Geomechanics and Engineering

Techno-Press (테크노프레스)
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Theoretical and numerical analysis of the influence of initial stress gradient on wave propagations

  • Tao, Ming (School of Resources and Safety Engineering, Central South University) ;
  • Chen, Zhenghong (School of Resources and Safety Engineering, Central South University) ;
  • Li, Xibing (School of Resources and Safety Engineering, Central South University) ;
  • Zhao, Huatao (School of Resources and Safety Engineering, Central South University) ;
  • Yin, TuBing (School of Resources and Safety Engineering, Central South University)
  • Received : 2015.08.30
  • Accepted : 2015.12.17
  • Published : 2016.03.25
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Abstract

The investigation of stress wave propagation in a medium with initial stress has very important application in the field of engineering. However, the previous research less consider the influence of initial stress gradient on wave propagation. In the present paper, the governing equation of wave propagation in elastic continuum material with inhomogeneous initial stress is derived, which indicated that the inhomogeneous initial stress changed the governing equation of wave propagation. Additionally, the definite problem of wave propagation in material with initial stress gradient is verified by using mathematical physics method. Based on the definite problem, the elastic displacement-time relationship of wave propagation is explored, which indicated that the inhomogeneous initial stress changed waveform and relationship of displacement-time histories. Furthermore, the spall process of blasting wave propagation from underground to earth surface is simulated by using LS-DYNA.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Asef, M.R. and Najibi, A.R. (2013), "The effect of confining pressure on elastic wave velocities and dynamic to static Young's modulus ratio", Geophysics, 78(3), 135-142.
  2. Biot, M.A. and Drucker, D.C. (1965), "Mechanics of incremental deformation", J. Appl. Mech., 32(4), 957.
  3. Bromwich, T.J. I'A. (1898), "On the influence of gravity on elastic waves, and, in particular on the vibrations of an elastic globe", Proceedings of the London Mathematical Society, 1(1), 98-120.
  4. Dhua, S. and Chattopadhyay, A. (2015), "Torsional wave in an initially stressed layer lying between two inhomogeneous media", Meccanica, 50, 1-15. https://doi.org/10.1007/s11012-014-0082-z
  5. Hallquist, J.O. (2007), LS-DYNA keyword user's manual, Livermore Software Technology Corporation, Version 970.
  6. Ji, S.C., Wang, Q., Marcotte, D., Salisbury, M.H. and Xu, Z.Q. (2007), "P wave velocities, anisotropy and hysteresis in ultrahigh-pressure metamorphic rocks as a function of confining pressure", J. Geophys. Res.: Solid Earth, 112(B9), 685-693.
  7. Ji, S.C., Li, A., Wang, Q., Long, C.X., Wang, H.C., Marcotte, D. and Salisbury, M.H. (2013a), "Seismic velocities, anisotropy, and shear-wave splitting of antigorite serpentinites and tectonic implications for subduction zones", J. Geophys. Res.: Solid Earth, 118(3), 1015-1037. https://doi.org/10.1002/jgrb.50110
  8. Ji, S.C., Shao, T.B., Michibayashi, K., Long, C.X., Wang, Q., Kondo, Y. and Salisbury, M.H. (2013b), "A new calibration of seismic velocities, anisotropy, fabrics, and elastic moduli of amphibole-rich rocks", J. Geophys. Res.: Solid Earth, 118(9), 4699-4728. https://doi.org/10.1002/jgrb.50352
  9. Kakar, R. and Kakar, S. (2014), "Electro-magneto-thermoelastic surface waves in non-homogeneous orthotropic granular half space", Geomech. Eng., Int. J., 7(1), 1-36. https://doi.org/10.12989/gae.2014.7.1.001
  10. Kumar, R. and Kumar, R. (2013), "Wave propagation at the boundary surface of elastic and initially stressed viscothermoelastic diffusion with voids media", Meccanica, 48(9), 2173-2188. https://doi.org/10.1007/s11012-013-9732-9
  11. Li, X.B. and Tao, M. (2015), "The influence of initial stress on wave propagation and dynamic elastic coefficients", Geomech. Eng., Int. J., 8(3), 377-390. https://doi.org/10.12989/gae.2015.8.3.377
  12. Mahmoud, S.R., Tounsi, A., Ahmed, T.A. and Al-Basyouni, K.S. (2014), "The effect of initial stress and magnetic field on wave propagation in human dry bones", Bound. Value Probl., 2014(1), 1-13. https://doi.org/10.1186/1687-2770-2014-1
  13. Ogden, R.W. and Singh, B. (2014), "The effect of rotation and initial stress on the propagation of waves in a transversely isotropic elastic solid", Wave Motion, 51(7), 1108-1126. https://doi.org/10.1016/j.wavemoti.2014.05.004
  14. Sethi, M., Bhardwaj, R. and kamal Sharma, A. (2014), "Surface waves in homogeneous visco-elastic media of higher order under the influence of gravity and surface stresses", Adv. Phys. Theor. Appl., 30, 65-77.
  15. Shen, J. and Karakus, M. (2015), "Simplified method for estimating the Hoek-Brown constant for intact rocks", J. Geotech. Geoenviron. Eng., 140(6), 971-984.
  16. Tao, M., Li, X.B. and Wu, C.Q. (2012), "Characteristics of the unloading process of rocks under high initial stress", Comput. Geotech., 45, 83-92. https://doi.org/10.1016/j.compgeo.2012.05.002
  17. Tao, M., Li, X.B. and Wu, C.Q. (2013), "3D numerical model for dynamic loading-induced multiple fracture zones around underground cavity faces", Comput. Geotech., 54, 33-45. https://doi.org/10.1016/j.compgeo.2013.06.002
  18. Tolstoy, I. (1982), "On elastic waves in prestressed solids", J. Geophys. Res.: Solid Earth, 87(B8), 6823-6827. https://doi.org/10.1029/JB087iB08p06823
  19. Vinh, P.C. and Linh, N.T.K. (2013), "Rayleigh waves in an incompressible elastic half-space overlaid with a water layer under the effect of gravity", Meccanica, 48(8), 2051-2060. https://doi.org/10.1007/s11012-013-9723-x
  20. Vinh, P.C. and Seriani, G. (2010), "Explicit secular equations of Stoneley waves in a non-homogeneous orthotropic elastic medium under the influence of gravity", Appl. Math. Computat., 215(10), 3515-3525. https://doi.org/10.1016/j.amc.2009.10.047
  21. Wang, Q., Ji, S.C., Sun, S.S. and Marcotte, D. (2009), "Correlations between compressional and shear wave velocities and corresponding Poisson's ratios for some common rocks and sulfide ores", Tectonophysics, 469(1), 61-72. https://doi.org/10.1016/j.tecto.2009.01.025
  22. Zhao, Z., Niu, Y., Christensen, N.I., Zhou, W., Hou, Q., Zhang, Z.M., Xie, H., Zhang, Z.C. and Liu, J. (2011), "Delamination and ultra-deep subduction of continental crust: constraints from elastic wave velocity and density measurement in ultrahigh-pressure metamorphic rocks", J. Metamor. Geol., 29(7), 781-801. https://doi.org/10.1111/j.1525-1314.2011.00941.x

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