However the cost of ultrasonic testing is much lower than. X-ray imaging systems. This paper presents experimental results of X-ray and ultrasonic tomographic ...
Daigle, M., Fratta, D., and Wang, L. B. (2005). “Ultrasonic and X-ray Tomographic Imaging of Highly Contrasting Inclusions in Concrete Specimens”. GeoFrontier 2005 Conference. Austin, TX.
Ultrasonic and X-ray Tomographic Imaging of Highly Contrasting Inclusions in Concrete Specimens by M. Daigle1, D. Fratta2 and L. B. Wang3 1
Undergraduate Research Assistant. Civil and Env. Engineering. Louisiana State University. Baton Rouge, LA 70803 2 Assistant Professor. ASCE Associate Member. Civil and Env. Engineering. University of Wisconsin-Madison. Madison, WI 53706-1691 3 JFAP LSU/SU Assistant Professor. Civil and Env. Engineering. Louisiana State University. Baton Rouge, LA 70803 Abstract: There are several techniques that may be used in the tomographic imaging of structural and geotechnical systems. X-ray tomography and ultrasonic imaging are two of the extreme techniques as functions of resolution and costs. On one hand, X-ray tomography allows the collection of high-resolution images in small specimens that may be removed from the structure. The application of X-rays in the field is not recommended due to cost and safety issues. On the other hand, ultrasonic testing may be used in the field to obtain stiffness images with lower resolution due to problems of high attenuation, diffraction and scattering around aggregates and inclusions. However the cost of ultrasonic testing is much lower than X-ray imaging systems. This paper presents experimental results of X-ray and ultrasonic tomographic imaging of concrete cylindrical specimens prepared with low-density and velocity and high-density and velocity inclusions. These specimens present the extremes of contrast for the two techniques. Quantitative and qualitative analysis of the results show that the results from each technique are complementary: X-ray tomography may be efficiently used for the collection of advanced model parameters while ultrasonic imaging may be used for the QC/QA of structural and geotechnical elements in the field. Keywords: ultrasonic imaging, x-ray tomographic imaging, inclusion, concrete
1. Introduction The imaging of structural and geotechnical engineering systems using non-destructive evaluation techniques is becoming more popular, not only in the scientific community but also in their engineering applications. Techniques such as X-ray tomography, electromagnetic methods, electrical resistivity tomography and sonic and ultrasonic-based testing are being used to locate defects, monitor processes and to estimate engineering properties of structural and geotechnical engineering systems (Santamarina and Fratta 1998; Prada et al. 2000; Fratta et al. 2001; Garboczi 2002; Jonsson et al. 2002; Massad et al. 2002; Wang et al. 2002a; Wang et al. 2002b). Many of the most advanced imaging techniques are also being used to numerically quantify internal parameters of structural and geotechnical systems (see for example Al-Al-Raoush and Willson 2004 for the evaluation of hydro geologic parameters and Fernandez 2000 and Fratta and deHay 2004 for the evaluation of internal state of stresses in soils). These types of techniques are very promising, and they may change the way we obtain design parameters in geotechnical and structural engineering. However, each of them has only a certain range of application. Therefore, it is important to characterize their performance not only in the technical but also in the economical aspects for their use in civil engineering research and practice. This paper presents two very different tomographic imaging techniques: X-ray computerized tomography and ultrasonic imaging techniques in concrete specimens. The experimental study evaluates the behavior of the imaging systems in concrete specimens with inclusions that are either low density and low velocity or high density and high velocity. These contrasts of density and velocity are the two extremes in the images for the transmission of X-rays and the propagation of elastic waves. The paper starts with a discussion of the two different techniques and an evaluation of their range of application. Then the specimen preparation and testing procedures are discussed. The procedure for the inversion is presented and results are compared. Three 10-cm diameter by 20-cm high cylindrical concrete specimens are tested: one homogeneous, one with a metal high density and velocity inclusion, and one with a foamy low density and velocity inclusion. The results show that both techniques have specific ranges of application. X-ray tomography yield high-resolution images that can be used to obtain model parameter for highly advanced numerical modeling. Ultrasonic tomography can be used as a preliminary way to locate inclusions and as a field quality control method. However due to the limitation on lowfrequency wave propagation physics, high resolution images should not be expected.
2. X-ray Computer Tomographic Techniques X-ray Computerized Tomography (XCT) is a powerful tool for the nondestructive evaluation of the microstructure of materials. It was developed in 1970 when G. Hounsfield combined powerful computer algorithms with X-ray projections for the 2-D and 3-D imaging of internal organs for medical diagnosis (Kak and Slaney 1988; Cho et al. 1993). Since then, researchers in civil engineering have been using the technique in the characterization of soil-water systems, rock, cement and asphalt concrete, and reinforced concrete structures (Alshibli et al. 2000a, 2000b; Pla-Rucki and Eberhard 1995; Braz et al. 1999; Masad et al. 2002; Wang 2003; Al-Raoush and Willson 2004; Al-Omari and Masad 2004). XCT systems used in the microstructure characterization of concrete usually have a large penetrating capability and high resolution up to 5-10 micrometers. Compared with other imaging methods, XCT has several advantages including the ability to acquire 3D data set, no need for sample preparation, and non-destruction to suit unique requirements of asphalt core analysis. Typically, the equipment occupies an entire room and special safety requirements are
required to operate it. The cost of these types of systems ranges from $300K to more than $1,000K. X-ray is a particular type of light particle at the atomic level. Because x-ray photons have higher energy than visible light, they can penetrate through thicker objects than visible light can (ASTM 1995). The data collected as the X-ray attenuate while penetrating a material medium may be used to obtain images of the medium, the contribution of the attenuation coefficient µ(x,y,z) along the X-ray’s path is: l
I = I oe
− ∫ µ (x , y , z )dl
(1)
0
where Io is the incident X-ray intensity and I is the X-ray intensity after traveling a distance l through the specimen (Figure 1a). Mathematical software using reconstruction techniques such as filtering back-projection, back-projection filtering, Fourier reconstruction or iterative methods (e.g., ART, SIRT, or MART – Kak and Slaney 1988; Cho et al. 1993) are used to solve Equation 1 and to estimate the distribution of the coefficients of attenuation along the travel length l and generates slices of 2-D images. The 2-D slices may be compiled to generate 3-D images. From the image given, one can observe the location of voids, defects, or inclusions.
medium
medium Source
Source
µ(x,y,z) inclusion
(a)
inclusion
Intensity distribution Projection screen
V(x,y,z)
(b)
Travel-time distribution Projection screen
Figure 1. (a) X-ray tomographic projection system (hard source) and (b) travel time tomographic projection system (soft source). The rendering considers a high density and velocity inclusion (Low density and velocity inclusion would yield opposite trends in the intensity and travel-time distributions).
3. Elastic-Wave Tomographic Techniques Elastic-wave tomography may be used to determine the distribution of elastic properties within cylindrical concrete specimens. The used technique is known as travel-time tomography. This technique evaluates the travel-time between sources and receivers at known locations to calculate the distribution of internal local velocities. The resulting travel times are the result of the shortest travel time paths that each wave needs to travel from sources to receivers (Moser 1991). Therefore, a specimen with an inclusion would cause the elastic wave to take more or less time to travel through, depending on the density and stiffness of the inclusion (Figure 1b - Fratta et al. 2000; Prada et al. 2000). l
dl 0 V (x , y, z )
t=∫
(2)
The ultrasonic tomography system provides the researcher with travel times; the solution of the problem is to assign local wave velocities in such a way that matches the measured projections of travel times (Santamarina and Fratta 1998). These techniques have been used in geotechnical and structural engineering to evaluate location of inclusion and defects and to evaluate the distribution of the state of stresses in soils (Santamarina and Potts 1994; PlaRucki and Eberhard 1995; Gheshlaghi et al. 1995; Rens et al. 2000, Fratta et al. 2000; Prada et al. 2000). Depending on the physical properties of the medium and the frequency of the propagating signals, different solutions are available for the elastic wave imaging. These solutions include: linear (hard sources), and non-linear and diffraction-based solutions (soft sources). In the case of travel-time tomographic imaging, the travel-time ti between a source and a receiver is the integral of the slowness along the ray path (Equation 2). If the medium is discretized into pixels, the integral travel-time equation can be written as a sum:
ti ≈ ∑ k
Li , k Vk
= ∑ Li , k ⋅ s k
or
t = L⋅s
(3)
k
where Li,k is the distance traveled by the ray i in the pixel k, Vk is the wave velocity at pixel k, and sk is the slowness (inverse of velocity) in pixel k. In these equations, the travel-time vector t is known, and the travel length matrix L is computed from geometric considerations assuming the ray paths (in the case of linear solution) or by using Snell’s law to trace the rays depending on the distribution of the medium wave velocity (in the case of non-linear solutions). The goal of travel time tomographic imaging is to solve Equation 3 to determine the slowness vector s. Once the slowness vector s is computed, pixel values are mapped onto a color scale to render the tomographic image, and the analyst relates these results to other physical properties in the medium. Procedures used to compute the pseudo inverse of L and to solve Equation 3 are reviewed in the literature (e.g., Santamarina and Fratta 1998). In linear problems, there are close-form solutions; while in the case of non-linear problems, Equation 3 is iteratively solved. Fernandez and Santamarina (2003) describe the limitations of linear solutions and give suggestions for the boundary for linear solutions implementations. These suggestions include the separation between consecutive sources and receivers and the angle-coverage of rays due to directivity of sensors, among other issues. In this paper a simple, straight ray-based solution was implemented. This solution provides first order approximation to the location of both types of inclusions, and it is consistent with the limited number of rays used during the data collection in field applications. The implication of small data sets in the travel-time tomographic imaging was studied elsewhere (see for example Prada et al. 2004).
4. Description of the Experimental Study Cylindrical concrete (10-cm diameter by 20-cm high) specimens are made using a 2:1 sand to cement mixture. These specimens are prepared with different types of inclusion: one homogeneous, one with a foam/low velocity inclusion, and one with a metal/high velocity inclusion. The cylinder foam inclusion is a 5 cm by 10 cm cylinder, and the metal inclusion is a 4.2 cm by 10 cm inclusion. Both inclusions are placed off-center in the concrete specimens. The three concrete specimens are analyzed, individually, first by using the ultrasonic method,
then by using the x-ray method. All data from both methods are evaluated, recorded and graphed on the computer. The data from the ultrasonic machine was evaluated and compared to the data from the x-ray machine. Observations and conclusions are made as to whether both methods are able to locate the inclusion and the quality of the image. X-Ray Tomographic Testing. In this paper, the data are collected and analyzed using a fifthgeneration X-ray tomographer. The fifth generation x-ray tomography image analyzer (Figure 2) used in this study is a dual energy system at 150 kV and 225 kV. It has a high penetrating capability and high resolution up to 5 µm. The system can perform traditional fan beam scanning and the advanced cone beam scanning. Image processing software is Image ProPlus 4.0. The tomographic and visualization algorithm is part of the software provided with the scanner and VoxBlast and IDL. Each specimen is scanned along a number of crosssections from the bottom to the top. Enough data is gathered to reconstruct 3D images of the specimen and their inclusion.
Figure 2: The ACTIS 150/225 Fifth Generation, Dual Energy CT Scanner used in this study. Ultrasonic Testing. The ultrasonic testing setup includes a Portable Ultrasonic NonDestructive Digital Indicating Tester (PUNDIT Plus) with 200 kHz piezocrystal probes. The PUNDIT Plus system is also a lightweight, small, and battery powered instrument that can be taken to any location. The data collected from both the sources and the receiver are sent to an Agilent 54624A digital storage oscilloscope for data collection and analysis. Receiver 3
2
Receiver 2
Receiver 4 0 Receiver 1
Receiver 1
Receiver 5
Amplitude [V]
Low-velocity inclusion
2
Receiver 2
4
Receiver 3
6
Receiver 4
8
10-cm diameter concrete specimen
Source
Receiver 5
10
(a)
0
5 .10
1 .10
5
Time [s]
4
1.5 .10
4
(b)
Figure 3: Ultrasonic testing: (a) Test setup and (b) Typical traces and first arrivals for wave traces around the concrete specimen with the low-velocity inclusion.
The ultrasonic data collection includes receiver positions for each of the twelve equallyspaced source locations (see Figure 3a). Figure 3b shows typical traces for a projection behind low-velocity inclusion. Note that as the wave moves from receiver 1 to receiver 3, the travel time increases (the travel lengths also increase). At receiver 4, the travel time further increases, although the direct travel length decreases from receiver 3 to receiver 4. This is clearly because the ray must travel through or most likely around the low velocity inclusion. Similarly the plot of the average measured velocities shows a dip in the measured velocity caused by the presence of the inclusion. Figure 4 shows the shadows of velocity for both low velocity and high velocity inclusions. Note that the trends in the shadows of average velocity are opposite are expected. This observation is caused by the presence of low-velocity versus high-velocity inclusions. Travel time data collection included twelve sources position projecting signals to seven receivers for a total of 84 rays. This type data collection arrangement yields a uniform information field as shown in Figure 5. The medium was divided in 49 square pixels. As Equation 3 yields a system of equations that are mix-determined (Santamarina and Fratta 1998), a damped least square solution was used to obtain tomographic imaging:
(
s = L ⋅ L + η⋅ I T
)
−1
⋅L ⋅t T
(4) 4000
Average velocity [m/s]
Average velocity [m/s]
4000 3150 3000
2000
1000
0
2
4
2000
1000
6
Receiver number [ ]
3150 3000
0
2
4
Receiver number [ ]
(a)
6
(b)
Figure 4: Shadows of average velocities on slides across the inclusion: (a) Low-velocity inclusion and (b) high-velocity inclusion (straight ray travel lengths are assumed). Receiver 4 Receiver 3
Receiver 5
Receiver 6
Receiver 2 30°
Receiver 7
Receiver 1
Source
(a)
(b)
Figure 5: (a) Travel-time tomography setup and (b) distribution of information content.
Ray length [m]
10.2⋅cm 0.1 7.2⋅cm
0.05
0
10
20
30
40 50 Ray number [ ]
60
70
80
Figure 6: Determined travel length from travel length matrix L (straight ray assumption).
where I is the identity matrix and η is damping coefficient. The ray lengths as obtained from summing the rows of the travel length matrix L are shown in Figure 6.
5. X-Ray Tomographic Imaging The presence of the inclusions is first evaluated with the X-ray tomographic system. The concrete specimens are scanned in a number of thin slices (1 mm-thick slices) to allow for the assembly of 3D images. The complete images of the concrete specimens may be viewed in full using digital radiography (DR) scans or in slices using a computer tomography (CT) scans. Figure 7 shows some of these images. Figures 7b and 7c show that the differences in colors show the difference in densities (and attenuation) of the two types of the inclusions with respect to density of the concrete matrix. The dark color shows the presence of the foam inclusion; the light color shows the presence of the steel inclusion (see also Figures 8 and 9). Figures 8 and 9 shows a set of X-ray tomographic slices arranged from the top of the specimens to the bottom. These images also show that the low velocity and density inclusion is located off-center, and it is not vertical but inclined towards the wall of the specimen. Figure 9 shows that the high-density and velocity inclusion is slightly off-center, and it is aligned parallel to the main axis of the concrete cylinder. The results from the X-ray tomographic imaging are then used to validate the results from the ultrasonic tomographic imaging.
(a)
(b)
(c)
Figure 7: Examples of x-ray tomography images: (a) full scan, (b) slice of the low-density inclusion, and (c) slice of the high-density inclusion.
Figure 8: X-ray tomographic slice images of the concrete specimen with a low-velocity and density inclusion (The slices are captured along cross-sections from zones with inclusion to zones without inclusion).
Figure 9: X-ray tomographic slice images of the concrete specimen with a high-velocity and density inclusion (The slices are captured along cross-sections from zones with inclusion to zones without inclusion).
Travel time [s]
6. Travel-Time Tomographic Imaging The quality of typical travel times collected using transducers are presented in Figure 10. These data show the travel time in the concrete with the high-velocity metal inclusions. For comparison the data from a slide where the inclusion is not present is plotted against the data from two slides where the inclusion is present. (c) Note that the high velocity sharply drops the travel time. This behavior of the data shows that waves do propagate through inclusion in spite of the impedance mismatch between the concrete and the steel. (a) (b) 3 .10
5
2.5 .10
5
2 .10
5
1.5 .10
Slice A with no inclusion
Slice B with highvelocity inclusion
Slice C with highvelocity inclusion
5
0
10
20
(c)
30
40 50 Ray number [ ]
60
70
80
Figure 10: Typical times: concrete specimen with the high-velocity metal inclusion.
Figures 11 and 12 summarize the results of applying Equation 4 to the travel time data from the two concrete specimens with the low density and velocity inclusion and with the highdensity and velocity inclusion. In spite of the simplification caused by the use of the straight
ray solution both inclusions are equally well located. However, some interpretation is needed to properly evaluate the data. The wave velocity in the foam used as low velocity and density inclusion is lower than 500 m/s per second, but the inverted velocity indicates an inclusion with a velocity ob about 2500 to 3000 m/s. In this case, there is large impedance mismatch and the waves propagate around the inclusion yielding a velocity that is lower than the velocity of the concrete but larger than the true velocity of the inclusion. That is, the elastic waves do not “see” the inclusion, but they go around it. Also the inverted image yields the size of an inclusion that is smaller than its true dimension. Slice A
Slice C
Slice C - Slice A
Slice A
inclusion
(a)
Inverted velocities [m/s]
Slice C
(b)
6000
Edge pixels
4000
Low velocity inclusion
2000
0
10
20 30 Pixel number [ ]
40
50
(c)
Figure 11: Travel time tomographic imaging of the concrete specimen with a lowvelocity inclusion: (a) Sketch of slices, (b) images from slice A (no inclusion), slice C (low velocity inclusion), and difference between images from slices C and A; (c) inverted velocities per pixel.
Figures 11b and c show the presence of outlier inverted velocity pixels. These pixels are located at the edge of the inverted image and they have the lowest information content, that is they are least constrained by the measurements. Then, the inversion algorithm “dumps” the noise at these pixels and in some cases distorts the image (see for example Santamarina and Reed 1994). Figure 12 shows the results of the inverted data for the concrete specimen with high-velocity inclusion. The results shows that the travel time inversion locates the inclusion at the slightly off-center as expected (see Figure 12b), but it also shows that inverted inclusion’s dimension is slightly larger than the real inclusion as the inclusion behaves as a diverging lenses. In this case the waves are attracted by the inclusion and they “see” it in great detail. These observations seem to indicate that ultrasonic waves and travel time data could be successfully used to find high-density and velocity inclusions such as rebars in concrete but they would have the tendency to mask low-density and velocity inclusion. For these types of evaluations, the analyst must place a great deal of attention to find problematic inclusion such
as necking and corroding rebars in drilled shafts infrastructure.
for the monitoring of the aging
Slice A
Slice B
Slide A
Slide C
Slice B - Slice A
Slice A
Slice B
inclusion
Slide C - Slide A
Slice C
(a)
(b)
Inverted velocity [m/s]
6000
4000
Slice A with no inclusion
2000
0
10
Slice B with highvelocity inclusion
20 30 Pixel number [ ]
Slice C with highvelocity inclusion
40
50
(c)
Figure 12: Travel time tomographic imaging of the concrete specimen with a lowvelocity inclusion: (a) Sketch of slices, (b) images from slice A (no inclusion), slice B (low velocity inclusion) slice C, and difference between images from slices C and A; (c) inverted velocities per pixel.
7. Conclusion Results show that ultrasonic travel time tomography, if properly interpreted, offers reasonable accuracy for determining sizes and locations of both high and low velocity inclusions. This technique provides a valid alternative to X-ray tomography in field applications where X-ray scanners cannot be deployed. However, the quality and the resolution of X-ray tomographic images are much higher than ultrasonic tomographic images; and they provide better data sets for the development of advanced numerical models.
Acknowledgments The support of the National Science Foundation (REU Site - Award number: 0097593), the Louisiana Board of Regents Research Competitiveness Subprogram (Award numbers:
LEQSF2003-06-RD-A-10 and LEQSF2002-05-RD-A-12), Louisiana Board of Regents Enhancement and the LSU Council on Research Summer Research Program is greatly acknowledged.
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