# Moisture Diffusion Coefficient of Concrete under Different Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Modeling

_{d}denotes the humidity reduction due to the drying effect, t denotes the drying time, x denotes the distance of the interior of the concrete from the drying surface, and D denotes the concrete diffusion coefficient.

_{d}can be expressed as:

_{e}denotes the ambient humidity of the concrete.

_{d}(x,t); therefore, its boundary conditions can be expressed as follows:

_{0}denotes the initial humidity inside the coagulation.

_{t}denotes the first-order partial derivative of the internal concrete humidity with respect to t and u

_{xx}denotes the second-order partial derivative of the internal concrete humidity with respect to x.

_{t}denotes the first-order partial derivative of the internal moisture diffusion of concrete with respect to t under infinite boundary conditions, U

_{xx}denotes the second-order partial derivative of the internal moisture diffusion of concrete with respect to x under infinite boundary conditions, X(x) denotes the change in humidity induced by the internal moisture diffusion of concrete on the x scale under infinite boundary conditions, and T(t) denotes the change in humidity induced by the internal moisture diffusion of concrete on the t scale under infinite boundary conditions.

_{α}satisfies the superposition principle, namely

_{0}yields the following equation:

_{d}and the relationship between H

_{d}and η, the humidity diffusion coefficient of the concrete can be calculated using Equation (34), as can the internal humidity of the concrete.

_{d}and η based on Akita’s research results [34]; by approximating the fitting of the test results, the humidity value is calculated as follows:

## 3. Experimental Design

#### 3.1. Concrete Mixing Ratio

_{2}, CaO, Al

_{2}O

_{3}, Fe

_{2}O

_{3}, MgO, and SO

_{3}in cement and fly ash is shown in Table 2. The specific surface area of cement and fly ash were 3471 and 4680 cm

^{2}/g. The density was 3.10 and 2.22 g/cm

^{3}, respectively.

#### 3.2. Basic Concrete Performance Tests

#### 3.3. Concrete Internal Humidity and Shrinkage

^{4}MPa, the yield strength was 400 × 10

^{4}MPa, and the ultimate strength was 580 × 10

^{4}MPa. Specific experimental information is tabulated in Table 4 (without constraints) and Table 5 (with constraints). All the components were tested at a room temperature of 25 °C. The internal humidity of the concrete test lasted for a total of 28 days. The internal humidity data of the concrete were automatically read and recorded by a computer every 0.5 days. Three specimens of each type were evaluated, and the data analyzed in the following sections were derived from the average of the data obtained from three specimens under the same test conditions.

#### 3.4. Pore Structure Test

## 4. Results and Discussion

#### 4.1. Concrete Internal Humidity

#### 4.2. Concrete Moisture Diffusion Coefficient

_{0}, a, b, c, and d represent calculation parameters of the humidity value fitting model (Equation (35)), and it can be obtained from the results of the fitting tests, as shown in Table 6. In addition, average fitting error is obtained between the experimental and fitted values of humidity diffusion at each age of the specimens.

^{2}/h. With the increase in external humidity to 50% and 65%, the humidity diffusion coefficient decreases to 68.9 mm

^{2}/h and 53.8 mm

^{2}/h, which is a decrease of 41.6 mm

^{2}/h and 56.7 mm

^{2}/h, respectively. This phenomenon occurs because when the concrete is poured, the internal humidity is significantly higher than the external humidity, and the lower the external humidity, the more significant the drying effect, which is reflected in the diffusion coefficient, and the higher the diffusion coefficient value. As can be seen in Figure 4, there is a linear relationship between the moisture diffusion coefficient of concrete and the external humidity. However, there are differences in the ratio between them at different strength classes as well as at different ages. In general, the effect of external humidity on the humidity diffusion coefficient decreases with age and concrete strength.

#### 4.3. Effect of Concrete Strength on Moisture Diffusion Coefficient

#### 4.4. Effect of Pore Structure on the Moisture Diffusion Coefficient of Concrete

_{s}is the modulus of elasticity of concrete, E

_{re}is the modulus of elasticity of steel reinforcement, ρ is the reinforcement ratio, μ is the Poisson’s ratio of concrete, and a and γ are calculation parameters. The above equation shows that the confining stress of the reinforcement increases with the increase in the reinforcement ratio. In this case, it will decrease the stress ensemble acting on the pore walls of the concrete. This indicates that the extent of decrease in the pore structure parameters of the concrete due to the action of capillary stresses decreases as the reinforcement ratio increases. This agrees with the experimental results that indicate that the pore structure size of the specimens increases with increasing reinforcement rate.

^{2}/h, 34.05 mm

^{2}/h, and 51.13 mm

^{2}/h, respectively.

## 5. Conclusions

- The internal humidity of concrete varies with age. As the age increases, the internal humidity of concrete decreases and gradually stabilizes. Due to more intense hydration, the internal humidity of high-strength concrete decreases more rapidly under sealed conditions. The internal humidity of specimens under dry conditions decreases faster than that of sealed specimens due to the drying effect. For the same concrete strength class, the lower the external humidity and the higher the reinforcement rate, the faster the internal humidity of the concrete decreases.
- The moisture diffusion coefficient of concrete can be divided into a rapid decline phase (0–1 day), a slow decline phase (1–8 days), and a stabilization phase (after 8 days) as the age increases. Due to the existence of a humidity gradient, the lower the external environmental humidity, the higher the humidity diffusion coefficient of concrete for the same concrete strength class and reinforcement ratio, and the two exhibit a linear relationship. With the increase in age and concrete strength, the influence of external humidity on the humidity diffusion coefficient of concrete weakens. Meanwhile, along with the gradual decrease in the internal humidity of concrete, the humidity diffusion coefficient of concrete also gradually decreases, and it is more difficult for the water in concrete to be transmitted to the external environment.
- At the same age, high-strength concrete has smaller pore structure parameters, which makes transporting water in high-strength concrete difficult. As a result, the moisture diffusion coefficient of concrete decreases as the concrete strength class increases for the same external humidity and reinforcement ratio. The method proposed in this study for calculating the internal humidity of concrete using the humidity diffusion coefficient is accurate.
- Reinforcing bars create confining tensile stresses inside the concrete, which changes the pore structure inside the concrete. For the same concrete strength, the higher the reinforcement rate, the larger the pore structure parameters of concrete (average pore diameter, median pore diameter, critical diameter of capillary, and porosity). Because the pore structure is the main transport channel for water in concrete, the higher the reinforcement ratio, the greater the moisture diffusion coefficient of the concrete and the faster the moisture in the concrete decreases for the same external humidity and concrete strength.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Krauss, P.D.; Rogalla, E.A. Transverse Cracking in Newly Constructed Bridge Decks; National Academy of Sciences: Washington, DC, USA, 1996. [Google Scholar]
- Chen, L.; Huang, L.; Hua, J.; Chen, Z.; Wei, L.; Osman, A.I.; Fawzy, S.; Rooney, D.W.; Dong, L.; Yap, P.-S. Green construction for low-carbon cities: A review. Environ. Chem. Lett.
**2023**, 21, 1627–1657. [Google Scholar] [CrossRef] - Zhou, F.; Jiang, H.; Huang, L.; Hu, Y.; Xie, Z.; Zeng, Z.; Liu, M.; Wang, B.; Zhou, X. Early Shrinkage Modeling of Complex Internally Confined Concrete Based on Capillary Tension Theory. Buildings
**2023**, 13, 2201. [Google Scholar] [CrossRef] - Huang, L.; Hua, J.; Kang, M.; Zhou, F.; Luo, Q. Capillary tension theory for predicting shrinkage of concrete restrained by reinforcement bar in early age. Constr. Build. Mater.
**2019**, 210, 63–70. [Google Scholar] [CrossRef] - Tran, N.P.; Gunasekara, C.; Law, D.W.; Houshyar, S.; Setunge, S.; Cwirzen, A. A critical review on drying shrinkage mitigation strategies in cement-based materials. J. Build. Eng.
**2021**, 38, 102210. [Google Scholar] [CrossRef] - Wang, X.; Song, P.; Yu, H.; Taylor, P.; Sadati, S.; Freeseman, K.; Ning, Y. Extended life concrete bridge decks utilizing internal curing to reduce cracking–Materials characterization and engineering demonstration. Constr. Build. Mater.
**2021**, 275, 122163. [Google Scholar] [CrossRef] - Miao, Y.; Lu, Z.; Wang, F.; Wang, H.; Li, Y.; Lin, J.; Jiang, J. Shrinkage cracking evolvement in concrete cured under low relative humidity and its relationship with mechanical development. J. Build. Eng.
**2023**, 72, 106670. [Google Scholar] [CrossRef] - Yu, S.; Sun, Z.; Qian, W.; Yu, J.; Yang, J. A meshless method for modeling the microscopic drying shrinkage cracking processes of concrete and its applications. Eng. Fract. Mech.
**2023**, 277, 109014. [Google Scholar] [CrossRef] - Shen, D.; Kang, J.; Jiao, Y.; Li, M.; Li, C. Effects of different silica fume dosages on early-age behavior and cracking resistance of high strength concrete under restrained condition. Constr. Build. Mater.
**2020**, 263, 120218. [Google Scholar] [CrossRef] - Klemczak, B.; Knoppik-Wróbel, A. Reinforced concrete tank walls and bridge abutments: Early-age behaviour, analytic approaches and numerical models. Eng. Struct.
**2015**, 84, 233–251. [Google Scholar] [CrossRef] - Chen, L.; Chen, Z.; Zhang, Y.; Liu, Y.; Osman, A.I.; Farghali, M.; Hua, J.; Al-Fatesh, A.; Ihara, I.; Rooney, D.W. Artificial intelligence-based solutions for climate change: A review. Environ. Chem. Lett.
**2023**, 21, 2525–2557. [Google Scholar] [CrossRef] - Chen, L.; Msigwa, G.; Yang, M.; Osman, A.I.; Fawzy, S.; Rooney, D.W.; Yap, P.-S. Strategies to achieve a carbon neutral society: A review. Environ. Chem. Lett.
**2022**, 20, 2277–2310. [Google Scholar] [CrossRef] - Farghali, M.; Osman, A.I.; Mohamed, I.M.; Chen, Z.; Chen, L.; Ihara, I.; Yap, P.-S.; Rooney, D.W. Strategies to save energy in the context of the energy crisis: A review. Environ. Chem. Lett.
**2023**, 21, 2003–2039. [Google Scholar] [CrossRef] [PubMed] - Deysel, R.C.; Boshoff, W.P.; Smit, M.S. Implementing capillary pressure control measures to prevent plastic shrinkage cracking in concrete. Constr. Build. Mater.
**2023**, 397, 132407. [Google Scholar] [CrossRef] - Liang, S.; Liu, Y.; Song, G.; Yan, H.; Song, B.; Liu, J. Effect of sulfoaluminate expansive additive on mechanical properties, internal relative humidity, and shrinkage of early-age mortar. Case Stud. Constr. Mater.
**2023**, 19, e02226. [Google Scholar] [CrossRef] - Wang, Y.; Zhu, J.; Guo, Y.; Wang, C. Early shrinkage experiment of concrete and the development law of its temperature and humidity field in natural environment. J. Build. Eng.
**2023**, 63, 105528. [Google Scholar] [CrossRef] - Persson, B. Moisture in concrete subjected to different kinds of curing. Mater. Struct.
**1997**, 30, 533–544. [Google Scholar] [CrossRef] - Kim, J.-K.; Lee, C.-S. Moisture diffusion of concrete considering self-desiccation at early ages. Cem. Concr. Res.
**1999**, 29, 1921–1927. [Google Scholar] [CrossRef] - Nilsson, L.-O. Long-term moisture transport in high performance concrete. Mater. Struct.
**2002**, 35, 641–649. [Google Scholar] [CrossRef] - Andrade, C.; Sarría, J.; Alonso, C. Relative humidity in the interior of concrete exposed to natural and artificial weathering. Cem. Concr. Res.
**1999**, 29, 1249–1259. [Google Scholar] [CrossRef] - Parrott, L. Some effects of cement and curing upon carbonation and reinforcement corrosion in concrete. Mater. Struct.
**1996**, 29, 164–173. [Google Scholar] [CrossRef] - Wang, J.; Li, H.; Wang, Z.; Yi, Z.; Huang, F. Humidity field and moisture transfer of concrete with different pre-saturated recycled sand. Constr. Build. Mater.
**2023**, 382, 131338. [Google Scholar] [CrossRef] - Shen, D.; Liu, C.; Wang, M.; Jin, X.; Tang, H. Prediction model for internal relative humidity in early-age concrete under different curing humidity conditions. Constr. Build. Mater.
**2020**, 265, 119987. [Google Scholar] [CrossRef] - Tazawa, E.-I.; Miyazawa, S. Influence of cement and admixture on autogenous shrinkage of cement paste. Cem. Concr. Res.
**1995**, 25, 281–287. [Google Scholar] [CrossRef] - Tazawa, E.-I.; Miyazawa, S. Experimental study on mechanism of autogenous shrinkage of concrete. Cem. Concr. Res.
**1995**, 25, 1633–1638. [Google Scholar] [CrossRef] - Aitcin, P.-C. Demystifying autogenous shrinkage. Concr. Int.
**1999**, 21, 54–56. [Google Scholar] - Ni, W.-M. The Mathematics of Diffusion; SIAM: Philadelphie, PA, USA, 2011. [Google Scholar]
- Park, S.-S.; Kwon, S.-J.; Jung, S.H.; Lee, S.-W. Modeling of water permeability in early aged concrete with cracks based on micro pore structure. Constr. Build. Mater.
**2012**, 27, 597–604. [Google Scholar] [CrossRef] - Linderoth, O.; Johansson, P.; Wadsö, L. Development of pore structure, moisture sorption and transport properties in fly ash blended cement-based materials. Constr. Build. Mater.
**2020**, 261, 120007. [Google Scholar] [CrossRef] - Huang, L.M.; Tang, L.P.; Lofgren, I.; Olsson, N.; Yang, Z.H.; Li, Y.Q. Moisture and ion transport properties in blended pastes and their relation to the refined pore structure. Cem. Concr. Res.
**2022**, 161, 106949. [Google Scholar] [CrossRef] - Bažant, Z.; Najjar, L. Nonlinear water diffusion in nonsaturated concrete. Matériaux Constr.
**1972**, 5, 3–20. [Google Scholar] [CrossRef] - Ayano, T.; Wittmann, F.H. Drying, moisture distribution, and shrinkage of cement-based materials. Mater. Struct.
**2002**, 35, 134–140. [Google Scholar] [CrossRef] - Sakata, K. A study on moisture diffusion in drying and drying shrinkage of concrete. Cem. Concr. Res.
**1983**, 13, 216–224. [Google Scholar] [CrossRef] - Akita, H.; Fujiwara, T.; Ozaka, Y. A practical procedure for the analysis of moisture transfer within concrete due to drying. Mag. Concr. Res.
**1997**, 49, 129–137. [Google Scholar] [CrossRef] - Ba, M.F.; Qian, C.X.; Gao, G.B. Nonlinear calculation of moisture transport in underground concrete. Comput. Concr.
**2014**, 13, 361–375. [Google Scholar] [CrossRef] - Rahimi-Aghdam, S.; Rasoolinejad, M.; Bažant, Z.P. Moisture diffusion in unsaturated self-desiccating concrete with humidity-dependent permeability and nonlinear sorption isotherm. J. Eng. Mech.
**2019**, 145, 04019032. [Google Scholar] [CrossRef] - Lin, G.; Liu, Y.; Xiang, Z. Numerical modeling for predicting service life of reinforced concrete structures exposed to chloride environments. Cem. Concr. Compos.
**2010**, 32, 571–579. [Google Scholar] [CrossRef] - Wang, A.; Sun, D.; Deng, M.; Chen, X.; Zhang, F. Influence of restraint on pore structures and air permeability of concrete containing MgO-type expansive agent. Asian J. Chem.
**2013**, 25, 5532. [Google Scholar] [CrossRef] - Zhang, R.; Wang, Q.; Ma, L. Relations between pore structure and creep characteristics of concrete under micro-expanding and lateral restraints. J. Chin. Ceram. Soc.
**2015**, 7, 585–593. [Google Scholar] - Yoo, D.-Y.; Park, J.-J.; Kim, S.-W.; Yoon, Y.-S. Influence of reinforcing bar type on autogenous shrinkage stress and bond behavior of ultra high performance fiber reinforced concrete. Cem. Concr. Compos.
**2014**, 48, 150–161. [Google Scholar] [CrossRef] - Sule, M.; van Breugel, K. The effect of reinforcement on early-age cracking due to autogenous shrinkage and thermal effects. Cem. Concr. Compos.
**2004**, 26, 581–587. [Google Scholar] [CrossRef] - Huang, L.; Hua, J.; Kang, M.; Zhang, A. Influence of reinforcement configuration on the shrinkage and cracking potential of high-performance concrete. Constr. Build. Mater.
**2017**, 140, 20–30. [Google Scholar] [CrossRef] - Yoo, D.-Y.; Park, J.-J.; Kim, S.-W.; Yoon, Y.-S. Early age setting, shrinkage and tensile characteristics of ultra high performance fiber reinforced concrete. Constr. Build. Mater.
**2013**, 41, 427–438. [Google Scholar] [CrossRef] - Ming, K. Research on Restrained Deformation Properties of Reinforced Concrete Members due to Early Shrinkage during Construction. Ph.D. Thesis, Chongqing University, Chongqing, China, 2010. [Google Scholar]
- Radlinska, A.; Weiss, J. Quantifying variability in assessing the risk of early-age cracking in restrained concrete elements. In Brittle Matrix Composites 8; Elsevier: Amsterdam, The Netherlands, 2006; pp. 331–342. [Google Scholar]
- Zhang, J.; Huang, Y.; Qi, K.; Gao, Y. Interior relative humidity of normal-and high-strength concrete at early age. J. Mater. Civ. Eng.
**2012**, 24, 615–622. [Google Scholar] [CrossRef] - Zhang, J.; Qi, K.; Huang, Y. Calculation of moisture distribution in early-age concrete. J. Eng. Mech.
**2009**, 135, 871–880. [Google Scholar] [CrossRef] - Deboodt, T.; Fu, T.; Ideker, J.H. Evaluation of FLWA and SRAs on autogenous deformation and long-term drying shrinkage of high performance concrete. Constr. Build. Mater.
**2016**, 119, 53–60. [Google Scholar] [CrossRef] - Shen, D.; Liu, K.; Ji, Y.; Shi, H.; Zhang, J. Early-age residual stress and stress relaxation of high-performance concrete containing fly ash. Mag. Concr. Res.
**2018**, 70, 726–738. [Google Scholar] [CrossRef] - GB/T50081-2002; Standard for Test Method of Mechanical Properties on Ordinary Concrete. Ministry of Construction of the People’s Republic of China and General Administration of Quality Supervision. Inspection and Quarantine of the People’s Republic of China: Beijing, China, 2003.

**Figure 3.**Development of the moisture diffusion coefficient of concrete with age: (

**a**) C30; (

**b**) C40; (

**c**) C50; (

**d**) C60.

**Figure 4.**Relationship between moisture diffusion coefficient and external humidity: (

**a**) C30; (

**b**) C40; (

**c**) C50; (

**d**) C60.

**Figure 5.**Development of diffusion coefficients of drying components at different internal humidities: (

**a**) C30; (

**b**) C40; (

**c**) C50; (

**d**) C60.

**Figure 6.**Comparison of calculated and actual internal humidity values of concrete without constraint conditions: (

**a**) C30-65; (

**b**) C40-65; (

**c**) C50-65; (

**d**) C60-65; (

**e**) C30-50; (

**f**) C40-50; (

**g**) C50-50; (

**h**) C60-50; (

**i**) C30-35; (

**j**) C40-35; (

**k**) C50-35; (

**l**) C60-35.

**Figure 7.**Comparison of calculated and actual internal humidity values of concrete under constraint conditions: (

**a**) C30-65-1; (

**b**) C30-65-3; (

**c**) C30-65-6; (

**d**) C60-65-1; (

**e**) C60-65-3; (

**f**) C60-65-6.

**Figure 8.**Effect of different concrete strengths on the humidity diffusion coefficient for the same external ambient humidity: (

**a**) RH = 35%; (

**b**) RH = 50%; (

**c**) RH = 65%.

**Figure 9.**Relationship between reinforcement ratio and pore structure parameters at 28 days: (

**a**) C30; (

**b**) C60.

**Figure 10.**Relationship between concrete pore structure parameters and humidity diffusion coefficient: (

**a**) C30; (

**b**) C60.

Concrete | Cement (kg/m^{3}) | Water (kg/m^{3}) | Fly Ash (kg/m^{3}) | Sand (kg/m^{3}) | Coarse Aggregate (kg/m ^{3}) | Water Reducing Agent (kg/m^{3}) |
---|---|---|---|---|---|---|

C30 | 336 | 195 | 69 | 705 | 1094 | 9.9 |

C40 | 365 | 185 | 65 | 685 | 1090 | 10.4 |

C50 | 394 | 175 | 61 | 665 | 1086 | 10.9 |

C60 | 423 | 166 | 58 | 645 | 1083 | 11.4 |

Composition (%) | Cement | Fly Ash |
---|---|---|

SiO_{2} | 21.47 | 49.47 |

CaO | 65.77 | 4.45 |

Al_{2}O_{3} | 5.47 | 20.67 |

Fe_{2}O_{3} | 4.28 | 14.32 |

MgO | 1.44 | 1.17 |

SO_{3} | 0.52 | 1.40 |

Basic Properties | Concrete Strength | Curing Condition | Age (Days) | ||
---|---|---|---|---|---|

3 | 7 | 28 | |||

Cube compressive strength (MPa) | C30 | Dry | 15.3 | 21.3 | 34.5 |

Sealed | 17.1 | 21.4 | 39.5 | ||

C40 | Dry | 25.1 | 31.0 | 45.4 | |

Sealed | 27.0 | 32.0 | 48.5 | ||

C50 | Dry | 34.0 | 40.6 | 55.0 | |

Sealed | 36.5 | 42.0 | 56.5 | ||

C60 | Dry | 44.0 | 53.0 | 63.0 | |

Sealed | 46.5 | 59.4 | 68.0 | ||

Splitting tensile strength (MPa) | C30 | Dry | 2.2 | 3.7 | 4.3 |

Sealed | 2.4 | 4.1 | 4.4 | ||

C40 | Dry | 2.5 | 4.1 | 4.7 | |

Sealed | 2.7 | 4.2 | 4.7 | ||

C50 | Dry | 2.9 | 4.4 | 5.0 | |

Sealed | 3.1 | 4.5 | 5.1 | ||

C60 | Dry | 3.4 | 4.7 | 5.4 | |

Sealed | 3.5 | 4.9 | 5.6 | ||

Static modulus of elasticity (×10^{4} MPa) | C30 | Dry | 1.6 | 1.7 | 2.9 |

Sealed | 1.7 | 2.0 | 2.9 | ||

C40 | Dry | 1.8 | 2.1 | 3.0 | |

Sealed | 1.6 | 2.2 | 3.0 | ||

C50 | Dry | 2.0 | 2.3 | 3.1 | |

Sealed | 2.1 | 2.4 | 3.2 | ||

C60 | Dry | 2.5 | 2.5 | 3.2 | |

Sealed | 2.4 | 2.6 | 3.4 |

No. | Concrete Strength | External Humidity (%) | Curing Condition |
---|---|---|---|

C30-35 | C30 | 35 | Dry |

C30-50 | C30 | 50 | Dry |

C30-65 | C30 | 65 | Dry |

C30-Sealed | C30 | - | Sealed |

C40-35 | C40 | 35 | Dry |

C40-50 | C40 | 50 | Dry |

C40-65 | C40 | 65 | Dry |

C40-Sealed | C40 | - | Sealed |

C50-35 | C50 | 35 | Dry |

C50-50 | C50 | 50 | Dry |

C50-65 | C50 | 65 | Dry |

C50-Sealed | C50 | - | Sealed |

C60-35 | C60 | 35 | Dry |

C60-50 | C60 | 50 | Dry |

C60-65 | C60 | 65 | Dry |

C60-Sealed | C60 | - | Sealed |

No. | Concrete Strength | External Humidity (%) | Reinforcement Ratio (%) | Curing Condition | Reinforcement Bar Diameter (mm) |
---|---|---|---|---|---|

C30-65-1 | C30 | 65 | 1.14 | Dry | 12 |

C30-65-3 | C30 | 65 | 3.24 | Dry | 20 |

C30-65-6 | C30 | 65 | 6.56 | Dry | 28 |

C60-65-1 | C60 | 65 | 1.14 | Dry | 12 |

C60-65-3 | C60 | 65 | 3.24 | Dry | 20 |

C60-65-6 | C60 | 65 | 6.56 | Dry | 28 |

No. | H_{0} | a | b | c | d | Average Fitting Error |
---|---|---|---|---|---|---|

C30-35 | 98.7 | 0.020 | 8.1 | 3.8 | 1.7 | 1.1% |

C30-50 | 98.5 | 0.014 | 7.6 | 3.5 | 1.9 | 0.3% |

C30-65 | 99.0 | 0.015 | 16 | 4.5 | 2.3 | 2.1% |

C40-35 | 98.5 | 0.015 | 8.5 | 3.0 | 2.0 | 0.9% |

C40-50 | 98.5 | 0.010 | 16.0 | 3.6 | 2.4 | 4.6% |

C40-65 | 98.6 | 0.013 | 21.0 | 3.5 | 2.6 | 6.5% |

C50-35 | 99.1 | 0.005 | 40.0 | 4.0 | 2.8 | 1.4% |

C50-50 | 98.5 | 0.008 | 18.0 | 3.8 | 2.6 | 0.7% |

C50-65 | 98.6 | 0.009 | 20.0 | 3.5 | 2.7 | 4.1% |

C60-35 | 98.8 | 0.010 | 15.0 | 2.5 | 2.6 | 2.9% |

C60-50 | 99.4 | 0.012 | 15.0 | 3.0 | 2.6 | 3.1% |

C60-65 | 99.6 | 0.015 | 15.0 | 3.2 | 2.6 | 5.2% |

C30-65-1 | 98.5 | 0.011 | 15.0 | 6.0 | 2.3 | 6.2% |

C30-65-3 | 99.4 | 0.010 | 19.0 | 6.0 | 2.3 | 4.2% |

C30-65-6 | 99.5 | 0.011 | 25.0 | 6.0 | 2.3 | 2.2% |

C60-65-1 | 98.5 | 0.016 | 10.0 | 3.0 | 2.3 | 0.05% |

C60-65-3 | 99.0 | 0.016 | 12.0 | 4.0 | 2.3 | 2.9% |

C60-65-6 | 99.0 | 0.015 | 13.0 | 5.0 | 2.3 | 5.6% |

Age (Days) | Average Pore Diameter (nm) | Median Pore Diameter (nm) | Critical Diameter of Capillary (nm) | Porosity (%) | D (mm^{2}/h) | |
---|---|---|---|---|---|---|

C30-65 | 3 | 24.45 | 65.17 | 61.79 | 22.52 | 13.21 |

7 | 21.94 | 46.13 | 52.30 | 20.32 | 10.24 | |

28 | 19.30 | 39.04 | 40.50 | 16.32 | 14.92 | |

C30-65-1 | 3 | 26.20 | 76.10 | 74.12 | 25.54 | 12.96 |

7 | 24.39 | 52.88 | 59.49 | 24.31 | 11.75 | |

28 | 20.58 | 45.25 | 52.34 | 19.21 | 13.19 | |

C30-65-3 | 3 | 30.17 | 82.02 | 79.03 | 27.56 | 11.22 |

7 | 27.41 | 64.04 | 66.60 | 25.64 | 11.34 | |

28 | 23.42 | 59.51 | 55.07 | 21.61 | 15.45 | |

C30-65-6 | 3 | 32.26 | 93.27 | 89.82 | 29.97 | 8.88 |

7 | 29.53 | 78.76 | 75.43 | 27.75 | 13.72 | |

28 | 26.35 | 64.83 | 62.46 | 23.84 | 16.31 | |

C60-65 | 3 | 21.35 | 53.61 | 44.13 | 21.52 | 10.08 |

7 | 17.41 | 36.53 | 29.55 | 18.47 | 17.80 | |

28 | 13.50 | 30.19 | 21.23 | 13.94 | 28.67 | |

C60-65-1 | 3 | 24.87 | 57.81 | 53.65 | 24.83 | 13.30 |

7 | 22.28 | 43.07 | 33.95 | 21.13 | 20.58 | |

28 | 17.14 | 36.83 | 26.78 | 17.74 | 17.25 | |

C60-65-3 | 3 | 27.85 | 66.13 | 57.29 | 25.94 | 11.89 |

7 | 24.75 | 51.46 | 37.99 | 22.88 | 17.49 | |

28 | 19.10 | 39.23 | 31.00 | 19.01 | 19.84 | |

C60-65-6 | 3 | 30.01 | 80.45 | 68.58 | 27.92 | 7.88 |

7 | 27.20 | 59.36 | 46.34 | 25.15 | 8.59 | |

28 | 19.90 | 45.04 | 38.91 | 21.41 | 12.69 |

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Zhou, F.; Li, W.; Hu, Y.; Huang, L.; Xie, Z.; Yang, J.; Wu, D.; Chen, Z.
Moisture Diffusion Coefficient of Concrete under Different Conditions. *Buildings* **2023**, *13*, 2421.
https://doi.org/10.3390/buildings13102421

**AMA Style**

Zhou F, Li W, Hu Y, Huang L, Xie Z, Yang J, Wu D, Chen Z.
Moisture Diffusion Coefficient of Concrete under Different Conditions. *Buildings*. 2023; 13(10):2421.
https://doi.org/10.3390/buildings13102421

**Chicago/Turabian Style**

Zhou, Fengbin, Wenhao Li, Ying Hu, Lepeng Huang, Zhuolin Xie, Jun Yang, Daifeng Wu, and Zhonghao Chen.
2023. "Moisture Diffusion Coefficient of Concrete under Different Conditions" *Buildings* 13, no. 10: 2421.
https://doi.org/10.3390/buildings13102421