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A conceptual modeling on the behavior of strain localization for brittle rocks

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Abstract

This paper captures the frequently encountered strain localization of brittle rocks in laboratory compression experiments under moderate confining pressures generally ranging from 10 to 60 MPa. The plastic volumetric strains are related to particle dislocations in shear bands strongly constrained by relatively undeformed neighboring materials. Accordingly, the dilatant behavior of shear bands, analogous to a rock joint shearing, is predicted by introducing a multiple-asperity joints model. By imposing the model, the dislocation of grain particles in bands is abstracted by an uneven interface shear to reflect admitted volumetric strain behavior. It also highlights key issues associated with the bands, i.e., the width, the boundary conditions and non-uniform grain sizes within the bands. To tackle these problems, appropriate hypotheses are further made to simplify analytical procedures. The solution can quantify triaxial stress–strain relations with the least number of model parameters. A comparison between predictions and published experimental data is claimed to be satisfactory.

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Data availability statement

Some or all data, models or code generated or used during the study are available from the corresponding author by request (the data in the graph and the code of calculation).

Abbreviations

H :

Height of prismatic specimen

D :

Diameter of cylinder specimen

W :

Equivalent width of cylinder sample

ε :

Global apparent strain

ε e :

Elastic strain

ε p :

Permanent strain

E :

Elasticity modulus

ν:

Poisson’s ratio

σ 1 :

Major principal stresses

σ 3 :

Minor principal stresses

W s :

Localized width of shear bands

R :

Radius of grains

r :

Radius of a cylindrical cavity.

L :

Total length of the primary joint profile

θ :

Inclination of asperities

l i :

Chord length of the ith asperities

l min :

Minimum chord length of asperity

l max :

Maximum chord length of asperity

n :

Total number of asperities

\(\xi_{i}^{cr}\) :

Critical shear displacement for ith asperity

c :

Cohesion of rocks

φ :

Internal friction angle of rocks

φ b :

Base friction angle of rocks

K :

Normal spring stiffness

ξ :

Displacement of the interface

l cr :

Critical chord length of failed asperities

τ i ,int :

Local shear strength of intact asperities

m :

Number of failed asperities

τ i ,res :

Local shear strength of failed asperities

φ r :

Residual frictional angle of rocks

A :

Nominal area of the joint

τ :

Global shear strength across the total joint

i cr :

Index of the biggest failed asperity

ψ :

Dilatancy angle of rocks

ω :

The angle of shear band with respect to the horizontal

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Acknowledgements

This research is a part of the work carried out by grants from the National Natural Science Foundation of China (Nos. 51978255 and 52108317).

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Authors and Affiliations

  1. College of Civil Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Heng Zhao, Jichao Hou & Wenzhe Peng

  2. Key Laboratory of Building Safety and Energy Efficiency, Ministry of Education, Hunan University, Changsha, 410082, People’s Republic of China

    Heng Zhao, Jichao Hou & Wenzhe Peng

  3. Hunan Provincial Key Laboratory of Geotechnical Engineering for Stability Control and Health Monitoring, Hunan University of Science and Technology, Xiangtan, 411201, People’s Republic of China

    Chao Zhang

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  1. Heng Zhao
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Correspondence to Wenzhe Peng.

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Zhao, H., Hou, J., Peng, W. et al. A conceptual modeling on the behavior of strain localization for brittle rocks. Acta Geotech. 17, 5239–5251 (2022). https://doi.org/10.1007/s11440-022-01652-z

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