·446 工程科学学报，第41卷，第4期 chanics /Geomechanics Symposium.San Francisco,2013:AR- [21]Ayatollahi M R,Moghaddam M R,Berto F.A generalized strain MA2013644 energy density criterion for mixed mode fracture analysis in brittle 2] Pu CZ.Cao P,Zhang C Y,et al.Fracture failure mechanism of and quasi-brittle materials.Theor Appl Fract Mech,2015,79: rock with closed crack and judging criterion of seepage pressure 70 under biaxial compression.Rock Soil Mech,2015,36(1):56 [22]Williams M L.On the stress distribution at the base of a stationa- (蒲成志，曹平，张春阳，等.双向压缩条件下闭合裂隙岩体 ry crack.J Appl Mech,1957,24:109 断裂破坏机制及渗透压环境判定准则.岩土力学，2015,36 [23]Khan S MA,Khraisheh M K.Analysis of mixed mode crack ini- (1):56) tiation angles under various loading conditions.Eng Fract Mech, [13]Li X B,He X Q,Chen H J.Crack initiation characteristics of 2000,67(5):397 opening-mode crack embedded in rock-ike material under seep- 24]Smith D J,Ayatollahi M R,Pavier M J.On the consequences of age pressure.Chin J Rock Mech Eng,2012,31 (7):1317 T-stress in elastic brittle fracture.Proc R Soc London A,2006, (李夕兵，贺显群，陈红江.渗透水压作用下类岩石材料张 462(2072):2415 开型裂纹启裂特性研究.岩石力学与工程学报，2012,31 25]Sih G C.Strain-energy-density factor applied to mixed mode (7):1317) crack problems.Int J Fract,1974,10(3):305 [14]Tang S B.Dong Z,Huang R Q.Determination of T-stress using 226]ANSYS Inc.ANSYS Mechanical Theory Reference:Release finite element analysis.Sci China Technol Sci,2017,60(8): 15.0.Canonsburg,2014 1211 27]Guo F,Morgenstern N R,Scott J D.Interpretation of hydraulic [15]Li S Y,He T M,Yin X C.Introduction of Rock Fracture Me- fracturing breakdown pressure //International Journal of Rock chanics.Hefei:University of Science and Technology of China Mechanics and Mining Sciences Geomechanics Abstracts.Perga- Pres5,2010 mom,1993:617 (李世愚，和泰名，尹祥础.岩石断裂力学导论.合肥：中国 8]Bruno M S,Nakagawa F M.Pore pressure influence on tensile 科学技术大学出版社，2010) fracture propagation in sedimentary rock //International Journal 6]Jin X C.An Integrated Geomechanies and Petrophysics Study of of Rock Mechanics and Mining Sciences Geomechanics Abstracts. 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[19]Wei Y J.An extended strain energy density failure criterion by Pergamon,1989:471 differentiating volumetric and distortional deformation.Int J Sol- B1]Haimson B,Fairhurst C.Hydraulic fracturing in porous-permea- ids Struct,2012,49(9）:1117 ble materials.J Petrol Technol,1969,21(7):SPE2354A [20]Ayatollahi M R,Moghaddam M R,Razavi S M J,et al.Geome- B2]da Silva B G,Einstein HH.Finite element study of fracture ini- try effects on fracture trajectory of PMMA samples under pure tiation in flaws subject to internal fluid pressure and vertical mode-loading.Eng Fract Mech,2016,163:449 stress.Int J Solids Struct,2014,51(23-24):4122工程科学学报，第 41 卷，第 4 期 chanics /Geomechanics Symposium． San Francisco，2013: AＲ- MA-2013-644 ［12］ Pu C Z，Cao P，Zhang C Y，et al． Fracture failure mechanism of rock with closed crack and judging criterion of seepage pressure under biaxial compression． Ｒock Soil Mech，2015，36( 1) : 56 ( 蒲成志，曹平，张春阳，等． 双向压缩条件下闭合裂隙岩体 断裂破坏机制及渗透压环境判定准则． 岩土力学，2015，36 ( 1) : 56) ［13］ Li X B，He X Q，Chen H J． Crack initiation characteristics of opening-mode crack embedded in rock-like material under seep￾age pressure． Chin J Ｒock Mech Eng，2012，31( 7) : 1317 ( 李夕兵，贺显群，陈红江． 渗透水压作用下类岩石材料张 开型裂纹启裂特性研究． 岩石力学与工程学报，2012，31 ( 7) : 1317) ［14］ Tang S B，Dong Z，Huang Ｒ Q． Determination of T-stress using finite element analysis． Sci China Technol Sci，2017，60 ( 8) : 1211 ［15］ Li S Y，He T M，Yin X C． Introduction of Ｒock Fracture Me￾chanics． Hefei: University of Science and Technology of China Press，2010 ( 李世愚，和泰名，尹祥础． 岩石断裂力学导论． 合肥: 中国 科学技术大学出版社，2010) ［16］ Jin X C． An Integrated Geomechanics and Petrophysics Study of Hydraulic Fracturing in Naturally Fractured Ｒeservoirs ［Disserta￾tion］． Norman: University of Oklahoma，2014 ［17］ Tang S B． The effect of T-stress on the fracture of brittle rock un￾der compression． Int J Ｒock Mech Min Sci，2015，79: 86 ［18］ Seweryn A． A non-local stress and strain energy release rate mixed mode fracture initiation and propagation criteria． Eng Fract Mech，1998，59( 6) : 737 ［19］ Wei Y J． An extended strain energy density failure criterion by differentiating volumetric and distortional deformation． Int J Sol￾ids Struct，2012，49( 9) : 1117 ［20］ Ayatollahi M Ｒ，Moghaddam M Ｒ，Ｒazavi S M J，et al． Geome￾try effects on fracture trajectory of PMMA samples under pure mode-I loading． Eng Fract Mech，2016，163: 449 ［21］ Ayatollahi M Ｒ，Moghaddam M Ｒ，Berto F． A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials． Theor Appl Fract Mech，2015，79: 70 ［22］ Williams M L． On the stress distribution at the base of a stationa￾ry crack． J Appl Mech，1957，24: 109 ［23］ Khan S M A，Khraisheh M K． Analysis of mixed mode crack ini￾tiation angles under various loading conditions． Eng Fract Mech， 2000，67( 5) : 397 ［24］ Smith D J，Ayatollahi M Ｒ，Pavier M J． On the consequences of T-stress in elastic brittle fracture． Proc Ｒ Soc London A，2006， 462( 2072) : 2415 ［25］ Sih G C． Strain-energy-density factor applied to mixed mode crack problems． Int J Fract，1974，10( 3) : 305 ［26］ ANSYS Inc． ANSYS Mechanical Theory Ｒeference: Ｒelease 15. 0． Canonsburg，2014 ［27］ Guo F，Morgenstern N Ｒ，Scott J D． Interpretation of hydraulic fracturing breakdown pressure / /International Journal of Ｒock Mechanics and Mining Sciences ＆ Geomechanics Abstracts． Perga￾mon，1993: 617 ［28］ Bruno M S，Nakagawa F M． Pore pressure influence on tensile fracture propagation in sedimentary rock / /International Journal of Ｒock Mechanics and Mining Sciences ＆ Geomechanics Abstracts． Pergamon，1991: 261 ［29］ Hossain M M，Ｒahman M K，Ｒahman S S． Hydraulic fracture initiation and propagation: roles of wellbore trajectory，perforation and stress regimes． J Petrol Sci Eng，2000，27( 3-4) : 129 ［30］ Ikeda Ｒ，Tsukahara H． Hydraulic fracturing technique: pore pressure effect and stress heterogeneity / /International Journal of Ｒock Mechanics and Mining Sciences ＆ Geomechanics Abstracts． Pergamon，1989: 471 ［31］ Haimson B，Fairhurst C． Hydraulic fracturing in porous-permea￾ble materials． J Petrol Technol，1969，21( 7) : SPE-2354-PA ［32］ da Silva B G，Einstein H H． Finite element study of fracture ini￾tiation in flaws subject to internal fluid pressure and vertical stress． Int J Solids Struct，2014，51( 23-24) : 4122 · 644 ·