CRACK DEPTH MEASUREMENT IN CONCRETE USING SURFACE
WAVE TRANSMISSION
J.S. Popovics and J. Zhu
Civil & Environmental Engineering Department
The University of Illinois
205 N. Mathews Ave., MC-250
Urbana, IL 61801
ABSTRACT. A technique to estimate the depth of surface-breaking cracks in concrete is presented.
The surface wave transmission coefficient across the crack plane is determined and used to estimate
the depth. A self-compensating testing scheme is applied to eliminate experimental difficulties. Here
the self-compensating testing scheme is introduced, and the approach used to estimate crack depth
from the measured surface wave transmission coefficient is described. Experimental results
obtained from concrete specimens with pre-placed surface-breaking notches are then presented.
BACKGROUND
Techniques that non-destructively detect defects, measure the mechanical properties, or
monitor the state of deterioration in concrete structures are of considerable interest to civil
engineers [1,2]. A distinct single surface-breaking crack is a common and significant
defect that can eventually lead to failure of a concrete structure. Thus it is important to
monitor in a non-destructive fashion the distance that the crack extends into the concrete.
Several studies on the time-of-flight technique to predict surface-breaking crack depth in
concrete have been reported. The time-of-flight method however is not effective when
realistic concrete cracks are tested, that is when the crack tip is ill defined and the crack is
tightly closed [3].
Wave transmission or attenuation measurements do show high sensitivity to realistic
cracking in concrete under laboratory conditions [4]. Practical one-sided surface wave
transmission coefficient measurements in relatively homogeneous materials such as metals
have been achieved through the use of a self-compensating testing scheme. In this paper,
the surface wave transmission coefficient obtained using a self-compensating scheme is
used to predict the depth of surface-breaking notches in concrete.
SELF-COMPENSATING THEORY
In the frequency domain, we can represent the surface wave signal sent at point i and
received at point j (Vy) as a simple product of terms
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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y = A 1 d S Sj
(1)
where AI describes the source, Sj the receiver and dy the general signal transmission
between points i and j. Consider a surface wave traveling from point 1 to 3, as illustrated
schematically in Figure 1. The wave travels from point 1, where it is generated as
described by the AI term. The wave propagates past point 2 to point 3, where it is received
as described by the 83 term. The general signal transmission between the points is
described by the product di2 d23. If a surface-breaking crack is located immediately
between points 2 and 3, it also will affect the signal received at point 3. The effect of the
crack is contained in the surface wave transmission coefficient T, which represents the
ratio of transmitted wave amplitude to incident surface wave amplitude as a result of wave
interaction with that particular crack. Thus
Vi 3 =
T d23 S3.
(2)
Similar expressions are derived for Vi2, V43 and V42. By obtaining four signals, we may
eliminate the extraneous source and receiver terms and outlying material signal
transmission terms that are normally coupled in the signal with the simple manipulation
= (V 42 Vi3/V4 3 V 12 )'0.5
(3)
A complementary measurement over a crack-free region of the same material gives an
expression for d23. Thus T may be determined by the quotient of the crack and crack-free
transmission data sets by eliminating d23. This final expression gives the transmission
coefficient of the crack as a function of frequency. Further detail on the approach,
including required signal processing, is given by Popovics et al. [5].
Because the manipulations are carried out in the frequency domain, one can use
individual wave pulses that contain a broad range of frequencies, thereby providing more
data to use in the computations. When using broad-band signals in concrete, it is important
to define the region of acceptably high signal to noise ratio within a given function is a
measure of the variability of repeated and nominally identical transmission data, from the
FIGURE 1. Plan view of self-compensating testing configuration showing source (circle) and receiver
(squares) point locations with respect to the crack.
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same testing location, computed at each frequency. High variability at a given frequency
indicates poor (low) signal to noise ratio and therefore unreliable data. Conversely, low
variability indicates reliable data. The signal consistency function is the quotient of the
geometric and arithmetic averages of the repeated data in the frequency domain. Previous
work indicates that acceptable signals are provided when signal consistency greater than
0.99 at a given frequency is achieved [5]. An example signal consistency plot from a
notched concrete slab is shown in Figure 2; the acceptable frequency region (5 kHz to 48
kHz) is indicated.
MODEL AND VERIFICATION
Previous work suggests that signal wave transmission is a sensitive indicator of surfacebreaking crack depth: signal transmission decreases at all frequencies as crack depth
increases. A unique relation between surface wave transmission coefficient and surfacebreaking crack depth normalized by the surface wave wavelength at a given frequency (a*)
has been observed in previous work on cracked concrete slabs (crosses in Figure 3) and
verified by boundary element (BEM) computations for a crack (solid line in Figure 3) [6].
These experimental results were obtained using the self-compensating scheme described
above, where the tests were performed on actual cracks in concrete slabs. The work shows
that T drops rapidly as a* increases from 0 to approximately 0.4. As a* increases beyond
0.4, T declines at a much slower rate, and also fluctuates, until it reaches a relatively
constant value for a* > 1.3. Note that the data indicate that T > 0.22 for a* < 0.4. Also it
was found that the notch and cracked cases give similar response for T > 0.4.
0.95
0
10000
20000 30000 40000
Frequency, hk
50000
60000
FIGURE 2. Signal consistency function obtained from concrete slab with 49 mm notch.
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X Experiment
——BEM
0
0.5
1
1.5
2
Normalized crack depth aAR
FIGURE 3. Experimental data (points) using self-compensating scheme and numerical prediction (line) of
relation between T and a* in concrete slabs containing surface breaking cracks.
INVERSION APPROACH
The observed relation between T and normalized crack depth suggests a possible
approach for the measurement of in situ crack depth (a). Self-compensating measurements
can be used to determine T. But then we need to develop an approach for inversion of the
data to solve for a from T. Here we use the relation between T and normalized crack depth
a* as determined by the BEM analysis. A unique and sensitive region of the observed
relation for this purpose is provided when a* < 0.35. A least-squares best-fit second-order
curve to the data in this region is given by
T = -2.2 a*2 -1.8 a* + 1.0.
(4)
Inverse expressions for a* are easily obtained from Eqn. 3 using the quadratic equation.
Based on these observations, the following approach is used to determine a from
experimentally-obtained values of T:
(1) Record T at each frequency datum that admits acceptable signal consistency and for
all values of T> 0.4
(2) Compute a* for each accepted value of T using the inverse expressions of Eqn.3.
(3) Compute a from a* using an appropriate value of wavelength at each frequency
datum. (Wavelength computed from quotient of surface wave velocity (constant)
and frequency).
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The described approach provides multiple redundant estimates of a from admissible data at
each frequency. The redundant values are averaged to provide a single estimate of a.
EXPERIMENTS
Experiments were carried out in order to verify the proposed inversion approach to
determine a from T obtained with the self-compensating approach.
Testing Setup and Specimens
Tests were carried out on concrete slabs that are 150cm x 150cm x 22cm in dimension.
The slabs are comprised of normal Portland cement concrete having a maximum aggregate
size of 25mm. 5mm wide notches of varying depth were cut into the top surface at the
center of each slab. Test results from slabs with three notch depths are reported here:
20mm, 49mm and 99mm. The notch depths were verified by direct examination. The
surface wave velocities of each concrete slab were measured [7] and found to be
approximately 2250 m/s in all cases. This constant value was used in the computations.
The surface waves were generated by the impact of small steel spheres on the surface of
the concrete. The tests were repeated for a 5mm sphere source and a 12mm sphere source.
The impact events were applied to locations 1 and 4 (see Fig. 1). The surface waves were
detected by miniature accelerometers mounted directly on the concrete surface at locations
2 and 3 (see Fig. 1). The accelerometers have nominal sensitivity of 1.02 mV/(m/s2) and
nominal ±10% flat frequency response over 1 to 25 kHz. The spacings between adjacent
points are 30mm, and the notch was centrally located between points 2 and 3. The transient
signals were captured by a digital oscilloscope (signal duration of 100 (isec, digitized with
sampling frequency of 5.12 MHz) and transferred to a computer via the GPIB connection.
Further data processing was carried out with a Lab Windows program on the computer.
Results From Concrete Specimens
Experimental data obtained across the 20mm notch (a = 20mm) are shown in Fig. 4. In
the plot, T values obtained using the self-compensating method are plotted in terms of a*;
a* is derived from known values of a and frequency. The data for the repeated cases of the
5mm and 12mm diameter spheres are shown as points and the predicted BEM response
(Eqn. 3) is shown as a line. The limit of acceptable signal consistency for this test is
denoted by the dashed line; the usable region for the inversion approach is that above and
to the right of the dotted lines. The data from the two impactors are in good agreement
within the usable region; this illustrates the effectiveness of the self-compensating
approach in eliminating the effects of varying source characteristics. The agreement
between the experimental data and BEM prediction is reasonable within that same region.
Each experimental datum within the usable region provides a prediction of a, and these
redundant predictions are averaged to provide a single prediction. The average predicted
depths are shown in Table 1; for the case of a=20mm, an error of 5mm is obtained. The
error for a = 49 is only 1mm. This level of error is acceptable for crack depth estimation in
concrete.
The data for a=99mm is shown in Fig. 5. In this case we see that no data fall within the
acceptable region, and therefore no depth prediction can be made with the described
approach. The reason for this shortcoming is the difficulty we encountered in obtaining
consistent and usable data, as defined by the signal consistency function, at low
frequencies. With the described approach, low frequency data are needed in order to size
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Small impactor (5mm OD)
arge impactor (12mm OfD)
0.05
0.1
0.15
0.2
0.25
0.35
Normalized notch depth, a*
FIGURE 4. Experimental data (points) using self-compensating scheme and numerical prediction (line) (of
relation between T and a* in concrete slabs containing 49mm surface breaking notch. Usable region is
defined above and to the right of the dotted lines.
deep notches. For example, our minimum consistent frequency data obtained by an
experiment was 5 kHz. At this frequency, the largest crack depth that can be sized with the
described approach is 115mm. In the case of a=99, the minimum usable frequency was
higher, so it could not be sized. In order to size deeper cracks, consistent data at lower
frequencies must be obtained. We are currently investigating alternative wave sources in
order to obtain the needed consistency at low frequencies.
CONCLUSIONS
The following conclusions are drawn based on the results presented in this paper:
(1) The self-compensating testing scheme allows reliable measurement of wave
transmission (T) for surface waves interacting with surface-breaking cracks and
notches in concrete slabs.
(2) T can be related to notch depth in concrete assuming appropriate frequency ranges
of data with acceptable signal consistency can be obtained.
TABLE 1. Comparison of predicted and actual notch depths for the 5mm sphere impactor.
Actual notch depth
(mm)
Predicted depth
(mm)
Error
(mm)
20
49
99
15
48
****
5
1
****
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Large impactpr (12 mm OD)
0.2
0.4
0.6
0.8
Normalized notch depth, a*
FIGURE 5. Experimental data (points) using self-compensating scheme and numerical prediction (line) (of
relation between T and a* in concrete slabs containing 99mm surface breaking notch. Usable region is
defined above and to the right of the dotted lines.
(3) The approach provides predictions with acceptable accuracy for small and medium
notch depths.
(4) The experimental aspects of the approach must be improved in order to measure the
depth of deep cracks and notches since acceptable signal consistency is difficult to
obtain at low frequencies.
REFERENCES
CRC Handbook on Nondestructive Testing of Concrete, edited by V.M. Malhotra
1.
and N.J. Carino, CRC Press, Boca Raton, 1991.
2.
Bungey, J.H. and Millard, S.G., Testing of Concrete in Structures, 3rd edition,
Blackie Academic & Professional, London, 1996.
Song, W., Popovics, J.S. and Achenbach, J.D., "Crack depth determination in
3.
concrete slabs using wave propagation measurements", in Proceedings of the
Federal Aviation Administration Technology Transfer Conference, Atlantic City,
NJ, April 1999.
4.
Suaris, W. and Fernando, V., "Ultrasonic pulse attenuation as a measure of damage
growth during cyclic loading concrete", ACIMaterials Journal, 84, 185-193
(1987).
5.
Popovics, J.S., Song, W., Ghandehari, M, Subramaniam, K.V., Achenbach, J.D.
and Shah, S.P., "Application of wave transmission measurements for crack depth
determination in concrete", ACI Materials Journal, 97, 127-135 (2000).
Song, W., Popovics, J.S., Aldrin, J.C., and Shah, S.P., "Measurement of surface
6.
wave transmission coefficient across surface-breaking cracks and notches in
concrete," submitted to Journal of the Acoustical Society of America. In review.
Popovics, J.S., Song, W., Achenbach, J.D., Lee, J. and Andre, R.F., "One-sided
7.
stress wave velocity measurement in concrete," ASCE Journal of Engineering
Mechanics, 124, 1346-1353 (1998).
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