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<p>Sandstone roof strata in deep coal mining are frequently subjected to impact disturbances, and their dynamic mixed-mode fracture response is closely related to crack initiation, propagation, and instability of surrounding rock. Previous studies have addressed rate-dependent dynamic fracture and angle-dependent mixed-mode fracture largely in isolation, but how loading rate and loading angle interact to govern the transition from opening-dominated to shear-dominated cracking, and how this coupled behavior manifests across different length scales has not been fully investigated. Therefore, this study conducted dynamic mixed-mode fracture tests on cracked straight-through Brazilian disc sandstone specimens with loading angles of 0°–90° and loading rates of 20–100 GPa/s using a split Hopkinson pressure bar system. High-speed photography, scanning electron microscopy, and three-dimensional fracture-surface fractal analysis were combined to characterize crack propagation, Mode I/II stress intensity factors, effective fracture toughness, and fracture morphology. The results indicate that the dynamic Mode I stress intensity factor decreases monotonically with increasing loading angle and changes sign near 45°, indicating a transition from opening-dominated to shear-dominated fracture. The dynamic Mode II stress intensity factor first increases and then decreases with loading angle, reaching its peak within approximately 45°. The dynamic effective fracture toughness follows a logarithmic relationship with loading rate within the tested range (R<sup>2</sup> = 0.94–0.99), with the strongest rate sensitivity coefficient&#xa0;a&#xa0;ranges from&#xa0;0.59 to 3.08&#xa0;across all loading angles and&#xa0;peaks at 3.08 near 45°, indicating the strongest rate sensitivity at the mixed-mode transition. The fracture-surface fractal dimension increases with loading rate and reaches its maximum within the 45–60° interval, where crack branching, grain pull-out, and local fragmentation are most pronounced. These findings demonstrate how loading rate and loading angle jointly govern dynamic mixed-mode I/II fracture in sandstone and provide laboratory-scale evidence for understanding rate-dependent fracture of sandstone roof strata under impact loading.</p>

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Loading-angle-dependent rate effects on dynamic mixed-mode I/II fracture behavior of coal-measure sandstone

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月15日

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  • Shankun Zhao,
  • Kaiwen Song,
  • Hao Sheng,
  • Yunpeng Li,
  • Quanhong Hu,
  • Jichao Wang,
  • Zhun Li,
  • Judong Jing

摘要

Sandstone roof strata in deep coal mining are frequently subjected to impact disturbances, and their dynamic mixed-mode fracture response is closely related to crack initiation, propagation, and instability of surrounding rock. Previous studies have addressed rate-dependent dynamic fracture and angle-dependent mixed-mode fracture largely in isolation, but how loading rate and loading angle interact to govern the transition from opening-dominated to shear-dominated cracking, and how this coupled behavior manifests across different length scales has not been fully investigated. Therefore, this study conducted dynamic mixed-mode fracture tests on cracked straight-through Brazilian disc sandstone specimens with loading angles of 0°–90° and loading rates of 20–100 GPa/s using a split Hopkinson pressure bar system. High-speed photography, scanning electron microscopy, and three-dimensional fracture-surface fractal analysis were combined to characterize crack propagation, Mode I/II stress intensity factors, effective fracture toughness, and fracture morphology. The results indicate that the dynamic Mode I stress intensity factor decreases monotonically with increasing loading angle and changes sign near 45°, indicating a transition from opening-dominated to shear-dominated fracture. The dynamic Mode II stress intensity factor first increases and then decreases with loading angle, reaching its peak within approximately 45°. The dynamic effective fracture toughness follows a logarithmic relationship with loading rate within the tested range (R2 = 0.94–0.99), with the strongest rate sensitivity coefficient a ranges from 0.59 to 3.08 across all loading angles and peaks at 3.08 near 45°, indicating the strongest rate sensitivity at the mixed-mode transition. The fracture-surface fractal dimension increases with loading rate and reaches its maximum within the 45–60° interval, where crack branching, grain pull-out, and local fragmentation are most pronounced. These findings demonstrate how loading rate and loading angle jointly govern dynamic mixed-mode I/II fracture in sandstone and provide laboratory-scale evidence for understanding rate-dependent fracture of sandstone roof strata under impact loading.