# Simulation of Real Defect Geometry and Its Detection Using Passive Magnetic Inspection (PMI) Method
## 3 Simulations and Results
Figure 13: Minimum values of Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm (values related to Hole 2), for different box mesh specifications with a fixed rebar mesh #8 (Table 4). According to Figures 7-9 and 12-14, the outcomes from the simulation of the rebar with mesh #8 and box mesh #5, the optimum mesh specifications, were chosen for the rest of the investigations. After the optimum mesh specifications, achieved by increasing the meshing accuracy, the biggest difference in the maximum and minimum values of magnetic flux densities (of the same place) are respectively less than 0.01 \(\upmu\)T and 0.04 \(\upmu\)T, which are considered negligible. Additionally, the same values are observed for the maximum and minimum values of magnetic data when the element accuracy is increased. The same magnetic values mean that the results converge and are independent of the mesh specifications. Carrying out simulations with optimum mesh specifications led to a graphical representation (Figure 15), which shows the behavior of the Z-component magnetic flux density at the location of Hole 2. Also, a planar slice of the magnetic field under the rebar in Figure 15 shows the conditions of the stray magnetic field around the rebar. As the distance from the rebar increases, the stray magnetic field around the rebar decreases relatively uniformly and symmetrically. Figure 16 shows the values of magnetic flux densities of rebar with optimum mesh specifications at different spacings from the center of the rebar, ranging from 8 mm (surface level) to 72 mm (maximum distance from the surface). The behavior of the Z-component magnetic flux density is distinguishable at Hole 2 at a maximum of 16 mm from the rebar's center (Figure 16), which is a distance equal to 8 mm from the rebar's surface (this distance represents how thick the concrete above the bar can be for detection of the buried defects). According to the simulation results, it seems that the technique can be used only for very thin concrete layers with a maximum thickness of 8 mm. Figure 14: Difference between the maximum and minimum values of Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm (values related to Hole 2), for different box mesh specifications with fixed rebar mesh #8 (Table 4). Figure 15: Behavior of Z-component magnetic flux density and normal magnetic field around the rebar (rebar mesh #8 and box mesh #5). It should be mentioned that the simulations were performed under the Earth's present magnetic field, but ferromagnetic materials are considered saturated by the natural magnetic field, and may show stronger magnetic behavior. For further investigation, the data-recording distance was increased to the maximum possible distance from the rebar, aligning with the inside edge of the box. At larger distances, the magnetic flux density trend becomes smoother and straighter, and approaches the background magnetic field. The minimum values of the Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm (values related to Hole 2), were considered for different distances. Increasing the vertical distance (in the Z direction) of the data recording line logarithmically decreased the minimum value of the Z-component magnetic flux density until this value reached an approximately constant value. The trend line showing the relation between the minimum values of the Z-component magnetic flux density and data recorded at various distances is a fourth-order polynomial equation (Figure 17). Figure 16: Values of magnetic flux densities of rebar mesh #8 and box mesh #5 at different vertical distances from the center of the rebar. Figure 17: Behavior of the minimum values of the Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm (values related to Hole 2), of rebar mesh #8 and box mesh #5, recorded at different vertical distances. We reviewed the different components of magnetic flux densities at the surface of the rebar, which were extracted from the optimum mesh specifications (Figure 18).