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Geomechanics and Engineering Volume 16, Number 2, October10 2018 , pages 169-176 DOI: https://doi.org/10.12989/gae.2018.16.2.169 |
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Surface wave propagation in an initially stressed heterogeneous medium having a sandy layer and a point source |
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Santanu Manna, J.C. Misra, Santimoy Kundu and Shishir Gupta
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| Abstract | ||
| An attempt has been made here to study the propagation of SH-type surface waves in an elastic medium, which is initially stressed and heterogeneous and has a point source inside the medium. The upper portion of the composite medium is a sandy layer. It is situated on an initially stressed heterogeneous half-space, whose density, rigidity and internal friction are function of depth. The analysis has been carried out by using Fourier transform and Green\'s function approach. The phase velocity has been investigated for several particular situations. It has been shown that the results of the study agree with those the case of Love wave propagation in a homogeneous medium in the absence of the sandy layer, when the initial stress is absent. In order to illustrate the validity of the analysis presented here, the derived analytical expression has been computed numerically, by considering an illustrative example and the variances of the concerned physical variables have been presented graphically. It is observed that the velocity of shear wave is amply influenced by the initial stress and heterogeneity parameters and the presence of the sandy layer. The study has an important bearing on investigations of different problems in the earth\'s interior and also in seismological studies. | ||
| Key Words | ||
| surface wave; green function; dispersion equation; phase velocity; heterogeneity | ||
| Address | ||
| Santanu Manna: 1.)Discipline of Mathematics, Indian Institute of Technology Indore, Simrol-453552, India 2.) Discipline of Civil Engineering, Indian Institute of Technology Indore, Simrol-453552, India J.C. Misra: Indian Institute of Engineering Science and Technology Shibpur, Howrah 711103, India Santimoy Kundu and Shishir Gupta: Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand-826004, India | ||