## 2 Control of Crack Width  
The purpose of crack control in RC structures includes maintaining good appearance, protecting rebars from corrosion, and having water tightness. Since the 1970s, various approaches have been used to control the width of cracks. From 1971 to 1995, the ACI 318 restrictions on the distribution of tension reinforcement were designed to limit the width of surface cracks. ACI 318-1995 [8] included provisions for keeping crack widths under 0.41 mm (16 mils) for interior and 0.30 mm (12 mils) for exterior applications, respectively. ACI 318-1995 [8] requirements for flexural crack control in beams and one-way slabs at the tensile reinforcement level were based on the equation proposed by [PERSON] [3], which was derived from regression analyses on data from several crack width studies.  
[PERSON] [16] re-evaluated [PERSON]'s model [2] and available crack width data [3] to suggest a model based on physical phenomena for determining the widths of flexural cracks in RC structures. The current ACI 318-2019 [17] crack control equation is based on [PERSON]'s study [6], and considers bar spacing, concrete cover, and bar stress to limit crack widths towards target level. [PERSON]'s study showed that previous crack width equations suggested by [PERSON] [18], [PERSON] [19], and [PERSON] [3] worked reasonably well for concrete covers up to 63.5 mm (2.5 inches). The equation proposed by [PERSON] [16] can be used for both beams and slabs if large deflection does not take place and the plane section remains plane. The crack width at the concrete surface can be calculated using the following equation:  
\[w_{c}=\psi_{s}\frac{f_{s}}{E_{s}}k\sqrt{d_{c}^{2}+\left(\frac{s}{2}\right)^{2}} \tag{1}\]  
where \(w_{c}\) is the crack width (mm), \(\psi_{s}\) is the crack spacing factor (1.0 for minimum, 1.5 for average, and 2.0 for maximum crack spacing; in this study the maximum crack spacing was used to calculate crack widths), \(f_{s}\) is calculated rebar stress (MPa), \(E_{s}\) is the modulus of steel, \(k\) is the ratio of distances to the neutral axis from extreme tension fiber and from  
Figure 1: Underground RC box culverts for power supply (unit: mm).  
the centroid of reinforcement \(\left(\frac{h-c}{d-c}\right)\), \(h\) is the slab thickness (mm), \(c\) is the distance to the neutral axis from the top face of the concrete (mm), \(d\) is the effective depth of the bottom reinforcement (mm), \(d_{c}\) is the distance from the center of the lowest bar to the bottom face of the concrete (mm), and \(s\) is the rebar spacing (mm).  
The Comite Euro-International du Beton and Federation Internationale de la Precontrainte (CEB-FIP 1990) [20] approach to predict crack width is similar to the ACI approach. The CEB-FIP model considers the average strain in reinforcing steel but within the bond transfer length. The characteristic crack width, \(w_{k}\), in flexural members (beams) is calculated in terms of the maximum bond transfer length, \(l_{s,max}\), over which a slip occurs between the steel reinforcement and the concrete. Eurocode EC2 [21] requires that cracking should be limited to a level that does not impair the proper functioning of the structure. It limits the maximum design crack width to 0.30 mm (12 mils) for sustained loads under normal environmental conditions. This study is performed for the crack width estimation of the flexural member of the underground RC box culverts used for power supply lines in Korea with a target crack width in the range between 0.3 to 0.5 mm (12 to 20 mils).