concrete in the 10.5, 21.0, and 42.0 g/L NaCl solutions were 13.13%, 17.85%, and 17.01%, respectively, after 300 freezethaw cycles. After 50 freeze-thaw cycles, the weight loss rates were 0.12%, 8.39%, 8.59%, respectively. The spalling due to the

Fig. 5. (a) Porosity of concrete in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions (b) critical pore diameter of concrete in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions (c) mode pore diameter of concrete in 10.5 g/L, 21.0 g/L and 42.0 g/L times NaCl solutions.

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tion) improved with an increasing number of freeze-thaw cycles. The porosity of the 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl samples increased by 3.01%, 5.17% and 7.3%, respectively. Due to the coupling action of freeze-thaw cycles and chloride ions, internal micro-cracks formed, and the pore structures of concrete showed signs of change, such as an increase in number and size. Similar results were observed in terms of the variation in pore size (Fig. 5 (b) and (c)). (2) Mercury injection was used to determine the curvilinear relationships and variations in the pore size distribution with different freeze-thaw cycles and ion contents (Figs. 6 and 7). Variations in the structural features of three types of pores in concrete, namely gel pores (1–10 nm), capillary pores (10–10000 nm) and macrospores (>10,000 nm), were monitored and analysed. According to the classical diffusion, permeation and electrical flux theory of chloride ion erosion, different size ranges of pores had various impacts on the durability properties of chloride ions in concrete. In general, small gel and capillary pores, which were classified as harmless pore structures, had no significant effect on chloride ion transportation. In this part of our study, we selected pore structures larger than 20 nm for durability analyses. The classification system used included smaller harmful pore structures (measuring between 20 nm and 50 nm), harmful pore structures (measuring between 50 and 200 nm) and more harmful structures (measuring larger than 200 nm) [39]. Combined with the variations in the volume percentage of pore structures, we analysed the coupling impact of freeze-thaw cycles and chloride ions on the diversification of different harmful pore structures. The volume percentage of pore structures can be determined as follows and is shown in Table 6:

R N ðTypeÞ ðTypeÞ T r dN ^ a ¼ 0R N sizeðAllÞ size ðAllÞ T size  r size dN 0

ð19Þ

^ is the volume percentage, T ðTypeÞ where a is the value of mercury size ðAllÞ

Fig. 6. (a) Mercury intrusion volume of concrete in 10.5 g/L NaCl conditions (b) mercury intrusion volume of concrete in 21.0 g/L NaCl conditions (c) mercury intrusion volume of concrete in 42.0 g/L NaCl conditions.

freeze-thaw cycles in the 21.0 g/L and 42.0 g/L NaCl solutions was an accelerated, progressive phenomenon, as it occurred more rapidly than the surface damage of the concrete in the 10.5 g/L NaCl solution. 4.2. Pore structure of concrete After all MIP experimental data of pore structure were obtained, the effects of freeze-thaw cycles and chloride ions on the mesoscopic structures of concrete were analysed. The following results were obtained. (1) As shown in Fig. 5, the porosity, critical pore diameter (the maximum pore level for connection between pores) and the mode pore diameter (the peak value of the pore distribu-

injected into various types of pore structures, T size is the cumulative amount of mercury injected into all pore structures. As shown in Table 6, the volume percentage of harmless pore structures decreased, and the volume percentages of smaller harmful, harmful and more harmful pore structures increased with the number of freeze-thaw cycles and chloride concentration. The volume percentages of different pore diameters (20 nm 6 r < 50 nm and 50 6 r < 200 nm) increased considerably, particularly for pores measuring 50 6 r < 200 nm, the percentage of which increased significantly. (3) As shown in Figs. 6 and 7 and Table 6, both the freeze-thaw cycles and chloride ion concentrations had a significant impact on the internal structures of the concrete specimens. For the same ion concentration, the peak amount of injected mercury increased with the number of freeze-thaw cycles, and the peak values of the pore size distribution in gel pores, capillary pores and macro-pores steadily increased. These results suggest that the rapid freeze-thaw cycles increased the volume and size of pores in the concrete. In addition, after comparing different chloride ion concentrations at the same number of freeze-thaw cycles, some analytical conclusions about the pore structure characteristics could be drawn. With increasing ion concentration, the pore sizes and cumulative mercury intrusion volume increased. The peak values of the cumulative mercury intrusion volume and pore size of the 42.0 g/L NaCl solution subjected to

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Fig. 7. (a) Pore size distribution of concrete in 10.5 g/L NaCl conditions (b) pore size distribution of concrete in 21.0 g/L NaCl conditions (c) pore size distribution of concrete in 42.0 g/L NaCl conditions.

Table 6 Pore size volume factors in different freeze-thaw cycles in 10.5 g/L 21.0 g/L and 42.0 g/L NaCl solutions (%). Freeze-thaw cycles

Pore size volume fraction (%) 1–20 nm

20–50 nm

50–200 nm

>200 nm

10.5 g/L NaCl 0 50 100 150 200 250 300

27.6 28.55 24.84 22.57 22.59 22.15 18.28

28.53 26.74 29.65 28.52 29.41 27.02 28.81

9.09 9.6 9.5 12.69 11.64 13.1 13.48

34.78 35.11 36.01 36.22 36.36 37.73 39.43

21.0 g/L NaCl 0 50 100 150 200 250 300

29.4 28.4 24.64 22.31 21.59 19.51 16.56

27.59 26.53 29.53 28.46 28.31 28.15 28.81

9.16 9.47 9.95 12.9 13.34 13.61 15.08

33.85 35.6 35.88 36.33 36.76 38.73 39.55

42.0 g/L NaCl 0 50 100 150

19 18.04 16.82 16.54

29.19 24.24 25.3 23.18

14.78 19.69 19.02 21.18

37.03 38.03 38.86 39.1

150 freeze-thaw cycles were nearly equivalent to the values measured for the 21.0 g/L NaCl and 10.5 g/L NaCl solutions subjected to 250 freeze-thaw cycles. The complex coupling between the freeze-thaw cycling and chloride ion concentration, variations in the chloride concentration could also affect and expand the pore structure of concrete. In previous

Fig. 8. The most content of chloride ion subjected to freeze-thaw cycles in 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions.

studies, this coupling has not been sufficiently significant and thus has often been ignored. In this study, however, changes in the salt solution concentrations also had a significant effect on the pore structure distributions and mesoscopic properties of concrete.

4.3. Diffusion parameters and contents To simulate the marine environment in Bohai Bay, 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl solutions were used as the calculated

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347

Fig. 9. (a) Diffusion content of chloride ion of concrete in 10.5 g/L NaCl conditions (b) diffusion content of chloride ion of concrete in 21.0 g/L NaCl conditions (c) diffusion content of chloride ion of concrete in 42.0 g/L NaCl conditions.

and analysed chloride concentrations. The highest diffusion of chloride in concrete [36–38] and contents of chloride ions subjected to different freeze-thaw cycles are shown in Figs. 8 and 9, respectively. In Fig. 8, the diffusion of chloride ions increased gradually in the 10.5 g/L and 21.0 g/L NaCl solutions at the end of the 150 freeze-thaw cycles. As indicated in Fig. 6, the pore structures of concrete expanded and developed such that the exhibited expansion and developments which is drastically accelerated chloride ion diffusion of chlorides. With an increasing number of

Fig. 10. (a) Coupling influence coefficients between freeze-thaw cycles and chloride ion corrosion (b) coefficients of freeze-thaw cycles (c) coefficients of chloride ion contents.

freeze-thaw cycles and pore structure evolution, the 10.5 g/L and 21.0 g/L NaCl solutions displayed similar increasing trends and peak values of 8.95% and 9.16%, respectively, in the diffusion

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Fig. 11. (a) Freeze-thaw stress (FT-S) of concrete in 10.5 g/L NaCl conditions (b) freeze-thaw stress (FT-S) of concrete in 21.0 g/L NaCl conditions (c) freeze-thaw stress (FT-S) of concrete in 42.0 g/L NaCl conditions.

Table 7 Parameter values employed in numerical simulations. Parameters

Notation

Value

Unit

Note

Feature pore size Maximum pore size

r0 rn

17.2

nm nm

Assumed on MIP Test

Water/cement Hydration degree Chloride concentration in NaCl solution

w/c H

0.36 0.61 10.5 21.0 42.0 400

Specimen length Diffusion parameter of concrete Weighted average of FT-S acceleration coefficient Weighted average of Ch-I acceleration coefficient Correlation coefficient Tortuosity of harmful pore structure

C mn 0

3:55  105

— — g/L

Da

2:50  1011

mm m2/s

K FTS

3.12

—

K ChI

3.84

—

R

0.97 0.06–0.2

— —

sr h

curves after 300 freeze-thaw cycles. However, the evolution of the critical chloride ion content in the 42.0 g/L NaCl solution showed marked differences. With an increase in the number of freezethaw cycles, the concentration increased exponentially, with a peak value of 8.83% after 150 freeze-thaw cycles. The combination of chloride ions and freeze-thaw conditions limited the chloride ion concentration and critical evolution of the pore structure. The coupling influence coefficients were determined using Matlab calculation programs based on the experimental results and are

shown in Fig. 10(a)–(c). The results of K show that the chloride ion content is the most significant factor affecting the diffusion depth and progress with the coupling between freeze-thaw cycles and chloride ion corrosion. A mesoscopic diffusion model of chloride ions based on Fick’s second law was established in this study. The boundary conditions of diffusion were as follows: (1) the diffusion depth x ranged from 5 mm to 20 mm; (2) the diffusion time t was as shown in Table 5; (3) the initial chloride ion contents were 10.5 g/L, 21.0 g/L and 42.0 g/L; (4) the freeze-thaw stress (FT-S) was calculated, as shown in Figs. 11 and 5) the parameters for numerical calculation in this paper are shown in Table 7. The results based on Eq. (16) were calculated by Matlab programs and compared with the experimental data shown in Fig. 12. Figs. 9 and 12 and Table 8 show that (a) freeze-thaw cycling had an accelerating effect on chloride ion erosion, which could be divided into an initial stage, an acceleration stage and a deceleration stage (Fig. 9(a) –(c)). For instance, as indicated by the 10.5 g/L NaCl curves in Fig. 9(a), the initial stage starting at the 5th freeze-thaw cycle and the acceleration stage occurred from the 55th to 255th freeze-thaw cycle. The deceleration stage ended at 285 cycles. Identical results were observed for the three different stages of the 21.0 g/L NaCl solution, as shown in Fig. 9(b). However, the 42.0 g/L NaCl solution showed some differences. Due to the function of the NaCl content, the effect of freeze-thaw cycling on chloride ions remained in the initial and accelerated stages, indicating that if the chlorine ion concentrations in the environment were variable, the effect of freezing and thawing on chloride ion diffusion could be drastically increased. (b) After 50 cycles, the calculated results for chloride ion

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Fig. 12. (a) Diffusion content of chloride ion subjected to 0 freeze-thaw cycle (b) diffusion content of chloride ion subjected to 50 freeze-thaw cycle (c) diffusion content of chloride ion subjected to 100 freeze-thaw cycle (d) diffusion content of chloride ion subjected to 150 freeze-thaw cycle (e) diffusion content of chloride ion subjected to 200 freeze-thaw cycle (f) diffusion content of chloride ion subjected to 250 freeze-thaw cycle (g) diffusion content of chloride ion subjected to 300 freeze-thaw cycle.

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Table 8 Calculated errors of Fick’s law and mesoscopic model (%). Cycles errors

10.5 g/L NaCl

21.0 g/L NaCl

Mesoscopic model

Fick’s law

Mesoscopic model

Fick’s law

Mesoscopic model

Fick’s law

0N 50 N 100 N 150 N 200 N 250 N 300 N Total errors

10.65% 14.24% 14.30% 13.55% 14.50% 13.70% 14.35% 12.40%

6.75% 14.20% 15.35% 17.13% 20.59% 21.68% 20.53% 13.59%

8.70% 8.80% 4.43% 4.48% 7.60% 14.45% 13.36% 9.60%

7.60% 7.44% 9.28% 11.63% 15.91% 21.43% 25.56% 14.12%

11.36% 13.20% 3.70% 7.68%

11.24% 18.30% 14.73% 19.80%

9.10%

15.01%

diffusion determined by Eq. (23) were greater than the experiment results due to the accelerating effect of freeze-thaw cycling on chloride ion erosion in the accelerated stage. After 200 cycles, the calculated error of the new model became larger. This increase in the error was observed because the spalling and damage of the concrete specimens caused by freeze-thaw cycling reduced the experimental chloride ion contents. Thus, freeze-thaw cycling has a strong effect on the calculation error. The total average errors for the 10.5 g/L, 21.0 g/L and 42.0 g/L NaCl conditions were 12.4%, 9.6% and 9.1%, respectively. Relative to the results calculated for chloride ions using Fick’s law, the total errors calculated for the various experimental conditions and the mesoscopic model are shown in Table 8. As shown, the errors for the Fick’s law calculations were 17.39%, 14.12% and 15.01%, respectively. Fick’s law showed high accuracy in calculating the low-concentration diffusion field and the single-environment field but produced relatively large errors in the calculations of the coupled field associated with freeze-thaw cycling and chloride ion concentration and multiconcentration gradients. The new mesoscopic model was incorporated with the accelerating effects of freeze-thaw cycles and chloride ions to make the results more accurate. (c) The high chloride ion concentration decreased the frost resistance of concrete. The concrete in the 42.0 g/L NaCl solution could only withstand 150 cycles. However, the diffusion equation remained accurate at the end of 300 cycles and beyond. The theoretical method for calculating the coupled erosion should be controlled by a threshold, such as weight loss, the elastic modulus or stress.

42.0 g/L NaCl

coupling between freeze-thaw cycles and chloride ion corrosion. Changes in chloride ion concentrations had the most significant effect in accelerating the depth of chloride ion diffusion. (3). Based on the variation of mesoscopic characteristics in concrete subjected to the aforementioned coupling environment, a mesoscopic diffusion equation was established for the theoretical calculation of chloride ion diffusion. Relative to the results calculated for chloride ions using Fick’s law, the total errors calculated for the various experimental conditions and the mesoscopic model are shown in Table 8. The total error of the mesoscopic model was 10.7% relative to compared with the experimental results. However, the total error for the Fick’s law calculations was 15.51%. Hence, the calculated results were closer to the actual results, and the mesoscopic diffusion equation could be employed in a future multi-scale study of chloride ion erosion. Acknowledgements The authors wish to acknowledge the financial support received for this work from the National Natural Science Foundation of China (50908059), the Natural Science Foundation of Heilongjiang Province of China (E201415), the Fundamental Research Funds for the Central Universities of China (HEUCF160207), and the Japan Society for the Promotion of Science (JSPS) (26.04058). References

5. Conclusions The pore size, pore distribution and mesoscopic pore structure of concrete and cement-based materials all have important effects on the transport of chloride ions in concrete. When concrete was subjected to freeze-thaw conditions and chloride corrosion, the macro-properties and mesoscopic structures changed considerably. The multiphase environment affected the mesoscopic pore structures, in which the diffusion of chloride could be represented by different mesoscopic properties. Based on the experimental results and the analysis of pore distribution and diameter alternation, the following conclusions can be drawn: (1). Freeze-thaw cycling accelerated chloride ion erosion, which could be divided into an initial stage, an acceleration stage and a deceleration stage. Simultaneously, chloride ions could reduce the frost resistance of concrete and cause early cracking and spalling. (2). The coupling between freeze-thaw cycling and chloride ion corrosion accelerated the erosion of chloride ions. The results of K show the coupling coefficients between chloride ion contents and freeze-thaw cycles. Results of K can also show that the chloride ion content is the most significant factor affecting the diffusion depth and progress with the

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