

浏览全部资源
扫码关注微信
1.北京工业大学城市安全与灾害工程教育部重点实验室,北京100124
2.北方工业大学土木工程学院,北京100144
Received:02 April 2022,
Revised:2022-05-09,
Published:15 October 2023
移动端阅览
徐静茹,李亮,宋佳.考虑惯性耦合的两相介质动力反应显式数值计算方法[J].防灾减灾工程学报,2023,43(05):1009-1015.
XU Jingru,LI Liang,SONG Jia.Time‑domain Full Explicit Numerical Algorithm of Fluid‑saturated Porous Media Considering Inertial Coupling[J].Journal of Disaster Prevention and Mitigation Engineering,2023,43(05):1009-1015.
徐静茹,李亮,宋佳.考虑惯性耦合的两相介质动力反应显式数值计算方法[J].防灾减灾工程学报,2023,43(05):1009-1015. DOI: 10.13409/j.cnki.jdpme.20220402003.
XU Jingru,LI Liang,SONG Jia.Time‑domain Full Explicit Numerical Algorithm of Fluid‑saturated Porous Media Considering Inertial Coupling[J].Journal of Disaster Prevention and Mitigation Engineering,2023,43(05):1009-1015. DOI: 10.13409/j.cnki.jdpme.20220402003.
基于包含惯性耦合(耦合质量密度系数)的
u
‑p
形式饱和两相介质弹性波动方程,开展了对饱和两相介质近场波动问题时域全显式数值计算方法的研究。通过对波动方程中的质量集中矩阵和流体压缩矩阵对角化处理,消除了方程中的动力耦联的影响。分别应用中心差分法和Newmark常平均加速度法求解固相位移和固相速度,基于向后差分法求解孔隙流体压力,建立了考虑惯性耦合的饱和两相介质的时域显式数值计算方法。将该方法的数值解与相应的解析解进行对比,二者符合良好,验证了该方法的正确性。将该方法应用于饱和两相介质自由场的地震反应问题,研究了惯性耦合对两相介质动力反应的影响。基于本文研究的两种情况表明,惯性耦合对饱和两相介质动力反应的影响程度有限。
Based on the
u
-p dynamic formulation of saturated two-phase media with considering inertial coupling (coupled mass density), the fully explicit algorithm intime domain for the near-field wave problem of fluid-saturated porous media is studied. The dynamic coupling in the equation is eliminated by diagonalizing the mass matrix and fluid compression matrix in the equation. The center difference method and Newmark constant average acceleration method are used to solve the solid phase displacement and velocity respectively, and the backward difference method is used to solve the fluid pressure. The numerical solution of the proposed method is compared with the analytical solution, with a strong agreement confirming the accuracy of the method employed. The method is applied to the seismic response of free field in saturated two-phase media and analyze the influence of inertial coupling on the dynamic response of two-phase media. Based on the two cases studied in this paper, the results show that the effect of inertial coupling on the dynamic reaction of fluid-saturated porous media is limited.
Biot M A . Theory of propagation of elastic waves in a fluid‑saturated porous solid [J]. The Journal of the Acoustical Society of America , 1956 , 28 ( 2 ): 168 ‑ 191 .
Zienkiewicz O C , Chang C T , Bettess P . Drained, undrained, consolidating and dynamic behaviour assumptions in soils [J]. Geotechnique , 1980 , 30 ( 4 ): 385 ‑ 395 .
Park K C . Stabilization of partitioned solution procedure for pore fluid‑soil interaction analysis [J]. International Journal for Numerical Methods in Engineering , 1983 , 19 ( 11 ): 1669 ‑ 1673 .
Zienkiewicz O C , Paul D K , Chan A H C . Unconditionally stable staggered solution procedure for soil‑pore fluid interaction problems [J]. International Journal for Numerical Methods in Engineering , 1988 , 26 ( 5 ): 1039 ‑ 1055 .
Zienkiewicz O C , Huang M S , Wu J , et al . A new algorithm for the coupled soil‑pore fluid problem [J]. Shock and Vibration , 1993 , 1 ( 1 ): 3 ‑ 14 .
Zienkiewicz O C , Huang M S , Pastor M . Computational soil dynamics‑A new algorithm for drained and undrained conditions [C]∥ Proceedings of the 8th International Conference on Computer Methods and Advances in Geomechanics , volume 1 , Morgantown, WV, United states: A.A. Balkema , 1994: 47 ‑ 59 .
段雪铭 , 李亮 , 杜修力 , 等 . 基于精细时程积分的饱和两相介质波动问题时域解法 [J]. 岩土力学 , 2015 , 36 ( 9 ): 2702 ‑ 2707,2715 .
Duan X M , Li L , Du X L , et al . A precise time‑integration method for wave propagation of fluid saturated porous media [J]. Rock and Soil Mechanics , 2015 , 36 ( 9 ): 2702 ‑ 2707,2715 . (in Chinese)
宋佳 , 许成顺 , 杜修力 , 等 . 基于精细时程积分的 u ‑ p 格式饱和两相介质动力问题的显‑显式时域算法 [J]. 工程力学 , 2017 , 34 ( 11 ): 9 ‑ 17 .
Song J , Xu C S , Du X L , et al . A temporal explicit‑explicit algorithm based on the precise time‑integration for solving the dynamic problems of fluid‑saturated porous media in u ‑ p form [J]. Engineering Mechanics , 2017 , 34 ( 11 ): 9 ‑ 17 . (in Chinese)
Xu C S , Song J , Du X L , et al . A completely explicit finite element method for solving dynamic u ‑ p equations of fluid‑saturated porous media [J]. Soil Dynamics and Earthquake Engineering , 2017 , 97 : 364 ‑ 376 .
李亮 , 李果 , 杜修力 , 等 . 饱和两相介质近场波动问题的一种时域全显式数值计算方法 [J]. 工程力学 , 2020 , 37 ( 8 ): 20 ‑ 31 .
Li L , Li G , Du X L , et al . A fully explicit numerical method in time domain for near‑field wave problems in saturated two‑phase media [J]. Engineering Mechanics , 2020 , 37 ( 8 ): 20 ‑ 31 . (in Chinese)
赵成刚 , 闫华林 , 李伟华 , 等 . 考虑耦合质量影响的饱和多孔介质动力响应分析的显式有限元法 [J]. 计算力学学报 , 2005 ( 5 ): 555 ‑ 561 .
Zhao C G , Yan H L , Li W H , et al . Dynamic analysis of fluid saturated porous media by using explicit finite element method considering the effects of coupling mass [J]. Chinese Journal of Computational Mechanics , 2005 ( 5 ): 555 ‑ 561 . (in Chinese)
Liao Z P , Wong H L . A transmitting boundary for the numerical simulation of elastic wave propagation [J]. Soil Dynamics and Earthquake Engineering , 1984 , 3 ( 4 ): 174 ‑ 183 .
王勖成 . 有限单元法 [M]. 北京 : 清华大学出版社 , 2003 .
Wang X C . Finite element method [M]. Beijing : Tsinghua University Press , 2003 . (in Chinese)
Simon B R , Zienkiewicz O C , Paul D K . An analytical solution for the transient response of saturated porous elastic solids [J]. International Journal for Numerical and Analytical Methods in Geomechanics , 1984 , 8 ( 4 ): 381 ‑ 398 .
Berryman J G . Comfirmation of Biot’ s throty [J]. Applied Physics Letters , 1980 , 37 ( 4 ): 382 ‑ 384 .
0
Views
0
下载量
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution
苏公网安备32010202012147号