Download Ultrasonic and X-ray Tomographic Imaging of Highly Contrasting

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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