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Damage Poro-Mechanics group at GeorgiaTech (DeeP MeLT)

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Georgia Tech
Poromechanics of Damage and Healing: A Philosophy of the Mesoscale
Chloé Arson

December 2015

Problems

Damage is an abstract concept, generally associated to  the  ideas  of  degradation,  decrease  of  performance  or  loss of reliability. Because damage is tied to the notion  of  deprivation,  its  definition  is  relative  to  a  reference  state  and  its  measure  depends  on  standards  considered  as  relevant  observation  tools  by  the  modeler.  Damage  prediction  relies  on  the  field  variables  chosen  to  describe  the  anticipated  "degradation",  "loss"  or  "deprivation".  That  is  the  reason  why  framing  a  damage  model  is  necessarily  a  dynamic  thinking  process,  well  described  by  Claude  Bernards' OHERIC approach: Observation‐Hypothesis‐ Experimentation‐Interpretation‐Conclusion.  Healing  can  be  understood  as  the  microscopic  processes  underlying  observable  compensation  (or  recovery)  of  damage. However, while  there is no consensus on  the  definition  of  healing  in  geomaterials,  proven  crack  "sintering"  and  "re‐bonding"  do  not  stem  from  the  same  physical  processes  as  the  ones  originating  damage.  The  fundamental  question  is:  "What  do  we  want  to  observe?"  In  other  words:  "What  is  the  mesoscale"?

Approach

We  formulate  energy‐based  damage  and  healing  models  for  geomaterials  - mainly  rock  and  cement‐ based  materials.  The  underlying  theoretical  background  comprises  fundamental  thermodynamics,  poromechanics,  Continuum  Damage  Mechanics,  micro‐mechanics  and  homogenization  schemes.  Starting  from  observations  reported  by  experimentalists,  we  postulate  the  form  of  thermodynamic potentials, and we define macroscopic  variables that can be coupled to microscopic variables  describing fabric evolution with crack opening, closure  and  healing.     Most  of  our work  focuses  on  damage  - induced anisotropy of stiffness and permeability.

Findings

The keys  for damage  and  healing  phenomenological 
modeling  are  (1)  the  choice  of  descriptors,  i.e.  the 
choice of a set of independent and complete variables 
relevant  to  the  macroscopic  properties  under  study, 
(2) the scales of the observation window, i.e. the length 
scales at which a continuum rheology may and need to 
be defined. Emphasis is put on how descriptors evolve 
across the observation scales.
• An  alternative  damage  model  was  formulated  in 
independent  strain  variables,  allowing  to  account 
for  thermo‐hydro‐mechanical  couplings  in 
unsaturated brittle rock,
• An  exploratory  damage  and  healing  model  was 
proposed, based on the evolution of an intermediate 
internal variable ‐ defined as the difference between 
a  rate‐independent  damage  variable  and  a  rate‐
dependent healing variable,
• A  novel  permeability  model  was  formulated  to 
update  microscopic  Pore  Size  Distribution  (PSD) 
parameters  with  macroscopic  deformation  and 
damage,
• A  thermodynamic  framework  was  proposed  to 
model  crack  opening,  closure  and  healing  for  one 
single crack embedded in a solid matrix.

Impact

The proposed  approach  allows  predicting  crack  patterns around geological storage facilities and ahead  of  fracture  tips, which  is  a  central  issue  in  energy  geotechnics.  Models are also expected to contribute to  the  design  of  self‐healing geomaterials  for  sustainable  infrastructure.  The  philosophical  question  is:  does  a (fixed) mesoscale exist, and is it unique?

Selected Publications

1.  J.‐M.  Pereira,  C.  Arson,  2012.  Retention  and  Permeability 
Properties  of  Damaged  Porous  Rocks,  Computers  & 
Geotechnics, DOI: 10.1016/j.compgeo.2012.08.003
2.  C.  Arson,  J.‐M.  Pereira,  2012.  Influence  of  Damage  on  Pore 
Size  Distribution  and  Permeability  of  Rocks,  International 
Journal for Numerical and Analytical Methods in Geomechanics,
DOI:10.1002/nag.1123
3.  C.  Arson,  H.  Xu,  F.M.  Chester,  2012.  On  The  Definition  Of 
Damage  In  Time‐Dependent  Healing  Models  For  Salt  Rock, 
Géotechnique Letters, vol.2, pp.67‐71
4.  C.  Arson,  B.  Gatmiri,  2010.  Numerical  study  of  a 
thermo‐hydro‐mechanical  damage  model  for 
unsaturated porous media, Annals of Solid and Structural 
Mechanics, vol.1, n.2, pp. 59‐78
5.  C.  Arson,  B.  Gatmiri,  2008.  On  damage  modelling  in 
unsaturated  clay  rocks,  Physics  and  Chemistry  of  the 
Earth, vol.33, pp. S407-S415


Core Competencies

  • Constitutive Modeling: damage and  healing in rock, influence of microstructure  on macroscopic properties, thermo‐hydro‐ chemo‐mechanical couplings in porous  media.
  • Numerical Modeling: MATLAB, Finite  Elements, Discrete Elements.
  • Energy Geotechnics: nuclear waste  disposals, compressed air storage, carbon  dioxide sequestration, geothermal systems,  hydraulic fracturing.

georgia-tech-photo-2012
Prediction of Damage and Healing of Salt Stiffness  (top). Creating new thermodynamic potentials for  multiple damage mechanisms (bottom).

Current Research Team Members:
• Chloé Arson (PI)
• Hao Xu (PhD student)
• Cheng Zhu (PhD student)

Recent  Graduates and Co‐workers:
• Nathalie Dufour (PhD 2011) : visiting Ph.D. 
student (Spring 2011), Ecole Nationale des 
Travaux Publics de l'Etat, France
• Benjamin Juge (supervised M.Sc. 2011) 
• Erin Berns (supervised Undergraduate 2011)
• Mathew Hong  (supervised Undergraduate 
2011)
• Abenezer Nida  (supervised Undergraduate 
2010)

Current Research Collaborations:
• Numerical algorithms for a constitutive model 
coupling damage and plasticity in unsaturated 
geomaterials - Solenn Le Pense, visiting PhD 
student, Navier Laboratory, Ecole des Ponts 
ParisTech, France
• Multi‐scale modeling of permeability in 
damaged rock ‐ Jean‐Michel Pereira,  
Researcher, Navier Laboratory, Ecole des Ponts 
ParisTech, France
• Stiffness Homogenization  of  the  hybrid layer in 
teeth  treated  with  resin  comppsites  - Elsa 
Vennat, Assistant Professor, MSSMat Laboratory, 
Ecole Centrale Paris, France
• Characterization  and Modeling  of  Cement  Paste 
Thermal  Damage  Using  Acoustic  Waves  ‐
Zoubeir  Lafhaj,  Professor,  Lille  Mechanical 
Laboratory, Ecole Centrale Lille, France
• Damage  and  healing‐induced  anisotropy  in  salt 
rock    ‐ Fred  Chester,  Professor,  Department  of 
Geology & Geophysics, Texas A&M University
• Role  of  AC  diffusion  potentials  in 
decontamination  using  poultices,  J.  Carlos 
Santamarina, School  of Civil and Environmental 
Engineering, Georgia Institute of Technology