基于精细时程积分的饱和两相介质波动问题时域解法

针对u-p形式的饱和两相介质的波动方程,采用精细时程积分方法计算固相位移u,采用向后差分算法求解流体压力p,建立了基于精细时程积分技术的饱和两相介质波动问题的时域求解方法。针对标准算例,将该方法的计算结果与可视为标准结果的Zienkiewicz隐式算法的计算结果进行比较分析,二者符合较好,表明了该方法具有良好的计算精度。同时,该方法的计算过程为交替迭代求解,避免了在每个时间分析步上求解耦联方程组,因而具有较高的计算效率。该方法具有时域显式计算方法的基本特点,是进行饱和两相介质动力问题计算与分析的一种有效方法。     

On Garg's solution of Biot's equations for wave propagation in a one-dimensional fluid-saturated elastic porous solid

Garg's approximate analytical solutions of Biot's equations for wave propagation in a fluid-saturated elastic porous solid of infinite extent subjected to a velocity boundary condition of a Heaviside function at one end are examined for small and large drag. Garg's approximations were apparently introduced to facilitate exact inversion of Laplace transforms of certain quantities. The approximate solutions are compared with carefully evaluated numerical inverses of the Laplace transform solutions for different soils with widely varying properties. It is seen that for most soils (clays, silts and, sands) the error in Garg's approximate solutions in insignificant, and the solutions can be used as benchmarks for verifying numerical analysis procedures such as finite element codes.     

Multi-scale simulation of wave propagation and liquefaction in a one-dimensional soil column: hybrid DEM and finite-difference procedure

The paper describes a multi-phase, multi-scale rational method for modeling and predicting free-field wave propagation and the weakening and liquefaction of near-surface soils. The one-dimensional time-domain model of a soil column uses the discrete element method (DEM) to track stress and strain within a series of representative volume elements (RVEs), driven by seismic rock displacements at the column base. The RVE interactions are accomplished with a time-stepping finite-difference algorithm. The method applies Darcy’s principle to resolve the momentum transfer between a soil’s solid matrix and its interstitial pore fluid. Different algorithms are described for the dynamic period of seismic shaking and for the post-shaking consolidation period. The method can analyze numerous conditions and phenomena, including site-specific amplification, down-slope movement of sloping ground, dissolution or cavitation of air in the pore fluid, and drainage that is concurrent with shaking. Several refinements of the DEM are described for realistically simulating soil behavior and for solving a range of propagation and liquefaction factors, including the poromechanic stiffness of the pore fluid and the pressure-dependent drained stiffness of the grain matrix. The model is applied to four sets of well-documented centrifuge studies. The verification results are favorable and highlight the importance of the pore fluid conditions, such as the amount of dissolved air within the pore water.

     

爆炸波在准饱和砂土中的传播规律

在文献[1]所建立的饱和砂土动力分析模型的基础上,将该模型编制成分析模块并与通用岩土分析软件FLAC接口。模拟分析饱和砂土在爆炸压缩波荷载作用下波的传播特性,分别考虑了准饱和砂土各组分含量等因素对饱和砂土中波传播的影响。数值模拟结果表明,准饱和土中含有的少量气体对爆炸压缩波传播以及饱和砂土动力特性具有重要影响。     

A mixed finite element approach for viscoelastic wave propagation

In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zeners model. We achieve its mathematical analysis: existence and uniqueness of solutions, energy decay and propagation with finite speed. For the numerical resolution, we extend a mixed finite element method proposed in [8]. This method combines mass lumping with a centered explicit scheme for time discretization. For the resulting scheme, we prove a discrete energy decay result and provide a sufficient stability condition. For the numerical simulation in open domains we adapt the perfectly matched layers techniques to viscoelastic waves [23]. Various numerical results are presented.     

软土非线性蠕变压缩模型

从土的力学行为与微观结构相结合的途径探讨滨海软土单向压缩的本构特征,旨在构造一个用于软土一维变形计算的合理形式.据多级加荷压缩试验成果,进一步证明了软土具有非线性蠕变特性;并用幂函数描述了软土压缩蠕变规律,用割线模量法概化了单向压缩的应力-应变的关系.提出了压缩蠕变率(CCR)的概念,并建立与土的结构定量参数(定向概率熵和孔隙分布分维数)、应力比之间的幂函数关系.在此基础上,建议了一个考虑非线性蠕变特性的单向压缩本构模型,并用试验资料初步验证了模型的有效性.建议的模型具有参数少、简便实用之特点,可用于软土地基的沉降计算分析.     

Effects of seismic wave propagation on a long and narrow building: Body wave and surface wave propagation

In the case of the dynamic analysis of the structures using the recorded earthquake ground motions, it is usually assumed that the ground motion consists of body waves propagating vertically. However, the response of a long and narrow structure may be influenced by the oblique propagation of body waves and the dispersion of surface waves. In this paper, the effects of the seismic wave propagation on the response of this kind of structure are investigated. The characteristics of the wave propagation were verified using the recorded motions and soil information at the building site. The ground motion at every input point of the building was evaluated using the difference of arrival time of seismic waves calculated by assuming the velocity and the direction of the wave propagation. Using these ground motions, response analyses of the lumped mass model for the structure were performed. By considering the characteristics of the seismic wave propagation, the average response decreased but the local response increased around the end of the roof. Further studies of the structure were also performed in order to restrain the response around the end of the roof.     

Analysis of wave propagation in dry granular soils using DEM simulations

In this paper, a three-dimensional particle-based technique utilizing the discrete element method (DEM) is proposed to study wave propagation in a dry granular soil column. Computational simulations were conducted to investigate the soil response to sinusoidal motions with different amplitudes and frequencies. Three types of soil deposits with different void ratios were employed in these simulations. Different boundary conditions at the base such as rigid bedrock, elastic bedrock, and infinite medium were also considered. Analysis is done in time domain while taking into account the effects of soil nonlinear behavior. The computational approach is able to capture a number of essential characteristics of wave propagation including motion amplification and resonance. Dynamic soil properties were then extracted from conducted simulations and used to predict the response of the soil using the widely used equivalent linear method program SHAKE and compare its predictions to DEM results. Generally, there was a good agreement between SHAKE and DEM results except when the exciting frequency was close to the resonance frequency of the deposit where significant discrepancy in computed shear strains between SHAKE predictions and DEM results was observed.     

条形荷载作用下梯度饱和土的动力响应分析

根据Biot波动理论,研究了条形均布荷载作用下非均匀饱和土地基的动力响应问题。利用Fourier积分变换,通过Helmholtz矢量分解原理,建立了饱和土层在动荷载作用下的回传射线矩阵法计算列式,考虑饱和土的物理力学性质沿深度方向按幂函数连续变化,采用数值Fourier逆变换获得了饱和土地基的位移、应力和孔隙压力等物理量的数值解。分析讨论了材料非均匀性对饱和土介质动力特性的影响。结果表明,非均匀饱和土的动力行为与均匀饱和土有着明显的不同,当土体的非均匀程度越高,条形荷载中点下流体压力和应力幅值越大,而位移、流体压力以及应力等物理量在水平方向的振动频率均随着土体非均匀变化程度的增强而增大。     

Shear wave propagation in granular assemblies

Shear wave velocity is a fundamental property of a granular assembly. It is a measure of the true elastic stiffness of a bulk specimen of discrete grains. Shear wave velocity is typically measured in the laboratory (e.g., using bender elements) or in-situ (e.g., using a seismic cone penetrometer, sCPT). In the current work, shear wave propagation is modeled numerically using the discrete element method (DEM). First, an appropriate method for measuring wave velocity is identified. Then the effects of particle size and elastic properties are investigated. Specimen fabric is then quantified before and after wave excitation and the elasticity of the response at the scale of the particle contacts is investigated. The results show that shear wave velocity may be robustly measured for discrete numerical specimens. The ability to measure shear wave velocity using DEM simulations may provide another tool for researchers seeking to link results from physical and numerical experiments.     

深层搅拌桩周围土体劈裂的研究与分析

现场测试结果表明：深层搅拌桩施工可以在周围土体中产生很高的超静孔隙水压力,其量值可能超过土体的静水劈裂压力。搅拌桩施工时和周围土体的相互作用可以用受剪的孔穴扩张过程来模拟。针对搅拌桩施工引起的周围土体的劈裂现象,提出了一种基于拉伸破坏原理的劈裂分析方法。分析结果表明：搅拌叶片的旋转对桩周围土体的劈裂起着很重要的作用。通过室内模型桩打设试验可以观测到搅拌桩周围土体的劈裂现象。分析现场搅拌桩施工时桩周土体中的孔隙水压力测试结果,表明现场施工可以引起劈裂。劈裂裂缝对于搅拌桩的性状有如下两方面的正面作用：其一,水泥浆体可以流入劈裂裂缝;其二,超静孔隙水压可以通过劈裂裂缝快速消散。这两者的作用加快了受扰动的周围土体的强度恢复。     

非饱和土中波的传播特性

基于已建立的非饱和土中的波动方程,第1次从理论上推证出非饱和土中存在4种体波,即1种S波和3种P波（P1波、P2波和P3波）,并导出了4种体波的波速以及衰减的解析表达式,分析了4种体波的波速、衰减与频率以及饱和度之间的关系。结果表明：3种P波中P3波波速最小,衰减最大;P1波波速最大,衰减最小;P2波则介于二者之间。4种体波都具有弥散性,一般而言,波速随频率的提高而有所减小,而衰减则有所增大。随含气量的提高,P1波的波速减小,P2波和S波的波速增大,而P3波则受含气量的影响很小;P1波和P3波的衰减都有所减小,但变化不是很显著,P2波的衰减基本不随含气量的变化而变化,S波几乎不存在衰减现象。     

有限二维饱和多孔介质因载荷诱发Biot固结的解析解

推导了有限矩形区域饱和多孔介质因表面载荷诱发的Biot固结的一个解析解。假设多孔介质为均匀各向同性和线弹性,并被单相流体所饱和;控制方程组采用不可压缩多孔介质模型;孔隙压力场采用狄利克雷边界条件,上下表面位移场符合物理边界,而左右侧面位移场边界条件则由人为特别给定。利用有限正余弦变换和拉普拉斯变换及数值反演获得了物理空间孔隙压力场和位移场的半解析解,其体现为双重级数和的封闭形式。最后以某软黏土层平面应变固结为例,利用有限元分析软件ABAQUS对所给出的解析解进行了验证,同时基于该解析解考察了孔隙压力场和位移场的时空演化规律。所给出的解析解可用于深入分析有限二维饱和多孔介质的流-固耦合力学行为。     

Coupled simulation of wave propagation and water flow in soil induced by high‐speed trains

The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water‐saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd.     

Parallel visualization of seismic wave propagation

Today parallel visualization of massive datasets from observation and numerical simulation of seismic waves is one of the major goals of geoscience community. A majority of these datasets are time-varying volume data (TVVD), also known as 4D field data. The difficulty of visualizing them on distributed parallel system mainly lies in the algorithm designing for distributed preprocessing of raw datasets, hierarchical point-to-point or collective communication implementation based on distributed data allocation, synchronous volume rendering techniques. In this work we present viable solutions for preprocessing of raw data sets, novel algorithms of parallel rendering and display matrix. Our main objective is focused on the parallel visualization of results coming from full 4D seismic wave propagation simulations.     

Instability of wave propagation in saturated poroelastoplastic media

In the present work, stationary discontinuities and fluttery instabilities of wave propagation in saturated poro‐elastoplastic media are analysed in the frame of Biot theory. The generalized Biot formulations are particularly employed for simulating non‐linear coupled hydro‐mechanical behaviour of the media. Inertial coupling effect between the solid and the fluid phases of the media is also taken into account. The non‐associated Drucker–Prager criterion to describe non‐linear constitutive behaviour of pressure dependent elasto‐plasticity for the solid skeleton of the media is particularly considered. With omission of compressibility of solid grains and the pore fluid, the critical conditions of stationary discontinuities and flutter instabilities occurring in wave propagation are given in explicit forms. It is shown that when the stationary discontinuity is triggered at the surface of discontinuity there still may exist real wave speeds. The wave speeds across the stationary discontinuity surface entirely cease to be real only in non‐associated plasticity, certain ranges of value of Poisson's ratio and when compression stress normal to the surface of discontinuity dominates the stress state at the surface. It is also indicated that the fluttery instabilities, under which some wave speeds cease to be real even in strain hardening stage, may occur prior to stationary discontinuities only for non‐associated plasticity under certain conditions. These conditions are: (1) both the porosity and the Poisson's ratio possess relatively low values and (2) the deviatoric part of the effective stress normal to the surface of discontinuity is compressive. A region in the porosity–Poisson's ratio plot, in which fluttery instabilities are possible to occur, is given. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of a rigid footing lying on three-layered soil using the finite difference method

A numerical procedure is described for the analysis of the vertical deformation and the stress distribution of the strip footings on layered soil media. Three layers of soil with different stiffness are considered with the middle soil layer the thinnest and most stiff layer. The soil media is discretized and using the theory of elasticity, the governing differential equations are obtained in terms of vertical and horizontal displacements. These equations along with appropriate boundary and continuity conditions are solved by using the finite difference method. The vertical and horizontal displacements, strains and stresses are found at various nodes in the soil media. Parametric studies are carried out to study the effect of the placement depth of the middle soil layer, the relative ratios of the moduli of deformation of the soil layers on the vertical displacement of the footing and the vertical stress distribution. These studies reveal that the middle thin but very stiff layer acts like a plate and redistributes the stresses on the lower soft soil layer uniformly. The displacement on the top and bottom of the middle soil layer is almost the same showing that the compression of the middle layer is negligible as it is very stiff.     

水平旋喷桩施工引起周围土体变形分析

水平旋喷桩施工期间,大量高压流体注入土层,引起土层内部产生较大的膨胀作用,致使周围一定区域的土体发生变形。水平旋喷桩施工引起土体变形可以归结为压力膨胀和体积膨胀共同作用的问题。依托单根水平旋喷桩施工的现场实例,建立了水平旋喷桩施工引起土体变形的数值模型。将水平旋喷桩施工引起的土体变形问题简化为圆孔的膨胀问题,可以统筹考虑注浆压力和注浆流量的影响。首先需要确定注浆压力的影响半径和注浆流量引起的体积膨胀比,然后可以通过数值模型计算膨胀引起的土体变形。数值分析结果与现场实测值的对比表明,当注浆压力影响半径为成桩半径的6倍时,数值计算结果与现场实测值吻合较好。     

A three‐phase soil model for simulating stress wave propagation due to blast loading

A three‐phase soil model is proposed to simulate stress wave propagation in soil mass to blast loading. The soil is modelled as a three‐phase mass that includes the solid particles, water and air. It is considered as a structure that the solid particles form a skeleton and their voids are filled with water and air. The equation of state (EOS) of the soil is derived. The elastic–plastic theory is adopted to model the constitutive relation of the soil skeleton. The damage of the soil skeleton is also modelled. The Drucker–Prager strength model including the strain rate effect is used to describe the strength of the soil skeleton. The model is implemented into a hydrocode Autodyn. The recorded results obtained by explosion tests in soil are used to validate the proposed model. Copyright © 2004 John Wiley & Sons, Ltd.