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Use of Ultrasound to Estimate Depth of Surface Opening Cracks in

Concrete Structures

Roberto C. A. PINTO1, Arthur MEDEIROS

1, Ivo J. PADARATZ

1, Patrícia B. ANDRADE

1

1

Civil Engineering Department, Federal University of Santa Catarina; Florianópolis; BrazilPhone: +55 483721 7768, Fax: +55 483721 5191; e-mail: [email protected], [email protected],

[email protected], [email protected]

AbstractThis study discusses the use of the ultrasound with the time-of-flight diffraction technique to estimate the depthof surface opening cracks. This technique is a very useful tool for practical applications. It is inexpensive,simple and easy to perform, giving a rapid indication of the extension of cracking. BS 1881:Part 203 presentssome mathematical expressions to estimate the depth of surface opening cracks. These expressions are based ontwo time-of-flight measurements performed using the indirect mode of transmission. However, BS 1881:Part

203 indicates that when such a mode of transmission is used, it is required at least four measurements to be ableto estimate the ultrasound pulse velocity (UPV). Due to this apparent incoherence, two graphically-basedmethods were developed, allowing for the use of several time-of-flight readings. All of these aforementioned

methods were applied to estimate the depth of surface opening cracks of artificially cracked samples produced inthe laboratory. The results indicated that the new developed methods can estimate vertical cracks with an errorof 10%; a smaller value compared to the error of 15% obtained for the BS 1881 method.

Keywords: ultrasound, surface opening cracks, non-destructive testing

1. Introduction

Surface opening cracks often occurs in concrete structures. They may appear as a

consequence of several degradation mechanisms such as repeated loading, differential

settlement, chemical attacks, drying shrinkage, and freeze-thaw cycles, among others. While

in some cases, surface opening cracks may only affect the aesthetics of the concrete surface,in most cases they are an indication of structural distress and/or decreased durability [1]. In

order to evaluate the damage of the concrete structure due to cracking, it is important to

quantify the crack geometric parameters including width, extension, and more importantly thedepth of penetration. Depending on the type of structure, the nature of the cracking, and the

crack penetration depth, surface opening cracks need to be repaired.

Crack depth determination can be performed non-destructively by the time-of-flight

diffraction technique [2-4]. In this technique, stress waves are generated on one side of thecrack, with wave arrival times monitored by a transducer placed on the opposite side of the

crack. Stress waves can be generated by a mechanical pulse, such as given by ultrasound

equipments, or by mechanical impact, as in the impact echo technique. Crack penetrationdepth is determined assuming a particular wave propagation path.

Although there are other techniques available to measure crack geometric characteristics [5-

7], the use of ultrasound with the time-of-flight refraction technique is very simple, easy to

perform, and gives a rapid indication of the extension of cracking. There are a significant

number of commercially ultrasound instruments available to be used in concrete structures.

They usually display the direct transit time of a longitudinal wave in microseconds.

Crack depth estimation by the time-of-flight diffraction technique using conventional

ultrasound equipment can be performed assuming a direct travel path of the stress wave from

the transmitter transducer to the receiver transducer, passing through the crack tip. The

transducers are placed on opposite sides of the crack.

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Bungey [3] presented a simple mathematical expression to calculate crack penetration depth

comparing two time-of-flight measurements through an indirect mode of transmission. The

first one is performed in sound concrete, while the second one is obtained with the transducers

placed equidistantly from the opening surface crack on opposite sides of the crack. In

Bungey´s method, it is necessary to know the ultrasound pulse velocity (UPV) in the concrete

which is usually obtained in a region away from the crack.

The former BS 1881 [2] also presented a mathematical expression based on twomeasurements with the transducers placed equidistantly from the opening surface crack. With

this special arrangement of transducers, it is possible to estimate both the crack depth and theUPV. However, when calculating UPV using the indirect mode of transmission, BS 1881

does require more than only two measurements.

In order to overcome this apparent incoherence, two graphically-based methods were

developed to obtain the depth of surface opening cracks based on several ultrasound time-of-

flight measurements. The first method is an extension of the method presented in BS 1881

but with more measurements taken. The second one was developed specifically when thecrack is close to the side of the concrete member such that there is not enough space availableto place both transducers equidistantly from the opening surface crack. Thus, one transducer

stays stationary whereas the other varies its position. This latter method is similar to theprocedure presented in BS 1881 to measure ultrasonic pulse velocity with both transducers on

the surface of the test specimen, through an indirect mode of transmission.

All four methods were applied to estimate the depth of artificial cracked samples in the

laboratory. Prismatic concrete specimens with vertical cracks were produced. It was

concluded that the graphically-based methods can better predict the depth of surface opening

cracks.

2. Methods to estimate crack depth

2.1 Existing Methods

Bungey [3] proposed a mathematical expression by comparing the time-of-flight of an

ultrasound longitudinal wave through a sound concrete to the one around a crack, considering

that the velocity of the longitudinal wave in the concrete is the same in both cases. Assuming

the wave travel path presented in Fig. 1a, the crack penetration depth “h” can be evaluated as:

2s

2c

s

T T T xh −

= ……..…………………. (1)

where: T c represents the travel time around the crack; T s is the surface travel time in sound

concrete, and x is the least distance between the transducers and the crack, measured on the

surface of the concrete. In order to use Eq. 1, it is necessary to previously obtain the surface

travel time of the longitudinal wave in a region without crack, T s, with transducers at a

distance 2 x apart from each other.

The assumption of the same ultrasonic pulse velocity through a sound surface concrete and

through a path around the crack may lead to errors in the estimate of the crack depth.Usually, top concrete layers are more porous than inner parts due to differences in settlement

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of aggregates, vibration and also humidity loss to the environment. Thus, it is common to

observe a smaller UPV in the surface of the concrete than in the inner parts of the structure.

Bungey [3] states that the depth of surface opening cracks using Eq. 1 can be estimated with a

precision of 15%.

Another method to estimate the depth of surface opening cracks is the one presented in BS1881: Part 203 [2]. This method uses two measurements taken with the transducers placed

equidistantly from the crack at the distances x, and 2x, according to Fig. 1b. Assuming thatthe ultrasonic pulse velocity is the same, it is possible to modify Eq. 1, as follows:

21

22

22

21

T T

T T 4 xh

−

−= ……..…………………. (2)

where T 1 and T 2 are the time-of-flight of the longitudinal wave with transducers at distances x,

and 2x from the crack, respectively. BS 1881 [2] suggests a distance x of 15 cm.

XX

h

XX

h

X X

a) b)

Fig.1. Transducer arrangements for Bungey’s and BS 1881 methods

This method does not require a complementary test in sound concrete. However, it is based

only in two measurements made with the indirect mode of transmission. In this arrangement,the exact travel path is uncertain. When calculating the ultrasound pulse velocity using the

indirect mode of transmission, in order to overcome the lack of precision of the travel path,

BS 1881 [2] requires a series of reading. The transmitter is fixed, and the receiver is moved

in a series of fixed incremental points along a chosen line. BS 1881 [2] indicates that the

velocity from the indirect transmission mode is often 5 to 20% smaller than the one obtained

from the direct transmission mode.

Yaman et al [8] recommended that when performing an indirect measurement, it is necessary

at least four readings in order to obtain variability smaller than 2% in the UPV. They alsoindicated that the first reading should have the transducers apart from themselves of at least

two times the wave-length “ λ”, with the subsequent readings at least one half wave lengthapart.

While BS 1881 [2] does require a series of measurements when using the indirect mode of

transmission to calculate the ultrasonic pulse velocity, it does not apply this requirement when

using the indirect mode of transmission to calculate estimate crack depth.

2.2 Proposed graphically-based methods to estimate crack depth

2.2.1 Method A

In this method, the transducers are placed in locations equidistantly from the surface opening

crack along a chosen line, similarly to the BS 1881 method, but with at least four positions as

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suggested by Yaman et al [8]. Fig. 2 shows a possible arrangement of the transducers. Time-

of-flight readings are performed at each transducer arrangement. Assuming the same

ultrasonic pulse velocity in all wave travel paths, the time-of-flight can be expressed by:

V

L2T i

i =

……………..…………………. (3)

where T i is the time-of-flight measured with transducers at a distance xi from the crack; V is

the ultrasonic pulse velocity; and Li is the assumed half travel length corresponding to T i,

which depends on the distances X i and h. If one substitutes Li in Eq. 3 by its dependence on X i

and h, the following expression can be found.

22

i22i h

4

T V X −=

………..…………………. (4)

X1X1

X3

X2

X3

h

X2

L3 L2 L1L4

X4 X4

L1 L2 L3 L4

Fig. 2. Transducer arrangements for graphically-based Method A

Equation 4 indicates a linear relationship between the parameters X i2

and T i2

. The crackpenetration depth, h, can be obtained by plotting the results. The slope of the best straight line

is proportional to the UPV while its intersection is proportional to the crack depth.

2.2.2 Method B

A variation of the above method can be used when the crack occurs close to one side of the

specimen. In this case, a procedure similar to the one used to obtain the ultrasonic pulse

velocity through the indirect transmission mode is followed. The transmitter is fixed in one

side of the crack, while the receiver is placed in several locations on the opposite side of thecrack, according to Fig. 3. The first position should have both transducers equidistantly from

the surface opening crack while for the other ones the receiver is moved in fixed increments.For each arrangement, a time-of-flight reading is taken.

Using similar assumptions regarding travel path and ultrasonic pulse velocity as used in the

previous method, the crack depth can be calculated by subtracting the time of flight from a

given reading to the time-of-flight obtained in the first reading, yielding:

221i

22i h)

2

T T (V X −−=

………....……………. (5)

This expression indicates a linear relationship between the parameters X i2

and (T i – T i /2)

2

.Similarly as in method A, the crack penetration depth can be obtained by plotting the results.

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X1

h L1L1L2 L3

X2

X3

L4

X4

X1

Fig. 3. Transducer arrangements for graphically-based Method B

4. Experimental program

In order to compare all the aforementioned methods to estimate crack depth, an experimental

program was designed. Concrete specimens with artificial cracks were produced in the

laboratory with time-of-flight measurements taken according to each of the four methods.

Three series of concrete specimens were cast. Series 1 consisted of 8 concrete prisms of 150x 250 x 700 mm with vertical cracks of 75 and 100 mm of depth and crack width of 6 mm,

with four replicates for each crack depth. Series 2 consisted of four concrete prisms of same

size, with vertical cracks of 50, 75, 100, and 150 mm, and crack widths of 0.5 mm. These

specimens were produced in order to verify the possible influence of crack widths in the

estimate of crack depths. In order to apply Method B, a third series comprising of concrete

prisms of greater length was produced. Four concrete prisms of 200 mm x 200 mm x 800 mm

with vertical crack of depths of 50, 75, and 100 mm, and crack width of 2 mm were chosen.

Table 1 presents a summary of the geometric characteristics of all the specimens.

Table 1 - Specimen characteristics

SpecimenSize

(mm x mm x mm)

crack depth

(mm)

crack width

(mm)

Series 1

S1-75-A

150 x 250 x 700

75 6

S1-75-B 75 6

S1-75-C 75 6

S1-75-D 75 6

S1-100-A 100 6

S1-100-B 100 6

S1-100-C 100 6

S1-100-D 100 6

Series 2S2-50 50 0.5S2-75 75 0.5

S2-100 100 0.5

S2-150 150 0.5

Series 3

S3-50

200 x 200 x 800

50 2

S3-75 75 2

S3-100 100 2

All cracks were artificially produced. During casting, plates with different thickness werepositioned on the sides of the specimen. At approximately six hours after casting, the plates

were removed and the artificial crack formed. Before performing time-of-flight

measurements, the specimens were rotated 90

o

. This procedure permitted that the ultrasound

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measurements could be performed on a flat and smooth surface; and that any line of testing

perpendicular to the crack would be at the same level of consolidation.

A 0.57 w/c concrete mixture was used to produce specimens for Series 1 and 2 while a higher

w/c of 0.63 was used to produce Series 3 specimens. The coarse aggregate used in both

concrete mixtures was a granite coarse aggregate with maximum nominal size of 19 mm.For each series, 10 x 20 cm concrete cylinders were also cast. These cylinders were

maintained under the same curing conditions as the prisms specimens. Concrete compressivestrength was evaluated after 28 days. The results indicated a compressive strength of 36 MPa

for concrete of Series 1 and 2, and 20 MPa for concrete of Series 3.

Ultrasound time-of-flight measurements were performed with a commercially available

equipment. For specimens of Series 1 and 2, two 54 kHz transducers were initially placed onopposite sides of the crack at a distance of 100 mm; afterwards both transducers were moved

simultaneously to the next test location at 50 mm increment following the transducer

arrangement presented in Fig. 2. For specimens of Series 3, the transmitter was fixed at a

distance of 100 mm from the crack, while the receiver was firstly placed at a distance of 100mm on the opposite side of the crack, and then moved away from the crack in 50 mm

increments. These transducers arrangement permitted that the first reading was performed

with the transducers at 200 mm apart from each other, which is greater than twice the wave

length λ, as suggested by Yaman et al [8]. The wave-length was in the order of 75 mm,considering an UPV of 4000 m/s.

For all specimens, UPV was also obtained using the indirect mode of transmission on the

surface of the specimen away from the crack according to recommendations of BS 1881 [2]

with at least four readings taken.

5. Results

Table 2 presents the time-of-flight results obtained by placing both transducers at equidistant

locations from the crack.

Table 2 - Time-of-flight readings with transducers equidistant from crack (in µµµµs)

SpecimenDistance x (mm)

100 150 200 250 300

S1-75-A 66.1 83.1 109.2 129.6 153.2

S1-75-B 61.4 80.7 102.6 124.4 145.9S1-75-C 60.0 78.6 105.6 124.2 147.8

S1-75-D 62.6 78.6 102.2 126.7 149.3

S1-100-A 71.7 88.3 111.2 130.6 151.5

S1-100-B 72.2 88.0 109.6 131.8 151.7

S1-100-C 71.3 87.1 111.2 131.6 155.4

S1-100-D 71.8 90.7 112.2 131.9 156.2

S2-50 52.5 77.6 97.7 122.5 144.4

S2-75 62.4 79.7 104.8 125.8 148.8

S2-100 80.3 90.2 108.3 132.8 152.1

S2-150 81.3 114.1 121.5 139.7 160.2

S3-50 60.4 90.0 113.8 136.5 -

S3-75 69.5 89.8 114.5 141.5 -

S3-100 75.6 91.7 114.6 135.1 -

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Table 3 presents the time-of-flight results obtained by fixing the transmitter at 100 mm from

the crack with the receiver at various distances from the crack. Table 4 presents the UPV

obtained by the indirect transmission mode performed in a region away from the crack, as

well as the ones obtained by the graphically-based methods A and B.

Table 3 - Time-of-flight readings with transmitter fixed at 100 mm from crack andreceiver at various distances (in µµµµs)

SpecimenDistance x (mm)

100 150 200 250 300 350 400 450

S3-50 62.6 73.9 86.7 98.9 110.1 125.8 136.0 149.1

S3-75 69.0 78.9 90.2 101.2 115.8 127.4 139.2 150.3

S3-100 77.0 87.2 98.0 105.8 120.2 133.6 144.8 159.4

Table 4 - Ultrasonic pulse velocity (m/s)

Specimen Indirect transmissionsound concrete

Method A Method B

S1-75-A 3900 4100 -

S1-75-B 3750 4250 -

S1-75-C 4250 4200 -

S1-75-D 4100 4150 -

S1-100-A 4150 4250 -

S1-100-B 4000 4200 -

S1-100-C 4000 4100 -

S1-100-D 3950 4100 -

S2-50 4100 4200 -

S2-75 4250 4150 -S2-100 3900 4300 -

S2-150 3950 4200 -

S3-50 3650 - 3860

S3-75 3500 - 3950

S3-100 3750 - 3850

6. Analysis and Discussion

6.1 Crack Depth Estimates by Different Methods

6.1.1 Bungey’s method

For the time-of-flight results with transducers positioned at 100 mm and 150 mm from thecrack tip, presented in Tables 2 and 3, crack penetration depth was estimated using Eq. 1. The

ultrasound pulse velocities were the ones obtained using the indirect mode of transmission on

sound concrete presented in Table 4. The obtained crack depth estimates were grouped

according to their actual crack depths, as presented in Fig. 4. Besides the estimated crack

depths, Fig. 4 also shows the actual depths and their 15% range for all specimens.

Fig. 4 indicates that although most of the individual results lies within 15% of the actual crack

depth, there were some poor estimates, specially the ones obtained for specimens S1-75-B,

and S3-75.

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0

50

100

150

200

S 2 - 5 0

S 3 - 5 0

S 1 - 7 5 -

A

S 1 - 7 5 - B

S 1 - 7 5 -

C

S 1 - 7 5 - D

S 2 - 7 5

S 3 - 7 5

S 1 - 1 0 0

- A

S 1 - 1 0 0

- B

S 1 - 1 0 0

- C

S 1 - 1 0 0

- D

S 2 - 1 0 0

S 3 - 1 0 0

S 2 - 1 5 0

specimen

E s t i m a t e d c r a c k d e p t h ( m m )

100mm 150mm ± 15% actual depth actual depth

Fig. 4. Crack depth penetration estimates by Bungey method with transducers at 100 and 150 mm from crack tip

6.1.2 BS 1881 Method

When applying the BS 1881 method to estimate crack depth, it was necessary to choose a pair

of time-of-flight measurements among those presented in Table 2 to be used in Eq. 2. Time-

of-flight measurements of transducers at the distances of 100 and 200 mm, and 150 and 300

mm were selected and used in Eq. 2 although others combinations could have also been

chosen. The results were grouped according to the crack depths, shown in Fig. 5.

Similarly to the results given by Bungey´s method, Fig. 7 indicates that most of the individualestimates lies within 15% of the actual depths.

0

50

100

150

200

250

S 2 - 5 0

S 1 - 7 5 -

A

S 1 - 7 5 - B

S 1 - 7 5 -

C

S 1 - 7 5 - D

S 2 - 7 5

S 1 - 1 0 0

- A

S 1 - 1 0 0

- B

S 1 - 1 0 0

- C

S 1 - 1 0 0

- D

S 2 - 1 0 0

S 2 - 1 5 0

specimen


100mm-200mm 150mm-300mm ± 15% actual depth actual depth

Fig. 5. Crack depth estimates by BS 1881 method

6.1.3 Graphically-based Methods A and B

For the proposed Methods A and B, time-of-flight measurements presented in Tables 2 and 3were used in Eqs. 4 and 5, respectively. Graphs relating the corresponding parameters were

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produced for each specimen with the depth penetration crack and the UPV estimated. Figure 6

presents the crack depth estimates for each specimen grouped according to their actual depths,

as well as, the 15% range of the actual depths for all specimens.

0

50

100

150

200

S 2 - 5 0

S 3 - 5 0

S 1 - 7 5 -

A

S 1 - 7 5 - B

S 1 - 7 5 -

C

S 1 - 7 5 - D

S 2 - 7 5

S 3 - 7 5

S 1 - 1 0 0

- A

S 1 - 1 0 0

- B

S 1 - 1 0 0

- C

S 1 - 1 0 0

- D

S 2 - 1 0 0

S 3 - 1 0 0

S 2 - 1 5 0

specimen


Method A Method B ± 15% actual depth actual depth

Fig. 6 Crack depth estimates by graphically-based Methods A and B

6.1.4 Comparison of all methods

Table 4 indicates that the ultrasound pulse velocities obtained by the graphically-based

methods A and B were consistently higher than the ones obtained through the indirect mode

of transmission in the surface of sound concrete. As previously discussed, the UPV in the

concrete surface is expected to be lower than the one in the inner part of the concrete member.

Although the concrete region close to the crack might be of lower quality due to the crackingprocess, the UPV´s estimated in that region were still higher than the ones in the surface of

the concrete, as the data from Table 4 indicate.

Table 5 presents a comparison between estimates given by each method. Crack penetration

depth estimates from Bungey’s method, with transducers at 150 mm; from the BS 1881

method, with transducers at 150-300 mm, and from graphically-based methods A and B are

presented. When the arrangement of 150-300 mm as proposed by BS 1881 was not possible

(S3-50, S3-75, and S3-100), the results presented in Table 5 came from the 100-200 mm

arrangement. In order to better compare the depth estimates given by the four aforementioned

methods, the average normalized error of the estimates was calculated by Eq. 6 for eachmethod. Table 5 also presents the calculated average errors, and their standard deviation.

n

h

hhen

1i i

ii

j

∑=

−

=∆

……..……………………. (6)

where j∆ is the normalized error given by method j; hei and hi are the estimated and actual

penetration depths for specimen i respectively, and n is the total number of specimen tested.

It can be seen that the graphically-based Method A yielded a smaller normalized error withsmaller standard deviation than the other methods. While an error of approximately 10% was

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obtained when Method A was applied, the other methods yielded errors of 16 to 24%. Such

results can be better visualized in Fig. 7.

Table 5- Actual and Estimated Penetration Depths (mm)

SpecimenActual

depth

Bungey BS 1881 Method A Method B

estim.error(%)

estim.error(%)

estim.error(%)

estim.error(%)

S1-75-A 75 61 18.7 75 0.0 88 17.3 - -

S1-75-B 75 20 73.3 85 13.3 86 14.7 - -

S1-75-C 75 73 2.7 64 14.7 77 2.7 - -

S1-75-D 75 59 21.3 58 22.7 73 2.7 - -

S1-100-A 100 105 5.0 111 11.0 115 15.0 - -

S1-100-B 100 92 8.0 108 8.0 113 13.0 - -

S1-100-C 100 89 11.0 92 8.0 102 2.0 - -

S1-100-D 100 98 2.0 109 9.0 109 9.0 - -

S2-50 50 53 6.0 70 40.0 55 10.0 - -

S2-75 75 79 5.3 68 9.3 80 6.7 - -

S2-100 100 92 8.0 119 19.0 130 15.0 - -

S2-150 150 168 12.0 217 44.7 158 5.3 - -

S3-50 50 67 34.0 42 16.0 67 34.0 72 44.0

S3-75 75 44 41.3 87 16.0 76 1.3 95 26.7

S3-100 100 86 14.0 115 15.0 115 15.0 96 4.0

mean error (%) 17.5 16.4 10.9 24.9

standard dev. (%) 19.2 11.8 8.5 20.1

0

25

50

75

100

125

150

175

200225

250

Actual Crack Depth (mm)

E s t i m a t e d C r a c k D e p t h ( m m ) Bungey - 150 mm

BS 150-300 mm

Method A

Method B

50 75 100 150

Fig. 7. Comparison between estimated and actual crack penetration depth

Table 5 also shows that there was not an apparent influence of different crack widths in the

estimates. The individual normalized errors for specimens of Series 1, 2 and 3 (crack width

of 6, 0.5 and 2 mm, respectively) did not differ significantly among themselves.

6. Conclusions

Two graphically-based methods have been developed to estimate crack penetration depths

from time-of-flight measurements. The results indicated that the method developed as anextension of the one in the BS 1881 standard with at least four readings was able to improve

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the overall estimation with an estimated error close to 10%, smaller than the errors from the

others methods. This method also permits the estimation of the ultrasound pulse velocity in

the region tested.

Finally, despite of the methods available to estimate geometric characteristics of surface

opening cracks [5-7], the ultrasound time-of-flight refraction technique may still be a veryuseful tool for practical applications. It is cheap, simple and easy to perform, and gives a rapid

indication of the extension of cracking.

Acknowledgments

Funding for this study was partially provided by the Brazilian National Council for Scientific

and Technological Development (CNPq), and by LEME Engenharia, Ltda, a Brazilian

consultant engineering company. The authors express special thanks to GPEND/LEE/UFSC

where this research was performed.

References

1. BS 1881: Part 203, Recommendations for measurement of the velocity of ultrasonic

pulses in concrete, London, 1986.2. J H Bungey, S G Millard, M G Grantham, Testing of concrete in structures, 4 ed. Taylor

& Francis, 2006.

3. ACI Committee 224. Causes, evaluation, and repair of cracks in concrete structures,

ACI 224.1R-07. American Concrete Institute, 2007.

4. M J Sansalone, J Lin, W B Street, “Determining the depth of surface-openings cracks

using impact-generated stress waves and time-of-flight techniques,” ACI Materials

Journal. V. 95. No. 2, 1998.

5. M Goueygou, O Abrahan, J-F Lataste, “A comparative study of two non-destructivetesting methods to assess near-surface mechanical damage in concrete structures,”

NDT&E International. 41, 2008.6. S W Shin, J Zhu, J Min, J S Popovics, “Crack depth determination in concrete using

energy transmission of surface waves,” ACI Materials. Vol. 105. No. 5, 2008.

7. Y-F Chang, C-Y Wang, “A 3-D image detection method of a surface opening crack in

concrete using ultrasonic transducer arrays,” Journal of Nondestructive Evaluation. Vol.

16. No. 4, 1997.

8. I O Yaman, G Inci, N Yesiller, H M Aktan, “Ultrasonic pulse velocity in concrete using

direct and indirect transmission,” ACI Materials Journal. Vol. 98. No. 6, 2001.

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