Analytical Solution of Transient Dynamic Response of Spherical Cavity in Viscoelastic and Saturated Soils

다국어 초록 (Multilingual 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.

참고문헌 (Reference)

1 Sherwin, J.-A., "Wavelengths of single-layer folds: A comparison between theory and observation" 266 (266): 167-179, 1968

2 Biot, M. A, "Theory of propagation of elastic waves in a fluidsaturated porous solid. I. Low-frequency range" 28 (28): 168-, 1956

3 Johnson, D. L, "Theory of frequency dependent acoustics in patchy-saturated porous media" 110 (110): 682-694, 2001

4 Rapoport, L., "Termination of the starting problem of dynamic expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium" 48 (48): 441-452, 2011

5 Lee, D. -S, "Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack" 40 (40): 2659-2671, 2003

6 Ai, Z. Y., "State space solution to threedimensional consolidation of multi-layered soils" 46 (46): 486-498, 2008

7 Wang, J., "State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media" 41 (41): 1799-1813, 2003

8 Xu, C., "Spherical wave propagation in saturated soils" 19 (19): 243-252, 1998

9 Durbin, F, "Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate's method" 17 (17): 371-376, 1974

10 Eringen, A. C., "Mechanics of continua" Robert E. Krieger Publishing Co. 1980

11 Philippacopoulos, A. J, "Lamb's problem for fluid-saturated, porous media" 78 (78): 908-923, 1988

12 Pan, E, "Green's functions in layered poroelastic half-spaces" 23 (23): 1631-1653, 1999

13 Biot, M. A, "General theory of three-dimensional consolidation" 12 (12): 155-164, 1941

14 Kaynia, A. M., "Fundamental solutions of Biot's equations of dynamic poroelasticity" 31 (31): 817-830, 1993

15 Yang, G, "Elasticity dynamics" Chinese Railway Press 1988

16 Durban, D, "Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium" 41 (41): 5697-5716, 2004

17 Zienkiewicz, O. C., "Drained, undrained, consolidating and dynamic behaviour assumptions in soils" 30 (30): 1980

18 Lee, D. -S, "Diffraction of torsional elastic waves by a peripheral edge crack around a spherical cavity" 46 (46): 433-439, 2009

19 Depollier, C., "Biot theory and stress-strain equations in porous sound-absorbing materials" 84 (84): 2277-2279, 1988

20 Bonnet, G, "Basic singular solutions for a poroelastic medium in the dynamic range" 82 (82): 1758-, 1987

21 Ogushwitz, P. R, "Applicability of the Biot theory. III. Wave speeds versus depth in marine sediments" 77 (77): 453-464, 1985

22 Ogushwitz, P. R, "Applicability of the Biot theory. II. Suspensions" 77 (77): 441-452, 1985

23 Ogushwitz, P. R, "Applicability of the Biot theory. I. Lowporosity materials" 77 (77): 429-440, 1985

24 Atalla, N., "A mixed displacementpressure formulation for poroelastic materials" 104 (104): 1444-1452, 1998

25 Wang, S., "A closed-form solution for a spherical cavity in the elastic–brittle–plastic medium" 26 (26): 236-241, 2011