Abstract
Based on the Biot’s theory of wave propagation in porous media, this paper studies the transient dynamic response of spherical cavity in viscoelastic and saturated soils. The analytical solution in transformed domain is obtained by the method of Laplace transformation, and numerical results are solved through inversed Laplace transformation. The displacements, stresses and pore water pressure developed in the viscoelastic soils are analyzed and compared with those from elastic model, and some new observations are discussed and interpreted from the perspective of material’s properties. The findings resulting from the current study are helpful to analyzing the transient dynamic responses of underground structures in the engineering practice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ai, Z. Y., Cheng Z. Y., and Han, J. (2008). “State space solution to three-dimensional consolidation of multi-layered soils.” International Journal of Engineering Science, Vol. 46, No. 5, pp. 486–498.
Atalla, N., Panneton, R., and Debergue, P. (1998). “A mixed displacementpressure formulation for poroelastic materials.” The Journal of the Acoustical Society of America, Vol. 104, No. 3, pp. 1444–1452.
Biot, M. A. (1941). “General theory of three-dimensional consolidation.” Journal of Applied Physics, Vol. 12, No. 2, pp. 155–164.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluidsaturated porous solid. I. Low-frequency range.” The Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 168.
Bonnet, G. (1987). “Basic singular solutions for a poroelastic medium in the dynamic range.” The Journal of the Acoustical Society of America, Vol. 82, No. 5, pp. 1758.
Depollier, C., Allard, J. F. and Lauriks, W. (1988). “Biot theory and stress-strain equations in porous sound-absorbing materials.” The Journal of the Acoustical Society of America, Vol. 84, No. 6, pp. 2277–2279.
Durbin, F. (1974). “Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate’s method.” The Computer Journal, Vol. 17, No. 4, pp. 371–376.
Durban, D. and Masri, R. (2004). “Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium.” International Journal of Solids and Structures, Vol. 41, No. 20, pp. 5697–5716.
Eringen, A. C. (1980). Mechanics of continua, Robert E. Krieger Publishing Co., Huntington, NY.
Johnson, D. L. (2001). “Theory of frequency dependent acoustics in patchy-saturated porous media.” The Journal of the Acoustical Society of America, Vol. 110, No. 2, pp. 682–694.
Kaynia, A. M. and Prasanta K. B. (1993). “Fundamental solutions of Biot’s equations of dynamic poroelasticity.” International Journal of Engineering Science, Vol. 31, No. 5, pp. 817–830.
Lee, D.-S. (2003). “Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack.” International Journal of Solids and Structures, Vol. 40, No. 11, pp. 2659–2671.
Lee, D.-S. (2009). “Diffraction of torsional elastic waves by a peripheral edge crack around a spherical cavity.” International Journal of Solids and Structures, Vol. 46, No. 2, pp. 433–439.
Ogushwitz, P. R. (1985a). “Applicability of the Biot theory. I. Low-porosity materials.” The Journal of the Acoustical Society of America, Vol. 77, No. 2, pp. 429–440.
Ogushwitz, P. R. (1985b). “Applicability of the Biot theory. II. Suspensions.” The Journal of the Acoustical Society of America, Vol. 77, No. 2, pp. 441–452.
Ogushwitz, P. R. (1985c). “Applicability of the Biot theory. III. Wave speeds versus depth in marine sediments.” The Journal of the Acoustical Society of America, Vol. 77, No. 2, pp. 453–464.
Pan, E. (1999). “Green’s functions in layered poroelastic half-spaces.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 23, No. 13, pp. 1631–1653.
Philippacopoulos, A. J. (1988). “Lamb’s problem for fluid-saturated, porous media.” Bulletin of the Seismological Society of America, Vol. 78, No. 2, pp. 908–923.
Rapoport, L., Katzir Z., and Rubin M. B. (2011). “Termination of the starting problem of dynamic expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium.” Wave Motion, Vol. 48, No. 5, pp. 441–452.
Sherwin, J.-A. and Chapple, W. M. (1968). “Wavelengths of single-layer folds: A comparison between theory and observation.” American Journal of Science, Vol. 266, No. 3, pp. 167–179.
Wang, J. and Fang, S. (2003). “State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media.” International Journal of Engineering Science, Vol. 41, No. 15, pp. 1799–1813.
Wang, S. and Yin, S. (2011). “A closed-form solution for a spherical cavity in the elastic-brittle-plastic medium.” Tunnelling and Underground Space Technology, Vol. 26, No. 1, pp. 236–241.
Xu, C. and Wu, S. M. (1998). “Spherical wave propagation in saturated soils.” Applied Mathematics and Mechanics, Vol. 19, No. 3, pp. 243–252.
Yang, G. and Zhang, S. (1988). Elasticity dynamics, Chinese Railway Press, Beijing
Zienkiewicz, O. C., Chang, C. T., and Bettess, P. (1980). “Drained, undrained, consolidating and dynamic behaviour assumptions in soils.” Géotechnique 30.4.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, C., Chen, Q., Zhou, J. et al. Analytical solution of transient dynamic response of spherical cavity in viscoelastic and saturated soils. KSCE J Civ Eng 19, 2035–2040 (2015). https://doi.org/10.1007/s12205-015-0552-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-015-0552-4