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Application of Three-Dimensional Explicit Discontinuous Deformation Analysis on Wave Propagation in Rock Masses Using Three Viscous Boundaries with the Remedy for Artificial Joints

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Abstract

The three-dimensional explicit discontinuous deformation analysis (3D-EDDA), namely the deformable distinct element method (3D-DDEM), is first applied to analyze the dynamic response of rock masses subject to wave incidence. Three existing viscous boundaries derived using the principle of minimum potential energy in DDA are reformulated with the virtual work principle, which firstly reveal that their major differences lie in the choice of maximum, average, and Newmark (ending) velocity for each time step. The force input method through a viscous boundary is integrated into EDDA/DDEM to simulate the infinite domain on the incidence side. Moreover, the impact of artificial joints on step size and absorbing efficiency is evaluated. A novel index, artificial joint ratio (AJR), is then applied to remedy the viscous boundary and achieves the expected improvement. Detailed numerical cases are performed, which cover the simulation of wave propagation in continuous, spalling, and fractured models. The desirable results warrant further investigation of EDDA/DDEM.

Highlights

  1. 1.

    Three viscous boundaries used in DDA are reformulated and compared.

  2. 2.

    Viscous boundaries are firstly applied and validated in 3D-EDDA/DDEM.

  3. 3.

    Influence of artificial joints on time step size and viscous boundary is quantified.

  4. 4.

    Wave propagation in continuous, spalling, and fractured rock masses is explored.

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Acknowledgements

The first author is grateful to Pro. Genhua Shi who originates the DDA method, and Pro. **aodong Fu whose study gives inspiration. This work was supported by the National Natural Science Foundation of China [41902275, 41827807, 41130751]; Joint Fund for Basic Research of High-speed Railway of National Natural Science Foundation of China, China Railway Corporation [U1934212]; the Special Fund for Basic Research on Scientific Instruments of the National Natural Science Foundation of China [4182780021]; Emeishan-hanyuan highway Program by Sichuan Lehan Expressway Co., Ltd. [SRIG2019GG0004]; Taihang mountain highway Program by China Power Construction Hebei Transportation Expressway Investment Development Co., Ltd. [TH-201908]; Department of Science and Technology of Guizhou Province ([2018]3011); China State Railway Group Co., Ltd.[P2019G038]; China Railway First Survey and Design Institute Group Co., Ltd. [2021RJ06, 19-21-1].

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Authors and Affiliations

  1. College of Civil Engineering, Tongji University, Shanghai, 200092, People’s Republic of China

    ** Wang, Wei Wu, Hehua Zhu & Hong Zhang

  2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, People’s Republic of China

    Wei Wu & Hehua Zhu

  3. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, People’s Republic of China

    Wei Wu & Hehua Zhu

  4. Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    Jeen-Shang Lin

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  5. Jeen-Shang Lin
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Correspondence to Wei Wu.

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Wang, X., Wu, W., Zhu, H. et al. Application of Three-Dimensional Explicit Discontinuous Deformation Analysis on Wave Propagation in Rock Masses Using Three Viscous Boundaries with the Remedy for Artificial Joints. Rock Mech Rock Eng 55, 5821–5843 (2022). https://doi.org/10.1007/s00603-022-02931-7

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