Skip to main content
SpringerLink
Log in

Development of New Three-Dimensional Rock Mass Strength Criteria

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Two new three-dimensional rock mass strength criteria are developed in this paper by extending an existing rock mass strength criterion. These criteria incorporate the effects of the intermediate principal stress, minimum principal stress and the anisotropy resulting from these stresses acting on the fracture system. In addition, these criteria have the capability of capturing the anisotropic and scale dependent behavior of the jointed rock mass strength by incorporating the effect of fracture geometry through the fracture tensor components. The new criteria are proposed after analyzing 284 numerical modeling results of the polyaxial, triaxial and biaxial compression tests conducted on the jointed rock blocks having one or two joint sets by the PFC3D software. Some of these simulation results were compared with experimental results to validate the developed PFC3D model that was used for numerical modeling of jointed blocks. In this research to have several samples with the same properties a synthetic rock material that is made out of a mixture of gypsum, sand and water was used. Altogether, 12 joint systems were chosen; some of them had one joint set and the rest had two joint sets. Joint sets have different dip angles varying from 15° to 45° at an interval of 15° with dip directions of 30° and 75° for the two joint sets. Each joint set also has three persistent joints with the joint spacing of 42 mm in a cubic sample of size 160 mm. The minimum and intermediate principal stress combination values were chosen based on the uniaxial compressive strength (UCS) value of the modeled intact synthetic rock. The minimum principal stress values were chosen as 0, 0.2, 0.4 and 0.6 of the UCS. For each minimum principal stress value, the intermediate principal stress value varies starting at the minimum principal stress value and increasing at an interval of 0.2 of the UCS until it is slightly lower than the strength of the sample under the biaxial loading condition with the same minimum principal stress value. To express the new rock mass strength criteria, it was also necessary to determine the intact rock strengths under the same confining stress combinations mentioned earlier. Therefore, the intact rock was also modeled for all three compression tests and the intact rock strengths were found for 33 different minimum and intermediate principal stress combinations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Abbreviations

A :

Disk area

\(a\), \({a_2}\), \({a_3}\), \(b\), \({b_2}\), \({b_3}\) :

Empirical coefficients

B :

An empirical constant

\({B^J}\) :

Constant coefficient of the modified smooth-joint contact model

\({C_J}\) :

Joint cohesion

D min, D max :

Minimum and maximum particle diameters

\({E_{\text{c}}}\), \({\bar {E}_{\text{c}}}\) :

Contact and bond Young’s modulus of the linear parallel bond model, respectively

\({F_{ij}}\), \(F_{{ij}}^{r}\), \(F_{{ij}}^{k}\) :

Fracture tensor, fracture tensor of the rock mass and fracture tensor of the kth joint set, respectively

\({F_{11}}\), \({F_{22}}\), \({F_{33}}\) :

Fracture tensor components in the maximum, intermediate and minimum principal stress directions, respectively

\(f\), \({f_2}\), \({f_3}\) :

Monotonically decreasing functions

\(K_{n}^{J}\), \(K_{s}^{J}\) :

Joint normal and shear stiffnesses, respectively

\(k_{n}^{J}\), \(k_{s}^{J}\) :

Joint normal and shear stiffnesses of the modified smooth-joint contact model, respectively

\(k_{{{n_{{\text{min}}}}}}^{J}\) :

Minimum joint normal stiffness of the modified smooth-joint contact model

k r ,\({\bar {k}_r}\) :

Ratio of the normal to shear stiffnesses of the contact and bond for the linear parallel bond model, respectively

m :

Number of parameters to be estimated

\({m^{\left( V \right)}}\) :

Number of fracture centers

N :

Total number of joint sets

n :

Total number of data sets

n :

Normal vector

\({n_i}\), \({n_j}\) :

Projection of the normal vector in the directions of i and j, respectively

p, \(~{p_2}\), \({p_3}\), q, \({q_2}\), \({q_3}\) :

Empirical coefficients

\({R^2}\) :

Coefficient of determination

r :

Equivalent radius

\({S_r}\) :

Strength ratio between the jointed rock mass and intact rock strengths

V :

Assumed volume

X, Y, Z :

Cartesian coordinates

\(\lambda\), \({\lambda _0}\), \({\lambda _2}\), \({\lambda _3}\) :

Empirical coefficients

\(\bar {\lambda }\) :

Bond radius fraction of the Linear Parallel Bond Model

\(\mu\) :

Friction coefficient of the Linear Parallel Bond Model

\(\mu^{J}\) :

Joint friction coefficient of the Modified Smooth-Joint Contact model

\({\sigma _1}\), \(~{\sigma _2}\), \(~{\sigma _3}\) :

Maximum, Intermediate and Minimum principal stresses, respectively

\({\sigma _c}\) :

Uniaxial compressive strength

\({\bar {\sigma }_c}\), \({\bar {\tau }_s}\) :

Bond tensile and shear strengths of the Linear Parallel Bond Model, respectively

\({\sigma _J}\), \({\sigma _I}\) :

Jointed rock mass and intact rock strengths, respectively

\(\sigma _{{J,i}}^{P}\) :

Predicted jointed rock block strength from the new rock mass strength criterion for data set i

\(\sigma _{{J,i}}^{{{\text{PFC}}}}\) :

Strength of the jointed rock block from the PFC3D modeling for data set i

\(\overline{\sigma } _{{J,i}}^{{{\text{PFC}}}}\) :

Average strength value of all the PFC3D data

\({\sigma _n}\) :

Normal stress

\(\sigma _{n}^{J}\) :

Normal stress on the Modified Smooth-Joint Contact

\({\varphi _J}\) :

Joint friction angle

CUMTB:

China University of Mining and Technology, Beijing

DEM:

Discrete element method

JSC:

Joint sides checking approach

LPBM:

Linear parallel bond model

LVDT:

Linear variable differential transformer

MSJCM:

Modified smooth-joint contact model

NIOSH:

National Institute for Occupational Safety and Health

PFC:

Particle flow code

PFC3D :

Three-dimensional particle flow code

SJCM:

Smooth-joint contact model

UCS:

Uniaxial compressive strength

3DEC:

Three-dimensional distinct element code

References

Download references

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).

Author information

Author notes

  1. Mohammad Hadi Mehranpour

    Present address: HPT-Laboratory, Faculty of Geosciences, Utrecht University, Utrecht, The Netherlands

Authors and Affiliations

  1. Rock Mass Modeling and Computational Rock Mechanics Laboratories, University of Arizona, Tucson, AZ, 85721, USA

    Mohammad Hadi Mehranpour & Pinnaduwa H. S. W. Kulatilake

  2. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing, China

    Ma Xingen & Manchao He

Authors
  1. Mohammad Hadi Mehranpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pinnaduwa H. S. W. Kulatilake
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ma Xingen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Manchao He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pinnaduwa H. S. W. Kulatilake.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mehranpour, M.H., Kulatilake, P.H.S.W., Xingen, M. et al. Development of New Three-Dimensional Rock Mass Strength Criteria. Rock Mech Rock Eng 51, 3537–3561 (2018). https://doi.org/10.1007/s00603-018-1538-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-018-1538-6

Keywords

Search

Navigation