Simulation of Real Defect Geometry and Its Detection Using ... - MDPI

applied sciences Article

Simulation of Real Defect Geometry and Its Detection Using Passive Magnetic Inspection (PMI) Method Milad Mosharafi 1, *, SeyedBijan Mahbaz 2 and Maurice B. Dusseault 2 1 2

*

Mechanical and Mechatronics Engineering Department, University of Waterloo, Ontario, N2L 3G1, Canada Earth and Environmental Sciences Department, University of Waterloo, Ontario, N2L 3G1, Canada; [email protected] (S.M.); [email protected] (M.B.D.) Correspondence: [email protected]; Tel.: +1-519-504-3499

Received: 26 May 2018; Accepted: 4 July 2018; Published: 14 July 2018







Abstract: Reinforced concrete is the most commonly used material in urban, road, and industrial structures. Quantifying the condition of the reinforcing steel can help manage the human and financial risks that arise from unexpected reinforced concrete structure functional failure. Also, a quantitative time history of reinforcing steel condition can be used to make decisions on rehabilitation, decommissioning, or replacement. The self-magnetic behavior of ferromagnetic materials is useful for quantitative condition assessment. In this study, a ferromagnetic rebar with artificial defects was scanned by a three-dimensional (3D) laser scanner. The obtained point cloud was imported as a real geometry to a finite element software platform; its self-magnetic behavior was then simulated under the influence of Earth’s magnetic field. The various passive magnetic parameters that can be measured were reviewed for different conditions. Statistical studies showed that 0.76% of the simulation-obtained data of the rebar surface was related to the defect locations. Additionally, acceptable coincidences were confirmed between the magnetic properties from numerical simulation and from experimental outputs, most noticeably at hole locations. Keywords: reinforce concrete; rebar; defect; self-magnetic behavior; magnetic flux density; probability paper method; Passive Magnetic Inspection (PMI)

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 from

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volumetric 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]. Similarly, radiographic and acoustic inspections can assess concrete conditions, but give no direct information related to rebar conditions [28]. Some active magnetic-based methods such as magnetic flux leakage (MFL) can provide information directly related to the rebar corrosion condition [29]. Such methods need an external source such as electromagnets to properly magnetize objects during inspection [30], which increases assessment time and energy costs. These methods are challenging to perform on structures with complicated geometries [31], and complex rebar geometries can hamper clear interpretation of different data sets collected over time. With the intent of providing a better measure that is quantitative and consistent, we introduce the passive magnetic method, which takes advantage of the Earth’s natural magnetic field in order to inspect ferromagnetic structures [32]. Passive magnetic methods require no special preparation [33] or artificial magnetic source [34], and use anomalies in the passive magnetic flux density to locate defects [35]. This method can detect rebar defects such as corrosion sites or cracks [33], and stress changes that impact the crystalline ferromagnetic structure [36]. We built a Passive Magnetic Inspection (PMI) tool to exploit the passive magnetic concept and examine the corrosion condition of embedded rebar by scanning from the external concrete surface [8]. Preliminary successes have been described [37] in which solid rebar was sketched in COMSOLR software version 5.3a (COMSOL Group, Stockholm, Sweden). based on a real rebar’s geometry. It was then magnetized, assuming a certain value of magnetic field. Next, the passive magnetic behavior was investigated at a fixed distance from the rebar. Building on that work, in this current paper, the same ferromagnetic steel rebar with artificial defects is scanned with a three-dimensional (3D) laser scanner to generate a detailed point cloud of the structure. This point cloud then serves as the geometry basis for the finite element method software (COMSOLR software), in studying how the Earth’s magnetic field affects the rebar. Different magnetic properties of the object are extracted and

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interpreted at several distances from the rebar, and the parameters influencing them are investigated. Additionally, a statistical detection method is presented as a new development in passive magnetic data processing and interpretation. 2. Theoretical Background and Methodology The Earth’s internal magnetic field is caused by liquid iron motions in the planetary core [38,39], plus contributions from other sources such as mantle movements, the nature of the lithosphere, etc. [40]. The magnetic field is a three-dimensional vector [41] with a harmonic pattern due to the globe’s rotational movement [42]. The vector originates from the surface of the Earth and extends beyond the atmosphere, and its magnitude and orientation are functions of location [41] and time [40]. Natural magnetic fields and other influential local magnetic sources [37], combined with internal and external stresses, can change the scattered stray magnetic field of ferromagnetic materials [43]. Internal domain walls’ displacement and magnetic-moment rotation in ferromagnetic materials happen under the influence of external magnetic fields [44], and there are relationships between the micro-magnetic characteristics of these materials and their mechanical responses [45]. For example, if the steel is deformed significantly in the presence of a magnetic field, the magnetization of the domains and their orientation within the steel are affected. Self-magnetic flux leakage (SMFL) is assumed to take place in the stress concentration areas of ferromagnetic materials affected by mechanical load under the Earth’s magnetic field [46], and this condition can remain even after removing the load, creating detectable magnetic leakage at the material surface [47]. Measuring SMFL at the surface of the materials helps in estimating their stress–strain states (SSSs), which is an important parameter in determining a structure’s reliability [48]. Therefore, the relation between localized stress and oriented magnetic domains is useful for detecting defects in ferromagnetic materials within the background magnetic field of the Earth [49]. Magnetic field parameters at a point in space are represented by magnetic flux density (B) and an external magnetic field (H). B and H are vectors with a proportional magnitude and parallel directions. Magnetic flux density (B) represents the closeness of the magnetic field lines, and shows the strength of the magnetic field [50]. Also, Gauss’s magnetic field law states that ∇B = 0 [51]. H and B may have a complex relationship in magnetic materials [52], but engineers usually invoke the relation established by Faraday and Maxwell, which demonstrates that B is produced in a magnetizable material due to the existence of a primary magnetic field (H) [53]. Numerical simulation of the PMI method is performed based on the stray magnetic field (Hd ) and the stray magnetic field energy (Ed ) [37]. Hubert and Schäfer in 1998 [54] presented the relation for calculating the stray magnetic field (Equation (1)), based on summarizing Gauss’s magnetic field law. In Equation (1), magnetic polarization (J) is the product of “volume-normalized magnetization” M, multiplied by “vacuum magnetic permeability of free space” µ0 . Additionally, a relation suggested for estimating the stray magnetic field energy uses the balance of the magnetic charges as well as their integration over the volume of the ferromagnetic material (Equation (2)). divHd = −div( Ed =

1 µ 2 0

Z all space

J ) µ0

1 Hd2 dV = − µ0 2

(1) Z

Hd · JdV

(2)

sample

Based on potential theory, volume charge density (λV )—Equation (3)—and surface charge density (σS )—equations (4) and (5)—are other parameters related to magnetization (M)—Equation (6)—and can be implemented for computing stray fields. Surface charge density is calculated by Equation (4) when there is just one magnetic medium; Equation (5) is applied when there are two varied different

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𝜎𝑆 = (𝑀1 − 𝑀2 ) ∙ 𝑛

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(5)

(6) 𝑀 (𝑟) = 𝐽(𝑟)⁄vector 𝐽𝑠 media with their own magnetization values and a specific perpendicular to the separation plane of those materials According to (n): Equation (7), the stray field energy at a position (r) can be also calculated through divM (3) V =− the negative gradient of the potential of theλstray field energy at a place (𝛷𝑑 (𝑟)) [55], where 𝛷𝑑 (𝑟)— Equation (8)—is a function of magnetizationσ saturation (𝐽𝑠 ), volume charge density (𝜆𝑉 ), surface (4) S = M·n charge density (𝜎𝑆 ), and the derivative of the position vector (𝑟 ˊ ). Next, the magnetic field energy is σS = ( M1 −functions M2 )·n of surface charge density and volume (5) obtained from Equation (9) through the integration charge density over the volume and surface, M (respectively. r ) = J (r )/J (6) s

(7) 𝐻𝑑 (𝑟) = −𝑔𝑟𝑎𝑑𝛷 According to Equation (7), the stray field energy 𝑑at(𝑟)a position (r) can be also calculated ˊ through the negative gradient of the𝐽𝑠potential ofˊ )the stray field at a place (Φd (r )) [55], 𝜆𝑉 (𝑟 𝜎𝑆 (𝑟energy ) 𝛷𝑑 (𝑟) = [∫ 𝑑𝑉 ˊ + ∫ 𝑑𝑆 ˊ ] (8) ˊ ˊ where Φd (r )—Equation (8)—is a function saturation |𝑟 − 𝑟 | |𝑟 − 𝑟(Js|), volume charge density (λV ), 4𝜋µ0of magnetization 0 surface charge density (σS ), and the derivative of the position vector (r ). Next, the magnetic field 𝐸𝑑 = 𝐽(9) 𝜆𝑉 (𝑟) the 𝛷𝑑 (𝑟)𝑑𝑉 + ∫ 𝜎𝑆functions (𝑟) 𝛷𝑑 (𝑟)𝑑𝑆 ] energy is obtained from Equation through integration of surface charge density and (9) 𝑠 [∫ volume charge density over the volume and surface, respectively. For conducting this research article, we scanned 373.87 mm of the surface of a ferromagnetic rebar (low-carbon steel), with a diameter anddtwo Hdof − gradΦ (r )16=mm, (r ) artificial defects (Table 1) [37], using(7)a high-resolution 3D laser scanner (Figure 1a) [56]. The shape was Z  created with cloud points Zof the rebar 0) 0) J λ r σ r ( ( s V S 0 0 (Figure 1b) that were Φ modified and converted by Mesh Lab V1.3.2 dV + to a 0mesh dS (8) d (r ) = 4πµ0 r 0 | produced r | was imported to COMSOLR |r − the |r −mesh (http://meshlab.sourceforge.net/). Subsequently,  Z Z software and converted to a discretized surface and solid, respectively (Figure 1c). The solid rebar (9) Ed R= Js λV (r )Φd (r )dV + σS (r )Φd (r )dS was simulated via COMSOL software with regard to the magnetic field of the Earth, different components of magnetic flux density were investigated at different spacing, related simulation For conducting this research article, we scanned 373.87 mm of the surface of a ferromagnetic results were compared with our previous experimental results, and statistical approaches were rebar (low-carbon steel), with a diameter of 16 mm, and two artificial defects (Table 1) [37], using a introduced. high-resolution 3D laser scanner (Figure 1a) [56]. The shape of the rebar was created with cloud points (Figure 1b) that were modified and converted to a mesh by Mesh Lab V1.3.2 (http://meshlab. Table 1. Specifications of the two holes in the rebar. sourceforge.net/). Subsequently, the produced mesh was imported to COMSOLR software and Diameter Depth Y-Location Rebar’s Start Point via converted to a discretized surface and solid, respectively (Figure 1c).from The the solid rebar was simulated Hole Name R (mm) field of the Earth, different (mm)components of magnetic COMSOL software with(mm) regard to the magnetic flux density were related simulation results Hole 1 investigated 0.58 at different spacing, 1.24 57.91were compared with our previousHole experimental results, approaches were introduced. 2 0.68 and statistical 0.57 282.67

Figure 1. 1. Process the rebar geometry to atosolid model: (a) scanning the rebar with threeFigure Processofofconverting converting the rebar geometry a solid model: (a) scanning the rebar with dimensional (3D) laser scanner; (b) cloud points of rebar, presented in MeshLab; (c) solid illustration three-dimensional (3D) laser scanner; (b) cloud points of rebar, presented in MeshLab; (c) solid illustration of rebar. rebar. of

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Table 1. Specifications of the two holes in the rebar. Hole Name

Diameter (mm)

Depth (mm)

Y-Location from the Rebar’s Start Point (mm)

Hole 1

0.58

1.24 0.57

57.91 282.67

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3. Simulations Simulations and and Results Results 3. R software, the magnetic behavior After converting convertingthethe rebar mesh to in solid in COMSOL R software, After rebar mesh to solid COMSOL the magnetic behavior simulation simulation was undertaken. Considering the of variations of Earth’sfield magnetic field inlocation, time andto location, was undertaken. Considering the variations Earth’s magnetic in time and obtain to obtain consistent and realistic results the average (within a year) of the different components of consistent and realistic results the average (within a year) of the different components of the magnetic the magnetic field for the Waterloo, Ontario region (the location of the experiments) was adopted for field for the Waterloo, Ontario region (the location of the experiments) was adopted for the simulations the simulations (Table 2).the Moreover, since themagnetic unitless permeability relative magnetic permeability low-carbon (Table 2). Moreover, since unitless relative of low-carbon steelsof(ASTM 1020) steels (ASTM 1020) range from 50 to 100 [57,58], a relative magnetic permeability of 75 was selected range from 50 to 100 [57,58], a relative magnetic permeability of 75 was selected for this study. for this study.

Table 2. Background magnetic field (magnetic field of the Earth): from August 2016 to August 2017 Table 2. Background field (magnetic field of the Earth): from August 2016 to August 2017 (Adapted from Naturalmagnetic Resources Canada (http://www.nrcan.gc.ca)). (Adapted from Natural Resources Canada (http://www.nrcan.gc.ca)). Background Magnetic Field Background Magnetic (X-Component)

Field (X-Component) 18 µT 18 µ T

Background Magnetic Field Background Magnetic (Y-Component)

Field (Y-Component) −3 µT −3 µ T

Background Magnetic Field Background Magnetic (Z-Component)

Field (Z-Component) 50 µT 50 µ T

The The duration duration of exposure exposure to to an an external external magnetic magnetic field field will will affect affect the the magnetic magnetic behavior behavior of of ferromagnetic materials. In reality, ferromagnetic materials are affected by the magnetic field of the ferromagnetic ferromagnetic the Earth Earth from from the the beginning beginning of of their their production production process. process. There may also be be some some unknown unknown external external magnetic magnetic sources sources in in the the surrounding surrounding environment environment that that affect affect the the magnetic magnetic behavior behavior of ferromagnetic objects [59]. However, as accurately as possible, we can apply the magnetic field of the Earth to the objects accurately object its magnetic behavior, although some divergence will existwill between simulation object and andsimulate simulate its magnetic behavior, although some divergence existthe between the and the experimental results. results. simulation and the experimental To To consider consider the the Earth’s Earth’s magnetic magnetic field field in in the the simulation, simulation, the the rebar rebar was located in a regular regular space space (Figure (Figure 2) 2) with with dimensions dimensions of of 100 100 mm mm×× 150 150 mm mm × × 410 mm, which included the magnetic magnetic field field presented in Table 2 and Figure 3. To have better control of simulation parameters, the box and rebar presented in Table 2 and Figure 3. To have better control of simulation parameters, the box were inin Table 3 (Figure 4a,b). weremeshed meshedseparately separatelywith withtetrahedral tetrahedralmeshes meshesaccording accordingtotothe thespecifications specifications Table 3 (Figure 4a, Then, the the rebar andand boxbox were jointly subjected to the simulation process as aas single system (Figure 4c). b). Then, rebar were jointly subjected to the simulation process a single system (Figure The values of the components (X, Y, Z) ofZ)the fluxflux densities were recorded for 4c). The values of different the different components (X,and Y, and of magnetic the magnetic densities were recorded the Y direction of the rebar (i.e.,(i.e., the the pathpath parallel to the rebar’s length). This path is at surface of for the Y direction of the rebar parallel to the rebar’s length). This path is the at the surface the rebar, andand extends from oneone sideside (Edge A) to other sideside of the boxbox (Edge B) (Figure 5). 5). of the rebar, extends from (Edge A)the to the other of the (Edge B) (Figure

Figure 2. 2. Solid Solid rebar rebar located located in in aa box. box. Figure

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Figure 3. 3. Box show the vector for for X, and Z Z components components of of Earth’s Earth’s Figure Box used used in in analysis; analysis; arrows arrows show the resultant resultant vector X, Y, Y, and magnetic field. Figurefield. 3. Box used in analysis; arrows show the resultant vector for X, Y, and Z components of Earth’s magnetic magnetic field. Table 3. 3. Mesh Mesh specifications specifications of of rebar rebar and and box box in in the the initial initial simulation. simulation. Table Table 3. Mesh specifications of rebar and box in the initial simulation.

Section Name Rebar Box Section Name Rebar Box Rebar MaximumSection elementName size (mm) 2 8Box Maximum element size (mm) 2 8 Maximum element size (mm) Minimum element size (mm) 12 4.18 Minimum element size (mm) 1 4.1 Minimum element size (mm) 1 4.1 Maximum element growth rate 1.45 1.45 Maximum element growth rate 1.45 1.45 Maximum element growth rate 1.45 1.45 Curvature factor 0.5 0.5 Curvature factor 0.5 0.5 Curvature factor 0.5 0.5 Resolution ofofnarrow regions 0.6 0.6 Resolution narrow regions 0.6 0.6 Number of degrees freedom (inregio total) 601,773 0.6 Resolution of narrow Number of degreesofof freedom (in total) 601,773 0.6

(a)

(b) (b)

(a)

(c) (c) Figure 4. Initial meshes of the system: (a) rebar mesh with its initial sizes; (b) box mesh with its initial Figure 4. Initial meshes of the system: (a) rebar mesh with its initial sizes; (b) box mesh with its initial Figure 4. Initial the system: rebarsystem mesh with its initial withfor its initial sizes; (c) rebar meshes and boxofmeshes as a(a) single (front face ofsizes; the (b) boxbox is mesh removed better sizes; (c) rebar and box meshes as a single system (front face of the box is removed for better sizes; (c) rebar and box meshes as a single system (front face of the box is removed for better visualization). visualization). visualization).

As observed in Figure 6, at first, the values of all of the components of magnetic flux densities are equal to the background magnetic flux (the magnetic field of the Earth). When the Y distance reaches

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about 18.065 mm, at the end of the rebar, the values of all of the components begin to reflect the impact of Appl. the magnetic of the ferromagnetic rebar on the magnetic fluxes. Sci. 2018, 8, xproperties FOR PEER REVIEW 7 of 20

Figure 5. Path of the data recording (at the surface of the rebar in the Y direction).

As observed in Figure 6, at first, the values of all of the components of magnetic flux densities are equal to the background magnetic flux (the magnetic field of the Earth). When the Y distance reaches about 18.065 mm, at the end of the rebar, the values of all of the components begin to reflect Figure5.5.Path Pathofofthe thedata data recording recording (at (at the in the the surface surfaceof ofthe therebar rebar theYYdirection). direction). the impact of Figure the magnetic properties of the ferromagnetic rebar on theinmagnetic fluxes.

80

70110 60100 50 90

Magnetic Flux density (Component (µT))

Magnetic Flux density (Component (µT))

As observed in Figure 6, at first, the values of all of the components of magnetic flux densities 110 are equal to the100background magnetic flux (the magnetic field of the Earth). When the Y distance reaches about 18.065 mm, at the end of the rebar, the values of all of the components begin to reflect 90 the impact of the magnetic properties of the ferromagnetic rebar on the magneticZ Component fluxes.

Z Component

40 80 30 70

X Component

20 60 10 50 0

-10 -20

Y Component

40 30

X Component

20 10

-30 0 -40 -100 -20

Y Component

30

60

90

120

150

180

210

240

270

300

330

360

390

420

450

Y direction (mm)

-30

Figure 6. Values of different components (X, Y and Z) of the magnetic flux densities in the Y direction Figure 6. Values-40of different components (X, Y and Z) of the magnetic flux densities in the Y direction 0 rebar 30 60 90 mesh 120 150of 180 210 240and 270 box). 300 330 360 390 420 450 at the the surface surface of of the the (initial the rebar rebar at rebar (initial mesh of the and box). Y direction (mm)

The values of all of the components have a harmonic variation because of the corrugated rebar Figure 6. Values componentshave (X, Y a and Z) of the magnetic flux densitiesofinthe the corrugated Y direction rebar The values of allofofdifferent the components harmonic variation because shape. at When the Yofdistance reaches theofend of the rebar, all of the components of magnetic flux the surface the rebar (initial mesh the rebar and box). shape. When the Y distance reaches the end of the rebar, all of the components of magnetic flux densities densities revert to the magnitudes of the background magnetic field. However, there is a revert to the magnitudes of the background magnetic field. However, there is a distinguishable distinguishable the direction and values ofvariation all of the components at the location The valuesirregularity of all of thein components have a harmonic because of the corrugated rebar of irregularity in the direction and values of all of the components at the location of Hole 2 (~301 mm Hole 2 (~301 mm Edge Areaches of the box). Thisofirregularity is in of a minimum peakflux in the shape. When thefrom Y distance the end the rebar, all of the the form components of magnetic from Edge Arevert of the box). This irregularity is in the form of a minimum peak inHowever, the valuesthere of theisZ and densities the magnitudes of the and background magnetic field.change a of values of the Z andto X magnetic flux densities, in the form of a sudden in the gradient X magnetic flux densities, andininthe thedirection form of aand sudden change in the the gradient of the Y-component of values of allthe of at the thedistinguishable Y-component irregularity of the magnetic flux density (a spike above zerocomponents line, followed by alocation suddenofdip theHole magnetic flux density (a spike above the zero line, followed by a sudden dip below the zero line, 2 (~301 A ofjump the box). irregularity below the zero mm line,from thenEdge a sharp backThis to the zero line).is in the form of a minimum peak in the then a sharp jump back to the zero line). values of the Z and X magnetic flux densities, and in the form ofofa magnetic sudden change in the gradient There are some outlier values in the different components flux densities, whichofare There are some outlier values in the different components of magnetic flux densities, which the Y-component of the magnetic density (a spike above the zero line, followed by amesh sudden dipare related to the specifications of the flux elements used in this simulation. In order to have element related to the specifications of the elements used in this simulation. In order to have mesh element below the zero line, then jump back to specifications the zero line). are implemented (Table 4). Then, the independent results, morea sharp accurate element independent more accurate element specifications are implemented (Table Then, the maximum There results, are some outlier values in the different components of magnetic flux4). densities, which are related to the specifications of the elements used in this simulation. In order to have mesh element independent results, more accurate element specifications are implemented (Table 4). Then, the

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Appl. Sci. 2018, 8, 1147 8 of 20 maximum and minimum values of the Z-component magnetic flux density (as a representative metric)

maximum andmm minimum values of the Z-component magnetic flux density (asofa Hole representative metric) from 295.0592 to 307.0592 mm (values symmetric about the fixed extent 2) are extracted. from 295.0592 mm to 307.0592 mm (values symmetric about the fixed extent of Hole 2) are extracted. The location of Hole 2 was chosen because of its importance in our investigation. The differences and minimum thechosen Z-component magnetic flux density (as investigation. a representative from The location of values Hole 2ofwas because of values its importance in our Themetric) differences between the maximum and minimum of these are also used to verify the convergence of the 295.0592 mm to 307.0592 mm (values symmetric about the fixed extent of Hole 2) are extracted. between theoutcomes. maximum and minimum of these values are also used to verify the convergence of the simulation The location of Hole 2 was chosen because of its importance in our investigation. The differences simulation outcomes. The values of the maximum and minimum magnetic flux densities become stable at mesh between the maximum and minimum of these values are flux also densities used to verify thestable convergence the The values the maximum and minimum at meshofand numbers 4 and 8of(Table 4), respectively (figures 7magnetic and 8). The difference become between the maximum simulation outcomes. numbers and 8 (Table respectively 7 and 8). The difference between the maximum and minimum4 magnetic flux4), densities in the(figures Z-component stabilize at rebar mesh #5 (Figure 9). Hence, The values of the maximum and minimum magnetic flux densities become stable at mesh minimum magnetic flux densities in the Z-component stabilize at rebar mesh #5 (Figure 9). Hence, the result of mesh #8 is used for continuing the simulation. The magnetic flux density values for numbers 4ofand 8 (Table 4), respectively (Figures 7 and 8). The difference between the maximum the result mesh #8 is used for the simulation. density values for mesh #8 have no out-of-range orcontinuing disorder trend, compared The withmagnetic the trendflux of rebar mesh #1, which and minimum magnetic flux or densities intrend, the Z-component stabilize at of rebar mesh #5#1, (Figure 9). mesh #8 have no out-of-range disorder compared with the trend rebar mesh which was the initial simulation (Figure 10). Hence, the result of mesh #8 is used for continuing the simulation. The magnetic flux density values for was the initial simulation (Figure 10). mesh #8 have no out-of-range or disorder trend, compared with the trend of rebar mesh #1, which was Table 4. Different mesh specifications of rebar, with the fixed mesh specifications of box mesh as #1. the initial 10). Tablesimulation 4. Different (Figure mesh specifications of rebar, with the fixed mesh specifications of box mesh as #1.

(µT) density flux Magnetic (µT) density flux Magnetic

Maximum Minimum Maximum Resolution Number of Curvature Maximum Minimum Maximum Resolution Number of Mesh Element Element Element of Narrow Degrees Table 4. Different mesh specifications of rebar, with theCurvature fixed mesh specifications of box mesh as #1.of Factor Mesh Element Element Element ofRegions Narrow Degrees of Size (mm) Size (mm) Growth Rate Freedom (in Total) Factor Size (mm) Size (mm) Growth Rate Regions Freedom (in Total) Minimum Maximum 1 2.000 1.000 1.450 0.500 0.600 601,773 Maximum Element Curvature Resolution of Number of Degrees Element Size Mesh Element Size 12 2.000 1.000 1.450 0.500 0.600 601,773 1.340 0.670 1.407Rate 0.450 0.636 1,267,526 Growth Factor Narrow Regions of Freedom (in Total) (mm) (mm) 23 1.340 0.670 1.407 0.450 0.636 1,267,526 0.898 0.449 1.364 0.405 0.674 3,324,359 13 2.000 1.000 1.450 0.500 0.600 601,773 0.898 0.449 1.364 0.405 0.674 3,324,359 0.602 0.301 1.323 0.365 0.715 9,764,894 24 1.340 0.670 1.407 0.450 0.636 1,267,526 0.602 0.301 1.323 0.365 0.715 9,764,894 34 0.898 0.449 1.364 0.405 0.674 3,324,359 5 0.571 0.286 1.310 0.361 0.722 10,441,703 45 0.602 0.301 1.323 0.365 0.715 9,764,894 0.571 0.286 1.310 0.361 0.722 10,441,703 6 0.5605 0.278 1.295 0.3505 0.746 10,995,911 5 0.571 0.286 1.310 0.361 0.722 10,441,703 6 0.5605 0.278 1.295 0.3505 0.746 10,995,911 0.550 0.270 1.280 0.340 0.770 11,594,725 67 0.5605 0.278 1.295 0.3505 0.746 10,995,911 0.550 0.270 1.280 0.340 0.770 11,594,725 77 0.550 0.270 1.280 0.340 0.770 11,594,725 8 0.530 0.240 1.260 0.330 0.780 12,877,797 88 0.530 0.240 1.260 0.330 0.780 12,877,797 0.530 0.240 1.260 0.330 0.780 12,877,797 0.500 0.200 1.250 0.320 0.790 15,173,763 99 0.500 0.200 1.250 0.320 0.790 15,173,763 9 0.500 0.200 1.250 0.320 0.790 15,173,763 10 0.460 0.160 1.220 0.280 0.810 19,243,609 10 0.460 0.160 1.220 0.280 0.810 19,243,609 11 0.446 0.141 1.100 0.240 0.830 20,879,674 10 0.460 0.160 1.220 0.280 0.810 19,243,609 11 0.446 0.141 1.100 0.240 0.830 20,879,674 11 0.446 0.141 1.100 0.240 0.830 20,879,674 100 100 99 99 98 98 97 97 96 96 95 95 94 94 93 93 1 1

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Figure 7. Maximum values of Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm Figure 7. Maximum Maximum values values of of Z-component Z-component magnetic flux flux density, from 295.0592 mm to 307.0592 307.0592 mm mm Figure mm to (values7.related to Hole 2), for different meshmagnetic specificationsdensity, of rebarfrom with295.0592 fixed box mesh #1. (values (values related related to to Hole Hole 2), 2), for for different different mesh mesh specifications specifications of of rebar rebarwith withfixed fixedbox boxmesh mesh#1. #1. 76 76 75 75 74 74 73 73 72 72 71 71 70 70 1 1

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Figure 8. Minimum values of Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm Figure Minimum values of flux from 295.0592 mm to 307.0592 mm Figure 8.related Minimum values of Z-component Z-component magnetic flux density, density, mm to 307.0592 mm (values8. to Hole 2), for different meshmagnetic specifications of rebarfrom with295.0592 fixed box mesh #1. (values related to Hole 2), for different mesh specifications of rebar with fixed box mesh #1. (values related to Hole 2), for different mesh specifications of rebar with fixed box mesh #1.

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T) Magnetic T) (µ density(µ fluxdensity Magneticflux

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Figure 9. Difference Difference between the maximum and minimumvalues valuesofof ofZ-component Z-component magnetic flux Figure 9. Difference betweenthe themaximum maximum and and minimum minimum magnetic fluxflux Figure 9. between values Z-component magnetic density, from 295.0592 mm toto307.0592 307.0592 mm (values relatedto toHole Hole2), 2),for fordifferent different mesh specifications density, from 295.0592 mm 307.0592mm mm(values (values related mesh specifications density, from 295.0592 mm to related to Hole 2), for different mesh specifications of rebar with fixed box mesh #1. of rebar with fixed box mesh #1. of rebar with fixed box mesh #1. 110 110

T)) Magnetic T)) (µ component(µ (Zcomponent density(Z fluxdensity Magneticflux

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Figure 10. 10. Comparison Comparison between between the values values of Z-component Z-component magnetic magnetic flux flux density density of of rebar rebar mesh mesh #8 Figure Figure 10. Comparison betweenthe the valuesof of Z-component magnetic flux density of rebar mesh #8 #8 and rebar rebar mesh mesh #1, #1, with with fixed fixed box mesh mesh (box mesh mesh #1). #1). and and rebar mesh #1, with fixedbox box mesh(box (box mesh #1).

To determine determine the the effect effect of spacing, values values of the the magnetic magnetic flux flux density density (rebar (rebar mesh mesh #8) #8) with To To determine the effectofofspacing, spacing, values of of the magnetic flux density (rebar mesh #8) withwith different spacing were investigated. It was understood that increasing the spacing between the rebar different spacing were investigated. thatincreasing increasingthe thespacing spacing between rebar different spacing were investigated.ItItwas wasunderstood understood that between thethe rebar and the the recording recording point point would would result result in some outliers outliers in in the the trend trend of of the the Z-component Z-component magnetic magnetic flux flux and and the recording point would resultininsome some outliers in the trend of the Z-component magnetic flux density, related toto the specifications of the thetetrahedral tetrahedral elements used in the the box. box. To make make the results results density, related to the the tetrahedral elements used in To the density, related thespecifications specifications of elements used in the box. To make the results of of the simulation independent of the element specifications, more accurate element specifications of the independentof of element specifications, accurate specifications the simulation simulation independent thethe element specifications, more more accurate elementelement specifications were were applied to the the (Table box (Table (Table 5). As aa representative representative result, theflux magnetic flux densities for the the ZZapplied to the box 5). As 5). a representative result, theresult, magnetic densities for densities the Z-component were applied to box As the magnetic flux for component at aa distance distance ofwere 16 mm mm were extracted extracted (Figure 11). The maximum maximum and minimum minimum values at a distance of 16 mm extracted (Figure 11). The 11). maximum and minimum values from component at of 16 were (Figure The and values from 295.0592 mm to 307.0592 mm (values related to Hole 2) were reviewed. Subsequently, the 295.0592 mm to 307.0592 mm (values related to Hole 2) were reviewed. Subsequently, the difference from 295.0592 mm to 307.0592 mm (values related to Hole 2) were reviewed. Subsequently, the betweenbetween the maximum and minimum was investigated, we found that values became difference between the maximum maximum andvalues minimum values was wasand investigated, andthewe we found that the the difference the and minimum values investigated, and found that stable with box mesh #5 (Figures 12–14). values became stable with box mesh #5 (figures 12–14). values became stable with box mesh #5 (figures 12–14).

Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 20 Appl.Appl. Sci. 2018, 8, x 8, FOR PEER REVIEW Sci. 2018, x FOR PEER REVIEW 1010ofof 2020 Appl. Sci. 2018, 8, 1147 10 of Table 5. Different mesh specifications of box, with the fixed mesh specifications of rebar 20

Table 5. Different mesh specifications ofof rebar rebar Table 5.# Different meshspecifications specificationsofof box, box, with with the the fixed fixed mesh specifications (rebar mesh 8). (rebar mesh # 8).# 8). (rebar mesh Table 5. Maximum Different meshMinimum specifications ofMaximum box, with the fixed mesh specifications of rebar (rebar mesh #8). Resolution Number of Degrees Curvature Maximum Minimum Minimum Maximum Maximum Resolution Number of Maximum Resolution Number ofDegrees Degrees Mesh Element Element Element of Narrow of Freedom Curvature Curvature Factor MeshMaximum Element Minimum Element Element of Narrow Narrow of Freedom Mesh Element Element Element of of Freedom Size (mm) Size (mm) Growth Regions (in Total) Maximum Rate Element Curvature Resolution of Number of Degrees Factor Factor Size Mesh Element Size(mm) Element Size Size (mm) Growth Rate Regions (in Total) Size (mm) Size (mm) Growth Rate Regions (in Total) Growth Rate Factor Narrow Regions of Freedom (in Total) 1 8.000 4.100 1.450 0.500 0.600 12,877,797 (mm) (mm) 1 8.000 4.100 1.450 0.500 0.600 12,877,797 1 8.000 4.100 1.450 0.500 0.600 12,877,797 7.720 3.400 1.330 0.410 0.620 13,794,957 12 8.000 4.100 1.450 0.500 0.600 12,877,797 7.720 3.400 1.330 0.410 0.620 13,794,957 2 2 7.720 3.400 1.330 0.410 0.620 13,794,957 23 7.720 3.400 1.330 0.410 0.620 13,794,957 6.820 2.300 1.300 0.400 0.650 14,188,984 6.820 2.300 1.300 0.400 0.650 14,188,984 33 3 6.820 2.300 1.300 0.400 0.650 14,188,984 6.820 2.300 1.300 0.400 0.650 14,188,984 4 4 5.810 1.400 1.250 0.350 0.680 15,058,001 4 5.810 5.810 1.400 1.250 0.350 0.680 15,058,001 1.400 1.250 0.350 0.680 15,058,001 4 5.810 1.400 1.250 0.350 0.680 15,058,001 4.110 1.100 1.190 0.290 0.710 17,446,126 55 5 4.110 1.100 1.190 0.290 0.710 17,446,126 4.110 1.100 1.190 0.290 0.710 17,446,126 5 4.110 1.100 1.190 0.290 0.710 17,446,126 66 2.840 0.850 1.150 0.250 0.730 22,627,445 2.840 0.850 1.150 0.250 0.730 22,627,445 6 2.840 0.850 1.150 0.250 0.730 22,627,445 76 2.250 0.820 1.140 0.230 0.730 28,481,960 2.840 0.850 1.150 0.250 0.730 22,627,445 2.250 0.820 1.140 0.230 0.730 28,481,960 87 7 2.210 0.815 1.130 0.230 0.740 29,650,862 2.250 0.820 1.140 0.230 0.730 28,481,960 2.250 0.820 1.140 0.230 0.730 28,481,960 87 8 2.210 0.815 1.130 0.230 0.740 29,650,862 2.210 0.815 1.130 0.230 0.740 29,650,862 8 2.210 0.815 1.130 0.230 0.740 29,650,862

16 16mm mm

16 mm

Figure Path data recording(with (withdistance distance16 16mm mm from from center center of the rebar). Figure 11.11. Path of of data recording of Figure 11. Path of data recording (with distance 16 mm from center of the the rebar). rebar). Figure 11. Path of data recording (with distance 16 mm from center of the rebar).

(µT) density flux Magnetic (µT) density flux Magnetic Magnetic flux density (µT)

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(µT) density flux Magnetic (µT) density flux Magnetic Magnetic flux density (µT)

mm12. (values related to Hole of 2), Z-component for different boxmagnetic mesh specifications with fixed295.0592 rebar mesh (Table 4). Figure Maximum values flux density, from mm#8to 307.0592 Figure 12. Maximum values ofofZ-component magnetic flux density, from 295.0592 mmmm to 307.0592 mm Figure 12. Maximum values Z-component magnetic flux density, from 295.0592 to 307.0592 mm (values related to Hole 2), for different box mesh specifications with fixed rebar mesh #8 (Table 4). (values related to Hole 2), for different box mesh specifications with fixed rebar mesh #8 (Table 4). 60 mm (values related to Hole 2), for different box mesh specifications with fixed rebar mesh #8 (Table 4). 60 59.8 60

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Figure 13. Minimum values of Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm Figure 13. Minimum Z-component magnetic flux from 295.0592 mm to to 307.0592 307.0592 mm (values related to Holevalues 2), forof different box mesh specifications with from a fixed rebar mesh #8 (Table 4).mm Figure 13. Minimum values of Z-component magnetic flux density, density, 295.0592 mm (values related to Hole 2), for different box mesh specifications with a fixed rebar mesh #8 (Table 4). (values related to Hole 2), for different box mesh specifications with a fixed rebar mesh #8 (Table 4).

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Figure 14. Difference between the maximum and minimum values of Z-component magnetic flux 0 between the maximum and minimum values of Z-component magnetic flux Figure 14. Difference 1 2 307.0592 3 4 5 8 density, from from 295.0592 295.0592 mm to to mm (values (values related to 6 Hole 2),7 for different box mesh density, mm 307.0592 mm Mesh numbersrelated of box to Hole 2), for different box mesh specifications with fixed rebar mesh #8 (Table 4). specifications with fixed rebar mesh #8 (Table 4). Figure 14. Difference between the maximum and minimum values of Z-component magnetic flux

According to figures 7–9 and the mm outcomes from the simulation of the box rebar with mesh #8 density, from 295.0592 mm 12–14, to 307.0592 (values related to Hole 2), for different mesh According to Figures 7–9 and 12–14, the outcomes from the simulation of the rebar with mesh specifications fixed rebar meshspecifications, #8 (Table 4). and box mesh #5, the with optimum mesh were chosen for the rest of the investigations. #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 Accordingmesh to figures 7–9 and 12–14,achieved the outcomes the simulation of the rebar with mesh #8biggest After the optimum specifications, by from increasing the meshing accuracy, the difference in the maximum and minimum values of magnetic flux densities (of the same place) are and box mesh #5, the optimum mesh specifications, were chosen for the rest of the investigations. difference in the maximum and minimum values of magnetic flux densities (of the same place) are respectively lessoptimum than 0.01 µT specifications, and 0.04 µT, which are considered Additionally, the same After the mesh by increasing the negligible. meshing accuracy, the biggest respectively less than 0.01 µT and 0.04 µT,achieved which are considered negligible. Additionally, the same values are observed the maximum and values minimum values ofdensities magnetic data when the difference in thefor maximum and minimum of magnetic flux (of the same place) areelement values are observed for the maximum and minimum values of magnetic data when the element respectively less The than same 0.01 µTmagnetic and 0.04 µT, which are considered negligible. Additionally, theindependent same accuracy is increased. values mean that the results converge and are accuracyvalues is increased. Thefor same mean that theofresults converge andthe areelement independent are observed the magnetic maximum values and minimum values magnetic data when of the mesh specifications. of the mesh specifications. accuracy is increased. The same magnetic values mean that the results converge and are independent Carrying out simulations with optimum mesh specifications led to a graphical representation of the mesh Carrying outspecifications. 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 out simulations with optimum mesh specifications led to aflux graphical representation (Figure 15), Carrying which shows the behavior of the Z-component magnetic density at the location of Hole 2. (Figure Also, a15), planar slice of the magnetic under the rebar in Figure 15 shows conditions of which shows the behavior offield the Z-component magnetic flux density at the the location of Hole 2. Also, a planar slice of the magnetic field under the rebar in Figure 15 shows the conditions of the strayHole magnetic around Asfield the distance the rebar15increases, the stray magnetic 2. Also, field a planar slice ofthe therebar. magnetic under the from rebar in Figure shows the conditions of the straythe magnetic field field around thethe rebar. As the distancefrom from the rebar increases, the stray magnetic stray around rebar. uniformly As the distance the rebar increases, the stray magnetic field around themagnetic rebar decreases relatively and symmetrically. field around the rebar decreases relatively uniformly and symmetrically. field around the rebar decreases relatively uniformly and symmetrically.

Figure 15. Behavior of Z-component magnetic flux density and normal magnetic field around the

Figure 15. Behavior of Z-component magnetic flux density and normal magnetic field around the rebar rebar (rebar mesh #8 and box mesh #5). (rebar #8 and box #5). Figuremesh 15. Behavior of mesh Z-component magnetic flux density and normal magnetic field around the Figure 16 shows thebox values of magnetic flux densities of rebar with optimum mesh specifications rebar (rebar mesh #8 and mesh #5). at different spacings from the center of the rebar, ranging mm (surface level) to 72 mm Figure 16 shows the values of magnetic flux densities of from rebar8with optimum mesh specifications (maximum distance from the surface). The behavior of the Z-component magnetic flux density is Figure 16 shows the values magnetic flux densities of rebar optimum mesh specifications at different spacings from the of center of the rebar, ranging fromwith 8 mm (surface level) to 72 mm distinguishable at Hole 2 at a maximum of 16 mm from the rebar’s center (Figure 16), which is a 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 distance equal to 8 mm from the rebar’s surface (this distance represents how thick the concrete above (maximum distance from thea surface). The behavior of the magnetic fluxthat density distinguishable 2 at maximum ofdefects). 16 mm from the rebar’s centerresults, (Figure 16), which is is a the bar canatbeHole for detection of the buried According toZ-component the simulation it seems distinguishable Hole 2used at the a only maximum of 16 mmdistance from rebar’s center (Figure which is a distance equal toat8 mm from rebar’s surface (this represents howthickness thick the concrete the technique can be for very thin concrete layersthe with a maximum of 16), 8 mm. It above should that the simulations were(this performed under present magnetic distance equal tomentioned 8detection mm from the rebar’s surface distance represents how thick the concrete above the bar can bebe for of the buried defects). According tothe theEarth’s simulation results, itfield, seems that can be can for detection of the buried defects). According the asimulation it seems that the bar technique be used only for very thin concrete layers to with maximumresults, thickness of 8 mm. the technique can be used only for very thin concrete layers with a maximum thickness of 8 mm. It should be mentioned that the simulations were performed under the Earth’s present magnetic field,

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It should be mentioned that the simulations were performed under the Earth’s present magnetic field, but ferromagnetic are considered saturated by the natural magnetic field, and12may Appl. Sci. 2018, 8, xmaterials FOR PEER REVIEW of 20 show stronger magnetic Appl. Sci. 2018, 8, behavior. x FOR PEER REVIEW 12 of 20 but ferromagnetic materials are considered saturated by the natural magnetic field, and may show For further investigation, the data-recording distance was increased to the maximum possible stronger magnetic behavior. but ferromagnetic materials are considered saturated by the natural magnetic field, and may show distance from the rebar, aligning with the inside edge of the box. At larger distances, the magnetic For further investigation, stronger magnetic behavior. the data-recording distance was increased to the maximum possible flux density trend andthe straighter, and approaches the background magnetic field. distance frombecomes theinvestigation, rebar, smoother aligning inside edge of the box. At larger the magnetic For further thewith data-recording distance was increased to distances, the maximum possible The minimum values of the Z-component magnetic flux density, from 295.0592 mm to 307.0592 flux density trend smoother and background field. mm distance from the becomes rebar, aligning withand thestraighter, inside edge ofapproaches the box. Atthe larger distances,magnetic the magnetic minimum values thesmoother Z-component magnetic flux from 295.0592 mm the tomagnetic 307.0592 mm (valuesThe related totrend Hole 2),ofwere considered for different distances. Increasing vertical distance flux density becomes and straighter, and density, approaches the background field. related values toof Hole were consideredmagnetic for Increasing themm vertical distancemm (in (in the(values Z direction) the data recording linedifferent logarithmically decreased the minimum value of The minimum of2),the Z-component fluxdistances. density, from 295.0592 to 307.0592 the Z direction) the 2), data recording line logarithmically decreased theapproximately minimum value of the (in Z- value. (values relatedmagnetic toofHole were considered for different distances. Increasing the vertical distance the Z-component flux density until this value reached an constant component magnetic flux density until this value reached an approximately constant value. The trend the Z direction) of the recording line logarithmically value of the Z- flux The trend line showing thedata relation between the minimumdecreased values ofthe theminimum Z-component magnetic line showing the relation betweenuntil the this minimum values an of the Z-component magnetic flux density component magnetic flux density value reached approximately constant value. The trend densityand and data recorded at various distances is a fourth-order polynomial equation (Figure 17). data recorded at various distances is a fourth-order polynomial equation (Figure 17). 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).

(Z component flux density Magnetic (µT))(µT)) (Z component flux density Magnetic

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Figure 16. Values of magnetic flux densities of rebar mesh #8 and box mesh #5 at different vertical

Figure 16. Values of magnetic flux densities of rebar mesh #8 and box mesh #5 at different vertical distances the of center of theflux rebar. Figure 16.from Values magnetic densities of rebar mesh #8 and box mesh #5 at different vertical distances from the center of the rebar. distances from the center of the rebar. 80

(Z component flux density Magnetic (µT))(µT)) (Z component flux density Magnetic

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60 60 50 y = 2E-05x4 - 0.0026x3 + 0.1655x2 - 4.6686x + 101.62 R²= 0.9982

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Figure 17. Behavior of the minimum values of the Z-component magnetic flux density, from 295.0592 mm to 307.0592 mm of (values related tovalues Hole 2), mesh #8 and box mesh recorded at different Figure 17. Behavior the minimum of of therebar Z-component magnetic flux#5, density, from 295.0592 Figurevertical 17. Behavior of the minimum values of the Z-component magnetic flux density, from 295.0592 mm distances. mm to 307.0592 mm (values related to Hole 2), of rebar mesh #8 and box mesh #5, recorded at different

to 307.0592 mm (values related to Hole 2), of rebar mesh #8 and box mesh #5, recorded at different vertical distances. vertical distances.

values at their minimum and results correlate well with the experimental results reported previously values at their minimum and results correlate well with the experimental results reported previously (Figure 19) [37]. The laboratory flux magnetic density measurements were conducted using the PMI (Figure 19) [37]. The laboratory flux magnetic density measurements were conducted using the PMI device that was specifically developed for this work in our lab, and is on its way to being device that was specifically developed for this work in our lab, and is on its way to being commercialized. The PMI device works through scanning the SMFL arising from ferromagnetic commercialized. The PMI device works through scanning the SMFL arising from ferromagnetic structures [37].1147 Appl. Sci. 2018, 8,[37]. 13 of 20 structures The patterns of laboratory and simulated outputs at the holes’ locations follow the same trend; The patterns of laboratory and simulated outputs at the holes’ locations follow the same trend; both curves generally have an up and down trend due to the corrugated shape of the rebar, along both curves generally have an up and down trend due to the corrugated shape of the rebar, along reviewedvalue the different components of 2. magnetic densities at top the hole surface with We a minimum at the center of the Hole As seen flux in Figure 18, the thatofis the ~301rebar, mm with a minimum value at the center of the Hole 2. As seen in Figure 18, the top hole that is ~301 mm which were extracted from the optimum mesh specifications (Figure 18). The noise and out-of-range from Edge A of the box (equal to ~282 mm from the rebar’s start point (Figure 19)) is substantially from Edge A of the box (equal to ~282 mm from the rebar’s start point (Figure 19)) is substantially values at detect their minimum and results well withFinding the experimental resultsinreported previously easier to than the hole on the correlate side of the rebar. the irregularity the magnetic data easier to detect than the hole on the side of the rebar. Finding the irregularity in the magnetic data (Figure 19) [37]. laboratory flux were conducted using the related to Hole 2 isThe easier because of themagnetic differencedensity betweenmeasurements the magnetic property of its surface (filled related to Hole 2 is easier because of the difference between the magnetic property of its surface (filled PMI device that was specifically developed for this work in our lab, and is on its way to being with air) and the rest of the rebar’s surface (which has a different magnetic property). No detectable with air) and the rest of the rebar’s surface (which has a different magnetic property). No detectable commercialized. PMIindevice worksmagnetic throughflux scanning the for SMFL frommore ferromagnetic irregularity can beThe sensed the surface densities Holearising 1, because metal lies irregularity can be sensed in the surface magnetic flux densities for Hole 1, because more metal lies structures between it[37]. and the scanning line. between it and the scanning line. 110 110 100 100 90 90 Z Component Z Component

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Figure 18. 18. Magnetic Magnetic flux density values values at at different different axes axes (X, (X, Y Y and Z) Z) in in the the Y Y direction direction at at the surface surface Figure flux density Figure 18. Magnetic flux density values at different axes (X,and Y and Z) in the Y direction the at the surface of the rebar (rebar mesh #8 and box mesh #5). of the rebar (rebar mesh #8 and boxbox mesh #5).#5). of the rebar (rebar mesh #8 and mesh

Figure 19. X-component of magnetic flux density resulting from the previous experiments; the square Figure X-component of magnetic flux density resulting from previous experiments; square Figure 19.19. X-component magnetic flux density resulting from thethe previous experiments; thethe square shows the Hole 2 locationof(modified from Mahbaz et al, 2017 [37]). shows the Hole 2 location (modified from Mahbaz et al, 2017 [37]). shows the Hole 2 location (modified from Mahbaz et al., 2017 [37]).

The patterns of laboratory and simulated outputs at the holes’ locations follow the same trend; both curves generally have an up and down trend due to the corrugated shape of the rebar, along with a minimum value at the center of the Hole 2. As seen in Figure 18, the top hole that is ~301 mm from Edge A of the box (equal to ~282 mm from the rebar’s start point (Figure 19)) is substantially easier to detect than the hole on the side of the rebar. Finding the irregularity in the magnetic data related to Hole 2 is easier because of the difference between the magnetic property of its surface (filled with air)

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and the rest of the rebar’s surface (which has a different magnetic property). No detectable irregularity can be sensed in the surface magnetic flux densities for Hole 1, because more metal lies between it and the scanning line. Appl. Sci. 2018, 8, x FOR PEER REVIEW

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4. Discussion 4. Discussion Assuming that the magnetic flux densities of different locations on the rebar are independent Assuming magneticgraph flux densities different locations rebar areflux independent of one another,that the the probability methodof was used for fittingon thethe magnetic values toof a one another, the probability graph method used the for empirical fitting the magnetic of flux values data to a probability distribution. This method involveswas equating distribution magnetic probability distribution. This method involves equating the empirical distribution of magnetic data (P i ) with the chosen cumulative distribution function (CDF). Next, the CDF function is written in (𝑃 ) with the chosen cumulative distribution function (CDF). Next, the CDF function The is written in 𝑖 linear form, which can be expressed as Equation (10) for Gamma CDF (GAMMADIS). linearity linear canfor be determining expressed aswhether Equationthe (10) forcan Gamma CDF (GAMMADIS). linearity is thenform, used which as a basis data be modeled by a particularThe distribution. 2 is then used as a basis for determining whether the data can be modeled by a particular distribution. Additionally, the goodness-of-fit of the model is given by the coefficient of determination R . Additionally, the goodness-of-fit of the model is given by the coefficient of determination 𝑅2 . Pi = GAMMADIS(magnetic data) → magnetic data = GAMMADISinverse ( Pi ) (10) (10) 𝑃𝑖 = 𝐺𝐴𝑀𝑀𝐴𝐷𝐼𝑆(𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑑𝑎𝑡𝑎) → 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑑𝑎𝑡𝑎 = 𝐺𝐴𝑀𝑀𝐴𝐷𝐼𝑆𝑖𝑛𝑣𝑒𝑟𝑠𝑒 (𝑃𝑖 ) The magnetic flux density data were plotted against various probability distributions distributions (normal, (normal, log-normal, Weibull, and gamma distributions); a gamma distribution distribution was was chosen based on the minimum least-squared (Figure 20). 20). This This distribution is based a function two parameters: least-squarederror error (Figure distribution is on based on a offunction of two α and β (Equation these were calculated by the mean and (SD), deviations which are parameters: 𝛼 and(11)); 𝛽 (Equation (11)); these were calculated bystandard the meandeviations and standard 87.8 and 25.6 AsµT, observed in Figure the gamma function correlates well function with the (SD),µT which are µT, 87.8respectively. µT and 25.6 respectively. As21, observed in Figure 21, the gamma histogram frequency and thisfrequency approximation may be useful for estimationmay in practical cases. correlates well with of thedata, histogram of data, and this approximation be useful for estimation in practical cases. 1 −x (11) f (x) = α 1 x α−1 e −β𝑥 𝑓(𝑥) = β 𝛼G (α) 𝑥 𝛼−1 𝑒 𝛽 (11) 𝛽 Г(𝛼) 120

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Figure 20. Probability plot for investigating the correlation of data with a gamma distribution. Figure 20. Probability plot for investigating the correlation of data with a gamma distribution.

According to Figure 18, a Z-component magnetic flux density of less than 76 µT (without considering the edge effect and background magnetic field) corresponds to the location of Hole 2. Importing this value into the obtained CDF shows that 0.76% of the data is related to the defective locations. In other words, 0.76% of the rebar surface (at the scanned section) can be considered imperfect. This result can

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0.09

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distribution) Probability density (based on gamma density (based on gamma distribution) Probability

(Z component) flux density Histogram frequency of magnetic of magnetic flux density (Z component) frequency Histogram

Appl. Sci. 2018, 8, 1147500

be verified by the Monte Carlo simulation method (based on inverse values of the obtained gamma 400 distribution function). Figure 22 presents the probability of defects considering the 0.07 mean, SD, and limit state, showing that 350 the probability of defectiveness fluctuates until the first 300 trails are completed, 0.06 and stabilizes theREVIEW value of ~0.75%. Appl. then Sci. 2018, 8, x FORat PEER 15 of 20 300 0.05 500 250

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Probability of being defective (%) Probability of being defective (%)

According to Figure 18, a Z-component magnetic flux density of less than 76 µT (without 50 considering the edge effect and background magnetic field) corresponds to the0.01 location of Hole 2. Importing this value into the obtained CDF shows that 0.76% of the data is related to the defective 0 0 74 76 78 80 the 82 rebar 84 86 surface 88 90 (at 92 the 94 scanned 96 98 100 102 locations. In other 72 words, 0.76% of section) can be considered Magnetic fluxMonte density (Z component (µT)) method (based on inverse values imperfect. This result can be verified by the Carlo simulation of the obtained gamma distribution function). Figure 22 presents the probability of defects Figure 21. Histogram frequency of data in conjunction with gamma distribution probability density. Figure 21. frequency of data in conjunction with gamma distribution probability density. considering theHistogram mean, SD, and limit state, showing that the probability of defectiveness fluctuates until the first 300 trails are completed, and then stabilizes at the value of ~0.75%. According to Figure 18, a Z-component magnetic flux density of less than 76 µT (without considering the edge effect and background magnetic field) corresponds to the location of Hole 2. 2 Importing this value into the obtained CDF shows that 0.76% of the data is related to the defective locations. In other words, 0.76% of the rebar surface (at the scanned section) can be considered imperfect. This result can be verified by the Monte Carlo simulation method (based on inverse values 1.6 of the obtained gamma distribution function). Figure 22 presents the probability of defects considering the mean, SD, and limit state, showing that the probability of defectiveness fluctuates until the first 300 trails are completed, and then stabilizes at the value of ~0.75%. 1.2 2

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For our statistical investigations, we considered the magnetic data as independent variables. For our statistical investigations, we considered the magnetic data as independent variables. Those independent variables were described by the chosen probability distribution with its particular Those independent variables were described by the chosen probability distribution with its particular distribution parameters, knowing that distribution allowed us to estimate an interval over which the 0 distribution parameters, knowing that distribution allowed us to estimate an interval over which the 0

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Figure 22. Defectiveness probability for the inspected rebar based on the Monte Carlo simulation method.

For our statistical investigations, we considered the magnetic data as independent variables.

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unknown future may lie (with a stipulated level of confidence). Using the CDF of the16gamma Appl. Sci. 2018, 8, x values FOR PEER REVIEW of 20 distribution, about 98% of all of the data are from 76 µT to 100 µT (Equation (12)). Hence, regarding the unknown future values may (with it a stipulated level of confidence). Using the that CDFifofthe the rebar gamma recorded magnetic data of thelierebar, can be predicted with 98% confidence was distribution, of all of thethe data are values from 76indicating µT to 100 µT (Equation (12)). Hence, longer (by howabout much98% is irrelevant), next a flawless rebar would be regarding somewhere the recorded data of the rebar, it canshould be predicted with 98% if the rebar was between 76–100magnetic µT. Values outside this range be reviewed asconfidence suspected that defect locations. longer (by how much is irrelevant), the next values indicating a flawless rebar would be somewhere between 76–100 µT. Values outside this should be(reviewed suspected defect GAMMADIS GAMMADIS 76 µT) =as 0.99 − 0.01 = 0.98 locations. (12) (100 µT ) −range

𝐺𝐴𝑀𝑀𝐴𝐷𝐼𝑆(100 µT) − 𝐺𝐴𝑀𝑀𝐴𝐷𝐼𝑆(76 µT) = 0.99 − 0.01 = 0.98

(12)

Figure 23 shows the values of different components of magnetic flux densities, 16 mm from the Figure 23 shows values of different of magnetic densities, theare center of the rebar. For the better observation of components the irregularities relatedflux to Hole 2, all16 ofmm the from graphs center of the rebar. For better observation of the irregularities related to Hole 2, all of the graphs presented from 200 mm to 370 mm at the appropriate scale. The anomaly in the magnetic values are at the presented from2200 to 370 mm scale.of The in flux the magnetic at 23 location of Hole canmm be detected inat allthe of appropriate the components theanomaly magnetic densities.values Figure the location of Hole 2 can be detected in all of the components of the magnetic flux densities. Figure indicates that the values of the X and Y-components of magnetic flux density still include some noise 23 indicates that the values of the X and Y-components of magnetic flux density still include some that is attributable to the mesh specifications. This issue can be investigated by increasing the mesh noise that is attributable to the mesh specifications. This issue can be investigated by increasing the density in both the rebar and the box containing the rebar. Additionally, increasing the quality of mesh density in both the rebar and the box containing the rebar. Additionally, increasing the quality clouds points defining the bar geometry can help achieve more accurate outcomes. For instance, Hole 1 of clouds points defining the bar geometry can help achieve more accurate outcomes. For instance, in the solid part produced from the captured cloud points was not as deep as the real depth (measured Hole 1 in the solid part produced from the captured cloud points was not as deep as the real depth directly), but directly), the meshbut was not corrected, the intentaswas partwas to test the laser cloudscan point (measured the mesh was notascorrected, the in intent in part to testscan the laser data without data input management. cloud pointadditional data without additional data input management.

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5. Conclusions Being able to detect defects in steel infrastructure would substantially improve risk management and condition evaluation over time. To this end, mathematical simulations were carried out on a pre-flawed specimen that was laser-scanned to generate a point cloud surface map. This map was then used as a basis to develop a model. The intent was to establish detectability limits for very small flaws in order to reduce Type I and Type II errors in anomaly detection. The magnetic behavior of the ferromagnetic rebar specimen was simulated with a finite element-based software considering the background magnetic field. Different components of magnetic flux densities on the surface showed consistent harmonic trends because of the corrugated shape of the rebar. However, there were specific irregularities in the direction and values for the different components of magnetic flux densities at the location of Hole 2. Simulated patterns could be correlated with the experimental data at the holes’ locations, so the top hole (Hole 2) was easily located, but Hole 1 was not, because of its orientation in the magnetic field and because the point cloud model did not replicate its true depth. The gamma probability distribution was chosen to statistically assess the magnetic flux density behavior of the rebar. Two main outcomes were extracted: 0.76% of the scanned section of the rebar was considered defective, and if the rebar specimen were longer, the Z-component magnetic flux density values indicating flawless rebar would be predicted to lie between 76–100 µT with 98% confidence. The values of the different components of magnetic flux densities at different distances from the rebar were reviewed. Increasing the vertical distance of the data recording line led to a logarithmic reduction of magnetic flux density values. As this distance was increased, the magnetic flux density values became approximately constant and close to the background magnetic field. In conclusion:

• • • • •

• •

The pattern of the simulation results at defect locations were similar to the outputs of previous physical experiments; The background magnetic field had a significant effect on the trend and values of different components of the magnetic flux density; All of the magnetic flux density components displayed correctly located anomalies corresponding to the defect on the top surface of the rebar; Increasing the distance from the rebar changed the trend and values of the magnetic flux densities such that at some distance, the anomaly became undetectable; To detect various shapes and sizes of defects at different places along a rebar specimen, additional magnetic parameters should be considered. For instance, the Z-component of the magnetic flux density was totally constant on the sides of the rebar, and could not detect the anomaly arising from Hole 1; The stray magnetic field around the rebar decreased relatively symmetrically by increasing the distance from the rebar; and The choice of the gamma distribution to model the Z-component magnetic flux density values of the numerical simulation resulted in valuable interpretations.

Author Contributions: Conceptualization, M.M., S.M. and M.B.D.; Data curation, M.M. and S.M.; Formal analysis, M.M.; Funding acquisition, M.B.D.; Investigation, M.M.; Methodology, S.M.; Supervision, M.B.D.; Writing—original draft, M.M.; Writing—review & editing, M.M., S.M., and M.B.D. Funding: This research received no direct funding. Acknowledgments: The authors would like to thank Inspecterra Inc. for providing access to the PMI device used in this study. We would like to acknowledge CMC Microsystems for the provision of products and services that facilitated this research, including the providing of a COMSOLR software license. In addition, we express our thanks to Professor Ralph Haas and Professor Carl T. Haas for permitting us to use their laboratory (Infrastructure and sensing analysis laboratory) during our studies. we also extend our thanks to their lab member Mr. Mohammad-Mahdi Sharif due to his support for scanning the rebar by the 3D-laser scanner. Conflicts of Interest: The authors declare no conflict of interest.

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