海洋地震工程流固耦合问题统一计算框架
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摘要
海底地震动的模拟以及海洋工程结构的地震反应分析中,涉及到海水、饱和海床、弹性基岩、结构之间的相互耦合.传统的方法分别采用声波方程描述理想流体、Biot方程描述饱和海床、弹性波方程描述基岩和结构,分别考虑相互之间的耦合,十分不便.本文基于理想流体、固体分别为饱和多孔介质的特殊情形(孔隙率分别为1和0),由饱和多孔介质的Biot方程可退化得到理想流体的声波方程和固体的弹性波方程.然后,以饱和多孔介质方程为基础,经集中质量有限元离散,考虑不同孔隙率的饱和多孔介质之间耦合的一般情形,建立了该耦合情形的求解方法.进一步论证了该一般情形的耦合计算方法可分别退化到流体与固体、流体与饱和多孔介质、固体与饱和多孔介质之间的耦合计算,从而将流体、固体、饱和多孔介质间的耦合问题纳入到统一计算框架,并编制了相应的三维并行分析程序.以P-SV波垂直入射时,半无限层状海水–饱和海床、海水–弹性基岩、海水–饱和海床–弹性基岩三种情形的动力分析为例,采用统一计算框架结合透射边界条件进行求解,并与传递矩阵方法得到的解进行对比,验证了该统一计算框架的有效性以及并行计算的可行性.
The simulation of seismic wavefield at seafloor and seismic response of marine structures involves the coupling between seawater, saturated seabed, elastic bedrock and structure. That means, we target simulation where several types of equations are involved such as fluid, solid and saturated porous media equation. The conventional method for this fluid-solid-saturated porous media interaction problem is to use exsisting solvers of different equations and coupling method, which needs data mapping, communication and coupling algorithm between different solvers. Here, we present an alternative method, in which the coulping between different solvers is avoided. In fact, when porosity equals to one and zero, the saturated porous media is reduced to fluid and solid respectively, so we can use the porous media equation to describe the ideal fluid and solid, and the coupling between porous media, solid and fluid turns to the coupling between porous media with different porosity. Based on this idea, firstly the Biot's equations are approximated by Galerkin scheme and the explicit lumped-mass FEM is chosen, that are well suited to parallel computation. Then considering the traction and velocity continuity on the interface between porous media with different porosity, the coupled algorithm is derived,which is proved to be suitable for the coupling between fluid,solid and saturated porous media. Thus, the coupling problem between fluid, solid and saturated porous media can be brought into a unified framework, in which only the solver of saturated porous media is used. The three-dimensional parallel code for this proposed method is programed,examples for analysis of layered water-saturated seabed, water-bedrock, and water-saturated seabed-bedrock semi-infinite systems subjected to plane P-SV wave are given, and the proposed unified framework is verified through comparison between the results obtained through the proposed unified framework combined with tansmitting boundary condition and those obtained through tansfer matrix method.
The simulation of seismic wavefield at seafloor and seismic response of marine structures involves the coupling between seawater, saturated seabed, elastic bedrock and structure. That means, we target simulation where several types of equations are involved such as fluid, solid and saturated porous media equation. The conventional method for this fluid-solid-saturated porous media interaction problem is to use exsisting solvers of different equations and coupling method, which needs data mapping, communication and coupling algorithm between different solvers. Here, we present an alternative method, in which the coulping between different solvers is avoided. In fact, when porosity equals to one and zero, the saturated porous media is reduced to fluid and solid respectively, so we can use the porous media equation to describe the ideal fluid and solid, and the coupling between porous media, solid and fluid turns to the coupling between porous media with different porosity. Based on this idea, firstly the Biot's equations are approximated by Galerkin scheme and the explicit lumped-mass FEM is chosen, that are well suited to parallel computation. Then considering the traction and velocity continuity on the interface between porous media with different porosity, the coupled algorithm is derived,which is proved to be suitable for the coupling between fluid,solid and saturated porous media. Thus, the coupling problem between fluid, solid and saturated porous media can be brought into a unified framework, in which only the solver of saturated porous media is used. The three-dimensional parallel code for this proposed method is programed,examples for analysis of layered water-saturated seabed, water-bedrock, and water-saturated seabed-bedrock semi-infinite systems subjected to plane P-SV wave are given, and the proposed unified framework is verified through comparison between the results obtained through the proposed unified framework combined with tansmitting boundary condition and those obtained through tansfer matrix method.
引文
1 Nakamura T,Takenaka H,Okamoto T,et al.FDM Simulation of seismic-wave propagation for an aftershock of the 2009 Suruga Bay earthquake:Effects of ocean-bottom topography and seawater layer.Bulletin of Seismological Society of America,2012,102(6):2420-2435
2 Petukhin A,Iwata T,Kagawa T.Study on the effect of the oceanic water layer on strong ground motion simulations.Earth Planets Space,2010,62:621-630
3 Jianhong Y,Seismic response of poroelastic seabed and composite breakwater under strong earthquake loading.Bulletin of Earthquake Engineering,2012,10:1609-1633
4 Cheng XS,Xu WW,Yue CQ,et al.Seismic response of fluidstructure interaction of undersea tunnel during bidirction earthquake.Ocean Engineering,2014,75:64-70
5 Jin HL,Seo SI,Mun HS.Seismic behaviors of a floating submerged tunnel with a rectangular cross-section.Ocean Engineering,2016,127:32-47
6 Farhat C,Lesoinne M,LeTallec P.Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces:Momentum and energy conservation,optimal discretization and application to aeroelasticity.Computer Methods in Applied Mechanics&Engineering,1998,157(1):95-114
7 Farhat C,Lesoinne M.Two effcient staggered algorithms for serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems.Computer Methods in Applied Mechanics&Engineering,2000,182:499-515
8 Farhat C,Zee KGVD,Geuzaine P.Provably second-order timeaccurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity.Computer Methods in Applied Mechanics&Engineering,2006,195(17):1973-2001
9 Bathe KJ,Zhang H.Finite element developments for general fluid flows with structural interactions.International Journal for Numerical Methods in Engineering,2010,60(1):213-232
10 Degroote J,Haelterman R,Annerel S,et al.Performance of partitioned procedures in fluid-structure interaction.Computers&Structures,2010,88(7):446-457
11 Hou G,Wang J,Layton A.Numerical methods for fluid-structure Interaction-A review.Communications in Computational Physics,2012,12(2):337-377
12 Habchi C,Russeil S,Bougeard D,et al.Partitioned solver for strongly coupled fluid-structure interaction.Computers&Fluids,2013,71(1):306-319
13 Mehl M,Uekermann B,Bijl H,et al.Parallel coupling numerics for partitioned fluid-structure interaction simulations.Computers&Mathematics with Applications,2016,71(4):869-891
14 Bungartz HJ,Lindner F,Gatzhammer B,et al.preCICE-A fully parallel library for multi-physics surface coupling.Computers&Fluids,2016,141:250-258
15 Banks JW,Henshaw WD,Kapila AK,et al.An added-mass partition algorithm for fluid-structure interactions of compressible fluids and nonlinear solids.Journal of Computational Physics,2016,305(C):1037-1064
16 Basting S,Quaini A,Glowinski R.Extended ALE Method for fluidstructure interaction problems with large structural displacements.Journal of Computational Physics,2016,331(C):312-336
17 Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid.Acoust Soc Am,1956,28:168-191
18 Biot MA.Mechanics of deformation and acoustic propagation in porous media.Journal of Applied Physics,1962,33(4):1482-1498
19 Komatitsch D,Barnes C,Tromp J.Wave propagation near a fluidsolid interface:A spectral-element approach.Geophysics,2000,65(2):623-631
20 Link G,Kaltenbacher M,Breuer M,et al.A 2D finite-element scheme for fluid-solid-acoustic interactions and its application to human phonation.Computer Methods in Applied Mechanics&Engineering,2009,198(41):3321-3334
21李伟华.考虑水-饱和土场地-结构耦合时的沉管隧道地震反应分析.防灾减灾工程学报,2010,30(6):607-613(Li Weihua.Seismic Response analysis of immersed tube tunnels considering water saturated soil site structure coupling.Journal of Disaster Prevention and Mitigation Engineering,2010,30(6):607-613(in Chinese))
22廖振鹏.工程波动理论导论.第2版.北京:科学出版社,2002:136-285(Liao Zhenpeng.Introduction to Wave Motion Theories in Engineering(2nd edn).Beijing:Science Press,2002:136-285(in Chinese))
23邢浩洁,李鸿晶.透射边界条件在波动谱元模拟中的实现:二维波动.力学学报,2017,49(4):894-906(Xing Haojie,Li Hongjing.Implementation of multi-transmitting boundary condition for wave motion simulation by spectral element method:Two dimension case.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):894-906(in Chinese))
24谷音,刘晶波,杜修力.三维一致粘弹性人工边界及等效粘弹性边界单元.工程力学,2007,24(12):31-37(Gu Lin,Liu Jingbo,Du Xiuli.Three-dimensional uniform viscoelastic artificial boundary and equivalent viscoelastic boundary element.Journal of Engineering Mechanics,2007,24(12):31-37(in Cinese))
25刘晶波,宝鑫,谭辉等.波动问题中流体介质的动力人工边界.力学学报,2017,49(6):1418-1427(Liu Jingbo,BaoXin,Tan Hui,et al.Dynamical artificial boundary for fluid medium in wave motion problems.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1418-1427(in Chinese))
26赵宇昕,陈少林.关于传递矩阵法分析饱和成层介质响应问题的讨论.力学学报,2016,48(5):1145-1158(Zhao Yuxin,Chen Shaolin.Discussion on the matrix propagator method to analyze the response od saturated layered media.Chinese Journal of Theoretical and Applied Mechanics,2016,48(5):1145-1158(in Chinese))
27刘晶波,谭辉,宝鑫等.土-结构动力相互作用分析中基于人工边界子结构的地震波动输入方法.力学学报,2018,50(1):32-43(Liu Jingbo,Tan Hui,Bao Xin,et al.The seismic wave input method for soil-structure dynamic interaction analysis based on the substructure of artificial boundaries.Chinese Journal of Theoretical and Applied Mechanics,2018,50(1):32-43(in Chinese))
28陈少林,廖振鹏,陈进.两相介质近场波动模拟的解耦方法,地球物理学报,2005,48(4):909-917(Chen Shaolin,Liao Zhenpeng,Chen Jin.Decoupling method for near-field wave simulation of two-phase media.Journal of Geophysics,2005,48(4):909-917(in Chinese))
29 Deresiewicz H,Rice JT.The effect of boundaries on wave propagation in a liquid-filled porous solid:V.Transmission across a plane interface.Bull Seis Soc Am,1964,54(1):409-416
30 Deresiewicz H.The effect of boundaries on wave propagation in a liquid-filled porous solid:VII.Surface waves in a half-space in the presence of a liquid layer.Bull Seis Soc Am,1964,54(1):425-430
31 Thomson WT.Transmission of elastic waves through a stratified solid media.Journal of Applied Physics,1950,21:89-93
32 Haskell NA.The dispersion of surface waves on multilayered media.Bull Seismol Soc Am,1953,43:17-34
33柯小飞,陈少林,张洪翔.P-SV波入射时海水-层状海床体系的自由场分析.振动工程学报,2018,录用(Ke Xiaofei,Chen Shaolin,Zhang Hongxiang.Freefield analysis of seawater-layered seabed system at P-SV wave incident.Journal of Vibration Engineering,2018,Accepted(in Chinese))
2 Petukhin A,Iwata T,Kagawa T.Study on the effect of the oceanic water layer on strong ground motion simulations.Earth Planets Space,2010,62:621-630
3 Jianhong Y,Seismic response of poroelastic seabed and composite breakwater under strong earthquake loading.Bulletin of Earthquake Engineering,2012,10:1609-1633
4 Cheng XS,Xu WW,Yue CQ,et al.Seismic response of fluidstructure interaction of undersea tunnel during bidirction earthquake.Ocean Engineering,2014,75:64-70
5 Jin HL,Seo SI,Mun HS.Seismic behaviors of a floating submerged tunnel with a rectangular cross-section.Ocean Engineering,2016,127:32-47
6 Farhat C,Lesoinne M,LeTallec P.Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces:Momentum and energy conservation,optimal discretization and application to aeroelasticity.Computer Methods in Applied Mechanics&Engineering,1998,157(1):95-114
7 Farhat C,Lesoinne M.Two effcient staggered algorithms for serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems.Computer Methods in Applied Mechanics&Engineering,2000,182:499-515
8 Farhat C,Zee KGVD,Geuzaine P.Provably second-order timeaccurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity.Computer Methods in Applied Mechanics&Engineering,2006,195(17):1973-2001
9 Bathe KJ,Zhang H.Finite element developments for general fluid flows with structural interactions.International Journal for Numerical Methods in Engineering,2010,60(1):213-232
10 Degroote J,Haelterman R,Annerel S,et al.Performance of partitioned procedures in fluid-structure interaction.Computers&Structures,2010,88(7):446-457
11 Hou G,Wang J,Layton A.Numerical methods for fluid-structure Interaction-A review.Communications in Computational Physics,2012,12(2):337-377
12 Habchi C,Russeil S,Bougeard D,et al.Partitioned solver for strongly coupled fluid-structure interaction.Computers&Fluids,2013,71(1):306-319
13 Mehl M,Uekermann B,Bijl H,et al.Parallel coupling numerics for partitioned fluid-structure interaction simulations.Computers&Mathematics with Applications,2016,71(4):869-891
14 Bungartz HJ,Lindner F,Gatzhammer B,et al.preCICE-A fully parallel library for multi-physics surface coupling.Computers&Fluids,2016,141:250-258
15 Banks JW,Henshaw WD,Kapila AK,et al.An added-mass partition algorithm for fluid-structure interactions of compressible fluids and nonlinear solids.Journal of Computational Physics,2016,305(C):1037-1064
16 Basting S,Quaini A,Glowinski R.Extended ALE Method for fluidstructure interaction problems with large structural displacements.Journal of Computational Physics,2016,331(C):312-336
17 Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid.Acoust Soc Am,1956,28:168-191
18 Biot MA.Mechanics of deformation and acoustic propagation in porous media.Journal of Applied Physics,1962,33(4):1482-1498
19 Komatitsch D,Barnes C,Tromp J.Wave propagation near a fluidsolid interface:A spectral-element approach.Geophysics,2000,65(2):623-631
20 Link G,Kaltenbacher M,Breuer M,et al.A 2D finite-element scheme for fluid-solid-acoustic interactions and its application to human phonation.Computer Methods in Applied Mechanics&Engineering,2009,198(41):3321-3334
21李伟华.考虑水-饱和土场地-结构耦合时的沉管隧道地震反应分析.防灾减灾工程学报,2010,30(6):607-613(Li Weihua.Seismic Response analysis of immersed tube tunnels considering water saturated soil site structure coupling.Journal of Disaster Prevention and Mitigation Engineering,2010,30(6):607-613(in Chinese))
22廖振鹏.工程波动理论导论.第2版.北京:科学出版社,2002:136-285(Liao Zhenpeng.Introduction to Wave Motion Theories in Engineering(2nd edn).Beijing:Science Press,2002:136-285(in Chinese))
23邢浩洁,李鸿晶.透射边界条件在波动谱元模拟中的实现:二维波动.力学学报,2017,49(4):894-906(Xing Haojie,Li Hongjing.Implementation of multi-transmitting boundary condition for wave motion simulation by spectral element method:Two dimension case.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):894-906(in Chinese))
24谷音,刘晶波,杜修力.三维一致粘弹性人工边界及等效粘弹性边界单元.工程力学,2007,24(12):31-37(Gu Lin,Liu Jingbo,Du Xiuli.Three-dimensional uniform viscoelastic artificial boundary and equivalent viscoelastic boundary element.Journal of Engineering Mechanics,2007,24(12):31-37(in Cinese))
25刘晶波,宝鑫,谭辉等.波动问题中流体介质的动力人工边界.力学学报,2017,49(6):1418-1427(Liu Jingbo,BaoXin,Tan Hui,et al.Dynamical artificial boundary for fluid medium in wave motion problems.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1418-1427(in Chinese))
26赵宇昕,陈少林.关于传递矩阵法分析饱和成层介质响应问题的讨论.力学学报,2016,48(5):1145-1158(Zhao Yuxin,Chen Shaolin.Discussion on the matrix propagator method to analyze the response od saturated layered media.Chinese Journal of Theoretical and Applied Mechanics,2016,48(5):1145-1158(in Chinese))
27刘晶波,谭辉,宝鑫等.土-结构动力相互作用分析中基于人工边界子结构的地震波动输入方法.力学学报,2018,50(1):32-43(Liu Jingbo,Tan Hui,Bao Xin,et al.The seismic wave input method for soil-structure dynamic interaction analysis based on the substructure of artificial boundaries.Chinese Journal of Theoretical and Applied Mechanics,2018,50(1):32-43(in Chinese))
28陈少林,廖振鹏,陈进.两相介质近场波动模拟的解耦方法,地球物理学报,2005,48(4):909-917(Chen Shaolin,Liao Zhenpeng,Chen Jin.Decoupling method for near-field wave simulation of two-phase media.Journal of Geophysics,2005,48(4):909-917(in Chinese))
29 Deresiewicz H,Rice JT.The effect of boundaries on wave propagation in a liquid-filled porous solid:V.Transmission across a plane interface.Bull Seis Soc Am,1964,54(1):409-416
30 Deresiewicz H.The effect of boundaries on wave propagation in a liquid-filled porous solid:VII.Surface waves in a half-space in the presence of a liquid layer.Bull Seis Soc Am,1964,54(1):425-430
31 Thomson WT.Transmission of elastic waves through a stratified solid media.Journal of Applied Physics,1950,21:89-93
32 Haskell NA.The dispersion of surface waves on multilayered media.Bull Seismol Soc Am,1953,43:17-34
33柯小飞,陈少林,张洪翔.P-SV波入射时海水-层状海床体系的自由场分析.振动工程学报,2018,录用(Ke Xiaofei,Chen Shaolin,Zhang Hongxiang.Freefield analysis of seawater-layered seabed system at P-SV wave incident.Journal of Vibration Engineering,2018,Accepted(in Chinese))