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Damage and Plastic Deformation Modeling of Beishan Granite Under Compressive Stress Conditions

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Abstract

Based on experimental investigations, we propose a coupled elastoplastic damage model to simulate the mechanical behavior of granite under compressive stress conditions. The granite is taken from the Beishan area, a preferable region for China’s high-level radioactive waste repository. Using a 3D acoustic emission monitoring system in mechanical tests, we focus on the cracking process and its influence on the macroscopic mechanical behavior of the granite samples. It is verified that the crack propagation coupled with fractional sliding along the cracks is the principal mechanism controlling the failure process and nonlinear mechanical behavior of granite under compressive stress conditions. Based on this understanding, the coupled elastoplastic damage model is formulated in the framework of the thermodynamics theory. In the model, the coupling between damage and plastic deformation is simulated by introducing the independent damage variable in the plastic yield surface. As a preliminary validation of the model, a series of numerical simulations are performed for compressive tests conducted under different confining pressures. Comparisons between the numerical and simulated results show that the proposed model can reproduce the main features of the mechanical behavior of Beishan granite, particularly the damage evolution under compressive stress conditions.

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Abbreviations

E:

Elastic modulus of intact rock

\(\tilde{E}\) :

Elastic modulus of damaged rock

v :

Poisson’s ratio

ε e :

Elastic strain

ε p :

Plastic strain

ɛ v :

Volumetric strain

σ 3 :

Minimum principal stress

ω :

Damage variable

k 0 :

Initial drained bulk of intact rock

μ 0 :

Initial shear modulus of intact rock

k(ω):

Effective drained bulk of damaged rock

μ(ω):

Effective shear modulus of damaged rock

H(e v):

Heaviside function of volumetric strain ɛ v

p :

Mean stress (compressive stress is taken as positive)

q :

Deviatoric stress

θ :

Lode’s angle

P a :

Normalizing coefficient in plastic yield surface

C s :

Parameter in plastic yield surface

η :

Parameter in plastic yield surface

m :

Parameter in plastic yield surface

η 0 and η m :

Initial and ultimate value of parameter η

γ p :

Equivalent plastic shear strain

b 1 :

Plastic hardening parameter

b2 :

Plastic hardening parameter

χ p :

Plastic hardening variable

δ ij :

Second-order unit tensor

μ c :

Parameter of plastic potential Q

\(\bar{p}_{0}\) :

Variable of plastic potential Q

C(ω):

Elastic stiffness tensor of damaged material

ψp :

Plastic hardening energy

λ p :

Plastic multiplier

Y ω :

Damage conjugate force

Y e ω :

Elastic damage conjugate force

Y p ω :

Plastic damage conjugate force

Y p,0 ω :

Threshold of plastic damage conjugate force

B ω :

Parameter of damage criterion controlling the kinetics of damage evolution

ω c :

Parameter of damage criterion that defines the asymptotic damage value

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Acknowledgments

This work was supported by the China Atomic Energy Authority through the geological disposal program and the National Natural Science Foundation of China (No. 11202069 and 51374148).

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Authors and Affiliations

  1. CNNC Key Laboratory of Geological Disposal of High-level Radioactive Waste, Beijing Research Institute of Uranium Geology, Beijing, 100029, China

    L. Chen, C. P. Wang, J. Liu & J. Wang

  2. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    J. F. Liu

  3. Laboratory of Mechanics of Lille, UMR8107 CNRS, University of Lille 1, 59660, Villeneuve d’Ascq, France

    Y. Jia & J. F. Shao

Authors
  1. L. Chen
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  2. C. P. Wang
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  3. J. F. Liu
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  4. J. Liu
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  5. J. Wang
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  6. Y. Jia
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  7. J. F. Shao
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Correspondence to L. Chen.

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Chen, L., Wang, C.P., Liu, J.F. et al. Damage and Plastic Deformation Modeling of Beishan Granite Under Compressive Stress Conditions. Rock Mech Rock Eng 48, 1623–1633 (2015). https://doi.org/10.1007/s00603-014-0650-5

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  • DOI: https://doi.org/10.1007/s00603-014-0650-5

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