Three-dimensional poro-elasto-plastic model for wave-induced seabed response around submarine pipeline

The evaluation of the wave-induced excess pore pressure around a buried pipeline is particularly important for pipeline engineers involved in the design of offshore pipelines. Existing models for the wave-induced seabed response around submarine pipeline have been limited to poro-elastic soil behavior and de-coupled oscillatory and residual mechanisms for the rise in excess pore water pressure. To overcome the shortcoming of the existing models, in this study a three-dimensional poro-elasto-plastic soil model with submarine pipeline is established, in which both oscillatory and residual mechanisms can be simulated simultaneously. With the proposed model, a parametric study is conducted to investigate the relative differences of the predictions of the wave-induced pore pressure with poro-elasto-plastic model. Based on numerical examples, it can be concluded that the poro-elasto-plastic behaviors of soil have more significant influence on wave-induced pore pressure of seabed around submarine pipeline. As the seabed depth increases, the normalized pore pressures decrease rapidly at the upper part of seabed, and then change slightly at the lower part of the seabed. Soil permeability and wave period have obvious influence on the wave-induced normalized pore pressure.     

Numerical analysis of liquefaction of porous seabed around pipeline fixed in space under seismic loading

Liquefaction of seabed under seismic loading is one of the main points that govern the overall stability of submarine pipeline. However, most previous investigations concerned only with free seabed and searched for seismic accumulative excess pore pressure by solving Terzaghi's consolidation equation containing pore pressure source term. It is not able to introduce two-dimensional structures such as submarine pipelines in one-dimensional problem, and it is also not able to obtain the distribution of seismic accumulative excess pore pressure in seabed around submarine pipelines by such a way. In this study, a FEM numerical analysis method for determining the liquefaction of sandy seabed around a buried pipeline under seismic loading is presented. The empirical mode of dynamic increase of pore pressure under undrained shearing induced by seismic loading is incorporated with two-dimensional dynamic consolidation equation and a numerical procedure based on FEM is developed to assess the accumulative excess pore pressure. By numerical computations, the accumulative process of pore pressure and liquefaction potential of seabed soil during seismic loading is evaluated. From a series of numerical computations based on the presented model with various parameters, the effects of soil characteristic parameters and pipeline geometry on seismic accumulative excess pore pressure around submarine pipeline and along the depth of seabed are explored in detail.     

Dynamic response of a porous seabed around pipeline under three-dimensional wave loading

The evaluation of the wave-induced pore pressure around a buried pipeline is particularly important for pipeline engineers involved in the design of offshore pipelines. Most previous investigations of the wave-induced dynamic response around an offshore pipeline have limited to two-dimensional cases. In this paper, a three-dimensional model including buried pipeline is established, based on the existing DYNE3WAC models. Based on the proposed numerical model and poro-elastic soil material assumption, the effects of wave and soil characteristics, such as wave period, water depth, shear modulus and permeability, and configuration of pipelines, such as pipeline radius and pipeline buried depth, on the wave-induced excess pore pressure will be examined. Numerical results indicated that the normalized excess pore pressures versus z/h near the pipeline increase as the obliquity angle, wave period and water depth increase, and they decrease as the burial depth and radius of pipeline increase above the pipeline. Soil permeability has obvious influence on the wave-induced normalized excess pore pressure, and different soil material will result in distinct computation results.     

Numerical modeling for wave–seabed–pipe interaction in a non-homogeneous porous seabed

An evaluation of the wave-induced pore pressures and effective stresses has been recognized by marine geotechnical engineers as an important factor in the design of marine pipelines. Most previous investigations for such a problem have considered the pipeline as a rigid material. Thus, the internal stresses within the pipeline have not been examined in the wave–seabed–pipe interaction problem. In this paper, we consider the pipeline itself to be an elastic material, and link the analysis of the pipeline with the wave–seabed interaction problem. Based on the numerical model presented, the effects of pipe geometry and variable soil characteristics on the wave-induced pore pressure and internal stresses will be discussed in detail. It is found that the internal normal stresses in the angular direction (σ_pθ) and shear stress (τ_p) within the pipe are much larger than the amplitude of wave pressure at the surface of the seabed.     

Finite element modelling for water waves-soil interaction

The soil permeability and shear modulus of many marine sediments vary with depth because of consolidation under overburden pressure. However, conventional theories for wave-induced soil response have assumed a homogeneous porous seabed, with constant soil permeability and shear modulus. This paper presents a finite element model for the wave-induced soil response in a porous seabed, with variable permeability and shear modulus as a function of burial depth. The soil matrix considered here is unsaturated and hydraulically anisotropic, and subjected to a three-dimensional short-crested wave system. The present finite element formulation is established by using a combination of semi-analytical techniques and the Galerkin method. The nodal effective stresses directly derived from the governing equations can be calculated accurately in the present model. Verification is available through the reduction to the simple case of homogeneous seabed. Three typical marine materials, course, fine sand and gravel, are considered in this study. The numerical results indicate that the soil permeability affects the wave-induced seabed response significantly especially for gravelled seabed, as does the soil shear modulus for sandy seabed.     

地基液化导致沉箱码头破坏及地基加固方法的非线性数值分析

地震作用引发的地基液化,往往导致沉箱基础的破坏。本文基于Biot两相饱和多孔介质动力耦合理论,采用FE-FD耦合数值分析方法,对液化海床沉箱基础的地震反应进行非线性有效应力分析。在数值分析过程中,建立了以土骨架位移和超静孔隙水压力表达的us-pw动力固结方程和循环弹塑性本构模型,该方法能够很好地模拟地震作用下沉箱码头的动力特性及液化破坏的影响。通过数值模拟计算,分析了采用碎石桩进行置换砂区域的防液化加固方法,并就碎石桩处理区域的选择提出了建议。     

波浪作用下成层海床孔隙水压力响应的简化分析

采用不排水条件下孔隙水压力发展模式,作为Terzagh i一维固结方程中考虑波浪循环作用所引起的孔隙水压力源项,对于成层海床建立了推广的一维动力固结方程,运用数理方程中的分离变量法与G reen函数求解了成层海床在波浪作用下残余孔隙水压力的发展规律,进而对成层海床的液化势进行了评判。对比计算与分析表明,海床表层土的渗透性及其厚度对于海床的整体抗液化性能具有显著的影响,低渗透性的表层导致海床孔隙水压力的显著积累,此时表层置换法是防治液化的有效途径。     

浪作用下海洋底床动态响应的研究

有关波浪作用下的底床动态响应越来越引起人们的重视。本文从海洋土的特点出发，针对各向同性底床和各向异性底床，详细论述了在线性波加载下，波浪衰减和底床动态响应这两方面的研究现状，在分析和比较已有研究成果的基础上，对今后的研究方向提出了自己的看法。     

A practical numerical method for large strain liquefaction analysis of saturated soils

Accurate prediction of the liquefaction of saturated soils is based on strong coupling between the pore fluid phase and soil skeleton. A practical numerical method for large strain dynamic analysis of saturated soils is presented. The u–p formulation is used for the governing equations that describe the coupled problem in terms of soil skeleton displacement and excess pore pressure. A mixed finite element and finite difference scheme related to large strain analysis of saturated soils based on the updated Lagrangian method is given. The equilibrium equation of fluid-saturated soils is spatially discretized by the finite element method, whereas terms associated with excess pore pressure in the continuity equation are spatially discretized by the finite difference method. An effective cyclic elasto-plastic constitutive model is adopted to simulate the non-linear behavior of saturated soils under dynamic loading. Several numerical examples that include a saturated soil column and caisson-type quay wall are presented to verify the accuracy of the method and its usefulness and applicability to solutions of large strain liquefaction analysis of saturated soils in practical problems.     

Dynamic response of an offshore pile to pseudo-Stoneley waves along the interface between a poroelastic seabed and seawater

A coupled model is developed to investigate the dynamic interaction between an offshore pile, a porous seabed and seawater when subjected to the pseudo-Stoneley wave along the seabed and the seawater interface. The pile and the seabed are treated as the porous medium governed by Biot's theory, while the seawater is considered as an acoustic medium and is described by the conventional Helmholtz equation. The free field solution of the incident pseudo-Stoneley wave is obtained using Biot's theory and the potential method. Based on the boundary element method (BEM) for the porous medium and the acoustic medium, three BEM formulations are constructed for the pile, the seabed and the seawater, respectively, which are combined together using the continuity conditions between the pile, the seabed and the seawater to formulate the coupled model for the system. As shown in numerical examples, when the system is subjected to the pseudo-Stoneley wave, the maximum pore pressure of the seabed usually occurs at the region near the interfaces between the seabed and the seawater.     

水域隧道地震响应分析

本文基于Biot动力固结理论和弹性动力学理论,考虑海床（土壤）的两相性、黏弹性人工边界及流（水）-固耦合作用,建立了隧道-土-流体相互作用的力学模型,讨论了P波作用下有无水的情况以及水深、水域隧道埋深、海床土性质和地震波入射角等因素对隧道及其周围海床应力的影响。结果表明:隧道周围海床土的孔隙水压力和隧道内应力随着水深的增加而增加;地震波特性和海床土特性对隧道的内应力和海床土的孔隙水压力均有较大的影响;海床土的渗透性和隧道埋深对隧道的内应力影响较小,而对隧道周围海床土的孔隙水压力影响较大;地震动的入射角对隧道的内应力和隧道附近土层的孔隙水压力均有较大影响。      

砂土液化引起大位移对地下管道影响的非线性分析

地下管线是生命线工程的主要部分,已经成为现代工农业生产和城镇生活的大动脉。已有震害调查表明,饱和砂土液化引起的地基大变形(侧向变形和沉降)是导致强震区生命线工程震害的主要原因。采用三维非线性有限差分分析方法来研究砂土液化引起的大位移对地下管道的破坏特征,分析砂土液化的斜坡变形特征、孔隙水的演化过程。结果表明,砂土液化引起的大位移对地下管道有破坏作用,导致管道变形规律与其斜坡的位移规律相同,地下管线的变形随着振动频率和幅值的增加其非线性增大。     

Analysis of attenuation and dispersion of propagating wave due to the coexistence of three fluid phases in the pore volume

In exploration geophysics, the efforts to extract subsurface information from wave characteristics exceedingly depend on the construction of suitable rock physics model. Analysis of different rock physics models reveals that the strength and magnitude of attenuation and dispersion of propagating wave exceedingly depend on wave-induced fluid flow at multiple scales. In current work, a comprehensive analysis of wave attenuation and velocity dispersion is carried out at broad frequency range. Our methodology is based on Biot's poroelastic relations, by which variations in wave characteristics associated with wave-induced fluid flow due to the coexistence of three fluid phases in the pore volume is estimated. In contrast to the results of previous research, our results indicate the occurrence of two-time pore pressure relaxation phenomenon at the interface between fluids of disparate nature, that is, different bulk modulus, viscosity and density. Also, the obtained results are compatible with numerical results for the same 1D model which are accounted using Biot's poroelastic and quasi-static equation in frequency domain. Moreover, the effects of change in saturation of three-phase fluids were also computed which is the key task for geophysicist. The outcomes of our research reveal that pore pressure relaxation phenomenon significantly depends on the saturation of distinct fluids and the order of saturating fluids. It is also concluded that the change in the saturation of three-phase fluid significantly influences the characteristics of the seismic wave. The analysis of obtained results indicates that our proposed approach is a useful tool for quantification, identification and discrimination of different fluid phases. Moreover, our proposed approach improves the accuracy to predict dispersive behaviour of propagating wave at sub-seismic and seismic frequencies.     

Transient dynamic response of fluid-saturated soil under a moving cyclic loading

Based on the Theory of Porous Media (TPM), a mathematical model of a two-dimensional incompressible fluid-saturated elastic soil is established, and the periodic boundary conditions are presented to analyze the transient dynamic response of this soil under a moving cyclic loading. The differential quadrature method (DQM) and the second-order backward difference scheme are applied to discretize the governing equations on the spatial and temporal domains, respectively. As application, a typical two-dimensional wave-induced transient problem with a seabed of finite thickness is analyzed, and the numerical results are compared with the analytical results presented in the present work. In addition, a transient dynamic response of fluid-saturated soil under limit moving vehicle loadings is studied. The effects of the velocity of vehicle and the volume fraction on the settlement and the pore water pressure are studied.     

遮帘式板桩码头地基地震液化破坏机理

遮帘式板桩码头作为一种新型的板桩结构型式,其抗震性能研究是设计建造过程中的重要环节。在FEM-FDM水土耦合计算的平台上引入循环弹塑性本构模型,借助FORTRAN编程软件形成饱和砂土动力液化分析的数值方法,可有效模拟饱和砂土在地震动力作用下的非线性及大变形特性,同时也可模拟砂土液化流动对遮帘桩和前墙的动土压力。研究表明:地震作用下可液化土层超孔隙水压力比增长并发生较大的水平流动变形,对前墙的水平破坏大于竖向破坏;前墙剪力最大值位于海床与前墙交界处;遮帘桩剪力最大值位移与前墙底平行的位置;后拉杆拉力逐渐变大,前拉杆拉力逐渐变小。通过对板桩码头地震液化灾害的分析,可为抗震和抗液化设计提供参考依据。     

Liquefaction characteristics of gap-graded gravelly soils in K0 condition

A series of undrained cyclic direct simple shear tests, which used a soil container with a membrane reinforced with stack rings to maintain the K₀ condition and integrated bender elements for shear wave velocity measurement, were performed to study the liquefaction characteristics of gap-graded gravelly soils with no fines content. The intergrain state concept was employed to categorize gap-graded sand–gravel mixtures as sand-like, gravel-like, and in-transition soils, which show different liquefaction characteristics. The testing results reveal that a linear relationship exists between the shear wave velocity and the minor fraction content for sand–gravel mixtures at a given skeleton void ratio of the major fraction particles. For gap-graded gravelly sand, the gravel content has a small effect on the liquefaction resistance, and the cyclic resistance ratio (CRR) of gap-graded gravelly sands can be evaluated using current techniques for sands with gravel content corrections. In addition, the results indicate that the current shear wave velocity (V_s) based correlation underestimates the liquefaction resistance for V_s values less than 160 m/s, and different correlations should be proposed for sand-like and gravel-like gravelly soils. Preliminary modifications to the correlations used in current evaluations of liquefaction resistance have thus been proposed.     

倾斜地层地震液化和滑移的有限元分析

应用饱和多孔介质动力学分析倾斜地层的土壤动力线性反应、液化和液化滑移问题，地下水位上的地层简化为单相介质层，饱和夹砂层看作是两相介质，水是可压缩的，采用双曲线非线性本构关系，考虑了砂土的剪胀性、刚度退化、滞回特性和土水相对运动等因素。基于土力学模型，建立了适用于分析非自由场地液化的动力方程组，基于是否考虑发生渗流问题，同时建立了两种离散形式：一种是以土骨架位移和水位移为未知量的矩阵方程，另一种是以土骨架位移、水位移和孔隙水压力为未知量的矩阵方程，初步分析了适用于多孔介质波动模拟的离散模型的人工边界问题，形成的方法将有助于问题的解决。     

Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians

A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant-Q (i.e. frequency-independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP-wave in the constant-Q viscoelastic anisotropic theory. For numerical simulations, the staggered-grid pseudo-spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional-order Laplacian approximation method is used to cope with spatial variable-order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant-Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional-order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.     

Rock-physics-based carbonate pore type characterization and reservoir permeability heterogeneity evaluation, Upper San Andres reservoir, Permian Basin, west Texas

The use of the shear wave velocity data as a field index for evaluating the liquefaction potential of sands is receiving increased attention because both shear wave velocity and liquefaction resistance are similarly influenced by many of the same factors such as void ratio, state of stress, stress history and geologic age. In this paper, the potential of support vector machine (SVM) based classification approach has been used to assess the liquefaction potential from actual shear wave velocity data. In this approach, an approximate implementation of a structural risk minimization (SRM) induction principle is done, which aims at minimizing a bound on the generalization error of a model rather than minimizing only the mean square error over the data set. Here SVM has been used as a classification tool to predict liquefaction potential of a soil based on shear wave velocity. The dataset consists the information of soil characteristics such as effective vertical stress (σ′_v0), soil type, shear wave velocity (V_s) and earthquake parameters such as peak horizontal acceleration (a_max) and earthquake magnitude (M). Out of the available 186 datasets, 130 are considered for training and remaining 56 are used for testing the model. The study indicated that SVM can successfully model the complex relationship between seismic parameters, soil parameters and the liquefaction potential. In the model based on soil characteristics, the input parameters used are σ′_v0, soil type, V_s, a_max and M. In the other model based on shear wave velocity alone uses V_s, a_max and M as input parameters. In this paper, it has been demonstrated that Vs alone can be used to predict the liquefaction potential of a soil using a support vector machine model.