Failure Evolution and Fractal Damage Characteristics of Bolt-Reinforced Rock Under True-Triaxial Single-Face Unloading

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Abstract
Deep excavation reduces lateral confinement and can increase tangential stress, promoting brittle failure in highly stressed rock. However, the effects of bolt number and spacing on mechanical response and damage evolution under this stress path remain insufficiently understood. In this study, parallel RFPA3D simulations were conducted for true-triaxial single-face unloading followed by continued axial loading, assuming perfect bonding at the bolt–rock interface. Two parameter series examined bolt numbers from zero to four (M0–M4) and bolt spacings from 10 to 80 mm. Stress–strain response, acoustic emission activity, failure morphology, damage area ratio (Ad), and box-counting fractal dimension (Df) were analysed. Bolt reinforcement increased post-unloading peak stress and restricted the inward extent of damage, while damage persisted near the unloaded face and within the inter-bolt regions. Peak stress increased from approximately 345 MPa in M0 to 363 MPa in M3, then decreased slightly to 358 MPa in M4, showing that reinforcement gains were not proportional to bolt number. Bolt spacing had a modest effect on peak stress but a clearer influence on damage continuity and inward extent. Among the tested spacings, the 40 mm case (D40) achieved the highest peak stress of 370.0 MPa and the lowest Ad of 23.85%, with a low Df of 1.431. In contrast, the 80 mm case (D80) exhibited more extensive and spatially complex damage (Ad = 30.78%, Df = 1.677). Ad and Df provided complementary descriptions of damage extent and spatial complexity. These numerical results provide a quantitative basis for comparing reinforcement configurations under the investigated specimen-scale conditions.
Funding Information
  • National Natural Science Foundation of China (U2244227)
  • China Geological Survey (DD202606101201)

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