1. Introduction
As one of the most commonly used building materials, concrete is inevitably subjected to various destructive factors, which stem from the production process or use environment of concrete. In addition, water is the most common substance accompanied by concrete, which always affects the durability of concrete [
1,
2]. Harmful ions dissolved in water (e.g., chloride ions, sulfate ions, or magnesium ions) are transported among the complex and disordered pores [
3]. Both theoretical and experimental results show that the capillary suction of unsaturated concrete absorbs chloride ions in water and accelerates the corrosion of reinforced concrete under the condition of wetting and drying alternation.
Additionally, sulfate attack also depends on the moisture entering concrete during the process of water transport [
4,
5,
6]. Water penetrating in and out actually exists in all the processes of deterioration resulting from the freeze-thaw cycle, and the damage extent of concrete shows an ultra-superposition effect under the alternation of wetting and drying [
7]. Obviously, water absorption behavior plays an important role in durability of concrete.
The rate at which water is absorbed into concrete by capillary suction can provide useful information relating to the pore structure, the permeation characteristics, and the durability of concrete surface zone [
8,
9]. Meanwhile, the pore structure of concrete is of great significance to the durability of the material, and the complexity of pore structure has a significant impact on the permeability. The pore size of concrete varies from nanometer scales to micrometer scales, and the pore morphology shown by scanning electron microscopy (SEM) is rather complex and disordered [
10].
Fractal theory, as a rising nonlinear science, may solve the problem of evaluating the complexity or roughness of self-similar or approximate self-similar objects effectively. The mathematical beauty of fractal is that it forms the infinite complexity with relatively simple equations and different information captured by test equipment and different definitions of fractal dimension (including the Hausdorff dimension, the box-counting dimension, etc.) [
11,
12]. Fractal theory has been applied to the study of concrete, and some valuable results have been obtained, especially in pore research, pore fractal dimension. It has a close relationship with the transport performance (chloride diffusion coefficient, depth of carbonation, etc.) as a parameter of the complex transport channel [
13,
14], which can be used as an index of pore structure damage [
15,
16]. If it is assumed that the pore can move by itself, the connecting behavior between the pore is a revolution from complexity to simplicity, so it can be inferred that the fractal dimension of the pore and the possibility of the connection correspond to each other. Microstructure parameters measured by MIP and X-ray CT images with different voxel sizes were compared [
17].
Fractal theory can better characterize the connectivity of pores. At present, there are few studies on quantitative analysis of pore connectivity by fractal theory. In this study, concrete specimens with different pore structures were prepared by adding different mineral admixtures. In order to obtain the relationship between the complexity of pore structure and the absorption capillary water in specific directions, a series of tests were carried out on the properties of concrete specimens, and the experimental results were compared and discussed by processing data obtained from the test of water absorption and MIP. Finally, fractal theory is used to analyze the relationship of the pore connectivity and water absorption.
2. Materials and Mixture Proportions
The 32.5. R ordinary Portland cement was used which is produced by Shenyang Jidong Cement Company, China. The physical properties of cement are shown in
Table 1. Additionally, the chemical compositions of fly ash and slag are shown in
Table 2. There are three specimens in each group. If the deviation of the test results of three specimens in each group is within 5%, the test results are considered to be valid, and the average value of the test results of the three specimens is taken as the final test results. All experimental results in this paper are based on this method.
Low air-induced water-reducing agent was used which is produced by Shenyang Dongling concrete admixture company, China. It is a polycarboxylate superplasticizer with solid content of 20%. The mix proportions are shown in
Table 3. The compressive strength test specimens were made of 100 mm × 100 mm × 100 mm. After curing for 24 h, the specimens were demolded and transported to the curing room for 7 and 28 days for testing. The workability and compressive strength of concrete are shown in
Table 4.
3. Water Absorption Test of Concrete
Duplicate specimens (40 mm × 40 mm × 160 mm) of mortar were used to determine the water absorption values of concrete at 7 and 28 days. The specimens were dried at 105 °C to constant, and the initial weight of all specimens was recorded. Then the surface of the specimens was coated with epoxy resin, except for an exposed surface. The cured specimens were immersed in water at 20 ± 2 °C, and the water head was maintained at 2.3 cm. Then the weight of the text specimens was recorded at a specified time interval, which can be set longer as the program continues. The schematic diagram of the water absorption test is shown in
Figure 1.
Due to the strong barrier effect of epoxy resin, only one bottom surface can directly contact with water, which ensures the one-way transmission path of water. We all realize that only when the pores in concrete are connected with each other, the liquid will transfer freely and rapidly between the pores. Therefore, the volume of the permeable pore equals to the volume of the cumulative water absorption and the connecting porosity in one direction, which can be obtained by Equation (1).
where
θ is connecting porosity,
mf is mass of fluid,
ρf is density of water, and
V is total volume of the tested specimen.
In addition, concrete is a kind of porous material, assuming that the capillary of concrete is multidimensional random parallel distribution, and the pore structure is cylindrical. The flow increment of concrete could be expressed as Equation (2) [
18].
where
W(
t) is flow increment,
n is mass of pores,
r is pore size,
ρ is density of water,
t is time,
γ is surface tension of water,
θ is contact angle of water,
η is viscosity of water,
s is coefficient of capillary absorption.
According to the characteristics of data collection and Equation (2), generalized least squares method could be used to calculate the capillary absorption rate of concrete.
Figure 2 and
Figure 3 show the experimental imbibition data (expressed as cumulative absorbed volume/unit inflow area vs.
t1/2).
As the curing time prolongs, the water absorption of all samples decreases (as shown in
Figure 4). Comparison sample has the highest water absorption, followed by fly ash. Slag sample and double mixing sample have the best water absorption resistance.
The results show that the water absorption of concrete can be effectively reduced by adding two mineral additives (fly ash and slag), and the water absorption reduction effect of slag powder is more remarkable than that of fly ash.
5. Results and Discussion
The investigations performed in this study showed that alterations of mineral admixture can seriously affect the water absorption of concrete as is shown in
Figure 13. Alterations of mineral admixture are not limited to macroscopic effect but act in the microstructure evolution of concrete. Mineral admixtures could refine the pore structures indeed, which is quantified as fractal dimension in this paper. Additionally, thinking about pore volume distribution from the perspective of the ideal fractal model, higher pore volume dimension means more complex pores distributed in concrete, under the same porosity conditions. The more complex the pore is, the longer the transmission path of water is, and also the transportation time which makes it a lower water absorption value of concrete [
20]. Due to these assumptions, total pore fractal dimension should have a good agreement with water absorption value. The relation between water absorption values and total pore dimension is as shown below:
However, this is not an ideal case. As shown in
Figure 13, there is no good correlation between the total pore volume size and the water absorption value (correlation coefficient is 0.78). Especially when the fractal dimension is 2.7308 and 2.7327, the water absorption rate is higher with the increase of the fractal dimension. It is concluded that the fractal dimension of total pore volume does contain all the information of the complex state of pores. In
Figure 9,
Figure 10,
Figure 11 and
Figure 12, there are inflection points in the relationship curve between Lg
r and Lg
V. Therefore, the total pore fractal dimension cannot accurately reflect the complex state of the pore. Therefore, the key factor to establish the objective relationship between pore complexity and water absorption value is to select the appropriate section of pore size, accurately characterize its complexity by pore fractal dimension, and explain the most possible pore size of concrete. The relationship of water absorption value and fractal dimension of 50~550 nm is shown in
Figure 14 and
Figure 15.
The fractal dimension of the comparing sample is obviously higher than that of the other samples with a most probable aperture near 671 nm. From another point of view, it is concluded that the fractal dimension of pore size of the comparing sample is the lowest between 50 and 550 nm, so there is another most possible pore size between 50 and 550 nm. From the mercury injection data, it can be seen the results of this analysis. Therefore, due to the inherent defects of MIP (high pressure, solid particle breakage, etc.), all samples have the maximum possible pore size between 50 and 550 nm. Compared with other sections, the middle section of pore diameter can always accurately describe the complex state of the pore, so that the fractal dimension of the pore between 50 and 550 nm has a good linear relationship with the water absorption value. The correlation coefficients of concrete cured on 7 and 28 d are greater than 0.95. Although the samples were tested at 28 days, there was a significant correlation between the absorption value of 7 days and the fractal volume dimension. The results show that the pore volume fractal dimension of 50–550 nm can be used to evaluate the water absorption of concrete. Furthermore, the pores with small fractal dimension correspond to low complexity of pores, which indicates that the pore tends to be simplified. Therefore, with the increase of pore fractal dimension, the probability of pore connectivity decreases. The relationship between connectivity probability of pores and pore volume dimension of 50~550 nm is shown in
Figure 16.
As shown in the figure above, the fractal dimension of pores in concrete is closely related to the probability of pore connectivity, and the correlation coefficient can reach 0.935. The above correlation can be explained by the quantification of pore fractal dimension between 50 and 550 nm, which quantifies the complexity of internal pores in concrete. The discovery of the relationship between fractal dimension and probability of pores distribution plays an important role in studying the internal possibility of concrete with the theory of chaos and fractal.