# Simulation of Real Defect Geometry and Its Detection Using Passive Magnetic Inspection (PMI) Method
## 1 Introduction  
Reinforced concrete as a composite infrastructure material is widely used in construction because of its excellent properties [1] and construction ease. Three factors control the behavioral responses of reinforced concrete: the reinforcing steel (generically referred to as rebar in this article), which has a noticeable ductile nature; the concrete itself, which has a noticeable brittle nature (low tensile strength but high compressive strength); and the condition of the rebar-concrete bonding (to achieve reliable stress transfer) [2]. Reinforced concrete is commonly used in infrastructure such as buildings, bridges, and highway construction [3]. The quality of a country's transportation system is mostly based on the conditions of its highway bridges, all of which contain steel. At the present time, apparently, approximately 28% of concrete bridge decks in the United States (US) and 33% of highway bridges in Canada can actually be considered operationally deficient or in a condition warranting the cessation of active service, mainly because of rebar corrosion [4]. Rebar corrosion is common in environmentally-exposed structures; it reduces the service life of these structures and impacts load-carrying capacity [5]. In the worst cases, structural failure occurs because corrosion reduces a stressed rebar's cross-sectional area [6] to the point of rupture. Rebar corrosion also degrades the bonding quality and can create cracks in the structure fromvolumetric expansion [7; 8]. Bond deterioration leaves structures more vulnerable to vibrations related to daily usage or earthquakes [9]. The corrosion of steel rebar embedded in concrete falls into two categories: one is related to the specifications of the rebar and the concrete; the other includes the environmental conditions (temperature, humidity, pH, salinity, etc.) to which the structure is exposed [10]. Exposure to chloride ions, usually mostly from environmental exposure, is the most significant reason for rebar corrosion [11]. Long-term exposure to chloride ions deteriorates the passive layer of oxide on the steel rebar, eventually causing significant deterioration or structural failure, which can carry substantial economic loss [10]. To reduce safety threats and financial impact, corrosion-threatened rebar condition should be monitored so that risks can be quantitatively managed (repair, replace, restore) [12]. The visual inspection method (VI) is commonly used to assess the conditions of reinforced structures [13]. VI evaluates the external surface of the structure without directly assessing the internal conditions [14]. Even with detailed rubrics and photo imagery, VI methods are weak and semi-quantitative at best, and they must be done in conjunction with other non-destructive methods [15]. Reinforced concrete can be inspected for different types of defects using various types of non-destructive testing (NDT) methods [16]; the most common methods are potential measurement survey [17], galvanic current measurement [18], ground penetrating radar (GPR) [19], rebound hammer [20], ultrasonic [21], and radiography [22]. Each NDT method has limitations [23]; for instance, the macro-current measurement is complicated to interpret, since its results are influenced by the distance between anode and cathode and humidity [24]. GPR results are influenced by the existence of voids and variable internal moisture conditions [25], which can confound interpretations in many ways, such as confusion with background structures, shadowing, or false identification of gaps or previously repaired sites as being corrosion sites (Type I errors) [4]. Half-cell potential surveys can only mark corrosion locations; they give no information about the corrosion extent [26]. Ultrasonic pulse velocity (UPV) or Schmidt hammer techniques assess the mechanical properties of concrete with no information directly related to rebar corrosion [27].