All over the world, particularly in severe environmental conditions, there are reinforced concrete structures that develop nonnegligible phenomena of durability problems. Most of the durability problems are related to hazardous substances invasion. Both engineering practice and scientific studies have revealed that the transport property of near-surface concrete is a main factor in the durability of concrete structures. Among many transport parameters, the chloride ion diffusion coefficient is the most important one, which provides important information on material design and service life prediction. In this paper, AC impedance spectroscopy technology was employed in the measurement of chloride ion diffusion coefficient. The relationship between mesostructure parameters and chloride ion diffusion coefficient was deduced by introducing a reasonable equivalent circuit model. Taking into account the conductivity difference caused by various cementitious material systems, the diffusion coefficient can be corrected, and a diffusion coefficient determination method based on AC impedance spectroscopy technique was established. For the convenience of application, a relationship between the newly proposed method and a widely recognized standard method was obtained. The proposed method can be applied to laboratory testing and establishes the theoretical basis for field tests.

Durability of concrete structures is one of the unsolved problems in the field of civil engineering and is an international research concern [

Concrete is a typical porous material. Its pore system includes C-S-H gel pores, capillary pores, microcracks, and micropores. Many ions, such as Ca^{2+}, Na^{+}, K^{+}, OH^{−}, Cl^{−}, and

To separate the desired mesostructure parameters from measured impedance data, researchers have proposed a number of equivalent circuit models [

The selected scale should not be small when considering the role of pores in ion diffusion. The C-S-H gel pore does not contribute to permeability. Therefore, only the capillary pores and the pores between C-S-H gels were considered. Basically, three conduction pathways exist for alternating current in concrete, that is, continuous conduction, discontinuous conduction, and the so-called “insulating” conduction paths. The continuous conduction path is a series of connected capillary pores or connected microcracks. If the pore connectivity is cut off by cementitious material or its hydration products, the discontinuous conduction path is formed. In addition to continuous and discontinuous conduction paths, isolated cementitious material particles and their hydration products or even the entire solid concrete block can also be conductive for alternating current. Based on the above considerations, the concrete mesostructure for AC conducting can be described in Figure

Concrete mesostructure for AC conducting.

The equivalent circuit model that corresponds to Figure

According to basic circuit theory, the equivalent circuit described in (

Converted equivalent circuit.

The conversion relationship of the two equivalent circuits is shown in

A parallel combination of a capacitor and a resistor produces a semicircle in the Nyquist plot. Therefore, two semicircles should appear on the plot of the equivalent circuit shown in Figure

Nyquist plot of the equivalent circuit model shown in Figure

Taking into account the second equation in (

High-frequency range Nyquist plot of typical concrete.

The left arc does not occur, which indicates that

Further simplified equivalent circuit and its Nyquist plot.

Further simplified equivalent circuit

Corresponding Nyquist plot of the simplified equivalent circuit

The above discussion indicates that

The relationship between AC impedance parameters and permeability can be established in two ways. An empirical relationship between the two can be mathematically regressed by conducting a large number of experiments. However, the disadvantage of this approach is the lack of reliable theoretical basis. Another way to derive some kind of quantitative relationship between the two is through theoretical derivation. This paper adopted the latter approach.

Einstein and Smoluchowski presented an equation on the diffusion of charged particles in solution in 1905 and 1906, respectively; this equation is known as the Einstein–Smoluchowski equation [^{2}/(V·s));

As for the most significant chloride ion diffusion coefficient

To use (

To further differentiate the contribution of chloride ions and sodium ions to the conductance, the contribution percentage of chloride ions is 61%, which is close to that of an infinitely diluted sodium chloride solution (60.4%), under the conditions of 25°C and 1 mol/L concentration; this information was verified by consulting a chemistry handbook. Combining (

Taking into account the relationship between resistance (

Therefore, the relationship between chloride ion diffusion coefficient and the interconnecting pore resistivity can be expressed as

In (

Chemical compositions of cement and mineral admixtures (% by weight).

Composition | SiO_{2} |
Al_{2}O_{3} |
Fe_{2}O_{3} |
CaO | MgO | SO_{3} |
Na_{2}O |
K_{2}O |
---|---|---|---|---|---|---|---|---|

Cement | 21.09 | 4.34 | 2.81 | 62.5 | 1.81 | 2.87 | 0.15 | 0.62 |

Slag | 34.55 | 14.36 | 0.45 | 33.94 | 11.16 | 1.95 | 0.28 | 0.35 |

Fly ash | 57.57 | 21.91 | 7.72 | 3.87 | 1.68 | 0.41 | 1.54 | 2.51 |

Silica fume | 92.63 | 1.05 | 1.17 | 0.34 | 0.73 | 0.30 | 0.22 | 0.93 |

A conductivity cell with a length of 6.92 cm and an electrode area of 9.62 cm^{2} was also made. This experiment aims to investigate the influence of different pore solutions caused by different cementitious materials used on conductance. Strictly speaking, to carry out pore solution conductivity tests, the pore solution should be squeezed out of the concrete block. However, given the complexity of the required equipment and the limited amount of the extracted pore solution, this research adopted the simulation approach by measuring high water-binder ratio paste that was prepared by using various cementitious materials. Before the age of 7 d, the paste will not solidify by shaking the container several times every day. The paste solution was shaken for 5 minutes the day before the test and then left undisturbed for 24 h. Then, the upper solution was taken and injected into the conductivity testing cell. The frequency of the alternating current is 2000 Hz, and the test ages are 28 and 90 d. Figure

Conductivity value of different paste solutions.

Figure

Diffusion coefficient correction factor.

Types of mineral admixtures | (Replacement ratio)/diffusion coefficient correction factor | ||
---|---|---|---|

Fly ash | (20%) 1.2 | (40%) 1.3 | (60%) 1.7 |

Slag | (25%) 1.1 | (50%) 1.3 | (75%) 1.8 |

Silicon fume | (5%) 1.1 | (10%) 1.3 | (15%) 1.4 |

Table

Concrete mix.

Specimen number | Materials used (unit: kg/m^{3}) | ||||||
---|---|---|---|---|---|---|---|

Cement | Fly ash | Slag | Silicon fume | Water | Fine aggr. | Coarse aggr. | |

C0 | 466.0 | 0 | 0 | 0 | 186.0 | 750.0 | 1125.0 |

FA1 | 372.8 | 92.3 | 0 | 0 | 186.0 | 735.7 | 1103.6 |

FA2 | 276.6 | 186.4 | 0 | 0 | 186.0 | 720.5 | 1080.9 |

FA3 | 186.4 | 276.6 | 0 | 0 | 186.0 | 705.3 | 1058.0 |

GS1 | 349.5 | 0 | 116.5 | 0 | 186.0 | 747.6 | 1121.4 |

GS2 | 233.0 | 0 | 233.0 | 0 | 186.0 | 744.2 | 1116.3 |

GS3 | 116.5 | 0 | 349.5 | 0 | 186.0 | 740.8 | 1111.2 |

SF1 | 442.7 | 0 | 0 | 23.3 | 186.0 | 747.6 | 1121.4 |

SF2 | 419.4 | 0 | 0 | 46.6 | 186.0 | 744.2 | 1116.3 |

SF3 | 396.1 | 0 | 0 | 69.9 | 186.0 | 740.8 | 1111.2 |

JH1 | 266.0 | 114.0 | 0 | 0 | 144.0 | 760.8 | 1141.2 |

JH2 | 190.0 | 95.0 | 95.0 | 0 | 144.0 | 761.2 | 1141.8 |

JH3 | 195.0 | 130.0 | 65.0 | 0 | 144.0 | 752.8 | 1129.2 |

First,

Then, a

Concrete blocks for the impedance test.

Stainless steel electrodes.

Electrode mounting.

Impedance tester.

Figure

Nyquist plot of spectroscopy test results of specimen number C0.

To verify the validity of the measured impedance data, a validation check by using linear Kramers–Kronig test [

Validation results.

Specimen number C0, 90 d

Specimen number FA2, 90 d

Specimen number GS2, 90 d

Specimen number SF2, 90 d

In Figure

Only measured data that passed the Kramers–Kronig test can be used for further numerical fitting. Figure

Parameters

The method of determining chloride ion diffusion coefficient based on the AC impedance technique is performed as follows:

Prepare ^{−} saturating using 1 mol/L NaCl solution (the saturating regime is the same as that of ASTM C1202).

Carry out AC impedance testing to obtain impedance spectroscopy data.

Perform data validation.

Obtain

Calculate chloride ion diffusion coefficient using (

Modify the diffusion coefficient according to the cementitious material that was used.

The rapid chloride permeability test ASTM C1202 has been adopted as national standard by many countries, including China, the United States, and Canada. The ASTM C1202 method specifies the rating of chloride permeability of concrete based on the charge passed through the specimen during 6 h of testing period. ASTM C1202 tests that use the same concrete blocks were conducted to perform a comparison. Figure

Relationship between chloride ion diffusion coefficient using ACIS and 6 h electric flux from ASTM C1202 tests.

As can be seen from Figure

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors acknowledge the support from National Natural Science Foundation of China (Grant nos. 51408379 and 51508350) and Natural Science Foundation of Hebei, China (Grant no. E2013210125).