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Acta Geotechnica

, Volume 13, Issue 2, pp 419–445 | Cite as

Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC3D simulations

  • Peng-fei He
  • Pinnaduwa H. S. W. Kulatilake
  • Xu-xu Yang
  • Dong-qiao Liu
  • Man-chao He
Research Paper

Abstract

Study of intact rock failure criteria is an important topic in rock mechanics. In this study, applicability of nine different intact rock failure criteria is investigated for intact coal strength data. PFC3D modeling was used to simulate the laboratory polyaxial tests for cubic intact coal blocks of side dimension 110 mm under different confining stress combinations. A modified grid search procedure is proposed and used to find the best-fitting parameter values and to calculate the coefficient of determination (R 2) values for each criterion. Detailed comparisons of the nine criteria are made using the following aspects: R 2 values, σ 1 − σ 2 plots for different σ 3, shapes on the deviatoric plane, linearity or nonlinearity on the meridian planes. Through the comparisons of R 2 values, σ 1 − σ 2 plots and meridian lines, the modified Wiebols–Cook and modified Lade criteria were found to fit the intact coal strength data best. The nine failure criteria are categorized into three types based on the appearances on the deviatoric plane.

Keywords

Deviatoric plane Failure criteria Intact coal strength Meridian planes PFC3D modeling 

List of symbols

σ1, σ2, σ3

Major, intermediate and minor principal stresses at failure, respectively

σ1′, σ2′, σ3

Major, intermediate and minor effective principal stresses at failure, respectively

I1, I3

First and third invariant of stress tensor

I1′, I3

Modified first and third invariant of stress tensor

J2

Second invariant of deviatoric stress tensor

σoct

Octahedral normal stress or mean stress

τoct

Octahedral shear stress

σm,2

(σ 1 + σ 3)/2

σci

Uniaxial compressive strength of the intact rock

σti

Uniaxial tensile strength of the intact rock

σbi

Strength of the intact rock under triaxial extension stress state for σ 3 = 0

τ

Shear stress

σn

Normal stress

τ13

Major principal shear stress

τ12

Intermediate principal shear stress or minor principal shear stress

τ23

Intermediate principal shear stress or minor principal shear stress

σ13

Normal stresses acting on the τ 13 plane

σ12

Normal stresses acting on the τ 12 plane

σ23

Normal stresses acting on the τ 23 plane

q

Material constant determined by a certain function of the coefficient of friction in the W–C criterion

c0

Cohesion of the intact rock

φ

Internal friction angle of the intact rock

mb

Hoek–Brown constant for the rock mass

mi

Hoek–Brown constant for the intact rock

s, a

Constants depending on the rock mass characteristics

D

Disturbance factor

GSI

Geological Strength Index

α, k

Material constants of the D–P criterion

ρc, ρt

Compressive and tensile meridian on the deviatoric planes

κ

Material constant depending on the density of the soil in Lade–Duncan criterion (1975)

pa

Atmospheric pressure

m′, η1

Material constants of the modified Lade criterion (1977)

S

Material constant related to the cohesion and internal friction angle of the rock in the modified Lade criterion (1999)

η

Material constant representing the internal friction of the rock

A, B, C

Parameters in the modified W–C criterion

β

Constant smaller than 1 in Mogi (1967) criterion

C

Parameter related to c 0 and φ in the linear unified failure criterion

δ

Parameter related to φ in the linear unified failure criterion

b

Intermediate stress parameter in both linear and nonlinear unified failure criteria

ω

Ratio of σ ci to σ ti for the intact rock in the linear unified failure criterion

θ

Lode angle

ρ, ξ

Abscissa and ordinate of the plots on the meridian planes

Notes

Acknowledgements

The research was funded by the National Institute for Occupational Safety and Health (NIOSH) of the Centers for Disease Control and Prevention (Contract No. 200-2011-39886) and the State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Beijing (Contract No. SKLGDUEK1416).

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Peng-fei He
    • 1
    • 2
    • 3
  • Pinnaduwa H. S. W. Kulatilake
    • 1
  • Xu-xu Yang
    • 1
    • 4
  • Dong-qiao Liu
    • 2
  • Man-chao He
    • 2
  1. 1.Rock Mass Modeling and Computational Rock Mechanics LaboratoriesUniversity of ArizonaTucsonUSA
  2. 2.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and Technology (Beijing)BeijingChina
  3. 3.Key Laboratory of Shale Gas and GeoengineeringInstitute of Geology and Geophysics, Chinese Academy of SciencesBeijingChina
  4. 4.State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouChina

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