Abstract
Lattice methods, namely the lattice Boltzmann method and the lattice spring model, can be successfully used to address acoustic wave propagation in dry and saturated porous media. The resulting code can upscale porous media properties or study direct time simulations in complex media. Only the second application is detailed here for various flat media which contain or not a cavity, which possess uniform properties or not; an explosion is simulated and the accelerations are measured at the surface. The data show that when the medium is simple, the cavity can be easily located, which is not true when it is heterogeneous.
Similar content being viewed by others
References
Adler PM, Jacquin CG, Quiblier JA (1990) Flow in simulated porous media. Int J Multiph Flow 16:691–712
Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511
Biot MA (1956a) Theory of propagation of elastic waves in a fluid-saturated porous solid. low-frequency range. J Acoust Soc Am 28:168
Biot MA (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid. Higer frequency range. J Acoust Soc Am 28:179
Boutin C, Auriault JL (1990) Dynamic behaviour of porous media saturated by viscoelastic fluid. Application to bituminous concretes. Int J Eng Sci 28:1157
Bouzidi M, Firdaouss M, Lallemand P (2001) Momentum transfer of a lattice-Boltzmann fluid with boundaries. Phys Fluids 13:3452
Buxton GA, Balazs AC (2004) Modeling the dynamic fracture of polymer blends processed under shear. Phys Rev B 69:054101
Buxton GA, Verberg R, Jasnow D, Balazs AC (2005) Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Phys Rev E 71:056707
d’Humières D, Ginzburg I, Krafczyk M, Lallemand P, Li-Shi L (2002) Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil Trans R Soc Lond A360:437
Faccioli E, Maggio F, Paolucci R, Quarteroni A (1997) 2D and 3D elastic wave propagation by a pseudo-spectral domain decomposition method. J Seismol 1:237–251
Ginzbourg I, Adler PM (1994) Boundary flow condition analysis for the three-dimensional lattice Boltzmann model. J Phys II Fr 4:191
Ginzburg I, d’Humières D (2003) Multireflection boundary conditions for lattice Boltzmann models. Phys Rev E 68:066614
Gochioco LM (1990) Seismic surveys for coal exploration and mine planning. Lead Edge 9:25–28
Grandjean G, Leparoux D (2004) The potential of seismic methods for detecting cavities and buried objects: experimentation at a test site. J Appl Geophys 56:93
Ladd AJC, Kinney JH (1997) Elastic constants of cellular structures. Physica A 240:349
Ladd AJC, Verberg R (2001) Lattice-Boltzmann simulations of particle-fluid suspensions. J Stat Phys 104:1191. https://doi.org/10.1023/A:1010414013942
Ladd AJC, Kinney JH, Breunig TM (1997) Deformation and failure in cellular materials. Phys Rev E 55:3271
Luo L-S (2000) Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases. Phys Rev E 62:4982. https://doi.org/10.1103/PhysRevE.62.4982
Malinouskaya I (2007) Propagation des ondes acoustiques dans les milieux hétérogènes. Ph. D. Thesis
McNamara GR, Zanetti G (1988) Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 61:2332
Nguyen N-Q, Ladd AJC (2002) Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys Rev E 66:046708
O’Brien GS, Bean CJ (2004) A discrete numerical method for modeling volcanic earthquake source mechanisms. J Geophys Res 109:B09301
Ostoja-Starzewski M (2002) Lattice models in micromechanics. Appl Mech Rev 55:35
Pazdniakou A, Adler PM (2012) Lattice spring models. Transp Porous Media 93: 243
Pazdniakou A, Adler PM (2013) Dynamic permeability of porous media by the lattice Boltzmann method. Adv Water Resour 62:292
Piwakowski B, Waletet JM, Moreaux D (1997) High resolution seismic prospection of old gypsum mines—evaluation of detection possibilities. Eur J Environ Eng Geophys 2:109–120
Sanchez-Palencia E (1980) Non homogeneous media and vibration theory. Springer, Berlin
Shtivelman V (2001) Shallow water seismic surveys for site investigation in the Haifa port extension area. Israel J Appl Geophys 46:147–162
Virieux J (1986) P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51:889–901
Wang J (1989) The bond-bending model in three dimensions. J Phys A Math Gen 22:L291
Wu J, Aidun CK (2010) Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force. Int J Numer Methods Fluids 62:765–783
Acknowledgements
This work was performed when P.M.A. was supported at the Mechanical Engineering Department, Technion, Haifa, Israel, by a fellowship of the Lady Davis Foundation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Adler, P.M., Pazdniakou, A. Wave Propagation in Heterogeneous Media with Cavities by an LSM/LBM-Coupled Model. Rock Mech Rock Eng 51, 3907–3923 (2018). https://doi.org/10.1007/s00603-018-1602-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-018-1602-2