Coupled-scale computational modelling of
permeability evolution in heterogeneous
rocks experiencing excavation damage
T.J. Massart, A.P.S. Selvadurai
Building, Architecture & Town Planning, Université Libre de
Bruxelles (ULB), Brussels, Belgium
Environmental Geomechanics, Civil Engineering, McGill
University, Montreal, Canada
Context - Motivation
[Souley et al., 2001]
[Rutqvist et al., 2009]
[Souley et al., 2001]
Can such effects be reproduced using computational homogenization tools,
assuming their microscale origin (microcrack dilatancy) ? [Zoback et al., 1975]
2
Periodic computational homogenization
Averaging relations for mechanical response
Strain
Stress
[Sanchez-Palencia ; Anthoine, 1995; Smit, 1998;
Feyel and Chaboche, 2000; Kouznetsova et al., 2001]
Energy
Averaging relations for fluid transport
[Ozdemir et al., 2008; Massart & Selvadurai 2012]
Average permeability
3
Local cracking–induced permeability evolution
Cracking represented by
local interfaces
[Lisjak, 2014; Mahabadi, 2012;
Massart & Selvadurai 2012]
Mohr-Coulomb criterion
Non associated Flow rule
with
with
with
[van Zijl, 1990]
Local permeability evolution
Permeability from hydraulic aperture
[Benjelloun, 1993; Nguyen & Selvadurai 1998]
with
0.5 <
<1
4
Lac du Bonnet Granite
 Volume fraction of species according to the experimentally observed mineralogic composition for the
considered granite
 Elastic properties of phases fitted to reproduce the elastic properties of the rock
 Random spatial distribution of mineral species in the RVE
 3D computations performed on RVEs under non proportional stress controlled loading (triaxial test)
 Analysis of the effect of dilatancy on the obtained permeability evolution
ft (MPa) Gf,I [N/mm] c [MPa] ϕ [°] Gf,II [N/mm]
ψ [°]
6
[20,40]**
1
26.4*
40
10
* Spatial lognormal distribution
** Assumed independent of confinement
[Massart & Selvadurai, 2014]
5
Lac du Bonnet Granite – associated response
[Souley et al., 2001; Massart & Selvadurai, 2014]
Mechanical response
Present approach
Jiang et al., 2010
Shao et al., 2006
6
Lac du Bonnet Granite – associated response
Permeability evolution
[Souley et al., 2001; Massart & Selvadurai, 2014]
σ3 = 10 MPa
Present approach
Jiang et al., 2010
Shao et al., 2006
7
Lac du Bonnet Granite – non associated response
Mechanical response
[Souley et al., 2001; Massart & Selvadurai, 2014]
8
Lac du Bonnet Granite – permeability
Permeability evolution
[Souley, 2001; Massart & Selvadurai, 2014]
9
Excavation damage at URL – Macro-scale
 2D problem, phased loading representing excavation process based on the initial in situ stress state
 Generalized Plane State assumption with scalar (nonlocal) damage model for localization
accounting for different behaviours in tension and compression
 Lower mechanical properties assumed to represent the effect of drill and blast operations & slight
variability introduced to promote localization
 Stress history of points along horizontal borehole extracted & used as loading history applied on
Σ = −11 MPa
representative volume elements
1
ν
ft [MPa]
fc [MPa]
lc (mm)
80 ± 3
0.2
0.25
20
700
Σ 2 = −50 MPa
1,75 m
E [MPa]
Σ3 = −57 MPa
2,2 m
Horizontal
borehole
10
Permeability evolution extracted from RVE
 Evolution of the geometrical mean of principal permeabilities
 Associated response of the cracks assumed at fine scale
 Degraded properties assumed at macroscale to capture a
proper damage patterns
 With such assumptions, stress history allows capturing
qualitatively the evolution of the permeability (horizontal
borehole)
[Rutqvist et al., 2009]
 Vertical borehole with higher permeability increase NOT
captured
 Further investigations required to couple crack dilatancy to
overall dilatancy linked to geometrical interlocking
11
Conclusion & Perspectives
 Computational homogenization used in combination with micro-scale
features (mineral species volume fractions, crack dilatancy, …)
 Computational homogenization allows capturing the order of
magnitude of permeability evolution in granite both in lab-scale and
in-situ configurations
 Macroscale degraded mechanical properties assumed to obtain
proper damage patterns
[Sonon et al., 2012, 2014]
 Further work required on overall dilatancy associated with
geometrical interlocking (non convexity of grains) using RVEs with
more realistic geometries
12