波浪作用下海床动力响应与液化的数值分析
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摘要
波浪作用下海床或海洋地基的动力稳定性是近海和离岸工程建筑物在设计和建造过程中必须考虑的重要问题之一。海洋表面传播的波浪在海水-海床的交界面处施加了循环波压力，在这种循环波压力作用下，海床内土骨架的变形与孔隙流体的渗流运动相互耦合。与常规陆上荷载不同，波压力不仅是外加的循环表面力，而且是海床表面的超静孔隙水压力边界条件。在长时间的风暴作用过程中，土中超静孔压不断累积，同时也会由于部分排水固结发生消散与扩散，超静孔压的累积发展可能导致砂质海床发生液化。本文着重研究砂质海床的自由场动力响应。
在过去三十多年的研究中，通常将问题分解为两个相对独立的问题分别进行处理，即弹性海床的自由场动力响应与残余孔压的数值模拟。对于第一个问题，一般基于Biot固结理论，将海床视为理想线弹性材料，重点考察瞬时超静孔压与瞬时有效应力幅值沿海床深度的分布，但不能给出波浪引起的累积变形与残余孔压；对于第二个问题大都根据地震动力响应有效应力分析法发展而来，将波浪引起的海床复杂应力状态简化为纯剪切应力，进而根据室内循环剪切试验确定海床土的等效粘弹性本构模型参数，然后进行动力方程与固结方程的解耦运算，每一计算小时段初引入时段不排水孔压增量，将海床表面视为自由排水面。上述两种方法采用的土体本构模型都不能再现砂土在暴风浪等非比例加载条件下的动力特性，本文基于广义Biot理论提出了波浪作用下海床线性或非线性动力响应的耦合计算模型与稳定、高效数值算法，分别针对土的弹性、粘弹性与弹塑性本构关系，对海床的动力响应进行了有限元数值模拟与分析。
广义Biot固结理论能够完整地描述静、动力荷载作用下多孔介质材料骨架变形与孔隙渗流的耦合作用，但其数值求解一直是土动力学中尚未很好解决的难点之一。本文针对海床动力响应边值问题，推导了广义Biot理论u～U和u～p两种形式的有限元列式，实现了通常认为很困难的u～p形式直接解法，并将交叉迭代法扩展至两种u～p形式的综合求解。详细比较广义Biot理论u～U形式直接解法、u～p形式直接解法与交叉迭代法求解弹性、弹塑性问题的收敛性、稳定性与计算效率，认为以往较少应用的u～U形式直接解法刚度阵病态性弱，求解效率高，更适合土工问题的数值模拟，
小风浪作用下海床的动力响应特性可视为弹性的。根据所提出的广义Blot固结理论计算模型，通过线性数值分析考察了加速度项对海床动力响应的影响范围及影响程度，指出对于高频波浪下的大厚度弹性海床，忽略加速度项可能低估某些范围内的有
效应力幅值，而传统的加速度作用判别准则并不总是成立的。实现了以往解析法和数
值法不能处理的非线性波浪、成层海床和斜坡海床等复杂工况的数值模拟。通过全面、
系统的变动参数比较研究，系统分析了海床动力响应的主要影响因素。探讨了海洋不
透水基础下超静孔压和有效应力的分布。
将线粘弹性本构关系引人所建立的计算模型和线性算法，考察了粘质上的粘滞性
对海床动力响应的影响。尽管忽略了粘土海床上波浪传播过程中的能量衰减，建立的
分析模型仍能定性解释波浪引起的淤泥质海床流动大变形。
波浪荷载属于非比例循环加载，并导致海床土体发生主应力轴旋转现象。为此本
文进一步采用应力增量与应变增量方向相关的亚塑性边界面模型描述波浪加载路径下
砂土的应力一应变关系。而现有的广义Bim理论算例大多局限于线弹性本构关系或本
构刚度阵与应变增量无关的传统弹塑性本构关系。亚塑性边界面模型增量形式的本构
刚度阵不仅不对称，而且强烈地依赖于应变增量，将其引入计算模型，并研制了收敛
性较好的、高效的增量一迭代算法。分析模型中不再需要采用基于土工试验的不排水
孔压经验模式。考察两种代表性砂质海床在不同幅值波压力作用下的动力响应，弹塑
性有限元计算得到的超静孔压和残余孔压发展规律与离心模型试验中观察到的现象定
性上一致。
辨析波浪作用下海床液化的两种机理解释。所提出的计算模型不需要专门的液化
判断准则，就能够成功模拟海床液化时的三种主要表象，初步再现了液化区的渐进扩
展过程。
本文对海床或海洋建筑物地基的动力响应与液化分析所进行的线性和非线性数值
分析研究不仅具有一定的学术意义，而且将为海洋工程场地和海洋地基的安全性评价
提供技术支持。
The analysis for dynamic stability of seabed or offshore foundation under wave loading is of practical significance in the design and construction of offshore and coastal structures. When waves propagate over the ocean surface, a sequence of wave pressure is induced on the mudline or seafloor, which causes the coupling interaction between the deformation of soil skeleton and seepage movements of porous fluid. Different from cyclic loading acted on onshore foundation, the wave pressure plays double roles as: the surface loading imposed on the mudline and the boundary condition of excess pore pressure. During long-time storm, the excess pore pressures will be built up, then dissipated and re-distributed simultaneously due to partial drainage. Then it is possible the developments of excess pore pressures cause the liquefiable sandy seabed be liquefied. In this dissertation, the methods of linear and nonlinear analysis for dynamic responses of sandy seabed under waves loading are developed.
During the past three decades, attentions have been paid to two different issues: analysis for free-field dynamic response of elastic seabed and numerical evaluation of residual pore pressure in the seabed. The former is based on Biot's consolidation theory, and the seabed soil is taken as linear-elastic material. According to this method, the distribution of amplitudes of transient pore pressures and transient effective stresses are assessed, while the residual pore pressure and accumulated deformation cannot be taken account. The latter is developed on the basis of the effective stresses analysis of dynamic response of soil structure and foundation under seismic loading in the field of earthquake engineering. The complex effective stress state of seabed soils under waves is simplified to pure shear stress. Accordingly, the parameters of equivalent visco-elastic model are determined through cyclic shear testing. The governing equation of the boundary-value issue for the response of seabed is separated into dynamic equation and consolidation equation, and the incremental excess pore pressure under undrained condition has to be included into calculation at the beginning of every time step. The mudline is treated as drained boundary. In fact, the constitutive models employed in both methods could not re-produce the dynamic behaviour of soil to non-proportional cyclic loading, such as waves loading. To simulate dynamic responses of elastic, visco-elastic and elasto-plastic sea beds, linear and/or non-linear numerical models based on generalized Biot's theory are developed together with stable and effective algorithm.
The difficulty in numerical computation made the generalized Biot's theory be difficult to be put into practice in the field of geotechnical engineering. For the boundary-value problem,
such as dynamic response of seabed, the finite element formulations of u~U and u~p forms of generalized Biot's theory are established in this dissertation. Usually the direct solution of u~p form is viewed as rather difficult. A procedure is developed by the author. In addition, the stagger solution procedure is enlarged to u~p form I and II. The direct solution for u~U and u~p form, the stagger solution for u~p form are compared in the convergency, stability and efficiency, from which it is concluded that the first solution used not widely before is characterized with weakly ill-conditioned stiffness and comparatively high efficiency. The finite element methods based on these three solving procedures are numerically implemented.
The seabed soil under wave pressure with small amplitude can be viewed as elastic material. Depending on the numerical model proposed, the effect of accelerations of soil skeleton and porous fluid on the dynamic response of elastic seabed is examined. It is possible that the amplitudes of effective stresses in large-thickness seabed to high-frequency waves would be underestimated in some regions if the accelerations were overlooked. The responses of layered seabed, seabed with gentle slope and the sea
在过去三十多年的研究中，通常将问题分解为两个相对独立的问题分别进行处理，即弹性海床的自由场动力响应与残余孔压的数值模拟。对于第一个问题，一般基于Biot固结理论，将海床视为理想线弹性材料，重点考察瞬时超静孔压与瞬时有效应力幅值沿海床深度的分布，但不能给出波浪引起的累积变形与残余孔压；对于第二个问题大都根据地震动力响应有效应力分析法发展而来，将波浪引起的海床复杂应力状态简化为纯剪切应力，进而根据室内循环剪切试验确定海床土的等效粘弹性本构模型参数，然后进行动力方程与固结方程的解耦运算，每一计算小时段初引入时段不排水孔压增量，将海床表面视为自由排水面。上述两种方法采用的土体本构模型都不能再现砂土在暴风浪等非比例加载条件下的动力特性，本文基于广义Biot理论提出了波浪作用下海床线性或非线性动力响应的耦合计算模型与稳定、高效数值算法，分别针对土的弹性、粘弹性与弹塑性本构关系，对海床的动力响应进行了有限元数值模拟与分析。
广义Biot固结理论能够完整地描述静、动力荷载作用下多孔介质材料骨架变形与孔隙渗流的耦合作用，但其数值求解一直是土动力学中尚未很好解决的难点之一。本文针对海床动力响应边值问题，推导了广义Biot理论u～U和u～p两种形式的有限元列式，实现了通常认为很困难的u～p形式直接解法，并将交叉迭代法扩展至两种u～p形式的综合求解。详细比较广义Biot理论u～U形式直接解法、u～p形式直接解法与交叉迭代法求解弹性、弹塑性问题的收敛性、稳定性与计算效率，认为以往较少应用的u～U形式直接解法刚度阵病态性弱，求解效率高，更适合土工问题的数值模拟，
小风浪作用下海床的动力响应特性可视为弹性的。根据所提出的广义Blot固结理论计算模型，通过线性数值分析考察了加速度项对海床动力响应的影响范围及影响程度，指出对于高频波浪下的大厚度弹性海床，忽略加速度项可能低估某些范围内的有
效应力幅值，而传统的加速度作用判别准则并不总是成立的。实现了以往解析法和数
值法不能处理的非线性波浪、成层海床和斜坡海床等复杂工况的数值模拟。通过全面、
系统的变动参数比较研究，系统分析了海床动力响应的主要影响因素。探讨了海洋不
透水基础下超静孔压和有效应力的分布。
将线粘弹性本构关系引人所建立的计算模型和线性算法，考察了粘质上的粘滞性
对海床动力响应的影响。尽管忽略了粘土海床上波浪传播过程中的能量衰减，建立的
分析模型仍能定性解释波浪引起的淤泥质海床流动大变形。
波浪荷载属于非比例循环加载，并导致海床土体发生主应力轴旋转现象。为此本
文进一步采用应力增量与应变增量方向相关的亚塑性边界面模型描述波浪加载路径下
砂土的应力一应变关系。而现有的广义Bim理论算例大多局限于线弹性本构关系或本
构刚度阵与应变增量无关的传统弹塑性本构关系。亚塑性边界面模型增量形式的本构
刚度阵不仅不对称，而且强烈地依赖于应变增量，将其引入计算模型，并研制了收敛
性较好的、高效的增量一迭代算法。分析模型中不再需要采用基于土工试验的不排水
孔压经验模式。考察两种代表性砂质海床在不同幅值波压力作用下的动力响应，弹塑
性有限元计算得到的超静孔压和残余孔压发展规律与离心模型试验中观察到的现象定
性上一致。
辨析波浪作用下海床液化的两种机理解释。所提出的计算模型不需要专门的液化
判断准则，就能够成功模拟海床液化时的三种主要表象，初步再现了液化区的渐进扩
展过程。
本文对海床或海洋建筑物地基的动力响应与液化分析所进行的线性和非线性数值
分析研究不仅具有一定的学术意义，而且将为海洋工程场地和海洋地基的安全性评价
提供技术支持。
The analysis for dynamic stability of seabed or offshore foundation under wave loading is of practical significance in the design and construction of offshore and coastal structures. When waves propagate over the ocean surface, a sequence of wave pressure is induced on the mudline or seafloor, which causes the coupling interaction between the deformation of soil skeleton and seepage movements of porous fluid. Different from cyclic loading acted on onshore foundation, the wave pressure plays double roles as: the surface loading imposed on the mudline and the boundary condition of excess pore pressure. During long-time storm, the excess pore pressures will be built up, then dissipated and re-distributed simultaneously due to partial drainage. Then it is possible the developments of excess pore pressures cause the liquefiable sandy seabed be liquefied. In this dissertation, the methods of linear and nonlinear analysis for dynamic responses of sandy seabed under waves loading are developed.
During the past three decades, attentions have been paid to two different issues: analysis for free-field dynamic response of elastic seabed and numerical evaluation of residual pore pressure in the seabed. The former is based on Biot's consolidation theory, and the seabed soil is taken as linear-elastic material. According to this method, the distribution of amplitudes of transient pore pressures and transient effective stresses are assessed, while the residual pore pressure and accumulated deformation cannot be taken account. The latter is developed on the basis of the effective stresses analysis of dynamic response of soil structure and foundation under seismic loading in the field of earthquake engineering. The complex effective stress state of seabed soils under waves is simplified to pure shear stress. Accordingly, the parameters of equivalent visco-elastic model are determined through cyclic shear testing. The governing equation of the boundary-value issue for the response of seabed is separated into dynamic equation and consolidation equation, and the incremental excess pore pressure under undrained condition has to be included into calculation at the beginning of every time step. The mudline is treated as drained boundary. In fact, the constitutive models employed in both methods could not re-produce the dynamic behaviour of soil to non-proportional cyclic loading, such as waves loading. To simulate dynamic responses of elastic, visco-elastic and elasto-plastic sea beds, linear and/or non-linear numerical models based on generalized Biot's theory are developed together with stable and effective algorithm.
The difficulty in numerical computation made the generalized Biot's theory be difficult to be put into practice in the field of geotechnical engineering. For the boundary-value problem,
such as dynamic response of seabed, the finite element formulations of u~U and u~p forms of generalized Biot's theory are established in this dissertation. Usually the direct solution of u~p form is viewed as rather difficult. A procedure is developed by the author. In addition, the stagger solution procedure is enlarged to u~p form I and II. The direct solution for u~U and u~p form, the stagger solution for u~p form are compared in the convergency, stability and efficiency, from which it is concluded that the first solution used not widely before is characterized with weakly ill-conditioned stiffness and comparatively high efficiency. The finite element methods based on these three solving procedures are numerically implemented.
The seabed soil under wave pressure with small amplitude can be viewed as elastic material. Depending on the numerical model proposed, the effect of accelerations of soil skeleton and porous fluid on the dynamic response of elastic seabed is examined. It is possible that the amplitudes of effective stresses in large-thickness seabed to high-frequency waves would be underestimated in some regions if the accelerations were overlooked. The responses of layered seabed, seabed with gentle slope and the sea
引文
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