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Critical Angles of Obliquely Incident Stress Wave Through a Single Joint with Different Mediums on Both Sides

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Abstract

This paper presents a study of the critical angles of obliquely incident stress wave through a single joint with different mediums on both sides. Based on the displacement discontinuity method (DDM) and Snell’s law, the propagation characteristics of obliquely incident stress wave through the joint with the different mediums on both sides are investigated. The existence of critical angles is judged, and the reflection and transmission of the stress wave before and after the critical angles are analyzed. The effects of the frequency of the incident wave, joint stiffness, and mechanical properties of mediums on the critical angles are studied. The results show that the first critical angle exists in the cases of the P wave velocity of medium II is larger than that of medium I, and both the first and second critical angles exist in the cases of the S wave velocity of medium II are larger than the P wave velocity of medium I. The first and second critical angles are only affected by the mechanical properties of mediums, and not affected by the frequency of the incident wave and joint stiffness. Both the first and second critical angles increase as the density of medium II increases, while both the first and second critical angles decrease as the Young’s modulus of medium II increases. It is noted that the first critical angle decreases while the second critical angle increases as the Poisson’s ratio of medium II increases.

Highlights

  • Critical angles of obliquely incident stress wave through a single joint with different mediums on both sides were studied.

  • The method for judging the existence of critical angles was proposed.

  • Reflection and transmission of stress wave before and after the critical angles were analyzed.

  • Effects of the parameters of the mediums and joint on the critical angles were investigated.

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Authors and Affiliations

  1. College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, 100124, China

    L. F. Fan, F. Jiang & M. Wang

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  1. L. F. Fan
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  2. F. Jiang
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  3. M. Wang
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Correspondence to L. F. Fan.

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The authors declare that they have no conflict of interest. Acknowledgments The research is supported by the National Natural Science Foundation of China (NSFC) (No. 12172019).

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Fan, L.F., Jiang, F. & Wang, M. Critical Angles of Obliquely Incident Stress Wave Through a Single Joint with Different Mediums on Both Sides. Rock Mech Rock Eng 55, 3317–3329 (2022). https://doi.org/10.1007/s00603-022-02840-9

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  • DOI: https://doi.org/10.1007/s00603-022-02840-9

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