**6. References**

[1] Kennett BLN (1983) Seismic wave propagation in stratified media. New York: Cambridge University Press. 497p.

<sup>\*</sup> Corresponding Author

[2] Miklowitz J, Achenbach JD (1978) Modern Problems in Elastic Wave Propagation. New York: John Wiley & Sons. 561p.

154 Wave Processes in Classical and New Solids

**Author details** 

Zheng-Hua Qian\*

**6. References** 

Corresponding Author

 \*

**Acknowledgement** 

computer memory required for a multilayered model is the same as that for a two-layer model. In case of the application of dynamic allocation of matrices and saving the global matrix propagators on hard drive, the array size assigned for calculating a two-layer model is sufficient for a multilayered model. In that case, the advantages of the boundary element method can be preserved, which implies that seismoacoustic scattering synthesis due to a

Furthermore, if a calculated model is only partially modified, such as increasing the number of layers below the uppermost fluid layer in the case of a plane wave incidence or changing the free surface profile in the case of a point source excitation, not all the matrices need recalculating. That is due to the two merits of the present method: the global matrix propagators for the layers above the source are calculated downwards; and the global matrix propagators for the layers below the source are independent of the rest of the model.

The support from the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, P. R. China is greatly appreciated. The financial support from the Global COE Program entitled "International Urban Earthquake Engineering Center for Mitigating Seismic Mega Risk", Tokyo Institute of Technology, Japan is gratefully acknowledged. The author (Qian) also appreciates very much the help of Prof. Chen X.F. from USTC and Prof. Ge Z. from Peking University for providing us with their program designed for multilayered solid media. And the author (Qian) thanks very much Prof. Fu L.Y. and Dr. Yu G.X. from the Institute of Geology and Geophysics, Chinese Academy of Science, P. R. China for their very much useful discussion and help on the application of BEM as well. The author (Qian) would also like to thank Prof. H. Takenaka from Kyushu University, Japan for giving the very constructive suggestions and comments on the research of seismoacoustic scattering simulation which help improve the introduced approach very much. The author (Qian) would like to appreciate the support from Prof. K. Kishimoto at Tokyo Institute of Technology, Japan. Finally, the author (Qian) would like to sincerely appreciate Prof. Sohichi Hirose from Tokyo Institute of Technolody, Japan for his so much inspiring discussion and

[1] Kennett BLN (1983) Seismic wave propagation in stratified media. New York:

high-frequency excitation can be modelled with reduced computer resources.

*State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China* 

comments on writing the programs of boundary element method.

Cambridge University Press. 497p.


[21] Lay T, Wallace TC (1995) Modern Global Seismology. San Diego: Academic Press. 521p.

**Chapter 7** 

© 2012 Sawangsuriya, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Wave Propagation Methods for** 

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0.1% (Kim and Stokoe 1992).

**1. Introduction** 

conditions.

**Determining Stiffness of Geomaterials** 

In many geoengineering design and analysis, the laboratory and field investigations are generally required to identify and classify geomaterials as well as to assess their engineering properties. One of the important engineering properties commonly used in geomechanical design and analysis is the stiffness of geomaterial. Such stiffness primarily describes the deformation characteristic of a geomaterial used to support engineered structures. Understanding the stiffness behaviour of geomaterials is therefore essential for improving design and analysis of structural behavior under varying loading and environmental

The importance of accurate stiffness measurements from small to large strains has gained increased recognition in both static and dynamic analyses over the past 20 years. In the static triaxial test, the local displacement transducer has been used to measure local axial strains (Goto et al. 1991). The resonant column and torsional shear devices have been widely used for many years to study cyclic and dynamic properties of geomaterials at strains ranging from 10=4 to 0.1% (Drnevich 1985, Saada 1988). The American Association of State Highway and Transportation Officials (AASHTO) has adopted the use of resilient modulus (MR) in pavement design, which is customarily used by the pavement community. The precise measurement of MR values of pavement materials is typically in the strain range from 10=2 to

Based on the typical variation of shear moduli with shear strain levels shown in Fig. 1 (after Atkinson and Sallförs 1991, Mair 1993, Ishihara 1996, Sawangsuriya et al. 2005), three strain ranges are defined: (1) very small strain, (2) small strain, and (3) large strain. The very small strain range corresponds to the range of strain less than the elastic threshold strain (γet), approximately between 10-3% and 10-2%, depending on plasticity index (Ip) for plastic soils (Vucetic and Dobry 1991) and on confining pressure (σo) for non-plastic soils (Ishibashi and

and reproduction in any medium, provided the original work is properly cited.


**Chapter 7** 
