Exact solution for the 1D transient response of saturated single-layer poroviscoelastic media

The basic equations for fluid-saturated porous media proposed by Biot are modified by replacing the classical linear elastic model of the solid skeleton with the Kelvin–Voigt model. Thus, the new theory can take into account the viscoelastic effect of the solid skeleton. After the establishment of appropriate boundary and initial conditions, a time-domain series solution for the transient response of a fluid-saturated single-layer poroviscoelastic medium is obtained by using the finite Fourier transform and the corresponding analytical inverse transform. Several numerical examples are provided to illustrate the validity of the exact solution and to investigate the influence of the viscosity coefficient, permeability coefficient, and load frequency on the transient response of a fluid-saturated single-layer poroviscoelastic medium.     

二维饱和土体动态孔隙率及相关动力响应特性研究

饱和多孔介质的动力响应研究在众多工程领域具有重要意义。充分考虑孔隙率的变化规律与影响因素,有利于合理揭示饱和多孔介质的相关力学行为。为此,将动态孔隙率模型与用于表征饱和多孔介质动力特性的u-U-p型方程结合,构建相应的非线性力学模型,利用Comsol Multiphysis PDE求取相应的数值解,以此研究不同透水条件下,受谐波载荷激励的二维饱和土体的孔隙率、变形量及孔隙水压力的变化规律。结果表明：孔隙率的变化与土骨架的体应变及孔隙水压力直接相关,土体压缩过程中,孔隙率相应减小,土骨架与孔隙流体的相互作用增强,土体运动时所受阻力增大,其无量纲竖向位移小于孔隙率被视为常数时的情况,在此条件下,由于土体的变形量减小,其孔隙水压力也相对减小。故充分考虑动态孔隙率,有利于更加精确地研究等饱土体和多孔介质的相关力学行为。此外,土体上表面透水条件下,孔隙流体可以从土体表面自由排出,土骨架承受的载荷更大,与不透水条件相比,土体孔隙率、竖向位移、孔隙水压力等变化更为显著。     

非饱和土中端承桩水平振动特性研究

针对非饱和土中桩的水平稳态振动问题,采用三相多孔介质波动方程,考虑固、液、气三相材料间的惯性和黏性耦合效应以及基质吸力的影响,通过Helmholtz矢量分解及分离变量法解耦波动方程,并将基桩等效为能描述其剪切变形和转动惯性效应的铁摩辛柯（Timoshenko）梁模型,采用Novak三维连续介质模型对非饱和土中端承桩的稳态水平振动进行了理论推导,获得了桩顶水平频域响应解析解,讨论了饱和度对土层和桩顶阻抗的影响以及桩身位移、内力沿深度的分布规律。结果表明,随着土体饱和度的升高,土层复阻抗和桩顶动力阻抗增大,桩身位移和内力则相应地减小;饱和度,包括渗透系数在内的影响仅在土体接近准饱和时才得以发挥;频率较低时,短桩拥有较大的刚度因子。桩长越长,阻抗因子越大,而共振频率越低。当长径比超过10时,桩顶阻抗不再随长径比的增加而改变。     

The effective stress concept and the evaluation of changes in pore air pressure under jacketed isotropic compression tests for dry sand based on the 2‐phase porous theory

The effective stress concept for solid‐fluid 2‐phase media was revisited in this work. In particular, the effects of the compressibility of both the pore fluid and the soil particles were studied under 3 different conditions, i.e., undrained, drained, and unjacketed conditions based on a Biot‐type theory for 2‐phase porous media. It was confirmed that Terzaghi effective stress holds at the moment when soil grains are assumed to be incompressible and when the compressibility of the pore fluid is small enough compared to that of the soil skeleton. Then, isotropic compression tests for dry sand under undrained conditions were conducted within the triaxial apparatus in which the changes in the pore air pressure could be measured. The ratio of the increment in the cell pressure to the increment in the pore air pressure, m, corresponds to the inverse of the B value by Bishop and was obtained during the step loading of the cell pressure. In addition, the m values were evaluated by comparing them with theoretically obtained values based on the solid‐fluid 2‐phase mixture theory. The experimental m values were close to the theoretical values, as they were in the range of approximately 40 to 185, depending on the cell pressure. Finally, it was found that the soil material with a highly compressible pore fluid, such as air, must be analyzed with the multi‐phase porous mixture theory. However, Terzaghi effective stress is practically applicable when the compressibilities of both the soil particles and the pore fluid are small enough compared to that of the soil skeleton.     

Implementation of a hydromechanical elastoplastic constitutive model for fully coupled dynamic analysis of unsaturated soils and its validation using centrifuge test results

Prediction of unsaturated soil behavior during earthquake loading has received increasing attention in geotechnical engineering research and practice in recent years. Development of a fully coupled analysis procedure incorporating a coupled hydromechanical elastoplastic constitutive model for dynamic analysis of unsaturated soils has, however, been limited. This paper presents the implementation of a coupled hydromechanical elastoplastic constitutive model into a fully coupled dynamic analysis procedure and its validation using a centrifuge test. First, the fully coupled finite element equations governing the dynamic behavior of unsaturated soils with the solid skeleton displacement, pore water pressure, and pore air pressure as nodal unknowns are briefly presented. The closest point projection method is then utilized to implement the coupled hydromechanical elastoplastic constitutive model into the finite element equations. The constitutive model includes hysteresis in soil–water characteristic curves, cyclic elastoplasticity of the solid skeleton, and the coupling mechanisms between the SWCCs and the solid skeleton. Finally, the analysis procedure is validated using the results from a dynamic centrifuge test on an embankment constructed of compacted unsaturated silt subjected to base shaking. Reasonable comparisons between the predicted and measured accelerations, settlements, and deformed shapes are obtained.

     

Numerical simulation of fully saturated porous materials

Fully coupled, porous solid–fluid formulation, implementation and related modeling and simulation issues are presented in this work. To this end, coupled dynamic field equations with u?p?U formulation are used to simulate pore fluid and soil skeleton (elastic–plastic porous solid) responses. Present formulation allows, among other features, for water accelerations to be taken into account. This proves to be useful in modeling dynamic interaction of media of different stiffnesses (as in soil–foundation–structure interaction). Fluid compressibility is also explicitly taken into account, thus allowing excursions into modeling of limited cases of non‐saturated porous media. In addition to these features, present formulation and implementation models in a realistic way the physical damping, which dissipates energy. In particular, the velocity proportional damping is appropriately modeled and simulated by taking into account the interaction of pore fluid and solid skeleton. Similarly, the displacement proportional damping is physically modeled through elastic–plastic processes in soil skeleton. An advanced material model for sand is used in present work and is discussed at some length. Also explored in this paper are the verification and validation issues related to fully coupled modeling and simulations of porous media. Illustrative examples describing the dynamical behavior of porous media (saturated soils) are presented. The verified and validated methods and material models are used to predict the behavior of level and sloping grounds subjected to seismic shaking. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

爆炸荷载作用下深埋圆形隧洞的饱和黏弹性土-衬砌系统动力响应

假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明：对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。     

Vertical ground motion analysis for submerged pore-elastic media with random void ratios

Recently, very strong vertical ground motions have been recorded during several earthquakes. The vertical motions are the consequence of compressional stresses which are mainly transmitted by pore fluids. For linear elastic analysis of a submerged soil layer, the permeability has a very minor effect on shear-wave response for which pore fluids are not taken into account. But on compressional-wave response, the permeability dominates the damping effect and is thought as the principal influential factor from pore fluids. In this study, the effect of changing permeability on damping is explored. In practice it is harder to obtain the coefficient of permeability, κ, than to measure the void ratio, e. In order to evaluate the permeability and explore its influence on vertical shaking, the formula relating κ–e for the saturated soil is selected for a 1D submerged pore-elastic model subjected to vertical sine-wave loading. The random, linear, linear-plus-random, logarithmic, and log-plus-random depth functions of void ratio are taken into account in this study. The intrinsic error due to the use of the arithmetic mean of permeability for a certain area with a heterogeneous distribution of permeability has also been assessed. Numerical simulations show that the five depth distributions of void ratio all result in the extra viscous forces. The damping effect on vertical shaking is mainly controlled by the harmonic mean of permeability and spatial distribution of permeability rather than the arithmetic mean of permeability. The harmonic mean is more appropriate than the arithmetic mean to be the representative permeability, because the damping coefficient is inversely proportional to permeability.     

A viscoelastic model for the dynamic response of soils to periodical surface water disturbance

In many instances soils can be assumed to behave like viscoelastic materials during loading/unloading cycles, and this study is aimed at setting up a viscoelastic model to investigate the dynamic response of a porous soil layer of finite thickness under the effect of periodically linear water waves. The waves and homogeneous water are described by potential theory and the porous material is described by a viscoelastic model, which is modified from Biot's poroelastic theory (1956). The distributions of pore water pressures and effective stresses of various soils such as silt, sand, and gravel are demonstrated by employing the proposed viscoelastic model. The discrepancies of the dynamic response between the simulations of viscoelastic model and elastic model are found to be strongly dependent on the wave frequency. Copyright © 2006 John Wiley & Sons, Ltd.     

Stress history effects on 1‐D consolidation of soft soils: a rheological model

Stress history plays an important role in controlling the consolidation behavior of soft clays, but few models exist that can provide quantitative estimate of its influence. In this paper, the Gibson–Lo rheological model is used to simulate the coupled processes of drainage and creep of soft soils that takes stress history into account. A hybrid combination of analytical and numerical methods is adopted to solve the governing equations of consolidation with the nonlinear rheological model. The methodology is applied to a saturated soft soil subjected to surface loading. The soil profile is separated into normally consolidated and overconsolidated layers by a boundary that is allowed to move. Comparisons of the model predictions and its simulations are used to evaluate the effects of stress history, model parameters, and loading pattern on consolidation behavior. It is shown that stress history influences the location of the moving boundary, variations of the profiles of excess pore water pressure dissipation, stress and deformation‐based average degrees of consolidation. Parametric studies conducted show that when soil is stiffer, the excess pore water pressure dissipates much more quickly, and thus the soil consolidates much faster especially at the early stages. The results also show that soil viscosity influences the deformation‐based average degree of consolidation at the latter stages. The consolidation process of soil layer under linear loading is shown to lag behind those under instantaneous loading: the longer the loading period is, the smaller the average degrees of consolidation are no matter how they are defined. Copyright © 2012 John Wiley & Sons, Ltd.     

基于细观分析的黏土本构模型

根据黏性土在固结排水条件下的加、卸载变形特征,分析了孔隙水,固体骨架在不同变形阶段的力学响应行为,按照细观力学分析中的自洽方法,建立了在固结排水条件下的黏土损伤本构模型。模型中考虑了孔隙水和固体骨架在加、卸载阶段的不同特性,认为在损伤阶段整体剪切模量的降低是由固体骨架颗粒接触面滑移而引起,与骨架中滑动相的体积百分比和滑动相的剪切模量有关,并给出了求解整体变形模量的解析方法,最后将模型预测与不同初始固结压力,不同应力路径的排水试验结果作了比较,证明该模型是合理的。     

低围压循环荷载作用下饱和粗粒土的动力特性与骨干曲线模型研究

基床层是铁路路基的核心组成部分,一般为粗颗粒土,厚约2.5～3.0 m,长期直接承受行车荷载的反复作用,其在动载反复作用下的变形特性是评价路基工作性能的关键要素之一。为研究粗粒土在列车循环荷载作用下的应力-应变特性,开展了一系列应力控制的单向循环加载大型动三轴试验,模拟列车动载和路基粗粒料填筑实际情况,包括不同动应力幅值（模拟不同列车轴重）、不同围压（模拟不同埋深）的动三轴持续振动试验。结果表明,在循环荷载作用下,土体刚度变化与振动次数、围压关系密切。根据动应力幅值大小的不同,循环荷载作用下饱和粗粒土的动应变随振次的发展形态可分为3种类型：稳定型、破坏型和临界型。根据试验所得出的动应力-应变关系曲线特点,建立了含围压和循环振次的骨干曲线模型。与传统的骨干曲线模型相比,该模型能反映土体刚度随循环振次的变化,更能反映列车往复作用的实际情况;同时该模型能用于估算路基土体动强度,对铁路路基核心层的动力变形稳定性评价和基于动力变形控制的路基设计具有参考价值。     

初始偏应力作用对萧山软黏土动弹模量与阻尼影响试验研究

通过对萧山正常固结饱和软黏土进行应力控制的循环三轴试验,着重研究了初始偏应力对动弹模量（土动剪模量）及阻尼比的影响。试验结果表明,在相同的动应变水平下,随着初始偏应力的增加,土体动模量Ed、Edmax 以及Ed /Edmax与阻尼比D都有较大幅度的增加。在试验的基础上,通过指数函数建立了反映动模量Ed、Edmax 以及Ed/Edmax与动应变之间关系的经验公式。同时,采用指数函数建立了阻尼比D与Ed /Edmax关系表达式来间接模拟初始偏应力作用下阻尼比的变化规律。与以往的二次函数曲线相比,得到了更为精确的结果。     

深厚覆盖层上土石坝抗震分析的三维真非线性方法及应用

针对强震区深厚覆盖层上土石坝工程的特点,基于土石料三维粘弹塑性动力本构模型,考虑孔隙水压力消散和扩散,建立了深厚覆盖层上土石坝地震反应分析的三维真非线性有效应力动力分析方法及抗震安全评价方法。利用土石料动力特性的大型三轴试验成果,对一深厚覆盖层上的土石坝进行了地震反应分析,给出了坝体及覆盖层地基的加速度反应、应力反应,并结合单元抗震安全系数、防渗墙动应力、地震残余变形、坝坡动力稳定性等进行了抗震评价,为大坝的抗震设计提供了有力的技术依据。     

循环荷载下黏弹性饱和土层的一维固结

针对单层黏弹性地基Merchant模型,运用Laplace变换,求得频域内单层黏弹性地基的一维固结解。通过Laplace逆变换,计算了单层黏弹性地基在任意循环荷载下的有效应力及平均固结度。此外,结合工程实例,研究了Merchant模型各参数对循环荷载下黏弹性地基固结的影响。结果表明,在黏弹性地基的固结过程中,有效应力和沉降的发展速率是不一致的,黏壶的存在使地基固结初期的有效应力增长加快,而使固结后期的有效应力增长减慢,同时使变形的发展滞后于有效应力的发展。研究结果亦表明,循环荷载下土体的固结对独立弹簧模量的变化要比Kelvin体中弹簧模量的变化敏感。     

基于达维坚科夫骨架曲线的软土非线性动力本构模型研究

试验研究表明,上海地区软土的动力变形特性符合“应变软化”规律,可用达维坚科夫（Давидеков）模型描述。首先以达维坚科夫骨架曲线为基础,采用Masing法则,构造了土体加载、再卸载的动应力-应变关系滞回曲线,推导了达维坚科夫骨架曲线和卸载、再加载滞回曲线的增量剪切模量表达式。随后将土体动应力-应变关系曲线从一维推广到三维应变空间,基于FLAC3D提供的二次开发平台,编制了基于达维坚科夫骨架曲线和符合广义Masing法则的土体非线性动力本构模型计算程序,并且通过复杂加载路径验证了编制程序的正确性和合理性。以相关文献中的土体动剪切模量比 随剪应变幅值 变化,以及阻尼比 随剪应变幅值 变化的试验结果为依据,运用编制程序计算了不同剪应变幅值下的 - 和 - 曲线,并与文献试验结果进行了对比。研究结果表明,相比于工程上广泛应用的Hardin-Drnevich模型,基于达维坚科夫骨架曲线构造的本构模型所得到的软土 - 和 - 曲线能与试验结果更符合,进而验证了所建立的本构模型的合理性与实用性,其结果可用于上海地区软土场地的动力计算反应分析。     

循环交通荷载下软土路基长期沉降理论解

基于循环交通荷载下软黏土累积塑性变形、累积孔压经验公式与分层总和法结合的方法,通过计算不排水循环累积塑性变形引起的沉降和不排水循环累积孔压消散引起的固结沉降叠加,建立了一个软土路基长期沉降拟静力计算模型。对交通荷载应力路径下的软黏土空心圆柱扭剪试验数据分析,获得了不排水累积塑性应变模型和不排水累积孔压公式的参数。基于弹性理论解积分计算交通荷载下路基中的动应力,再结合分层总和法计算了路基沉降与循环周次的关系。通过工程实例分析,对比了计算沉降结果与实测结果并与以往理论分析结果,验证了所建立模型的合理性。     

粉土循环累积应变和残余动模量的试验研究

粉土地基上建造的铁路或公路在交通荷载作用下易产生各种病害,导致基础设施不能正常工作。为研究交通循环荷载作用下粉土的累积变形和动力性能,针对钱塘江粉土开展一系列的循环三轴试验,探讨土体物理条件（相对压实度、含水率）和应力特征（频率、围压、动应力比）等对粉土累积轴向应变、动模量和阻尼比等的影响。试验结果表明,钱塘江粉土的临界动应力比约为0.11,当轴向动应力小于临界动应力时,粉土的动模量变化很小,相应的累积轴向应变也很小;当动应力超过临界动应力后,土样的动模量快速下降,残余动模量约为初始弹性模量的20%,同时,动模量和阻尼比随着累积轴向应变（或名义振次）的发展变化显著。粉土的动模量和阻尼比在归一化后可得到统一规律：在轴向应变（或名义振次）小于一定值时,动模量几乎不变,而后呈指数形式衰减,最终趋于稳定值;粉土阻尼比随着轴向应变（或名义振次）的发展呈指数关系增长。