Noise Filtration of Shockwave Propagation in Multi-Layered Soils

Noise Filtration of Shockwave Propagation in Multi-Layered Soils

Laith I. Namiq Yousof Q. Abdaljalil

Retired Professor, Geotechnical Department, AKRF, Inc., USA

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Numerical methods, and especially the finite-element method (FEM), are usually adopted for the analyses of shockwave propagation in nonlinear inelastic media. Noise or spurious oscillations, in the calculated stresses and displacements, frequently appear in the FEM solutions. This article introduces and describes a numeric filter based on least-square analysis that can smooth out such fictitious noise. The sliced least-square method (SLSM) filter is implemented in a finite elements program that solves 1D time integration of dynamic equilibrium sets of equations that simulate shockwave propagation in multi-layered soils supported by a hard stratum. Elastic and elasto-viscoplastic material models with dynamic yield surface constitutive relations are invoked to model sand, clay, and concrete materials in the analyses. Results of the analyses of shockwave propagation in layers of soil and concrete without the filter are compared with identical conditions with the inclusion of the new filter in the finite-element program. Oscillations in calculated stresses and displacements were observed in the results when no filter was included in the solution program. Solution results showed little or no noise with the application of the new filter. The predicted FEM analyses results were compared with physical test results with very good to excellent comparisons obtained.


elasto-viscoplastic material model, finite elements, implicit time integration, spatial filter, spurious oscillations, wave propagation


[1] Belytschko, T. & Mullen, R., Mesh partitions of explicit-implicit time integration. Formulations and Computational Algorithm in Finite Element Analysis, ed. K.J. Bathe, T. Oden & W. Wunderlich, MIT Press: Cambridge, Massachusetts, U.S.A., pp. 672–690, 1978.

[2] Pain, H.G., The Physics of Vibrations and Waves, John Wiley and Sons Ltd.: London, 1976.

[3] Kreig, R.D. & Key, S.W., Transient shell response by numerical time integration. Advances in Computational Methods in Structural Mechanics and Design, eds J.T. Oden, W.W. Clough & Y. Yamamoto, UAH Press: Huntsville, Alabama, U.S.A., 1972.

[4] Ham, S. & Bathe, K.J., A finite element method enriched for wave propagation prob- lems. Computers and Structures, 94–95, pp. 1–12, 2012.

[5] Schmicker, D., Duczek, S., Liefold, S. & Gabbert, U., Wave propagation analysis using high-order finite element methods: spurious oscillations excited by internal element eigenfrequencies. Technische Mechanik, 34(2), pp. 51–71, 2014.

[6] Okrouhlik, M., Ptak, S. & Valdek, U., Self-assessment of finite element solutions applied to transient phenomena in solid continuum mechanics. Engineering Mechancis, 16(2), pp. 103–121, 2009.

[7] Martel, L., Love wave propagation across a step by finite elements and spatial filtering. Geophysical Journal of the Royal Astronomical Society, 61, pp. 659–677, 1980.

[8] Cope, R.J., Sawko, F. & Tickell, R.G., Computer Methods for Civil Engineers, McGraw- Hill Book Company, Ltd.: U.K., 1982.

[9] Hendron, A.J. & Auld, H.E., The effect of soil properties on the attenuation of air- blast-induced ground motions. Proceedings of Symposium on Wave Propagation, The University of New Mexico, Albuquerque, New Mexico, U.S.A., 1978.

[10] Belytschko, T., Chiapetta, R.L. & Bartel, H.D., Efficient large scale non-linear transient analysis by finite elements. International Journal of Numerical Methods in Engineering, 10, pp. 579–596, 1976.

[11] Atkinson, J.H. & Bransby, P.L., The Mechanics of Soils: An Introduction to Critical State Soil Mechanics, McGraw-Hill Ltd.: U.K., 1978.