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17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China
Evaluation of Depth of Deterioration of Concrete Structure after Fire Using Stress Wave Method
Chia-Chi CHENG,
Department of Construction Engineering; Chaoyang University of Technology, Taichung County,
Chinese Taiwan
Phone: +886 4 23323000ext 4243, Fax: +886 4 23742325; e-mail: [email protected]
Abstract
The aim of the present research is to evaluate the degree of deterioration by means of
stress waves. In this study, the stress waves generated by the impact of a steel ball on
concrete surface are recorded by a displacement receiver 200 mm away. The received
signal is analyzed in the frequency domain. The frequencies of the dominant response
in the spectrum are used to evaluate the depth of deterioration for concrete specimens
experienced various high temperatures. Two types of specimens were used for
investigation. One is small specimen with dimensions 40*40*15 cm3. These
specimens were heated with the temperatures 300 to 800. The other is a large
concrete plate with the size 240*130*15 cm3. The specimen is heated by fire with the
highest temperature 600. The principal frequencies obtained from the small
specimens were compared to the depth of deterioration evaluated by drilled core. The
cores were sliced into thin disks and the depth of the deterioration was evaluated by
the dynamic elastic modulus of the disks. The test procedures were also applied to the
big plate specimen to obtain the depth of deterioration. The test results show the depth
of deterioration can not be evaluated when it is less than 2 cm. A linear relationship
can be found between the lowest peak frequency and the depth of deterioration.
Keywords: stress waves, concrete, fire, depth of deterioration
1. Introduction
Immediate collapse is usually not the case for reinforced concrete structure damaged
by fire. The damage assessment for RC structures after fire is important for engineers
to decide the strategies of retrofit or repair. For damage assessment, the issue
concerned most would be the depth of concrete deterioration. When the damage of
concrete reaches the surrounding of the steel bars, the bond between the steel bar and
concrete would decrease so would the bearing capacity of the structure member. The
typical way to evaluate the depth of the concrete deterioration is by core drilling. The
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method can not be generally applied because it will locally damage the structure. Thus,
it is important to develop techniques for evaluating the depth of concrete damages
in-situ non-destructively after fire.
The aim of this study is to evaluate the depth of deterioration by stress wave
related method. In this study, the stress waves generated by the impact of a steel ball
on concrete surface are recorded by a displacement receiver 200 mm away. The
received signal is analyzed in the frequency domain. The frequencies of the dominant
response in the spectrum are used to evaluate the depth of deterioration for concrete
specimens experienced various high temperatures.
2. Experimental Design
Two types of specimens were cast in this study. Small block specimens with
dimensions 40*40*15cm3 were designed for studying the effects of variations of
concrete mixtures and oven temperatures to the test responses and establishing the
empirical relationship between the measured response and depth of deterioration. The
large plate specimens with dimensions 240×130×15cm3 were constructed to study the
effect of lateral dimensions to the response. Moreover, as the small block specimens
were placed in an electrical oven for heating and the large plate specimens were
placed in a flame chamber in the simulating fire environment, the frequency-depth
relationship established by the small specimens can be verified by the tests performed
on the large plate specimens. The concrete mixtures were listed in Table 1. There are
four w/c ratios, 0.45, 0.55, 0.6, and 0.65 and five highest oven heating temperatures,
namely 300°C, 400°C, 500°C, 600°C, 800°C used for the block specimens. All the
specimens were exposed to the highest oven temperature for two hours. For the plate
specimens, the w/c ratio is 0.6. In the heating process, the temperature elevation
followed the standard fire curve [1] to the highest chamber temperature 600°C. The
specimen experienced the highest temperature for two hours and naturally cooled
down to room temperature.
The small blocks were cured in water for 28 days, air dried, and heated at the age
90 days. To ensure a complete dryness, the specimens were preheated in oven at 60
for 24 hours before the regular heating process. The specimens were heated by one
side only to simulate the condition in fire site. To achieve that, four blocks with
different w/c ratios were arranged back to back and surrounded by ceramic sheets and
gypsum plates as shown in Figure 1. The plate specimen was also heated on one sided
in the gas oven.
For block specimens, the impact tests were performed by 3 mm-dia. steel ball on
the heated surface along the four test lines shown in Figure 2. In the test, a
displacement receiver is placed 20 cm away from the impactor. The displacement was
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recorded in every 1.334 µs. There are 2048 data been recorded, which leads to 0.732
kHz for frequency resolution of the amplitude spectrum. For every test line, three
repetitive tests were performed to obtain the averaged amplitude spectrum.
After performing the non-destructive tests, one drilled core with diameter 8.1 cm
was taken from each specimen. Each core was cut through the depth and sliced into
1.5 cm-thick pieces. The depth of the concrete deterioration after high temperature
was estimated by the dynamic elastic modulus (Ed) of the disks. The dynamic elastic
modulus (Ed) of the disk is estimated by the fundamental flexural vibrational modal
frequency (f) of the disk. F was measured by an accelerometer placed on the side
surface of the disk which was hung by a string, as shown in Figure 3, following the
test method demonstrated in ref. [2]. The vibration is triggered by a 3mm-diameter
steel ball impacting on the center of the disk. Ed was estimated by Eq. (1). In the
formula, the diameter (d) and density (ρ) were measured for individual disk and the
poisson ratio (ν) was assigned as 0.2. The fundamental modal frequency parameter
(Ω0) for the disk with specific height and diameter was obtained from the eigenvalue
of the numerical model constructed by a finite-element program ANSYS.
Ω+=
0
)1(2fd
Ed
πρν (1)
3. Experimental Results
To reduce the effect of wave reflections from the side boundaries of the block
specimens, only the first 512 data was used for spectrum analysis. The waveforms are
added to 8192 points with the rest of the data set to zero to increase the resolution of
the response in frequency domain. The amplitude spectra are normalized by adjusting
the highest peak amplitude to 1. To illustrate the effects of different oven temperatures
to the test responses, the amplitude spectra averaged from three repetitive tests
obtained from the w/c 0.65 specimens are shown in Figure 4. For the specimen
without heating, shown in Figure 4(a), a dominant response can be found at 18.39
kHz corresponding to the major modal vibration generated by the impact. The
principal frequency becomes lower for higher oven temperature. As shown in Figure
4(b) to (f), the lowest dominant frequencies move to 17.39, 14.0, 13.18、11.16 及8.97
kHz, for oven temperatures 300, 400, 500, 600, 800°C. Moreover, there are some
secondary higher amplitude peaks at the frequencies range 20-50 kHz for oven
temperature 300-500°C. For oven temperatures 600 and 800°C, the responses at the
previous mentioned frequency range are suppressed and those at lower frequencies
are dominant.
As the frequencies of the dominant peak are affected by the surface deterioration,
4
the frequencies of the peak amplitude larger than 0.8, which are defined as the
dominant frequencies, for all of the test responses are recorded. Figure 5 shows the
distribution of the dominant frequencies with respect to the oven temperatures for all
the specimens with various w/c ratios. In the figure, we can find the lowest dominant
frequency decreases with the oven temperature for all the w/c ratios. For the
specimens with w/c 0.45, 0.55 and 0.6, single dominant frequency near the one of
room temperature is found for oven temperature less than 400°C. In contrast, for w/c
0.65 specimen, multiple dominant frequencies spreading at a large frequency range
are found at oven temperature 400°C. The presence of the multiple dominant
frequencies indicates the existence of micro-cracks which complicates the wave
propagation. Thus, the test results show the concrete with lower strength, such as the
case of w/c 0.65, was damaged at lower temperature. On the other hand, for the oven
temperature 800°C, narrower dominant frequency ranges were found for all the w/c
ratios. It may imply higher frequency contents of the stress waves generated by an
impact can not be propagate through the damaged layer, so the damaged layer acts as
the low-pass filter.
The depth of the concrete deterioration is evaluated from the dynamic modulus
of the sliced disks obtained from the drilled cores. Figures 6(a) and (b) show the
amplitude spectra obtained from the solid and damaged disks. The dominant peak
frequency is about 11 kHz for the solid disk corresponding to the fundamental
flexural vibrational mode. For the badly damaged disk, such as the case shown in
Figure 6(b), multiple peaks are found in spectra due to the existence of cracks inside
the disk. When the disk has only minor damages, one dominant peak was found but
the peak frequency is usually lower than 10 kHz indicating lower dynamic modulus.
Thus, concluded from the test results, the depth of concrete deterioration is defined by
the deepest position of the slice with the spectrum having multiple dominant peaks or
mono-peak frequency less than 10 kHz. Table 2 shows the estimated depths of
deterioration for all the specimens. In Table 2, the second column shows the lowest
dominant frequency obtained from the specimen-impact-tests and the third column
shows the estimated depth of deterioration. The relation between the lowest dominant
frequency and the depth of deterioration is shown in Figure 7. Because the lowest
dominant frequency are all around 17 kHz for the depth of deterioration less than 2
cm, the modal vibration of the specimens still controls the response for these cases
with shallow damages. For the depth larger than 2 cm, the depth of the lowest
dominant frequency decreases with the depth of deterioration and the corresponding
empirical formula is shown in Eq. (2).
521.28991.1 +−= fd R2=0.8463 (2)
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The same experimental process is applied to the large concrete plate specimen.
As the spectra are unlikely affected by the mode shape of the specimen, the
displacement waveforms did not set to zero after the 512 data point like those for
small block specimens. As shown in Figure 8, there are six positions been tested after
fire exposure. Three positions labeled as A, B, and C are at the area without surface
spalling and the three positions labeled as BR1, BR2, and BR3 are at the area with
surface spalling. The orientation of the test lines are also indicated in Figure 8. The
depth of deterioration estimated by Eq.(2) is compared with the real depth estimated
by the core slicing technique. The results and the errors are shown in Table 3. It was
found the error in estimation is less than 1.1 cm for the cases with lowest dominant
frequency less than 10 kHz. For the other cases, the depths of damage are all around
10 cm but the lowest dominant frequencies are not very stable and usually higher than
expected. It was suspected the orientation between the test line and the major cracks
may affect the value of the lowest dominant frequencies.
4. Conclusions
The test results show this innovational test method is easy in operation and has
large potential in estimating the depth of the deterioration larger than 2 cm. As
whether the depth of deterioration is larger than the concrete cover is the major
concern for engineers, the method may be proper for fire-site evaluations. However,
more studies are needed for obtaining the correct lowest dominant frequency and the
effect of internal reinforcement to the test response.
Acknowledgements
The research was sponsored by the National Science Council of the Republic of China,
Taiwan, under contract no. NSC 95-2211-E-324-050-.
Reference
[1] Lin, Y. and Su. W.C., “The Use of Stress Waves for Determining the Depth of
Surface-Opening Cracks in Concrete Structures,” Materials Journal of the
American Concrete Institude, Vol.93, No.5, pp.494-505 (1996).
[2] Leming, M. L., Nau, J. M., and Fukuda, J., “Nondestructive determination of the
dynamic modulus of concrete disks,” ACI Mater. J., 95(1), pp. 50–57 (1998).
Table 1 concrete mixtures for laboratory specimens
concrete mixtures(kg/m3)
6
w/c water cement fine aggregate coarse
aggregate
0.65 241 372 592 1044
0.6 235 392 592 1044
0.55 227 415 592 1044
0.45 208 469 592 1044
Table 2 The lowest dominant frequency and the measured depth of deterioration for
small block specimens
w/c 0.45 w/c 0.55
ambient temp.
lowest dominant
freq.
depth of deterioration
ambient temp.
lowest dominant
freq.
depth of deterioration
(°C) (kHz) (cm) (°C) (kHz) (cm)
23 19.491 - 23 18.3014 -
300 18.9419 - 300 18.1184 -
400 18.6674 - 400 17.4778 0.8
500 17.8439 1.8 500 17.294 1.9
600 16.1967 1.8 600 11.6214 2.6
800 10.0658 9.8 800 9.1507 9.8
w/c 0.55 w/c 0.65
ambient temp.
lowest dominant
freq.
depth of deterioration
ambient temp.
lowest dominant
freq.
depth of deterioration
(°C) (kHz) (cm) (°C) (kHz) (cm)
23 18.4844 - 23 17.9354 -
300 17.4778 - 300 17.4778 -
400 17.1118 0.8 400 13.9091 0.8
500 16.83 1.5 500 15.922 1.8
600 12.2619 4.3 600 11.0723 8.5
800 9.88275 9.7 800 8.51015 10.5
Table 3 Comparison between the estimated and measured depth of deterioration
Test position
Lowest dominant freq.(kHz)
depth from eq. (2) (cm)
depth from drilled
core(cm) errors(cm)
A 10.98 6.66 8.61 2.0
B 14.64 -0.63 11.24 11.9
C 10.98 6.66 10.11 3.5
7
BR1 11.71 5.20 9.99 4.8
BR2 9.52 9.57 8.43 -1.1
BR3 7.32 13.95 13.72 -0.2
Figure 1 Four blocks with different w/c ratio were arranged back to back and
surrounded by ceramic sheets and gypsum plates before put into the oven
Figure 2 Positions of four test lines for small
block specimen
Figure 3 Experimental setup for measuring
the dynamic elastic modulus
0-0.6518.39
00.20.40.60.8
11.2
0 10 20 30 40 50 60
Frequency (kHz)
Am
plit
ude
(
300-0.6521.87
17.75
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60Frequency (kHz)
Am
plit
ude (
400-0.6517.8414.00
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60Frequency(kHz)
Am
plitude (
gypsum
Ceramic
sheet
8
500-0.6513.1815.37
24.07 49.6043.83
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60Frequency (kHz)
Am
plitude
(
600-0.6511.1613.09
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60Frequency (kHz)
Am
plit
ude
(
800-0.658.97
11.44
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60Frequency (KHz)
Am
plitude
(
Figure 4 Amplitude spectra for w/c 0.65 specimens experiencing different temp.
w/c 0.45
0
10
20
30
40
50
0 200 400 600 800
Temperature()
Fre
quency
(kH
z) (
w/c 0.55
0
10
20
30
40
50
0 200 400 600 800
Temperature()Fre
quency
(kH
z) (
w/c 0.60
0
10
20
30
40
50
0 200 400 600 800
Temperature()
Fre
quen
cy(k
Hz)
(
w/c 0.65
0
10
20
30
40
50
0 200 400 600 800
Temperature()
Fre
quency
(kH
z) (
Figure 5 The distribution of the dominant frequencies w.r.t. the oven temperatures for
the specimens with various w/c ratios
0.45-23-1
11.71
0
1000000
2000000
3000000
4000000
0 20 40 60 80 100
Frequency(kHz)
Am
plitude
0.45-500-1
6.5813.54
0
500000
1000000
1500000
2000000
0 20 40 60 80 100
Frequency(kHz)
Am
plitu
de
(a) (b)
Figure 6 The amplitude spectra obtained from (a) the solid and (b) the damaged disks.
17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China
y = -1.991x + 28.521R2 = 0.8463
02468
101214
0 5 10 15 20
Frequency (kHz)
Dept
h (c
m)
(
Figure 7 The relation between the depth
of deterioration and the lowest dominant
frequency
Figure 8 Test positions labeled as A, B,
C, BR1, BR2, and BR3 are at the area
with surface spalling.