Rock Mechanics and Rock Engineering

, Volume 51, Issue 6, pp 1777–1787 | Cite as

Characterizing Fracturing of Clay-Rich Lower Watrous Rock: From Laboratory Experiments to Nonlocal Damage-Based Simulations

  • N. Guy
  • D. M. Seyedi
  • F. Hild
Original Paper


The work presented herein aims at characterizing and modeling fracturing (i.e., initiation and propagation of cracks) in a clay-rich rock. The analysis is based on two experimental campaigns. The first one relies on a probabilistic analysis of crack initiation considering Brazilian and three-point flexural tests. The second one involves digital image correlation to characterize crack propagation. A nonlocal damage model based on stress regularization is used for the simulations. Two thresholds both based on regularized stress fields are considered. They are determined from the experimental campaigns performed on Lower Watrous rock. The results obtained with the proposed approach are favorably compared with the experimental results.


Crack network Fracture toughness Nonlocal damage Rock fracturing Weibull model 

List of Symbols

\({\varvec{\sigma }}\)

Stress tensor

\(\overline{{\varvec{\sigma }}}\)

Regularized stress tensor

\(\ell _{\mathrm{c}}\)

Characteristic length

\({\varDelta }\)

Laplacian operator


Normal to surface


Crack initiation probability


Crack initiation stress

\(\frac{\sigma _{0}^{m}}{\lambda _{0}}\)

Scale parameter


Volume of an element


Weibull modulus

\(\sigma _{\ell _{\mathrm{c}}}\)

Nominal stress


Crack growth stress


Fracture toughness

\({\varGamma }\)

Gamma function


Mass density



\(\psi _{\mathrm{e}}\)

State potential

\({\mathcal {C}}\)

Hooke’s tensor

\({\varvec{\epsilon }}\)

Infinitesimal strain tensor


Thermodynamic force associated with damage


Heaviside function

\({\overline{\sigma }}_{\mathrm{I}}\)

Maximum principal regularized stress


Half-length of critical defect

\(\sigma _{\mathrm{w}}\)

Weibull stress

\(\sigma _{\mathrm{w}i}\)

Weibull stress associated with sample i


Failure probability


Failure probability associated with sample i


Critical maximum principal stress


Stress heterogeneity factor


Sample volume


Stress heterogeneity factor for Brazilian test


Sample volume for Brazilian test


Stress heterogeneity factor for three-point flexural test


Sample volume for three-point flexural test


Total number of samples


Radius of Brazilian test sample


Length of Brazilian test sample


Mode I stress intensity factor


Mode II stress intensity factor


Ratio between mode II and mode I stress intensity factors



This work was funded by BRGM through an “Institut Carnot” research Grant. The authors wish to thank Dr. Steve Whittaker and Saskatchewan Industry and Resource for kindly providing the samples of Lower Watrous caprock.


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Copyright information

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

Authors and Affiliations

  1. 1.BRGM, Natural Risks and CO2 Storage Safety DivisionOrléansFrance
  2. 2.IFP Energies NouvellesRueil-Malmaison CedexFrance
  3. 3.Andra, R & D DivisionChatenay-MalabryFrance
  4. 4.LMT, ENS Paris-Saclay / CNRS / Université Paris-SaclayCachan CedexFrance

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