Acoustic Nondestructive Testing and Measurement of Tension for Steel Reinforcing Members

Transcription

1 Acoustic Nondestructive Testing and Measurement of Tension for Stee Reinforcing Members Part 1 Theory by Michae K. McInerney PURPOSE: This Coasta and Hydrauics Engineering Technica Note (CHETN) describes theoretica work supporting the deveopment of a nondestructive evauation (NDE) technoogy that can quantitativey measure tension in structura stee reinforcing members. In arge concrete structures such as ocks and dams, the corrosion of tensioned stee components can ead to oss of tension and consequent severe probems such as cracking of the concrete or fracturing of the stee. The theory and appication address the probem of determining tension in concreteembedded pre- and post-tensioned stee reinforcement rods. BACKGROUND: Many concrete structures contain interna pre- and post-tensioned stee structura members that are subject to fracturing and corrosion. Corrosion of stee components can ead to oss of tension and consequent severe probems, such as cracking of the concrete or fracturing of the stee. The major probem with conventiona tension-measurement techniques is that they use indirect and non-quantitative methods to determine whether there has been a oss of tension. We have deveoped an acoustics-based technoogy and method for making quantitative tension measurements of an embedded, tensioned stee member. Acoustic waves are nondestructive, are capabe of traveing ong distances in engineered structures, and can thoroughy interrogate a structure s integrity. Acoustics are dua purpose: they can determine buk materia properties, such as tension; and they can detect sma defects, such as fractures. Measurements can be performed very quicky, usuay in rea time, athough postprocessing may be required. In this Technica Note, a theoretica basis for buk tension measurements and an acoustic propagation mode is described. The theory and mode are verified using simpe stee rods as test specimens. A companion Technica Note, ERDC/CHL CHETN-IX-38 (Part 2 Fied Testing), describes the fied testing of a technoogy appication that addresses the probem of determining tension in the concrete-embedded pre- and post-tensioned reinforcement rods used in arge Civi Works structures. BASIC ULTRASONIC THEORY: A materia s utrasonic properties are fundamenta to the understanding of wave behavior. There is much iterature describing the theory and appications of utrasonic waves. Some common references are Aud 1990, Ensminger 1973, Fiipczynski et a. 1966, and Krautkramer and Krautkramer Utrasonic waves can propagate as both ongitudina and shear waves. The two different propagation modes are dispayed in Figure 1. For ongitudina waves, the direction of partice motion is the same as the direction of propagation. For shear waves, the direction of partice motion is perpendicuar to the direction of propagation. Longitudina waves can exist in a media; shear waves exist ony in soids. In stee, shear waves move about haf the speed of ongitudina waves. The shear wave is 4 10 times more attenuated than the ongitudina wave. Approved for pubic reease; distribution is unimited.

2 Report Documentation Page Form Approved OMB No Pubic reporting burden for the coection of information is estimated to average 1 hour per response, incuding the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and competing and reviewing the coection of information. Send comments regarding this burden estimate or any other aspect of this coection of information, incuding suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arington VA Respondents shoud be aware that notwithstanding any other provision of aw, no person sha be subject to a penaty for faiing to compy with a coection of information if it does not dispay a currenty vaid OMB contro number. 1. REPORT DATE SEP REPORT TYPE 3. DATES COVERED to TITLE AND SUBTITLE Acoustic Nondestructive Testing and Measurement of Tension for Stee Reinforcing Members: Part 1-Theory 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) U.S. Army Engineer Research and Deveopment Center,,Vicksburg,,MS 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for pubic reease; distribution unimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 11. SPONSOR/MONITOR S REPORT NUMBER(S) 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT uncassified b. ABSTRACT uncassified c. THIS PAGE uncassified Same as Report (SAR) 18. NUMBER OF PAGES 10 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

3 Figure 1. Iustration of acoustic wave propagation ( TENSION-MEASUREMENT THEORY: Derivation and deveopment of the acoustic tensionmeasurement technique are described in detai in Carye et a. 2004a and Carye et a. 2004b. Given equations describing inear eastic deformation and utrasonic wave veocity, an equation describing how to determine tension inside a homogeneous materia using pure utrasonic measurements can be derived. The eastic deformation quantities incude Hooke s Law, the buk moduus, Young s moduus, the shear moduus, and Poisson s ratio. Genera inear eastic deformation is described using Hooke's Law, which reates stress to strain: σ = c ε k where σ is the stress in the i, j direction, ε k is the strain in the k, direction, and c k is the easticity tensor (which has 36 independent stiffness constants). For the isotropic case, Equation 1 reduces to a much simper form of Hooke's Law that invoves ony two independent constants: aa k σ = λδ ε + 2µ ε where δ is the Kronecker deta, and λ and μ are known as Lame s constants. Lame s constants can be used to cacuate severa other important materia properties, such as the buk moduus: K = λ + 2µ / 3 = σ / 3ε = σ / 3ε = σ / ε xx xx yy yy zz 3 zz (1) (2) (3) Young's moduus: ( 3λ + 2 µ ) / ( λ + µ ) σ / ε zz zz E = µ = (4) The shear moduus: And Poisson's ratio: σ zx = 2µ ε zx ( λ µ ) υ = λ / 2 + (5) (6) 2

4 A fundamenta property of utrasonic waves is that their propagation veocity, v, is a function of the stiffness constants, c, and the density of the materia, ρ, in which they are traveing: v = v = s ( c / ρ) 1/2 11 ( c / ρ) 1/2 44 (7) (8) where v is the ongitudina wave veocity, v s is the shear wave veocity, c 11 is the stiffness constant governing osciatory motion aong the direction of wave propagation, and c 44 is the stiffness constant governing osciatory motion transverse to the direction of wave propagation. The definitions for buk moduus, Young s moduus, shear moduus and Poisson s ratio given by Equations 3 6 are substituted into Equation 2 aong with the ongitudina and shear wave veocities (given by Equations 7 and 8). The seven fundamenta equations shown in Figure 2 were used to derive Equation 9, which reates tension to the veocities of the ongitudina and shear waves. Hooke s Law σ = λ δ ε aa + 2 μ ε Young s Moduus E = μ ( 3 λ + 2 μ ) / (λ + μ ) = σ zz / ε zz Buk Moduus K = λ + 2 μ / 3 = σ xx / ( 3 ε xx ) = σ yy / ( 3 ε yy ) = σ zz / ( 3 ε zz ) Shear Moduus Poisson s Ratio σ zx = 2 μ ε zx v = λ / 2 (λ + μ ) Longitudina Wave Speed Shear Wave Speed V = (c 11 / ρ ) 1/2 V s = (c 44 / ρ ) 1/2 Figure 2. Fundamenta aws and equations governing materia properties. R = C 2 2 ( v C vs ) 2 2 ( v v ) σ (9) Tension (σ ) is dependent on acoustic ongitudina ( v ) and shear ( v s ) wave veocities (Equation 9), and materia properties R and C (Equation 10): s C = c 11 c 44 (10) where c 11 and c 44 are two of the materia s thirty-six stiffness constants. 3

5 R and C are constants, and do not vary with changes in tension. Thus one needs ony to determine, either through measurement or modeing, the veocities of the ongitudina and shear waves. ULTRASONIC SIMULATION: A modeing and ray-tracing software package, Imagine3D 1, was used to mode a 19 in. pain stee rod measuring 1.25 in. diameter. This seemingy simpe object actuay invoves a great dea of compexity due to beam divergence and mode conversion 2. The experimenta setup and the acoustic wave propagation simuation of the rod are shown in Figure 3. The transducer is mounted on the eft end of the rod. The acoustic energy traves down the rod, refects off the right end of the rod, and traves back to the transducer. The utrasonic beam from the transducer diverges (i.e., spreads) as it traves. The beam divergence is represented in the ower pot of Figure 3, where the bue rays emitting from the transducer have a cear conica shape. As the beam interacts with the ongitudina surface of the rod it refects and mode-converts in accordance with Sne's Law 3. The refected utrasonic rays are shown in green. Because of the number of rays invoved, the refected beam seems to fi the rod, but in reaity each ray is traveing at an ange to the surface of the rod. Mode conversion is aso taking pace when the surface refection occurs, and athough the software simuation is producing rays that correspond to shear waves, they are not seen in the chosen simuation view. Figure 3. Utrasonic instrument showing received signa from transducer mounted on eft end of rod (top); simuation of signa propagation within the rod (bottom) 1 Microsoft Windows version discontinued by Impuse, Inc., after this modeing project was competed. 2 Conversion from a ongitudina to a shear wave and vice versa. 3 According to Sne s Law, the wave aso refracts into the adjacent medium. When the adjacent medium is water, for exampe, 12.17% of the wave energy refracts and 87.83% refects back into the stee. However, when the adjacent medium is air, ony a vanishingy sma portion of the energy (0.0036%) refracts, with % of it refecting back into the stee. In our simpe mode, the adjacent medium is air, so we negect the minuscue oss of energy due to refraction of the wave at the ongitudina surface. 4

6 Figure 4 shows the resuts of the beam divergence and mode conversion taking pace inside the test rod when the simuator sums a of the received echoes. The rod is 19 in. ong so, as expected, a strong echo appears at 19 in. from the transducer This is produced by the ongitudina wave traveing straight down the rod, refecting off the far end of the rod, and echoing back to the transducer. Figure 4. Simuation of echoes in sampe rod (top) and actua screen shot from utrasonic instrument dispay (bottom). Note that other echoes appear after 19 in. These are caused by mode conversion of the origina ongitudina utrasonic beam into shear waves, as the diverging beam interacts with the ongitudina surface of the rod. Since shear waves trave in stee about haf as fast as ongitudina waves, when they arrive back at the transducer they wi ag behind the faster ongitudina. The agreement between the simuation and the resut obtained from the measurement is very good. In addition to pacing a the echoes at the proper distance, the modeing software aso did a good job of cacuating the expected ampitude for the echoes. The ony significant disagreement between the resut obtained from the measurement and simuation appears in the echo at 20 in. The measurement recorded a stronger echo than predicted by the simuation. A the other echoes, from about in., agree we between measurement and simuation. TENSION MEASUREMENTS USING ULTRASOUND: The key to computing tension in a component is to obtain the necessary utrasonic measurements with a high degree of accuracy. There are two ways to do this: (1) modeing software can be used to compute the vaue of the shear veocity from two echoes and the measured veocity of the ongitudina wave, and (2) the ongitudina and shear wave veocities can be measured directy. 5

7 The tension-measurement mode consists of an equation together with an accurate utrasonic echo mode. Our equation cacuates a materia s buk stress, σ, in terms of utrasonic quantities. This equation permits us to measure the tension in an embedded stee rod, such as a tainter gate anchor rod, by measuring two utrasonic properties and dividing the cacuated stress vaue by the circuar area (i.e., cross section) of the rod. The physica changes produced by tension in a rod can be determined using the isotropic version of Hooke's Law, σ E = zz ε zz (11) Stress, σ, is force (tension) divided by area, whie strain, ε, is change in ength divided by the origina ength. The foowing equation shows the reationship for the ength change that resuts from a given tension in a rod: where F = appied force L = origina ength of the rod A = circuar area of the rod E = Young s moduus. L = FL AE The change in ength for various appied oads to a 19 x 1.25 in. (diameter) stee rod is cacuated using Equation 4 and presented in Tabe 1. Tabe 1. Load-induced ength change in a 19 x 1.25 in. (diameter) stee rod. Load (b) Length Change (in. 100 pounds inch 500 pounds inch 1000 pounds inch 5000 pounds inch pounds inch From the information in Tabe 1, the modeing software can be used to predict the exact position of the utrasonic echoes that wi resut when the ength of the exampe rod is increased by these engths. Thus, the effect of tension on utrasound echoes in the stee bar can be observed. This accompishes two things: (1) it permits us to see the magnitude change of any given tension state and (2) it permits us to see the effect of tension on any particuar echo. The first point is important because it aows us to determine the precision with which the utrasonic veocity measurements wi need to be conducted. The echoes shown in Figure 5 are produced in the modeing software by specifying the wave modes that can exist in the rod. The first echo, at 19 in., is the resut of a ongitudina wave propagating down the ength of the rod and another ongitudina wave refecting off the far end and returning to the transducer. This can be seen ceary in the top and bottom pots of Figure 5; the bue rays are the ongitudina wave propagating down the ength of the rod and the green rays correspond to this ongitudina wave, refecting off the far end and returning to the transducer. (12) 6

8 There are no shear waves in the first echo because the shear waves are created by mode conversion of the refecting ongitudina wave, and they trave at about the haf the veocity of the ongitudina wave. Figure 5. Mode of 19 x 1.25 in. (diameter) stee rod showing how first echo (green rays) and second echo (magenta) form (top); mode showing how the first echo (green rays) and third echo (gray rays) form (bottom). The second, third, and higher echoes consist of a mix of ongitudina waves and shear waves. The top pot of Figure 5 aso shows how the second echo is created. A ongitudina wave (bue) propagates down the rod, a refected ongitudina wave (green) refects off the far end, and a refected shear wave (dark purpe) is created when the refected ongitudina wave mode-converts at the ongitudina surface of the rod. Another refected ongitudina wave (magenta) is created when this shear wave mode-converts on the opposite surface of the rod. This ast ongitudina wave returns to the transducer to create echo 2. This event can be expressed with the foowing equation for the time of echo 2, t e2. where v and x, x, x, and x x x x x t e = + (13) v v vs v v s are the ongitudina and the shear wave veocities, respectivey, and are the path engths for their respective rays in the rod. The bottom pot of Figure 5 shows how the third echo is created. A ongitudina wave (bue) propagates down the rod and a refected ongitudina wave (green) refects off the far end. A refected shear wave (dark purpe) is created when the refected ongitudina wave mode-converts at the ongitudina surface of the rod, and another refected shear wave (magenta) is created when the first refected shear wave refects off the opposite side of the rod. Finay, a refected ongitudina wave (gray) is created when this second shear wave mode-converts on the opposite side of the rod. This ast ongitudina wave returns to the transducer to create echo 3. This can be expressed with the foowing equation for the time of echo 3, t e3. x x x x x t e = (14) v v vs vs v where v and v s are the ongitudina and the shear wave veocity, respectivey, and x 2, x3, x6, and x7 are the path engths for their respective rays in the rod. Note that x 2, x3, and x4 are common to echoes 2 and 3. 7

9 An equation for the veocity of the shear wave as a function of the veocity of the ongitudina wave and the echoes in the rod is obtained by subtracting Equation 13 from Equation 14. v ( v x ) ( v 6 s = (15) ( te3 te2) + x5 x7 ) The modeing software can compute the vaues of the four path engths x 4, x5, x6, and x7. The software can aso provide the times of the two required echoes, t e2 and t e3. These computed quantities, in combination with the measured vaue of the ongitudina wave veocity, v, are a that is needed to obtain the ast desired quantity, v s. To obtain the tension in the rod one uses Equation 9 and the measured ongitudina veocity, v, and the computed shear veocity, v s. MEASUREMENT ISSUES: There are many possibe difficuties with utrasonicay measuring the tension of anchor rods in situ. The greatest is the attenuation of the acoustic signas, especiay that of the shear wave. Additiona wave propagation probems are refection, refraction, beam spread and couping of the signa to the rod from the transducer. Unfortunatey these difficuties are entirey due to the physics of the probem and are very difficut to overcome. The measurement wi aso be dependent on the medium surrounding the rod, e.g., air, grease, or grout. The preferred measurement method is to measure the ongitudina and shear wave veocities directy and compute the tension using the formua in Equation 1. This gives a quantitative resut. Athough modeing software can be used to compute the vaue of the shear veocity from the measured veocity of the ongitudina wave and two echoes, this is considered quantitative since the technique is dependent on the mode used. For exampe, the current mode did not take into account the media surrounding the rod. The mode woud need to be redone to incorporate the resuts of the grouted rod tests. SUMMARY: A theory and testing technique was deveoped for quantitativey determining tension in concrete-embedded structura stee members. In this work, a theoretica basis was estabished for buk tension measurements and an acoustic propagation mode was deveoped and impemented using commerciay avaiabe software. The technoogy and method of appication were awarded a U.S. patent (McInerney et a. 2009). When perfected, the benefits of this acoustic NDE tension-measurement technoogy wi incude rapid, noninvasive tension measurement of embedded stee rods in the fied ease of measurement where at east one rod end is avaiabe, even where access is difficut cost reduction by a factor of 10 compared with the present ift-off testing method faciitation of more frequent testing and improved structura evauation. FUTURE WORK: Further aboratory studies of wave propagation wi be done using the ERDC Anchor Rod Test Bed, ocated at the Engineer Research and Deveopment Center, Coasta and Hydrauics Laboratory, Vicksburg, MS. This faciity accommodates the testing of rods approximatey 60 ft ong under tension with severa different types of conduit-fier materias. 8

10 POINTS OF CONTACT: This CHETN is a product of the Acoustic Nondestructive Testing work unit of the Navigation Systems Research Program (NavSys) being conducted at the U.S. Army Engineer Research and Deveopment Center, Construction Engineering Research Laboratory, Champaign, IL. Questions about this technica note can be addressed to Mr. Michae K. McInerney at ; e-mai Michae.K.Mcinerney@usace.army.mi. For information about the NavSys Research Program, contact the Program Manager, Chares E. (Eddie) Wiggins at ; e-mai Chares.E.Wiggins@usace.army.mi. This CHETN shoud be cited as foows: REFERENCES McInerney, M.K Acoustic Nondestructive Testing and Measurement of Tension for Stee Reinforcing Members. Coasta and Hydrauics Engineering Technica Note ERDC/CHL CHETN-IX-37. Vicksburg, MS: U.S. Army Engineer Research and Deveopment Center. Aud, B.A Acoustic Fieds and Waves in Soids, Vo I & II, 2d edition. Maabar, FL: Krieger Pubishing Company. Carye, J.M., V. Hock, M. McInerney, and S. Morefied Mathematica Tension / Corrosion Prediction Modes for Tainter Gate Tendon Rods. Fina Report to the U.S. Army Corps of Engineers, Contract DACW42-03-P Champaign, IL: U.S. Army Engineer Research and Deveopment Center, Construction Engineering Research Laboratory (ERDC-CERL). Carye, J.M., V. Hock, M. McInerney, and S. Morefied Nondestructive Testing for Service Life Prediction of Reinforced Concrete Structures. Fina Report to the U.S. Army Corps of Engineers, Champaign, IL: U.S. Army Engineer Research and Deveopment Center, Construction Engineering Research Laboratory (ERDC-CERL). Ensminger, D Utrasonics. New York: Marce Dekker, Inc. Fiipczynski, L., Z. Pawowski, and J. Wehr Utrasonic Methods of Testing Materias. London: Butterworth & Co. Krautkramer, Josef, and Herbert Krautkramer Utrasonic Testing of Materias, 4th edition Springer-Verag. McInerney, Michae K., Sean W. Morefied, Vincent F. Hock, Victor H. Key, and John M. Carye. Device for Measuring Buk Stress via Insonification and Method of Use Therefor. U.S. Patent Number 7,614,303 B2, issued 10 November Wave Propagation, NDT Resource Center, Iowa State University, CommunityCoege/Utrasonics/Physics/wavepropagation.htm, verified 5 February NOTE: The contents of this technica note are not to be used for advertising, pubication, or promotiona purposes. Citation of trade names does not constitute an officia endorsement or approva of the use of such products. 9