## 1 Introduction  
In Japan, concrete structures (including those of port facilities) that were built during the intensive post-war construction period and are associated with high economic growth are now ageing remarkably. Such circumstances suggest that a future increase in the number of associated services such as inspections and diagnoses will be needed, along with the development of laws and ordinances related to the maintenance and management of these structures [1]. Reinforced concrete (RC) structures located in coastal areas, such as port and harbor facilities, are vulnerable to corrosion by chloride ions, which cause serious structural deterioration [2; 3; 4; 5]. In principle, corroded reinforcing bars in concrete cause cracks to propagate by pressure expansion [6], which not only degrades the appearance of the structure but also induces damage to the surrounding areas or entities as the concrete cover peels and spalls [7]. Moreover, progressive corrosion of the reinforcing bars eventually leads to the structural performance of the concrete deteriorating rapidly [8]. Therefore, evaluating the residual performance of the deteriorated facility is essential for implementing inspection and diagnosis work on the facilities. Because the structural and durability performances of a structure depend strongly on the amount of reinforcing bar corrosion [9; 10], a method should be established to accurately evaluate that amount. Currently, the standard way to diagnose structural deterioration is through visual inspection [11]. With this method, the residual structural performance is evaluated quantitatively if the amount of corrosion of the reinforcing bars in the immediate vicinity of the crack can be estimated from the width of the corrosion crack on the concrete surface. The subsequent deterioration progress can be predicted, and repair and reinforcement timing can be determined, thereby helping to improve the structure's maintenance and management. Such estimation can be established via several representative studies incorporating various cases, among which a numerical study is very effective. There have been many numerical studies of crack width evaluation regarding the corrosion of reinforcing bars in concrete. The approaches that have been used include (i) the meshless method [12], (ii) a model of corrosion-induced crack initiation and propagation focused on corrosion products [13], (iii) predicting the cover cracking time with a numerical model [14; 15; 16; 17], (iv) evaluating the crack width related to the amount of corrosion [18], and (v) simulating the damage development due to steel bar corrosion with a sustained load [19]. Other approaches related to structural performance include (vi) a fatigue flexural model of a corroded RC beam [20], (vii) a seismic-capacity degradation model [21; 22], and (viii) a cracking model considering predictive models of the bond-strength loss of a corroded deformed bar [23]. Recently, schemes have been developed for the fracture of RC structures using damage models based on fracture mechanics [24; 25]. With that approach, all parameters (e.g., calculated strain and stress output) become less susceptible to the influence of element dimensions. On that basis, an analysis carried out with finite elements of very fine dimensions would still yield generally correct results. Furthermore, because the distribution of the damage variable indicating the degree of damage can be regarded as being approximately equal to the crack distribution, the appearance of the concrete close to the actual crack can be visualized in 3D [25]. Recently, cases have been reported in which the development of 3D cone-shaped internal cracks from the nodes of deformed reinforcing bars subjected to tensile action was simulated through a numerical analysis of the uniaxial tension and bending of RC with deformed bars shaped as nodes and ribs.