Document Type : Original Research Paper


1 Department of Mining and Metallurgical Engineering, Faculty of Engineering, Yazd University, Yazd, Iran.

2 School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran.


In this work, an effective methodology is introduced for simulation of the crack propagation in linear poroelastic media. The presence of pores and saturated cracks that can be accompanied by fluid flow makes the use of poroelastic media inevitable. In this work, involvement of the time parameter in crack propagation is of particular importance. The order of doing the work is such that first, derives the fundamental solutions of a poroelastic higher order displacement discontinuity method (PHODDM). Then will be provided a numerical formulation and implementation for PHODDM in a code named linear element poroelastic DDM (LEP-DDM). Analytical solutions use different times to check the correctness and validity of the proposed solution and the newly developed code. The numerical results show a good agreement and coordination with the analytical results in time zero and 5000 seconds . The code is able to pursue crack-propagation in time and space. This topic is introduced and shown in an example.


[2]. Portela. A, Aliabadi M.H., and Rooke DP. (1992).The dual boundary element method: effective implementation for crack problems. Int J Numer Methods Eng ;33 (6): 1269–87.
[4]. Santana .E. and Portela. A. (2016). Dual boundary element analysis of fatigue crack growth, interaction and linkup. EngAnal Bound Elem ;64:176–95. 10.1016/j.enganabound.2015.12.002.
[5]. dell’Erba. D.N. and Aliabadi .M.H. (2000). Three-dimensional thermo-mechanical fatigue crack growth using BEM. Int J Fatigue ;22:261–73. S0142-1123(00)00011-6.
[6]. Cisilino. A.P. and Aliabadi .M.H. (2004). Dual boundary element assessment of three-dimensional fatigue crack growth. Eng Anal BoundElem;28:1157–73.https://doi. org/10.1016/j.enganabound.2004.01.005.
[7]. Wang. P.B. and Yao .Z.H. (2006). Fast multipole DBEM analysis of fatigue crackgrowth.ComputMech ;38(3):22333.
[8]. Crouch. S.L.(1976). Engineering U of MD of C and M, Program NSF (U. S). RA to NN. Analysis of Stresses and Displacements Around Underground Excavations.
[10]. Chaoxi. L, Suaris. W.(1991). Hadamard’s principle for displacement discontinuity modeling of cracks. Eng Fract Mech ;39:141–5. 7944 (91)90029-Z.
[11]. Fatehi Marji. M. (2011). On the crack propagation mechanism of brittle rocks under various loading conditions.
[17]. Abdollahipour. A. and Fatehi Marji. M. (2020). A thermo-hydromechanical displacement discontinuity method to model fractures in high-pressure, high-temperature environments. RenewEnergy;153:1488–503.
[26]. Li. J, Sladek J, Sladek. V, and Wen PH. (2020).Hybrid meshless displacement discontinuity method (MDDM) in fracture mechanics: static and dynamic. Eur J Mech ;83: 104023.
[29]. Naredran .V.M and Cleary .M.P.(1`989). Analysis of growth and interaction of multiple hydraulic fractures. Reserv. Stimul. Symp., San Francisco.
[31]. Ito. T.(2008). Effect of pore pressure gradient on fracture initiation in fluid saturated porous media: Rock. Eng Fract Mech ;75:1753–62. doi:10.1016/j.engfracmech.2007.03.028.
[32]. Huang. J, Griffiths. D.V.V, and Wong. S. (2012). Initiation pressure, location and orientation of hydraulic fracture. Int J Rock Mech Min Sci ;49:59–67.2011.11.014.
[33]. Yu. W., Luo. Z., Javadpour. F., and Varavei. A., Sepehrnoori. K.(2013). Sensitivity analysis of hydraulic fracture geometry in shale gas reservoirs. J Pet Sci Eng2014;113:1–7. doi:10.1016/j.petrol.2013.12.005.
[38]. Reinicke. A, Zimmermann. G .(2010). Hydraulic stimulation of a deep sandstone reservoir to develop an enhanced geothermal system:laboratory and field experiments. Geothermics39:70–77. doi:10.1016/j.geothermics.2009.12.003.
[39]. Davis. R. and Carter. L.(2013). Fracking Doesn’t Cause Significant Earthquakes. Durham Univesity.
[42]. Boonei. T.J, Ingrffea. A.R, Roegiers. J-C .(1991). Simulation of hydraulic fracture propagation in poroelastic rock with application to stress measurement techniques. Int J Rock Mech Min Sci Geomech abstr 28:1–14.
[45]. Bobet A and Yu H. (2015). Stress field near the tip of a crack in a poroelastic transversely anisotropic saturated rock. Eng Fract Mech 141:1–18.
[52]. Lobao. M, Eve. R, Owen. D.R.J et al. (2010). Modelling of hydrofracture flow in porous media. Engng Comput 27:129–154. doi:10.1108/02644401011008568.
[54]. Darvish. H, Nouri-Taleghani. M, Shokrollahi. A, and Tatar. A (2015). Geo-mechanical modeling and selection of suitable layer for hydraulic fracturing operation in an oil reservoir (south west of Iran). J African Earth Sci; 111:409–20.
[56]. Sanford. R.J (2003). Principles of fracture mechanics. Prentice Hall, Upper Saddle River.
[57]. Fatehi Marji. M, Hosseini Nasab. H, and Kohsary. A.H (2006). On the uses of special crack tip elements in numerical rock fracture mechanics. Int J Solids. Struct43:1669–1692.doi:10.1016/j.ijsolstr.2005.04.042.
[58]. Lawn. R and Wilshaw. R (1975). Review indentation fracture: principles and applications. J Mater Sci 10:1049–1081.
[59]. Pollard. D.D and Aydin. A (1988). Progress in understanding jointing over the past century. Geol Soc Am Bull 100:1181–1204.
[60]. Morozov. V.A and Savenkov. G.G. (2013). Limiting velocity of crack propagation in dynamically fractured materials. J Appl Mech Tech Phys 54:142–147.
[61]. Erdogan. F, Sih. G.C. (1963). On the crack extension in plates under plate loading and transverse shear. J Basic Eng 85:519–27
[71]. Atkinson. B.K (1984). Subcritical crack growth in geological minerals. J Geophys Res 89:4077–4114.