On the higher-order thermal vibrations of FG saturated porous cylindrical micro-shells integrated with nanocomposite skins in viscoelastic medium

Since the multi-layered structures are widely used nowadays, and due to interesting applications of cylindrical shells, this study is dedicated to analyzing free vibrational behaviors of functionally graded saturated porous micro cylindrical shells with two nanocomposite skins. Based on Biot's assumptions, constitutive relations for the core are presented and effective properties of the skins are determined via the rule of mixture. A sinusoidal theory is used to capture the shear deformation effects, and to account for the scale effects, the modified couple stress theory is employed which suggests a material length-scale parameter for predicting the results in small-dimension. With the aid of extended form of Hamilton's principle for dynamic systems, differential equations of motion are extracted. Fourier series functions are used to obtain natural frequencies and after validating them, a set of parametric studies are carried out. The results show the significant effects of porosity and Skempton coefficient, pores placement patterns, CNTs addition and distribution patterns, temperature variations, material length-scale parameter and viscoelastic medium on the natural frequencies of the microstructure. The outcomes of this work could be used to design and manufacture more reliable micro cylindrical structures in thermo-dynamical environments.

Solution of a Green's function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green＇s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters （permeability, frequency, etc.） under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner＇s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two- phase saturated medium in engineering.

Dynamic analysis of slab track on multi-layered transversely isotropic saturated soils subjected to train loads

The dynamic responses of a slab track on transversely isotropic saturated soils subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate the rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground systems are solved using the double Fourier transform, and the dynamic responses in the time domain are obtained by the inverse Fourier transform. The results show that a train load with high velocity will generate a larger response in transversely isotropic saturated soil than the lower velocity load, and special attention should be paid on the pore pressure in the vicinity of the ground surface. The anisotropic parameters of a surface soil layer will have greater influence on the displacement and excess pore water pressure than those of the subsoil layer. The traditional design method taking ground soil as homogeneous isotropic soil is unsafe for the case of RE 〈 1 and RG 〈 1, so a transversely isotropic foundation model is of great significance to the design for high train velocities.

Humic acid-mediated transport of a typical soil passivation remediation product(chloropyromorphite)in saturated porous media

Conversion of labile Pb species into chloropyromorphite(CPY)using phosphorus-bearing amendments was considered to be an ideal strategy in soil passivation remediation.However,the fate and transport of CPY in the soil are poorly understood.This study aims to fill the knowledge gap by evaluating the fate and transport of CPY under environmentally relevant conditions of humic acid(HA),pH,electrolyte concentration,and species through the saturated sandy medium.Results showed that bare CPY colloids are basically immobile in sandy porous media while the co-existence of HA made the transport of CPY improved by30%-93.5%.Facilitated transport of CPY was attributed to the increased stability of CPY and the repulsive interaction between CPY particles and sands due to HA adsorption.The mobility of CPY was also increased with increasing pH from 5.0 to 9.0.When the pH was 9 with a10 mmol/L NaCl background solution,the stronger energy barrier between CPY and sand led to enhanced transport behavior.The divalent Ca^(2+)had a more dramatic effect than monovalent Na^(+)on the aggregation and sedimentation of CPY colloids due to its effectivescreening of the surface charge of CPY and bridging interaction with CPY particles.Derjaguin-LandauVerwey-Overbeek theory and attachment efficiency calculation indicated that high energy barriers were responsible for the high mobility of CPY colloids,while the retention of CPY in sands was mainly caused by secondary energy minimum and physically straining.The findings of this work can help to evaluate the fate of soil passivation remediation products in natural water and soil.

Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

Abstract An analytical solution to the three-dimen-sional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expan-sion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot＇s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn： （1） there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; （2） the nor-malized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; （3） with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

饱和土中多孔洞对SH波的散射与动应力集中分析

根据Biot波动理论,采用复变函数法和多极坐标法下饱和土中多个非圆形孔洞的应力、位移边界条件下的基本解,求解SH波在饱和土中孔洞周围的散射和动应力集中的数值解,建立了一种求解饱和土孔洞对稳态SH波散射的理论方法.算例结果表明:随波数的增加,动应力集中系数和孔压集中系数都减小.波数在低频范围内,动应力集中系数随孔间距的增加而减小,而孔压集中系数随孔间距的增加而增加.另外,动应力集中系数和孔压集中系数随椭圆度的增加而减小.

饱和土中Biot波动方程与混合物理论波动方程的比较

本文比较了混合物理论推导出的饱和土一般波动方程与Biot饱和上波动方程，证明两者之间完全一致，但混合物理论无需关于a≥0的限制，在此基础上，本文推导出两种波动理论之间的正确系数对应关系，使混合物理论获得的结果与工程实践相吻合．

考虑竖向荷载作用时液化土中高桩基础水平动阻抗分析

考虑竖向荷载与水平荷载的耦合作用,基于Biot饱和多孔介质理论,结合Novak薄层法,建立饱和土体中高桩基础的水平振动分析模型,引入势函数解耦,利用微分算子分解法和参数分离法,得到非液化饱和土中桩段的水平振动解析解。将上部液化土视作无黏性不可压缩流体,建立柱坐标下的流体运动方程,求解得到液化土中桩段的水平振动解析解。利用位移连续条件,通过矩阵传递法得到高桩桩顶的动力阻抗表达式,并退化与已有文献解进行对比验证,讨论液化土性质、竖向荷载等因素对桩顶动阻抗的影响。结果表明,高桩阻抗随液化土厚度的增加而减小;液化土厚度不变时,液化土密度在高频阶段对高桩阻抗影响更显著;竖向荷载的存在主要影响桩基动刚度,对桩基动阻尼几乎无影响。

饱和土的球对称固结与Mandel-Cryer效应

饱和土的固结问题是土力学的一个基本问题,在饱和土固结过程中往往伴有Mandel-Cryer效应,对Mandel-Cryer效应的理论研究尚不完善.以Biot饱和土理论为基础,通过直接求解饱和土球对称Biot固结方程,得到了球对称固结方程在真实空间的解析解.数值计算结果充分表现了饱和土三维固结过程中孔隙水压力在空间的分布和随时间的变化,直观反映了Mandel-Cryer效应的发展过程,同时给出了土体泊松比对Mandel-Cryer效应的影响规律.

移动荷载作用下饱和土体上筏板—上部结构的动力响应分析(英文)

根据饱和土Biot理论与最小势能原理及薄板理论,采用子结构法,把上部结构、基础和地基作为一个共同作用的整体,在接触界面上满足变形协调条件,建立移动荷载作用下饱和土体地基—筏板—上部结构共同作用的积分方程.对积分方程的数值求解和相应的Fourier逆变换,得到任意时刻上部结构、筏板的内力和位移以及地基反力.最后通过数值计算,分析了饱和土体参数、移动荷载的速度等对上部结构水平、垂直方向的振动的影响特点.数值结果表明,上部结构各层的水平位移、竖向位移都随荷载速度增大而增加.竖向位移随楼层增加变化不大,当荷载速度较低时,水平位移随上部结构高度的变化曲线平滑少弯折,说明振动较稳定.但当荷载速度较高时,水平位移随楼层变化曲折越明显,层间差异大.

饱和土中单桩受移动荷载作用的动力响应

根据Biot动力理论,采用Fourier和Hankel变换方法得到了半空间饱和土受移动荷载及土体内受垂直简谐荷载作用下的变换域内基本解.再根据虚拟桩法,得出了移动载荷作用下桩基的第二类Fredholm积分方程.最后应用IFFT方法得到时间、空间域内单桩的动力响应.数值结果表明,移动荷载会引起桩身的负摩擦力;桩身最大轴力、孔压随移动荷载速度增加而增大;此外,在桩上端部会出现孔压集中现象.

求解饱和半空间上弹性圆板固结沉降的积分方程

本文采用解析方法分析了弹性圆板在饱和半空间上的固结沉降。考虑弹性圆板与饱和半空间的接触面上无摩擦力,且饱和半空间表面为全部透水的。运用Biot固结理论和积分方程技术,在Laplace变换域上建立了弹性圆板固结沉降的对偶积分方程,并化此对偶积分方程为第二类Fredholm积分方程。通过对其核函数的有效数值积分得到第二类Fredholm积分方程的解,再利用Laplace反演技术获得弹性板在时间域中的固结沉降值。文末给出弹性板中心点固结沉降的固结度的数值算例。

固结和流变的饱和土—筏板—单桩共同作用分析

根据Biot固结理论,采用Laplace和Hankel变换方法得到了半空间饱和土表面和土体内受垂直环形载荷作用下的变换域内基本解.再根据虚拟桩法,得出了土—筏板—桩的第二类Fredholm积分方程.求解积分方程并进行相应的数值逆变换可得单桩的变形、轴力、孔压以及筏板与土的接触正应力随时间的变化情况.数值结果表明:随着土体的逐步固结与流变,筏板与土的接触正应力将减小,而桩所分担的荷载比例增加;同时桩周孔压逐步消散;桩身位移随着时间的推移会增大.

饱和孔隙介质中的格林函数及边界积分方程

根据Biot理论,利用势函数方法建立了频域内孔隙介质的二维格林函数;利用格林函数和孔隙介质中的互易定理,建立了孔隙介质的边界积分方程.通过引入二维弹性静力学解和二维La-place方程的基本解,处理了边界积分方程中的柯西主值积分问题.笔者的研究为应用边界元方法求解孔隙介质中的二维动力问题提供了理论基础.

Finite element implementation of coupled hydro-mechanical modeling of transversely isotropic porous media in DEAL.II

In geotechnical engineering,modeling geo-structures is challenging,particularly in cases where the interaction between the structures and soil or rock is complex.Most wellknown commercial modeling software is based on homogenous and isotropic materials.However,soil and rock are often modeled in heterogeneous and anisotropic media because of the inherent anisotropy of sedimentary rock masses and their stratified structure.In recent decades,coupled hydro-mechanical(HM)interactions in isotropic porous media have been studied;however,the behavior of transversely isotropic porous media is rarely considered.In addition,it is difficult for commercial software such as Plaxis and Flac3D to express complex rock formation where the anisotropy of the material and the associated cracks and fractures could be assembled into a single model.In this study,a finite element implementation using Differential Equation Analysis Library(DEAL.II),an open-source library of finite element codes,was developed to model the fully coupled HM behavior of transversely isotropic porous media.The proposed implementation can be applied to both isotropic and transversely isotropic porous media based on Biot’s theory.The developed code can be used to model poroelastic media with(1)equations of linear elasticity for the solid matrix and(2)diffusion equations for fluid flow based on mass and linear-momentum conservation laws.We verified the performance and accuracy of the code through two examples,i.e.,Mandel’s problem with a compared analytical solution and a tunnel excavation process with the Flac3D software.On the basis of these numerical applications,we present the code to model the behavior of various geo-structures such as tunnels and pile–soil interactions with anisotropic materials.

半空间饱和孔隙介质在P、SV波入射下的波场解

基于Biot理论,利用Fourier变换和势函数方法,将Biot波动方程化为一组Helmholtz方程。通过入射波和反射波的波势函数表达式及边界条件,可得波势函数的幅值,进而可得位移、应力、孔压。数值算例给出了P和SV波入射的波场解及其随饱和孔隙介质参数的变化。本文的结果是研究饱和土在地震波作用下土的液化以及利用积分方程或边界元方法研究桩在地震波作用下的动力响应的基础。