Rock Mechanics and Rock Engineering

, Volume 51, Issue 7, pp 2095–2114 | Cite as

Statistical Analysis of Rock Fracture Toughness Data Obtained from Different Chevron Notched and Straight Cracked Mode I Specimens

  • M. R. M. Aliha
  • E. Mahdavi
  • M. R. Ayatollahi
Original Paper


In laboratory fracture toughness studies, the crack growth resistance of rock materials may be influenced by different factors such as specimen geometry, loading conditions, and also the type of pre-notch cut in the test sample. In this paper, a large number of mode I fracture toughness experiments are conducted on an Iranian white rock “Harsin marble” with six different mode I specimens. The selected test specimens are in the shape of cylindrical rod, rectangular beam, and circular Brazilian disk containing either chevron notch or straight crack. The effect of specimen geometry and pre-notch type was investigated statistically, and it was found that the average fracture toughness values of notched specimens were higher than those of the similar specimens but containing straight crack. Meanwhile, the scatters of fracture toughness data for chevron notched specimens were smaller than those for the straight cracked samples. For each set of experimental fracture toughness results, probability of fracture was investigated using two- and three-parameter Weibull statistical distributions. Comparison of the Weibull fitted curves for chevron notched and straight cracked samples with the same geometries demonstrated that the discrepancy between the corresponding curves can be described with a good accuracy by a simple shift factor. In addition, using the extended maximum tangential strain criterion which takes into account the influence of both KI and T-stress terms, the statistical fracture toughness data of chevron notched specimens were predicted in terms of the Weibull distribution parameters of the straight cracked specimens.


Extended maximum tangential strain (EMTSN) criterion Mode I fracture resistance Rock Statistical analysis Weibull probability model 



Crack length


Critical crack length


Initial length of chevron notch


Final length of chevron notch


Dimensionless critical stress intensity factor of the CB specimen


Thickness of specimen


Biaxiality ratio


Dimensionless compliance of specimen


Diameter of specimen


Modulus of elasticity


Geometry factor of the SENB specimen




Fracture load


Number of test specimen


Shear transfer function


Stress intensity factor


Fracture toughness


Mode I fracture toughness


Mode I fracture resistance


Location parameter of fracture resistance distribution


Scale parameter of fracture resistance distribution


Length of specimen


Shape parameter for describing the scatter of KIf


Total number of tests for each specimen


Shape or geometry factor of the SCCBD specimen


Failure probability


Distance from the crack tip


Critical distance from the crack tip


Radius of specimen


Support span


Critical value of T-stress


Load-point displacement


Height of the CNBB and SENB specimens


Normalized critical stress intensity factor of CCNBD specimen


Normalized critical distance


Critical value of tangential strain


Tangential strain


Chevron notch angle


Direction of fracture in polar coordinates


Shift factor between two sets of data


Poisson’s ratio


Characteristic stress in the specimen


Tensile strength of rock material


Chevron bend specimen


Cracked chevron notched Brazilian disk specimen


Chevron notched bend beam


Extended maximum tangential strain criterion


Fracture process zone


International Society for Rock Mechanics


Maximum tangential strain criterion


Straight center cracked Brazilian disk specimen


Single edge cracked round bar bend specimen


Single edge notched beam specimen


Stress intensity factor


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • M. R. M. Aliha
    • 1
  • E. Mahdavi
    • 2
  • M. R. Ayatollahi
    • 2
  1. 1.Welding and Joining Research Center, School of Industrial EngineeringIran University of Science and Technology (IUST)Narmak, TehranIran
  2. 2.School of Mechanical EngineeringIran University of Science and Technology (IUST)Narmak, TehranIran

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