DOI QR코드

DOI QR Code

Application of Fracture Toughness for Scaled Model Test

파괴인성의 축소모형실험 적용 연구

  • 김종관 (한국광물자원공사 볼레오사업실)
  • Received : 2020.02.03
  • Accepted : 2020.02.25
  • Published : 2020.02.29

Abstract

Fracture toughness of rock is a constant that can indicate the initiation and propagation of cracks due to blasting, excavation, etc. Scaled model tests have been applied to the behavior of tunnels and the stability of limestone mines. Through the scaled model, damaged zone evaluation due to blasting is also carried out, and the scale factor is not applied to the failure-related factors. In this study, DCT (diametral compression test) and finite element method ATENA2D numerical analysis results were compared to determine whether the scale factor could be applied to the fracture toughness of rock. The theoretical values of the scale factor applied to the fracture toughness of the rock and the DCT test results and the numerical results are 0.21~0.46, 0.40, and 0.99MPa ${\sqrt{m}}$ respectively, so these three values should be considered when determining scale factor. It is necessary to derive a suitable scale factor in consideration of the length, time, and mass to which the scale factor is applied, as well as the values of the scale factor of major design factors such as uniaxial compressive strength and density.

암석의 파괴인성은 발파, 굴착 등으로 인한 균열의 개시와 전파를 나타낼 수 있는 상수이다. 터널의 거동, 석회석 광산의 안정성 평가 등에 축소모형실험이 다양하게 적용되고 있다. 축소모형을 통해 발파로 인한 손상영역평가도 이뤄지고 있는데, 파괴 관련 인자에 대한 축소율 적용은 이뤄지지 않고 있다. 본 연구에서는 DCT(diametral compression test) 값과 유한요소법인 ATENA2D 수치해석 결과를 비교하여 암석의 파괴인성에 축소율을 적용할 수 있는지 확인하였다. 암석의 파괴인성에 이론적으로 계산된 축소율을 적용한 값과 DCT 시험결과 및 수치해석 결과가 각각 0.21~0.46, 0.40, 0.99MPa ${\sqrt{m}}$ 로 편차가 있으므로 암석의 파괴인성에 축소율을 적용 시에는 이 세 가지 값을 고려하여 적합한 축소율을 도출해야 하고, 축소모형 제작 시 축소율 적용 대상이 되는 길이, 시간, 질량과 함께 이로부터 산출되는 일축압축강도, 밀도 등의 주요 설계인자들의 축소율이 적용된 값을 함께 검토해야 할 것이다.

Keywords

References

  1. Andre, F.A. and Rafael, A.S, 2016, Analysis and Design of Reinforced Concrete Deep Beams by a Manual Approach of Stringer-Panel Method, Latin American Journal of Solids and Structures, 13, 1126-1151. https://doi.org/10.1590/1679-78252623
  2. Atahan, H.N., M. Kizilaslan, M.A. Tasdemir and S. Akyuz, 1997, Size effect on the failure of concrete under Mode I loading condition, Proceedings of 10th National Mechanics Congress, Istanbul, Turkey, 105-115.
  3. Atahan, H.N., M.A. Tasdemir, C. Tasdemir, N. Ozyurt and S. Akyuz, 2005, Mode I and mixed mode fracture studies in brittle materials using the Brazilian disc specimen, Materials and Structures, Vol. 38, 305-312. https://doi.org/10.1007/BF02479295
  4. Atkinson, B.K., 1976, Fracture toughness of Tennesses sandstone and Carrara marble using the double torsion testing method, Int. J. Rock Mech. & Geomech. Abstr., Vol. 16, 49-53. https://doi.org/10.1016/0148-9062(79)90774-5
  5. Atkinson, C., R.E. Smelser and J. Sanchez, 1982, Combined Mode Fracture via the Cracked Brazilian Disk Test, International Journal of Fracture, 18.4, 279-281. https://doi.org/10.1007/BF00015688
  6. Baek, Y. and W.S. Kim, 2017, Technological Development Trends for Underground Safety in Urban Construction, TUNNEL & UNDERGROUND SPACE, Vol. 27, No. 6, 2017, 343-350. https://doi.org/10.7474/TUS.2017.27.6.343
  7. Barker, L.M., 1983, Compliance calibration of a family short rod and short bar fracture toughness specimens, Energ. Fracture mech., Vol. 17, 289-312. https://doi.org/10.1016/0013-7944(83)90081-4
  8. Bazant, Z.P., 1996, Analysis of work of fracture method for measuring fracture energy of concrete, Journal of Engineering Mechanics, ASCE 122, 138-144. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:2(138)
  9. Bieniawski, Z.T., 1968, Mechanism of brittle fracture of rock, part II, Theory of the fracture process, Int. J. Rock Mech. Vol. 5, 529-549. https://doi.org/10.1016/0148-9062(68)90040-5
  10. Chang, S.H. and C.I. Lee, 1999, Measurement of rock fracture toughness under Mode I, II, & Mixed-mode conditions by using disc-typed specimens, J. of Korean Society for Rock Mech., 9, 315-327.
  11. Cotterell, B., 1972, Brittle fracture in compression, Int. J. Fract. Mech., Vol. 8, 195-208. https://doi.org/10.1007/BF00703881
  12. Hwang, J.S., J.H. Kim and J.W. Kim, 2018, Stability estimation of the closely-spaced twin tunnels located in fault zones, Tunnel and Underground Space, 28.2, 170-185. https://doi.org/10.7474/TUS.2018.28.2.170
  13. Ingraffea, A.R., 1977, Discrete fracture propagation in rocks : Laboratory test and finite element analysis, Ph.D Thesis, University of Colorado.
  14. Jeong, J.H., 2007, A Numerical Verification Study on Fracture Toughness Test, Master Thesis, Chonnam National University.
  15. Kim, J.D. and S.K. Baek, 1992, The size effect in measuring the fracture toughness of rock using chevron bend specimen, Tunnel and Underground Space, Vol.2, 251-264.
  16. Kim, J.G, H.S. Yang, 2016, Stability analysis of the inclined pillars by scaled model test, Tunnel and Underground Space, 26.6, 508-515. https://doi.org/10.7474/TUS.2016.26.6.508
  17. Kim, J.W., 2018, Evaluation of reinforcement effect of rock bolts in anisotropic rock mass using tunnel scaled model tests, Tunnel and Underground Space, 28.5, 442-456. https://doi.org/10.7474/TUS.2018.28.5.442
  18. Ko, T.Y., T.K. Kim and D.H. Lee, 2019, Determination of Mode I fracture toughness of rocks using wedge splitting test, Tunnel and Underground Space, 29.6, 523-531. https://doi.org/10.7474/TUS.2019.29.6.523
  19. Kobayashi, R., K. Matsuki and N. Otsuka, 1980, Fracture toughness of rock in splitting test - size effect of tuff specimen on fracture toughness, J. Min. Metallurgical Ins. Japan 96, 131-318. https://doi.org/10.2473/shigentosozai1953.96.1105_131
  20. Libatskii, L.L. and S.E. Kovchig, 1967, Fracture of discs containing cracks, Fiziko-Khimicheskaya Mekhanika Materialov, 458-464.
  21. O, S.H., H.S. Kim, B.A. Jang and M.C. Suh, 2000, A comparative study on dynamic & static elastic modulus of cement mortar specimens, Journal of the Korean Geophysical society, 3.2, 127-138.
  22. Otsuka, N. and R. Kobayashi, 1982, Studies on fracture toughness of various rock, J. Min. Metallurgical Ins. Japan 98, 1-6. https://doi.org/10.2473/shigentosozai1953.98.1127_1
  23. Park, H.J., H.S. Jang, S.H. Lee and C.S. Jin, 2004, Fracture toughness of a center notched concrete disk, Journal of the Korea Concrete Institute, 16.6, 851-858. https://doi.org/10.4334/JKCI.2004.16.6.851
  24. Randi, R.P., Almeida, L.C., Trautwein, L.M., Munhoz, F.S., 2018, Analysis of the influence of column reinforcement anchorage length in a concrete two-pile cap, Ibracon Structures and Materials Journal, 11.5, 1122-1150.
  25. Schmidt, R.A., 1976, Fracture toughness testing of limestone, Exp. Mech. Vol. 16, 161-167. https://doi.org/10.1007/BF02327993
  26. Tesi di Laurea, 2014, Calibration and validation of ATENA concrete material model with respect to experimental data, UNIVERSITA DEGLI STUDI DI PADOVA, 16-17.
  27. Yang, H.S. and J.G. Kim, 2007a, Fracture toughness of mortar and scaled model design, Korean society explosives engineering's proceedings, 53-59.
  28. Yang, H.S. and J.G. Kim, 2007b, Trends of research in fracture toughness of rocks, J. of Korean Society for Rock Mech., 17(6), 448-452.
  29. Yang, H.S., J.G. Kim, M.J. Choi, B.H. Choi and C.H. Ryu, 2007, Detonating cord as a controllable source for scaled model blasting test, Tunnel and Underground Space, 17.4, 295-300.
  30. Yarema, S.Ya. and G.S. Krestin, 1966, Determination of the modulus of cohesion of brittle materials by compressive tests on disc specimens containing cracks, Fiziko-Khimieheskaya Mekhanika Materialov, 2(1), 10-14.
  31. Yarema, S.Ya., G.S. Ivanitskaya, A.L. Maistrenko and A.I. Zboromirskii, 1984, Crack development in a sintered carbide in combined deformation of types I and II, Problemy Prochnosti 8, 51-56.
  32. Yoon, J.S. and S.W. Jeon, 2003, An experimental study on Mode ll fracture toughness determination of rock, Tunnel and Underground Space, 13.1, 64-75.