A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.

THE NON-AXISYMMETRICAL DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED POROELASTIC MEDIA

The Blot's wave equations of transversely isotropic saturated poroelastic media excited hy non-axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot's wave equations. The method of research on non-axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.

Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space

Heat source function method is adopted in the present paper to derive elementary solutions of coupled thermo-hydro-mechanical consolidation for saturated porous media under conjunct actions of instantaneous point heat source, instantaneous point fluid source and constant volume force. By using the so-called fictitious heat source method and images method, the solutions of a semi-infinite saturated porous medium subjected to a local heat source with time-varied intensity on its free surface are developed from elementary solutions. The numerical integral methods for calculating the unsteady temperature, pore pressure and displacement fields are given. The thermomechanical response are analyzed for the case of a circular planar heat source. Besides, the thermal consolidation characteristics of a saturated porous medium subjected to a harmonic thermal loading are also given, and the fluctuation processes of the field variables located below the center of heat source are analyzed.

THE NON-AXISYMMETRICAL DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED POROELASTIC MEDIA

The Biot’s wave equations of transversely isotropic saturated poroelastic media excited by non_axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot’s wave equations. The method of research on non_axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.

PARAMETERS INVERSION OF FLUID-SATURATED POROUS MEDIA BASED ON NEURAL NETWORKS

The multi- layers feedforward neural network is used for inversion ofmaterial constants of fluid-saturated porous media. The direct analysis of fluid-saturated porousmedia is carried out with the boundary element method. The dynamic displacement responses obtainedfrom direct analysis for prescribed material parameters constitute the sample sets training neuralnetwork. By virtue of the effective L-M training algorithm and the Tikhonov regularization method aswell as the GCV method for an appropriate selection of regu-larization parameter, the inversemapping from dynamic displacement responses to material constants is performed. Numerical examplesdemonstrate the validity of the neural network method.

Petroleum Hydrocarbon Transport through Saturated-unsaturated Media: A Numerical Model and Practice

The mathematical model of migration of total petroleum hydrocarbons in unsaturated media was described,including convection,molecular diffusion,mechanical dispersion and adsorption,and chemical reactions.By finite element method,a numerical model of evaluating petroleum hydrocarbon migration through contaminated soils was created and applied to the environmental investigations of a relocated mechanical factory in Shanghai.The model consisted of three compacted soil layers:plain fill,sandy silt and silty clay.The results showed that pollutants in the sandy silt traveled faster than that in the plain fill and silty clay.The same decreasing trend of migration velocity was observed in all of the three soil layers.After 180 d,the concentrations of pollutants in the sandy silt can be as low as 40% of the original maximum,while its counterpart in the silty clay is 64%.

Vibrating Liquefaction Experiment and Mechanism Study in Saturated Granular Media

By the vibrating liquefaction experiment of tailings and fine-ores of iron, it is observed and noted that the change of pore water pressure when the vibrating liquefaction takes place. Based on relevant suppositions, the equation of wave propagation in saturated granular media is obtained. This paper postulates the potential vector equation and the velocity expression of three kinds of body waves under normal conditions. Utilizing the wave theory and the experimental results, the influence of three body waves on pore water pressure and granules has been analyzed in detail. This revealed the rapid increment mechanism of pore water pressure and the wave mechanism of vibrating liquefaction.

Interaction of Airy–Gaussian beams in saturable media

Based on the nonlinear Schr o¨dinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure.

Water transfer characteristics during methane hydrate formation and dissociation processes inside saturated sand

Gas hydrates formation and dissociation processes inside porous media are always accompanied by water transfer behavior, which is similar to the water behavior of ice freezing and thawing processes. These processes have been studied by many researchers, but all the studies are so far on the water transfer characteristics outside porous media and the water transfer characteristics inside porous media have been little known. In this study, in order to study the water transfer characteristics inside porous media during methane hydrate formation and dissociation processes, a novel apparatus with three pF-meter sensors which can detect water content changes inside porous media was applied. It was experimentally observed that methane hydrate formation processes were accompanied by water transfer from bottom to top inside porous media, however, the water behavior during hydrate dissociation processes was abnormal, for which more studies are needed to find out the real reason in our future work.

Experimental Study on Mechanism of Depressurizing Dissociation of Methane Hydrate under Saturated Pore Fluid

Sediment-hosted hydrate reservoir often contains saturated pore fluid, which changes the heat transfer and mass transfer characteristics of the hydrate reservoir. The exploitation of hydrate under saturated pore fluid using depressurization is simulated experimentally to investigate the influence of particle size of porous media, dissociation temperature, pressure drop and injected fluid type on gas production behavior. Homogeneous methane hydrate was firstly formed in frozen quartz sand. With the formed hydrate sample, hydrate dissociation experiments by depressurization were conducted. The test results showed that the gas production rate of hydrate under saturated pore fluid was substantially influenced by the particle size, the pressure drop and the injected fluid type, while it was influenced little by the dissociation temperature. The hydrate dissociates faster under larger pressure drop and in the presence of smaller porous media within the experimental region. The dissociation rate increases with an increasing fluid salinity in the initial stage, while it decreases in the later stage. The increase of gas diffusion resistance resulted from ionic hydration atmosphere in saturated chloride solution impeded the dissociation of hydrate. It can be solved by increasing the pressure drop and decreasing the fluid salinity in the process of gas recovery from hydrate reservoir.

Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam

Based on the three-dimensional Gurtin-type variational principle of the incompressible saturated porous media, a one-dimensional mathematical model for dynamics of the saturated poroelastic Timoshenko cantilever beam is established with two assumptions, i.e., the deformation satisfies the classical single phase Timoshenko beam and the movement of the pore fluid is only in the axial direction of the saturated poroelastic beam. Under some special cases, this mathematical model can be degenerated into the Euler-Bernoulli model, the Rayleigh model, and the shear model of the saturated poroelastic beam, respectively. The dynamic and quasi-static behaviors of a saturated poroelastic Timoshenko cantilever beam with an impermeable fixed end and a permeable free end subjected to a step load at its free end are analyzed by the Laplace transform. The variations of the deflections at the beam free end against time are shown in figures. The influences of the interaction coefficient between the pore fluid and the solid skeleton as well as the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam are examined. It is shown that the quasi-static deflections of the saturated poroelastic beam possess a creep behavior similar to that of viscoelastic beams. In dynamic responses, with the increase of the slenderness ratio, the vibration periods and amplitudes of the deflections at the free end increase, and the time needed for deflections approaching to their stationary values also increases. Moreover, with the increase of the interaction coefficient, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Timoshenko beam.

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the halfspace is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Predhohn integral equations of the second kind and solved by numerical procedures. In the numerical extortples, the dynamic colnpliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

Bending of simply supported incompressible saturated poroelastic beams with axial diffusion

Based on the mathematical model of the bending of the incompressible saturated poroelastic beam with axial diffusion, the qUasi-static bendings of the simply supported poroelastic beam subjected to a suddenly applied constant load were investigated, and the analytical solutions were obtained for different diffusion conditions of the pore fluid at the beam ends. The deflections, the bending moments of the solid skeleton and the equivalent couples of the pore pressures were presented in figures. It is also shown that the behavior of the saturated poroelastic beams depends closely on the diffusion conditions at the beam ends, especially for the equivalent couples of the pore pressures. It is found that the Mandel-Cryer effect also exists in the bending of the saturated poroelastic beams under specific diffusion conditions at the beam ends.

双重孔隙流体饱和介质弹性波散射二维IBIEM模拟

基于平面波势函数,采用间接边界积分方程法(indirect boundary integral equation method, IBIEM)研究了双孔隙流体饱和介质中弹性波入射下二维孔洞的散射特性。推导得到了双孔隙介质中全空间二维线源动力格林函数,并给出了各散射波的位移场和应力场。在数值精度验证的基础上,以双孔隙二维饱和全空间中孔洞为例,解决了平面P、SV波入射下的地震波散射问题。数值结果表明:双重孔隙介质中的位移幅值、环向应力幅值、孔隙压力变化规律与不同入射波形,入射频率,孔隙率和边界排水条件密切相关,位移幅值在低频(无量纲频率η≤2)入射时出现峰值。环向应力幅值与干土条件相比更为复杂,基质孔压与裂缝孔压的存在增大了双重孔隙饱和介质的能量效应,总体震动趋势大于干土条件,环向应力放大可达62%。

孔隙率对多孔介质模型内水-气两相驱替规律的影响

多孔介质的孔隙率是影响水气两相驱替模式和注液饱和度的重要因素,饱和度是决定离子型稀土矿浸出率的关键指标。开展四种孔隙率的多孔介质中水气两相驱替微流体模型试验,确定了水气两相驱替模式,分析了气体团簇的形成机理及其分布特征,研究了孔隙率对模型内注液饱和度的影响。结果表明:水气两相驱替为毛细管指进模式,孔隙率高的多孔介质中指进现象更显著;随着毛细管数的增大,渗流模式逐渐趋于稳定。毛细管指进过程容易在多孔介质孔隙中形成气体团簇,低孔隙率模型中的气体团簇小而多;高孔隙率模型内的气体团簇大而少。模型内的注液饱和度随着孔隙率的增大而减小,随着注液强度的增大而增大。

库水-淤砂层-坝体-坝基体系地震响应分析

针对我国西部水利工程结构面临的地震安全问题,特别是混凝土高拱坝的抗震安全设计,以小湾水电站混凝土高拱坝为研究对象,进行了库水-淤砂层-坝体-坝基体系的耦合动力分析,同时考虑了复杂的坝基地形、正常蓄水位的库水以及常年运行而堆积的淤沙层的影响。主要内容有:①基于传递矩阵法及二维有限元,实现了复杂峡谷地形的自由场计算;②基于水-饱和多孔介质-固体的统一计算框架,实现了库水-淤沙层-坝体-坝基体系的三维地震响应分析算法。最后,分别以脉冲波和地震波作为输入,探讨了小湾拱坝的地震响应规律及库水淤沙层对拱坝地震响应的影响。结果表明:坝体顶部中心区域会承受较大的拉、压应力;而库水底部淤砂层对坝体的位移及应力影响并不显著。

地下水位对核电结构地震反应的影响分析

核电结构大多沿海或沿江、河而建,在地下水位以下,土体孔隙中的流体对土层的地震响应有较大影响,进而影响核电结构的响应。本文采用饱和多孔介质模型,考虑土-结相互作用效应,分析地下水位对核电结构地震反应的影响。通过传递矩阵方法,得到干土-饱和土水平成层场地的自由场,并结合透射人工边界,实现土-结相互作用分析的波动输入;采用土-结相互作用的分区并行计算方法,实现饱和土和结构相互作用分析。其中,含地下水位的场地土体采用广义饱和多孔介质模型描述,通过自编FORTRAN程序用集中质量显式有限元结合透射人工边界进行模拟,结构通过ANSYS中的隐式有限元进行分析。以某一核电结构为例,分析了0,−10,−20,−30,−40 m不同地下水位的五种场地上,土-基础-核电结构体系的动力响应。结果表明,地下水位对基础和结构的位移影响不大,对加速度的影响较大。