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Influence of Intermittent Artificial Crack Density on Shear Fracturing and Fractal Behavior of Rock Bridges: Experimental and Numerical Studies

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Abstract

Shear-box experiments, Rock Failure Process Analysis (RFPA) simulations, and box-counting fractal analysis on rock-like models are conducted to investigate the influence of intermittent artificial crack density on the shear fracturing and fractal behavior of rock bridges in jointed rock slopes. The artificial crack geometry of the conceptual rock bridge model is a combination of two edge-notched artificial cracks and imbedded artificial cracks with different intermittent artificial crack densities. By numerical shear-box tests, deep insight into the mesoscopic mechanism of crack evolution is gained, and the simulated failure patterns are in accordance with experimental results. Three types of failure patterns are identified: shear mode, mixed shear/tensile mode, and tensile mode. The RFPA simulations demonstrate that macroscale shear cracks form as damage belts consisting of many tensile/shear mesocracks, as typically observed in microscopic experimental work. The failure pattern is mostly influenced by the intermittent artificial crack density, whereas the peak shear strength is related to the failure pattern. As the intermittent artificial crack density increases, the failure pattern changes from shear mode to mixed shear/tensile mode and then to tensile mode, resulting in a decrease in the peak shear strength. The regression analysis shows that the relationship between the peak shear strength and intermittent artificial crack density can be expressed by an exponential decay model. Furthermore, digital image processing and box-counting fractal analyses are performed on the shear fracture surfaces of the physical and numerical models to describe the fractal behavior. The relationships between the fractal dimension and peak shear strength are analyzed, and strong correlations that display an exponential decay function are found.

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Abbreviations

CNL:

Constant normal load

OEDF:

One-phase exponential decay function

RFPA:

Rock failure process analysis

A :

Rock bridge area

a1, b1, and t1 :

Undetermined coefficients

a2, and b2 :

Undetermined coefficients

a3, b3, x3, and t3 :

Undetermined coefficients

b :

Edge-notched artificial crack half-length

D :

Fractal dimension

E m0 :

Elastic modulus of the undamaged mesoscopic element

f c0 :

Compressive strength of the mesoscopic element

f t0 :

Tensile strength of the mesoscopic element

l :

Imbedded en-echelon artificial crack half-length

m :

Shape of the distribution function

N :

Number of artificial cracks

N(δ):

Number of boxes

P :

Axial loading applied by the machine

P n :

Compressive loading

P s :

Shear loading

u :

Mechanical property of the mesoscopic element

u 0 :

Mean mechanical property of the mesoscopic element

α :

Die angle

β :

Imbedded artificial crack inclination

δ :

Scale length of box

ε f :

Intermittent artificial crack density

λ :

Residual strength coefficient

v :

Poisson’s ratio

σ c :

Uniaxial compressive strength

σ t :

Tensile strength

τ p :

Peak shear strength

φ :

Friction angle

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Acknowledgements

The authors would like to acknowledge the China National Natural Science Foundation (Project Nos. 41762021, 11862024), the China Postdoctoral Science Foundation (Project No. 2017T100715). and the Open Research Fund Program of the State Key Laboratory of Groundwater Protection and Utilization in Coal Mining (Project No. SHGF-17-13-09), which collectively funded this project. The authors are grateful to the anonymous reviewers for their useful comments and constructive suggestions.

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Authors and Affiliations

  1. Faculty of Electric Power Engineering, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China

    Ke Zhang & Xianghua Liu

  2. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China

    Yulong Chen & Hebing Luan

  3. School of Resources and Safety Engineering, Central South University, Changsha, 410083, Hunan, China

    Wencheng Fan

  4. State Key Laboratory of Groundwater Protection and Utilization in Coal Mining, China Energy Group, Beijing, 100011, China

    Hebing Luan

  5. Department of Civil Engineering, Yunnan University, Kunming, 650500, Yunnan, China

    Jianbin Xie

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  1. Ke Zhang
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Correspondence to Ke Zhang.

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Zhang, K., Chen, Y., Fan, W. et al. Influence of Intermittent Artificial Crack Density on Shear Fracturing and Fractal Behavior of Rock Bridges: Experimental and Numerical Studies. Rock Mech Rock Eng 53, 553–568 (2020). https://doi.org/10.1007/s00603-019-01928-z

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