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<p>Quantifying the time-dependent deformation and failure of asperities on rock fracture surfaces is crucial for revealing the evolution of internal structure of fractures and ensuring the long-term safety of deep underground engineering. The classical rheological models developed for intact, regular-shaped rock specimens cannot be directly applied to characterize the time-dependent deformation behavior of irregular-shaped specimens that are conceptualized based on asperities found on rock fracture surfaces. Here, we generalize asperities into semi-ellipsoids with varying initial height-to-radius ratios (HRR). Time-dependent compression experiments (TCE) on artificial asperities were conducted using homogenous rock-like materials, and evolutions of stress and strain over time at multiple constant normal load (CNL) stages were obtained. Experimental results reveal that asperities with a smaller initial HRR require greater strains to enter the nonlinear deformation stage. The normal loads at the first accelerating creep for the four different asperities exhibit exponential decrease&#xa0;to 2.808, 1.54, 1.056, and 0.7&#xa0;kN, yet their proportion relative to the maximum elastic load conversely&#xa0;increases, reaching 52, 70, 88, and 100%, respectively. Under an identical normal load for a period of time, their strains tend to converge over time. The maximum elastic load appears at a point where the HRR of compressed part <i>λ</i>(<i>t</i>) reaches a peak. Based on Hertzian contact theory, an improved hyperbolic sine power-law function was proposed to predict the time-dependent elastic compressive deformation of asperities. Our experimental results highlight the control of morphology in the evolution of asperity deformation and the need for more sophisticated modeling of asperity contact on natural rock fractures.</p>

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Time-Dependent Deformation of Fracture Asperities with Different Height-to-Radius Ratios Subject to Normal Loading

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Song Zhenyu,
  • Li Bo,
  • Chen Xingwei,
  • Kong Deheng,
  • Wang Ju

摘要

Quantifying the time-dependent deformation and failure of asperities on rock fracture surfaces is crucial for revealing the evolution of internal structure of fractures and ensuring the long-term safety of deep underground engineering. The classical rheological models developed for intact, regular-shaped rock specimens cannot be directly applied to characterize the time-dependent deformation behavior of irregular-shaped specimens that are conceptualized based on asperities found on rock fracture surfaces. Here, we generalize asperities into semi-ellipsoids with varying initial height-to-radius ratios (HRR). Time-dependent compression experiments (TCE) on artificial asperities were conducted using homogenous rock-like materials, and evolutions of stress and strain over time at multiple constant normal load (CNL) stages were obtained. Experimental results reveal that asperities with a smaller initial HRR require greater strains to enter the nonlinear deformation stage. The normal loads at the first accelerating creep for the four different asperities exhibit exponential decrease to 2.808, 1.54, 1.056, and 0.7 kN, yet their proportion relative to the maximum elastic load conversely increases, reaching 52, 70, 88, and 100%, respectively. Under an identical normal load for a period of time, their strains tend to converge over time. The maximum elastic load appears at a point where the HRR of compressed part λ(t) reaches a peak. Based on Hertzian contact theory, an improved hyperbolic sine power-law function was proposed to predict the time-dependent elastic compressive deformation of asperities. Our experimental results highlight the control of morphology in the evolution of asperity deformation and the need for more sophisticated modeling of asperity contact on natural rock fractures.