Rahman M M,Rahman M K.A review of hydraulic fracture models and development of an improved pseudo-3D model for stimulating tight oil gas sand[J].Energy Sources,Part A:Recovery,Utilization,and Environmental Effects,2010,32(1):1416–1436.
[2]
Hu Y J,Chen G l,Cheng W P,et al.Simulation of hydraulic fracturing in rock mass using a smeared crack model[J].Computers and Structures,2013,137(1):72-77.
[3]
Pak A.Numerical modeling of hydraulic fracturing[D].Edmonton:University of Alberta,1997.
[4]
Dugdale D S.Yielding of steel sheets containing slits[J].Journal of the Mechanics and Physics of Solids,1960,8(2):100-104.
[5]
Barenblatt G L.The mathematical theory of equilibrium cracks in brittle fracture[J].Advances in Applied Mechanics,1962,7(1):55-129.
[6]
Mohammadnejad T,Khoei A R.An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model[J].Finite Elements in Analysis and Design,2013,73(1):77-95.
[7]
Lecampion B.An extended finite element method for hydraulic fracture problems[J].Communications in Numerical Methods in Engineering,2009,25(1):121-133.
[8]
Adachi J,Siebrits E,Peirce A,et al.Computer simulation of hydraulic fractures[J].International Journal of Rock Mechanics & Mining Sciences,2007,44(5):739-754.
[9]
Bazant Z P,Lin F B.Nonlocal smeared cracking model for concrete fracture[J].Journal of Structural Engineering,1988,114(11):2493-2510.
[10]
Bazant Z P ,Oh B H.Crack band theory for fracture of concrete[J].Matériaux et Constructions,1983,16(3):155-177.
[11]
Wang S Y,Sun L,Au A S,et al.2D-numerical analysis of hydraulic fracturing in heterogeneous geo-materials[J].Construction and Building Materials,2009,23(1):2196–2206.
[12]
Zhu W,Montesi L G ,Wong T F.A probabilistic damage model of stress-induced permeability anisotropy during cataclastic flow[J].Journal of Geophysical Research,2007,112(1):1-20.
[13]
Brace W F,Paulding B,Scholz C.Dilatancy in the fracture of crystalline rocks[J].Journal of Geophysical Research,1966,71(16):3939–3953.
[14]
冷雪峰,唐春安,杨天鸿.岩石水压致裂过程的数值模拟分析[J].东北大学学报:自然科学版,2002,23(11):1104-1107.(Leng Xue-feng,Tang Chun-an,Yang Tian-hong.Numerical simulation and analysis on heterogeneous and permeable rocks under hydraulic fracturing[J].Journal of Northeastern University:Natural Science,2002,23(11):1104-1107.)
[15]
Lasry D,Belytschko T.Localization limiters in transient problems[J].International Journal of Solids and Structures,1988,24(6):581-597.
[16]
Fernandes R,Chavant C.Evaluating the reliability of hydro-mechanical :a benchmark of numerical techniques carried out by research group of MoMas[J].Laboratoire de Mécanique des Structures Industrielles Durables,Clamart Cedex,2005,37(1):211-212.
[17]
Oliver J.A consistent characteristic length for smeared cracking models[J].International Journal for Numerical Methods in Engineering,1989,28(2):461-474.
[18]
Mosalam K M,Paulino G H.Evolutionary characteristic length method for smeared cracking finite element models[J].Finite Elements in Analysis and Design,1997, 27(1):99-108.