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A Model for Pore Pressure Response of a Claystone due to Liberated Residual Stress Dilation

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Abstract

The hydromechanical response of Opalinus Clay is being studied as a potential host formation for the long-term geological storage of nuclear waste. Two separate mine-by field experiments were conducted at Mont Terri rock laboratory, Switzerland: one in 1997–1998 (HD-B) and one in 2008 (MB Niche) to observe the claystone’s response to tunnel excavation. The data from both mine-by tests revealed an undrained pore pressure response dominated by significant pore pressure drop (i.e., a dilational tendency), even in instrumentation locations where stress-induced damage (‘failure’) was not anticipated. This response is not reproducible by conventional hydromechanical models unless very low yield envelopes are used to predict the onset of dilation. An alternative mechanism for the undrained dilational response of Opalinus Clay due primarily to unloading in the low confining stress regime is presented in this paper. The mechanism is derived from observed behaviour of the Opalinus Clay in the field and laboratory, and an understanding of the composition and geological history of the material. The model is based on mechanisms associated with liberation of latent strain energy, and associated residual stress (‘locked-in stress’ or ‘stress memory’) through microcrack formation. Mobilization of this internal stress on the undrained response of Opalinus Clay results in distinct regimes of hydromechanical response, dependent on confining stress levels, that is accounted for in the model. The model was implemented into the continuum finite difference code FLAC3D and produced good agreement with mine-by test observations.

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Fig. 1

Modified after Martin et al. (2015)

Fig. 2

Modified from Martin and Christiansson (2009)

Fig. 3
Fig. 4

Data from Olalla et al. (1999)

Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

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Notes

  1. Itasca Consulting Group, Inc. (https://www.itascacg.com).

Abbreviations

EDZ:

Excavation Damaged Zone

EdZ:

Excavation Disturbed Zone

LRSD:

Liberated Residual Stress Dilation

REV:

Representative Elementary Volume

UCS:

Unconfined Compressive Strength

w :

Water content

\(\nu \) :

Poisson ratio

E :

Young’s modulus

\(E_\mathrm{c}\) :

Young’s modulus (secant) in crack closure region

K :

Bulk modulus of rock matrix

\(K_\mathrm{s}\) :

Bulk modulus of rock grains

\(K_\mathrm{w}\) :

Bulk modulus of water

\(\epsilon _\mathrm{a}\) :

Axial strain

\(\epsilon _\mathrm{cc}\) :

Crack Closure strain

\(\epsilon _x,\epsilon _y,\epsilon _z\) :

Normal strain components

\(\epsilon _\mathrm{v}\) :

Volumetric strain

\(\epsilon _\mathrm{vc}\) :

Crack volumetric strain

\(\sigma _x,\sigma _y,\sigma _z\) :

Normal stresses components

\(\sigma _1,\sigma _2,\sigma _3\) :

Principal stresses

\(\sigma _\mathrm{m}\) :

Mean stress

\(\sigma _\mathrm{a}\) :

Axial stress

\(\sigma _\mathrm{cc}\) :

Crack Closure stress in UCS test

\(\sigma _\mathrm{ci}\) :

Crack Initiation stress in UCS test

\(\sigma _\mathrm{cd}\) :

Crack Damage stress in UCS test

\(\sigma _\mathrm{p}\) :

Peak stress (strength) in UCS test

\(\sigma '\) :

Effective stress (with components)

\(\sigma ^*\) :

Microstress (with components)

\(\sigma _\mathrm{r}\) :

Residual (locked-in) stress

\(\sigma _\mathrm{cr}\) :

Liberated residual stress

\(\sigma _\mathrm{n}\) :

Net stress acting on REV

\(\alpha \) :

Biot’s pore pressure coefficient

p :

Pore pressure

\(p_\mathrm{e}\) :

Excess pore pressure components

\(p_\mathrm{s}\) :

Static pore pressure components

V :

Volume (total)

\(V_\mathrm{c}\) :

Crack volume

k :

Hydraulic conductivity

X / D :

Distance from tunnel face/tunnel diameter

l :

Length of REV

\(k_1,k_2\) :

Spring stiffness constants

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Acknowledgements

Professor C.D. Martin provided generous support throughout the study. Dr P. Blümling and Nagra staff provided helpful insight and resources. Professor N.R. Morgenstern suggested the potential role of diagenetic bonding and latent strain energy in the unique behaviour of claystones. Several colleagues kindly provided helpful comments and suggestions and the Journal’s reviewers helped to improve the manuscript.

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  1. Dalhousie University, Halifax, Nova Scotia, Canada

    A. G. Corkum

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Corkum, A.G. A Model for Pore Pressure Response of a Claystone due to Liberated Residual Stress Dilation. Rock Mech Rock Eng 53, 587–600 (2020). https://doi.org/10.1007/s00603-019-01938-x

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