.. Simulations-numériques, 71 3.3.5 Solutions semi-analytiques pour le calcul des facteurs d'intensité de contraintes en régime stationnaire

H. Abe, T. Mura, and L. M. Keer, Growth rate of a penny-shaped crack in hydraulic fracturing of rocks, Journal of Geophysical Research, issue.29, pp.81-5335, 1976.

J. I. Adachi and E. Detournay, Plane strain propagation of a hydraulic fracture in a permeable rock, Engineering Fracture Mechanics, vol.75, issue.16, pp.75-4666, 2008.
DOI : 10.1016/j.engfracmech.2008.04.006

J. I. Adachi, E. Detournay, and A. A. Savitski, Simulation of hydraulic fracturing using an explicit moving mesh algorithm, The 38th US Symposium on Rock Mechanics (USRMS), 2001.

J. I. Adachi, E. Siebrits, A. Peirce, and J. Desroches, Computer simulation of hydraulic fractures, International Journal of Rock Mechanics and Mining Sciences, vol.44, issue.5, pp.739-757, 2007.
DOI : 10.1016/j.ijrmms.2006.11.006

S. H. Advani, T. S. Lee, R. H. Dean, C. K. Pak, and J. M. Avasthi, CONSEQUENCES OF FLUID LAG IN THREE-DIMENSIONAL HYDRAULIC FRACTURES, International Journal for Numerical and Analytical Methods in Geomechanics, vol.7, issue.4, pp.229-240, 1997.
DOI : 10.1002/(SICI)1096-9853(199704)21:4<229::AID-NAG862>3.0.CO;2-V

B. Amadei and S. Saeb, Constitutive models of rock joints, Rock joints. Proceedings of the international symposium on rock joints, pp.4-6, 1990.

T. Backers, Fracture toughness determination and micromechanics of rock under Mode I and Mode II loading, 2004.

S. C. Bandis, A. C. Lumdsen, and N. R. Barton, Fundamentals of rock joint deformation, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.20, issue.6, pp.249-268, 1983.
DOI : 10.1016/0148-9062(83)90595-8

G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture Advances in Applied Mechanics, pp.55-129, 1962.

G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], Journal of Applied Mathematics and Mechanics, vol.24, issue.5, pp.1286-1303, 1960.
DOI : 10.1016/0021-8928(60)90107-6

N. R. Barton and S. C. Bandis, Effect of block size on the behavior of jointed rock, Proceedings of the 23 rd U.S. Symposium on Rock Mechanics, pp.739-760, 1982.

N. Barton, Review of a new shear strength criterion for rock joints. Engineering Geology, pp.287-332, 1973.

J. Bass, Elasticity of minerals, glasses, and melts, American Geophysical Union Online Reference Shelf, vol.20, pp.45-63, 1995.
DOI : 10.1029/RF002p0045

B. Yazdi and P. , Modélisation de la stabilité des massifs rocheux avec prise en compte de l'endommagement des joints et des effets hydromécaniques, p.237, 2009.

I. Berchenko and E. Detournay, Deviation of hydraulic fractures through poroelastic stress changes induced by fluid injection and pumping, International Journal of Rock Mechanics and Mining Sciences, vol.34, issue.6, pp.1009-1019, 1997.
DOI : 10.1016/S1365-1609(97)80010-X

Y. Bernabé, The effective pressure law for permeability in Chelmsford granite and Barre granite, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.23, issue.3, pp.267-275, 1986.
DOI : 10.1016/0148-9062(86)90972-1

J. G. Berryman, Effective stress for transport properties of inhomogeneous porous rock, Journal of Geophysical Research, vol.59, issue.B12, pp.17409-17424, 1992.
DOI : 10.1029/92JB01593

M. A. Biot, General Theory of Three???Dimensional Consolidation, Journal of Applied Physics, vol.12, issue.2, pp.155-164, 1941.
DOI : 10.1063/1.1712886

URL : https://hal.archives-ouvertes.fr/hal-01368635

M. A. Biot and D. G. Willis, The elastic coefficients of the theory of consolidation, Journal of Applied Mechanics, vol.24, pp.594-601, 1957.
URL : https://hal.archives-ouvertes.fr/hal-01368677

A. W. Bishop, The use of the Slip Circle in the Stability Analysis of Slopes, G??otechnique, vol.5, issue.1, pp.7-17, 1955.
DOI : 10.1680/geot.1955.5.1.7

L. Bjerrum, J. K. Nash, R. M. Kennard, and R. E. Gibson, Hydraulic fracturing in field permeability testing, G??otechnique, vol.22, issue.2, pp.319-332, 1972.
DOI : 10.1680/geot.1972.22.2.319

T. J. Boone and A. R. Ingraffea, A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media, International Journal for Numerical and Analytical Methods in Geomechanics, vol.24, issue.1, pp.27-47, 1990.
DOI : 10.1002/nag.1610140103

D. F. Boutt, L. Goodwin, and B. J. Mcpherson, Role of permeability and storage in the initiation and propagation of natural hydraulic fractures, Water Resources Research, vol.263, issue.2, 2009.
DOI : 10.1029/2007WR006557

W. F. Brace, Laboratory studies of stick-slip and their application to earthquakes, Tectonophysics, vol.14, issue.3-4, pp.189-200, 1972.
DOI : 10.1016/0040-1951(72)90068-6

A. Brencich and A. Carpinteri, Interaction of a main crack with ordered distributions of microcracks: a numerical technique by displacement discontinuity boundary elements, International Journal of Fracture, vol.48, issue.4, pp.373-389, 1986.
DOI : 10.1007/BF00039784

D. Broek, Elementary engineering fracture mechanics The Hague, The Netherlands, 1982.

M. S. Bruno and F. M. Nakagawa, Pore pressure influence on tensile fracture propagation in sedimentary rock, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.28, issue.4, pp.261-273, 1991.
DOI : 10.1016/0148-9062(91)90593-B

H. D. Bui, Mécanique de la rupture fragile, p.215, 1978.

A. P. Bunger, E. Detournay, and D. I. Garagash, Toughness-dominated Hydraulic Fracture with Leak-off, International Journal of Fracture, vol.400, issue.1, pp.175-190, 2005.
DOI : 10.1007/s10704-005-0154-0

J. D. Byerlee, The fracture strength and frictional strength of Weber Sandstone, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.12, issue.1, pp.1-4, 1975.
DOI : 10.1016/0148-9062(75)90736-6

I. Carol, P. C. Prat, and C. M. López, Normal/Shear Cracking Model: Application to Discrete Crack Analysis, Journal of Engineering Mechanics, vol.123, issue.8, pp.123765-773, 1997.
DOI : 10.1061/(ASCE)0733-9399(1997)123:8(765)

A. Carpinteri, Softening and snap-back instability in cohesive solids, International Journal for Numerical Methods in Engineering, vol.85, issue.7, pp.1521-1537, 1989.
DOI : 10.1002/nme.1620280705

A. Carpinteri and I. Monetto, Snap-back analysis of fracture evolution in multi-cracked solids using boundary element method, International Journal of Fracture, pp.98-101, 1999.

B. Carrier and S. Granet, Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model, Engineering Fracture Mechanics, vol.79, pp.312-328, 2012.
DOI : 10.1016/j.engfracmech.2011.11.012

URL : https://hal.archives-ouvertes.fr/hal-00670787

S. Cesca, F. Grigoli, S. Heimann, A. Gonzalez, E. Buforn et al., The 2013 seismic sequence close to gas injection platform of the Castor project, offshore Spain, EGU General Assembly Conference Abstracts, p.7171, 2014.

B. Cotterell and J. Rice, Slightly curved or kinked cracks, International Journal of Fracture, vol.2, issue.2, pp.155-169, 1980.
DOI : 10.1007/BF00012619

C. A. Coulomb, Essai sur une application des règles de maximis & minimis à quelques problèmes de statique, relatifs à l'architecture, 1776.

O. Coussy, Poromechanics, p.315, 2004.
DOI : 10.1002/0470092718

URL : https://hal.archives-ouvertes.fr/hal-00586279

J. L. Chaboche, F. Feyel, and Y. Monerie, Interface debonding models: a viscous regularization with a limited rate dependency, International Journal of Solids and Structures, vol.38, issue.18, pp.383127-3160, 2001.
DOI : 10.1016/S0020-7683(00)00053-6

M. Chalhoub, Apports des méthodes d'homogénéisation numérique sur la classification des Massifs Rocheux Fracturés, p.225, 2006.

N. Chandra, H. Li, C. Shet, and H. Ghonem, Some issues in the application of cohesive zone models for metal???ceramic interfaces, International Journal of Solids and Structures, vol.39, issue.10, pp.39-2827, 2002.
DOI : 10.1016/S0020-7683(02)00149-X

H. Chang, Hydraulic fracturing in particulate materials. Doctoral dissertation, Georgia Institute of Technology, 2004.

C. R. Chen and Y. W. Mai, Comparison of cohesive zone model and linear elastic fracture mechanics for a mode I crack near a compliant/stiff interface, Engineering Fracture Mechanics, vol.77, issue.17, pp.773408-3417, 2010.
DOI : 10.1016/j.engfracmech.2010.09.009

P. Dangla and O. Coussy, Non linear poroelasticity for unsaturated porous materials: an energy approach, Proceedings of Biot Conference on Poromechanics, pp.53-64, 1998.

N. H. Dao and M. N. Vu, Load sequence effects on the fatigue crack growth in a cylinder subjected to combined rotary bending moment and axial force loads. Theoretical and Applied Fracture Mechanics, 2015.

C. J. De-pater, M. P. Cleary, T. S. Quinn, D. T. Barr, D. E. Johnson et al., Experimental Verification of Dimensional Analysis for Hydraulic Fracturing, SPE Production & Facilities, vol.9, issue.04, pp.9-230, 1994.
DOI : 10.2118/24994-PA

E. Detournay and D. I. Garagash, The near-tip region of a fluid-driven fracture propagating in a permeable elastic solid, Journal of Fluid Mechanics, vol.494, pp.1-32, 2003.
DOI : 10.1017/S0022112003005275

A. Ducellier, D. Seyedi, and E. Foerster, A coupled hydromechanical fault model for the study of the integrity and safety of geological storage of CO 2, Proceedings of GHGT10, pp.19-23, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00560485

D. S. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-104, 1960.
DOI : 10.1016/0022-5096(60)90013-2

M. Elices, G. V. Guinea, J. Gomez, and J. Planas, The cohesive zone model: advantages, limitations and challenges, Engineering Fracture Mechanics, vol.69, issue.2, pp.137-163, 2002.
DOI : 10.1016/S0013-7944(01)00083-2

F. Erdogan and G. C. Sih, On the Crack Extension in Plates Under Plane Loading and Transverse Shear, Journal of Basic Engineering, vol.85, issue.4, pp.519-525, 1963.
DOI : 10.1115/1.3656897

D. Garagash and E. Detournay, The Tip Region of a Fluid-Driven Fracture in an Elastic Medium, Journal of Applied Mechanics, vol.67, issue.1, pp.183-192, 2000.
DOI : 10.1115/1.321162

S. K. Garg and A. Nur, Effective stress laws for fluid-saturated porous rocks, Journal of Geophysical Research, vol.70, issue.26, pp.5911-5921, 1973.
DOI : 10.1029/JB078i026p05911

E. E. Gdoutos, Fracture mechanics: An introduction, 2005.
DOI : 10.1007/978-94-015-8158-5

J. Geertsma, The effect of fluid pressure decline on volumetric changes of porous rocks. Transactions of the Metallurgical Society of AIME, pp.331-340, 1957.

J. Geertsma, Problems of rock mechanics in petroleum production engineering, 1st ISRM Congress. International Society for Rock Mechanics, 1966.

J. Geertsma and F. De-klerk, A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures, Journal of Petroleum Technology, vol.21, issue.12, pp.1571-1581, 1969.
DOI : 10.2118/2458-PA

S. Géniaut, Calcul des facteurs d'intensité des contraintes par extrapolation du champ de déplacement, 2009.

S. Ghabezloo, Comportement thermo-poro-mécanique d'un ciment pétrolier, Thèse de doctorat, Ecole Nationale des Ponts et Chaussées, 2008.

S. Ghabezloo and J. Sulem, Stress dependent thermal pressurization of a fluid-saturated rock. Rock Mechanics and Rock Engineering, pp.1-24, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00315383

S. Ghabezloo, J. Sulem, S. Guédon, and F. Martineau, Effective stress law for the permeability of a limestone, International Journal of Rock Mechanics and Mining Sciences, vol.46, issue.2, 2008.
DOI : 10.1016/j.ijrmms.2008.05.006

URL : https://hal.archives-ouvertes.fr/hal-00315562

A. Ghassemi, X. X. Zhou, and C. Rawal, A three-dimensional poroelastic analysis of rock failure around a hydraulic fracture, Journal of Petroleum Science and Engineering, vol.108, 2013.
DOI : 10.1016/j.petrol.2013.06.005

R. E. Goodman, Methods of Geological Engineering in Discontinuous Rock, p.472, 1976.

G. Y. Gor, H. A. Stone, and J. H. Prévost, Fracture Propagation Driven by Fluid Outflow from a Low-Permeability Aquifer, Transport in Porous Media, pp.69-82, 2013.
DOI : 10.1007/s11242-013-0205-3

Y. N. Gordeyev and V. M. Entov, The pressure distribution around a growing crack, Journal of Applied Mathematics and Mechanics, vol.61, issue.6, pp.61-1025, 1997.
DOI : 10.1016/S0021-8928(98)80005-1

A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.221, issue.582-593, pp.163-198, 1921.
DOI : 10.1098/rsta.1921.0006

C. Guiducci, A. Pellegrino, J. P. Radu, F. Collin, and R. Charlier, Numerical modeling of hydro-mechanical fracture behavior Balkema, NUMOG VIII, pp.293-299, 2002.

J. Hagoort, B. D. Weatherill, and A. Settari, Modeling the Propagation of Waterflood-Induced Hydraulic Fractures, Society of Petroleum Engineers Journal, vol.20, issue.04, pp.293-303, 1980.
DOI : 10.2118/7412-PA

B. Haimson and C. Fairhurst, Hydraulic Fracturing in Porous-Permeable Materials, Journal of Petroleum Technology, vol.21, issue.07, pp.811-817, 1969.
DOI : 10.2118/2354-PA

L. Harrington and R. R. Hannah, Fracturing Design Using Perfect Support Fluids for Selected Fracture Proppant Concentrations in Vertical Fractures, Fall Meeting of the Society of Petroleum Engineers of AIME, 1975.
DOI : 10.2118/5642-MS

R. J. Hartranft and G. C. Sih, Alternating method applied to edge and surface crack problems, Methods of Analysis and Solutions of Crack Problems, pp.179-238, 1973.
DOI : 10.1007/978-94-017-2260-5_4

M. Hassanizadeh and W. G. Gray, General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow, Advances in Water Resources, vol.3, issue.1, pp.25-40, 1980.
DOI : 10.1016/0309-1708(80)90016-0

R. Hill, The Elastic Behaviour of a Crystalline Aggregate, Proceedings of the Physical Society. Section A, vol.65, issue.5, pp.349-354, 1952.
DOI : 10.1088/0370-1298/65/5/307

A. Hillerborg, M. Modéer, and P. E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, vol.6, issue.6, pp.773-781, 1976.
DOI : 10.1016/0008-8846(76)90007-7

O. Hoffman, Zur Frage des Auftriebes in Talsperren, Die Wasserwirtschaft, vol.22, pp.562-566, 1929.

G. C. Howard and C. R. Fast, Optimum fluid characteristics for fracture extension, 1957.

M. K. Hubbert and W. W. Rubey, ROLE OF FLUID PRESSURE IN MECHANICS OF OVERTHRUST FAULTING, Geological Society of America Bulletin, vol.70, issue.2, pp.115-206, 1959.
DOI : 10.1130/0016-7606(1959)70[115:ROFPIM]2.0.CO;2

M. A. Hussain, S. L. Pu, and J. Underwood, Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II, Fracture Analysis, vol.560, issue.1, 1974.
DOI : 10.1520/STP33130S

Y. Ida, Analysis of stick-slip and earthquake mechanism, Physics of the Earth and Planetary Interiors, vol.11, issue.2, pp.147-156, 1975.
DOI : 10.1016/0031-9201(75)90008-4

C. Inglis, Stress in a plate due to the presence of cracks and sharp corners, Transactions of the Royal Institution of Naval Architects, vol.55, pp.219-241, 1913.

G. R. Irwin, Fracturing of metals, ASM, vol.147, pp.19-28, 1948.

G. R. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics, vol.24, issue.82, pp.361-364, 1957.

G. W. Jaworski, J. M. Duncan, and H. B. Seed, Laboratory study of hydraulic fracturing, Journal of Geotechnical and Geoenvironmental Engineering, p.107, 1981.

Z. H. Jin, G. H. Paulino, and R. H. Dodds, Cohesive Zone Modelling of elastic?plastic crack growth in functionally graded materials, Engineering Fracture Mechanics, issue.14, pp.701885-1912, 2003.

L. M. Kachanov, Time of the rupture process under creep conditions, Isv. Akad. Nauk. SSR. Otd Tekh. Nauk, vol.8, pp.26-31, 1958.

M. F. Kanninen and C. H. Popelar, Advanced fracture mechanics, 1985.

N. Khalili, R. Witt, L. Laloui, L. Vulliet, and A. Koliji, Effective stress in double porous media with two immiscible fluids, Geophysical Research Letters, vol.45, issue.23???24, pp.32-15309, 2005.
DOI : 10.1029/2005GL023766

G. Kirsch and . Die, Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre, Veit. Ver. Deut. Ing, vol.42, pp.797-807, 1898.

Y. Kovalyshen, Fluid-driven fracture in poroelastic medium, Thèse de doctorat, 2010.

S. A. Kristianovitch and Y. P. Zheltov, Formation of vertical fractures by means of highly viscous fluids, Proceedings of the 4th World Petroleum Congress, p.579, 1955.

B. Ladanyi and G. Archambault, Simulation of the shear behaviour of a jointed rock mass, Proceedings of the 11th U.S. Symposium on Rock Mechanics, pp.105-125, 1969.

J. B. Leblond, Mécanique de la rupture fragile et ductile, p.197, 2003.

B. Lecampion and E. Detournay, An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.49-52, pp.4863-4880, 2007.
DOI : 10.1016/j.cma.2007.06.011

D. Leguillon, Strength or toughness? A criterion for crack onset at a notch, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.61-72, 2002.
DOI : 10.1016/S0997-7538(01)01184-6

J. Lemaitre, Evaluation of Dissipation and Damage in Metals Submitted to Dynamic Loading, Proceedings I.C.M.I, 1971.

J. Lemaître and J. L. Chaboche, Mécanique des matériaux solides. 2 ème édition: Dunod, 2004.

P. A. Liolios and G. E. Exadaktylos, A solution of steady-state fluid flow in multiply fractured isotropic porous media, International Journal of Solids and Structures, vol.43, issue.13, pp.43-3960, 2006.
DOI : 10.1016/j.ijsolstr.2005.03.021

S. A. Mathias and M. Van-reeuwijk, Hydraulic Fracture Propagation with 3-D Leak-off, Transport in Porous Media, pp.499-518, 2009.
DOI : 10.1007/s11242-009-9375-4

T. Mohammadnejad and A. R. Khoei, An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elements in Analysis and Design, pp.77-95, 2013.

O. Mohr, Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials, Zeitschrift des Vereins Deutscher Ingenieure, pp.1524-1530, 1900.

T. Mori and H. Kawamura, Simulation Study of Spatiotemporal Correlations of Earthquakes as a Stick-Slip Frictional Instability, Physical Review Letters, vol.94, issue.5, p.58501, 2005.
DOI : 10.1103/PhysRevLett.94.058501

L. C. Murdoch and L. N. Germanovich, Analysis of a deformable fracture in permeable material, International Journal for Numerical and Analytical Methods in Geomechanics, vol.185, issue.6, pp.529-561, 2006.
DOI : 10.1002/nag.492

N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, Noordhoff, vol.704, 1953.
DOI : 10.1007/978-94-017-3034-1

E. Nauleau, Évolution au cours du temps des propriétés physiques et mécaniques des matériaux cimentaires d'un puits géothermique basse énergie, Thèse de doctorat, p.248, 2013.

A. Needleman, A Continuum Model for Void Nucleation by Inclusion Debonding, Journal of Applied Mechanics, vol.54, issue.3, pp.525-531, 1987.
DOI : 10.1115/1.3173064

S. Nielsen, J. Taddeucci, and S. Vinciguerra, Experimental observation of stick-slip instability fronts, Geophysical Journal International, vol.180, issue.2, pp.697-702, 2010.
DOI : 10.1111/j.1365-246X.2009.04444.x

R. P. Nordgren, Propagation of a Vertical Hydraulic Fracture, Society of Petroleum Engineers Journal, vol.12, issue.04, pp.306-314, 1972.
DOI : 10.2118/3009-PA

A. Nur and J. D. Byerlee, An exact effective stress law for elastic deformation of rock with fluids, Journal of Geophysical Research, vol.70, issue.2, pp.6414-6419, 1971.
DOI : 10.1029/JB076i026p06414

F. Orr, Storage of Carbon Dioxide in Geologic Formations, Journal of Petroleum Technology, vol.56, issue.09, pp.90-97, 2004.
DOI : 10.2118/88842-JPT

P. C. Papanastasiou, An efficient algorithm for propagating fluid-driven fractures, Computational Mechanics, vol.24, issue.4, pp.258-267, 1999.
DOI : 10.1007/s004660050514

K. Park and G. H. Paulino, Computational implementation of the PPR potential-based cohesive model in ABAQUS: Educational perspective, Engineering Fracture Mechanics, vol.93, pp.239-262, 2012.
DOI : 10.1016/j.engfracmech.2012.02.007

F. D. Patton, Multiple modes of shear failure in rock, proc. 1 st Congress of the International Society for Rock Mechanics, pp.503-513, 1966.

T. W. Patzek and D. B. Silin, Water Injection into a Low -Permeability Rock -1, 2001.

N. Perez, Fracture mechanics, 2004.
DOI : 10.1007/978-3-319-24999-5

T. K. Perkins and L. R. Kern, Widths of Hydraulic Fractures, Journal of Petroleum Technology, vol.13, issue.09, pp.937-949, 1961.
DOI : 10.2118/89-PA

Z. G. Philip, J. J. Jennings, J. E. Olson, S. E. Laubach, and J. Holder, Modeling Coupled Fracture-Matrix Fluid Flow in Geomechanically Simulated Fracture Networks, pp.300-309, 2005.

B. Pichler and L. Dormieux, Micromechanical Interpretation of the Dissipation Associated With Mode I Propagation of Microcracks in Brittle Materials, Journal of Applied Mechanics, vol.76, issue.4, p.41003, 2009.
DOI : 10.1115/1.3086594

B. Pichler and L. Dormieux, Instability during cohesive zone growth, Engineering Fracture Mechanics, vol.76, issue.11, pp.1729-1749, 2009.
DOI : 10.1016/j.engfracmech.2009.03.011

A. Pouya, Three-dimensional flow in fractured porous media: A potential solution based on singular integral equations, Advances in Water Resources, vol.35, pp.30-40, 2012.
DOI : 10.1016/j.advwatres.2011.10.009

URL : https://hal.archives-ouvertes.fr/hal-00668190

A. Pouya, A finite element method for modeling coupled flow and deformation in porous fractured materials, International Journal for Numerical and Analytical Methods in Geomechanics, 2015.

A. Pouya and P. Bemani-yazdi, A damage-plasticity model for cohesive fractures, International Journal of Rock Mechanics and Mining Sciences, vol.73, pp.194-202, 2015.
DOI : 10.1016/j.ijrmms.2014.09.024

A. Pouya and Z. Bendjeddou, Homogénéisation des effets hydrauliques et hydromécaniques, p.44, 2011.

A. Pouya, V. L. Nguyen, and S. Ghabezloo, Modélisation théorique et numérique de la propagation des fractures sous sollicitations hydromécaniques, Séance technique du 16 Octobre 2014, Comité français de mécanique des roches, CNAM, 2014.

A. Pouya and M. N. Vu, Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method, Transport in Porous Media, pp.475-493, 2012.
DOI : 10.1007/s11242-012-9968-1

URL : https://hal.archives-ouvertes.fr/hal-00790536

A. Pouya and M. N. Vu, Fluid flow and effective permeability of an infinite matrix containing disc-shaped cracks, Advances in Water Resources, vol.42, pp.37-46, 2012.
DOI : 10.1016/j.advwatres.2012.03.005

URL : https://hal.archives-ouvertes.fr/hal-00700099

A. Pouya, M. N. Vu, S. Ghabezloo, and Z. Bendjeddou, Effective permeability of cracked unsaturated porous materials, International Journal of Solids and Structures, vol.50, issue.20-21, pp.3297-3307, 2013.
DOI : 10.1016/j.ijsolstr.2013.05.027

URL : https://hal.archives-ouvertes.fr/hal-00946086

A. Pouya, M. N. Vu, and D. Seyedi, Modelling effective permeability of fracture networks in permeable rock formations by singular integral equations method, Computational Methods in Multiphase Flow VI, pp.287-298, 2011.
DOI : 10.2495/MPF110241

A. Pouya and S. Ghabezloo, Flow Around a Crack in a Porous Matrix and Related Problems, Transport in Porous Media, pp.511-532, 2010.
DOI : 10.1007/s11242-009-9517-8

URL : https://hal.archives-ouvertes.fr/hal-00627357

B. Prabel, Modélisation avec la méthode X-FEM de la propagation dynamique et de l'arrêt de fissure de clivage dans un acier de cuve REP, Thèse de doctorat, 2007.

Y. U. Rabotnov, Creep rupture, Proceedings of the XII International Congress on Applied Mechanics, pp.342-349, 1968.
DOI : 10.1007/978-3-642-85640-2_26

S. Rangaraj and K. Kokini, A Study of Thermal Fracture in Functionally Graded Thermal Barrier Coatings Using a Cohesive Zone Model, Journal of Engineering Materials and Technology, vol.126, issue.1, pp.103-115, 2004.
DOI : 10.1115/1.1631028

H. W. Reinhardt and H. A. Cornelissen, Post-peak cyclic behaviour of concrete in uniaxial tensile and alternating tensile and compressive loading, Cement and Concrete Research, vol.14, issue.2, pp.263-270, 1984.
DOI : 10.1016/0008-8846(84)90113-3

J. Réthoré, R. De-borst, and M. A. Abellan, A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks, Computational Mechanics, vol.53, issue.4???6, pp.227-238, 2008.
DOI : 10.1007/s00466-007-0178-6

J. M. Rice and M. P. Cleary, Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents, Reviews of Geophysics, vol.80, issue.4, pp.227-241, 1976.
DOI : 10.1029/RG014i002p00227

J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, vol.35, issue.2, pp.379-386, 1968.
DOI : 10.1115/1.3601206

J. Rohmer and D. Seyedi, Coupled large scale hydromechanical modelling for caprock failure risk assessment of CO 2 storage in deep saline aquifers. Oil & Gas Science and Technology -Revue d'IFP Energies nouvelles, pp.503-517, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00533062

J. Rutqvist and O. Stephansson, The role of hydromechanical coupling in fractured rock engineering, Hydrogeology Journal, vol.80, issue.1, pp.7-40, 2003.
DOI : 10.1007/s10040-002-0241-5

M. Sanchez, O. L. Manzoli, and L. J. Guimarães, Modeling 3-D desiccation soil crack networks using a mesh fragmentation technique, Computers and Geotechnics, vol.62, pp.27-39, 2014.
DOI : 10.1016/j.compgeo.2014.06.009

M. Sanchez, A. Atique, S. Kim, E. Romero, and M. Zielinski, Exploring desiccation cracks in soils using a 2D profile laser device, Acta Geotechnica, vol.57, issue.1, pp.583-596, 2013.
DOI : 10.1007/s11440-013-0272-1

J. C. Santamarina, K. A. Klein, and M. A. Fam, Soils and Waves: Particulate materials behavior, characterization and process monitoring, 2001.

E. Sarris and P. C. Papanastasiou, The influence of the cohesive process zone in hydraulic fracturing modelling, International Journal of Fracture, vol.42, issue.9, pp.33-45, 2011.
DOI : 10.1007/s10704-010-9515-4

E. Sarris and P. C. Papanastasiou, Modeling of Hydraulic Fracturing in a Poroelastic Cohesive Formation, International Journal of Geomechanics, vol.12, issue.2, pp.160-167, 2012.
DOI : 10.1061/(ASCE)GM.1943-5622.0000121

E. Sarris and P. C. Papanastasiou, Numerical modeling of fluid-driven fractures in cohesive poroelastoplastic continuum, International Journal for Numerical and Analytical Methods in Geomechanics, vol.46, issue.12, pp.1822-1846, 2012.
DOI : 10.1002/nag.2111

J. M. Segura and I. Carol, Coupled HM analysis using zero-thickness interface elements with double nodes. Part I: Theoretical model, International Journal for Numerical and Analytical Methods in Geomechanics, vol.7, issue.1, pp.32-2083, 2008.
DOI : 10.1002/nag.730

A. Settari, A New General Model of Fluid Loss in Hydraulic Fracturing, Society of Petroleum Engineers Journal, vol.25, issue.04, pp.491-501, 1985.
DOI : 10.2118/11625-PA

D. M. Seyedi, M. N. Vu, and A. Pouya, A two-scale hydromechanical model for fault zones accounting for their heterogeneous structure, Computers and Geotechnics, vol.68, pp.8-16, 2015.
DOI : 10.1016/j.compgeo.2015.03.001

URL : https://hal.archives-ouvertes.fr/hal-01355430

D. M. Seyedi, A. Ducellier, M. N. Vu, and A. Pouya, A Two-scale Model For Simulating the Hydromechanical Behavior of Faults During CO2 Geological Storage Operation, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00581742

C. Shet and N. Chandra, Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes, Journal of Engineering Materials and Technology, vol.124, issue.4, pp.440-450, 2002.
DOI : 10.1115/1.1494093

H. Shin and J. C. Santamarina, Fluid-driven fractures in uncemented sediments: Underlying particle-level processes, Earth and Planetary Science Letters, vol.299, issue.1-2, pp.180-189, 2010.
DOI : 10.1016/j.epsl.2010.08.033

G. C. Sih, Some basic problems in fracture mechanics and new concepts, Engineering Fracture Mechanics, vol.5, issue.2, pp.365-377, 1973.
DOI : 10.1016/0013-7944(73)90027-1

G. C. Sih, P. C. Paris, and G. R. Irwin, On cracks in rectilinearly anisotropic bodies, International Journal of Fracture Mechanics, vol.1, issue.3, pp.189-203, 1965.
DOI : 10.1007/BF00186854

A. W. Skempton, Terzaghi's discovery of effective stress. From Theory to Practice in Soil Mechanics: Selections from the Writings of Karl Terzaghi, pp.42-53, 1960.

A. W. Skempton, Effective stress in soils, concrete and rocks. Proceeding of the Conference: Pore Pressure and Suction in Soils, pp.4-16, 1960.

A. W. Skempton and A. W. Bishop, Soils, Building Materials, their Elasticity and Plasticity, 1954.

V. Slowik, V. E. Saouma, and A. Thompson, Large scale direct tension test of concrete, Cement and Concrete Research, vol.26, issue.6, pp.949-954, 1996.
DOI : 10.1016/0008-8846(96)00062-2

I. N. Sneddon, The Distribution of Stress in the Neighbourhood of a Crack in an Elastic Solid, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.187, issue.1009, pp.229-260, 1009.
DOI : 10.1098/rspa.1946.0077

J. E. Streit and R. R. Hillis, Estimating fault stability and sustainable fluid pressures for underground storage of CO2 in porous rock, Energy, vol.29, issue.9-10, pp.1445-1456, 2004.
DOI : 10.1016/j.energy.2004.03.078

C. T. Sun and Z. H. Jin, Chapter 9 -Cohesive zone model. Fracture mechanics, pp.227-246, 2012.

H. Tada, P. Paris, and G. Irwin, The stress analysis of cracks handbooks, 2000.

J. L. Thiébaut, Contribution à l'étude des sédiments argilo-calcaires du Bassin de Paris, Thèse de doctorat, p.170, 1925.

T. Todd and G. Simmons, Effect of pore pressure on the velocity of compressional waves in low-porosity rocks, Journal of Geophysical Research, vol.23, issue.20, pp.3731-3743, 1972.
DOI : 10.1029/JB077i020p03731

V. Tvergaard, Theoretical investigation of the effect of plasticity on crack growth along a functionally graded region between dissimilar elastic???plastic solids, Engineering Fracture Mechanics, vol.69, issue.14-16, pp.69-1635, 2002.
DOI : 10.1016/S0013-7944(02)00051-6

S. Valente, Bifurcation phenomena in cohesive crack propagation, Computers & Structures, vol.44, issue.1-2, pp.55-62, 1992.
DOI : 10.1016/0045-7949(92)90222-L

P. J. Van-ruth, E. Nelson, and R. R. Hillis, Fault reactivation potential during CO2 injection in the Gippsland Basin, Australia, Exploration Geophysics, vol.37, issue.1, pp.50-56, 2006.
DOI : 10.1071/EG06050

V. Terzaghi and K. , Die Berechnung der Durchlässigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen, Math.-Naturwis, pp.125-138, 1923.

V. Terzaghi and K. , The shearing resistance of saturated soils and the angle between the planes of shear, First International Conference of Soil Mechanics, pp.54-56, 1936.

M. N. Vu, Modélisation des écoulements dans des milieux poreux fracturés par la méthode des équations aux intégrales singulières, Thèse de doctorat, p.148, 2012.

M. N. Vu, A. Pouya, and D. M. Seyedi, Theoretical and numerical study of the steady-state flow through finite fractured porous media, International Journal for Numerical and Analytical Methods in Geomechanics, vol.25, issue.23-24, pp.221-235, 2014.
DOI : 10.1002/nag.2200

URL : https://hal.archives-ouvertes.fr/hal-01157354

M. N. Vu, A. Pouya, and D. M. Seyedi, Modelling of steady-state fluid flow in 3D fractured isotropic porous media: application to effective permeability calculation, International Journal for Numerical and Analytical Methods in Geomechanics, vol.454, issue.11, pp.2257-2277, 2012.
DOI : 10.1002/nag.2134

URL : https://hal.archives-ouvertes.fr/hal-00795809

M. N. Vu, A. Pouya, and D. Seyedi, Etude numerique de l'ecoulement dans un milieu poreux fissure : Application au calcul de la permeabilite equivalente, Journées Nationales de Géotechnique et de Géologie de l'Ingénieur JNGG2012, pp.1015-1023, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00795805

M. N. Vu, S. T. Nguyen, and M. H. Vu, Modeling of fluid flow through fractured porous media by a single boundary integral equation, Engineering Analysis with Boundary Elements, vol.59, pp.166-171, 2015.
DOI : 10.1016/j.enganabound.2015.06.003

M. N. Vu, S. T. Nguyen, M. H. Vu, A. M. Tang, and V. T. To, Heat conduction and thermal conductivity of 3D cracked media, International Journal of Heat and Mass Transfer, vol.89, pp.1119-1126, 2015.
DOI : 10.1016/j.ijheatmasstransfer.2015.05.113

URL : https://hal.archives-ouvertes.fr/hal-01271134

M. N. Vu, S. Geniaut, P. Massin, and J. J. Marigo, Numerical investigation on corner singularities in cracked plates using the G-theta method with an adapted ?? field, Theoretical and Applied Fracture Mechanics, pp.59-68, 2015.
DOI : 10.1016/j.tafmec.2015.02.003

URL : https://hal.archives-ouvertes.fr/hal-01246477

C. H. Wang, Introduction to Fracture Mechanics. Aeronautical and Maritime Research Laboratory, p.82, 1996.

J. T. Wang, Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics. National Aeronautics and Space Administration, 2010.

N. Weber, P. Siebert, K. W. Willbrand, M. Feinendegen, C. Clauser et al., The XFEM with an Explicit-Implicit Crack Description for Hydraulic Fracture Problems, ISRM International Conference for Effective and Sustainable Hydraulic Fracturing, 2013.
DOI : 10.5772/56383

H. M. Westergaard, Bearing pressure and cracks, Journal of Applied Mechanics, vol.22, pp.49-53, 1939.

M. William, Stress singularities from various boundary conditions in angular corners of plates in extension, Journal of Applied Mechanics, ASME, vol.19, issue.4, pp.526-528, 1952.

M. William, The Bending Stress Distribution at the Base of a Stationary Crack, Journal of Applied Mechanics, vol.28, issue.1, pp.109-114, 1957.
DOI : 10.1115/1.3640470

M. William, The stresses around a fault or crack in dissimilar media, pp.199-204, 1959.

M. Wrobel and G. Mishuris, Efficient pseudo-spectral solvers for the PKN model of hydrofracturing, International Journal of Fracture, pp.1-20, 2013.

W. Xu and Y. Wei, Strength and interface failure mechanism of adhesive joints, International Journal of Adhesion and Adhesives, vol.34, pp.80-92, 2012.
DOI : 10.1016/j.ijadhadh.2011.12.004

X. Xu and A. Needleman, Void nucleation by inclusion debonding in a crystal matrix, Modelling and Simulation in Materials Science and Engineering, vol.1, issue.2, p.111, 1993.
DOI : 10.1088/0965-0393/1/2/001

B. Yang, S. Mall, and K. Ravi-chandar, A cohesive zone model for fatigue crack growth in quasi-brittle materials, International Journal of Solids and Structures, issue.22, pp.38-3927, 2001.

T. Yang, W. Zhu, Q. Yu, and H. Liu, O papel da press??o nos poros em processos de fratura????o hidr??ulica e implica????es em irrup????es de ??gua subterr??nea em minas e t??neis, Hydrogeology Journal, vol.6, issue.1, pp.995-1008, 2011.
DOI : 10.1007/s10040-011-0731-4

Z. J. Zhang and G. H. Paulino, Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials, International Journal of Plasticity, vol.21, issue.6, pp.1195-1254, 2005.
DOI : 10.1016/j.ijplas.2004.06.009

R. W. Zimmerman, W. H. Somerton, and M. S. King, Compressibility of porous rocks, Journal of Geophysical Research: Solid Earth, vol.14, issue.EM5, pp.12765-12777, 1986.
DOI : 10.1029/JB091iB12p12765