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An Improved Smoothed Particle Hydrodynamics Method and Its Application in Rock Hydraulic Fracture Modelling

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Abstract

In this study, the smoothed particle hydrodynamics method was modified to the two-phase-improved kernel of smoothed particle hydrodynamics (2P-IKSPH). By mapping the water pressure of the water base particles to the solid base particles, the hydraulic fracturing processes of rock masses were realised in a set of unified equations, which could reduce the amount of calculation and improve calculation efficiency. The kernel function in the traditional SPH method was improved to realise the brittle fracture characteristics of solids. A solid–water coupling algorithm was also proposed to automatically transform the damaged solid base particles to water base particles; therefore, eliminating the need to search and regenerate the water base particles. The particle domain searching method was used to realise arbitrary generations of the initial fissure base particles, initial tunnel base particles, and initial water base particles. Three numerical examples are presented to illustrate the effectiveness of 2P-IKSPH, and the correctness of the proposed method was verified by comparison with previous experiments and numerical results. Finally, an engineering example of the progressive failure of a horseshoe-shaped tunnel during stress balance, tunnel excavation, and water filling was numerically simulated, indicating that 2P-IKSPH can be effectively applied to rock engineering.

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Availability of data and material

All data generated or analyzed during this study are included in this published article [and its supplementary information files].

Code availability

The 2P-IKSPH codes are currently not public.

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Funding

This work was supported by the National Natural Science Fund (Grant no. U1765204), the National Natural Science Found (51409170) and “the Fundamental Research Funds for the Central Universities” (B210203078). Meanwhile, the authors greatly wish to express their thanks to Professor Bi Jing for his technical support in the 2P-IKSPH programming.

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Authors and Affiliations

  1. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China

    Shuyang Yu, Xuhua Ren & Jixun Zhang

  2. School of Transportation and Civil Engineering, Nantong University, 9 Seyuan Road, Nantong, 226019, China

    Shuyang Yu & Zhaohua Sun

  3. State Key Laboratory of Hydrology-Water Resource and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing, 210029, China

    Haijun Wang

Authors
  1. Shuyang Yu
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  2. Xuhua Ren
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  3. Jixun Zhang
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  4. Haijun Wang
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  5. Zhaohua Sun
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Contributions

SY completed the numerical analysis and wrote the paper; XR, JZ and HW provided the writing ideas and supervised the study; ZS did the statistical analysis.

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Correspondence to Xuhua Ren.

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Yu, S., Ren, X., Zhang, J. et al. An Improved Smoothed Particle Hydrodynamics Method and Its Application in Rock Hydraulic Fracture Modelling. Rock Mech Rock Eng 54, 6039–6055 (2021). https://doi.org/10.1007/s00603-021-02594-w

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  • DOI: https://doi.org/10.1007/s00603-021-02594-w

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