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Overhanging Rock: Theoretical, Physical and Numerical Modeling

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Abstract

Overhanging rock instability is a serious geological problem in mountainous regions. The initiation and propagation of a controlling crack are the fundamental causes of overhanging rock failure. In the view of fracture mechanics, the instability of toppling overhanging rock can be equivalent to the effect of pure shear and pure bending moment. This paper analyzes the evolution of displacement–load curves and failure modes of overhanging rock models at different crack lengths, crack angles, and load distances based on fracture tests of the toppling overhanging rock model. Maximum circumferential stress theory is used as the fracture criterion of mixed mode I–II fractures to calculate the stress intensity factor (SIF) of the crack tip and the theoretical failure load of the overhanging rock model. The fracture mode mechanism is analyzed by the calculated SIF. We use the extended finite element method to simulate the crack propagation path and analyze the change process from equivalent stresses of the numerical model using propagation steps. Comparisons between the physical tests, theoretical calculations, and numerical simulations verify the rationality of the experimental results.

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Abbreviations

T :

External vertical load on the overhanging rock

G :

Weight of the overhanging rock

a 0 :

Length of the controlling crack

b :

Locking section length of the overhanging rock

H :

Thickness of the overhanging rock slab

β :

Inclination angle of the controlling crack

x 1, x 2 :

Horizontal distances from the load to the controlling crack

K IC :

Fracture toughness

σ rr, σ θθ, τ rθ :

Radial stress, circumferential tensile stress, and shear stress at the crack tip

θ :

Crack deviation angle (positive counterclockwise, negative clockwise)

r :

Distance from the crack tip

SIF:

Stress intensity factor

K I, K II :

Mode I and II stress intensity factors

a :

Half-length of the crack

σ ∞, τ ∞ :

Far-field tensile stress and far-field shear stress

K e :

Equivalent stress intensity factor

t :

Thickness of the model

F :

Boundary correction factor

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Acknowledgements

We thank the Funds for Creative Research Groups of China (no. 41521002) and the National Natural Science Foundation of China (no. 41672282), and State Key Laboratory of Geohazard Prevention and Geoenvironment Prevention Independent Research Project (SKLGP2017Z003) for supporting this project. The first author thanks the Innovative Team of Chengdu University of Technology.

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  1. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, 610059, Sichuan, People’s Republic of China

    L. Z. Wu, G. Q. Shao, R. Q. Huang & Q. He

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  1. L. Z. Wu
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  2. G. Q. Shao
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  3. R. Q. Huang
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  4. Q. He
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Correspondence to R. Q. Huang.

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Wu, L.Z., Shao, G.Q., Huang, R.Q. et al. Overhanging Rock: Theoretical, Physical and Numerical Modeling. Rock Mech Rock Eng 51, 3585–3597 (2018). https://doi.org/10.1007/s00603-018-1543-9

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  • DOI: https://doi.org/10.1007/s00603-018-1543-9

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