IJE TRANSACTIONS B: Applications Vol. 15, No. 2 (July 2002) 125-134   

downloaded Downloaded: 144   viewed Viewed: 1926

A. Nouri and A. Pak

Department of Civil Engineering, Sharif University of Technology
Tehran, Iran, pak@sina.sharif.ac.ir
( Received: September 30, 1999 – Accepted in Revised Form: May 03, 2001 )

Abstract    Hydraulic fracturing is a phenomenon in which cracks propagate through the porous medium due to high pore fluid pressure. Hydraulic fracturing appears in different engineering disciplines either as a destructive phenomenon or as a useful technique. Modeling of this phenomenon in isothermal condition requires analysis of soil deformation, crack and pore fluid pressure interactions. In this paper a numerical scheme is presented for analysis of soil stresses and deformations and fluid flow in a coupled manner, which is also capable to detect the initiation of fracture in the medium. Applications of the model are shown by illustrative examples.


Keywords    Hydraulic Fracturing, Finite Element Method, Effective Stress Analysis, Mohr-Coulomb Criterion, Hyperbolic Model



1. Terzaghi, K., "Erbaumechanik Auf Bodenphysikalischer Grundlage (Leipzig F. Deuticke 1925)", Principles of Soil Mechanics, Eng. News Record, A Series of Articles,(1925).

2. Biot, M.A., "General Theory of Three Dimensional Consolidation", J. Appl. Physics, Vol. 12, (1941), 155-164.

3. Biot, M.A., "General Solutions of The Equations of Elasticity and Consolidation For A Porous Material", J. Applied Mech., Trans. ASME, Vol. 78, (1956a), 91-96.

4. Biot, M.A., "Theory of Deformation of A Porous Viscoelastic Anisotropic Solid", J. Applied Physics, Vol.27, (1956b), 459-467.

5. Sandhu, R.S., "Fluid Flow in Saturated Porous Elastic Media", Ph.D. Thesis, Department of Civil Engineering, University of California, Berkeley, (1968).

6. Christian, J.T., "Undrained Stress Distribution By Numerical Methods", J. Of Soil Mech. Found. Eng. Div., ASCE, Vol. 94, SM 6, (1968), 1333-1345.

7. Christian, J.T. and Boehmer, J.W., "Plane Strain Consolidation By Finite Elements", J. Of Soil Mech. Found. Eng. Div., ASCE, Vol. 96, SM 4, (1970), 1435-


8. Carter, J.P., Small, J.C. and Booker, J.R., "A Theory of Finite Elastic Consolidation", Int. J. Of Solids Structures, Vol. 13, (1977), 467-478.

9. Carter, J.P., Booker, J.R. and Small, J.C., "The Analysis of Finite Elastoplastic Consolidation", Int. J. Of Num. Anal. Methods in Geomech., Vol. 3, (1979), 107-129.

10. Lewis, R.W., Roberts, G.K. and Zienkiewicz, O.C., "A Nonlinear Flow and Deformation Analysis of Consolidation Problems", 2nd Int. Con. on Num.Methods in Geomechanics, Blacksburg, Virginia, Vol. 2, (1976), 1106-1118.

11.Zheltov, Y.P. and Khristianovitch, S.A., "On The Mechanism of Hydraulic Fracturing of An Oil-Bearing Stratum", hvest. Akad. Nauk SSR, OTN, Vol. 5, (1955), 3-41 (in Russian).

12. Perkins, T.K. and Kern, L.R., "Width of Hydraulic Fractures", JPT, Trans., AIME, 222, (Sept. 1961), 937- 949.

13. Geertsma, J. And deklerk, F.A., "Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures", JPT, Trans., AIME, 246, (Dec. 1969), 1571-1581.

14. Settari, A. And Raisbeck, J.M., "Fracture Mechanics Analysis in In-Situ Oilsand Recovery", JCPT, (April-June1979), 85-94.

15. Settari, A. And Raisbeck, J.M.,"Analysis and Numerical Modeling of Hydraulic Fracturing During Cyclic Steam Stimulation in Oilsands", JPT, (Nov. 1981), 2201-2212.

16. Settari, A., Kry, P.R. and Yee, C.T., "Coupling of Fluid Flow and Soil Behavior To Model Injection into Uncemented Oilsands"; JCPT, 28(1), 81-92, Jan.-Feb.(1989).

17. Advani, S.H., Lee, T.S. and Lee, J.K., "Three-Dimensional Modeling of Hydraulic Fractures In Layered Media, Part I and Part II", Journal of Energy Resources Technology, Vol. 112, (1990), 1-19.

18. Pak. A., "Numerical Modeling of Hydraulic Fracturing", Ph.D. Thesis, Department of Civil and Environmental Engineering, University of Alberta, Canada, (1997).

19. Nouri, A., "Numerical Study of Hydraulic Fracturing in Two- Phases Porous Media", M.Sc. Thesis, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran, (1998).

20. Duncan, J.M. and Chang, C.Y., "Nonlinear analysis of Stress and Strain in Soils", Journal of Soil Mechanics and Foundation Engineering Division, ASCE, Vol. 96,

SM5,(1970), 1629-1653.

21. Britto, A.M. and Gunn, M.J., "Critical State Soil Mechanics Via Finite Elements", Ellis Horwood Limited, (1987).

22. Atkinson, B.K. (editor), "Fracture Mechanics of Rocks", Academic Press, Geology Series, (1987).

23. Komak- Panah, A. and Yanagisawa, E., "Laboratory study of Hydraulic Fracturing Criteria in Soils", Soils and Foundation, vol. 29. No. 4, (1989), 14-22.

24. Vermeer, P.A. and Verruijit, A., "An Accuracy Condition for Consolidation Analysis by FEM", Int. J. for Num. and Anal. Methods in Geomech. Vol. 5, (1981), 1-14.

25. Gatmiri, B., "Validation Du Code UDAM, UDAM: A Finite Element Software for the Analysis of Unsaturated Porous Media", Internal Report CERMES-ENPC, Paris,


26. Christian, J.T., "Two- and Three Dimensional Consolidation", in Numerical Methods in Geomechanical Engineering (eds. C.S. Desai and J.T. Christian), London McGraw-Hill, (1977), 399-426.

27. Settari, A., Raisbeck, J.M., "Fracture Mechanics Analysis in In-Situ Oilsand Recovery", JCPT, April- June, (1979) 85-94.

28. Pak, A., SadrNejad, A., and Nouri, A., "Influence of the Initial Effective Principal Stresses on Hydraulic Fracture in Soils ", Sclentia Iranica, Vol. 5, No. 3,4, (1999).

29. Settari, A., Raisbeck, J.M., "Analysis and Numerical Modeling of Hydraulic Fracturing during cyclic steam simulation in oilsands", JPT, Nov. (1981), 2201-2212.

30. Settari, A., "Simulation of Hydraulic Fracturing Process", SPE Journal, (Dec. 1980), 2187-500.

31. Chan, D. and Pak, A., "Numerical Modeling of Hydraulic Fracturing in a Porous medium". International Conference on Geomechanics/Ground Control in Mining and Underground Construction, Wollongong, Australia, (1998).

32. Lewis, R. W., Roberts.G.K. and Zienkiewicz, O.C., "A Nonlinear  Flow  and   Deformation  Analysis  of Consolidation Problems", 2nd. Int. Conf. On Num. Methods in Geomech., Blacksburg, Virginia, Vol. 2, (1976), 1106-1118.

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir