Numerical Study on Wave-Induced Oscillatory Liquefaction in Anisotropic Seabed
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摘要: 为探究各向异性海床在波浪作用下的瞬态液化问题，采用有限元法求解RANS （reynolds averaged navier-stokes）方程及k-ε湍流模型进行数值造波，通过求解Biot多孔弹性方程获得海床瞬态响应，进而建立了波浪-各向异性海床耦合作用的二维数值仿真模型. 在完成对新建模型的验证后，基于此模型系统地研究了波浪及海床特性对各向异性海床瞬态液化的影响. 研究结果表明：海床瞬态液化深度随波高、周期增大而增大，随海床饱和度增大而减小；当海床垂向渗透系数在一定范围内时，海床最大液化深度随垂向渗透系数增大而减小，超出该范围时，海床垂向渗透系数对海床最大液化深度的影响不明显；海床瞬态液化深度对水平方向渗透系数的改变不敏感.Abstract: In order to investigate the wave-induced oscillatory liquefaction in an anisotropic seabed, a two-dimensional numerical model for wave-seabed interactions is proposed. The reynolds-averaged navier-stokes (RANS) equation with the standard k-ε turbulence model was used to describe wave motions, and Biot’s poro-elastic equation was taken as the governing equation for the seabed model. After validation with previous experimental data and analytical solution, the proposed model was further applied to investigate the effects of wave and soil characteristics on anisotropic soil liquefaction. Numerical results show that the maximum liquefaction depth increased with an increase in wave height and wave period, and decreased with the degree of soil saturation. When the value of the soil permeability coefficient along the vertical direction is within a certain range, the effects of soil permeability along the vertical direction on the wave-induced soil response are obvious. Beyond the range, however, the effects of soil permeability along the vertical direction are almost negligible. Besides, the wave-induced oscillatory liquefaction depth in an anisotropic seabed is not sensitive to the variations in soil permeability along the horizontal direction.
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Key words:
- liquefaction /
- RANS equation /
- Biot’s equation /
- seabed /
- anisotropy
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图 2 不同网格密度时A点孔隙水压力时程曲线
Figure 2. Variations of pore pressure with time at point A for various mesh systems
图 3 最大孔隙水压力（|ps|/p0）沿海床深度（z/h）分布规律
Figure 3. Distribution of the maximum pore pressure (|ps|/p0) along the seabed depth (z/h)
图 6 海床液化深度随海床饱和度变化规律
Figure 6. Variations of the liquefaction depth with the degree of soil saturation
图 7 不同波浪高度下海床液化深度随Kz的变化规律（Kx = 1 × 10–7 m/s）
Figure 7. Variations of the liquefaction depth with the vertical permeability coefficient (Kz) under different wave heights (Kx = 1 × 10–7 m/s)
图 8 不同波浪周期下海床液化深度随Kz的变化规律（Kx = 1 × 10–7 m/s）
Figure 8. Variations of the liquefaction depth with the vertical permeability coefficient (Kz) under different wave periods (Kx = 1 × 10–7 m/s)
图 9 不同饱和度下海床液化深度随Kz的变化规律（Kx = 1 × 10–7 m/s）
Figure 9. Variations of the liquefaction depth with the vertical permeability coefficient (Kz) under different degrees of soil saturation (Kx = 1 × 10–7 m/s)
图 10 不同波浪高度下海床液化深度随Kx的变化规律（Kz = 1 × 10–7 m/s）
Figure 10. Variations of the liquefaction depth with the horizontal permeability coefficient (Kx) under different wave heights (Kz = 1 × 10–7 m/s)
图 11 不同波浪周期下海床液化深度随Kx的变化规律（Kz = 1 × 10–7m/s）
Figure 11. Variations of the liquefaction depth with the horizontal permeability coefficient (Kx) under different wave periods (Kz = 1 × 10–7 m/s)
图 12 不同饱和度下海床液化深度随Kx的变化规律（Kz = 1 × 10–7 m/s）
Figure 12. Variations of the liquefaction depth with the horizontal permeability coefficient (Kx) under different degrees of soil saturation (Kz = 1 × 10–7 m/s)
表 1 数值案例所取参数
Table 1. Parameters used in numerical examples
类型 参数 数值 波浪 H/m 2 d/m 10 T/s 12 h/m 20 海床土体 n 0.4 Kx/（m•s–2） 1 × 10–7 Kz/（m•s–1） 1 × 10–6 Sr 0.97 μs/（N•m–2） 1 × 107 
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