Failure Evolution and Fractal Damage Characteristics of Bolt-Reinforced Rock Under True-Triaxial Single-Face Unloading
- 1School of Civil Engineering, Tianjin University, Tianjin 300350, China
- 2Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
- 3Institute of Exploration Technology, Chinese Academy of Geological Sciences, Chengdu 611734, China
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.
Related
- Effect of Turning Structure on Spatiotemporal Evolution Characteristics of Outburst Gas–Solid Two-Phase Flow Dynamic Disasters
- TRISDUCTION: A Linguistically, Topologically, and Mathematically Sealed Verification Architecture · Triaxial Orthogonality, Twelve-Gate Closure, the Quaternionic Completion, the Root Axiom, and the Master Pre-Sealed Proposition Ledger
- A Study on the Migration Law of Overburden and Fracture Fractal Evolution Characteristics Under the Influence of Remaining Coal Pillar in Gently Inclined Multi-Coal-Seam Mining
- Once-reinforced random walk on ℤd has range exponent at least d/(d+1)
- Laws of the iterated logarithm for the range of once-reinforced random walk on ℤ
BibTeX
@article{yang2026failure,
title = {{Failure Evolution and Fractal Damage Characteristics of Bolt-Reinforced Rock Under True-Triaxial Single-Face Unloading}},
author = {Nan Yang and Bin Li and Yang Gao and Qing He and Jinyang Li and Jiawei Wan and Jun Li},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100699},
url = {https://www.mdpi.com/2504-3110/10/10/699},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Failure Evolution and Fractal Damage Characteristics of Bolt-Reinforced Rock Under True-Triaxial Single-Face Unloading
AU - Nan Yang
AU - Bin Li
AU - Yang Gao
AU - Qing He
AU - Jinyang Li
AU - Jiawei Wan
AU - Jun Li
PY - 2026
DA - 2026/10/04
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100699
UR - https://www.mdpi.com/2504-3110/10/10/699
AB - 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.
SN - 2504-3110
ER -