Corrosion Detection of Steel Cables Using Time Domain. Reflectometry

Transcription

1 Corrosion Detection of Steel Cables Using Time Domain Reflectometry By Wei Liu 1, Robert G. Hunsperger, Michael J. Chajes 3, Associate Member, ASCE, Kevin J. Folliard 4, and Eric Kunz 5 ABSTRACT: Corrosion of steel cables and reinforcing steel in concrete structures is a major cause of structural deterioration. The current methods for corrosion detection suffer from several significant drawbacks. In this paper, a nondestructive evaluation technique is developed that is capable of determining the location and severity of corrosion of embedded or encased steel rebar and cables. This technique utilizes time domain reflectometry (TDR), which has been traditionally used to detect electrical discontinuities in transmission lines. By installing a sensor wire along side steel reinforcement, the reinforcement can be modeled as an asymmetric, twin-conductor transmission line. Physical defects of the reinforcement, such as abrupt pitting corrosion, general surface corrosion, and grouting voids, will change the electromagnetic properties of the line. They can be modeled analytically, and identified using TDR. TDR measurement results from several fabricated bridge cable sections with built-in defects are reported. Based on the initial results, the TDR corrosion detection method has proven to be more robust than the existing methods because it allows one to detect, locate and identify the extent of corrosion damage. KEYWORDS: corrosion detection, nondestructive evaluation, time domain reflectometry (TDR), transmission line INTRODUCTION The corrosion of steel cables and reinforcing steel in concrete represents one of the leading causes of durability problems affecting the civil infrastructure. Reinforced, prestressed, and post-tensioned concrete structures have all suffered significantly from corrosion damage, especially in aggressive environments. One of the most challenging aspects of this durability problem is the detection of corrosion of steel cables used in bridges. The National Cooperative Highway Research Program (NCHRP) has identified a concern regarding the structural 1 Grad. Res. Asst., Dept. of Electrical and Computer Engineering, Univ. of Delaware, Newark, DE Prof., Dept. of Electrical and Computer Engineering, Univ of Delaware, Newark, DE Assoc. Prof., Dept. of Civ. and Envir. Engrg., Univ of Delaware, Newark, DE Asst. Prof., Dept. of Civ. Engrg., Univ of Texas, Austin, TX Industry Representative, 6 Oak Road, Elkton, MD 191.

2 integrity of steel components used in cable-stayed bridges (NCHRP 1986). While visual inspection is an effective method for detecting corrosion in some types of structures, it cannot be used for embedded or encased steel cables, such as those used in cable-stayed bridges. A nondestructive method to determine the location and extent of corrosion-induced damage is needed. Several indirect electromagnetic nondestructive corrosion detection methods have been developed. Electromagnetic methods are based on the fact that the high-strength steel cables are very good electrical conductors. Mechanical damage to the cable will change its electrical properties. One can use resistance measurement, potential measurement (utilizing electrochemical reaction due to active corrosion) (Wietek and Kunz 1995), or magnetic inductance scanning to detect corrosion (Zahn and Bitterli 1995). To date, these methods have had varying degrees of success in detecting the presence of corrosion, but all have disadvantages, and many are uneconomical. One common drawback to these methods is that the location and nature of the corrosion is very difficult to determine. In this paper, a nondestructive evaluation technique for detecting damage in steel rebar and cables using time domain reflectometry (TDR) is described. The method being developed has the advantage over existing methods in that it can detect, locate, and identify the extent of corrosion. TDR is a well-established technique in the field of electrical engineering that has been used for many years to detect faults in transmission lines (Hewlett-Packard 1988). It involves sending an electrical pulse along the transmission line and using an oscilloscope to observe the echoes. Any discontinuity will cause a reflection. From the transit time, magnitude, and polarity of the reflection, it is possible to determine the spatial location and nature of the discontinuity. TDR has also been used in some other fields such as geotechnical engineering and mining. Typical applications of TDR include soil moisture measurements (Topp et al. 1994), water level changes (Hokett et al. 1994), and rock mass deformation (Dowding et al. 1989). There are obvious similarities between bridge cables and transmission lines. The bridge cable can be modeled as an asymmetric, twin-conductor transmission line by applying a sensor wire along with the cable (Bhatia

3 et al. 1998). Physical defects of the bridge cable, such as abrupt pitting corrosion, general surface corrosion, and voids in the grout, will change the electromagnetic properties of the line. These defects, which can be modeled as different kinds of discontinuities, can be detected by TDR. ANALYTICAL MODELS Modeling Bridge Cables Time domain reflectometry is traditionally used in the field of electrical engineering to detect discontinuities in a transmission line. A transmission line is a wave guiding system along which electromagnetic waves can travel. It typically has at least two parallel conductors. Examples are telephone lines and television cables. The key difference between transmission lines and conventional circuits is the size. A transmission line can be miles long. Therefore, it is long compared to the signal wavelength. As a result, signals cannot travel instantaneously from one end to the other, as there will be a propagation delay. For a thorough analysis of the wave propagation in a transmission line, one needs to solve Maxwell's equations with boundary conditions imposed by the physical nature of the system under investigation. It is also possible to represent a line by the distributed parameter equivalent circuit and discuss wave propagation in terms of voltage and current. A bridge cable is a good conductor embedded in a dielectric (grout). By applying a sensor wire along side the steel cable, the twin-conductor transmission line geometry is obtained (see Figure 1). However, there are still some important differences between this system and the classic transmission line. First, the two conductors have different diameters. Next, they are embedded in concrete and encased in a tube; this imposes a complicated boundary condition. However, if the dimension of the concrete grout is much larger than the dimension of the steel cable and the sensor wire, one can assume these two conductors are in a uniform concrete medium, i.e., the influence of the tube is neglected. This simplification will not appreciably affect the analysis since the electromagnetic field is concentrated between the two conductors and does not significantly extend through the grout to the tube.

4 A distributed parameter model is used to study the wave propagation in this transmission line. The distributed parameter equivalent circuit is shown in Figure. It possesses a uniformly distributed series resistance R, series inductance L, shunt capacitance C, and shunt conductance G. (R, L, C, and G are defined per unit length.) By studying this equivalent circuit, several characteristics of the transmission line can be determined. The transmission line equations can be obtained by applying Kirchhoff's voltage and current laws to the distributed equivalent circuit. They are given by v z i z = = Ri + L i t Gv + C v t (1) () in which v and i are the instantaneous values of the line voltage and current at an arbitrary point z. They are functions of time t and position z. For the sinusoidal steady-state condition, v and i are given by Ve jωt and Ie jωt respectively, where V and I are the amplitudes of the voltage and current at the point z. The radian frequency, ω, is given by ω=πf, where, f is frequency in Hz. Making these substitutions, and eliminating I, the following differential equation results z V = ( R + jω L)( G + jωc) V = γ V (3) where ( R + jωl)( G jωc ) γ = α + jβ = + (4) and γ is the propagation constant that defines the phase shift β and attenuation α per unit length. The velocity at which the voltage travels down the line can be defined in terms of β: v p = ω β (5)

5 V and I are related by I = V Z 0 (6) where Z 0 is the characteristic impedance of the line. It is given by Z 0 = R G + + jωl jωc (7) Distributed Parameters To study the electrical properties of the cable, it is desirable to obtain the distributed parameters associated with the cable. The capacitance per unit length is calculated by considering the electric field of two parallel infinitely long straight line charges of equal and opposite uniform charge densities. The equipotential surfaces are cylinders with axes parallel to the line charges. If a perfectly conducting cylinder is placed in any equipotential surface, the electric field will not be disturbed. By placing the two conductors in two equipotential surfaces, and calculating the potential difference, the capacitance per unit length of the line is obtained to be (Liu 1998) C = cosh 1 πε d a b ab (8) Since L and C are related by LC=µε (the product of permeability and permittivity), one can get inductance per unit length from the expression L = µ π cosh 1 d a b ab (9) The resistance per unit length R has two parts, R a and R b, which are the resistance of the bridge cable and sensor wire respectively. To calculate the resistance at high frequency, skin effects must be taken into account. When the operating frequency is f, the resistance of the transmission line is

6 R = R a + R b = fµ π a σ a b σ b (10) where, σ is the conductivity of the conductor. Characteristic Impedance At very high frequencies R increases as the square root of f, whereas ωl increases directly as f, and the ratio R/ωL decreases as the square root of f. It will be useful to consider the case of a single 7-wire prestressing strand (a=0.635cm), the sensor wire being used (b=0.05cm), and a typical distance between them (d=3.175cm). At f=50mhz, the ratio R/ωL is , which is negligible compared with unity; it will clearly become still more negligible at higher frequencies. This result, which is based on reasonably realistic data, shows that R+ jωl jωl in the frequency range of TDR operation. For grout with low water content, the conductance is quite small. Additionally, there is an isolating layer of plastic insulation around the sensor wire. Therefore, the conductance G can be considered to be zero, and G/ ωc will therefore be approximately zero. Under these circumstances the characteristic impedance is given to a high degree of accuracy by the simplified expression Z 0 = R G + + jωl jωc L C (11) Upon substituting for C and L the following expression for Z 0 results Z 0 = 1 π µ ε cosh 1 d a b ab (1) The characteristic impedance of the line is a function of a, b, and d. Note that b is much smaller than a and d (see Figure 1), and it remains the same value along the line. However, the radius of the steel cable, a, may be changed if corrosion occurs. A plot of characteristic impedance Z 0 versus the radius of the bridge cable a is shown in Figure 3. When b<<d,

7 dz da π µ ε a d d + a a (13) This expression has a negative value, which means that the characteristic impedance will increase for a small decrease of a as shown in Figure 3. Since radius a always decreases at a corrosion site, corrosion will cause higher characteristic impedance. This change of impedance can be detected by time domain reflectometry. It is also noticed that dz 0 /da depends on the value of d -a. When the sensor wire is close to the steel cable, d -a is small, and dz 0 /da is large. In this case, the characteristic impedance will have a greater change for the same decrease of a, and hence the TDR method will be more sensitive. Time Domain Reflectometry Time domain reflectometry can be used to detect discontinuities in a transmission line. It involves sending an electrical pulse along a transmission line and using an oscilloscope to observe the echoes returning back from the system being tested. A time domain reflectometer is usually configured as shown in Figure 4. The pulse generator generates a fast rising step wave or pulse. This wave is launched into the transmission line. A high impedance oscilloscope is connected to monitor the wave. The wave travels down the transmission line at v p, the velocity of propagation. At every point that the excitation signal crosses, the transmission line equations must be obeyed. For a line terminated by a load Z l, if Z l is different from Z 0, the transmission line equations are not satisfied unless a second wave is considered to originate at the load and propagate back up the line, i.e., a reflection is generated at this point. The ratio of reflected voltage to the incident voltage is defined as voltage reflection coefficient, Γ, and is related to Z l and Z 0 by the equation V Γ = V r i = Z Z l l Z + Z 0 0 (14)

8 The reflected wave is superimposed on the incident wave. However, they are separated in time. This time, T, is the transit time from the monitoring point to the mismatch and back again. Therefore, the distance from the monitoring point to the mismatch is calculated to be D=v p T/. Modeling different types of corrosion In order to utilize TDR to detect corrosion, the damage sites of a bridge cable need to be modeled as electrical discontinuities in a transmission line. Several physical defects are of great interest when considering the durability of bridge cables. Among them are abrupt pitting corrosion, general surface corrosion, and voids in the grout. Pitting corrosion Pitting corrosion is a serious defect characterized by severe localized damage. It greatly reduces the cross-sectional area of the steel cable, and the localized impedance should increase abruptly if pitting corrosion occurs. Note that pitting corrosion is not uniform and hence, the shape will not be circular. An equivalent radius needs to be used to calculate the localized impedance. When the length of pitting corrosion is small compared to the wavelength of the excitation signal, it can be modeled as a lump inductor in series with the line. From the discussion of TDR in the previous section, a positive reflection from the site of pitting corrosion is expected. The reflection amplitude gives indications of the severity of the damage. The location of the corrosion site is obtained from the transit time. Surface corrosion Surface corrosion tends to reduce the radius of the cable on the order of a few percent over a part of length of the line. Its length is longer than the wavelength of the excitation signal. Therefore, it is modeled as a section of transmission line with slightly increased characteristic imp edance. A small positive reflection in the TDR waveform indicates the beginning of a surface corrosion site, while a negative step denotes the end. The extent and length of the corrosion can be determined from the magnitude and duration of the reflection, respectively.

9 Voids in grout Although a void in the grout will not change the strength of the reinforcing cable, it leaves a section of the cable vulnerable to corrosion. The characteristic impedance also depends on ε, which is the dielectric constant of the system. A void in the grout will change this dielectric constant since the contents of the void, usually air and some water, have different electrical properties. Voids tend to reduce the dielectric constant and therefore increase the characteristic impedance. Also, voids will also change the velocity of propagation in the transmission line. EXPERIMENTAL APPROACH AND RESULTS A thorough theoretical analysis of the problem has been presented. The model involves representing the bridge cable as an asymmetric, twin-conductor transmission line by applying a sensor wire along with the cable. The distributed parameters of the transmission line can be calculated from the geometry and material parameters of the cable. Physical defects of the bridge cable change the electromagnetic properties of the line and are modeled as different kinds of discontinuities, which can theoretically be detected by TDR. The following focuses on an experimental study at verifying the use of TDR. Sample Fabrication For the present study, several 1-meter and 3-meter steel strand and rebar specimens with built-in defects were used to study the ability of TDR to detect pitting corrosion. The pitting corrosion was simulated by locally grooving the rebar specimens or severing several wires of a strand specimen. Preliminary testing was performed on both grouted and ungrouted specimens. The steel specimen was placed in the center of a PVC pipe with the plastic insulated monitoring wire wound around it. To increase the applicability of the laboratory testing, a typical grout used in cable-stayed bridges was used. The TDR measurements were also made on bare specimens. Without the grout, the dielectric constant changed, thus changing the velocity of propagation. On the other hand, the relative magnitude of the impedance difference did not change. As a result, it was found that damage detection for the ungrouted specimens was very similar to that of grouted specimens. Because the researchers have access to the corrosion site when measuring specimens that are not embedded in concrete, such specimens are more convenient to

10 use to study the electromagnetic properties of the simulated corrosion. As a result, only bare specimens were used to investigate several aspects related to TDR damage detection. The specific specimens used are listed in Table 1. Instrumentation TDR measurements can be made either using an oscilloscope/pulse generator combination or using a commercially available TDR tester. An inexpensive time domain reflectometer can be assembled using a conventional oscilloscope and a general-purpose pulse generator. A functional block diagram for a typical time domain reflectometer is shown in Figure 4. A Tektronix 45A 100MHz oscilloscope and an Interstate Electronics Corporation P5 pulse generator were used in some of the early experiments. The pulse generator can generate pulses as narrow as 10ns. However, the electrical length of the 1-meter samples is around 10ns. A narrower pulse is desirable to avoid the overlap of the transmitted and reflected pulses. Additionally, the peak distortion of the pulse generator is also a limiting factor. If the reflections from corrosion sites have a magnitude of the same order as the peak distortions, it may be difficult to identify them. Major oscilloscope companies, such as Hewlett-Packard and Tektronix, have all built dedicated TDR instruments or oscilloscopes that include TDR capabilities. TDR results discussed in this paper were obtained using the Hewlett-Packard 54750A digitizing oscilloscope with Hewlett-Packard 54753A single ended TDR plug-in. This system has a built-in step generator that generates a 40ps rise time, 00mV step pulse. The rise time, T r, is the time required for the voltage to rise from 10 percent to 90 percent of the final value. Theoretical analysis shows that T r is an important factor in determining whether or not a small mismatch can be detected. Experimental Results The steel cable specimens were connected to the time domain reflectometer through standard 50Ω coaxial cables. The far end of the steel cable sample was connected to a terminating resistive load. A pulse was then sent

11 down the sample and the reflections were viewed on the oscilloscope. The terminating load was changed from an open to a short to determine where the end of the sample was. The propagation velocity was then calculated. Figure 5 shows the TDR reflection from a 3-meter steel rebar sample (specimen 1). This sample has one simulated 50% pitting corrosion site 1.55m from the front end. The pitting corrosion was simulated by circularly grooving the rebar and removing 50% of its cross-sectional area. The TDR measurement was made on the bare specimen (without grout). The first step in the waveform corresponds to the generation of the step wave (A). The wave is launched into a coaxial cable, which is used to connect the sample to the measuring system. The characteristic impedance of this coaxial cable is 50Ω. However, the sample has higher impedance. As a result, there is a positive reflection at the beginning of the sample (B). At the end of the sample, the wave goes up because the line is terminated by an open circuit (D). Right in the middle of the sample there is a simulated corrosion site. A positive reflection from that site is observed at location (C). The time interval between points B and D is 3.0ns, which gives a propagation velocity of m/s, i.e. about 87% of speed of light. The location of the damage site is accurately determined as 1.58m from point B since T C - T B =1.1ns. The accuracy of the distance measurement can be further improved with better coaxial cable-to-specimen connections. TDR can not only locate the corrosion, but also reveal the severity of corrosion. Figure 6 shows TDR returns from two seven-wire strand steel cable samples (specimen 3 and 4). The steel cables are 0.95m long and 1.7cm in diameter. Corrosion was simulated by cutting several strands. The damage was produced over a 7.5cm length, 44cm from the end of the sample. The first marker indicates the initial reflection from the front of the sample, and the third marker indicates the reflection from the end of sample 9.94ns later. The propagation velocity is m/s. The second marker indicates the reflection from the simulated corrosion site. Note that accurate location is identified. Experimental results indicate that the magnitude of the reflection depends on the severity of the damage. The sample on the right has severe damage in which six strands are severed, while the other sample has two severed strands. Another advantage of TDR is its ability to deal with multiple discontinuities. Figure 7 shows the TDR reflection from a 3-meter steel rebar sample (specimen ). The sample has a simulated 70% pitting corrosion site

12 one meter from the end of the sample and a simulated 40% pitting corrosion site a meter further down. The simulated pitting corrosion is a circular groove 1.cm in length. The two markers in Figure 7 indicate the pulse reflections from the damage sites. Both of them are detected through a single measurement. The reflections are small because the damage extends over only a short length. Even though the reflections are relatively small, if compared to the signal from an undamaged specimen, it is clearly identifiable. Characteristic impedance also depends on the cable-to-wire distance. The closer the two conductors, the more sensitive the measurement will be. This effect is shown in Figure 8. In the figure, the distance d is the distance between the sensor wire and the strand (see Figure 1). The reflection is stronger when the sensor wire is close to the severed strand. This result is consistent with the theoretical analysis. Laboratory experiments also indicate that the TDR measuring system must have a small system rise time to produce acceptable results. TDR measurements were made on the 1-meter seven-wire strand cable sample with two strands severed at the middle with rise times varying from 500ps to 3ns. When T r is greater than ns, the 7.5cm long breakage of two strands at the center point is not detectable as shown in Figure 9. In field applications for more complex structures like an actual bridge, noise, energy loss, and wave dispersion can be problematic for TDR measurements. Testing of the prestressed girders in the field has indicated that energy loss and wave dispersion are not significant. Whether in the lab, or in the field, small amounts of random noise will be present. To deal with this, one can repeat measurements and average the results to effectively mask the noise. In fact, the TDR results shown in Figure 5 through Figure 9 are the average results of 16 measurements. Another kind of noise in the signal can be created by electric field disturbance caused by steel components near the cable being tested, variations in d, the distance between the steel cable and the sensing wire, since the characteristic impedance depends on d.

13 The noise magnitude can be relatively large. However, once the concrete element is instrumented, the location of the steel components causing noise, and the distance d between the steel cable and sensing wire will remain unchanged. Therefore, the noise will be repeatable. Differential TDR measurement can be used to effectively distinguish corrosion sites from repeatable noise. If several TDR measurements are made for the same cable over a long time period, the later TDR results should be identical to the former ones except for the corrosion sites. A differential comparison of stored signals with newly measured ones can reveal corrosion that occurred between the two measurements. The differential TDR method has been tested experimentally. Figure 10 shows TDR results obtained from a 1-meter seven-wire strand sample (specimen 5). This sample has two severed strands over a 4.0cm length, 48cm from the front end of the sample. From waveform 1, it is hard to tell whether or not the sample is damaged and where the damage is. However, if this waveform is differentially compared with waveform, which is the TDR return obtained from the same sample when it did not have any electrical discontinuities, the damage site can be easily identified. Currently this differential TDR method is being used to monitor prestressed concrete bridge girders for Bridge 8F in Fredrica, Delaware (Liu et al. 001). Using External Sensor Wire to Detect Corrosion The discussion to this point has been limited to a sensor wire in grout. In this case the sensor wire is very close to the steel cable and d -a is very small. The characteristic impedance is very sensitive to the change of the radius a according to equation 13. Although the internal sensor wire makes the TDR measurement more sensitive, it is not practical for existing structures. For detecting corrosion in existing structures, a sensor wire can be placed outside the concrete grout as long as the wire is parallel to the steel cable and the distance d is not too large. This method is very easy to use, however, the biggest disadvantage of the external sensor wire is that the TDR measurement is less sensitive, as mentioned above. For corrosion that reduces the radius of a single strand (0.635cm) by.5 percent to 0.49cm, the characteristic impedance will change from 51.9Ω to 68.0Ω if an internal sensor wire is applied. However, for an

14 external sensor wire, the change of impedance is only 134.4Ω Ω=5.6Ω. Surface corrosion and small pitting corrosion may not be detectable under this circumstance. However, there is no big difference between internal and external sensor wires if a (radius of the steel cable) is small. It means that the external sensor wire can be used to detect serious corrosion as well as the internal wire. This fact is of great significance because it allows the evaluation of existing structures. CONCLUSIONS A novel nondestructive evaluation technique for detecting damage in steel cables and reinforcing steel in concrete structures using time domain reflectometry (TDR) has been developed and demonstrated. Both analytical models and laboratory tests have been used to demonstrate the effectiveness of TDR in locating and characterizing simulated corrosion sites. Based on the work, the following results have been shown: 1. The system (steel strand/rebar and sensor wire) can be modeled as a transmission line and evaluated analytically. Experimental results showed that the analytical model gave an accurate prediction of the characteristic impedance of the sample.. TDR can detect the location of damage sites on a steel strand or reinforcing bar and provide indications as to the severity of the damaged region. 3. TDR measurements can be used for both new and existing structures. External sensing wires applied outside of the protective sheathing can be used for already existing structures, but with reduced measurement sensitivity. The TDR nondestructive evaluation technique need not be limited to the application of bridge cables or reinforcing steel. It can also be applied to other structures that utilize steel to detect and locate hidden corrosion damage or other defects such as fatigue cracks. ACKNOWLEDGMENTS This work was supported in part by the National Science Foundation under grant CMS and the Delaware Transportation Institute under grant No.99.

15 APPENDIX. REFERENCES Bhatia, S. K., Hunsperger, R. G., and Chajes, M. J. (1998). Modeling Electromagnetic Properties of Bridge Cables for Non-destructive Evaluation. Proc. of Int. Conference on Corrosion and Rehabilitation of Reinforced Concrete Structures, Orlando, Florida. Dowding, C. H., Su, M. B., and O Connor, K. M. (1989). Measurement of Rock Mass Deformation with Grouted Coaxial Antenna Cables. Rock Mechanics and Rock Engineering, v., No. 1, pp.1-3. Time Domain Reflectometry Theory" (1998). Hewlett-Packard Application Note 1304-, Hewlett-Packard Company, Palo Alto, Calif. Hokett, S.L., Russell, C.E., and Gillespie, D.R. (1994). Water Level Detection During Drilling Using Time Domain Reflectometry, Proc. of Symposium and Workshop on Time Domain Reflectometry in Environmental, Infrastructure, and Mining Applications, Evanston, Illinois. Liu, W. (1998). "Nondestructive Evaluation of Bridge Cables Using Time Domain Reflectometry." Master s thesis, University of Delaware. Liu, W., Hunsperger, R. G., Chajes, M. J., Li, D., and Kunz, E. (001). Nondestructive Corrosion Monitoring of Prestressed HPC Bridge Beams Using Time Domain Reflectometry, Proc. of TRB 80th Annual Meeting, Washington, DC. Nondestructive Methods for Field Inspection of Embedded or Encased High Strength Steel Rods and Cables. (1986). Final Report, NCHRP Project 10-30, Manchester, England. Topp, G.C., Zegelin, S.J., White, I. (1994). Monitoring Soil Water Content Using TDR: an Overview of Progress Proc. Of Symposium and Workshop on Time Domain Reflectometry in Environmental, Infrastructure, and Mining Applications, Evanston, Illinois. Wietek, B. and Kunz, E. (1995). Permanent Corrosion Monitoring for Reinforced and Prestressed Concrete Structures." Proc. of IABSE Symposium, San Francisco, Calif. Zahn, F. A. and Bitterli, B. (1995). "Developments in Non-Destructive Stay Cable Inspection Methods", Proc. of IABSE Symposium, San Francisco, Calif.

16 Table 1 Specimens used in the experiment. Specimen Type Length Damages Sites 1 rebar 3-m 50% at 1.55m rebar 3-m 70% at 1.0m, 40% at.0m 3 strand 0.95-m severed wires 7.5 cm wide at 0.44m 4 strand 0.95-m 6 severed wires 7.5 cm wide at 0.44m 5 strand 0.95-m severed wires 4.0 cm wide at 0.48m

17 Grout Tube Steel cable Sensor wire a d b Figure 1. Twin-conductor transmission line geometry of a bridge cable with sensor wire, where a is the radius of the steel cable, b is the radius of the sensor wire, and d is the center-tocenter distance between the cable and wire.

18 R D Z L D Z R D Z L D Z G D Z C DZ G D Z C DZ Z Z+ Z Z+ Z Figure. Distributed parameter equivalent circuit of a transmission line

19 Figure 3. Characteristic impedance as a function of radius a, where d=0.80cm, b=0.03cm

20 Pulse Generator Transmission Line Z l Load Oscilloscope Figure 4. Functional block diagram for a typical time domain reflectometer

21 A B C D Figure 5. TDR return of a 3-meter rebar sample (specimen 1). The sample has 50% pitting corrosion in the middle.

22 Two Severed Strands Six Severed Strands Figure 6. TDR returns from 95cm seven-wire strand cable samples (specimen 3 and 4).

23 Figure 7. TDR returns from 3-meter reinforcing steel sample (specimen ).

24 d = d 1 d = d = d 3 d Figure 8. TDR returns from 1-meter seven-wire strand cable sample, where d1<d<d3.

25 Tr=500ps Tr=1.0ns Tr=.0ns Tr=3.0ns Figure 9. Comparison of TDR returns with different rise time Tr. The sample is 0.95m long and has two severed strands at 0.44m.

26 Figure 10. TDR results obtained from a 95cm seven-wire strand sample before (waveform ) and after (waveform 1) a simulated damage is made to the sample. The differential comparison in the bottom reveals the damage site.

27 LIST OF FIGURES Figure 11. Twin-conductor transmission line geometry of a bridge cable with sensor wire, where a is the radius of the steel cable, b is the radius of the sensor wire, and d is the center-to-center distance between the cable and wire. Figure 1. Distributed parameter equivalent circuit of a transmission line Figure 13. Characteristic impedance as a function of radius a, where d=0.80cm, b=0.03cm Figure 14. Functional block diagram for a typical time domain reflectometer Figure 15. TDR return of a 3-meter rebar sample (specimen 1). The sample has 50% pitting corrosion in the middle. Figure 16. TDR returns from 95cm seven-wire strand cable samples (specimen 3 and 4). Figure 17. TDR returns from 3-meter reinforcing steel sample (specimen ). Figure 18. TDR returns from 1-meter seven-wire strand cable sample, where d1<d<d3. Figure 19. Comparison of TDR returns with different rise time Tr. The sample is 0.95m long and has two severed strands at 0.44m. Figure 0. TDR results obtained from a 95cm seven-wire strand sample before (waveform ) and after (waveform 1) a simulated damage is made to the sample. The differential comparison in the bottom reveals the damage site.