Constitutive modelling of fine-grained gassy soil: A composite approach

Fine-grained marine sediments containing large undissolved gas bubbles are widely distributed around the world. Presence of the bubbles could degrade the undrained shear strength (s_u ) of the soil, when the gas pressure u_g is relatively high as compared with the effective stress in the saturated soil matrix. Meanwhile, the addition of bubbles may also increase s_u when the difference between u_g and pore water pressure u_w becomes smaller than the water entry value, causing partial water drainage from the saturated matrix into the bubbles (bubble flooding) during globally undrained shearing. A new constitutive model for describing the two competing effects on the stress-strain relationship of fine-grained gassy soil is proposed within the framework of critical state soil mechanics. The gassy soil is considered as a three-phase composite material with compressible cavities, which allows water entry from the saturated matrix. Bubble flooding is modelled by introducing an additional positive volumetric strain increment of the saturated clay matrix, which is dependent on the difference between pore gas and pore water pressure based on experimental observations. A modified hardening law based on that of the modified Cam clay model is employed, which in conjunction with the expression for bubble flooding, can describe both the detrimental and beneficial effects of gas bubbles on soil strength and plastic hardening in shear. Only two extra parameters in addition to those in the modified Cam clay model are used. It is shown that the key features of the stress-strain relationship of three fine-grained gassy soils can be reproduced satisfactorily.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

基于单相流的减饱和砂土流固耦合改进算法

减饱和法是一种通过减小饱和砂土地基中水的饱和度来处置可液化砂土地基的方法。基于单相流-固耦合理论,将减饱和砂中水-气两相流体等效为单相流体,提出一种可以考虑加载过程中孔隙流体体积模量变化的减饱和砂土静态液化的单相流改进算法,用其进行单调荷载作用下三轴不排水压缩试验数值模拟研究,分析了不同饱和度条件下的减饱和砂土的不排水反应并与饱和砂土三轴不排水试验结果进行对比。研究结果表明,单相流改进算法能够很好地反映减饱和法的抗液化特性。此外,对比不同数值分析方法模拟结果,得出以下结论：采用单相流简化算法分析减饱和砂土的不排水反应时,因为不考虑加载过程中的孔隙流体体积模量变化,所以初始的流体体积模量取值会影响减饱和砂土的强度,初始围压为100 kPa、饱和度为96%的减饱和砂土在单调荷载作用下,气体体积模量取值从100 kPa增加至200 kPa时,减饱和砂试样的峰值偏应力会减小约30%,孔隙压力会增加约40%;通过对比同等条件下的单相流改进算法和两相流算法的应力-应变关系曲线以及饱和度和体积应变变化曲线,两者结果相近,误差在5%以内。综上所述,单相流改进算法是一种较为合理而简洁地模拟减饱和砂土静态液化的计算方法。     

Numerical study of the deformation of saturated soil in the vicinity of a vibrating pile

The paper presents a dynamic finite-element analysis of the deformation of saturated cohesionless soil in the vicinity of the toe of a vibrating cylindrical pile. The soil behaviour is described by a hypoplastic constitutive model with intergranular strain assuming locally undrained conditions for the pore fluid. Emphasis is placed on the detailed analysis of stresses and displacements in the soil. It is shown that, starting from a homogeneous stress state, the first several cycles of vibration lead to the formation of a permanent liquefaction zone with vanishing effective stresses at a certain distance from the pile. The displacement field reveals an accumulation of residual displacements in the soil in the form of rotation. The influence of the initial stress state, the pore fluid compressibility, the pile displacement amplitude and the soil density on the formation of a liquefaction zone, on the stress amplitude in the soil and on the intensity of the permanent rotation is investigated.     

Simulation of liquefaction of unsaturated soil using critical state soil model

Several researchers have reported that the mean effective stress of unsaturated soils having a relatively high degree of saturation gradually decreases under fully undrained cyclic loading conditions, and such soils can be finally liquefied like saturated soils. This paper describes a series of simulations of fully undrained cyclic loading on unsaturated soils, conducted using an elastoplastic model for unsaturated soils. This model is a critical state soil model formulated using effective stress tensor for unsaturated soils, which incorporates the following concepts: (a) the volumetric movement of the state boundary surface containing the critical state line owing to the variation in the degree of saturation; (b) the soil water characteristic curve considering the effects of specific volume and hydraulic hysteresis; and (c) the subloading surface concept for considering the effect of density. Void air is assumed to be an ideal gas obeying Boyle's law. The proposed model is validated through comparisons with past results. The simulation results show that the proposed model properly describes the fully undrained cyclic behavior of unsaturated soils, such as liquefaction, compression, and an increase in the degree of saturation. Finally, the effects of the degree of saturation, void ratio, and confining pressure on the cyclic strength of unsaturated soils are described by the simulation results. The liquefaction resistance of unsaturated soils increases as the degree of saturation and the void ratio decrease, and as the confining pressure increases. Furthermore, the degree of saturation has a greater effect on the liquefaction resistance than the confining pressure and void ratio. Copyright © 2017 John Wiley & Sons, Ltd.     

Application of a high-cycle accumulation model to the analysis of soil liquefaction around a vibrating pile toe

High residual pore pressure observed in the vicinity of piles driven in saturated soil indicates that the soil around the pile may be liquefied. In the present paper, the problem of deformation of saturated sand around a vibrating pile is formulated with the use of a high-cycle accumulation model capable of describing a large number of cycles. The problem is solved numerically for locally undrained conditions in spherically symmetric formulation suitable for the lower part of a cylindrical closed-ended pile near the toe. The aim of the study is to calculate the evolution of the liquefaction zone around the pile for a large number of cycles. A parametric study is carried out to show how the growth of the liquefaction zone depends on the pile displacement amplitude, the relative soil density, the effective stress in the far field and the pore fluid compressibility.     

Hydromechanical Behaviour of Fontainebleau Sandstone

Summary. The hydromechanical behaviour of Fontainebleau sandstone is studied on the basis of isotropic and triaxial compression tests in drained and undrained conditions on water saturated samples. The effect of the evolution of the compressibility of the rock with the applied stress on the poromechanical parameters is shown. On the basis of micro-mechanical considerations, a new expression for the Skempton coefficient B is proposed as a function of the porosity, the drained bulk compressibility and the grain and fluid compressibility. The relation between rock deformation and pore-pressure evolution in undrained deviatoric tests is analysed. An elasto-plastic constitutive model with stress-dependent elasticity and damage is proposed to describe the behaviour of the rock and validated through back analysis of drained and undrained tests.     

饱和土体静态液化失稳理论预测

通过在屈服准则和剪胀性方程中引入材料状态参数,建立了一个与材料状态相关的本构模型,用于模拟不同初始孔隙比和围压下土体的应力-应变关系。基于二阶功理论,建立了饱和土体静态液化失稳理论判别准则。通过预测一系列饱和松砂三轴不排水试验结果,验证了所建立的本构模型及判别预测准则的合理性。分析结果表明,静态液化发生于土体硬化阶段,静态液化触发伴随着剪应力达到峰值,其后剪应力降低且孔隙水压力持续增长。进一步地,模拟了充分降解的城市固体废弃物在不排水条件下的应力-应变特性,并预测到了潜在失稳线及静态液化触发点。     

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.     

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

不饱和土动弹塑性本构模型研究

以饱和度与有效应力为状态变量,通过引入描述不饱和与饱和土孔隙比差的状态变量,将Zhang等提出的饱和土体应力诱导各向异性动弹塑性本构模型推广到不饱和土体中,使其可描述不饱和土在动力循环荷载作用下的力学特性行为。通过对已有不饱和土体在完全不排水条件下的动三轴试验进行理论模拟,验证了所提出不饱和土本构模型的正确性。最后基于所提出本构模型,讨论了在不排水条件下初始饱和度对不饱和土动力特性研究。结果表明,不饱和土在动力荷载作用下,土体的孔隙比将减少,导致饱和度增加;当初始饱和度较高时,不饱和土会转化为饱和土,从而发生液化现象。该研究成果对研究不饱和土在地震等动力荷载作用下的力学特性行为具有重要意义。     

Static Liquefaction Analysis Considering Principal Stress Directions and Anisotropy

Static liquefaction failure of a sloping ground occurs when the shear stress applied by a monotonic triggering load exceeds the undrained yield (peak) shear strength of the saturated liquefiable cohesionless soil. Current practices for determining the in-situ undrained yield strength for ground subject to static shear stress either rely on a suite of costly laboratory tests on undisturbed field samples or empirical correlations based on in-situ penetration tests which do not account for the effects of anisotropic consolidation, intermediate principal stress, and mode of shear on the degree of strain-softening and brittleness of cohesionless soils. This study investigates the effects of variations in the direction and relative magnitudes of principal stresses associated with different modes of shear and ground slopes on static liquefaction failure of cohesionless soils. Empirical relationships are developed between soil brittleness index and maximum excess pore water pressure ratio to characterize soil shearing behavior observed in a database of 271 undrained laboratory shear tests collected from the past literature. The application of these relationships for estimating the static liquefaction triggering strength of cohesionless soils under sloping grounds is described for plane-strain boundary conditions and the results are compared with those back-calculated for several cases of static liquefaction flow failures. The proposed procedure incorporates variations in mode of shear and initial stress anisotropy in an empirical formulation based on in-situ penetration tests.     

Analysis of liquefaction susceptibility of nearly saturated sands

A new constitutive formulation for simulating the behaviour of nearly saturated sands under seismic loads is presented. The formulation is based on combining the Henry's law for dissolution of gas in water, the ideal or perfect gas law and the law of conservation of mass. The effects of transient air dissolution in water on the compressibility of partially saturated soils are also taken into account. The model was calibrated based on numerical simulations of isotropically consolidated cyclic triaxial tests conducted on partially saturated samples of Toyoura sand. A multi‐yield plasticity soil constitutive model implemented in the finite element code DYNAFLOW was used for these numerical simulations. It is shown that the formulation proposed here is able to reasonably predict the soil cyclic undrained behaviour at various degrees of saturation (95% and higher). Copyright © 2006 John Wiley & Sons, Ltd.     

Effects of medium and pore‐fluid compressibility on chemical‐dissolution front instability in fluid‐saturated porous media

Theoretical analysis and computational simulations have been carried out to investigate how medium and pore‐fluid compressibility affects the chemical‐dissolution front propagation, which is associated with a fully‐coupled nonlinear problem between porosity, pore‐fluid pressure, pore‐fluid density and reactive chemical‐species transport within a deformable and fluid‐saturated porous medium. When the fully‐coupled nonlinear system is in a subcritical state, some analytical solutions have been derived for a special case, in which the ratio of the equilibrium concentration to the solid molar density of the chemical species is approaching zero. To investigate the effect of either medium compressibility or pore‐fluid compressibility on the evolutions of chemical dissolution fronts in supercritical chemical dissolution systems, numerical algorithms and procedures have been also proposed. The related theoretical and numerical results have demonstrated that: (i) not only can pore‐fluid compressibility affect the propagating speeds of chemical dissolution fronts in both subcritical and supercritical systems, but also it can affect the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; (ii) medium compressibility may have a little influence on the propagating speeds of chemical dissolution fronts, but it can have significant effects on the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; and (iii) both medium and pore‐fluid compressibility may stabilize irregular chemical‐dissolution‐fronts in supercritical chemical dissolution systems. Copyright © 2011 John Wiley & Sons, Ltd.     

饱和粉土静态液化性能试验研究

通过固结不排水三轴压缩试验,分析了围压、固结比和干密度等因素对饱和粉土静态液化特性的影响。试验结果表明,在干密度较小时,饱和粉土的偏应力-应变曲线呈现明显的硬变软化型,随轴向应变增大超静孔隙水压力增加、有效应力减小而发生静态液化,当干密度达到1.58 g· cm-3时,饱和粉土的偏应力-应变曲线表现出硬变硬化现象,超静孔隙水压力为负值或接近0,饱和粉土不再发生静态液化,即饱和粉土存在静态液化的干密度临界值;其他条件不变,随着围压、固结比或干密度的增大,偏应力峰值和残余强度均增大,静态液化势降低;根据有效应力路径建立了流滑面以作为饱和粉土稳定区与非稳定区的分界面。     

Crack nucleation in saturated porous media

Crack nucleation has been the subject of important contributions in the last two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question addressed in the present paper which is devoted to nucleation in traction mode. From a physical point of view, nucleation is a sudden phenomenon, so that the material response is both adiabatic and undrained. In the spirit of the variational approach, the nucleated crack is viewed as the final state of a region of space in which the material undergoes a full damage process. In traction mode, the opening of a saturated crack in undrained condition induces a drop of fluid pressure. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapor pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.     

Performance-based assessment of earthquake-induced catastrophic landslide hazard in liquefiable soils

This paper outlines a methodology for evaluating the likelihood of catastrophic landslide occurrence on gentle slopes in liquefiable soils during earthquake. The approach is based on a modified Newmark sliding block model of assessing the earthquake-induced undrained landslide displacements for conditions of no shear stress reversals on the sliding surface. By employing the shear resistance-displacement relationship from undrained monotonic ring shear tests, the simulation model incorporates the sensitivity of computed displacements to variations in yield acceleration. The proposed approach involves an examination of undrained seismic slope performance under various horizontal seismic waveforms scaled to different specific values of the peak earthquake acceleration. An example problem illustrates how the proposed methodology may be used to demarcate, based on the magnitude of permanent seismic displacement, the levels of low, moderate and high risk of catastrophic landslide on a gentle slope in a saturated cohesionless soil susceptible to liquefaction during earthquake.     

Laboratory Investigation into the Effects of Silty Fines on Liquefaction Susceptibility of Chlef (Algeria) Sandy Soils

In a number of recent case studies, the liquefaction of silty sands has been reported. To investigate the undrained shear and deformation behaviour of Chlef sand–silt mixtures, a series of monotonic and stress-controlled cyclic triaxial tests were conducted on sand encountered at the site. The aim of this laboratory investigation is to study the influence of silt contents, expressed by means of the equivalent void ratio on undrained residual shear strength of loose, medium dense and dense sand–silt mixtures under monotonic loading and liquefaction potential under cyclic loading. After an earthquake event, the prediction of the post-liquefaction strength is becoming a challenging task in order to ensure the stability of different types of earth structures. Thus, the choice of the appropriate undrained residual shear strength of silty sandy soils that are prone to liquefaction to be used in engineering practice design should be established. To achieve this, a series of undrained triaxial tests were conducted on reconstituted saturated silty sand samples with different fines contents ranging from 0 to 40 %. In all tests, the confining pressure was held constant at 100 kPa. From the experimental results obtained, it is clear that the global void ratio cannot be used as a state parameter and may not characterize the actual behaviour of the soil as well. The equivalent void ratio expressing the fine particles participation in soil strength is then introduced. A linear relationship between the undrained shear residual shear strength and the equivalent void ratio has been obtained for the studied range of the fines contents. Cyclic test results confirm that the increase in the equivalent void ratio and the fines content accelerates the liquefaction phenomenon for the studied stress ratio and the liquefaction resistance decreases with the increase in either the equivalent void ratio or the loading amplitude level. These cyclic tests results confirm the obtained monotonic tests results.     

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.     

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.