The 3-D non-axisymmetrical Lamb’s problem in transversely isotropic saturated poroelastic media
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Based on Biot’s theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biot’s wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic media into two—one 6-order and one 2-order—uncoupling differential governing equations. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, the systematic study on Lamb’s problems for the transversely isotropic saturated poroelastic media is performed. Integral solutions for surface radial, vertical and circumferential displacements are obtained in both cases of drained surface and undrained surface under the vertical and horizontal harmonic excitation force. In the end of this paper, the numerical examples are presented. The calculation results indicate that the difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media is obvious.
Keywordstransversely isotropic saturated poroelastic media Biot’s wave equations Lamb’s problems
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- 5.Philippacopoulous, A. J., Lamb’s problem for fluid-saturated porous media, Bull. Seism. Soc. Am., 1988, 78: 908–932.Google Scholar
- 7.Kaynia, A. M., Banerjee, P. K., Fundamental solution of Biot’s equations of dynamic poroelasticity, Int. J. Engng. Sci., 1992, 77: 12–23.Google Scholar
- 10.Wang Lizhong, Chen Yunmin, Wu Shiming et al., The integral solution under the low-frequency harmonic concentrated force on the saturated elastic half-space. J of Hydraulic Engineering (in Chinese), 1996, (2): 84–88.Google Scholar
- 11.Yan Jun, Wu Shiming, Chen Yunmin, Steady state response of elastic soil layer and saturated layered half-space, China Civil Engineering Journal (in Chinese), 1997, 30(3): 39–47.Google Scholar
- 13.Zhang Yinke, Huang Yi, The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media, Applied Mathematics and Mechanics (in Chinese), 2002, 35(3): 41–45.Google Scholar
- 15.Liu Yinbin, Li Youming, Wu Rushan, Seismic wave propagation in transversely isotropic porous media, Geophysica Sinica, 1994, 37(4): 499–514.Google Scholar
- 16.Wang Yuesheng, Zhang Zimao, Propagation of plane waves in transversely isotropic fluid-saturated porous media. Acta Mechanica Sinica, 1997, 29(30): 257–268.Google Scholar
- 17.Hu Yayuan, Wang Lizhong, Zhang Zhongmia et al., The pragmatic wave equations of transversely isotropic saturated soil, J. of Vibration Engineering, 1998, 12(2): 170–176.Google Scholar
- 18.Zhang Yinke, Huang Yi, The non-axisymmetrical dynamic response of transversely isotropic saturated poroelastic media, Applied Mathematic and Mechanics, 2001, 22(1): 56–70.Google Scholar
- 20.Hu Haichang, On the three-dimensional problems of the theory of elasticity of a transversely isotropic body, Acta Physica Sinica, 1953, 9(2): 130–147.Google Scholar