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Fracturing and Energy Evolution of Rock Around Prefabricated Rectangular and Circular Tunnels Under Shearing Load: A Comparative Analysis

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Abstract

Mechanical behavior and energy evolution of rock around the tunnel are critical for evaluating the instability of geotechnical engineering. To reveal the influence of tunnel section shape on deformation, stress distribution, and fracturing mechanism of rock around the tunnel, a series of physical model shear tests for rock around prefabricated rectangular and circular tunnels were carried out, and corresponding fracturing and energy evolution analysis were also presented. In the shear test, the cracking evolution of rock around tunnel specimens was monitored and recorded by a high-speed camera and acoustic emission monitor to reveal the macro- and meso-fracture features. In addition, to examine the continuous-discontinuous shear process, four typical numerical models of rock around the tunnel were exploited to explore meso-mechanical behavior and fracturing mechanism. In light of the first law of thermodynamics, energy conversion process, damage characteristics and rockburst tendency of rock around tunnel specimens were investigated. The test results manifested that fracturing evolution, energy characteristic conversion, and micro-cracks evolution of rock around tunnel specimens generally were classified as four unified stages. In terms of fracturing evolution, rock around tunnel specimens experienced shearing compression stage (stage I), elastic stage (stage II) dominated by crack initiation, shearing fracture stage (stage III) dominated by crack propagation, coalescence and shear-induced rockburst, and shearing friction stage (stage IV). In the aspect of energy characteristic conversion, rock around tunnel specimens were mainly elastic deformation before peak shearing load, and the plastic deformation was relatively small. Partial dissipated strain energy acted on closing hole and crack initiation, and the rest was stored as elastic strain energy. After peak shearing load, the shear strength dropped rapidly, and a large amount of strain energy was converted into dissipated strain energy for crack propagation, coalescence and shear-induced rockburst. In the evolution of micro-cracks, the specimens underwent crack quiet period (stage I), crack initial increase stage (stage II), crack rapid increase stage (stage III), and crack stable stage (stage IV). Interestingly, the damage stress and rockburst tendency of rock around prefabricated rectangular tunnels were superior to those of rock around prefabricated circular tunnels, indicating that the bearing capacity of rock around prefabricated rectangular tunnels was superior to that of rock around prefabricated circular tunnels, related to the deviatoric stress distribution and confining pressure. In addition, a novel impact tendency index (Sp et) was presented for evaluating shear-induced rockburst tendency, which carved the proportional relationship between elastic strain energy and dissipative strain energy at peak shearing load. The research results were conducive to recognize the fracturing mechanism of rock around a tunnel subjected to shear condition and provided a theoretical basis for the prevention and control of geotechnical engineering.

Highlights

  • Shear characteristic, energy characteristic conversion and micro-cracks number evolution of rock around tunnel specimens generally were classified as four unified stages.

  • Bearing capacity of rock around a prefabricated rectangular tunnel was superior to that of rock around a prefabricated circular tunnel, related to the deviatoric stress distribution and confining pressure.

  • A novel damage variable was proposed to quantify the damage degree of rock

  • A novel impact tendency index (Sp et) was presented for evaluating the shear-induced rockburst tendency

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Abbreviations

δ h :

Shear displacement

\(\delta_{h}^{t}\) :

Shear displacement at time t

δ v :

Normal displacement

\(\delta_{v}^{t}\) :

Normal displacement at time t

γ p :

Shear peak strain

μ :

Particle friction coefficient

v :

Poisson ratio

ρ :

Particle density

σ n :

Parallel-bond normal strengths

τ :

Shear stress

τ n :

Parallel-bond shear strengths

τ p,:

Shear strength

\(\Delta U_{{\text{d}}}\) :

Dissipative strain energy increment

AE:

Acoustic emission

D :

Damage variable

DEM:

Discrete element method

E :

Elastic modulus

E c :

Particle contact modulus

E c′:

Parallel bond modulus

E t :

Tensile modulus

G :

Shear modulus

ISRM:

International society for rock mechanics

k n/ks :

Ratio of normal to shear stiffness of the particle

K n′/k s′:

Ratio of normal to shear stiffness of parallel bond

PFC:

Particle flow code

R max/R min :

Ratio of maximum to minimum of radius

R min :

Minimum radius of the particle

Sp et:

Impact tendency index

U :

Total energy

U e :

Elastic strain energy

U d :

Dissipated strain energy

U n :

Work of normal force

U s :

Work of shear force

V P :

Wave velocity

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Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. 52325905) and the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (No. Z020005).

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Jie Xin, Quan Jiang, Shaojun Li, Pengfei Chen & Herui Zhao

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Jie Xin, Pengfei Chen & Herui Zhao

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  1. Jie Xin
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  2. Quan Jiang
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  3. Shaojun Li
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  4. Pengfei Chen
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  5. Herui Zhao
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Contributions

JX conceptualization, methodology, writing-original draft, and writing-review and editing; QJ conceptualization, resources, supervision, and funding acquisition; SL resources, supervision, and data curation; PC resources, formal analysis; HZ resources, formal analysis.

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Correspondence to Quan Jiang.

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Xin, J., Jiang, Q., Li, S. et al. Fracturing and Energy Evolution of Rock Around Prefabricated Rectangular and Circular Tunnels Under Shearing Load: A Comparative Analysis. Rock Mech Rock Eng 56, 9057–9084 (2023). https://doi.org/10.1007/s00603-023-03532-8

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