## 1 Introduction  
Strength and serviceability are the two main criteria to be satisfied in the design of reinforced concrete (RC) structures. Strength is the ability of the structure to carry the design ultimate loads without collapse while serviceability covers the functionality, durability, and sustainability of the structural members. Surface crack width is one of the important serviceability criteria in RC members. The deterioration of RC structures can be caused by steel rebar corrosion which occurs due to the cracking of concrete. In underground RC box culverts, the cracking of the concrete may reduce the service life of the structure by permitting the penetration of corrosive factors, such as high humidity, repeated saturation with moisture, and water with reacting agents, to reach the reinforcement. Cracking also reduces the stiffness of culverts and crack widths can potentially increase even under normal service loads. This study is conducted to develop a probability-based crack width estimation model for flexural members of underground RC box culverts utilized in power supply lines. The stress in the steel reinforcement is proportional to the width of the cracks and is one of the most important factors for the cracking behavior of RC members [1]. [PERSON] [1] identified the importance of stress in the steel reinforcement and observed that crack width can be prevented from growing by using a large number of smaller reinforcement bars and by increasing the reinforcement ratio. [PERSON] [2] found that the difference in crack width between the concrete surface and the reinforcing bar is small at low tensile stresses (just after crack formation), and this difference increases as the tensile stress increases in bars. Therefore, the crack width at the reinforcing bar increases more slowly than the width at the concrete surface with an increase in load. [PERSON] and [PERSON] [3] performed an extensive statistical evaluation of data from six different investigations and proposed an empirical model as the result of correlation and regression analyses. The major parameter controlling the cracking behavior of a two-way system, apart from the reinforcement stress level, is the spacing of the intersecting bars or wires in the two orthogonal directions, and the diameter of the reinforcement and the concrete cover are the two other parameters that influence the cracking behavior [4]. [PERSON] [5] stated that crack patterns can be controlled by the depth to which the cracks penetrate to or by the proximity of the reinforcement. He showed that the spacing of transverse reinforcement had a strong influence on the crack width and crack spacing. After some initial cracks have formed, the tensile stress on the concrete that would widen the cracks is resisted by the area of concrete immediately surrounding the steel, which is less than the total area of the concrete in the tensile zone of the member subjected to pure flexure [2]. Due to the formation of cracks in reinforced concrete elements, the compatibility of deformations between reinforcing bars and concrete is not maintained. The bond stress-slip characteristics of the reinforcing bar have a significant influence on crack width, crack spacing, and the stiffening of tensioned concrete [6]. [PERSON] and [PERSON] [7] investigated the effect of thick concrete cover on maximum flexural crack width under service loads and further examined the validity of crack width prediction formulas given in old provisions such as the ACI 318-1995 [8] and BS8110: part 2-1985 [9]. The maximum acceptable crack width depends on the structural type, the location of the crack within the structure, the surrounding environment, and the consequences of excessive cracking. [PERSON] and [PERSON] [10] found that cracks up to 0.25-0.38 mm (10-15 mils) may be aesthetically acceptable. The ACI Committee 224R-01 [11] has recommended tolerable crack widths for various exposure conditions which can protect reinforcement against corrosion.