随机和非线性波浪作用下海床动力响应和液化分析
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摘要
波浪作用下海床和海洋地基的动力稳定性是近海及海洋工程建筑物在设计和建造时必须考虑的重要问题之一。目前结合波浪荷载特点和海洋土的实际工程特性的研究和设计并不多见。作者考虑波浪和波浪荷载的随机和非线性特性，同时考虑波浪-海床相互作用，建立了求解实际波浪荷载作用下海床动力响应和液化深度的精确计算模型，对应完善了解析解法和有限元数值解法，通过大量数值计算和对比分析，着重讨论了波浪在传播过程中受多孔介质海床消能的影响，以及波浪荷载的随机和非线性特性对于海床动力响应和液化深度的定量影响程度，为实际海洋环境条件下海床液化与稳定性评价提供理论基础和技术储备。论文的主要研究内容如下：
1．重新推导和验证了基于准静态模式和完全动力响应模式的海床响应解析解，并给出两种模型的适用条件，为后续章节的研究内容奠定了理论基础；
2．采用复变量解析法，基于准静态模式和完全动力响应模式推导和建立了能够考虑多孔介质海床对波浪传播影响的波散方程。通过变动海床和波浪的主要特征参数，进行数值计算和对比分析，探讨和归纳了多孔介质海床对于波浪传播影响的规律和特性。结果表明，海洋土体和波浪参数的变动对波长比L／L_0和能量衰减系数e_α都有不同程度的影响；基于两种计算模式计算得到的波长比L／L_0和能量衰减系数e_α随海洋土体及波浪参数的变化趋势基本相同；相同海况下，与准静态模式计算结果相比，基于完全动力响应模式计算得到的波长比L／L_0和能量衰减系数e_α更小；水深的变化对波长比L／L_0影响相对规则，与深水区相比，浅水区内的波浪传播更容易受到海床的消能影响，深水区波浪传播几乎不受到海床消能的影响；海洋土体参数的变动对波长比L／L_0变化的影响程度基本相同，但渗透系数和剪切模量变动引起能量衰减系数e_α的变化更明显；多孔介质海床对低频波浪传播的影响明显高于对高频波浪传播的影响；
3．应用线性叠加法，采用平均JONSWAP谱模拟随机波浪，并考虑随机波浪-海床的相互作用，建立了新的求解随机波浪荷载作用下海床动力响应和液化深度的精确数值分析模型，并采用复变量解析法进行求解。结果表明，在随机波浪荷载作用下，海床动力响应具有较强的不规则性。同时由于波压力向海床内部传播具有时滞性，海床动力响应的峰值在时程上与随机波浪幅值的瞬时峰值不同步；由随机波浪理论计算得到的海床动力响应最大幅值沿海床深度方向的分布趋势与根据线性规则波浪理论得到的分布趋势基本相同，但数值上存在差异。其中采用传统随机分析方法的计算结果幅值最大，采用传统线性规则波浪理论的计算结果幅值最小，基于改进的随机分析模型的计算结果介于两者之间，三者之间的差值比较明显；根据随机波浪理论计算得到的海床最大液化深度明显大于线性规则波浪理论的计算结果，其中基于改进的随机分析模型得到的液化深度介于其他两种分析方法的结果之间。因此在海洋地基设计和自由场地安全评估时应该合理地考虑波浪荷载的随机特性。
4．应用一阶椭圆余弦波和二阶Stokes波等非线性波浪理论，考虑浅水区波浪传播的非线性效应，在时域上采用有限单元法对非线性波浪荷载作用下饱和砂质海床的动力响应进行了数值求解，并与线性规则波浪荷载作用下海床动力响应进行了对比分析。计算结果表明：当波浪由深部向近岸浅部传播而发生变形时，随着无量纲参数L／d与T(g/d)~(1/2)的增大，波浪的非线性程度增大，海床中孔隙水压力和有效应力的幅值明显地增大；不同波浪理论计算结果表明，海床中有效应力和孔隙水压力幅值沿海床深度方向的变化趋势基本相同，但数值存在差异，根据非线性波浪理论计算所得到的海床动力响应均大于线性规则波浪理论的计算结果；由一阶椭圆余弦波与二阶Stokes波两种非线性波浪理论所得到的海床动力响应之间相互大小关系并不唯一，具体取决于波浪和海床条件的组合。
The analysis of dynamic response of seabed due to wave loading is of practical significance in design and construction of marine structures and offshore installations. Reccently Considerable efforts for this problem have been made with growing interest by many researchers and marine engineers, and many representative results have been achieved. It is obvious that wave loading plays a significant role in the evaluation of construction safety and seabed instability. But there are few results of research and engineering design that can consider the feature of wave loading and soil parameters together. The purpose of this thesis is to establish a reasonable numerical model to simulate the characteristics of randomness and non-linearity of wave loading. The dynamic correaltion between wave and seabed can also be described through this model. Comparative parametric studies are principally made between the proposed analysis considering actual feature of ocean situation and conventional analysis based on linear theory of regular wave. The effect of randomness and non-linearity of wave loading on the dynamic response of seabed is investigated. The necessity is discussed about considering the influence of eliminating energy on propagating wave by porous seabed. The main investigations consist of the following parts:
1. The analytical solutions based on quasic-static model and dynamic model are derived and verified. The necessary condition of adoping dynamic model is discussed. Modifed expression provides the acdemic basis for the following research.
2. Based on quasi-static model and dynamic model, the analytical method with complex value is adopted to derive and establish wave dispertion eqaution, which can be used to consider the influence of porous seabed on wave propagating. The interactions between seabed and wave are described through numerous compared numerical resluts of parametric studies. The results show that the variation of soil parameters and wave diagnostic parameters have great effects on wave length ratio L/L_0 and the coefficient of energy attenuation e_α.The results of aforementioned two non-dimensional parameters based on dynamic solution are less than the results based on quasic-static solution. The distributions of L/L_o and e_αverus the parameters of wave and seabed are same with each other between analitcal results based on two kinds of model. When wave propagates over shallow water region, the wave energy loses much rapidly than on deep water region. It is expected that porous seabed almost has no effect on wave propagating in the region of very deep water. Among the parameters of soil, permeabilty and shear modulus have distinct effects on the coefficient of energy attenuation e_α. Compared with the sea wave of high frequence, the sea wave with low frequence is more readily to be influenced by porous seabed. The difference between proposed wave dispertion equation and traditional wave dispertion equation is checked, which is uesful for pratical marine engineering.
3. In conventional analyses of seabed dynamics, wave loading is basically treated as a deterministic process and is usually taken into consideration by using linear theory of regular wave. In fact, ocean wave is of intrinsic randomness in both time sequences and spatial distribution. The random nature of both wave and wave-induced loading will subsequently affect dynamic behavior of seabed. In this thesis, the analyses which can consider characteristics of randomness of wave loading and dynamic interaction between seabed and wave together, are formulated in a stochastic framework. Integrated numerical analysis model is established by employing wave spectrum. The comparative studies are conducted among the methods of traditional random analysis, modified random analysis, and linear regular wave theory. The results show that the amplitudes of dynamic response of seabed subjected to random wave loading are larger than that of regular linear wave loading. Therefore the stochastic feature of wave loading has to be duly taken into account in the analysis for dynamic response of seabed.
4. The numerical analyses adopting finite element method are performed for dynamic response of sandy seabed subjected to non-linear wave loading in the shallow water region. The non-linear wave loading is represented by second-order Stokes wave theory and first-order cnoidal-wave theory. Numerical results are calculated for comparative studiesbased on two non-dimensional parameters, L/d and T(1/2)g/d . Compared with the numericalresults from the linear wave theory, the amplitudes of dynamic responses computed by non-linear wave theories increase. It is shown that the linear theory of wave usually underestimate the dynamic response of seabed in the shallow water region. Therefore, the effect of non-linear characteristics of wave loading should be taken into consideration in planning and design of various marine or offshore constructions and facilities.
1．重新推导和验证了基于准静态模式和完全动力响应模式的海床响应解析解，并给出两种模型的适用条件，为后续章节的研究内容奠定了理论基础；
2．采用复变量解析法，基于准静态模式和完全动力响应模式推导和建立了能够考虑多孔介质海床对波浪传播影响的波散方程。通过变动海床和波浪的主要特征参数，进行数值计算和对比分析，探讨和归纳了多孔介质海床对于波浪传播影响的规律和特性。结果表明，海洋土体和波浪参数的变动对波长比L／L_0和能量衰减系数e_α都有不同程度的影响；基于两种计算模式计算得到的波长比L／L_0和能量衰减系数e_α随海洋土体及波浪参数的变化趋势基本相同；相同海况下，与准静态模式计算结果相比，基于完全动力响应模式计算得到的波长比L／L_0和能量衰减系数e_α更小；水深的变化对波长比L／L_0影响相对规则，与深水区相比，浅水区内的波浪传播更容易受到海床的消能影响，深水区波浪传播几乎不受到海床消能的影响；海洋土体参数的变动对波长比L／L_0变化的影响程度基本相同，但渗透系数和剪切模量变动引起能量衰减系数e_α的变化更明显；多孔介质海床对低频波浪传播的影响明显高于对高频波浪传播的影响；
3．应用线性叠加法，采用平均JONSWAP谱模拟随机波浪，并考虑随机波浪-海床的相互作用，建立了新的求解随机波浪荷载作用下海床动力响应和液化深度的精确数值分析模型，并采用复变量解析法进行求解。结果表明，在随机波浪荷载作用下，海床动力响应具有较强的不规则性。同时由于波压力向海床内部传播具有时滞性，海床动力响应的峰值在时程上与随机波浪幅值的瞬时峰值不同步；由随机波浪理论计算得到的海床动力响应最大幅值沿海床深度方向的分布趋势与根据线性规则波浪理论得到的分布趋势基本相同，但数值上存在差异。其中采用传统随机分析方法的计算结果幅值最大，采用传统线性规则波浪理论的计算结果幅值最小，基于改进的随机分析模型的计算结果介于两者之间，三者之间的差值比较明显；根据随机波浪理论计算得到的海床最大液化深度明显大于线性规则波浪理论的计算结果，其中基于改进的随机分析模型得到的液化深度介于其他两种分析方法的结果之间。因此在海洋地基设计和自由场地安全评估时应该合理地考虑波浪荷载的随机特性。
4．应用一阶椭圆余弦波和二阶Stokes波等非线性波浪理论，考虑浅水区波浪传播的非线性效应，在时域上采用有限单元法对非线性波浪荷载作用下饱和砂质海床的动力响应进行了数值求解，并与线性规则波浪荷载作用下海床动力响应进行了对比分析。计算结果表明：当波浪由深部向近岸浅部传播而发生变形时，随着无量纲参数L／d与T(g/d)~(1/2)的增大，波浪的非线性程度增大，海床中孔隙水压力和有效应力的幅值明显地增大；不同波浪理论计算结果表明，海床中有效应力和孔隙水压力幅值沿海床深度方向的变化趋势基本相同，但数值存在差异，根据非线性波浪理论计算所得到的海床动力响应均大于线性规则波浪理论的计算结果；由一阶椭圆余弦波与二阶Stokes波两种非线性波浪理论所得到的海床动力响应之间相互大小关系并不唯一，具体取决于波浪和海床条件的组合。
The analysis of dynamic response of seabed due to wave loading is of practical significance in design and construction of marine structures and offshore installations. Reccently Considerable efforts for this problem have been made with growing interest by many researchers and marine engineers, and many representative results have been achieved. It is obvious that wave loading plays a significant role in the evaluation of construction safety and seabed instability. But there are few results of research and engineering design that can consider the feature of wave loading and soil parameters together. The purpose of this thesis is to establish a reasonable numerical model to simulate the characteristics of randomness and non-linearity of wave loading. The dynamic correaltion between wave and seabed can also be described through this model. Comparative parametric studies are principally made between the proposed analysis considering actual feature of ocean situation and conventional analysis based on linear theory of regular wave. The effect of randomness and non-linearity of wave loading on the dynamic response of seabed is investigated. The necessity is discussed about considering the influence of eliminating energy on propagating wave by porous seabed. The main investigations consist of the following parts:
1. The analytical solutions based on quasic-static model and dynamic model are derived and verified. The necessary condition of adoping dynamic model is discussed. Modifed expression provides the acdemic basis for the following research.
2. Based on quasi-static model and dynamic model, the analytical method with complex value is adopted to derive and establish wave dispertion eqaution, which can be used to consider the influence of porous seabed on wave propagating. The interactions between seabed and wave are described through numerous compared numerical resluts of parametric studies. The results show that the variation of soil parameters and wave diagnostic parameters have great effects on wave length ratio L/L_0 and the coefficient of energy attenuation e_α.The results of aforementioned two non-dimensional parameters based on dynamic solution are less than the results based on quasic-static solution. The distributions of L/L_o and e_αverus the parameters of wave and seabed are same with each other between analitcal results based on two kinds of model. When wave propagates over shallow water region, the wave energy loses much rapidly than on deep water region. It is expected that porous seabed almost has no effect on wave propagating in the region of very deep water. Among the parameters of soil, permeabilty and shear modulus have distinct effects on the coefficient of energy attenuation e_α. Compared with the sea wave of high frequence, the sea wave with low frequence is more readily to be influenced by porous seabed. The difference between proposed wave dispertion equation and traditional wave dispertion equation is checked, which is uesful for pratical marine engineering.
3. In conventional analyses of seabed dynamics, wave loading is basically treated as a deterministic process and is usually taken into consideration by using linear theory of regular wave. In fact, ocean wave is of intrinsic randomness in both time sequences and spatial distribution. The random nature of both wave and wave-induced loading will subsequently affect dynamic behavior of seabed. In this thesis, the analyses which can consider characteristics of randomness of wave loading and dynamic interaction between seabed and wave together, are formulated in a stochastic framework. Integrated numerical analysis model is established by employing wave spectrum. The comparative studies are conducted among the methods of traditional random analysis, modified random analysis, and linear regular wave theory. The results show that the amplitudes of dynamic response of seabed subjected to random wave loading are larger than that of regular linear wave loading. Therefore the stochastic feature of wave loading has to be duly taken into account in the analysis for dynamic response of seabed.
4. The numerical analyses adopting finite element method are performed for dynamic response of sandy seabed subjected to non-linear wave loading in the shallow water region. The non-linear wave loading is represented by second-order Stokes wave theory and first-order cnoidal-wave theory. Numerical results are calculated for comparative studiesbased on two non-dimensional parameters, L/d and T(1/2)g/d . Compared with the numericalresults from the linear wave theory, the amplitudes of dynamic responses computed by non-linear wave theories increase. It is shown that the linear theory of wave usually underestimate the dynamic response of seabed in the shallow water region. Therefore, the effect of non-linear characteristics of wave loading should be taken into consideration in planning and design of various marine or offshore constructions and facilities.
引文
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