考虑渗流应力耦合的XFEM水压致裂模拟
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摘要
推导了含裂隙饱和多孔介质的水压致裂全耦合问题的扩展有限元增量迭代求解格式。通过对含中心裂纹无限大平板的裂尖位移场解析解的分析,按Ⅰ型和Ⅱ型变形特征进行提取,构建了一种新型的内聚裂尖加强函数,使传统扩展有限元中受裂尖加强影响的节点由每个节点8个裂尖加强自由度缩减到2个(平面问题),大大减小了计算规模。以含中心斜裂纹的多孔介质平板为例,验证了内聚裂尖加强模式的正确性,并对两种裂尖加强模式的雅克比矩阵条件数进行了计算。结果表明:内聚裂尖加强模式下扩展有限元的计算精度与传统扩展有限元的计算精度同阶,且网格较密时,本文处理方法的计算精度高于传统模式的。最后将改进的内聚裂尖加强模式应用到混凝土重力坝的水压致裂模拟中,取得了良好的计算效果。
An extended finite element incremental iterative solution scheme for the hydraulic fracturing problem with saturated porous media was derived. Based on the analysis of analytical solutions of crack tip displacement field of infinite plate with central crack, a new cohesive crack tip strengthening function was constructed according to the deformation characteristics of modelⅠand modelⅡ, which reduced the degree of freedom of the nodes affected by the crack tip strengthening from 8 to 2 in the traditional extended finite element method(for plane problem). The issue has greatly reduced the computation scale. Taking a porous medium plate with a central oblique crack as an example, the correctness of the cohesive crack tip strengthening model was verified. The condition numbers of Jacobian matrices of two kinds of crack tip strengthening modes were calculated. The results show that the accuracy of the extended finite element method under the cohesive crack tip strengthening mode is the same as that of the traditional extended finite element method. When the grid is denser, the accuracy of this method is higher than that of the traditional one. Finally, the improved cohesive crack tip strengthening model is applied to the hydraulic fracturing simulation of concrete gravity dam and good results are obtained.
An extended finite element incremental iterative solution scheme for the hydraulic fracturing problem with saturated porous media was derived. Based on the analysis of analytical solutions of crack tip displacement field of infinite plate with central crack, a new cohesive crack tip strengthening function was constructed according to the deformation characteristics of modelⅠand modelⅡ, which reduced the degree of freedom of the nodes affected by the crack tip strengthening from 8 to 2 in the traditional extended finite element method(for plane problem). The issue has greatly reduced the computation scale. Taking a porous medium plate with a central oblique crack as an example, the correctness of the cohesive crack tip strengthening model was verified. The condition numbers of Jacobian matrices of two kinds of crack tip strengthening modes were calculated. The results show that the accuracy of the extended finite element method under the cohesive crack tip strengthening mode is the same as that of the traditional extended finite element method. When the grid is denser, the accuracy of this method is higher than that of the traditional one. Finally, the improved cohesive crack tip strengthening model is applied to the hydraulic fracturing simulation of concrete gravity dam and good results are obtained.
引文
[1] KHOEI A R .Extended Finite Element Method:Theory and Applications[M].[S.l.]:[s.n.],2014:409-460.
[2] 柳占立,庄茁,孟庆国,等.页岩气高效开采的力学问题与挑战[J].力学学报,2017,49(3):507-516.
[3] 杨克己,韩理安.桩基工程[M].北京:人民交通出版社,1992:2-10.
[4] MOHAMMADI S.Extended Finite Element Method:for Fracture Analysis of Structures[J].Xfem Fracture Analysis of Composites,2007,45(22):5675-5687.
[5] 李录贤,王铁军.扩展有限元法(XFEM)及其应用[J].力学进展,2005(1):5-20.
[6] 夏晓舟,赵睿祺,章青.基于扩展有限元方法的含裂纹结构在动力荷载作用下的数值仿真[C]//南方计算力学联络委员会,江苏省力学学会.第十一届南方计算力学学术会议(SCCM-11)摘要集.南方计算力学联络委员会,江苏省力学学会,2017:1.
[7] 江守燕,杜成斌.一种XFEM断裂分析的裂尖单元新型改进函数[J].力学学报,2013,45(1):134-138.
[8] 王荣华,章青,夏晓舟.含裂隙饱和多孔介质流-固耦合的扩展有限元分析[J].岩土力学,2017,38(5):1489-1496.
[9] 王忠福,刘汉东,周敏,等.黄河大堤丁坝流固耦合分析研究[J].人民黄河,2008,30(8):16-17.
[10] RETHORE J,DE BORST R,ABELLAN M A.A Two-Scale Approach for Fluid Flow in Fractured Porous Media[J].International Journal for Numerical Methods in Engineering,2007,71(7):780-800.
[11] 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,2013,73:77-95.
[2] 柳占立,庄茁,孟庆国,等.页岩气高效开采的力学问题与挑战[J].力学学报,2017,49(3):507-516.
[3] 杨克己,韩理安.桩基工程[M].北京:人民交通出版社,1992:2-10.
[4] MOHAMMADI S.Extended Finite Element Method:for Fracture Analysis of Structures[J].Xfem Fracture Analysis of Composites,2007,45(22):5675-5687.
[5] 李录贤,王铁军.扩展有限元法(XFEM)及其应用[J].力学进展,2005(1):5-20.
[6] 夏晓舟,赵睿祺,章青.基于扩展有限元方法的含裂纹结构在动力荷载作用下的数值仿真[C]//南方计算力学联络委员会,江苏省力学学会.第十一届南方计算力学学术会议(SCCM-11)摘要集.南方计算力学联络委员会,江苏省力学学会,2017:1.
[7] 江守燕,杜成斌.一种XFEM断裂分析的裂尖单元新型改进函数[J].力学学报,2013,45(1):134-138.
[8] 王荣华,章青,夏晓舟.含裂隙饱和多孔介质流-固耦合的扩展有限元分析[J].岩土力学,2017,38(5):1489-1496.
[9] 王忠福,刘汉东,周敏,等.黄河大堤丁坝流固耦合分析研究[J].人民黄河,2008,30(8):16-17.
[10] RETHORE J,DE BORST R,ABELLAN M A.A Two-Scale Approach for Fluid Flow in Fractured Porous Media[J].International Journal for Numerical Methods in Engineering,2007,71(7):780-800.
[11] 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,2013,73:77-95.