摘要
为研究层理面对页岩Ⅰ型裂纹扩展的影响,利用裂纹尖端应力场Williams解,推导了页岩Ⅰ型裂纹沿层理方向的新分叉裂纹尖端应力场.基于最大周向应力判据,建立了考虑T应力的Ⅰ型裂纹沿层理起裂扩展准则,探讨了不同层理角度下裂纹沿层理面起裂与扩展规律.研究结果表明:T应力对含层理页岩裂纹扩展角,以及反映裂纹转向层理扩展难易程度指标起裂临界强度比Sc^i和扩展临界强度比Sc^c都具有影响。解析得到反映T应力大小的无量纲参数Bα=0.375是层理倾角β=0时Ⅰ型裂纹发生转向的一个分界点.β>0时,Bα=±0.375是Ⅰ-Ⅱ复合型分叉裂纹Sc^i和Sc^c发生变化的分界点:当Bα<-0.375时,Sc^i和Sc^c随着层理角度的增加先减小后增加,当Bα>0.375时,Sc^i和Sc^c随着层理角度的增加先增加后减小,而当-0.375≤Bα≤0.375时,Sc^i和Sc^c随着层理角度的增加而减小.基于此建立了综合反映T应力和层理角度对临界强度比影响的临界面.将理论预测裂纹沿层理面扩展结果与试验及数值模拟结果进行比较,吻合较好.
In order to study the effect of bedding plane on the propagation of mode Ⅰ crack in shale, the new bifurcation crack tip stress field of mode Ⅰ crack along the bedding of shale was derived by using Williams solution. Based on the criterion of the maximum circumferential stress, the mode Ⅰ crack initiation and propagation criterion considering T-stress was established, and the law of the crack initiation and propagation along the bedding plane with different bedding angles were discussed. The results indicate that T-stress has an effect on the crack propagation angle of bedding shale, as well as the crack initiation critical strength ratio Sc^i and the crack propagation critical strength ratio Sc^c, both of Sc^i and Sc^c reflect the difficulty of crack propagation along the bedding plane. The dimensionless parameter B α=0.375 representing the magnitude of T-stress was obtained analytically, which is a dividing point for mode Ⅰ crack deflecting for shale with bedding angle β=0. And B α=±0.375 is also a dividing point for the bifurcation cracks of the bedding which is mode Ⅰ-Ⅱ composite cracking at the bedding angle β>0. When B α<-0.375,Sc^i and Sc^c decrease first and then increase with the increase of β;B α>0.375, Sc^i and Sc^c increase first and then decrease with the increase of β, but if-0.375≤B α≤0.375, Sc^i and Sc^c decrease with the increase of β. Based on above results, the critical interface was established which comprehensively reflects the influence of T-stress and bedding angle on critical strength ratio. The experimental and numerical simulation results were used to validate the proposed crack propagation criterion. Reasonable agreement was obtained which provided the validations of the proposed criterion.
作者
李英杰
钟立博
左建平
LI Yingjie;ZHONG Libo;ZUO Jianping(School of Mechanics and Civil Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China)
出处
《中国矿业大学学报》
EI
CAS
CSCD
北大核心
2020年第3期488-498,共11页
Journal of China University of Mining & Technology
基金
国家自然科学基金青年基金项目(51604275)
中央高校基本科研业务费专项资金项目(2016QL02)
中国矿业大学(北京)越崎青年学者奖励计划项目
中国矿业大学(北京)越崎杰出学者奖励计划项目
大学生创新训练项目北京市重点项目(C201706375)。
关键词
层理页岩
裂纹扩展
T应力
解析解
断裂力学
bedding shale
crack propagation
T-stress
analytical solution
fracture mechanics