Arabian Journal of Geosciences

, 12:578 | Cite as

Study on Mohr–Coulomb-based three-dimensional strength criteria and its application in the stability analysis of vertical borehole

  • Aditya SinghEmail author
  • K. Seshagiri Rao
  • Ramanathan Ayothiraman
Original Paper


In the present study, the six extensions for the Mohr–Coulomb criterion into three-dimensional stress state are discussed in detail. The prediction of strength from these criteria are compared with the experimental data of true-triaxial tests from 16 rocks. These extended criteria are Mogi–Coulomb, Modified Mohr–Coulomb A and B, and Mohr–Coulomb criterion with three different deviatoric functions (elliptical, hyperbolic, and spatial mobilized plane functions). The strength parameters of these criteria are calculated using the triaxial compression points from the true-triaxial tests data. Such consideration is taken because in general triaxial compression tests, data are only available for the majority of rocks. It is observed from the comparison that on average Mohr–Coulomb criterion with elliptical smoothening (MC-ED) performed better than other criteria (considered in the study). Hence, MC-ED is considered for vertical borehole stability analysis. MC-ED criterion also satisfies the Drucker stability postulate. To demonstrate the application of MC-ED criterion in the borehole stability analysis, four cases are considered. Results from the MC-ED criterion are compared with the Mohr–Coulomb criterion. The Mohr–Coulomb analysis calculates the higher minimum overbalance pressure required as compared to the MC-ED and lower fracture pressure. It is observed that MC-ED results are relatively closer to the actual values used in the case study considered in this paper.


Three-dimensional stress state Borehole stability Mohr–Coulomb criterion Mogi–Coulomb criterion Modified Mohr–Coulomb A and B criteria Lode angle dependency 


ξ, r, θ

Haigh–Westergaard coordinate system parameters


Lode angle


First stress invariant


Second stress invariants of the deviatoric stress tensor


Third stress invariants of the deviatoric stress tensor


Major principal stress


Intermediate principal stress


Minor principal stress


Angle of shearing resistance



a and b

Mogi–Coulomb parameters

a1 and b1

Modified Mohr–Coulomb A parameters

a2 and b2

Modified Mohr–Coulomb B parameters


Lode dependent function/deviatoric function


Aspect ratio


Funding information

The research is supported by the parents of Dr. Aditya Singh. His father Thakur Kirpal Singh Ji and mother Vimlesh Singh Ji gave the financial and emotional support to accomplish this work.


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Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  • Aditya Singh
    • 1
    Email author
  • K. Seshagiri Rao
    • 2
  • Ramanathan Ayothiraman
    • 2
  1. 1.Independent ResearcherAligarhIndia
  2. 2.Department of Civil EngineeringIndian Institute of Technology DelhiNew DelhiIndia

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