# Design of Magnetic Concrete for Inductive Power Transfer System in Rail Applications
## 3 Materials and Methods  
### Magnetic Concrete Mix Design and Permeability Test  
The primary objective of the current study is to examine how variations in the content of ferromagnetic materials--such as carbon steel fiber, ferrite powder (particle size 0.05 mm and magnetic permeability 2000 H/m), and ferrite chips--affect the magnetic permeability of the concrete and, in turn, influence magnetic field interactions within the IPT system. For the experimental study, a series of specimens were fabricated, each differing in the composition of ferromagnetic materials. Carbon steel fiber, known for its high magnetic permeability and mechanical strength, was used to improve the magnetic properties of the concrete while also adding structural strength and integrity. Ferrite powder, widely used in magnetic applications due to its excellent magnetic properties and high relative permeability, was included to enhance magnetic field concentration within the concrete. Ferrite chips, similar in function to ferrite powder, were incorporated to further improve the magnetic properties of the concrete and ensure effective magnetic flux guidance toward the receiver coil. The specimens included varying percentages of these materials, as detailed in Table 1. The magnetic inclusions--carbon steel fiber, ferrite powder, and ferrite chips--are depicted in Figure 3.  
Figure 3: Magnetic inclusions. (**a**) Carbon steel fiber. (**b**) Ferrite powder. (**c**) Ferrite chips. Figure 2: The view of an IPT system’s transmitter coil embedded between the tracks and receiver coil mounted under a battery-powered train. Seven different specimen mixes, designated as S1 through S7, were tested to quantify the effects of varying concentrations and combinations of ferromagnetic materials on magnetic permeability. The mixing method uses a concrete bench mixer, and the specimens are allowed to cure for 28 days prior to demolding. To ensure uniform distribution of ferrite powder in the mix, the powder was applied to the concrete mix using hand spraying slowly. Table 1 summarizes the composition of each magnetic concrete specimen. For instance, S1 was designed for high strength (25% steel fiber) and low cost without ferrite material, while S2 aimed for higher strength and increased magnetic permeability by incorporating 12% ferrite powder and reducing carbon steel fiber to 12%. Other specimens, such as S4 and S5, were designed to determine which material contributes most to relative permeability, with S4 using 8% ferrite powder and no carbon steel fiber and S5 using 8% ferrite chips and no carbon steel fiber. Specimens S6 and S7 prioritized achieving the highest permeability by eliminating carbon steel fiber, albeit at the expense of structural strength. Magnetic permeability tests were used to calculate the relative permeability (\(\mu_{r}\)) of each specimen. The relative permeability was calculated using the toroid inductance equation:  
\[\mu_{r}=2\pi L/\mu_{0}N^{2}h\mathrm{ln}\left(\frac{b}{a}\right) \tag{1}\]  
where \(L\) represents the inductance measured using an LCR meter, \(\mu_{0}\) is the permeability constant of free space, \(N=10\) is the total number of coil windings, \(h=1.9\) cm is the axial length of the toroidal core, and \(b=10\) cm and \(a=6.5\) cm are the outer and inner radii of the toroid, respectively. The toroid's inherently closed magnetic circuit minimized external magnetic field interactions, ensuring precise and reliable measurements, as shown in Figure 4.