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Analysis of dynamic stress concentration in three different types of poro-viscoelastic rock medium

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Abstract

The propagation of shear waves inside/at the Earth’s crust during earthquake may cause the progression of punch in the rock medium. In this study, the movement of semi-infinite punch due to the propagation of the shear wave in a pre-stressed vertically transversely isotropic poro-viscoelastic medium has been analyzed. Based on Wiener–Hopf technique and two-sided Fourier integral transformations, the dynamic stress concentration due to moving punch is determined in closed form. The significant effects of various affecting parameters viz. velocity of moving punch, horizontal initial stress, vertical initial stress, anisotropy parameter, porosity, and viscoelasticity on dynamic stress concentration have been discussed. It is noteworthy that as the punch propagates with higher velocity, dynamic stress concentration in the considered poro-viscoelastic medium escalates. It is also found that horizontal tensile and vertical compressive initial stresses have an adverse impact on the dynamic stress concentration. On the other hand, the horizontal compressive and vertical tensile initial stresses have a favorable influence on the dynamic stress concentration. Also, its values increase with the increase of porosity, while it gets decreased as anisotropic parameter prevails in the considered medium. The behavior of dynamic stress concentration in three different types of pre-stressed vertically transversely isotropic poro-viscoelastic media viz. sandstone (a sedimentary rock), granite (an igneous rock), and marble (a metamorphic rock) has been compared. From this comparison, it is obtained that the dynamic stress concentration attains maximum value if the rock medium is marble and minimum value if the rock medium is sandstonel. Some graphical illustrations and numerical computations have also been established. Furthermore, some important properties are identified from the obtained dynamic stress concentration expressions.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati, India

    Piu Kundu & Anil Negi

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  1. Piu Kundu
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  2. Anil Negi
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Contributions

Dr. Anil Negi explores the mathematical model for the problem and works to explore the data for realistic rock materials. Dr. Piu Kundu solves the mathematical model, draw the graphs, and wrote the paper. Dr. Anil Negi again reviewed the papers and made some changes to enhance the readability of the manuscript.

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Correspondence to Anil Negi.

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Kundu, P., Negi, A. Analysis of dynamic stress concentration in three different types of poro-viscoelastic rock medium. J Eng Math 144, 13 (2024). https://doi.org/10.1007/s10665-023-10312-4

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