# Curable Area Substantiation of Self-Healing in Concrete Using Neutral Axis
## 1 Introduction  
Self-healing of concrete is attracting attention as a solution for reducing maintenance costs and environmental issues. Conventionally, studies in the literature on concrete development have focused mainly on improving the properties of concrete such as strength; durability; resistance against acid, chlorides, corrosion, etc. [1]. Ultra-high-strength concrete of over 100 MPa has been developed [2], and the strength of the concrete used in actual applications has been increased [3; 4]. Moreover, various admixtures are being applied to improve the durability of concrete [5; 6; 7; 8; 9]. These efforts ultimately aim to reduce construction costs by reducing the section areas of a framework. By contrast, there is a debate about reducing maintenance costs of an increasing cumulative number of old concrete structures [10; 11; 12]. In addition, research on mitigating environmental problems is required in the concrete industry based on the notion that environmental issues should be assessed at any cost [13]. Self-healing of concrete presents advantages in terms of reducing costs and solving environmental problems. The main aim is to reduce maintenance costs through automatic crack detection and recovery in general, and multiple self-healing methods are available to this end. Moreover, the increased lifetime of concrete structures due to self-healing reduces the overall usage of cement in the long term, thereby gradually mitigating the environmental harm arising from the CO2 generated during cement production.  
Self-healing of concrete has been studied from various viewpoints over the past decade. The most famous study involved the active method of using capsules containing an adhesive [14; 15; 16; 17; 18; 19; 20]; this methodis classified as active because it uses additives that are not used in normal concrete. Another famous active method was proposed based on the use of microorganisms [21; 22; 23; 24], which help deposit crack-restoring substances. Moreover, many passive methods exist, for example, improvement of self-healing environment using fibers that prevent the occurrence of a single large crack and induce multiple cracks of small width [25; 26; 27; 28]. The recovery due to self-healing is not only general strength recovery but also durability recovery such as decreased water permeability [29; 30; 31; 32; 33]. Furthermore, self-healing techniques have been studied in various ways depending on the types and shapes of cracks that can occur in a structure, and various methods for verifying the healing effect have been proposed. However, existing studies have generally measured the degree of healing by an indirect method because direct observation of cracks and post-healing conditions is not easy and has various limitations.  
The most important part of self-healing assessment is to measure efficiently and quantify accurately the healing effects. Indirect measurements, such as strength measurement, permeability estimation, and ultrasonic pulse velocity measurement, can easily quantify the healing effect by comparing the measured values before and after healing. However, these measurements are limited to relative comparison because the generated cracks are not directly measured and compared after healing. In addition, it is difficult to exclude the influence of the portion with no cracking because the measurement range covers the entire specimen as opposed to only the area around the generated crack. Especially, the age effect, which is necessarily accompanied by healing time, makes it difficult to evaluate only the healing effect accurately. Therefore, to distinguish the self-healing effect more clearly, a more direct measure is required.