A DR-BEM Model for a Half-Space Including the Cavity under Scalar Surface Pulse

Document Type : Original Article

Authors

1 Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran

Abstract

In this paper, a two-dimensional half-space model is presented in the presence of a subsurface circular cavity under a uniform surface scalar pulse. In this regard, a dual reciprocity boundary element method (DR-BEM) was successfully developed, in which the discretizing process was only applied to the boundary of the model as well as a few internal points. The simple formulation and step-by-step transient analysis in the absence of time-domain fundamental solutions were some of the characteristics of the implemented approach. First, by introducing the method and briefly presenting the formulation, a time-domain algorithm was prepared based on the mentioned approach, then it was validated by comparing with the existing analytical solutions. Moreover, by modeling a half-space domain including a subsurface circular cavity, the transient displacement was obtained at different points of the ground surface and the cavity wall, subjected to the surface pulse of the Ricker wavelet type function. The results showed that the presence of the cavity was effective not only in changing the distribution pattern, but also in the formation of safe areas behind the wave front. The efficient approach is recommended to all researchers in the field of geotechnical earthquake engineering, especially in the analysis of surface explosions.

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References

  1. Kramer, S., Geotechnical Earthquake Engineering, Prentice Hall, London, 1996.
  2. Charles, E., Anderson, Jr., Behner, T., and Carl, E. W., “Mine Blast Loading Experiments”, International Journal of Impact Engineering, Vol. 38, pp. 697-706, 2011.
  3. An, J., Tuan, C. Y., ASCE, F., Cheeseman, B. A., and Gazonas, G. A., “Simulation of Soil Behavior under Blast loading”, International Journal of Geotechnics, Vol. 10, pp. 323-334, 2011.
  4. Feldgun, V. R., Kochetkov, A. V., Karinski, Y. S., and Yankelevsky, D. Z., “Blast Response of a Lined Cavity in a Porous Saturated Soil”, International Journal of Impact Engineering, Vol. 35, pp. 953-966, 2008.
  5. Abedi, A. S., Hataf, N., and Ghahramani, A., “Analytical Solution of the Dynamic Response of Buried Pipelines Under Blast Wave”, International Journal of Rock Mechanics & Mining Sciences, Vol. 88, pp. 301-306, 2016.
  6. Wu, Z., Rao, P., Nimbalkar, S., Chen, Q., Cui, J., and Ouyang, P., “A Semi-Analytical Solution for Shock Wave Pressure and Radius of Soil Plastic Zone Induced by Lightning Strikes”, Materials, Vol. 15, No. 2239, pp. 2-18, 2022.
  7. Huang, B., Gao, Q., Wang, J., Jiang, X., Wang, X., Jiang, B., and Wu, W., “Dynamic Analysis of Pile-Soil-Structure Interaction System Under Blasting Load”, Applied Mechanics and Materials, Vol. 638, pp. 433-436, 2014.
  8. Seyedan, M. J., and Seyedi Hosseininia, E., “Significance of Soil Compaction on Blast Resistant Behavior of Underground Structures: A Parametric Study”, Civil Engineering Infrastructures Journal, Vol. 48, No. 2, pp. 359-372, 2015.
  9. Malekshahi, M., and Akhaveissy, A. H., “Experimental Study of Masonry Structure under Impact Loading and Comparing it with Numerical Modeling Results via Finite Element Model Updating”, Journal of Rehabilitation in Civil Engineering, Vol. 8, pp. 90-105, 2020.
  10. Mandal, J., and Goel, M. D., “Effect of Geo-Material on Dynamic Response of Tunnel Subjected to Surface Explosion”, Geotechnics, Vol. 2, pp. 635-648, 2022.
  11. Banerjee, P. K., and Butterfield, R., Boundary Element Method in Geomechanics, Wiley, London, 1977.
  12. Brebbia, C. A., and Dominguez, J., Boundary Elements an Introductory Course, Computational Mechanics Publications, ISBN: 1562520873, 1992
  13. Dominguez J., Boundary Element in Dynamics. Computational Mechanics Publications. ISBN: 1562521829, 1993.
  14. Auersch, L., and Schmid, G., “A simple Boundary Element Formulation and Its Application to Wavefield Excited Soil-Structure Interaction”, Earthquake Engineering and Structural Dynamics, Vol. 19, pp. 931-947, 1990.
  15. Chen, H., Zhou, J., Fan, H., Jin, F., Xu, Y., Qiu, Y., Wang, P., and Xie, W., “Dynamic Responses of Buried Arch Structure Subjected to Subsurface Localized Impulsive Loading: Experimental Study”, International Journal of Impact Engineering, 1-57, 2013.
  16. Abtahi, F., Hosseini, M., and Shah Hosseini, A., “Effect of Blast Loading on Stability of Ghareh Changool Ramp in Zehabad Lead and Zinc Mine”, Journal of Engineering Geology, Vol. 13, No. 3, pp. 339-364, 2019.
  17. Panji, M., and Ansari, B., “Modeling Pressure Pipe Embedded in Two-Layer Soil by a Half-Plane BEM”, Computers and Geotechnics, Vol. 81, pp. 360-367, 2017a.
  18. Panji, M., and Ansari, B., “Transient SH-Wave Scattering by the Lined Tunnels Embedded in an Elastic Half-Plane”, Engineering Analysis with Boundary Elements, 84, pp. 220-230, 2017b.
  19. Nardini, D., and Brebbia, C. A., “A New Approach to Free Vibration Analysis using Boundary Elements”, Applied Mathematical Modelling, Vol. 7, pp. 157-162, 1983.
  20. Wrobel, L. C., and Brebbia, C. A., “The dual Reciprocity Boundary Element Formulation for Nonlinear Diffusion Problems”, Computer Methods in Applied Mechanics and Engineering, Vol. 65, pp. 147-164, 1987.
  21. Partridge, P. W., Brebbia, C. A., and Wrobel, L. C., The Dual Reciprocity Boundary Element Method. Computational Mechanics Publications, ISBN: 0945824823, 1992.
  22. T, “Wave Propagation In Homogeneous Elastic Half-Space Using The Dual Reciprocity Boundary Element Method”, Ph.D Thesis, Faculty of Civil Engineering of the Ruhr University Bochum, 2005 .
  23. F, Feng. X. and Zhou. H, “A Dual Reciprocity Hybrid Radial Boundary Node Method Based on Radial Point Interpolation Method”, Computational Mechanics, Vol. 45, pp. 541-552, 2010.
  24. Yu, B., Cao, G., Huo, W., Zhou, H., and Atroshchenko, E., “Isogeometric Dual Reciprocity Boundary Element Method for Solving Transient Heat Conduction Problems with Heat Sources”, Journal of Computational and Applied Mathematics, Vol, 385, No. 113197, pp. 1-20, 2021.
  25. A. F., Prada. D. M., Moura. L. S., Zavaglia. C., Foster. J. M., Sollero. P., and Wrobel. L. C., “BESLE: Boundary Element Software for 3D Linear Elasticity”, Computer Physics Communications, Vol. 265, p. 108009, 2021.
  26. J., Lei. Z., Yao. Q., Zhou. F., and Pan. X., “A Bounded Randomly Variable Shape Multi-Quadric Interpolation Method in Dual Reciprocity Boundary Element Method”, Engineering Analysis with Boundary Elements, Vol. 134, pp. 377-387, 2022.
  27. Newmark, N. M., “A Method of Computation for Structural Dynamics”, Journal of the Engineering Mechanics Division, Vol. 85, No. 3, pp. 67-94, 1959.
  28. Loeffler, C. F., and Mansur, W. J., Dual Reciprocity Boundary Element Formulation for Potential Problems in Infinite Domains, in Boundary Elements X, Computational Mechanics Publications, Vol 2, Berlin and New York. 1988.
  29. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 194.
  30. Partridge, P. W., and Brebbia, C. A., Computer Implementation of the BEM Dual Reciprocity Method for the Solution of General Field Equations”, Communications in Applied numerical methods, Vol. 6, pp. 83-92, 1990.
  31. Nardini, D., and Brebbia, C. A., Boundary Integral Formulation of Mass Matrixes for Dynamic Analysis, In Topics in Boundary Research. Springer-Verlag, Berlin and New York, 1985.
  32. Dominguez, J., and Meise, T., “On the Use of the BEM for Wave Propagation in Infinite Domains”, Engineering Analysis with Boundary Elements, Vol. 8, No. 3, pp. 132-138, 1991.
  33. Nardini, D., and Brebbia, C. A., Transient Boundary Element Elastodynamics Using Dual Reciprocity Method and Model Superposition, Boundary Elements VIII, Vol1, Springer-Verlag, Berlin and New York. 1986.
  34. Johnson, D. E., “A Proof of the Stability of the Houblot Method”, American Institute of Aeronautics and Astronautics, Vol. 4, No. 8, pp. 1450-1451, 1996.

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