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Engineering infrastructure nondestructive testing with Rayleigh waves: case studies in

transportation and archaeology

View the table of contents for this issue, or go to the journal homepage for more

2007 J. Geophys. Eng. 4 268

(http://iopscience.iop.org/1742-2140/4/3/S05)

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IOP PUBLISHING JOURNAL OF GEOPHYSICS AND ENGINEERING

J. Geophys. Eng. 4 (2007) 268–275 doi:10.1088/1742-2132/4/3/S05

Engineering infrastructurenondestructive testing with Rayleighwaves: case studies in transportation andarchaeologyJinzhong Sun, Xiang Chen and Xiaofu Tian

China University of Geosciences, Beijing 100083, People’s Republic of China

E-mail: sunjinz@126.com

Received 31 August 2006Accepted for publication 4 June 2007Published 31 August 2007Online at stacks.iop.org/JGE/4/268

AbstractNondestructive testing with Rayleigh waves has been widely applied to engineeringinfrastructures and archaeological objects. Depending on the size of the objects under test andthe spacial precision requirement, Rayleigh waves with different frequencies can be used. Thekey is to identify the stable and reliable dispersion features of the entire frequency band,especially those of high frequencies. The approach taken is the precise analysis of phasedifferences between waves of different frequencies on two measuring points. In this paper, wereport two case studies associated with urban infrastructures. One is the test for the groutingtreatment effect of a road foundation which has been disturbed by culvert propulsion across ahighway. The other is the investigation of the weathering degree of a marble fence plate in theForbidden City, Beijing. These two case studies offer our insight into the application ofRayleigh waves for investigating engineering objects in accordance to different sizes, theprecision requirement, and other engineering interests.

Keywords: nondestructive testing, Rayleigh waves, frequency band, dispersion, size andprecision

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Nondestructive testing using seismic waves has been widelyapplied to engineering infrastructures and archaeologicalobjects (Zhao et al 1998, Liu and Guo 2005, Chen et al 2005).The dispersive nature of Rayleigh waves, one of the mainconstituents in a seismic wave train, was discovered in the early1950s. Since then the study of the interior structure of theearth by Rayleigh waves in the records of natural earthquakewaves began (Haskell 1953, Ewing and Press 1954, Kovachand Anderson 1964). Only after the 1970s, Rayleigh wavesstimulated by manpower were used in engineering geologicalproblems of shallow strata (Nazarian et al 1983, Wu et al 1988,Yang 1989, Chen et al 1993, Liu and Wang 1996).

Seeking dispersion curves from dispersion equations hasalways been an important topic stressed by seismologists.In order to overcome the digital loss in high frequencycomponents, Knopoff (1964), Thrower (1965) and Dunkin(1965) put forward a d-matrix method in three successivepapers, but the highest frequency of the results obtained bythis method is only several tens of Hz. Subsequently, themethod was improved by many scholars (Abo-Zena 1979,Vardoulakis and Vretto 1988, Vretto 1990a, 1990b), so that thehighest frequency of the results from the dispersion equationwas enhanced to about 800 Hz, which could basically satisfythe tests for large dimension engineering bodies, but it is stillnot high enough to perform tests for small dimension bodies,such as the test for the weathering grade of lithoid cultural

1742-2132/07/030268+08$30.00 © 2007 Nanjing Institute of Geophysical Prospecting Printed in the UK 268

Engineering infrastructure nondestructive testing with Rayleigh waves

relics, the test for the qualities of concrete structures etc. Inrecent years, the multiple rank property and its influence ondispersion curves of Rayleigh waves were revealed (Zhanget al 2000, Chen et al 2004). When a soft interlayer existsin strata, the influence of high rank surface waves will resultin a notable difference between theoretical dispersion curvesand measured ones. This problem brings many hazes anddifficulties to the calculation and interpretation of Rayleighwave dispersion curves. In order to resolve this problem, Parket al (1999), Ryden et al (2004) and Chen et al (2006) broughtforward many methods which are convenient in practice.More recently, Zhao et al (2007) using the microtremor arraymethod observed the fundamental and predominant frequencyassociated with a basin structure. Theoretical studies revealthat Rayleigh waves are one of the main causes of the observedmicrotremors.

So far, there are few case studies in which the resolutiondetail of the object detected with surface waves is smaller thanseveral millimetres. The frequency band of surface waveshas to be shifted from low to high as the size of resolutiondetail changes from large to small. This results in a seriesof technical requirements for surface wave methods such asstimulation, observation and analysis etc. Therefore, the studyof surface wave detection of objects with different sizes is apractical subject with widely applied values.

2. Theory of the detecting method with Rayleighwaves

The detecting method with Rayleigh waves is based on thefollowing physical phenomena: the phase velocities (VR) ofRayleigh waves are closely relative to the properties of themedium in which the waves are propagating; and the phasevelocities (VR) correspond to certain frequencies (f ) of thewaves (dispersion of Rayleigh waves). The distribution ofelastic wave velocities within an object can be obtained fromthe dispersion feature of the Rayleigh waves propagating in theobject. Furthermore, the engineering estimation of the objectcan be deducted from the relationship between the mediumproperties of the object and the elastic wave velocities.

2.1. Drawing the phase velocities from recordedwaveform data

2.1.1. Basic theory. Consider a coherent wave propagatingalong a surface of a medium with phase velocity VR as follows(Yang 1989):

w = A cos(ωt − kx), (1)

where A is the amplitude of the wave; k = ω/VR, ω = 2π f,f is the frequency of the wave and VR is a function of f; x isthe distance and t is time, the wave phase ϕ = ωt − kx. Ata moment t = t1 = t2, the phase difference �ϕ between thewave phases on two different sites x1 and x2 is

�ϕ = ω(x2 − x1)

VR= 2πf · �x

VR. (2)

So the formula for the phase velocity VR is as follows:

VR = 2πf · �x

�ϕ. (3)

2.1.2. Defects in traditional drawing methods for phasevelocity of Rayleigh waves. According to formula (3), thekey to drawing phase velocities from wave data is to get �ϕ.The traditional method to calculate �ϕ is cross-correlationanalysis (Wu 1997).

Let w1(t) and w2(t) represent the records respectively onsite x1 and site x2 of the same wave propagating from x1 to x2.The cross-correlation function r21(τ ) of w1(t) and w2(t) is asfollows:

r21 =∫ +∞

−∞w1(t + τ) · w2(t) dt . (4)

The Fourier transform R21(f ) of the cross-correlation functionr12(τ ) is

R21(f ) =∫ +∞

−∞r21(τ ) · e−i(2πf )τ dτ = W ∗

2 (f ) · W1(f )

= |W2(f )| · |W1(f )| · ei(ϕ1−ϕ2) = |R21(f )| · ei�ϕ (5)

in which W2(f ) and W1(f ) are the Fourier transform spectraof w2(t) and w1(t) respectively, and W ∗

2 (f ) is the conjugatespectrum of W2(f ).

Now we can see that the phase of cross-correlationspectrum R21(f ) is just the phase difference �ϕ betweensignals w1(t) and w2(t). However, we should be aware that�ϕ from formula (5) is in a defined region of tangent function,say (π/2, 3π/2). This means that �x = x2 − x1 should be inthe range (λR/4, 3λR/4), in which λR = VR/f is the Rayleighwavelength. If we want to detect something with a very highresolution, very high wave frequencies will be necessary. Asa result, the interval �x between two measuring points will beso small that there is not enough room to place two receivingtransducers on the points. In other words, the actual intervalbetween two measuring points has to be much bigger than thewavelength. This will result in a big error in the value of �ϕ

so that the phase velocity will also not be reliable.

2.1.3. Improvement in the calculation of phase difference �ϕ.In order to get reliable phase velocities of high frequencycomponents, we have to determine the value of �ϕ accurately.In fact, as shown in figure 1, the wave phase ϕ1 and ϕ2 informula (5) are the initial phases relative to the arrival timet1 and t2 of wave signal w1(t) and w2(t) respectively. Sothe phase difference �ϕ in formula (5) is only the differencebetween two initial phases, here we write it as �ϕ0, and a largeportion of phase difference caused by arrival time differenceτ = t2 − t1 is neglected. The higher the frequency is, the largerthe portion will be. The contribution of arrival time differenceτ to the phase difference should be 2π fτ . Therefore the phasedifference �ϕ should be calculated as follows:

�ϕ = �ϕ0 + 2πfτ . (6)

By this method, we can greatly enhance the precision of �ϕ

so that a much more reliable phase velocity will be derived (Qiet al 2001).

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τ

0 20 40 60 80

-40.0

0.0

40.0

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0.00

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t / ms

0.00 0.05 0.10-4.0

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4.0ϕ 1( f2 )

t /ms

t 1

t2

0.00

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0.0

4.0ϕ 2( f2 )

t /ms

0

20 40 60

80

-50.0

0.0

50.0 w2(t)

t /ms

Figure 1. Phase difference calculation.

2.2. Interpretation method of measured dispersion curves

In the light of the theoretical relationship between the featuresof dispersion curves and the medium models, the rationalexplanation about the actual medium situation of an object canbe derived from measured dispersion curves of the Rayleighwaves recorded on the object. So far, the velocity–depth curvemethod is still an easy and effective explanation method ofmeasured dispersion curves.

In this method, the curve of velocity versus frequency(dispersion curve) is first converted into the curve of velocity(VR) versus wavelength (λR) according to the relationshipbetween frequency and wavelength, and then transformedfurther into the curve of velocity versus depth in the light ofthe relationship between wavelength and effective detectingdepth (D) as follows:

D = β · λR (7)

where β is called the converting coefficient for the wavelengthto the effective penetrating depth, and is a function of Poisson’sratio. At last, the properties of media within a certain extentof depth can be explained with the curve of velocity versusdepth.

The velocity–depth curve method is somewhat imperfectin theory, though it is simple and convenient, and can alsosolve a series of problems in engineering. A better approach

is continually adjusting the medium model so as to get thetheoretical dispersion curve that is the best match with themeasured one, and the medium model corresponding tothe theoretical dispersion curve shall be the interpretationresult for the detected object (Chen and Sun 2006, Xia et al1999). In this way, not only is the theoretical rationality of theinterpretation assured, but also the information in measuredwaves is fully considered.

3. Test for the grouting treatment effect of a roadfoundation

A test for the qualities of road foundations and road surfacelayers of highways or airports deals with the depth scopesfrom several metres to several centimetres, and in the light ofthe propagating velocities (300–1000 m s−1) of surface wavesin such kinds of engineering objects, the frequency band ofthe elastic waves applied to the test should be hundreds tothousands of Hz. This kind of test in construction engineeringis of medium scale. Here a case study on the application of theRayleigh wave method is introduced to test for the groutingtreatment effect of a road foundation.

The road foundation tested is near Wulidian, Fengtaidistrict in Beijing, on the highway from Beijing toShijiazhuang. The road foundation was disturbed by culvertpropulsion in order to make a natural gas pipeline go throughthe highway (figure 2). The culvert consists of a series ofconcrete tubes which are forced into the foundation by an oiljack. The size of a single tube is as follows: axial length3 m, inner diameter 1.5 m, wall thickness about 16 cm. Thetotal length of the culvert is about 50 m; the distance fromthe top of the culvert to the ground surface of the highway isabout 7 m. After the culvert propulsion, the road foundationabove the culvert is grouted with a slurry of cement and fly-ashthrough the holes in the top wall of the concrete tubes preparedbeforehand, so as to eliminate the influence of the culvertpropulsion. In order to ensure the safety of the transportationon the highway, the grouting treatment effect of the roadfoundation should be evaluated.

SWG multiple seismic wave apparatus with 12 detectorchannels is used to record the signals of Rayleigh waves. Theobserving system of the test is shown in figure 3. In thetest, Rayleigh waves are stimulated by a 0.5 kg hand hammerknocking on the top wall inside the concrete tube so that allfrequencies of interest are covered. The measuring line is alsodistributed on the top wall parallel to the axis of the culvert.Twelve wave detectors with a natural resonance frequency of100 Hz are fixed on the top wall of the culvert with gypsumto form a detecting array in which the interval between twoadjacent detectors is 0.5 m so that each array of detectors maycover 5.5 m of the measuring line. The end detector of an arrayis set as the first detector of the next array so as to ensure therecorded wave data continuously cover the whole measuringline. So there are 9 arrays across the highway from south tonorth.

The phase velocity distribution along the depth betweentwo adjacent measuring points (the curve of phase velocityversus depth) may be obtained from the dispersion curve drawn

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Engineering infrastructure nondestructive testing with Rayleigh waves

Figure 2. Location of the road section where the gas pipeline crosses (in red circle). http://en.beijing2008.cn/06/78/emap.shtml, copyrightThe Beijing Organizing Committee for the Games of the XXIX Olympiad.

Roadfoundation

Concrete culvert

Section A–A

X / m

⋅⋅⋅⋅⋅⋅⋅Concrete culvert

Road foundation

Source Detector

H / m

N S

0

A

A(a) (b) Section S–N

Figure 3. Schematic for observing a system of Rayleigh waves inside the concrete culvert.

0.5

1.0

1.5

2.0

2.5

3.0

0.0800 1200 1600 2000

H / m

VR / m⋅s-1

VR H curve at – x = 38.75 m (a) (b) Waveforms in the 8th array

12345678910 11 12

0 2.5 5.0 7.5 10 / ms

Figure 4. Measurement of VR–H curve of the road foundation above the concrete pipe.

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5 10 15 20 25 30 35 40 45

1

3

1

3

200 600 1000 1400 1800 2200

NSH / m H / m

X / m

VR / m⋅s-1

Figure 5. Distribution of Rayleigh wave velocities in the road foundation above the concrete pipe.

CT measuring line

Surface wave measuring line

Figure 6. The first marble fence plate on the west side in front of Wuying Hall, Forbidden City, Beijing.

Pulse Transducer

15 cm ∆X = 5cm

X = 0

H

E

Marble plate 15cm thick

X

Figure 7. Schematic of the observation system of Rayleigh waveson the top of the marble plate.

from the two waveforms recorded on these two measuringpoints as shown in figure 4. Actually, there are 9 arrays ofwaveforms, and 99 curves of phase velocity versus depth canbe obtained.

The distribution of Rayleigh wave velocities in the roadfoundation across the highway is formed by the combinationof the 99 curves of phase velocity versus depth obtained fromall measurements (as shown in figure 5), and from the first twomeasurement points in the first array to the last two measuringpoints in the 9th array, the range of the road foundation detectedby Rayleigh waves is about 0.25–49 m.

Generally, the density of soil mass is in direct ratio to itselastic wave velocity. So, based on the distribution of Rayleigh

0 400 800 1200 1600 2000

1

2

3

4

5

6

7

8

t / µs

Rayleigh wave

Figure 8. Waveforms measured on the top of the marble plate.

wave velocities in the road foundation, we can further analyzethe influence of the culvert propulsion construction on the roadfoundation.

According to the distribution of Rayleigh wave velocitiesin the road foundation, we can make the following observationsabout the influence of the culvert propulsion construction onthe road foundation.

(1) The disturbance of culvert propulsion to the soil mass ofthe road foundation is very small, and the road foundationis in normal condition.

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Engineering infrastructure nondestructive testing with Rayleigh waves

X = 15 cm

0

5

10

15

20

25

30

400 800 1200 1600 2000VR /m⋅s-1

H / cm X = 20 cm

0

5

10

15

20

25

30

0 400 800 1200 1600

H / cm

VR / m⋅s-1

X = 25 cm

0

5

10

15

20

25

30

400 600 800 1000 1200

H / cm

VR / m⋅s-1

X = 10 cm

0

5

10

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20

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30

200 400 600 800 1000 1200

H / cm

VR / m⋅s-1

X = 5 cm

0

5

10

15

20

25

30

400 600 800 1000 1200 1400

H / cm

VR / m⋅s-1

X = 0 cm

0

5

10

15

20

25

200 400 600 800 1000 1200

H / cm

VR / m⋅s-1

X = 30 cm

0

5

10

15

20

25

30

700 800 900 1000 1100 1200

H / cm

VR / m⋅s-1

Figure 9. VR–H curves interpreted from Rayleigh waves measured on the top of the marble plate (X = 0–30 cm).

(2) The grouting effect is evident, and the soil mass near theculvert is obviously consolidated.

(3) After culvert propulsion construction and groutingreinforcement, the road foundation above the top ofculvert is in a good physical and mechanical state so thatsafe continuation of the highway can be guaranteed.

The detected results above show that the Rayleigh wavemethod is very effective when testing for the quality of roadfoundation.

4. Assessment of the degree of weathering for lithoidcultural relics

The Forbidden City, a world-class cultural heritage sitewith a large number of white marble fence plates and rareinscriptions, has important historical significance and is highlyworthy of protection. Owing to their great age and theinfluence of the environment, these lithoid cultural relics arebecoming seriously eroded, and some of them have evenpartially become powder.

The height of the marble fence is less than 60 cm, andthe thickness is about 15 cm. The request for the spatialresolution of weathering degree detection is on the level ofcentimetres or even millimetres. Such small scale detectingrequires elastic waves of a much higher frequency than that inthe road foundation test. For this reason, Rayleigh waves ofultrasonic frequency are applied in the investigation of the firstplate of the marble fence on the west side in front of WuyingHall in the Forbidden City (as shown in figure 6).

The observation system of Rayleigh waves is as shownin figure 7. The measuring points from right to left aresuccessively numbered as 1 to 8. DB16 Multiwave ParameterApparatus is used in wave data observing and recording.Waves are stimulated by a slight pulse generated with a verysmall hammer weighing 0.2 kg on the top surface of thefence plate. The distance between the stimulating point andthe first measuring point is about 10 cm (approximately onewavelength). To pick up the ultrasonic waves, 8 piezoelectricporcelain transducers with a natural resonance frequency of50 kHz are stuck on 8 measuring points distributed on the

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VR /m⋅s-1

100

300

500

700

900

1100

1300

1500

1700

cm H /cm

X /cm 0510 15 20 2530

5

10

15

20

25

5

10

15

20

25

E

A A

Figure 10. Vertical section of VR distribution across the first marble fence plate on the west side in front of Wuying Hall, Forbidden City,Beijing (A–A orientation: CT section line).

measuring line with intervals �X = 5 cm, and the wavesignals picked up are transformed into digital records withtime intervals �t = 2 µs by the apparatus. The measuredwaveforms on eight measuring points are as shown infigure 8.

Analyzing the recorded wave signals two by two from8 measuring points may result in 7 curves of phase velocityversus depth (VR–H) as shown in figure 9. Combining these 7curves will form a section of wave velocity distribution beneaththe measuring line in a certain range of depth as shown infigure 10.

Figure 10 reveals that there are three seriously weatheredareas in the marble plate: one is at the bottom near the middleof the section, and the other two are at the east end on the topof the marble plate. The influence depths of the two seriouslyweathered areas on the top are 5–8 cm. There is a highvelocity area from the western top to the eastern bottom of thesection between the high and low seriously weathered areas,which reflects the light weathering degree in the middle partof the marble plate. The velocity isolines densely distributedbetween high and low velocity areas are relative to the gradebelt of velocity variation in the marble plate.

The observation of the marble plate on site shows that thepositions where the dense velocity isolines are distributed arejust in accordance with a developing area of natural veins inthe marble plate, and the extending direction of the naturalveins is parallel to the isolines. This indicates the rationalityof the result detected by the Rayleigh wave method, and alsotells us that the weathering degree of the marble plate is closelyrelated to its natural texture.

In order to check the result from the Rayleigh wavemethod, the CT wave velocity reconstruction method withultrasonic transmitting waves is also applied to the samemarble plate. The observation system of CT on the plateis as shown in figure 11. The velocity distribution section

E Transducer

15 cm

∆X=5 cm

H=15 cm

X = 0

X

A A

X

YA–A orientation

North side

0

Stimulating transducer

Receiving transducer

15 c

m

Figure 11. Schematic for the observation system of ultrasonic CTon the marble plate.

resulting from the ultrasonic CT method is shown in figure 12.Compared with the result from the Rayleigh wave method,the CT section (figure 12) vertically cuts the section fromthe Rayleigh wave method (figures 10 and 11) at a depth of15 cm.

As shown in figure 12 there is also a relatively highvelocity zone in the middle part of the section, and P-wavevelocity (Vp) distribution in the CT section is accordantwith R-wave velocity (VR) distribution in the section fromthe Rayleigh wave method as shown in figure 10. Thisagain confirms the feasibility of the Rayleigh wave methodto weathering degree detection in lithoid cultural relics.

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Engineering infrastructure nondestructive testing with Rayleigh waves

0510152025300

5

10

15

0

5

10

15 2200

2600

3000

3400

3800

4200

4600

X /cm

Y / cm

VP / m⋅s-1

Figure 12. Horizontal CT section of the first marble fence plate on the west side in front of Wuying Hall, Forbidden City, Beijing.

5. Conclusions

In this paper, according to the relationship between wavefrequency and detecting scale, the Rayleigh wave detectionmethod is applied in a test for the grouting treatment effectof a road foundation and in detection of the weatheringdegree of a marble fence plate in the Forbidden City. Thefeasibility of the Rayleigh wave method for engineeringmass bodies of different dimension scales or for differentrequirements of spatial resolution is tested. Stimulation,observation and explanation of Rayleigh waves with differentfrequency bands are explored so that a methodological seriesof Rayleigh wave detection with low to high frequencies isformed. This offers a foundation for the application of theRayleigh wave method in nondestructive testing for variousprojects.

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