为探究波浪荷载作用下渗透率各向异性的海床的瞬态液化问题，分别以雷诺平均Navier-Stokes(RANS)方程和Biot多孔弹性方程作为波浪运动和海床响应的控制方程，采用LSM (Level Set Method)法对自由表面进行追踪，以保证波浪运动模拟的准确性，并建立了波浪-海床相互作用的二维耦合数值模型.在验证数值模型合理性的基础上，进一步分析了波浪参数、海床土体的饱和度和渗透性对海床瞬态液化的影响.结果表明：波浪参数和海床土体饱和度对海床瞬态液化的影响显著；海床的瞬态最大液化深度随着波浪的高度、周期的增大而增加，随着海床土体饱和度的增大而减小；相比于海床土体的水平方向渗透系数，海床的瞬态最大液化深度对垂直方向渗透系数的变化更加敏感.
In order to investigate the wave-induced seabed liquefaction with variation in permeability anisotropy, a two-dimensional integrated model for wave-seabed interactions was proposed in this paper. In the model the Reynolds-Averaged Navier-Stokes (RANS) equations and the Biot’s poro-elastic equations were taken as the governing equations for the wave model and seabed model respectively. The level set method (LSM) was used to track the free surface of water for modeling wave motion accurately. After the feasible of the present models were validated, the effects of wave parameters, soil saturation and permeability on the seabed liquefaction with variation in permeability anisotropy were further discussed. The analysis results indicated that both the wave parameters and soil saturation of seabed can significantly affect the wave-induced seabed liquefaction and the depth of maximum transient liquefaction of seabed increases with the increment of wave height, wave period and the decrement of degree of soil saturation. Maximum transient liquefaction of seabed depth is more sensitive to the variations of the permeability in vertical direction than the horizontal permeability.
［1］BIOT M A. General theory of three-dimensional consolidation［J］. Journal of Applied Physics, 1941, 12(2): 155-164.
［2］JENG D S. Porous models for wave-seabed interactions［M］. Heideberg: Springer, 2013.
［3］JENG D S, LIN Y S. Finite element modeling for water waves-soil interaction［J］. Soil Dynamics and Earthquake Engineering, 1996, 15(5): 283-300.
［4］JENG D S, YE J H, ZHANG J S, et al. An integrated model for the wave-induced seabed response around marine structures: Model verifications and applications［J］. Coastal Engineering, 2013, 72(2): 1-19.
［5］YE J H, JENG D S, WANG R, et al. A 3-D semi-coupled numerical model for fluid-structures-seabed-interaction (FSSI-CAS 3D): Model and verification［J］. Journal of Fluids and Structures, 2013, 40(7): 148-162.
［6］陈海锋. 波浪作用下的三维海床响应及液化分析［D］. 天津: 天津大学, 2009.
CHEN Haifeng. Study on wave-induced response of progresssive pore pressure and liquefaction in seabed［D］. Tianjin: Tianjin University, 2009.
［7］LIAO C C, TONG D G, CHEN L H. Pore pressure distribution and momentary liquefaction in vicinity of impermeable slope-type breakwater head［J］. Applied Ocean Research, 2018, 78: 290-306.
［8］LIAO C C, TONG D G, JENG D S, et al. Numerical study for wave-induced oscillatory pore pressures and liquefaction around impermeable slope breakwater heads［J］. Ocean Engineering, 2018, 157: 364-375.
［9］MADSEN O S. Wave-induced pore pressures and effective stress in a porous bed［J］. Geotechnique, 1978, 28(4): 377-393.
［10］YAMAMOTO T, SELLMEIHER H L, HIJUM E V. On the response of a porous-elastic bed to water waves［J］. Journal of Fluid Mechanics, 1978, 87(1): 193-206.
［11］MEI C C, FODA M A. Wave-induced responses in a fluid-filled poro-elastic solid with a free surface—A boundary layer theory［J］. Geophysical Journal of the Royal Astronomical Society, 1981, 66(3): 597-631.
［12］王栋, 栾茂田, 郭莹. 波浪作用下海床动力反应有限元数值模拟与液化分析［J］. 大连理工大学学报, 2001, 41(2): 216-222.
WANG Dong, LUAN Maotian, GUO Ying. FEM-based numerical simulation of dynamic response and liquefaction analysis of seabed under wave-induced loading［J］. Journal of Dalian University of Technology, 2001, 41(2): 216-222.
［13］ZEN K, YAMAZAKI H. Mechanism of wave-induced liquefaction and densification in seabed［J］. Soils and Foundations, 1990, 30(4): 90-104.
［14］SAKAI T, HANTAAKA K, MASE H. Wave-induced effective stress in seabed and its momentary liquefaction［J］. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1992, 118(2): 202-206.
［15］LIN Y S, JENG D S. Short-crested wave-induced liquefaction in porous seabed［J］. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(5): 481-494.
［16］SUZUKI K, TAKAHASHI S. Liquefaction of loosely deposited sandbed behind a breakwater due to wave overtopping［C］∥Coastal Structures 2003. Portland, USA: ASCE, 2003: 656-662.
［17］黄光爵, 郑永来, 武伯弢. 波浪作用下可液化海床最大液化深度［J］. 地震工程与工程振动, 2012, 32(5): 146-151.
HUANG Guangjue, ZHENG Yonglai, WU Botao. The maximum liquefaction depth of liquefiable seabed under loading［J］. Journal of Earthquake Engineering and Engineering Vibration, 2012, 32(5): 146-151.
［18］JENG D S, SEYMOUR B R. Response in seabed of finite depth with variable permeability［J］. Journal of Geotechnical and Geoenvironment Engineering, 1997, 123(10): 902-911.
［19］张金凤, 张庆河, 秦崇仁. 波浪作用下非均质各向异性海床响应的数值模拟［J］. 天津大学学报, 2006, 39(2): 159-164.
ZHANG Jinfeng, ZHANG Qinghe, QIN Chongren. Numerical simulation of wave-induced response of inhomogeneous and anisotropic seabed［J］. Journal of Tianjin University, 2006, 39(2): 159-164.
［20］WEN F, WANG J H. Response of layered seabed under wave and current loading［J］. Journal of Coastal Research, 2015, 31(4): 907-919.
［21］LIU B, JENG D S, YE G L, et al. Laboratory study for pore pressures in sandy deposit under wave loading［J］. Ocean Engineering, 2015, 106: 207-219.
［22］HSU J R C, JENG D S. Wave-induced soil response in an unsaturated anisotropic seabed of finite thickness［J］. International Journal for Numerical and Analytical Methods in Geomechanics, 1994, 18(11): 785-807.
［23］CHOWDHURY B, DASARI G R, NOGAMI T. Laboratory study of liquefaction due to wave-seabed interaction［J］. Journal of Geotechnical and Geoenvi-ronmental Engineering, 2006, 132(7): 842-851.
