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The 3D Numerical Simulation for the Propagation Process of Multiple Pre-existing Flaws in Rock-Like Materials Subjected to Biaxial Compressive Loads

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Abstract

General particle dynamics (GPD), which is a novel meshless numerical method, is proposed to simulate the initiation, propagation and coalescence of 3D pre-existing penetrating and embedded flaws under biaxial compression. The failure process for rock-like materials subjected to biaxial compressive loads is investigated using the numerical code GPD3D. Moreover, internal crack evolution processes are successfully simulated using GPD3D. With increasing lateral stress, the secondary cracks keep growing in the samples, while the growth of the wing cracks is restrained. The samples are mainly split into fragments in a shear failure mode under biaxial compression, which is different from the splitting failure of the samples subjected to uniaxial compression. For specimens with macroscopic pre-existing flaws, the simulated types of cracks, the simulated coalescence types and the simulated failure modes are in good agreement with the experimental results.

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Abbreviations

D :

A disturbance coefficient

E :

Young’s modulus

f :

Interaction factor

\(D_{1}\) :

Damage factor

G :

Shear modulus

U :

Undamaged particles

D a :

Damaged particles

h :

Smoothing length

μ :

Poisson ratio

ρ :

Real time mass density

ρ 0 :

The initial density

k :

The modulus of volume elasticity

\(v_{i}\) :

Particle velocity at ith particle

\(\dot{R}^{\alpha \beta }\) :

Rotation rate

\(x^{\alpha }\) :

Spatial coordinate (X)

\(\dot{\varepsilon }^{\alpha \beta }\) :

Strain rate

c i :

The elastic wave speed

\(W_{ij,\,\beta }\) :

The kernel gradient with smoothing length h

\({{\text{d}} \mathord{\left/ {\vphantom {{\text{d}} {{\text{d}}t}}} \right. \kern-0pt} {{\text{d}}t}}\) :

The time derivative

m :

The value of \(m_{s}\) (in the Hoek–Brown criterion)

\(\sigma_{c}\) :

Uniaxial compressive strength

\(v^{\alpha }\) :

Velocity vector (V)

\(c_{i}\) :

The elastic wave speed at the ith particle

\(\sigma^{\alpha \beta }\) :

Cauchy stress tensor (\(\sigma\))

\(\tau^{\alpha \beta }\) :

Material frame in different objective rate

\(\dot{\tau }^{\alpha \beta }\) :

Stress rate

\(\alpha ,\,\,\beta\) :

Indices for the three spatial directions

a :

The half-length of flaw

c :

The non-overlapping length

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Acknowledgments

This work was supported by project 973 (Grant No. 2014CB046903), the National Natural Science Foundation of China (Nos. 51325903 and 51279218), and the Natural Science Foundation Project of CQ CSTC (Nos. CSTC, cstc2013kjrcljrccj0001 and cstc2013jcyjys30002).

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Authors and Affiliations

  1. School of Civil Engineering, Chongqing University, 400045, Chongqing, People’s Republic of China

    J. Bi & X. P. Zhou

  2. School of Resources and Environmental Engineering, Hefei University of Technology, 230009, Hefei, People’s Republic of China

    J. Bi & X. P. Zhou

  3. Engineering Institute of Engineering Crops, PLA University of Science and Technology, 210007, Nanjing, People’s Republic of China

    X. P. Zhou & Q. H. Qian

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  1. J. Bi
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Correspondence to X. P. Zhou.

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Bi, J., Zhou, X.P. & Qian, Q.H. The 3D Numerical Simulation for the Propagation Process of Multiple Pre-existing Flaws in Rock-Like Materials Subjected to Biaxial Compressive Loads. Rock Mech Rock Eng 49, 1611–1627 (2016). https://doi.org/10.1007/s00603-015-0867-y

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