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Non-Destructive Evaluation for Sectional Loss of External Tendon of Prestressed Concrete Structures Using Total Flux Leakage

Non-Destructive Evaluation for Sectional Loss of External Tendon of Prestressed Concrete... applied sciences Article Non-Destructive Evaluation for Sectional Loss of External Tendon of Prestressed Concrete Structures Using Total Flux Leakage Imjong Kwahk, Kwang-Yeun Park, Ji-Young Choi, Hungjoo Kwon and Changbin Joh * Department of Infrastructure Safety Research, Korea Institute of Civil Engineering and Building Technology, 283, Goyangdae-Ro, Goyang-Si, Gyeonggi-Do 10223, Korea; kwakim@kict.re.kr (I.K.); kypark@kict.re.kr (K.-Y.P.); legion@kict.re.kr (J.-Y.C.); kwonhj3@kict.re.kr (H.K.) * Correspondence: cjoh@kict.re.kr; Tel.: +82-31-910-0332 Received: 22 September 2020; Accepted: 19 October 2020; Published: 22 October 2020 Abstract: A non-destructive evaluation method is proposed to identify the sectional loss of the external tendon of prestressed concrete structures by detecting the change of the magnetic flux in the external tendon exposed to a magnetic field. The method uses a solenoid-shaped device with two coils: a primary coil for producing magnetic field and secondary coil for damage detection, wrapping the external tendon. A current applied to the primary coil in the device causes the magnetic field. Then, the change in the magnetic flux by the damage in the external tendon is detected by the variation of the voltage in the secondary coil in the device as the device moves along the tendon. An alternating current is applied to the primary coil to minimize the e ect of the moving speed of the device. As a result, the damaged area can be detected with a low-level energy current. In addition, a wrapping solenoid-shaped device that is easy to disassemble and assemble was developed for in situ inspection. The measured signal from the secondary coil has a sinusoidal form with the same frequency as the applied current to the primary coil, and the peak curve of the measured signal provides enough information to detect the damage. It is shown that the proposed method can quantitatively identify one or multiple damaged-tendon locations as well as damages of at least 2 cm. Keywords: total flux leakage; non-destructive evaluation(NDE); Prestressed Concrete (PSC); corrosion of the prestressing tendon; section loss of external tendon 1. Introduction The extensive application of prestressed concrete (PSC) in structures can be credited to its structural and economic eciency. In the PSC structure, the tendon plays a critical role to introduce prestress. The tendon is anchored to the concrete member at its ends and is inserted in a duct generally made of HDPE (High Density PolyEthylene) duct filled with grout to protect it from external ingress. However, the corrosion of the prestressing tendon accelerates in corrosive environments as the tension force becomes higher [1]. There is a long list of structures that su ered severe degradation or even collapse because of the rupture or sectional loss of the corroded tendons’ strands [2,3]. Following the risk of such corrosion-induced damages, Germany and Japan implemented large-scale investigations on their PSC bridge inventories, which made it possible to detect numerous damages, from minor damage like early corrosion to severe damage like tendon failure [4,5]. The common causes of damage in the external tendon of PSC structures are known to be the low quality of grouting, the formation of air voids in the duct, and the chemical reaction of deicing chemical and chloride ion [6,7]. For example, corrosion of the tendons near their anchorage and cracks in the HPDE duct occurred at the Mid-Bay Bridge, Florida, USA, in 2000. One external tendon Appl. Sci. 2020, 10, 7398; doi:10.3390/app10217398 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 7398 2 of 12 failed completely, another one experienced partial damage, a tendon su ered severe corrosion near its anchorage, and huge quantities of air voids were found in the ducts at mid-span and around their anchorages [8]. In 2007, two tendons among the 480 tendons with grouted post-tensioned strands of Varina Enon Bridge, Virginia, USA, were replaced because of the formation of voids at their high ends which compromised the corrosion protection of the tendons [9]. In 2016, an external tendon of Jeongneungcheon Bridge, Seoul, Korea, broke due to corrosion and the investigation could attribute it to the poor quality of the grouting [10–12]. Later in 2019, corrosion literally exploded a 1000-ft cable on Wando River Bridge, South Carolina, USA, and sent scraps of grout and plastic as far as 30 m. The corrosion was caused by water seeping through the concrete deck [13]. From these examples, the poor quality of the grouting in the PSC structure appears to be one major initiator of the corrosion or damage of the tendon. Periodic non-destructive evaluation (NDE) of the PSC structure is thus necessary for proper maintenance, and repair shall be implemented when the sectional loss reaches a definite level. Accordingly, the FHWA guideline(FHWA-HRT-13-027) states that the tendon must be replaced when the sectional loss exceeds 5% [14]. This study pays attention to the non-destructive method to detect the change of the magnetic flux induced by the delivered magnetic field at the sectional loss area. Typical NDE methods delivering the magnetic field to the tendon are RMF (Remnant Magnetic Field), MFL (Magnetic Flux Leakage), and IMF (Induced Magnetic Field). These methods have shown the potential to evaluate the corrosion in the tendon section [15,16]. The disadvantage of the MFL method is that the Hall sensor measuring the leakage of the magnetic field is sensitive to the distance to the damage in the tendon. In other words, a weak signal from the Hall sensor cannot tell if the damage exists or if the distance to the intact tendon from the Hall sensor is far. According to the research using the MFL method on the external tendon, the existence of the sectional loss was well identified, but the di erence between the estimated amount of sectional loss and the actual amount of the sectional loss was bigger as the amount of sectional loss increased [17]. In another study for improving the MFL method, a method to measure the residual flux leakage induced by a permanent magnet was sensitive to the magnetization of the tendon [18]. Another method proposed to measure the variation of the total magnetic field flux through the yoke rather than measuring the magnetic field leakage is MMF (Main Magnetic Flux). Since the MMF method can quantify the section loss of the tendon, it can be utilized in combination with the MFL method [19]. Although the MMF method basically estimates the relative sectional loss, a method to figure out the absolute sectional loss by measuring the maximum and minimum of the magnetic flux change after delivering a strong bi-polar magnetic field to the tendon was proposed [20]. Another study proposed to quantify the sectional loss by comparing the slope of the B-H loop with the reference slope [21]. However, there was a diculty in distinguishing the slope change resulting from the sectional loss and the tensile stress in the tendon. The IMF method that is conceptually similar to the MMF method has shown a capability of detecting the damage location but there remains some doubt about the quantification of the damage [22]. In addition, another method called spontaneous MFL was suggested to estimate the sectional loss by measuring the magnetic flux delivered by the Earth’s magnetic field instead of an artificial magnetic field to the tendon [23,24]. However, the leaked magnetic flux was so small that an extremely sensitive magnetic sensor had to be used to measure it and the method also required separating the measured signal from the noise and the external magnetic field source. For the external tendon of the PSC structure, a heavy magnetizing system using a yoke for NDE is not suitable practically. It is also dicult to move the magnetizing system along the length of the tendon with a constant speed. Accordingly, this research adopts a simple solenoid to generate the magnetic field instead of the heavy yoke. In this framework, when the DC (direct current) is delivered to the solenoid, the induced voltage of the secondary coil related to the sectional change can be influenced by the moving speed of the device. Therefore, the AC (alternating current) is delivered to the primary coil to reduce the e ect of the moving speed of the device and generate larger induced Appl. Sci. 2020, 10, 7398 3 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  3  of  13  Appl. Sci. 2020, 10, x FOR PEER REVIEW  3  of  13  voltage in the secondary coil so that the flux leakage can be measured easily. The proposed method is voltage in the secondary coil so that the flux leakage can be measured easily. The proposed method  voltage in the secondary coil so that the flux leakage can be measured easily. The proposed method  expected to identify the sectional damage of the external tendon e ectively by increasing the sensitivity is  expected  to  identify  the  sectional  damage  of  the  external  tendon  effectively  by  increasing  the  is  expected  to  identify  the  sectional  damage  of  the  external  tendon  effectively  by  increasing  the  of the secondary coil. sensitivity of the secondary coil.  sensitivity of the secondary coil.  This paper proposes a novel damage-detecting method for an external tendon of PSC structures This paper proposes a novel damage‐detecting method for an external tendon of PSC structures  This paper proposes a novel damage‐detecting method for an external tendon of PSC structures  using a solenoid-shaped device. The principle of detecting sectional loss using a magnetic field is using a solenoid‐shaped device. The principle of detecting sectional loss using a magnetic field is  using a solenoid‐shaped device. The principle of detecting sectional loss using a magnetic field is  explained in Section 2, and the experimental demonstration of the method is presented in Section 3. explained in Section 2, and the experimental demonstration of the method is presented in Section 3.  explained in Section 2, and the experimental demonstration of the method is presented in Section 3.  The discussion of the experimental results and the conclusion of the research are drawn in Sections 4 The discussion of the experimental results and the conclusion of the research are drawn in Sections 4  The discussion of the experimental results and the conclusion of the research are drawn in Sections 4  and 5. and 5.  and 5.  2. TFL Method 2. TFL Method  2. TFL Method  The proposed TFL (Total Flux Leakage) method employs a solenoid similar to the EM The  proposed  TFL  (Total  Flux  Leakage)  method  employs  a  solenoid  similar  to  the  EM  The  proposed  TFL  (Total  Flux  Leakage)  method  employs  a  solenoid  similar  to  the  EM  (electromagnetic) sensor with a primary and secondary coil in order to estimate the sectional loss in (electromagnetic) sensor with a primary and secondary coil in order to estimate the sectional loss in  (electromagnetic) sensor with a primary and secondary coil in order to estimate the sectional loss in  the external tendon. The EM sensor was introduced to measure the residual stress in the tendon for the external tendon. The EM sensor was introduced to measure the residual stress in the tendon for  the external tendon. The EM sensor was introduced to measure the residual stress in the tendon for  NDE. The EM sensor consists of the primary coil to generate a magnetic field on the external tendon NDE. The EM sensor consists of the primary coil to generate a magnetic field on the external tendon  NDE. The EM sensor consists of the primary coil to generate a magnetic field on the external tendon  and the secondary coil installed at the center to detect the generated magnetic field. The governing and the secondary coil installed at the center to detect the generated magnetic field. The governing  and the secondary coil installed at the center to detect the generated magnetic field. The governing  equation of the EM sensor is well established [25,26]. Once a current is passed through the primary equation of the EM sensor is well established [25,26]. Once a current is passed through the primary  equation of the EM sensor is well established [25,26]. Once a current is passed through the primary  coil installed at the surface of HDPE duct of the external tendon, a magnetic field is generated inside coil installed at the surface of HDPE duct of the external tendon, a magnetic field is generated inside  coil installed at the surface of HDPE duct of the external tendon, a magnetic field is generated inside  and outside of the duct as shown in Figure 1. and outside of the duct as shown in Figure 1.  and outside of the duct as shown in Figure 1.  Figure 1. Magnetic flux distribution around electromagnetic solenoid.  Figure 1. Magnetic flux distribution around electromagnetic solenoid. Figure 1. Magnetic flux distribution around electromagnetic solenoid.  If a ferromagnetic material like the tendon is placed inside the duct along the longitudinal direction If  a  ferromagnetic  material  like  the  tendon  is  placed  inside  the  duct  along  the  longitudinal  If  a  ferromagnetic  material  like  the  tendon  is  placed  inside  the  duct  along  the  longitudinal  direc of thetion solenoid  of the so aslenoid shown as in shown Figur in e Figure 2, and 2, if and the if tendon  the tend is on intact,  is intthe act, magnetic the magne flux tic fldeveloped ux developed by  direction of the solenoid as shown in Figure 2, and if the tendon is intact, the magnetic flux developed  the current in the primary coil will be distributed along the longitudinal direction of the tendon. by the current in the primary coil will be distributed along the longitudinal direction of the tendon.  by the current in the primary coil will be distributed along the longitudinal direction of the tendon.  From From th thee perspect perspective ive of of ma magnetic gnetic ma material, terial, th thee gr grout out f fill illing ing the the ex external ternal ten tendon don ha hass the the sa same me re relative lative  From the perspective of magnetic material, the grout filling the external tendon has the same relative  permeability with the air ( = 1) and has thus no e ect on the magnetic flux developed by the current permeability with the air (μr = 1) and has thus no effect on the magnetic flux developed by the current  permeability with the air (μr = 1) and has thus no effect on the magnetic flux developed by the current  in in th thee prim primary ary coil. coil.  in the primary coil.  Figure 2. Magnetic flux of solenoid installed on surface of tendon of the prestressed concrete (PSC)  Figure 2. Magnetic flux of solenoid installed on surface of tendon of the prestressed concrete (PSC)  Figure 2. Magnetic flux of solenoid installed on surface of tendon of the prestressed concrete structure.  structure.  (PSC) structure. If, additionally, a secondary coil is installed at the center of the solenoid as shown in Figure 3a,  If, additionally, a secondary coil is installed at the center of the solenoid as shown in Figure 3a, If, additionally, a secondary coil is installed at the center of the solenoid as shown in Figure 3a,  any change in the magnetic flux can be detected by the change in the induced voltage in the secondary  any any chan change ge in in th thee ma magneti gneticc flux flux ca can n be be de detected tected by by the the change change in in the the induce induced d voltage voltage in in the the seconda secondary ry  coil. Unlike the undamaged tendon case (Figure 3a), when the tendon suffers partial damage like a  coil. Unlike the undamaged tendon case (Figure 3a), when the tendon su ers partial damage like a coil. Unlike the undamaged tendon case (Figure 3a), when the tendon suffers partial damage like a  sectional loss due to the rupture of some strands, a part of the magnetic flux around the damaged  sectional sectional loss loss due dueto tothe  ther uptur ruptur e e of of some  some strands,  strands a, part a paof rt the of the magnetic  magnet flux ic fl ar ux ound  around the damaged the damaged area  area is absorbed by the neighboring and undamaged strands and the remaining part of the magnetic  area is absorbed by the neighboring and undamaged strands and the remaining part of the magnetic  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 4 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  4  of  13  is absorbed by the neighboring and undamaged strands and the remaining part of the magnetic flux is flux is leaked (Figure 3b). In such a case, the secondary coil around the damaged area detects the  leaked (Figure 3b). In such a case, the secondary coil around the damaged area detects the remaining remaining magnetic flux that has not been leaked.  magnetic flux that has not been leaked. (a)  (b)  Figure 3. Change in magnetic flux distribution of solenoid according to eventual sectional loss of Figure 3. Change in magnetic flux distribution of solenoid according to eventual sectional loss of  external tendon: (a) undamaged tendon; (b) damaged tendon. external tendon: (a) undamaged tendon; (b) damaged tendon.  The electromotive force of the secondary coil induced by the current in the primary coil of the The electromotive force of the secondary coil induced by the current in the primary coil of the  solenoid is expressed in Equation (1). The induced electromotive force, V , is simply the product of ind solenoid is expressed in Equation (1). The induced electromotive force, 𝑉 , is simply the product of  dF the number N of turns in the secondary coil and , the first time derivative of the magnetic flux. 2nd dt the number 𝑁   of turns in the secondary coil and  , the first time derivative of the magnetic flux.  Note that V acts in the direction opposite the change of the magnetic flux. The magnetic flux F is ind Note that 𝑉   acts in the direction opposite the change of the magnetic flux. The magnetic flux 𝛷   is  represented as the integration of the magnetic flux density, B, over the total internal cross-sectional represented as the integration of the magnetic flux density, 𝐵 , over the total internal cross‐sectional  area, A, of the solenoid. ! ! dF d area, 𝐴 , of the solenoid.  V (t) = N = N BdA (1) ind 2nd 2nd dt dt 𝑑𝛷 𝑑 ⃗ ⃗ 𝑉 𝑡 𝑁 𝑁 𝐵 ∙𝑑 𝐴   (1) where the total internal cross-sectional area of the solenoid A = A + A + A + A ; A is tendon air duct concrete air 𝑑𝑡 𝑑𝑡 the cross-sectional area of air in the cross-section of the solenoid; A is the cross-sectional area of the duct where  the  total  internal  cross‐sectional  area  of  the  solenoid 𝐴𝐴 𝐴 𝐴 𝐴 ;  HDPE duct in the cross-section of the solenoid; A is the cross-sectional area of concrete in the concrete 𝐴   is the cross‐sectional area of air in the cross‐section of the solenoid; 𝐴   is the cross‐sectional  cross-section of the solenoid; and, A is the cross-sectional area of the tendon in the cross-section of tendon area of the HDPE duct in the cross‐section of the solenoid; 𝐴   is the cross‐sectional area of  the solenoid. concrete in the cross‐section of the solenoid; and, 𝐴   is the cross‐sectional area of the tendon in  When a time-variant AC flows in the primary coil of the solenoid, the magnetic field changes the cross‐section of the solenoid.  together and results in the change of the magnetic flux around the solenoid. The magnitude of When a time‐variant AC flows in the primary coil of the solenoid, the magnetic field changes  the induced electromagnetic field is a function of A = A + (A + A + A ) = A + A . concrete tendon air duct together and results in the change of the magnetic flux around the solenoid. The magnitude of the  Since A , A and A in A can be assumed as constants A , the induced electromotive force a air duct concrete induced  electromagnetic  field  is  a  function  of 𝐴𝐴 𝐴 𝐴 𝐴 𝐴 𝐴 .  function of A = A . Compared to the permeability  of the ferromagnetic tendon, the permeability tendon Since 𝐴 , 𝐴   and 𝐴   in 𝐴   can be assumed as constants 𝐴 , the induced electromotive  of the air, concr ete, and HDPE duct is very small and practically identical to the permeability in vacuum, force a function of 𝐴 𝐴 . Compared to the permeability 𝜇   of the ferromagnetic tendon, the  . Considering that all the parameters at the exception of A are controllable or constant, V in 0 ind permeability  of  the  air,  concrete,  and  HDPE  duct  is  very  small  and  practically  identical  to  the  Equation (1) can be expressed as a function of the area of the tendon, A as shown in Equation (2). permeability  in  vacuum,  𝜇 .  Considering  that  all  the  parameters  at  the  exception  of  𝐴   are  2 3 Z Z Z ! ! ! ! ! ! 6 7 controllable or constant, 𝑉   ind Equation (1) can be expressed as a function d  of the area of the tendon,  6 7 6 7 V (t) = N 6 HdA + BdA 7  N BdA (2) ind 2nd 0   2nd 4 0 5 𝐴   as shown in Equation (2).  dt dt A A A 𝑑 𝑑 where H is magnetic field intensity. ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ 𝑉 𝑡 𝑁 𝜇 𝐻 ∙𝑑 𝐴 𝐵 ∙𝑑 𝐴 ≅𝑁 𝐵 ∙𝑑 𝐴   (2) 𝑑𝑡 𝑑𝑡 where 𝐻   is magnetic field intensity.  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 5 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  5  of  13  Appl. Appl. Appl. Appl. Appl. Appl.   Sci.  Sci.  Sci.  Sci.  Sci. Sci.   2020  2020  2020  2020  2020 2020 ,, , 10 , 10 , 10 , 10 10 ,10 , , x, x, x , x FOR  x FOR x FOR  FOR  FOR FOR   P P P EER PEER  PEER PEER EER EER   RE  RE  RE  RE  RE RE VVVV IV IE V IEIEIW EIW EW EW W W      555 5 5 of 5 of of of of  of 13 13 13 13 13 13      Equation (2) indicates that the measured variation of the induced voltage in the second coil by  Equation (2) indicates that the measured variation of the induced voltage in the second coil by moving the solenoid throughout the length of the external tendon gives a means to detect the change  moving the solenoid throughout the length of the external tendon gives a means to detect the change Equation Equation Equation Equation Equation Equation  (2 (2 (2 (2 (2 )(2 ) ) )indi ) indi  )indi  indi  indi indi cat cat cat cat cat cat eeesesese s sth sth th th th th aaaatta ta tthe t the  tthe  the  the the  mea  mea  mea  mea  mea mea sssured sured sured sured ured ured  va  va  va  va va va riat riat riat riat riat riat ion ion ion ion ion ion  of of of of of of  the  the  the  the  the the  ind  ind  ind  ind  ind ind uuuuced uced uced ced ced ced  vo  vo  vo  vo  vo vo lltltlatlatltaagtg ag agegege e ein ein in in in in  the  the  the  the  the the  second  second  second  second  second second  co co co co co co ilililil il il by  by  by  by  by by       of the sectional area of the tendon.  of the moving moving sectional  the  the sar osolenoid ea lenoid of  the thro  thro tendon. uugghout hout the  the len  lenggthth of of the  the ex external ternal tendon  tendon gives  gives a a mea  meanns sto to detect  detect the  the change  change   moving moving moving moving  the the   the the  ss o sosolenoid olenoid lenoid lenoid  thro thro   thro thro uuugugghout ghout hout hout  the the   the the  len len   len len gggth gth th th  of of  of of  the the   the the  ex ex  ex ex ternal ternal ternal ternal  tendon tendon   tendon tendon  gives gives   gives gives  aa   a amea mea   mea mea nnnsns s to sto  to to  detect detect   detect detect  the the   the the  change change   change change     of of of of of of  th th th th th th eee e esecti  esecti  secti  secti  secti secti oooona ona ona na na na ll l lar lar lar ar ar ar ea ea ea ea ea ea  of of of of of of  the  the  the  the  the the  tendon.  tendon.  tendon.  tendon.  tendon. tendon.       3. Experiment  3. Experiment 3.3. Ex Expe peririme mentnt   3. 3.3. 3.  Ex Ex   Ex Ex pe pe pe pe riririri me me me me nt nt nt nt     Recalling that the tendon is made up of a bundle of strands and each strand is made up of wires,  Recalling that the tendon is made up of a bundle of strands and each strand is made up of wires, Rec Rec Rec Rec Rec Rec aaaallaling laling lling lling lling ling  tha  tha  tha  tha  tha tha tt t tthe t the  tthe  the  the the  tend  tend  tend  tend  tend tend on on on on on on  is is is is is is ma  ma  ma  ma  ma ma de de de de de de  up  up  up  up  up up  of of of of of of  a a a a   abundle  abundle  bundle  bundle  bundle bundle  of of of of of of  strands  strands  strands  strands  strands strands  and  and  and  and  and and  ea ea ea ea ea ea ccchchchch h str h str  str  str  str str aaaand nd and and nd nd  is is is is is is ma  ma  ma  ma  ma ma de de de de de de  up  up  up  up  up up  of of of of of of  wires,  wires,  wires,  wires,  wires, wires,       the tendon considered in this study is made of fifteen 7‐wire strands. The sectional loss of the external  the tendon considered in this study is made of fifteen 7-wire strands. The sectional loss of the external the the the the the the  tendon  tendon  tendon  tendon  tendon tendon  co co co co co co nsider nsider nsider nsider nsider nsider ed ed ed ed ed ed  in in in in in in  th th th th th th is isis isis is study  study  study  study  study study  is is is is is is ma  ma  ma  ma  ma ma ddddedede e eof of e of of of of  fi fi fi fift fift fiftftft een een fteen een een een  7 7 7 7‐ ‐7wire ‐7wire ‐‐wire wire ‐wire wire  st st st st st ra st ra ra ra ra ra nds. nds. nds. nds. nds. nds.  The  The  The  The  The The  secti  secti  secti  secti  secti secti oooonal onal onal nal nal nal  los  los  los  los  los los sss s of s of s of of of of  the  the  the  the  the the  external  external  external  external  external external       prestressing tendon is simulated as shown in Figure 4 by the number of snapped strands and the  prestressing tendon is simulated as shown in Figure 4 by the number of snapped strands and the prest prest prest prest prest prest rrressing ressing ressing ressing essing essing  tendon  tendon   tendon tendon  tendon tendon   is is is is is is  si si si si si mu si mu mu mu mu mu la la la la la tla tetetted etd ed ed d das as  as as as as  sho  sho   sho sho  sho sho w w w w w n w nnn n n in in in in in in   Fi Fi Fi Fi Fi gu Fi gu gu gu gu gu rrrererer e e 4e 4 44   4 by 4 by by by  by by   th th th th th th eee e e number e number  number number  number number   of of of of of of  snap  snap   snap snap  snap snap ped ped ped ped ped ped   st st st st st ra st ra ra ra ra ra nds nds nds nds nds nds  and  and   and and  and and   the  the  the the  the the       length of the damage in the tendon. For the convenience of the experiment, the HDPE duct of the  length of the damage in the tendon. For the convenience of the experiment, the HDPE duct of the leng lengthth of of the  the damage  damage in in th the etendon  tendon. .For  For the  the convenience  convenience of of th the eex experiment, periment, the  the HDPE  HDPE du  ductc tof of the  the   leng leng leng leng th th th th  of of of of  the  the  the the  damage  damage  damage damage  in in in in  th th th th ee e etendon  tendon  tendon tendon ..  .For . For  For For  the  the  the the  convenience  convenience  convenience convenience  of of of of  th th th th ee e eex ex ex ex periment, periment, periment, periment,  the  the  the the  HDPE  HDPE  HDPE HDPE  du  du  du du cctctc t of t of of of  the  the  the the     external tendon is replaced with a transparent acrylic duct having similar relative permeability to  external tendon is replaced with a transparent acrylic duct having similar relative permeability to extern extern extern extern extern extern al al al al al al  tend  tend  tend tend  tend tend on on on on on on   is is is is is is  re re re re re re pla pla pla pla pla pla ccced ced ced ced ed ed   with  with  with with  with with   a a aa   a tr a tr tr tr tr an tr an an an an an sp sp sp sp sp sp aren aren aren aren aren aren tt t tt a at aa ccacarylic crylic crylic crylic rylic rylic   duc  duc  duc duc  duc duc tt t tt ha ha t ha ha  ha ha vvvviviv ng ing ing ing ing ng   si si si si si mil si mil mil mil mil mil aaaarrara r r re r re re re re re lat lat lat lat lat lat iive ive ive ive ive ve   perme  perme  perme perme  perme perme aaaabbababili bili bili ili ili ili ty ty ty ty ty ty   to to to to to to       HDPE. The tendon is placed inside the acrylic duct, and the length of the damage near the center of  HDPE. The tendon is placed inside the acrylic duct, and the length of the damage near the center of the HDPE. HDPE. HDPE. HDPE. HDPE. HDPE.  The  The  The  The  The The  te te te te te ndon te ndon ndon ndon ndon ndon  is is is is is is pla  pla  pla  pla  pla pla ccced ced ced ced ed ed  insi  insi  insi  insi  insi insi de de de de de de  th th th th th th eee e eacryli  eacryli  acryli  acryli  acryli acryli ccc c cduc  cduc  duc  duc  duc duc tt,t,t t, ,and t ,and  ,and  and  and and  the  the  the  the  the the  len  len  len  len  len len ggggth gth gth th th th  of of of of of of  the  the  the  the  the the  da  da  da  da  da da mage mage mage mage mage mage  near  near  near  near  near near  the  the  the  the  the the  cen  cen  cen  cen  cen cen tter ter tter er ter er  of of of of of of       the tendon is changed from 0 to 10 cm. The number of snapped strands is increased from one to three  tendon is changed from 0 to 10 cm. The number of snapped strands is increased from one to three to the the the the the the  tendon  tendon  tendon  tendon  tendon tendon  is is is is is is changed  changed  changed  changed  changed changed  from  from  from  from  from from  0 0 0 0   0to 0to to to to to  10 10 10 10 10 10  cm.  cm.  cm.  cm.  cm. cm.  Th  Th  Th  Th  Th Th eee e enumber  number e number  number  number number  of of of of of of  sna  sna  sna  sna  sna sna pped pped pped pped pped pped  st st st st st rands st rands rands rands rands rands  is is is is is is incre  incre  incre  incre  incre incre aaaassasaesesesd ed ed ed d from d from  from  from  from from  one  one  one  one  one one  to to to to to to  three  three  three  three  three three       to observe the secondary coil output according to the amount of damage. Table 1 describes the cases  observe to to to to to to  observe  observe  observe  observe  observe observe the secondary   th th th th th th eee e esecond  esecond  second  second  second second coil ar ar ar ar ar ar yyyy y co y co output  co co co co iilili li loutput i loutput  loutput  output  output output accor   acc  acc  acc  acc  acc acc o ding ooording ording ording rding rding rding to  to to to to to the to  th th th th th th eee e amount  eam  eam  am  am  am am oun oun oun oun oun oun tt t tof t of tof of of of of  dama  dama  dama  dama damage.  dama dama ggggegege.e.e .e .Tab  Tab . Tab . Tab  Tab Tab Tllable elelel el e1 e1 1 1   1descr  1descr  descr  descr  descr 1descr describes iibes ibes ibes ibes ibes bes  th th th th th th eee e ecases  ecases  cases  cases the  cases cases  cases      setup for the 3‐strand damage case.  setup setup setup setup setup setup  fo fo fo fo fo fo rrr r th r th r th th th th eee e e3 e3 3 3‐ ‐3str ‐3str ‐‐str str ‐str str aaaand nd and and nd nd  dam  dam  dam  dam  dam dam aaaage ge age age ge ge  case.  case.  case.  case.  case. case.       setup for the 3-strand damage case. 1, 1,1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3 3 3  3  3da 3da da  da da da m m m m m m aaage age age age ge ge dddd d str d str  str  str  str str aaan ananandndnddsdsdssss 1, 2, 3 damaged strands 15 15 15 15 15 15  str  str  str  str  str str aaand and and and nd nd ssssss 15 strands 0, 0,0, 0, 0,  0, 2, 2, 2, 2, 2,  2, 4, 4, 4, 4, 4,  4, 6, 6, 6, 6, 6,  6, 8, 8, 8, 8, 8,  8, 10 10 10 10 10 10  cm  cm  cm  cm  cm cm 163 163 163 163 163 163  cm  cm  cm  cm  cm cm 0, 2, 4, 6, 8, 10 cm 163 cm 330 330 330 330 330 330  cm  cm  cm  cm  cm cm 330 cm        Figure Figure Figure Figure Figure Figure   4. 4. 4. 4. 4.  4. Cons  Cons  Cons  Cons Cons Cons idered idered idered idered idered idered   sect  sect  sect  sect sect sect io io io io io nal io nal nal nal nal nal   d d d dad ad amage amage amage amage mage mage   ca ca ca ca ca ses ca ses ses ses ses ses   of of of of of of  external  external  external  external external external   PSC  PSC  PSC  PSC PSC PSC   tendon  tendon  tendon  tendon tendon tendon   (1 (1 (1 (1 (1 5(1 55‐5‐5strand ‐5strand ‐strand ‐strand ‐strand strand   tendon,  tendon,  tendon,  tendon, tendon, tendon,   7 7 7 ‐7‐7wire ‐7wire ‐wire ‐wire ‐wire wire       strand). strand). strand). strand). strand). strand).       Figure  4.  Considered  sectional  damage  cases  of  external  PSC  tendon  (15‐strand  tendon,  7‐wire  Figure 4. Considered sectional damage cases of external PSC tendon (15-strand tendon, 7-wire strand). strand).  Table Table Table Table Table Table  1. 1. 1. 1. 1.  1. Damage  Damage  Damage  Damage  Damage Damage  case  case  case  case  case case sss s for s for s for  for  for for  3 3 3 ‐3‐ 3strand ‐3strand ‐strand ‐strand ‐strand strand  d d d da d ad amage amage amage amage mage mage  of of of of of of 15 15 15 15 15 15‐‐strand ‐strand ‐strand ‐strand ‐strand strand  te te te te te ndon. te ndon. ndon. ndon. ndon. ndon.       Table 1. Damage cases for 3-strand damage of 15-strand tendon. Length Length Length Length Length Length  of of of of of of  S S S S eSeSeectio ctio ectio ectio ctio ctio nnnn n n Loss  Loss  Loss  Loss  Loss Loss  (c (c (c (c (c m) (c m) m) m) m) m)       Table 1. Damage cases for 3‐strand damage of 15‐strand tendon.  Length of Section Loss (cm) 0000  0 0    2222  2 2    4444  4 4    6666  6 6    8888  8 8    10 10 10 10 10 10       0 2 4 6 8 10 Length of Section Loss (cm)  0  2  4  6  8  10                                              The The The The The The  dev  dev   dev dev  dev dev iice ice ice ice ice ce  d d  dd ededeliver eliver eliver eliver liver liver ing ing ing ing ing ing  the  the   the the  the the  ma  ma   ma ma  ma ma gnet gnet gnet gnet gnet gnet ic icic ic ic ic fi fi  fifi eld field field eld eld eld  to to  to to to to  the  the   the the  the the  ex ex  ex ex ex ex ter ter ter ter ter ter nnnnal nal nal al al al tendon  tendon   tendon tendon  tendon tendon  and  and   and and  and and  de  de   de de  de de tec tec tec tec tec tec ttin tin ttin in tin in gggg g gthe  the   the the  the the  va  va   va va  va va riation riation riation riation riation riation  of of  of of of of          The device delivering the magnetic field to the external tendon  and detecting the variation of the   the the the the the the  magnetic  magnetic   magnetic magnetic  magnetic magnetic  flux  flux   flux flux  flux flux  is is  is is is is ma  ma   ma ma  ma ma ddddedede e eby  eby   by by  by by  the  the   the the  the the  assem  assem   assem assem  assem assem bbbblage blage blage lage lage lage  of of  of of of of  two  two   two two  two two  37 37  37 37 37 37‐‐cm ‐cm ‐‐cm cm ‐cm cm  lon  lon   lon lon  lon lon gggg g gplastic  plastic   plastic plastic  plastic plastic  half  half   half half  half half‐‐cy‐cy‐‐cy cy‐cy cy linders linders linders linders linders linders  as as  as as as as  sho  sho   sho sho  sho sho w w w w w n w nnn n nin in  in in in in       Fig Fig Fig Fig Fig Fig uuuure ure ure re re re  5a 5a  5a 5a 5a 5a .. . .Th  .Th  . Th Th  Th Th eee e esecond  esecond   second second  second second ary ary ary ary ary ary  co co  co co co co iilili li liwi  lwi  l wi wi  wi wi tth th tthh t h h18 18  18 18 18 18  turns  turns   turns turns  turns turns  is is  is is is is ins  ins   ins ins  ins ins ttatattaalle tlle alle alle lle lle dddd d dat at  at at at at the  the   the the  the the  ce ce  ce ce ce ce nnnntntner ter tter er ter er  of of  of of of of  the  the   the the  the the  fr fr  fr fr fr am fr am am am am am eee e efor  efor   for for  for for  de  de   de de  de de tectin tectin tectin tectin tectin tectin gggg g gthe  the   the the  the the       magnetic flux is made by the assemblage of two 37-cm long plastic half-cylinders as shown in Figure 5a. The device delivering the magnetic field to the external tendon and detecting the variation of  ma ma ma ma ma ma gnet gnet gnet gnet gnet gnet ic icic ic ic ic fl fl  flfl u flufluuxuxuxx  xsignal  xsignal   signal signal  signal signal  and  and  and  and  and and  the  the  the  the  the the  prim  prim   prim prim  prim prim aaaarrarayryryry y yco co  co co co co iilili li liwit  lwit  l wit wit  wit wit hhhh h h40 40 40  40 40 40 0000  0turns  0turns  turns  turns  turns turns  over  over   over over  over over  a a a a   alengt  alengt   lengt lengt  lengt lengt hhhh h hof of  of of of of  30 30 30 30 30 30  cm  cm   cm cm  cm cm  is is  is is is is pl pl  pl pl pl pl aaaaccacaecececd ed ed ed d dove  ove   ove ove  ove ove rrr r rthe  rthe   the the  the the       The secondary coil with 18 turns is installed at the center of the frame for detecting the magnetic flux the magnetic secondary secondary secondary secondary secondary secondary  flux   co co co co co co ilililil il  to ilto  to is to to to  gen   gen  gen ma  gen  gen gen eeed rate erate erate erate erate rate  by  the  the  the  the  the  the the   ma  ma  ma  ma  ma ma gnetic assem gnetic gnetic gnetic gnetic gnetic  fifi b fi field. fi eld. filage eld. eld. eld. eld.  The  The  The   The  The of The   sta  sta  two sta  sta  sta sta bbbbili bili bili ili ili 37 ili ttytyttyyt y‐ of y of cm of of of of  th th th th th th eelon e e ema  ma e ma  ma  ma ma ggn gn gn gn gn plastic gn eeeteteiteitcticitci ci field c field c field  field  field field  half   alo alo   alo  alo alo  alo ‐ncy nnngngngg linders g th g th th th th th eee e elon  lon e lon  lon  lon lon gg ggigas itgitiu tiu tituu t dudusho ddina dina dina ina ina ina lw l l l l l n  in  signal and the primary coil with 400 turns over a length of 30 cm is placed over the secondary coil to axi axi axi axi axi axi sss s s mea s mea  mea  mea mea mea sssured sured sured sured ured ured   at at at at at at  the  the  the  the the the   ce ce ce ce ce ce nnnntntnetetteretrere r r of r of of of of of   the  the  the  the the the   cro  cro  cro  cro cro cro sssssssss s s secti s secti  secti  secti secti secti oooonononn n n is is is isis is  verified  verified  verified  verified verified verified   in in in in in in   Figure  Figure  Figure  Figure Figure Figure   5b 5b 5b 5b 5b 5b   by  by  by  by by by   co co co co co co mpa mpa mpa mpa mpa mpa rrririrsisrisiosiososonononn n n wi  wi  wi  wi wi wi tth th tthh t h h the  the  the  the the the       Figure 5a. The secondary coil with 18 turns is installed at the center of the frame for detecting the  generate the magnetic field. The stability of the magnetic field along the longitudinal axis measured theore theore theore theore theore theore tic tic tic tic tic tic aaaalla la l lva va l va va va va llu lu lu lules ues ues es es es .. . . Howev . Howev . Howev  Howev Howev Howev eeer, er, er, er, r, r, the  the  the  the the the   devic  devic  devic  devic devic devic eee e e in e in in in in in   Figur  Figur  Figur  Figur Figur Figur eee e e 5e 5 5 5  5 5is is is isis is  un  un  un  un un un su su su su su su itabl itabl itabl itabl itabl itabl eee e e for e for  for  for for for   in in in in in in   situ  situ  situ  situ situ situ   in in in in in in spect spect spect spect spect spect iion ion ion ion ion on   tha  tha  tha  tha tha tha tt t tt needs  needs t needs  needs needs needs       magnetic flux signal and the primary coil with 400 turns over a length of 30 cm is placed over the  at the center of the cross section is verified in Figure 5b by comparison with the theoretical values. freq freq freq freq freq freq uen uen uen uen uen uen tt t tas t as tas as as as se se se se se se m m m m m m bbbbly bly bly ly ly ly  an an an  an an an dddd d d d d d d idid sassembly isassembly isassembly isassembly isassembly sassembly  due  due  due  due  due due  to to to to to to  the  the  the  the  the the  la la la la la rge la rge rge rge rge rge  nu  nu  nu  nu  nu nu mbe mbe mbe mbe mbe mbe rrr r of r of r of of of of  numerous  numerous  numerous  numerous  numerous numerous  turns.  turns.  turns.  turns.  turns. turns.       secondary coil to generate the magnetic field. The stability of the magnetic field along the longitudinal  However, the device in Figure 5 is unsuitable for in situ inspection that needs frequent assembly and axis  measured  at  the  center  of  the  cross  section  is  verified  in  Figure  5b  by  comparison  with  the  disassembly due to the large number of numerous turns. theoretical values. However, the device in Figure 5 is unsuitable for in situ inspection that needs  frequent assembly and disassembly due to the large number of numerous turns.  Appl. Appl. Appl. Appl. Appl. Appl.   Sci.  Sci.  Sci.  Sci.  Sci. Sci.   2020  2020  2020  2020  2020 2020 ,, , 10 , 10 , 10 , 10 10 ,10 , , x; , x; , x; , x;  x; doi: x; doi:  doi:  doi:  doi: doi:   FOR  FOR  FOR  FOR  FOR FOR   PEE  PEE  PEE  PEE  PEE PEE RRRR R REVIEW R REVIEW  REVIEW  REVIEW  REVIEW REVIEW        www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ jjournal/applsci ournal/applsci jjournal/applsci journal/applsci ournal/applsci journal/applsci        Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  6  of  13  Appl. Sci. 2020, 10, 7398 6 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  6  of  13  (a)  (b)  Figure 5. Fabrication and installation of solenoid‐shape device: (a) installed device; (b) distribution of  theoretical and measured longitudinal magnetic fields at center of device.  Accordingly, our research team developed a mountable frame where the primary and secondary  can be easily connected by plugging as shown in Figure 6a to avoid the repeated winding of the coils  in situ. This so‐called wrapping solenoid‐shaped device also exhibited stable magnetic field through  the comparison of the measured and theoretical values (Figure 6b). Nevertheless, the original setup  (a)  (b)  of Figure 5 is employed here for evaluating the feasibility of the TFL method in detecting the sectional  loss Figure in  the 5.  ext Fabrication ernal  ten and don. installation   Research of solenoid-shape about  the  improved device: (a ) de installed vice  shown device; (in b) distribution Figure  6  will of   be  Figure 5. Fabrication and installation of solenoid‐shape device: (a) installed device; (b) distribution of  implemen theoretical ted in and the measur  future ed to longitudinal  investigat magnetic e its accu fields racy at and center  perform of device. ance. In addition, the operation of  theoretical and measured longitudinal magnetic fields at center of device.  the solenoid‐shape device with a battery will be tested in the future to verify the stableness of the  Accordingly, our research team developed a mountable frame where the primary and secondary device’s results with a less stable power supply for in situ inspection.  Accordingly, our research team developed a mountable frame where the primary and secondary  can be easily connected by plugging as shown in Figure 6a to avoid the repeated winding of the coils can be Although  easily connected  an autom aby tic plugging  movement  as  shown of the devic  in Figur e caen 6a re duce to avoid  the  the unce rertain peatteyd from  windin  theg  iof nc th ons e ta coils nt   in situ. This so-called wrapping solenoid-shaped device also exhibited stable magnetic field through moving speed of the device, the automation of the device movement is not considered in this study.  in situ. This so‐called wrapping solenoid‐shaped device also exhibited stable magnetic field through  the comparison of the measured and theoretical values (Figure 6b). Nevertheless, the original setup of In the gener  comp al,arison  near  th ofe the  ancho  measured rage where  and  th is eoret damaica gel sva are lue often s (Fig fo urund, e 6b) .tendons  Nevert he are les close s, thely or space iginadl  setu withp   Figure 5 is employed here for evaluating the feasibility of the TFL method in detecting the sectional loss each other, and an available space that the device can use is limited. The automation equipment also  of Figure 5 is employed here for evaluating the feasibility of the TFL method in detecting the sectional  in the external tendon. Research about the improved device shown in Figure 6 will be implemented in incre loss ain ses  the  the  weigh externta of l  ten thed device on.  Resea  thatr is ch anothe   aboutr  limi the tat improved ion for fie  de ld vice appl ica shown tion.  Therefore in  Figure,  th6e  will device   be   the future to investigate its accuracy and performance. In addition, the operation of the solenoid-shape was designed to remove inessential function in order to fit into the limited space and weight. But the  implemented in the future to investigate its accuracy and performance. In addition, the operation of  device with a battery will be tested in the future to verify the stableness of the device’s results with a au the tom  soaleno tionid eq‐shape uipme de ntvi can ce  be with  in staal ba led tte witho ry willu tbe di fftes ictul edty in if  necessa the futury re.  to verify the stableness of the  less stable power supply for in situ inspection. device’s results with a less stable power supply for in situ inspection.  Although an automatic movement of the device can reduce the uncertainty from the inconstant  moving speed of the device, the automation of the device movement is not considered in this study.  In general, near the anchorage where is damages are often found, tendons are closely spaced with  each other, and an available space that the device can use is limited. The automation equipment also  increases the weight of the device that is another limitation for field application. Therefore, the device  was designed to remove inessential function in order to fit into the limited space and weight. But the  automation equipment can be installed without difficulty if necessary.  (a)  (b)  Figure 6. Mountable wrapping solenoid-shaped device for in situ inspection: (a) mounted wrapping Figure 6. Mountable wrapping solenoid‐shaped device for in situ inspection: (a) mounted wrapping  device; (b) distribution of theoretical and measured longitudinal magnetic fields at the center of device; (b) distribution of theoretical and measured longitudinal magnetic fields at the center of the  the device. device.  Although an automatic movement of the device can reduce the uncertainty from the inconstant Figure 7 shows the external tendon specimen with the installed device. During the inspection,  moving speed of the device, the automation of the device movement is not considered in this study. the distance travelled by the device along the axis of the tendon was measured in real time with  In general, near the anchorage where is damages are often found, tendons are closely spaced with respect  to  the  reference  point  using  a  laser  distance  meter.  An  AC  with  frequency  of  10  Hz  and  (a)  each other, and an available space that the device can use is limited. The automation equipment also (b)  amplitude  of  ±0.6  A  was  delivered  continuously  to  the  primary  coil  of  the  device  using  the  NI  increases the weight of the device that is another limitation for field application. Therefore, the device Figure 6. Mountable wrapping solenoid‐shaped device for in situ inspection: (a) mounted wrapping  was designed to remove inessential function in order to fit into the limited space and weight. But the Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  device; (b) distribution of theoretical and measured longitudinal magnetic fields at the center of the  automation equipment can be installed without diculty if necessary. device.  Figure 7 shows the external tendon specimen with the installed device. During the inspection, the distance travelled by the device along the axis of the tendon was measured in real time with respect Figure 7 shows the external tendon specimen with the installed device. During the inspection,  to the reference point using a laser distance meter. An AC with frequency of 10 Hz and amplitude of the distance travelled by the device along the axis of the tendon was measured in real time with  0.6 A was delivered continuously to the primary coil of the device using the NI (National Instrument) respect  to  the  reference  point  using  a  laser  distance  meter.  An  AC  with  frequency  of  10  Hz  and  equipment as shown in Figure 8. The signal was generated by the LabVIEW program on a laptop and amplitude  of  ±0.6  A  was  delivered  continuously  to  the  primary  coil  of  the  device  using  the  NI  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  7  of  13  Appl. Sci. 2020, 10, x FOR PEER REVIEW  7  of  13  Appl. Sci. 2020, 10, 7398 7 of 12 (National Instrument) equipment as shown in Figure 8. The signal was generated by the LabVIEW  (National Instrument) equipment as shown in Figure 8. The signal was generated by the LabVIEW  program on a laptop and the NI PXI‐5412 AWG (arbitrary waveform generator). The generated signal  program on a laptop and the NI PXI‐5412 AWG (arbitrary waveform generator). The generated signal  the NI PXI-5412 AWG (arbitrary waveform generator). The generated signal was magnified by the NF was magnified by the NF BP bipolar DC power supply. The output voltage from the secondary coil  was magnified by the NF BP bipolar DC power supply. The output voltage from the secondary coil  BP bipolar DC power supply. The output voltage from the secondary coil of the device was measured of  the  device  was  measured  by  the  NI  PXI‐4462  DAQ  (data  acquisition)  system.  The  device  was  of  the  device  was  measured  by  the  NI  PXI‐4462  DAQ  (data  acquisition)  system.  The  device  was  by the NI PXI-4462 DAQ (data acquisition) system. The device was moved manually and slowly along moved manually and slowly along the length of the tendon by the operator without a specific power  moved manually and slowly along the length of the tendon by the operator without a specific power  the length of the tendon by the operator without a specific power unit. unit.  unit.  Figure 7. View of external PSC tendon installed for measurement test of sectional loss by the Total  Figure 7. View of external PSC tendon installed for measurement test of sectional loss by the Total  Figure 7. View of external PSC tendon installed for measurement test of sectional loss by the Total Flux Flux Leakage (TFL) method.  Flux Leakage (TFL) method.  Leakage (TFL) method. Figure 8. Equipment used to deliver AC to the primary coil of the device and measure the output of  Figure 8. Equipment used to deliver AC to the primary coil of the device and measure the output of  Figure 8. Equipment used to deliver AC to the primary coil of the device and measure the output of the secondary coil.  the secondary coil.  the secondary coil. 4. Results 4. Results  4. Results  Figur Figure e 99 shows shows aa typical typicalpattern  patternof ofthe  theoutput  output signal  signal measur  measured ed in in the the secondary  secondarcoil y coin il in the th case e cas ofe  Figure 9 shows a typical pattern of the output signal measured in the secondary coil in the case  damaged external tendon. As the AC is delivered to the primary coil, the output signal of the secondary of damaged external tendon. As the AC is delivered to the primary coil, the output signal of the  of damaged external tendon. As the AC is delivered to the primary coil, the output signal of the  coil secondary has a form  coil similar has a form to the siinput milar  signal to thedeliver  input ed sigto nal the delivere primary d to coil the with  prima the same ry coil fr equency with the and same is  secondary coil has a form similar to the input signal delivered to the primary coil with the same  symmetric with reference to the horizontal axis. In the case where the DC is delivered to the primary frequency  and  is  symmetric  with  reference  to  the  horizontal  axis.  In  the  case  where  the  DC  is  frequency  and  is  symmetric  with  reference  to  the  horizontal  axis.  In  the  case  where  the  DC  is  coil delive instead red  toof  the an  prima AC and ry the coilmoving   insteadspeed   of  an of AC the  and device   the is mov irregular ing  speed , undesir   of  th ed e  device disturbance   is  irre would gular,  delivered  to  the  primary  coil  instead  of  an  AC  and  the  moving  speed  of  the  device  is  irregular,  occur in the induced voltage on the secondary coil. In this research, a suciently stable magnetic flux undesired disturbance would occur in the induced voltage on the secondary coil. In this research, a  undesired disturbance would occur in the induced voltage on the secondary coil. In this research, a  was suffic generated iently staby blemeans  magnet ofic AC  flux that was inverted  generated the dir by ection  mean ofs the of AC power  thasour t inver ce as ted much  the di asre its ctifroequency n of the  sufficiently stable magnetic flux was generated by means of AC that inverted the direction of the  even though the operator was moving the device without specific speed control. Since the device power source as much as its frequency even though the operator was moving the device without  power source as much as its frequency even though the operator was moving the device without  was specif moved ic speeslowly d contro from l. Sin the ce lef the t end device to the was right  moved end sl of owl the y external from thetendon,  left enda to very  the lar righ get number end of the of  specific speed control. Since the device was moved slowly from the left end to the right end of the  positive and negative peaks of the secondary coil output signal was recorded according to the distance external tendon, a very large number of positive and negative peaks of the secondary coil output  external tendon, a very large number of positive and negative peaks of the secondary coil output  travelled signal waduring s recorded the acco totalrding time of to the motion.  distance The tr measur avelled ed durin secondary g the tot coil al tim output e of motion. takes thus  The the  measured form of  signal was recorded according to the distance travelled during the total time of motion. The measured  the compressed sinusoidal wave along the horizontal axis shown in Figure 9. Only the positive peaks secondary coil output takes thus the form of the compressed sinusoidal wave along the horizontal  secondary coil output takes thus the form of the compressed sinusoidal wave along the horizontal  wer axise  shown picked  fr inom   Fig the uremeasur   9.  Only ed  the signal   positive for the  pea convenience ks  were  pi ofck the ed analysis. from  the  measured  signal  for  the  axis  shown  in  Figure  9.  Only  the  positive  peaks  were  picked  from  the  measured  signal  for  the  convenience of the analysis.  convenience of the analysis.  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  8  of  13  Appl. Sci. 2020, 10, 7398 8 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  8  of  13  Figure 9. Induced voltage and its peaks in the secondary coil.  The peak curves of the voltage induced in the secondary coil in accordance with the change in  length of one‐strand damage of the external tendon are presented in Figure 10. The lowest point in  the curves corresponds the center of the damage length. The centerline of the damage length is shifted  slightly to the right due to the fixed left end of the damage as shown in Figure 4. It is observed that  this phenomenon is reflected on the measured peak curves.  In the same manner, the peak curves of the voltage induced in the secondary coil in accordance  with the change in length of two‐ and three‐strand‐damage of the external tendon are presented in  Figure 11 and Figure 12 Figure , respectively  9. Induced.  In vo ad ltage di tion, and its the peaks  second  in the ary se vo condary ltage  red coil.u  ction ratios of the one  Figure 9. Induced voltage and its peaks in the secondary coil. to three‐strands damage with respect to the damage length are presented in Figure 13. The damage  The peak curves of the voltage induced in the secondary coil in accordance with the change in The peak curves of the voltage induced in the secondary coil in accordance with the change in  detectable level in Figure 13 was visually suggested as the peak curve for the 1‐strand damage with  length of one-strand damage of the external tendon are presented in Figure 10. The lowest point in the length of one‐strand damage of the external tendon are presented in Figure 10. The lowest point in  0 cm damage length in Figure 10 is difficult to be distinguished and can be hidden if the signal to  curves corresponds the center of the damage length. The centerline of the damage length is shifted the curves corresponds the center of the damage length. The centerline of the damage length is shifted  noise ratio decreases. The decrement ratio in Figure 13 is the voltage change due to the damage to the  slightly to the right due to the fixed left end of the damage as shown in Figure 4. It is observed that this slightly to the right due to the fixed left end of the damage as shown in Figure 4. It is observed that  voltage value just before the decrement.  phenomenon is reflected on the measured peak curves. this phenomenon is reflected on the measured peak curves.  In the same manner, the peak curves of the voltage induced in the secondary coil in accordance  with the change in length of two‐ and three‐strand‐damage of the external tendon are presented in  Figure 11 and Figure 12, respectively. In addition, the secondary voltage reduction ratios of the one  to three‐strands damage with respect to the damage length are presented in Figure 13. The damage  detectable level in Figure 13 was visually suggested as the peak curve for the 1‐strand damage with  0 cm damage length in Figure 10 is difficult to be distinguished and can be hidden if the signal to  noise ratio decreases. The decrement ratio in Figure 13 is the voltage change due to the damage to the  voltage value just before the decrement.  Figure 10. Secondary coil output peak induced by 1‐strand damage according to damage length.  Figure 10. Secondary coil output peak induced by 1-strand damage according to damage length. In the same manner, the peak curves of the voltage induced in the secondary coil in accordance with the change in length of two- and three-strand-damage of the external tendon are presented in Figures 11 and 12, respectively. In addition, the secondary voltage reduction ratios of the one to three-strands damage with respect to the damage length are presented in Figure 13. The damage Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  detectable level in Figure 13 was visually suggested as the peak curve for the 1-strand damage with 0 cm damage length in Figure 10 is dicult to be distinguished and can be hidden if the signal to noise ratio decreases. The decrement ratio in Figure 13 is the voltage change due to the damage to the voltage value just before the decrement. Figure 10. Secondary coil output peak induced by 1‐strand damage according to damage length.  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  9  of  13  Appl. Sci. 2020, 10, x FOR PEER REVIEW  9  of  13  Appl. Sci. 2020, 10, 7398 9 of 12 Figure 11. Secondary coil output peak induced by 2‐strand damage according to damage length.  Figure Figure 11. 11. Secondary  Secondary coil coil output  output peak  peak induced  induceby d by 2-strand  2‐strand damage  damage accor  accordi dingnto g to damage  damage length.  length.  Figure 12. Secondary coil output peak induced by 3‐strand damage according to damage length.  Figure 12. Secondary coil output peak induced by 3-strand damage according to damage length. Figure 12. Secondary coil output peak induced by 3‐strand damage according to damage length.  The location of the sectional loss can be estimated simply and intuitively. Moreover, the change in the damage length is also well reflected in Figures 10–12. The reduction of the magnitude of the voltage induced in the secondary coil caused by the magnetic flux leaked from the damaged section that is not permeating the secondary coil shown in Figure 3 can be clearly distinguished in the graphs. In addition, it appears that deeper and longer damage introduces stronger magnetic flux leakage as well as increases the magnitude of the decrement of the voltage induced in the secondary coil as shown in Figure 13. The ratio of decrement in induced voltage of the secondary coil for all cases except for the 1-strand damage with a length of 0 cm case were above the designated damage detectable level. However, as such the case is neglectable as the external tendon is always in tension and the damage length would not be zero when cut. Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 10 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  10  of  13  Figure 13. Rate of decrement in induced voltage of secondary coil.  Figure 13. Rate of decrement in induced voltage of secondary coil. The The maximum location of peak the sec curve tiona of l lo the ss voltage can be estimated induced in simpl the secondary y and intuicoil tivemeasur ly. More ed over, by moving  the change the  device throughout the length of the external tendon can provide information about the damage location in the damage length is also well reflected in Figures 10–12. The reduction of the magnitude of the  by voltage identif ind ying ucethe d inv the ariation  secondary of the coil curve.  cauThe sed by reduction  the magnet of the ic fl voltage ux leake induced d from in the the  dam secondary aged section coil  by the rupture of 1 or more strands or damage length of 2 cm or longer can be intuitively identified. that is not permeating the secondary coil shown in Figure 3 can be clearly distinguished in the graphs.  Hence, In additthis ion, validates it appearsthat  thatthe  deeper method  and measuring longer damag theechange  introduce of the s strong totaler flux  macan gnetbe ic fl used ux leto akdetect age as  damage in the external tendon. This result satisfies the FHWA guideline of tendon replacement at 5% well as increases the magnitude of the decrement of the voltage induced in the secondary coil as  sectional shown inloss  Figu asre well  13. as The the ra pr tio oject’s  of decre detection ment in accuracy  induced of volt figuring age of out the 1 out second of 15 ary tendons.  coil for all cases  The external tendon of the PSC structure has a limited profile and size inside the structure section except  for  the  1‐strand  damage  with  a  length  of  0  cm  case  were  above  the  designated  damage  unlike detectable other lev cases el. However with a complicated , as such the pr case ofile is and  neglectable size. Since asthe  thedevice  external wraps  tendon the is entir  always e section  in tensi of the on  external tendon, the secondary coil can measure almost any change of the magnetic flux induced by and the damage length would not be zero when cut.  the change The ma ofximum the sectional  peak curve area of inside  the voltage the tendon.  induce The d in pr the oposed  second method ary coil has mea shown suredthe  by potent moving ial the to  identify and quantify the sectional loss in the external tendon by using a solenoid-shaped device fed device  throughout  the  length  of  the  external  tendon  can  provide  information  about  the  damage  with location AC  and by  ipr dent esenting ifying ath simple e  variat shape ion  of and  the light   cur weight ve.  The even   reduc though tion  the of  the uncertainty   voltage  of induce the pr doposed   in  the  method increases if a strong exterior magnetic source is close to the device or the power supply is secondary  coil  by  the  rupture  of  1  or  more  strands  or  damage  length  of  2  cm  or  longer  can  be  unstable. intuitivelyThe  identi prfie oposed d. Hence TFL, th method is valida o te ers s tha thet the advantage  method of mea a low-power suring the change source of which  the to makes tal flux it  convenient for actual NDE conditions in terms of portability and long-term usage. can be used to detect damage in the external tendon. This result satisfies the FHWA guideline of  tendon replacement at 5% sectional loss as well as the project’s detection accuracy of figuring out 1  5. Conclusions out of 15 tendons.  The  external  tendon  of  the  PSC  structure  has  a  limited  profile  and  size  inside  the  structure  A new TFL method is proposed to estimate the location and amount of damage in the external section  unlike  other  cases  with  a  complicated  profile  and  size.  Since  the  device  wraps  the  entire  tendon of PSC structures. This TFL method uses AC-delivering solenoid with a secondary coil inserted section of the external tendon, the secondary coil can measure almost any change of the magnetic flux  in an external primary coil enclosing the tendon. The primary coil is fed with a current in the device induced by the change of the sectional area inside the tendon. The proposed method has shown the  to cause the magnetic field, and the change in the magnetic flux at the damaged area of the external potential to identify and quantify the sectional loss in the external tendon by using a solenoid‐shaped  tendon is detected and quantified by the variation of the voltage in the secondary coil. Unlike the MMF device fed with AC and presenting a simple shape and light weight even though the uncertainty of  (Main Magnetic Flux) method, which usually uses a heavy magnetic yoke, the proposed TFL method the proposed method increases if a strong exterior magnetic source is close to the device or the power  uses a light solenoid-shaped device. In addition, the proposed TFL method can provide a stable output supply is unstable. The proposed TFL method offers the advantage of a low‐power source which  due to the AC input signal and can be applied to any cable system with minor modification. makes it convenient for actual NDE conditions in terms of portability and long‐term usage.  The following conclusions can be derived from a series of experiments considering various degrees and lengths of damage in the tendon. 5. Conclusions  (1) Sucient output signal could be acquired from the secondary coil for identifying the damage on the A new TFL method is proposed to estimate the location and amount of damage in the external  external tendon even when using the device with light and simple structure and fed with low-level tendon  of  PSC  structures.  This  TFL  method  uses  AC‐delivering  solenoid  with  a  secondary  coil  inserted in an external primary coil enclosing the tendon. The primary coil is fed with a current in the  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 11 of 12 AC. The proposed method was proved to satisfy the simplicity, portability, and low-energy power requirements for detecting damage in the external tendon of the PSC structure. (2) There is concern about the occurrence of undesired disturbance in the induced voltage from the secondary coil if the moving speed is not constant in the process of detecting the damage location by moving the device throughout the length of the external tendon. In this research, a suciently stable magnetic flux was generated by means of AC that inverted the direction of the power source as much as its frequency even though the operator was moving the device without specific speed control. (3) The signal induced in the secondary coil by the AC delivered to the primary coil of the device is an AC signal with the same frequency as the input signal on the primary coil and is governed only by the tendon area in the duct. The signal measured in the secondary coil reflected the change of the total flux throughout the length of the external tendon. The location of the damage could be identified by analyzing only the peaks of the induced signal measured when moving the device throughout the length of the external tendon. Intuitive detection of the rupture of 1 or more strands or damage length of 2 cm or longer could be achieved by identifying the reduction of the amplitude of the signal measured in the secondary coil. The proposed method proved its feasibility in e ectively detecting the damage by measuring the change of the total flux in the external tendon. Author Contributions: Conceptualization, I.K. and C.J.; methodology, I.K. and J.-Y.C.; software, H.K. and K.-Y.P.; validation, I.K., H.K., and C.J.; resources, J.-Y.C.; data curation, K.-Y.P.; writing—original draft preparation, I.K.; writing—review and editing, C.J.; visualization, K.-Y.P.; project administration, C.J. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Korea Institute of Civil Engineering and Building Technology (KICT) of the Republic of Korea, Project No. 2020-0033. Conflicts of Interest: The authors declare no conflict of interest. References 1. Lee, B.Y.; Koh, K.T.; Ismail, M.A.; Ryu, H.-S.; Kwon, S.J. Corrosion and strength behaviors in prestressed tendon under various tensile stress and impressed current conditions. Adv. Mater. Sci. Eng. 2017, 2017, 1–7. [CrossRef] 2. Mahmoodian, M.; Li, C.Q. Failure assessment of a pre-stressed concrete bridge using time dependent system reliability method. In Proceedings of the 29th Annual International Bridge Conference, Pittsburgh, PA, USA, 10–13 June 2012. 3. Naito, C.; Sause, R.; Hodgson, I.; Pessiki, S.; Macioce, T. Forensic Examination of a Noncomposite Adjacent Precast Prestressed Concrete Box Beam Bridge. J. Bridg. Eng. 2010, 15, 408–418. [CrossRef] 4. 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[CrossRef] 25. Sun, Z. Cable tension sensor based on magneto-elastic e ect. In Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, 12–17 October 2008. 26. Cho, S.; Yim, J.; Shin, S.W.; Jung, H.-J.; Yun, C.-B.; Wang, M.L. Comparative Field Study of Cable Tension Measurement for a Cable-Stayed Bridge. J. Bridg. Eng. 2013, 18, 748–757. [CrossRef] Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional aliations. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute

Non-Destructive Evaluation for Sectional Loss of External Tendon of Prestressed Concrete Structures Using Total Flux Leakage

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Abstract

applied sciences Article Non-Destructive Evaluation for Sectional Loss of External Tendon of Prestressed Concrete Structures Using Total Flux Leakage Imjong Kwahk, Kwang-Yeun Park, Ji-Young Choi, Hungjoo Kwon and Changbin Joh * Department of Infrastructure Safety Research, Korea Institute of Civil Engineering and Building Technology, 283, Goyangdae-Ro, Goyang-Si, Gyeonggi-Do 10223, Korea; kwakim@kict.re.kr (I.K.); kypark@kict.re.kr (K.-Y.P.); legion@kict.re.kr (J.-Y.C.); kwonhj3@kict.re.kr (H.K.) * Correspondence: cjoh@kict.re.kr; Tel.: +82-31-910-0332 Received: 22 September 2020; Accepted: 19 October 2020; Published: 22 October 2020 Abstract: A non-destructive evaluation method is proposed to identify the sectional loss of the external tendon of prestressed concrete structures by detecting the change of the magnetic flux in the external tendon exposed to a magnetic field. The method uses a solenoid-shaped device with two coils: a primary coil for producing magnetic field and secondary coil for damage detection, wrapping the external tendon. A current applied to the primary coil in the device causes the magnetic field. Then, the change in the magnetic flux by the damage in the external tendon is detected by the variation of the voltage in the secondary coil in the device as the device moves along the tendon. An alternating current is applied to the primary coil to minimize the e ect of the moving speed of the device. As a result, the damaged area can be detected with a low-level energy current. In addition, a wrapping solenoid-shaped device that is easy to disassemble and assemble was developed for in situ inspection. The measured signal from the secondary coil has a sinusoidal form with the same frequency as the applied current to the primary coil, and the peak curve of the measured signal provides enough information to detect the damage. It is shown that the proposed method can quantitatively identify one or multiple damaged-tendon locations as well as damages of at least 2 cm. Keywords: total flux leakage; non-destructive evaluation(NDE); Prestressed Concrete (PSC); corrosion of the prestressing tendon; section loss of external tendon 1. Introduction The extensive application of prestressed concrete (PSC) in structures can be credited to its structural and economic eciency. In the PSC structure, the tendon plays a critical role to introduce prestress. The tendon is anchored to the concrete member at its ends and is inserted in a duct generally made of HDPE (High Density PolyEthylene) duct filled with grout to protect it from external ingress. However, the corrosion of the prestressing tendon accelerates in corrosive environments as the tension force becomes higher [1]. There is a long list of structures that su ered severe degradation or even collapse because of the rupture or sectional loss of the corroded tendons’ strands [2,3]. Following the risk of such corrosion-induced damages, Germany and Japan implemented large-scale investigations on their PSC bridge inventories, which made it possible to detect numerous damages, from minor damage like early corrosion to severe damage like tendon failure [4,5]. The common causes of damage in the external tendon of PSC structures are known to be the low quality of grouting, the formation of air voids in the duct, and the chemical reaction of deicing chemical and chloride ion [6,7]. For example, corrosion of the tendons near their anchorage and cracks in the HPDE duct occurred at the Mid-Bay Bridge, Florida, USA, in 2000. One external tendon Appl. Sci. 2020, 10, 7398; doi:10.3390/app10217398 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 7398 2 of 12 failed completely, another one experienced partial damage, a tendon su ered severe corrosion near its anchorage, and huge quantities of air voids were found in the ducts at mid-span and around their anchorages [8]. In 2007, two tendons among the 480 tendons with grouted post-tensioned strands of Varina Enon Bridge, Virginia, USA, were replaced because of the formation of voids at their high ends which compromised the corrosion protection of the tendons [9]. In 2016, an external tendon of Jeongneungcheon Bridge, Seoul, Korea, broke due to corrosion and the investigation could attribute it to the poor quality of the grouting [10–12]. Later in 2019, corrosion literally exploded a 1000-ft cable on Wando River Bridge, South Carolina, USA, and sent scraps of grout and plastic as far as 30 m. The corrosion was caused by water seeping through the concrete deck [13]. From these examples, the poor quality of the grouting in the PSC structure appears to be one major initiator of the corrosion or damage of the tendon. Periodic non-destructive evaluation (NDE) of the PSC structure is thus necessary for proper maintenance, and repair shall be implemented when the sectional loss reaches a definite level. Accordingly, the FHWA guideline(FHWA-HRT-13-027) states that the tendon must be replaced when the sectional loss exceeds 5% [14]. This study pays attention to the non-destructive method to detect the change of the magnetic flux induced by the delivered magnetic field at the sectional loss area. Typical NDE methods delivering the magnetic field to the tendon are RMF (Remnant Magnetic Field), MFL (Magnetic Flux Leakage), and IMF (Induced Magnetic Field). These methods have shown the potential to evaluate the corrosion in the tendon section [15,16]. The disadvantage of the MFL method is that the Hall sensor measuring the leakage of the magnetic field is sensitive to the distance to the damage in the tendon. In other words, a weak signal from the Hall sensor cannot tell if the damage exists or if the distance to the intact tendon from the Hall sensor is far. According to the research using the MFL method on the external tendon, the existence of the sectional loss was well identified, but the di erence between the estimated amount of sectional loss and the actual amount of the sectional loss was bigger as the amount of sectional loss increased [17]. In another study for improving the MFL method, a method to measure the residual flux leakage induced by a permanent magnet was sensitive to the magnetization of the tendon [18]. Another method proposed to measure the variation of the total magnetic field flux through the yoke rather than measuring the magnetic field leakage is MMF (Main Magnetic Flux). Since the MMF method can quantify the section loss of the tendon, it can be utilized in combination with the MFL method [19]. Although the MMF method basically estimates the relative sectional loss, a method to figure out the absolute sectional loss by measuring the maximum and minimum of the magnetic flux change after delivering a strong bi-polar magnetic field to the tendon was proposed [20]. Another study proposed to quantify the sectional loss by comparing the slope of the B-H loop with the reference slope [21]. However, there was a diculty in distinguishing the slope change resulting from the sectional loss and the tensile stress in the tendon. The IMF method that is conceptually similar to the MMF method has shown a capability of detecting the damage location but there remains some doubt about the quantification of the damage [22]. In addition, another method called spontaneous MFL was suggested to estimate the sectional loss by measuring the magnetic flux delivered by the Earth’s magnetic field instead of an artificial magnetic field to the tendon [23,24]. However, the leaked magnetic flux was so small that an extremely sensitive magnetic sensor had to be used to measure it and the method also required separating the measured signal from the noise and the external magnetic field source. For the external tendon of the PSC structure, a heavy magnetizing system using a yoke for NDE is not suitable practically. It is also dicult to move the magnetizing system along the length of the tendon with a constant speed. Accordingly, this research adopts a simple solenoid to generate the magnetic field instead of the heavy yoke. In this framework, when the DC (direct current) is delivered to the solenoid, the induced voltage of the secondary coil related to the sectional change can be influenced by the moving speed of the device. Therefore, the AC (alternating current) is delivered to the primary coil to reduce the e ect of the moving speed of the device and generate larger induced Appl. Sci. 2020, 10, 7398 3 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  3  of  13  Appl. Sci. 2020, 10, x FOR PEER REVIEW  3  of  13  voltage in the secondary coil so that the flux leakage can be measured easily. The proposed method is voltage in the secondary coil so that the flux leakage can be measured easily. The proposed method  voltage in the secondary coil so that the flux leakage can be measured easily. The proposed method  expected to identify the sectional damage of the external tendon e ectively by increasing the sensitivity is  expected  to  identify  the  sectional  damage  of  the  external  tendon  effectively  by  increasing  the  is  expected  to  identify  the  sectional  damage  of  the  external  tendon  effectively  by  increasing  the  of the secondary coil. sensitivity of the secondary coil.  sensitivity of the secondary coil.  This paper proposes a novel damage-detecting method for an external tendon of PSC structures This paper proposes a novel damage‐detecting method for an external tendon of PSC structures  This paper proposes a novel damage‐detecting method for an external tendon of PSC structures  using a solenoid-shaped device. The principle of detecting sectional loss using a magnetic field is using a solenoid‐shaped device. The principle of detecting sectional loss using a magnetic field is  using a solenoid‐shaped device. The principle of detecting sectional loss using a magnetic field is  explained in Section 2, and the experimental demonstration of the method is presented in Section 3. explained in Section 2, and the experimental demonstration of the method is presented in Section 3.  explained in Section 2, and the experimental demonstration of the method is presented in Section 3.  The discussion of the experimental results and the conclusion of the research are drawn in Sections 4 The discussion of the experimental results and the conclusion of the research are drawn in Sections 4  The discussion of the experimental results and the conclusion of the research are drawn in Sections 4  and 5. and 5.  and 5.  2. TFL Method 2. TFL Method  2. TFL Method  The proposed TFL (Total Flux Leakage) method employs a solenoid similar to the EM The  proposed  TFL  (Total  Flux  Leakage)  method  employs  a  solenoid  similar  to  the  EM  The  proposed  TFL  (Total  Flux  Leakage)  method  employs  a  solenoid  similar  to  the  EM  (electromagnetic) sensor with a primary and secondary coil in order to estimate the sectional loss in (electromagnetic) sensor with a primary and secondary coil in order to estimate the sectional loss in  (electromagnetic) sensor with a primary and secondary coil in order to estimate the sectional loss in  the external tendon. The EM sensor was introduced to measure the residual stress in the tendon for the external tendon. The EM sensor was introduced to measure the residual stress in the tendon for  the external tendon. The EM sensor was introduced to measure the residual stress in the tendon for  NDE. The EM sensor consists of the primary coil to generate a magnetic field on the external tendon NDE. The EM sensor consists of the primary coil to generate a magnetic field on the external tendon  NDE. The EM sensor consists of the primary coil to generate a magnetic field on the external tendon  and the secondary coil installed at the center to detect the generated magnetic field. The governing and the secondary coil installed at the center to detect the generated magnetic field. The governing  and the secondary coil installed at the center to detect the generated magnetic field. The governing  equation of the EM sensor is well established [25,26]. Once a current is passed through the primary equation of the EM sensor is well established [25,26]. Once a current is passed through the primary  equation of the EM sensor is well established [25,26]. Once a current is passed through the primary  coil installed at the surface of HDPE duct of the external tendon, a magnetic field is generated inside coil installed at the surface of HDPE duct of the external tendon, a magnetic field is generated inside  coil installed at the surface of HDPE duct of the external tendon, a magnetic field is generated inside  and outside of the duct as shown in Figure 1. and outside of the duct as shown in Figure 1.  and outside of the duct as shown in Figure 1.  Figure 1. Magnetic flux distribution around electromagnetic solenoid.  Figure 1. Magnetic flux distribution around electromagnetic solenoid. Figure 1. Magnetic flux distribution around electromagnetic solenoid.  If a ferromagnetic material like the tendon is placed inside the duct along the longitudinal direction If  a  ferromagnetic  material  like  the  tendon  is  placed  inside  the  duct  along  the  longitudinal  If  a  ferromagnetic  material  like  the  tendon  is  placed  inside  the  duct  along  the  longitudinal  direc of thetion solenoid  of the so aslenoid shown as in shown Figur in e Figure 2, and 2, if and the if tendon  the tend is on intact,  is intthe act, magnetic the magne flux tic fldeveloped ux developed by  direction of the solenoid as shown in Figure 2, and if the tendon is intact, the magnetic flux developed  the current in the primary coil will be distributed along the longitudinal direction of the tendon. by the current in the primary coil will be distributed along the longitudinal direction of the tendon.  by the current in the primary coil will be distributed along the longitudinal direction of the tendon.  From From th thee perspect perspective ive of of ma magnetic gnetic ma material, terial, th thee gr grout out f fill illing ing the the ex external ternal ten tendon don ha hass the the sa same me re relative lative  From the perspective of magnetic material, the grout filling the external tendon has the same relative  permeability with the air ( = 1) and has thus no e ect on the magnetic flux developed by the current permeability with the air (μr = 1) and has thus no effect on the magnetic flux developed by the current  permeability with the air (μr = 1) and has thus no effect on the magnetic flux developed by the current  in in th thee prim primary ary coil. coil.  in the primary coil.  Figure 2. Magnetic flux of solenoid installed on surface of tendon of the prestressed concrete (PSC)  Figure 2. Magnetic flux of solenoid installed on surface of tendon of the prestressed concrete (PSC)  Figure 2. Magnetic flux of solenoid installed on surface of tendon of the prestressed concrete structure.  structure.  (PSC) structure. If, additionally, a secondary coil is installed at the center of the solenoid as shown in Figure 3a,  If, additionally, a secondary coil is installed at the center of the solenoid as shown in Figure 3a, If, additionally, a secondary coil is installed at the center of the solenoid as shown in Figure 3a,  any change in the magnetic flux can be detected by the change in the induced voltage in the secondary  any any chan change ge in in th thee ma magneti gneticc flux flux ca can n be be de detected tected by by the the change change in in the the induce induced d voltage voltage in in the the seconda secondary ry  coil. Unlike the undamaged tendon case (Figure 3a), when the tendon suffers partial damage like a  coil. Unlike the undamaged tendon case (Figure 3a), when the tendon su ers partial damage like a coil. Unlike the undamaged tendon case (Figure 3a), when the tendon suffers partial damage like a  sectional loss due to the rupture of some strands, a part of the magnetic flux around the damaged  sectional sectional loss loss due dueto tothe  ther uptur ruptur e e of of some  some strands,  strands a, part a paof rt the of the magnetic  magnet flux ic fl ar ux ound  around the damaged the damaged area  area is absorbed by the neighboring and undamaged strands and the remaining part of the magnetic  area is absorbed by the neighboring and undamaged strands and the remaining part of the magnetic  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 4 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  4  of  13  is absorbed by the neighboring and undamaged strands and the remaining part of the magnetic flux is flux is leaked (Figure 3b). In such a case, the secondary coil around the damaged area detects the  leaked (Figure 3b). In such a case, the secondary coil around the damaged area detects the remaining remaining magnetic flux that has not been leaked.  magnetic flux that has not been leaked. (a)  (b)  Figure 3. Change in magnetic flux distribution of solenoid according to eventual sectional loss of Figure 3. Change in magnetic flux distribution of solenoid according to eventual sectional loss of  external tendon: (a) undamaged tendon; (b) damaged tendon. external tendon: (a) undamaged tendon; (b) damaged tendon.  The electromotive force of the secondary coil induced by the current in the primary coil of the The electromotive force of the secondary coil induced by the current in the primary coil of the  solenoid is expressed in Equation (1). The induced electromotive force, V , is simply the product of ind solenoid is expressed in Equation (1). The induced electromotive force, 𝑉 , is simply the product of  dF the number N of turns in the secondary coil and , the first time derivative of the magnetic flux. 2nd dt the number 𝑁   of turns in the secondary coil and  , the first time derivative of the magnetic flux.  Note that V acts in the direction opposite the change of the magnetic flux. The magnetic flux F is ind Note that 𝑉   acts in the direction opposite the change of the magnetic flux. The magnetic flux 𝛷   is  represented as the integration of the magnetic flux density, B, over the total internal cross-sectional represented as the integration of the magnetic flux density, 𝐵 , over the total internal cross‐sectional  area, A, of the solenoid. ! ! dF d area, 𝐴 , of the solenoid.  V (t) = N = N BdA (1) ind 2nd 2nd dt dt 𝑑𝛷 𝑑 ⃗ ⃗ 𝑉 𝑡 𝑁 𝑁 𝐵 ∙𝑑 𝐴   (1) where the total internal cross-sectional area of the solenoid A = A + A + A + A ; A is tendon air duct concrete air 𝑑𝑡 𝑑𝑡 the cross-sectional area of air in the cross-section of the solenoid; A is the cross-sectional area of the duct where  the  total  internal  cross‐sectional  area  of  the  solenoid 𝐴𝐴 𝐴 𝐴 𝐴 ;  HDPE duct in the cross-section of the solenoid; A is the cross-sectional area of concrete in the concrete 𝐴   is the cross‐sectional area of air in the cross‐section of the solenoid; 𝐴   is the cross‐sectional  cross-section of the solenoid; and, A is the cross-sectional area of the tendon in the cross-section of tendon area of the HDPE duct in the cross‐section of the solenoid; 𝐴   is the cross‐sectional area of  the solenoid. concrete in the cross‐section of the solenoid; and, 𝐴   is the cross‐sectional area of the tendon in  When a time-variant AC flows in the primary coil of the solenoid, the magnetic field changes the cross‐section of the solenoid.  together and results in the change of the magnetic flux around the solenoid. The magnitude of When a time‐variant AC flows in the primary coil of the solenoid, the magnetic field changes  the induced electromagnetic field is a function of A = A + (A + A + A ) = A + A . concrete tendon air duct together and results in the change of the magnetic flux around the solenoid. The magnitude of the  Since A , A and A in A can be assumed as constants A , the induced electromotive force a air duct concrete induced  electromagnetic  field  is  a  function  of 𝐴𝐴 𝐴 𝐴 𝐴 𝐴 𝐴 .  function of A = A . Compared to the permeability  of the ferromagnetic tendon, the permeability tendon Since 𝐴 , 𝐴   and 𝐴   in 𝐴   can be assumed as constants 𝐴 , the induced electromotive  of the air, concr ete, and HDPE duct is very small and practically identical to the permeability in vacuum, force a function of 𝐴 𝐴 . Compared to the permeability 𝜇   of the ferromagnetic tendon, the  . Considering that all the parameters at the exception of A are controllable or constant, V in 0 ind permeability  of  the  air,  concrete,  and  HDPE  duct  is  very  small  and  practically  identical  to  the  Equation (1) can be expressed as a function of the area of the tendon, A as shown in Equation (2). permeability  in  vacuum,  𝜇 .  Considering  that  all  the  parameters  at  the  exception  of  𝐴   are  2 3 Z Z Z ! ! ! ! ! ! 6 7 controllable or constant, 𝑉   ind Equation (1) can be expressed as a function d  of the area of the tendon,  6 7 6 7 V (t) = N 6 HdA + BdA 7  N BdA (2) ind 2nd 0   2nd 4 0 5 𝐴   as shown in Equation (2).  dt dt A A A 𝑑 𝑑 where H is magnetic field intensity. ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ 𝑉 𝑡 𝑁 𝜇 𝐻 ∙𝑑 𝐴 𝐵 ∙𝑑 𝐴 ≅𝑁 𝐵 ∙𝑑 𝐴   (2) 𝑑𝑡 𝑑𝑡 where 𝐻   is magnetic field intensity.  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 5 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  5  of  13  Appl. Appl. Appl. Appl. Appl. Appl.   Sci.  Sci.  Sci.  Sci.  Sci. Sci.   2020  2020  2020  2020  2020 2020 ,, , 10 , 10 , 10 , 10 10 ,10 , , x, x, x , x FOR  x FOR x FOR  FOR  FOR FOR   P P P EER PEER  PEER PEER EER EER   RE  RE  RE  RE  RE RE VVVV IV IE V IEIEIW EIW EW EW W W      555 5 5 of 5 of of of of  of 13 13 13 13 13 13      Equation (2) indicates that the measured variation of the induced voltage in the second coil by  Equation (2) indicates that the measured variation of the induced voltage in the second coil by moving the solenoid throughout the length of the external tendon gives a means to detect the change  moving the solenoid throughout the length of the external tendon gives a means to detect the change Equation Equation Equation Equation Equation Equation  (2 (2 (2 (2 (2 )(2 ) ) )indi ) indi  )indi  indi  indi indi cat cat cat cat cat cat eeesesese s sth sth th th th th aaaatta ta tthe t the  tthe  the  the the  mea  mea  mea  mea  mea mea sssured sured sured sured ured ured  va  va  va  va va va riat riat riat riat riat riat ion ion ion ion ion ion  of of of of of of  the  the  the  the  the the  ind  ind  ind  ind  ind ind uuuuced uced uced ced ced ced  vo  vo  vo  vo  vo vo lltltlatlatltaagtg ag agegege e ein ein in in in in  the  the  the  the  the the  second  second  second  second  second second  co co co co co co ilililil il il by  by  by  by  by by       of the sectional area of the tendon.  of the moving moving sectional  the  the sar osolenoid ea lenoid of  the thro  thro tendon. uugghout hout the  the len  lenggthth of of the  the ex external ternal tendon  tendon gives  gives a a mea  meanns sto to detect  detect the  the change  change   moving moving moving moving  the the   the the  ss o sosolenoid olenoid lenoid lenoid  thro thro   thro thro uuugugghout ghout hout hout  the the   the the  len len   len len gggth gth th th  of of  of of  the the   the the  ex ex  ex ex ternal ternal ternal ternal  tendon tendon   tendon tendon  gives gives   gives gives  aa   a amea mea   mea mea nnnsns s to sto  to to  detect detect   detect detect  the the   the the  change change   change change     of of of of of of  th th th th th th eee e esecti  esecti  secti  secti  secti secti oooona ona ona na na na ll l lar lar lar ar ar ar ea ea ea ea ea ea  of of of of of of  the  the  the  the  the the  tendon.  tendon.  tendon.  tendon.  tendon. tendon.       3. Experiment  3. Experiment 3.3. Ex Expe peririme mentnt   3. 3.3. 3.  Ex Ex   Ex Ex pe pe pe pe riririri me me me me nt nt nt nt     Recalling that the tendon is made up of a bundle of strands and each strand is made up of wires,  Recalling that the tendon is made up of a bundle of strands and each strand is made up of wires, Rec Rec Rec Rec Rec Rec aaaallaling laling lling lling lling ling  tha  tha  tha  tha  tha tha tt t tthe t the  tthe  the  the the  tend  tend  tend  tend  tend tend on on on on on on  is is is is is is ma  ma  ma  ma  ma ma de de de de de de  up  up  up  up  up up  of of of of of of  a a a a   abundle  abundle  bundle  bundle  bundle bundle  of of of of of of  strands  strands  strands  strands  strands strands  and  and  and  and  and and  ea ea ea ea ea ea ccchchchch h str h str  str  str  str str aaaand nd and and nd nd  is is is is is is ma  ma  ma  ma  ma ma de de de de de de  up  up  up  up  up up  of of of of of of  wires,  wires,  wires,  wires,  wires, wires,       the tendon considered in this study is made of fifteen 7‐wire strands. The sectional loss of the external  the tendon considered in this study is made of fifteen 7-wire strands. The sectional loss of the external the the the the the the  tendon  tendon  tendon  tendon  tendon tendon  co co co co co co nsider nsider nsider nsider nsider nsider ed ed ed ed ed ed  in in in in in in  th th th th th th is isis isis is study  study  study  study  study study  is is is is is is ma  ma  ma  ma  ma ma ddddedede e eof of e of of of of  fi fi fi fift fift fiftftft een een fteen een een een  7 7 7 7‐ ‐7wire ‐7wire ‐‐wire wire ‐wire wire  st st st st st ra st ra ra ra ra ra nds. nds. nds. nds. nds. nds.  The  The  The  The  The The  secti  secti  secti  secti  secti secti oooonal onal onal nal nal nal  los  los  los  los  los los sss s of s of s of of of of  the  the  the  the  the the  external  external  external  external  external external       prestressing tendon is simulated as shown in Figure 4 by the number of snapped strands and the  prestressing tendon is simulated as shown in Figure 4 by the number of snapped strands and the prest prest prest prest prest prest rrressing ressing ressing ressing essing essing  tendon  tendon   tendon tendon  tendon tendon   is is is is is is  si si si si si mu si mu mu mu mu mu la la la la la tla tetetted etd ed ed d das as  as as as as  sho  sho   sho sho  sho sho w w w w w n w nnn n n in in in in in in   Fi Fi Fi Fi Fi gu Fi gu gu gu gu gu rrrererer e e 4e 4 44   4 by 4 by by by  by by   th th th th th th eee e e number e number  number number  number number   of of of of of of  snap  snap   snap snap  snap snap ped ped ped ped ped ped   st st st st st ra st ra ra ra ra ra nds nds nds nds nds nds  and  and   and and  and and   the  the  the the  the the       length of the damage in the tendon. For the convenience of the experiment, the HDPE duct of the  length of the damage in the tendon. For the convenience of the experiment, the HDPE duct of the leng lengthth of of the  the damage  damage in in th the etendon  tendon. .For  For the  the convenience  convenience of of th the eex experiment, periment, the  the HDPE  HDPE du  ductc tof of the  the   leng leng leng leng th th th th  of of of of  the  the  the the  damage  damage  damage damage  in in in in  th th th th ee e etendon  tendon  tendon tendon ..  .For . For  For For  the  the  the the  convenience  convenience  convenience convenience  of of of of  th th th th ee e eex ex ex ex periment, periment, periment, periment,  the  the  the the  HDPE  HDPE  HDPE HDPE  du  du  du du cctctc t of t of of of  the  the  the the     external tendon is replaced with a transparent acrylic duct having similar relative permeability to  external tendon is replaced with a transparent acrylic duct having similar relative permeability to extern extern extern extern extern extern al al al al al al  tend  tend  tend tend  tend tend on on on on on on   is is is is is is  re re re re re re pla pla pla pla pla pla ccced ced ced ced ed ed   with  with  with with  with with   a a aa   a tr a tr tr tr tr an tr an an an an an sp sp sp sp sp sp aren aren aren aren aren aren tt t tt a at aa ccacarylic crylic crylic crylic rylic rylic   duc  duc  duc duc  duc duc tt t tt ha ha t ha ha  ha ha vvvviviv ng ing ing ing ing ng   si si si si si mil si mil mil mil mil mil aaaarrara r r re r re re re re re lat lat lat lat lat lat iive ive ive ive ive ve   perme  perme  perme perme  perme perme aaaabbababili bili bili ili ili ili ty ty ty ty ty ty   to to to to to to       HDPE. The tendon is placed inside the acrylic duct, and the length of the damage near the center of  HDPE. The tendon is placed inside the acrylic duct, and the length of the damage near the center of the HDPE. HDPE. HDPE. HDPE. HDPE. HDPE.  The  The  The  The  The The  te te te te te ndon te ndon ndon ndon ndon ndon  is is is is is is pla  pla  pla  pla  pla pla ccced ced ced ced ed ed  insi  insi  insi  insi  insi insi de de de de de de  th th th th th th eee e eacryli  eacryli  acryli  acryli  acryli acryli ccc c cduc  cduc  duc  duc  duc duc tt,t,t t, ,and t ,and  ,and  and  and and  the  the  the  the  the the  len  len  len  len  len len ggggth gth gth th th th  of of of of of of  the  the  the  the  the the  da  da  da  da  da da mage mage mage mage mage mage  near  near  near  near  near near  the  the  the  the  the the  cen  cen  cen  cen  cen cen tter ter tter er ter er  of of of of of of       the tendon is changed from 0 to 10 cm. The number of snapped strands is increased from one to three  tendon is changed from 0 to 10 cm. The number of snapped strands is increased from one to three to the the the the the the  tendon  tendon  tendon  tendon  tendon tendon  is is is is is is changed  changed  changed  changed  changed changed  from  from  from  from  from from  0 0 0 0   0to 0to to to to to  10 10 10 10 10 10  cm.  cm.  cm.  cm.  cm. cm.  Th  Th  Th  Th  Th Th eee e enumber  number e number  number  number number  of of of of of of  sna  sna  sna  sna  sna sna pped pped pped pped pped pped  st st st st st rands st rands rands rands rands rands  is is is is is is incre  incre  incre  incre  incre incre aaaassasaesesesd ed ed ed d from d from  from  from  from from  one  one  one  one  one one  to to to to to to  three  three  three  three  three three       to observe the secondary coil output according to the amount of damage. Table 1 describes the cases  observe to to to to to to  observe  observe  observe  observe  observe observe the secondary   th th th th th th eee e esecond  esecond  second  second  second second coil ar ar ar ar ar ar yyyy y co y co output  co co co co iilili li loutput i loutput  loutput  output  output output accor   acc  acc  acc  acc  acc acc o ding ooording ording ording rding rding rding to  to to to to to the to  th th th th th th eee e amount  eam  eam  am  am  am am oun oun oun oun oun oun tt t tof t of tof of of of of  dama  dama  dama  dama damage.  dama dama ggggegege.e.e .e .Tab  Tab . Tab . Tab  Tab Tab Tllable elelel el e1 e1 1 1   1descr  1descr  descr  descr  descr 1descr describes iibes ibes ibes ibes ibes bes  th th th th th th eee e ecases  ecases  cases  cases the  cases cases  cases      setup for the 3‐strand damage case.  setup setup setup setup setup setup  fo fo fo fo fo fo rrr r th r th r th th th th eee e e3 e3 3 3‐ ‐3str ‐3str ‐‐str str ‐str str aaaand nd and and nd nd  dam  dam  dam  dam  dam dam aaaage ge age age ge ge  case.  case.  case.  case.  case. case.       setup for the 3-strand damage case. 1, 1,1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3 3 3  3  3da 3da da  da da da m m m m m m aaage age age age ge ge dddd d str d str  str  str  str str aaan ananandndnddsdsdssss 1, 2, 3 damaged strands 15 15 15 15 15 15  str  str  str  str  str str aaand and and and nd nd ssssss 15 strands 0, 0,0, 0, 0,  0, 2, 2, 2, 2, 2,  2, 4, 4, 4, 4, 4,  4, 6, 6, 6, 6, 6,  6, 8, 8, 8, 8, 8,  8, 10 10 10 10 10 10  cm  cm  cm  cm  cm cm 163 163 163 163 163 163  cm  cm  cm  cm  cm cm 0, 2, 4, 6, 8, 10 cm 163 cm 330 330 330 330 330 330  cm  cm  cm  cm  cm cm 330 cm        Figure Figure Figure Figure Figure Figure   4. 4. 4. 4. 4.  4. Cons  Cons  Cons  Cons Cons Cons idered idered idered idered idered idered   sect  sect  sect  sect sect sect io io io io io nal io nal nal nal nal nal   d d d dad ad amage amage amage amage mage mage   ca ca ca ca ca ses ca ses ses ses ses ses   of of of of of of  external  external  external  external external external   PSC  PSC  PSC  PSC PSC PSC   tendon  tendon  tendon  tendon tendon tendon   (1 (1 (1 (1 (1 5(1 55‐5‐5strand ‐5strand ‐strand ‐strand ‐strand strand   tendon,  tendon,  tendon,  tendon, tendon, tendon,   7 7 7 ‐7‐7wire ‐7wire ‐wire ‐wire ‐wire wire       strand). strand). strand). strand). strand). strand).       Figure  4.  Considered  sectional  damage  cases  of  external  PSC  tendon  (15‐strand  tendon,  7‐wire  Figure 4. Considered sectional damage cases of external PSC tendon (15-strand tendon, 7-wire strand). strand).  Table Table Table Table Table Table  1. 1. 1. 1. 1.  1. Damage  Damage  Damage  Damage  Damage Damage  case  case  case  case  case case sss s for s for s for  for  for for  3 3 3 ‐3‐ 3strand ‐3strand ‐strand ‐strand ‐strand strand  d d d da d ad amage amage amage amage mage mage  of of of of of of 15 15 15 15 15 15‐‐strand ‐strand ‐strand ‐strand ‐strand strand  te te te te te ndon. te ndon. ndon. ndon. ndon. ndon.       Table 1. Damage cases for 3-strand damage of 15-strand tendon. Length Length Length Length Length Length  of of of of of of  S S S S eSeSeectio ctio ectio ectio ctio ctio nnnn n n Loss  Loss  Loss  Loss  Loss Loss  (c (c (c (c (c m) (c m) m) m) m) m)       Table 1. Damage cases for 3‐strand damage of 15‐strand tendon.  Length of Section Loss (cm) 0000  0 0    2222  2 2    4444  4 4    6666  6 6    8888  8 8    10 10 10 10 10 10       0 2 4 6 8 10 Length of Section Loss (cm)  0  2  4  6  8  10                                              The The The The The The  dev  dev   dev dev  dev dev iice ice ice ice ice ce  d d  dd ededeliver eliver eliver eliver liver liver ing ing ing ing ing ing  the  the   the the  the the  ma  ma   ma ma  ma ma gnet gnet gnet gnet gnet gnet ic icic ic ic ic fi fi  fifi eld field field eld eld eld  to to  to to to to  the  the   the the  the the  ex ex  ex ex ex ex ter ter ter ter ter ter nnnnal nal nal al al al tendon  tendon   tendon tendon  tendon tendon  and  and   and and  and and  de  de   de de  de de tec tec tec tec tec tec ttin tin ttin in tin in gggg g gthe  the   the the  the the  va  va   va va  va va riation riation riation riation riation riation  of of  of of of of          The device delivering the magnetic field to the external tendon  and detecting the variation of the   the the the the the the  magnetic  magnetic   magnetic magnetic  magnetic magnetic  flux  flux   flux flux  flux flux  is is  is is is is ma  ma   ma ma  ma ma ddddedede e eby  eby   by by  by by  the  the   the the  the the  assem  assem   assem assem  assem assem bbbblage blage blage lage lage lage  of of  of of of of  two  two   two two  two two  37 37  37 37 37 37‐‐cm ‐cm ‐‐cm cm ‐cm cm  lon  lon   lon lon  lon lon gggg g gplastic  plastic   plastic plastic  plastic plastic  half  half   half half  half half‐‐cy‐cy‐‐cy cy‐cy cy linders linders linders linders linders linders  as as  as as as as  sho  sho   sho sho  sho sho w w w w w n w nnn n nin in  in in in in       Fig Fig Fig Fig Fig Fig uuuure ure ure re re re  5a 5a  5a 5a 5a 5a .. . .Th  .Th  . Th Th  Th Th eee e esecond  esecond   second second  second second ary ary ary ary ary ary  co co  co co co co iilili li liwi  lwi  l wi wi  wi wi tth th tthh t h h18 18  18 18 18 18  turns  turns   turns turns  turns turns  is is  is is is is ins  ins   ins ins  ins ins ttatattaalle tlle alle alle lle lle dddd d dat at  at at at at the  the   the the  the the  ce ce  ce ce ce ce nnnntntner ter tter er ter er  of of  of of of of  the  the   the the  the the  fr fr  fr fr fr am fr am am am am am eee e efor  efor   for for  for for  de  de   de de  de de tectin tectin tectin tectin tectin tectin gggg g gthe  the   the the  the the       magnetic flux is made by the assemblage of two 37-cm long plastic half-cylinders as shown in Figure 5a. The device delivering the magnetic field to the external tendon and detecting the variation of  ma ma ma ma ma ma gnet gnet gnet gnet gnet gnet ic icic ic ic ic fl fl  flfl u flufluuxuxuxx  xsignal  xsignal   signal signal  signal signal  and  and  and  and  and and  the  the  the  the  the the  prim  prim   prim prim  prim prim aaaarrarayryryry y yco co  co co co co iilili li liwit  lwit  l wit wit  wit wit hhhh h h40 40 40  40 40 40 0000  0turns  0turns  turns  turns  turns turns  over  over   over over  over over  a a a a   alengt  alengt   lengt lengt  lengt lengt hhhh h hof of  of of of of  30 30 30 30 30 30  cm  cm   cm cm  cm cm  is is  is is is is pl pl  pl pl pl pl aaaaccacaecececd ed ed ed d dove  ove   ove ove  ove ove rrr r rthe  rthe   the the  the the       The secondary coil with 18 turns is installed at the center of the frame for detecting the magnetic flux the magnetic secondary secondary secondary secondary secondary secondary  flux   co co co co co co ilililil il  to ilto  to is to to to  gen   gen  gen ma  gen  gen gen eeed rate erate erate erate erate rate  by  the  the  the  the  the  the the   ma  ma  ma  ma  ma ma gnetic assem gnetic gnetic gnetic gnetic gnetic  fifi b fi field. fi eld. filage eld. eld. eld. eld.  The  The  The   The  The of The   sta  sta  two sta  sta  sta sta bbbbili bili bili ili ili 37 ili ttytyttyyt y‐ of y of cm of of of of  th th th th th th eelon e e ema  ma e ma  ma  ma ma ggn gn gn gn gn plastic gn eeeteteiteitcticitci ci field c field c field  field  field field  half   alo alo   alo  alo alo  alo ‐ncy nnngngngg linders g th g th th th th th eee e elon  lon e lon  lon  lon lon gg ggigas itgitiu tiu tituu t dudusho ddina dina dina ina ina ina lw l l l l l n  in  signal and the primary coil with 400 turns over a length of 30 cm is placed over the secondary coil to axi axi axi axi axi axi sss s s mea s mea  mea  mea mea mea sssured sured sured sured ured ured   at at at at at at  the  the  the  the the the   ce ce ce ce ce ce nnnntntnetetteretrere r r of r of of of of of   the  the  the  the the the   cro  cro  cro  cro cro cro sssssssss s s secti s secti  secti  secti secti secti oooonononn n n is is is isis is  verified  verified  verified  verified verified verified   in in in in in in   Figure  Figure  Figure  Figure Figure Figure   5b 5b 5b 5b 5b 5b   by  by  by  by by by   co co co co co co mpa mpa mpa mpa mpa mpa rrririrsisrisiosiososonononn n n wi  wi  wi  wi wi wi tth th tthh t h h the  the  the  the the the       Figure 5a. The secondary coil with 18 turns is installed at the center of the frame for detecting the  generate the magnetic field. The stability of the magnetic field along the longitudinal axis measured theore theore theore theore theore theore tic tic tic tic tic tic aaaalla la l lva va l va va va va llu lu lu lules ues ues es es es .. . . Howev . Howev . Howev  Howev Howev Howev eeer, er, er, er, r, r, the  the  the  the the the   devic  devic  devic  devic devic devic eee e e in e in in in in in   Figur  Figur  Figur  Figur Figur Figur eee e e 5e 5 5 5  5 5is is is isis is  un  un  un  un un un su su su su su su itabl itabl itabl itabl itabl itabl eee e e for e for  for  for for for   in in in in in in   situ  situ  situ  situ situ situ   in in in in in in spect spect spect spect spect spect iion ion ion ion ion on   tha  tha  tha  tha tha tha tt t tt needs  needs t needs  needs needs needs       magnetic flux signal and the primary coil with 400 turns over a length of 30 cm is placed over the  at the center of the cross section is verified in Figure 5b by comparison with the theoretical values. freq freq freq freq freq freq uen uen uen uen uen uen tt t tas t as tas as as as se se se se se se m m m m m m bbbbly bly bly ly ly ly  an an an  an an an dddd d d d d d d idid sassembly isassembly isassembly isassembly isassembly sassembly  due  due  due  due  due due  to to to to to to  the  the  the  the  the the  la la la la la rge la rge rge rge rge rge  nu  nu  nu  nu  nu nu mbe mbe mbe mbe mbe mbe rrr r of r of r of of of of  numerous  numerous  numerous  numerous  numerous numerous  turns.  turns.  turns.  turns.  turns. turns.       secondary coil to generate the magnetic field. The stability of the magnetic field along the longitudinal  However, the device in Figure 5 is unsuitable for in situ inspection that needs frequent assembly and axis  measured  at  the  center  of  the  cross  section  is  verified  in  Figure  5b  by  comparison  with  the  disassembly due to the large number of numerous turns. theoretical values. However, the device in Figure 5 is unsuitable for in situ inspection that needs  frequent assembly and disassembly due to the large number of numerous turns.  Appl. Appl. Appl. Appl. Appl. Appl.   Sci.  Sci.  Sci.  Sci.  Sci. Sci.   2020  2020  2020  2020  2020 2020 ,, , 10 , 10 , 10 , 10 10 ,10 , , x; , x; , x; , x;  x; doi: x; doi:  doi:  doi:  doi: doi:   FOR  FOR  FOR  FOR  FOR FOR   PEE  PEE  PEE  PEE  PEE PEE RRRR R REVIEW R REVIEW  REVIEW  REVIEW  REVIEW REVIEW        www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ www.mdpi.com/ jjournal/applsci ournal/applsci jjournal/applsci journal/applsci ournal/applsci journal/applsci        Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  6  of  13  Appl. Sci. 2020, 10, 7398 6 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  6  of  13  (a)  (b)  Figure 5. Fabrication and installation of solenoid‐shape device: (a) installed device; (b) distribution of  theoretical and measured longitudinal magnetic fields at center of device.  Accordingly, our research team developed a mountable frame where the primary and secondary  can be easily connected by plugging as shown in Figure 6a to avoid the repeated winding of the coils  in situ. This so‐called wrapping solenoid‐shaped device also exhibited stable magnetic field through  the comparison of the measured and theoretical values (Figure 6b). Nevertheless, the original setup  (a)  (b)  of Figure 5 is employed here for evaluating the feasibility of the TFL method in detecting the sectional  loss Figure in  the 5.  ext Fabrication ernal  ten and don. installation   Research of solenoid-shape about  the  improved device: (a ) de installed vice  shown device; (in b) distribution Figure  6  will of   be  Figure 5. Fabrication and installation of solenoid‐shape device: (a) installed device; (b) distribution of  implemen theoretical ted in and the measur  future ed to longitudinal  investigat magnetic e its accu fields racy at and center  perform of device. ance. In addition, the operation of  theoretical and measured longitudinal magnetic fields at center of device.  the solenoid‐shape device with a battery will be tested in the future to verify the stableness of the  Accordingly, our research team developed a mountable frame where the primary and secondary device’s results with a less stable power supply for in situ inspection.  Accordingly, our research team developed a mountable frame where the primary and secondary  can be easily connected by plugging as shown in Figure 6a to avoid the repeated winding of the coils can be Although  easily connected  an autom aby tic plugging  movement  as  shown of the devic  in Figur e caen 6a re duce to avoid  the  the unce rertain peatteyd from  windin  theg  iof nc th ons e ta coils nt   in situ. This so-called wrapping solenoid-shaped device also exhibited stable magnetic field through moving speed of the device, the automation of the device movement is not considered in this study.  in situ. This so‐called wrapping solenoid‐shaped device also exhibited stable magnetic field through  the comparison of the measured and theoretical values (Figure 6b). Nevertheless, the original setup of In the gener  comp al,arison  near  th ofe the  ancho  measured rage where  and  th is eoret damaica gel sva are lue often s (Fig fo urund, e 6b) .tendons  Nevert he are les close s, thely or space iginadl  setu withp   Figure 5 is employed here for evaluating the feasibility of the TFL method in detecting the sectional loss each other, and an available space that the device can use is limited. The automation equipment also  of Figure 5 is employed here for evaluating the feasibility of the TFL method in detecting the sectional  in the external tendon. Research about the improved device shown in Figure 6 will be implemented in incre loss ain ses  the  the  weigh externta of l  ten thed device on.  Resea  thatr is ch anothe   aboutr  limi the tat improved ion for fie  de ld vice appl ica shown tion.  Therefore in  Figure,  th6e  will device   be   the future to investigate its accuracy and performance. In addition, the operation of the solenoid-shape was designed to remove inessential function in order to fit into the limited space and weight. But the  implemented in the future to investigate its accuracy and performance. In addition, the operation of  device with a battery will be tested in the future to verify the stableness of the device’s results with a au the tom  soaleno tionid eq‐shape uipme de ntvi can ce  be with  in staal ba led tte witho ry willu tbe di fftes ictul edty in if  necessa the futury re.  to verify the stableness of the  less stable power supply for in situ inspection. device’s results with a less stable power supply for in situ inspection.  Although an automatic movement of the device can reduce the uncertainty from the inconstant  moving speed of the device, the automation of the device movement is not considered in this study.  In general, near the anchorage where is damages are often found, tendons are closely spaced with  each other, and an available space that the device can use is limited. The automation equipment also  increases the weight of the device that is another limitation for field application. Therefore, the device  was designed to remove inessential function in order to fit into the limited space and weight. But the  automation equipment can be installed without difficulty if necessary.  (a)  (b)  Figure 6. Mountable wrapping solenoid-shaped device for in situ inspection: (a) mounted wrapping Figure 6. Mountable wrapping solenoid‐shaped device for in situ inspection: (a) mounted wrapping  device; (b) distribution of theoretical and measured longitudinal magnetic fields at the center of device; (b) distribution of theoretical and measured longitudinal magnetic fields at the center of the  the device. device.  Although an automatic movement of the device can reduce the uncertainty from the inconstant Figure 7 shows the external tendon specimen with the installed device. During the inspection,  moving speed of the device, the automation of the device movement is not considered in this study. the distance travelled by the device along the axis of the tendon was measured in real time with  In general, near the anchorage where is damages are often found, tendons are closely spaced with respect  to  the  reference  point  using  a  laser  distance  meter.  An  AC  with  frequency  of  10  Hz  and  (a)  each other, and an available space that the device can use is limited. The automation equipment also (b)  amplitude  of  ±0.6  A  was  delivered  continuously  to  the  primary  coil  of  the  device  using  the  NI  increases the weight of the device that is another limitation for field application. Therefore, the device Figure 6. Mountable wrapping solenoid‐shaped device for in situ inspection: (a) mounted wrapping  was designed to remove inessential function in order to fit into the limited space and weight. But the Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  device; (b) distribution of theoretical and measured longitudinal magnetic fields at the center of the  automation equipment can be installed without diculty if necessary. device.  Figure 7 shows the external tendon specimen with the installed device. During the inspection, the distance travelled by the device along the axis of the tendon was measured in real time with respect Figure 7 shows the external tendon specimen with the installed device. During the inspection,  to the reference point using a laser distance meter. An AC with frequency of 10 Hz and amplitude of the distance travelled by the device along the axis of the tendon was measured in real time with  0.6 A was delivered continuously to the primary coil of the device using the NI (National Instrument) respect  to  the  reference  point  using  a  laser  distance  meter.  An  AC  with  frequency  of  10  Hz  and  equipment as shown in Figure 8. The signal was generated by the LabVIEW program on a laptop and amplitude  of  ±0.6  A  was  delivered  continuously  to  the  primary  coil  of  the  device  using  the  NI  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  7  of  13  Appl. Sci. 2020, 10, x FOR PEER REVIEW  7  of  13  Appl. Sci. 2020, 10, 7398 7 of 12 (National Instrument) equipment as shown in Figure 8. The signal was generated by the LabVIEW  (National Instrument) equipment as shown in Figure 8. The signal was generated by the LabVIEW  program on a laptop and the NI PXI‐5412 AWG (arbitrary waveform generator). The generated signal  program on a laptop and the NI PXI‐5412 AWG (arbitrary waveform generator). The generated signal  the NI PXI-5412 AWG (arbitrary waveform generator). The generated signal was magnified by the NF was magnified by the NF BP bipolar DC power supply. The output voltage from the secondary coil  was magnified by the NF BP bipolar DC power supply. The output voltage from the secondary coil  BP bipolar DC power supply. The output voltage from the secondary coil of the device was measured of  the  device  was  measured  by  the  NI  PXI‐4462  DAQ  (data  acquisition)  system.  The  device  was  of  the  device  was  measured  by  the  NI  PXI‐4462  DAQ  (data  acquisition)  system.  The  device  was  by the NI PXI-4462 DAQ (data acquisition) system. The device was moved manually and slowly along moved manually and slowly along the length of the tendon by the operator without a specific power  moved manually and slowly along the length of the tendon by the operator without a specific power  the length of the tendon by the operator without a specific power unit. unit.  unit.  Figure 7. View of external PSC tendon installed for measurement test of sectional loss by the Total  Figure 7. View of external PSC tendon installed for measurement test of sectional loss by the Total  Figure 7. View of external PSC tendon installed for measurement test of sectional loss by the Total Flux Flux Leakage (TFL) method.  Flux Leakage (TFL) method.  Leakage (TFL) method. Figure 8. Equipment used to deliver AC to the primary coil of the device and measure the output of  Figure 8. Equipment used to deliver AC to the primary coil of the device and measure the output of  Figure 8. Equipment used to deliver AC to the primary coil of the device and measure the output of the secondary coil.  the secondary coil.  the secondary coil. 4. Results 4. Results  4. Results  Figur Figure e 99 shows shows aa typical typicalpattern  patternof ofthe  theoutput  output signal  signal measur  measured ed in in the the secondary  secondarcoil y coin il in the th case e cas ofe  Figure 9 shows a typical pattern of the output signal measured in the secondary coil in the case  damaged external tendon. As the AC is delivered to the primary coil, the output signal of the secondary of damaged external tendon. As the AC is delivered to the primary coil, the output signal of the  of damaged external tendon. As the AC is delivered to the primary coil, the output signal of the  coil secondary has a form  coil similar has a form to the siinput milar  signal to thedeliver  input ed sigto nal the delivere primary d to coil the with  prima the same ry coil fr equency with the and same is  secondary coil has a form similar to the input signal delivered to the primary coil with the same  symmetric with reference to the horizontal axis. In the case where the DC is delivered to the primary frequency  and  is  symmetric  with  reference  to  the  horizontal  axis.  In  the  case  where  the  DC  is  frequency  and  is  symmetric  with  reference  to  the  horizontal  axis.  In  the  case  where  the  DC  is  coil delive instead red  toof  the an  prima AC and ry the coilmoving   insteadspeed   of  an of AC the  and device   the is mov irregular ing  speed , undesir   of  th ed e  device disturbance   is  irre would gular,  delivered  to  the  primary  coil  instead  of  an  AC  and  the  moving  speed  of  the  device  is  irregular,  occur in the induced voltage on the secondary coil. In this research, a suciently stable magnetic flux undesired disturbance would occur in the induced voltage on the secondary coil. In this research, a  undesired disturbance would occur in the induced voltage on the secondary coil. In this research, a  was suffic generated iently staby blemeans  magnet ofic AC  flux that was inverted  generated the dir by ection  mean ofs the of AC power  thasour t inver ce as ted much  the di asre its ctifroequency n of the  sufficiently stable magnetic flux was generated by means of AC that inverted the direction of the  even though the operator was moving the device without specific speed control. Since the device power source as much as its frequency even though the operator was moving the device without  power source as much as its frequency even though the operator was moving the device without  was specif moved ic speeslowly d contro from l. Sin the ce lef the t end device to the was right  moved end sl of owl the y external from thetendon,  left enda to very  the lar righ get number end of the of  specific speed control. Since the device was moved slowly from the left end to the right end of the  positive and negative peaks of the secondary coil output signal was recorded according to the distance external tendon, a very large number of positive and negative peaks of the secondary coil output  external tendon, a very large number of positive and negative peaks of the secondary coil output  travelled signal waduring s recorded the acco totalrding time of to the motion.  distance The tr measur avelled ed durin secondary g the tot coil al tim output e of motion. takes thus  The the  measured form of  signal was recorded according to the distance travelled during the total time of motion. The measured  the compressed sinusoidal wave along the horizontal axis shown in Figure 9. Only the positive peaks secondary coil output takes thus the form of the compressed sinusoidal wave along the horizontal  secondary coil output takes thus the form of the compressed sinusoidal wave along the horizontal  wer axise  shown picked  fr inom   Fig the uremeasur   9.  Only ed  the signal   positive for the  pea convenience ks  were  pi ofck the ed analysis. from  the  measured  signal  for  the  axis  shown  in  Figure  9.  Only  the  positive  peaks  were  picked  from  the  measured  signal  for  the  convenience of the analysis.  convenience of the analysis.  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  8  of  13  Appl. Sci. 2020, 10, 7398 8 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  8  of  13  Figure 9. Induced voltage and its peaks in the secondary coil.  The peak curves of the voltage induced in the secondary coil in accordance with the change in  length of one‐strand damage of the external tendon are presented in Figure 10. The lowest point in  the curves corresponds the center of the damage length. The centerline of the damage length is shifted  slightly to the right due to the fixed left end of the damage as shown in Figure 4. It is observed that  this phenomenon is reflected on the measured peak curves.  In the same manner, the peak curves of the voltage induced in the secondary coil in accordance  with the change in length of two‐ and three‐strand‐damage of the external tendon are presented in  Figure 11 and Figure 12 Figure , respectively  9. Induced.  In vo ad ltage di tion, and its the peaks  second  in the ary se vo condary ltage  red coil.u  ction ratios of the one  Figure 9. Induced voltage and its peaks in the secondary coil. to three‐strands damage with respect to the damage length are presented in Figure 13. The damage  The peak curves of the voltage induced in the secondary coil in accordance with the change in The peak curves of the voltage induced in the secondary coil in accordance with the change in  detectable level in Figure 13 was visually suggested as the peak curve for the 1‐strand damage with  length of one-strand damage of the external tendon are presented in Figure 10. The lowest point in the length of one‐strand damage of the external tendon are presented in Figure 10. The lowest point in  0 cm damage length in Figure 10 is difficult to be distinguished and can be hidden if the signal to  curves corresponds the center of the damage length. The centerline of the damage length is shifted the curves corresponds the center of the damage length. The centerline of the damage length is shifted  noise ratio decreases. The decrement ratio in Figure 13 is the voltage change due to the damage to the  slightly to the right due to the fixed left end of the damage as shown in Figure 4. It is observed that this slightly to the right due to the fixed left end of the damage as shown in Figure 4. It is observed that  voltage value just before the decrement.  phenomenon is reflected on the measured peak curves. this phenomenon is reflected on the measured peak curves.  In the same manner, the peak curves of the voltage induced in the secondary coil in accordance  with the change in length of two‐ and three‐strand‐damage of the external tendon are presented in  Figure 11 and Figure 12, respectively. In addition, the secondary voltage reduction ratios of the one  to three‐strands damage with respect to the damage length are presented in Figure 13. The damage  detectable level in Figure 13 was visually suggested as the peak curve for the 1‐strand damage with  0 cm damage length in Figure 10 is difficult to be distinguished and can be hidden if the signal to  noise ratio decreases. The decrement ratio in Figure 13 is the voltage change due to the damage to the  voltage value just before the decrement.  Figure 10. Secondary coil output peak induced by 1‐strand damage according to damage length.  Figure 10. Secondary coil output peak induced by 1-strand damage according to damage length. In the same manner, the peak curves of the voltage induced in the secondary coil in accordance with the change in length of two- and three-strand-damage of the external tendon are presented in Figures 11 and 12, respectively. In addition, the secondary voltage reduction ratios of the one to three-strands damage with respect to the damage length are presented in Figure 13. The damage Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  detectable level in Figure 13 was visually suggested as the peak curve for the 1-strand damage with 0 cm damage length in Figure 10 is dicult to be distinguished and can be hidden if the signal to noise ratio decreases. The decrement ratio in Figure 13 is the voltage change due to the damage to the voltage value just before the decrement. Figure 10. Secondary coil output peak induced by 1‐strand damage according to damage length.  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x FOR PEER REVIEW  9  of  13  Appl. Sci. 2020, 10, x FOR PEER REVIEW  9  of  13  Appl. Sci. 2020, 10, 7398 9 of 12 Figure 11. Secondary coil output peak induced by 2‐strand damage according to damage length.  Figure Figure 11. 11. Secondary  Secondary coil coil output  output peak  peak induced  induceby d by 2-strand  2‐strand damage  damage accor  accordi dingnto g to damage  damage length.  length.  Figure 12. Secondary coil output peak induced by 3‐strand damage according to damage length.  Figure 12. Secondary coil output peak induced by 3-strand damage according to damage length. Figure 12. Secondary coil output peak induced by 3‐strand damage according to damage length.  The location of the sectional loss can be estimated simply and intuitively. Moreover, the change in the damage length is also well reflected in Figures 10–12. The reduction of the magnitude of the voltage induced in the secondary coil caused by the magnetic flux leaked from the damaged section that is not permeating the secondary coil shown in Figure 3 can be clearly distinguished in the graphs. In addition, it appears that deeper and longer damage introduces stronger magnetic flux leakage as well as increases the magnitude of the decrement of the voltage induced in the secondary coil as shown in Figure 13. The ratio of decrement in induced voltage of the secondary coil for all cases except for the 1-strand damage with a length of 0 cm case were above the designated damage detectable level. However, as such the case is neglectable as the external tendon is always in tension and the damage length would not be zero when cut. Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 10 of 12 Appl. Sci. 2020, 10, x FOR PEER REVIEW  10  of  13  Figure 13. Rate of decrement in induced voltage of secondary coil.  Figure 13. Rate of decrement in induced voltage of secondary coil. The The maximum location of peak the sec curve tiona of l lo the ss voltage can be estimated induced in simpl the secondary y and intuicoil tivemeasur ly. More ed over, by moving  the change the  device throughout the length of the external tendon can provide information about the damage location in the damage length is also well reflected in Figures 10–12. The reduction of the magnitude of the  by voltage identif ind ying ucethe d inv the ariation  secondary of the coil curve.  cauThe sed by reduction  the magnet of the ic fl voltage ux leake induced d from in the the  dam secondary aged section coil  by the rupture of 1 or more strands or damage length of 2 cm or longer can be intuitively identified. that is not permeating the secondary coil shown in Figure 3 can be clearly distinguished in the graphs.  Hence, In additthis ion, validates it appearsthat  thatthe  deeper method  and measuring longer damag theechange  introduce of the s strong totaler flux  macan gnetbe ic fl used ux leto akdetect age as  damage in the external tendon. This result satisfies the FHWA guideline of tendon replacement at 5% well as increases the magnitude of the decrement of the voltage induced in the secondary coil as  sectional shown inloss  Figu asre well  13. as The the ra pr tio oject’s  of decre detection ment in accuracy  induced of volt figuring age of out the 1 out second of 15 ary tendons.  coil for all cases  The external tendon of the PSC structure has a limited profile and size inside the structure section except  for  the  1‐strand  damage  with  a  length  of  0  cm  case  were  above  the  designated  damage  unlike detectable other lev cases el. However with a complicated , as such the pr case ofile is and  neglectable size. Since asthe  thedevice  external wraps  tendon the is entir  always e section  in tensi of the on  external tendon, the secondary coil can measure almost any change of the magnetic flux induced by and the damage length would not be zero when cut.  the change The ma ofximum the sectional  peak curve area of inside  the voltage the tendon.  induce The d in pr the oposed  second method ary coil has mea shown suredthe  by potent moving ial the to  identify and quantify the sectional loss in the external tendon by using a solenoid-shaped device fed device  throughout  the  length  of  the  external  tendon  can  provide  information  about  the  damage  with location AC  and by  ipr dent esenting ifying ath simple e  variat shape ion  of and  the light   cur weight ve.  The even   reduc though tion  the of  the uncertainty   voltage  of induce the pr doposed   in  the  method increases if a strong exterior magnetic source is close to the device or the power supply is secondary  coil  by  the  rupture  of  1  or  more  strands  or  damage  length  of  2  cm  or  longer  can  be  unstable. intuitivelyThe  identi prfie oposed d. Hence TFL, th method is valida o te ers s tha thet the advantage  method of mea a low-power suring the change source of which  the to makes tal flux it  convenient for actual NDE conditions in terms of portability and long-term usage. can be used to detect damage in the external tendon. This result satisfies the FHWA guideline of  tendon replacement at 5% sectional loss as well as the project’s detection accuracy of figuring out 1  5. Conclusions out of 15 tendons.  The  external  tendon  of  the  PSC  structure  has  a  limited  profile  and  size  inside  the  structure  A new TFL method is proposed to estimate the location and amount of damage in the external section  unlike  other  cases  with  a  complicated  profile  and  size.  Since  the  device  wraps  the  entire  tendon of PSC structures. This TFL method uses AC-delivering solenoid with a secondary coil inserted section of the external tendon, the secondary coil can measure almost any change of the magnetic flux  in an external primary coil enclosing the tendon. The primary coil is fed with a current in the device induced by the change of the sectional area inside the tendon. The proposed method has shown the  to cause the magnetic field, and the change in the magnetic flux at the damaged area of the external potential to identify and quantify the sectional loss in the external tendon by using a solenoid‐shaped  tendon is detected and quantified by the variation of the voltage in the secondary coil. Unlike the MMF device fed with AC and presenting a simple shape and light weight even though the uncertainty of  (Main Magnetic Flux) method, which usually uses a heavy magnetic yoke, the proposed TFL method the proposed method increases if a strong exterior magnetic source is close to the device or the power  uses a light solenoid-shaped device. In addition, the proposed TFL method can provide a stable output supply is unstable. The proposed TFL method offers the advantage of a low‐power source which  due to the AC input signal and can be applied to any cable system with minor modification. makes it convenient for actual NDE conditions in terms of portability and long‐term usage.  The following conclusions can be derived from a series of experiments considering various degrees and lengths of damage in the tendon. 5. Conclusions  (1) Sucient output signal could be acquired from the secondary coil for identifying the damage on the A new TFL method is proposed to estimate the location and amount of damage in the external  external tendon even when using the device with light and simple structure and fed with low-level tendon  of  PSC  structures.  This  TFL  method  uses  AC‐delivering  solenoid  with  a  secondary  coil  inserted in an external primary coil enclosing the tendon. The primary coil is fed with a current in the  Appl. Sci. 2020, 10, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/applsci  Appl. Sci. 2020, 10, 7398 11 of 12 AC. The proposed method was proved to satisfy the simplicity, portability, and low-energy power requirements for detecting damage in the external tendon of the PSC structure. (2) There is concern about the occurrence of undesired disturbance in the induced voltage from the secondary coil if the moving speed is not constant in the process of detecting the damage location by moving the device throughout the length of the external tendon. In this research, a suciently stable magnetic flux was generated by means of AC that inverted the direction of the power source as much as its frequency even though the operator was moving the device without specific speed control. (3) The signal induced in the secondary coil by the AC delivered to the primary coil of the device is an AC signal with the same frequency as the input signal on the primary coil and is governed only by the tendon area in the duct. The signal measured in the secondary coil reflected the change of the total flux throughout the length of the external tendon. The location of the damage could be identified by analyzing only the peaks of the induced signal measured when moving the device throughout the length of the external tendon. Intuitive detection of the rupture of 1 or more strands or damage length of 2 cm or longer could be achieved by identifying the reduction of the amplitude of the signal measured in the secondary coil. The proposed method proved its feasibility in e ectively detecting the damage by measuring the change of the total flux in the external tendon. Author Contributions: Conceptualization, I.K. and C.J.; methodology, I.K. and J.-Y.C.; software, H.K. and K.-Y.P.; validation, I.K., H.K., and C.J.; resources, J.-Y.C.; data curation, K.-Y.P.; writing—original draft preparation, I.K.; writing—review and editing, C.J.; visualization, K.-Y.P.; project administration, C.J. 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Published: Oct 22, 2020

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