All Issue

2007 Vol.9, Issue 4 Preview Page
Guidedwave-induced rockbolt integrity using Fourier and wavelet transforms

유도파에 대한 푸리에 및 웨이브렛 변환을 이용한 록볼트의 건전도 평가

In-Mo Lee1*
,
Hyun-Jin Kim2
,
Shin-In Han3
,
Jong-Sub Lee4
이 인모1*
,
김 현진2
,
한 신인3
,
이 종섭4
1고려대학교 공과대학 건축사회환경공학과 교수
2고려대학교 공과대학 건축사회환경공학과 석사과정
3고려대학교 공과대학 건축사회환경공학과 박사과정
4고려대학교 공과대학 건축사회환경공학과 조교수
*교신저자. *Corresponding Author. 
31 December 2007. pp. 403-413
PDF XML Citation
Abstract

As rock bolts become one of the main support systems in tunnels and underground structures, the integrity of the rock bolts affects the safety of these types of structures. The purpose of this study is the evaluation of rock bolt integrity using Fourier and wavelet transforms of the guided ultrasonic waves. After five rock bolt specimens with various defect ratios are embedded into a large scale concrete block, guided waves are generated by a PZT (lead zirconate titanate) element and measured by an acoustic emission (AE) sensor. The captured signals are analyzed in the frequency domain using the Fourier transform, and in the time-frequency domain using the wavelet transform based on a Gabor wavelet. The spectrum obtained from the Fourier transform shows that a portion of high frequency contents increases with increase in the defect ratio. Peak values in the time-frequency domain represent the interval of travel time of each echo. The energy velocities of the guided waves increase with the defect ratio. This study shows that the spectrum ratio and the energy velocity may be indicators for the evaluation of rock bolt integrity.

Keywords
Energy velocity
Fourier transform
guided wave
non-destructive test
spectrum
wavelet transform

터널과 같은 지하공간 구조물에 있어서 록볼트는 숏크리트와 함께 주요 지보재 중의 하나이며, 그러므로 록볼트 시공품질 정도에 따라 이러한 지중구조물의 안정성에 큰 영향을 미치게 된다. 본 연구의 목적은 록볼트를 따라 전파되는 유도파에 대하여 푸리에 및 웨이브렛 변환을 이용하여 록볼트의 건전도를 평가하는데 있다. 각기 다른 결함비율을 가진 다섯 개의 록볼트 시험체를 제작하여 콘크리트 블록에 매설한 후, PZT(Pb[ZrxTi1-x]O3: lead zirconate titanate) 엘리먼트로 유도파를 발생시키고 AE(acoustic emission) 센서를 이용하여 신호를 측정하였다. 수집된 신호는 푸리에 변환을 이용하여 주파수 영역에서 분석하였고, 가버 웨이브렛을 사용한 웨이브렛 변환을 이용하여 시간-주파수영역에서 분석하였다. 푸리에 변환을 이용하여 얻은 스펙트럼을 분석하면 록볼트의 결함비율이 증가함에 따라 고주파 대역 에너지의 비율이 증가하는 것을 알 수 있다. 또한, 시간-주파수 영역에서의 각 파군별 최대 에너지가 나타나는 지점의 시간차는 각 반사파군 간의 이동 시간차를 나타내며, 이를 통해 계산된 유도파의 에너지 속도는 록볼트의 공동결함비율이 증가함에 따라 증가하는 것으로 나타났다. 본 연구는 스펙트럼 비와 에너지 속도가 록볼트의 건전도 평가에 있어서 하나의 지표가 될 수 있음을 보여준다.

키워드
에너지 속도
푸리에 변환
유도파
비파괴 시험
스펙트럼
웨이브렛 변환
References
1
1.Beard, M. D., Lowe, M. J. S., Cawley, P. (2003), “Ultra-sonic guided waves for inspection of grouted tendon and bolts.”, Journal of Materials in Civil Engineering, ASCE, Vol. 15, No. 3, pp. 212-218.
2
2.Douka, E., Loutridis, S., Trochidis, A. (2003), “Crack identi-fication in beams using wavelet analysis.”, International Journal of Solids and Structures, Vol. 40, pp. 3557-3569.
3
3.Han, S. I., Lee, I. M., Lee, Y. J., Lee, J. S. (2006), “Integrity evaluation of rockbolts encapsulated by cement-mortar grouting using ultrasonic guided waves.”, Proc., 27th Sym-posium on Ultrasonic Electronic, 27, Nagoya, pp. 177-178.
4
4.Hong, J. C., Kim, Y. Y. (2004), “Determination of the optimal Gabor wavelets shape for the best time-frequency localization using the entropy concept.”, Experimental Mechanics, Vol. 44, No. 4, pp. 387-395.
5
5.Inoue, H., Kishimoto, K., Shibuya, T. (1996), “Experi-mental wavelet analysis for flexural waves in beams.”, Experimental Mechanics, Vol. 36, No. 3, pp. 212-217.
6
6.Jeong, H. J., Jang, Y. S. (2000), “Fracture source location in thin plates using the wavelet transform of dispersive waves.”, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 47, No. 3, pp. 612-619.
7
7.Kim, H., Melhem, H. (2003), “Fourier and wavelet analyses for fatigue assessment of concrete beams.”, Experimental Mechanics, Vol. 43, No. 2, pp. 131-140.
8
8.Kim, Y. Y. and Kim, E. H. (2001), “Effectiveness of the continuous wavelet transform in the analysis of some dispersive elastic waves.”, Journal of Acoustical Society of America, Vol. 110, No. 1, pp. 86-94.
9
9.Kishimoto, K., Inoue, H., Hamada, M., Shibuya, T. (1995), “Time-frequency analysis of dispersive waves by means of wavelet transform”, Journal of Applied Mechanics, Vol. 62, pp. 841-846.
10
10.Kumar, P., Foufoula-Georgiou, E. (1994), “Wavelet analysis in geophysics: An introduction, Wavelet analysis and its application”, Volumn 4 - Wavelets in Geophysics, Foufoula- Georgiou and Kumar eds., Academic Press. New York.
11
11.Lee, I. M., Bae, G. J., Lee, S. W., Lee, J. G. (2004), “Soundness evaluation of a tunnel concrete lining by using the hammer impact-induced sound wave.”, Key Engineering Materials, Vol. 270-273, pp. 1500-1505.
12
12.Newland, D. E. (1993), “Harmonic wavelet analysis.”, Proc., Mathematical and Physical Science, Vol. 443, No. 1917, pp. 203-225.
13
13.Onsay, T., Haddow, A.G. (1994), “Wavelet transform analy-sis of transient wave propagation in a dispersive medium.”, Journal of Acoustical Society of America, Vol. 95, No. 3, pp. 1441-1449.
14
14.Santamarina. J. C., Fratta, D. (2005), “Discrete signals and inverse problems: An introduction for engineers and scientists”, Wiley, New York.
15
15.Sato, M. (1991), “Mathematical foundation of wavelets.”, Journal of Acoustical Society of Japan, Vol. 47, No. 6, pp. 405-423 (in Japanese).
16
16.Thurner, H. F. (1988), “Boltometer-instrument for non- destructive testing of grouted rock bolts.”, Proc., 2nd Inter-national Symposium on Field Measurements in Geome-chanics, Sakurai(ed.), Rotterdam, pp. 135-143.
17
17.Wang, L. (2004), “Elastic wave propagation in composites and least-square damage location technique”, MSc Thesis, North Carolina State University, NC.
18
18.Zhang, C. S., Zou, D. H., and Madenga, V. (2006), “Nu-merical simulation of wave propagation in grouted rock bolts and the effects of mesh density and wave frequency.”, International Journal of Rock Mechanics and Mining Sciences, Vol. 43, No. 4, pp. 634-639.
Information
  • Publisher :Korean Tunneling and Underground Space Association
  • Publisher(Ko) :한국터널지하공간학회
  • Journal Title :Journal of Korean Tunnelling and Underground Space Association
  • Journal Title(Ko) :한국터널지하공간학회 논문집
  • Volume : 9
  • No :4
  • Pages :403-413
Journal Informaiton Journal of Korean Tunnelling and Underground Space Association Journal of Korean Tunnelling and Underground Space Association
Online Submission & Review System
  • NRF
  • KOFST
  • KISTI Current Status
  • KISTI Cited-by
  • crosscheck
  • orcid
  • open access
  • ccl
Journal Informaiton Journal Informaiton - close