# Water Impermeability of Self-Compacting Fly-Ash-Containing Concrete
## 1 Introduction  
The water impermeability of concrete is determined based on the permissible filtration losses through the concrete and its corrosion resistance. Filtration losses are significant in hydraulic constructions, such as high-rise pressure dams, canal hinings, etc. [1; 2; 3; 4]. Four methods of determining water impermeability can be used [5; 6]:  
* By \"wet spot\";
* By filtration coefficient;
* By penetration depth of water under pressure;
* By air permeability. According to Ukrainian standards, the primary method for determining the water impermeability of concrete is the \"wet spot\" method. The water impermeability class of concrete (W) indicates the maximum water pressure (in MPa\(\cdot 10^{-1}\)) at which no water filtration occurs on at least four out of six samples by visual assessment. Several calculation dependencies have been proposed for the predicted water impermeability, depending on the concrete structure parameters [7]. For cement stone, the equation [8; 9] for the dependence between the filtration coefficient (FC) and the values of the hydraulic pore radius and porosity, reflecting the main features of its pore structure, was proposed:  
\[lgFC=38.45+4.08 lg\left(P\cdot r^{2}\right), \tag{1}\]  
where \(r\) is the hydraulic radius and \(P\) is the porosity. However, the practical use of this dependence is problematic due to the difficulty of calculating the hydraulic radius, which is the average size of the capillaries at the endsof which there is a pressure drop. The hydraulic radius of capillaries in cement stone is usually calculated by dividing the amount of filtered water by the wetted surface area. To experimentally define the radius of capillaries in concrete, it is necessary to know the maximum capillary pressure P and the surface tension value \(\sigma\) at the liquid-gas border. According to [PERSON] [10], \(r\) is equal to:  
\[r=\frac{4\sigma}{2.028\cdot 10^{6}\cdot\mathrm{P}} \tag{2}\]  
The formula is proposed [11] to calculate the filtration coefficient:  
\[FC=K_{W}\cdot P_{28}, \tag{3}\]  
where \(P_{28}\) is the concrete porosity at 28 days and \(K_{W}\) is the coefficient of water velocity. Calculations using this formula allow the determination of the filtration coefficient for each class of concrete water impermeability depending on its total porosity. Formula (3) has a several drawbacks [12]. The velocity coefficient \(K_{w}\) was calculated under standard conditions to determine the concrete water impermeability using cylinder specimens with a diameter and height of 15 cm. It is assumed that the water velocity in concrete obeys [PERSON]'s law [13], which is valid only for viscous (Poiseuille) flow. This equation is valid for the \"liquid-concrete\" system with a pore radius \(r=10^{-4}\)-\(10^{-3}\) cm. According to the data obtained using mercury porosimetry, in a cement stone with W/C = 0.3, the volume of pores less than \(10^{-4}\) cm is 15%, and at W/C = 0.5, it is 25% [12]. It is also known that the content of pores less than \(10^{-4}\) cm in a cement-sand mortar during wet-air hardening is more than 60%, and during water hardening--almost 90%. It is considered to be experimentally proven [14] that the water impermeability of concrete is determined not by the total but by the permeable or effective porosity. It means the ratio of the volume of pores, which are the ways of water filtration, to the volume of the specimen. As opposed to total and capillary porosity, effective porosity varies widely depending on the duration of the specimen's interaction with water. The relationship between the filtration coefficient of concrete and its compressive strength has been experimentally substantiated. The presence of this relationship made it possible to propose a method for determining the strength of concrete by water impermeability.