Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils

The paper presents an approach to predicting variation of a degree of saturation in unsaturated soils with void ratio and suction. The approach is based on the effective stress principle for unsaturated soils and several underlying assumptions. It focuses on the main drying and wetting processes and does not incorporate the effects of hydraulic hysteresis. It leads to the dependency of water retention curve (WRC) on void ratio, which does not require any material parameters apart from the parameters specifying WRC for the reference void ratio. Its validity is demonstrated by comparing predictions with the experimental data on four different soils taken over from the literature. Good correlation between the measured and predicted behaviour indirectly supports applicability of the effective stress principle for unsaturated soils. Copyright © 2009 John Wiley & Sons, Ltd.     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Analytical derivation of water retention for random monodisperse granular media

The mechanics of water retention in unsaturated granular media is of critical importance to a broad range of disciplines including soil science, geotechnical engineering, hydrology and agriculture. Fundamental to water retention is the relationship between degree of saturation and suction, referred to as the water retention curve (WRC). The majority of WRC models are empirically based and seldom incorporate physically meaningful parameters. This study presents an analytical model for the WRC that considers separate contributions from fully filled pores and partially filled pores containing liquid bridges. A recently established unique k-gamma pore volume distribution function for randomly assembled monodisperse granular materials is adopted to determine the contributions of fully filled pores. Calculation of the contribution of residual pore water retained in partially filled pores is undertaken by representing pores as individual cells shaped as platonic shapes of various sizes and determining the volume of all liquid bridges suspended between particles within the pore cells. Weighting factors for the various cell types are obtained from the pore volume distribution to determine the relative contribution of different pore cell geometries to the total residual pore water. The combined model accurately describes experimental data for monodisperse spherical glass beads for both wetting and drying, even though the underlying assumptions do not reflect exactly the complex, interconnected and highly irregular geometry of the pore space. A single parameter provides the lateral shift between the wetting and drying curves. The results of this study provide a geometric understanding of the mechanisms of water retention in granular media.     

Insights into the water retention behaviour of GMZ bentonite pellet mixture

Bentonite pellets are recognized as good buffer/backfill materials for sealing technological voids in high-level radioactive waste (HLW) repository. Compared to that of a traditional compacted bentonite block, one of the most important particularities of this material is the initially discrete pellets and the inevitable heterogeneous porosity formed, leading to a distinctive water retention behaviour. In this paper, water retention and mercury intrusion porosimetry (MIP) tests were conducted on pellet mixture (constant volume), single pellet (free swelling) and compacted block (constant volume) of GMZ bentonite, water retention properties and pore structure evolutions of the specimens were comparatively investigated. Results show that the water retention properties of the three specimens are almost similar to each other in the high suction range (>?10 MPa), while the water retention capacity of pellet mixture is lower than those of the compacted block and single pellet in the low suction range (<?10 MPa). Based on the capillary water retention theory (the Young–Laplace equation), a new concept ‘saturated void ratio’ that was positively related to water content and dependent on pore size distribution of the specimen was defined. Then, according to the product of saturated void ratio and water density in saturated void, differences of water retention properties for the three specimens at low suctions were explained. Meanwhile, MIP tests indicate that as suction decreases, the micro- and macrovoid ratios of pellet mixture and compacted block decrease as the mesovoid ratio increases, while all the void ratios of single pellets increase. This could be explained that upon wetting, water is successively adsorbed into the inter-layer, inter-particle and inter-pellet voids, leading to the subdivision of particles and swelling of aggregates and pellets. Under constant volume condition, aggregates and pellets tend to swell and fill into the inter-aggregates or inter-pellets voids. While under free swelling condition, the particles and aggregates in a single pellet tend to swell outward rather than squeezing into the inter-aggregate voids, leading to the expansion of the pores and even formation of cracks. Results including the effects of initial conditions (initial dry density and fabric) and constraint conditions (constant volume or free swelling) on the water retention capacity and pore structure evolution reached in this work are of great importance in designing of engineering barrier systems for the HLW repository.

     

A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd.     

A probabilistic approach for computing water retention of particulate systems from statistics of grain size and tessellated pore network

The paper offers an analytical determination of the hydraulic properties of an unsaturated soil with reference to its retention curve, which describes the relationship between the volumetric water content and capillarity through matric suction. The analysis combines a particulate approach focused on the physics at the pore scale, including microstructural aspects, with a probabilistic approach where the void space and grain size are considered as random variables. In the end, the soil water characteristic curve of an unsaturated granular medium along a drying path can be derived analytically based on the sole information of particle size distribution. The analysis hinges on the tessellation of a wet granular system into an assemblage of tetrahedral unit cells revealing a pore network upon which capillary physics are computed with respect to pore throat invasion by a non-wetting fluid with evolving pendular capillary bridges. The crux of the paper is to pass from particle size probability distribution to a matching void space distribution to eventually reveal key information such as void cell and solid volume statistics. Making reasonable statistically based assumptions to render calculations tractable, the water retention curve can be readily constructed. Model predictions compare quite favourably with experimental data available for actual soils, especially in the high saturation range. Having a sound scientific basis, the model can be made amenable to address a variety of soils with a wider range of particle sizes.     

Derivation of soil water retention curve incorporating electrochemical effects

Water retention of clayey soils with wide particle size distributions involves a combination of capillary and adsorbed layers effects that result into suction–saturation relations spanning over multiple decades of matric suction values. The present study provides a physics-based analysis to reproduce the water retention curve of such soils based solely on particle size distribution and porosity. The distribution of inter-particle pore sizes is inferred through a probabilistic treatment of the particle size distribution, which is then used, together with an assigned pore entry pressure, to estimate the inter-particle water volume at a given suction. The contribution to water content from adsorbed layers is also taken into account by considering the balance of electrochemical forces between water and clay material. The total water content is therefore found by summing up the contribution of inter-particle water, as well as adsorbed layers that form around clay particles and around the individual clay platelets. Comparisons with experimental results on nine different soil samples verify the capability of the model in accurately predicting the wide water retention curves without any prior calibration. Additional to capturing the essential features of the water retention curve with remarkable detail, the analytical model also provides insights into the relative contributions of capillary and adsorbed waters to the overall saturation at different suction regimes. Being based upon easily accessible information such as particle size distribution and void ratio, the model can therefore be considered as a substitute for costly and lengthy laboratory and in situ measurements of water retention curve.

     

A bounding surface model for unsaturated soils considering the microscopic pore structure and interparticle bonding effect due to water menisci

The interparticle bonding effect due to water menisci plays an important role in the hydromechanical coupling properties of unsaturated soils. This paper presents an unsaturated hydromechanical coupling model that considers the influence of matric suction, degree of saturation, and microscopic pore structure on the interparticle bonding effect. The enhanced effective stress and bonding variable are selected as constitutive variables. The bonding variable is correlated with the ratio between unsaturated void ratio and saturated void ratio. The deformation characteristics of unsaturated soils are described based on the bounding surface plasticity theory. A soil–water characteristic model that considers deformation and hydraulic hysteresis is integrated into the constitutive model to achieve hydromechanical coupling. The proposed model can effectively describe the hydromechanical coupling characteristics and the meniscus bonding force of unsaturated bimodal structure soils; the model parameters can be easily obtained through routine experiments. The experimental results of unsaturated isotropic compression, the wetting/drying cycle, and unsaturated triaxial shear tests are used to validate the capability of the proposed model.

     

Consequences on water retention properties of double-porosity features in a compacted silt

The paper deals with an experimental investigation aimed at studying microstructural features and their consequences on water retention properties of statically compacted unsaturated silt. The evolution of the microstructure of the aggregate fabric induced by compaction is investigated by studying the pore size distribution changes under different initial conditions (void ratio and water content). The material used is low plasticity silt from Jossigny near Paris, France. A series of mercury intrusion porosimetry tests (MIP) were performed at different void ratios and water contents to provide microstructural information. The arrangement of aggregation/particles and pore network was also investigated with environmental scanning electron microscopy (ESEM). The MIP data were used to determine the water retention curve on drying for the specific pore network configuration induced on compaction. The MIP data were used to formulate and calibrate a multimodal water retention model for a specific pore network configuration, which is obtained by linear superposition of subcurves of a modified van Genuchten type. The study is then complemented with controlled suction oedometer tests on compacted samples to obtain the water retention properties of the material at two different void ratios. Finally, we compare the water retention properties obtained by the simulated progression of the different pore network configurations induced on the hydraulic path with the water retention properties under suction-controlled conditions. Good agreement between the two methods for the drying path is reached.     

真三轴条件下Q3原状黄土的力学特性

为了模拟实际工程中黄土在不排水条件下的破坏,在控制含水率不变条件下,利用非饱和土真三轴仪对不同初始吸力非饱和原状黄土进行了等向固结试验和不同中主应力参数b值的剪切试验,研究了非饱和原状黄土的力学特性。研究结果表明：真三轴等向压缩屈服应力随着初始吸力的增大而增大,吸力随着净平均应力的增大而减小,净平均应力对吸力的影响程度随着初始吸力的增大而增大。不同 值条件下,广义剪应力和净平均应力破坏状态线近似呈平行直线关系,广义剪应力和有效净平均球应力试验点可归一为饱和土的排水剪切破坏状态线;剪切破坏时吸力随着b值的增大基本呈线性增大趋势;孔隙比和净平均应力对数临界状态线近似呈线性平行关系,其斜率比饱和土大,且大于等向压缩屈服前的斜率;非饱和土孔隙比和有效净平均球应力对数临界状态线与饱和土的临界状态线近似呈线性平行关系;不同净围压条件下,不同 值非饱和土与饱和土的破坏状态孔隙比的比值与气体饱和度的试验点分布于1.0～1.2的直线带内,但同一净有效球应力条件下可以归一为一条非线性曲线。     

沉积泥砂非线性大变形固结沉降计算模型

沉积形成的水底黏性泥砂自重固结过程表现出显著非线性大变形固结特征,应采用大变形固结理论进行泥砂沉积固结计算。基于软黏土一维非线性大应变固结理论,应用有效应力、渗透系数与孔隙比间扩展幂次函数固结本构关系,由达西定律、有效应力原理、连续介质方程等建立大变形固结控制方程,根据固结单元孔隙水渗流、单元变形与泥砂沉积层固结沉降耦合关系形成黏性泥砂大变形自重固结数值模型。泥砂自重作为固结荷载,数值模型假定沉积泥砂各向同性且固结沉降应变、孔隙水渗流仅发生于竖直方向,为一维单向沉积固结过程;采用泥砂沉降柱试验确定泥砂非线性扩展幂次函数关系参数。模型应用中,划分竖向固结单元,由沉积泥砂固结本构关系确定各固结单元有效应力及超孔隙水应力,通过超孔隙水应力时间维度上的消散过程及各固结参数间的耦合关系计算泥砂固结沉降。数值模型计算结果表明,沉积黏性泥砂自重固结初期表现为有效应力调整过程,初始有效应力与孔隙比根据固结本构关系匹配调整为扩展幂次函数关系;沉积泥砂应变与应力固结度存在20%左右误差,泥砂固结沉降发展快于超孔隙水应力消散过程,证明沉积泥砂固结沉降变形的发展与超孔隙水应力消散并非同步耦合。计算模型应用于室内沉降柱试验模拟淤积黏性泥砂自重固结沉降预测中,模型输出与试验结果符合良好。     

脱湿状态下南京下蜀土的土水-力学特性

用经改造的GDS非饱和土三轴仪测得下蜀土在不同净围压下的变形特性和持水特性,并以van Genuchten模型对试验数据的拟合结果为基础,分析了净围压对下蜀土吸力应力特征曲线的影响,全面系统地研究了脱湿状态下南京下蜀土的土水-力学特性。研究表明,下蜀土的变形特性受净围压与基质吸力影响,基质吸力越高,下蜀土的压缩性越低,可以用二元指数函数本构模型分析孔隙比与应力状态变量间的关系。净围压使下蜀土持水能力增强,净围压与进气值呈幂函数关系。土的压缩性越高,净围压对其持水特性的影响越显著;随着净围压的增大,下蜀土孔隙比趋同,净围压对持水特性的影响逐渐减弱。外部荷载对下蜀土吸力应力特征曲线的影响是分段的,在边界效应区范围内,净围压增大时,吸力应力特征曲线间的差异逐渐减小;在过渡区范围内,吸力应力随状态变量变化的快慢程度不受外部荷载影响。根据双电层理论分析了高吸力时吸力应力的物理意义与计算方法,提出以界限有效饱和度作为吸力应力函数的分界点。     

Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model

The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.     

Coupled hydro-mechanical model for partially saturated soils predicting small strain stiffness

In the paper, we present newly developed hydro-mechanical hypoplastic model for partially saturated soils predicting small strain stiffness. Hysteretic void ratio dependent water retention model has been incorporated into the existing hypoplastic model. This required thorough revision of the model structure to allow for the hydro-mechanical coupling dependencies. The model is formulated in terms of degree of saturation, rather than of suction. Subsequently, the small strain stiffness effects were incorporated using the intergranular strain concept modified for unsaturated conditions. New features included degree of saturation-dependent size of the elastic range and an updated evolution equation for the intergranular strain. The model has been evaluated using two comprehensive data sets on completely decomposed tuff from Hong-Kong and Zenos Kaolin from Iran. It has been shown that the modified intergranular strain formulation coupled with the hysteretic water retention model correctly reproduces the effects of both the stress and suction histories on small strain stiffness evolution. The model can correctly predict also different other aspects of partially saturated soil behaviour, starting from the very small strain range up to the asymptotic large-strain response.     

初始孔隙比对高吸力下非饱和土土水特性的影响

在我国西北干旱半干旱地区,处于高吸力范围内的非饱和土广泛存在于各种岩土工程中。非饱和土土水特性的研究是非饱和土渗流、强度与变形研究的基础。为研究高吸力下不同初始孔隙比非饱和土的土水特性,以一种粉土试样作为研究对象,采用饱和盐溶液蒸汽平衡法控制土试样的吸力,利用阿基米德原理量测不规则土试样的体积,通过修正的Van-Gen...     

Analysis of water seepage in a pavement system using the particulate approach

A particulate model has been developed to analyze the effects of transient and steady state seepage of water through a randomly-packed coarse-grained soil as an alternative to conventional seepage analysis based on continuum models. In this model, the soil skeleton and the pore water are volumetrically coupled in the transient and steady-state conditions. The concept of relative density has been used to define different compaction levels of the soil layers forming a pavement filter system and observe the seepage response to compaction. First, Monte–Carlo simulation is used to randomly pack discrete spherical particles from a specified particle size distribution (PSD) to achieve a desired relative density based on the theoretical minimum and maximum void ratios. Then, a water pressure gradient is applied across one two-layer unit to trigger water seepage. The interstitial pore water motion is idealized using Navier–Stokes (NS) equations with provision to incorporate the drag forces acting between the pore fluid and soil particles. The NS equations are discretized using finite differences and applied to discrete elements in a staggered, structured grid. The model predicted hydraulic conductivities are validated using widely used equations.     

不排水循环荷载作用过程中累积孔压对细砂弹性剪切模量Gmax的影响

在土工结构物地震有效应力分析中,往往采用Hardin经验公式计算动荷作用过程中由于孔压变化对砂土初始弹性剪切模量Gmax的影响,但由于以往试验手段的限制,这种方法的有效性至今没有得到验证。为此,采用多功能三轴仪和压电陶瓷弯曲元剪切波速测试系统,研究了不排水循环荷载过程中孔压对细砂Gmax的影响。试验结果表明,细砂Gmax可由 Hardin型经验公式计算,但材料参数应通过试验确定;不排水循环荷载作用过程中,细砂Gmax随孔压上升而降低,其值可由其实际平均有效应力和固结后的孔隙比通过由试验得到的Hardin型经验公式计算。     

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.     

Predicting Hysteresis of the Water Retention Curve from Basic Properties of Granular Soils

The water retention curve (WRC), which represents the relationship between volumetric water content (θ) and suction (ψ), is required to analyze the hydro-geotechnical response of unsaturated soils. The laboratory (or field) determination of the WRC can however be time consuming and difficult to conduct. A practical alternative, particularly useful at the preliminary stages of a project, is to estimate the WRC using a predictive model based on basic geotechnical properties that are easy to obtain. One common limitation of such predictive models is due to hysteresis effects, which are not taken into account by most of these models. The authors present in this paper an extended version of the Modified Kovács (MK) predictive model that incorporates hysteresis of the WRC along different paths, including the main wetting and drying curves and the wetting and drying scanning curves for granular soils. The model formulation is presented, and predictions are compared to experimental data obtained on different granular soils. The results show a good agreement for the main and scanning curves.     

Hydromechanical characteristics and microstructure of unsaturated loess under high suctionEI北大核心

联合压力板仪和蒸汽平衡法在全吸力范围内对原状与重塑黄土进行持水特性试验,使用非饱和三轴仪对高吸力下的原状与重塑黄土进行剪切试验,同时采用扫描电镜仪(scanning electron microscope,SEM)和压汞仪(mercury injection apparatus,MIP)进行微观试验,探讨了非饱和黄土结构性差异对其水力力学特性的影响。试验结果表明:随着吸力的增大,原状和重塑土的饱和度、含水率均减小,孔隙比稍有减小。由于原状及重塑黄土的初始孔隙比基本一致,因此两者压汞试验总进汞量接近。由扫描电镜和压汞试验得到的原状及重塑黄土的孔隙结构形态及优势孔径范围不一样,结构性有所差异,导致土-水特征曲线在不同吸力范围内呈现不一样的规律。原状和重塑土的应力-应变关系多呈软化现象,吸力为3.29 MPa的重塑土呈硬化现象。且随着吸力的增大,原状和重塑土的黏聚力和峰值强度均明显增加,体变由剪缩趋向剪胀现象。由于原状土具备一定结构性,胶结作用较强,其黏聚力的增幅会大于重塑土,峰值强度也高于重塑土,而两者的内摩擦角基本一致。