# Influence of Cracking on the Durability of Reinforced Concrete with Carbon Nanotubes
## 1 Introduction  
Concrete is a quasi-brittle material highly prone to crack formation throughout its service life [1, 2]. The reasons behind crack appearance in concrete include poor design, mechanical actions, hygrothermal changes, shrinkage, and others [3, 4]. Cracks tend to form in concrete when the internal tensile stresses surpass its optimum tensile strength. The newly created paths may increase concrete permeability to water and deleterious agents, negatively affecting its durability. Various investigations have been carried out to study the effect of cracks on the durability behavior of conventional concrete [5, 6, 7, 8, 9, 10]. Studies involving pre-cracking via splitting tensile tests indicated that the permeability was significantly affected for crack widths over 0.05 mm [6, 8], especially up to 0.2 mm [5, 6]. For crack widths wider than 0.2 mm, the permeability increase continued but at a lower rate. In another study [11], considering concrete specimens with natural and artificial cracks, the coefficient of permeability increased parabolically with the crack width (0.1-0.5 mm). Factors affecting the concrete penetrability include orientation, depth, and geometry of the cracks, which makes it difficult to precisely evaluate the cracking influence on the overall concrete durability. In order to overcome this issue, investigators have attempted to estimate threshold crack widths, above which, chloride and carbonation of cracked concrete is significantly increased [7, 9, 10, 12]. Critical crack widths of 0.05-0.08 mm were determined for chloride diffusion in cracked concrete specimens [10, 13]. In a study by [PERSON] et al. [5], the depth of chloride penetration and carbonation of concrete were related to the crackwidth through proposed expressions. Other investigators have related the crack width to CO\({}_{2}\) diffusion ability [12], or connected the crack width to the carbonation depth with an S-shaped curve [7], where the carbonation is greatly increased up to an upper limit, above which the further increase of the crack width has lower influence on this property. The rising demand for concrete and higher durability requirements increased the research efforts in order to enhance the performance of this material. An answer to the structural and durability challenges of concrete is the incorporation of reinforcing fibers in the cementitious matrix, aiming to improve the concrete ductility and control over cracks [14; 15]. However, due to their size, the most common fibers are unable to act at a micro level, preventing small microcracks from becoming larger and propagating into macroracks. During the last decade, carbon nanotubes (CNT) have been studied as a reinforcement material for cement-based composites [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. The growing interest in this field comes from the desire to modify the cement matrix at the scale of their main compounds, by taking advantage of the outstanding properties of CNT. On the one hand, CNT have ultra-high strength and stiffness, with Young's modulus up to 1 TPa and exceptional tensile strength up to 100 GPa [27]. On the other hand, they have extremely high aspect ratios (1:1000) and surface area (up to 1000 m\({}^{2}\)/g), as well as very low density (1500 kg/m\({}^{3}\)). Therefore, CNT are ideal candidates for cement nano-reinforcement, being potentially able to retain the propagation of nano-cracks and improving some negative features of cement-based materials, such as the low tensile strength and low strain capacity. In fact, CNT have been proven to enhance the fracture properties and early age strain capacity of cement pastes and mortars, reducing or preventing crack initiation [25; 26]. Due to their significant capillary forces, the small pores up to about 50 nm have a great impact in the shrinkage and creep of concrete, as well as on durability [28; 29]. Due to their small dimensions, CNT are able to affect the concrete porous structure and work as fillers and nucleation sites, reducing the number of pores below 50 nm [30].