中文摘要：

以非线性断裂力学理论为基础，通过应力叠加原理，推导出了ⅠⅡ型复合水力裂缝起裂角的解析模型。利用该模型计算了裂缝与最大水平主应力方向夹角为0°、30°、60°和90°时的裂缝端部塑性区域范围，并将利用该模型计算出的起裂角与利用最大周向应力准则计算出的起裂角进行了对比。结果表明：裂缝与最大水平主应力方向夹角为0°、30°、60°和90°时的裂缝端部塑性区域的范围分别是0～0.18，0～0.45，0～0.45和0～0.18倍半缝长；裂缝与最大水平主应力方向夹角为0°时，裂缝的起裂角为180°；当裂缝与最大水平主应力方向夹角增大至90°时，起裂角降为0°；在裂缝与最大水平主应力方向夹角及缝内流体压力相同的情况下，利用该模型计算出的起裂角比利用最大周向应力准则计算出的大0°～20°；在裂缝与最大水平主应力方向夹角相同的情况下，缝内流体压力为55 M Pa时的起裂角比缝内流体压力为45 M Pa时的大0°～40°。研究表明，利用非线性断裂力学研究泥页岩地层起裂是可行的，研究结果可以为水平井分段压裂优化提供一定的理论指导。

英文摘要：

Muddy shale is ductile rock ,the initiation angle of muddy shale formation was researched to en-hance the effect of hydraulic fracturing .In this work ,an analytic model for plastic core region and fracture initiation ofⅠ Ⅱ mixed mode hydraulic fractures was proposed base on Plastic Mechanics and superposition principle .Based on the model ,the plastic core region of fracture was calculated considering the fracture and maximum horizontal principal stress inclination angle of 0° ,30° ,45° and 60° .The calculated initiation angles were compared with the ini-tiation angles by adopting maximum tangential stress criterion .Results showed that when inclination angles were 0° ,30° ,45° and 60° ,the regime of plastic core regions is 0-0.18 ,0-0.45 ,0-0.45 and 0-0.18 times that of half-length of fracture respectively .When the inclination was 0° ,the initiation angle was 180° ,and the initiation angle decreased to 0° when the inclination angle was 90° .Given the same inclination angle and pressure ,the fracture initi-ation angle of the new model was 0°-20° larger than the initiation angle based on maximum tangential stress crite-rion .With the same inclination angle ,the initiation angle under 55 M Pa w as 0° -40° larger than that under 45 MPa .The research results showed that Plastic Mechanics was a feasible method for researching initiation of ductile formation ,and the results could provide theoretical reference to the optimization of perforation angle and fractu-ring pressure of horizontal well multistage fracturing in muddy shale formation .