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.

     

土-水特征曲线滞后阻塞模型

基于Young-Laplace方程利用土-水特征曲线估算孔隙分布,借鉴非饱和渗流统计模型,建立了土-水特征曲线的滞后模型。在某一基质吸力下对应的毛细半径上限的毛细水对更大孔隙半径的毛细水具有阻塞作用,阻塞概率与孔隙分布函数直接相关。孔隙分布函数自身属性体现了土体孔隙空间分布的非均匀性。该模型显示：在高基质吸力与低基质吸力阶段,脱湿曲线与吸湿曲线趋近相等;中等基质吸力阶段,脱湿曲线饱和度高于吸湿曲线饱和度,两者的差值存在一个明显的峰值。并采用实例验证了该模型的可靠性,发现该模型对中、细粒土预测效果较好,而砂类土因孔隙分布不符合假设,导致存在较大误差。对于砂类土等特征尺寸较大的土质,引入阻塞概率修正系数,发现最佳修正系数与土-水特征曲线半对数坐标下的土-水特征曲线最大斜率呈反比例关系。     

A new and simple stress-dependent water retention model for unsaturated soil

The water retention curve (WRC) is an important hydraulic property of unsaturated soil needed for seepage analysis. Experimental evidence shows that the WRC is affected by various factors such as net stress and soil type. Many attempts have been made to describe the effects of net stress by including the void ratio in a water retention model. But the void ratio (i.e., soil density) is not the only parameter altered by the application of net stress. The pore structure, including the pore size distribution, pore shape and pore orientation, is also changed. Thus the influence of net stress on the WRC should not be treated as equivalent to density effects. In this study, it is verified that the inclusion of the void ratio cannot adequately capture the effects of net stress on the water retention behaviour. A new and simple water retention model is thus developed by considering the stress effects on the void ratio as well as the pore structure. The model is then applied to simulate the WRCs of three different soils tested over a wide range of stress conditions, including isotropic and anisotropic stress conditions. The results show that better predictions of experimental data can be made by incorporating the effects of net stress on both the void ratio and the pore structure.     

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.     

关于基质吸力及几个相关问题的一些思考

基质吸力是非饱和土力学中一个非常重要的概念,也是初学者学习中的一个难点,要把它理解透彻并不容易。本文从表面物理化学的基本公式,亦即Young-Laplace公式和Kelvin公式出发,对基质吸力概念和与基质吸力有关的若干问题进行了一些思考和初步探讨。研究表明,基质吸力的大小受土的孔径大小的影响;在环境条件下,基质吸力的大小受外界平衡相对深度的影响;土的孔径分布决定了土水特征曲线的特征。     

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.     

The role of pore water in the mechanical behavior of unsaturated soils

Deformation and failure of soils are governed by the stresses acting on the soil skeleton. The isotropic stress acting on the soil skeleton can be divided into two components. One is the stress component which is transmitted through the soil skeleton. This skeleton stress is influenced by the pore water (bulk water) in the soil. The other is the internal stress component which does not contribute to equilibrium with a given external force. The internal stress is induced by the capillary tension of meniscus water clinging to the contact point of soil particles and acts so as to connect the soil particles tightly. Therefore, in modeling the stress and strain relations for unsaturated soils, it is of much importance to quantitatively evaluate how the pore water exists in the soil. This paper discusses the role of pore water on the mechanical behaviour of the soil. In particular, the significance of the water retention curve is emphasized from a mechanical viewpoint. Essential features required in modeling of the constitutive relations for unsaturated soils are discussed and presented.     

基于分层核磁测试新技术的未冻水变化规律研究——以砂土冻融过程为例北大核心CSCD

土体冻融过程中的未冻水动态变化与冰-水相变过程密切相关,是冻融过程中非饱和土研究的重要基础。利用在线控温以及分层扫描的核磁共振新技术直观测试冻融过程中非饱和砂土的未冻水含量。结合T_(2)分布曲线(曲线上不同的T;值对应着孔隙水类别特性,曲线下方的面积对应试样水分含量)在冻融过程中的峰值大小和峰面积数据反演土体中含水量的大小与赋存的位置,而曲线的峰形态以及弛豫范围(各峰起始值以及终止值)等信息反演不同类型水分(吸附水与毛细水)以及土体结构的分布。在处理试验结果时,首先依据测试得到的冻结温度划分试样冻结区与未冻区。冻结区与未冻区未冻水含量及其孔隙变化差异明显,究其原因是冰水相变与水分迁移。在土样冻结区域冰水相变占主导地位,水分主要由未冻区向冻结锋面附近的e、f层迁移。首先以中大孔隙中毛细水迁移为主,其次以小孔隙中的吸附水迁移为辅。依据水相变成冰体积增大和孔隙体积占比数据分析可知,冻结区微小孔隙会在冻结过程中连通形成中大孔隙;而在未冻区水分迁移占主导地位。未冻区受固结作用中大孔隙压缩形成为小孔隙。试验过程中冻结锋面附近的e、f层孔隙变化最为剧烈。     

An approach to characterisation of multi-scale pore geometry and correlation with moisture storage and transport coefficients in cement-stabilised soils

An experimental approach to the characterisation of the complex, multi-scale pore geometry in cement-stabilised soils is presented, in which the pore size distribution inclusively spans at least six orders of magnitude from ~3 nm up to >3 mm. These most likely result from the combined effects of granular inter-particle packing, clay/cement clothing and bridging effects, cement hydration and clay/cement pozzolanic reactions, and alteration of larger pore geometries as a result of solid mass mobilisation and transport following capillary wetting/drying regimes. Experimental data are presented and were obtained through a combination of X-ray computed tomography, mercury intrusion porosimetry and N₂ physisorption supported by ‘wet mode’ environmental scanning electron microscopy. Data strongly suggest that macropore/capillary pore size distribution, mean pore size, sorptivity and transport coefficients are a function of particle size distribution (when compaction energy is constant). Mesopore size distribution, which dominates hygric sorption/desorption behaviour, occurs within the clay/cement matrix and also appears to be strongly influenced by the particle size distribution of the granular phase. All other factors being equal, manipulation of granular particle size distribution can be used to engineer the hygric (vapour) and capillary (liquid) potentials and also the fluid transport coefficients of these materials.     

Revisiting the thermodynamics of hardening plasticity for unsaturated soils

A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here.     

延安压实黄土土−水特征曲线的快速预测方法

传统测试土−水特征曲线（soil-water characteristic curve,简称SWCC）方法耗时较长,开发快速确定非饱和土的SWCC具有重要的实践意义。为了实现压实黄土SWCC快速预测,对不同干密度压实黄土进行了水势和水分测试,并且运用核磁共振（nuclear magnetic resonance,简称NMR）技术对其孔径分布曲线进行了测试。根据测试结果建立了基于孔隙比的延安压实黄土土−水特征曲线快速预测方法,并利用实测数据验证了方法的准确性。结果表明：预测模型中的分形维数D可用孔径分布曲线上两点（峰值点和半幅点）的累计孔隙体积与孔径在双对数坐标中连成直线的斜率确定;基于孔隙比和优势孔径在双对数坐标中的线性关系,D可用孔隙比进行表示。SWCC进气值受大孔隙直径控制;过渡段斜率受中孔隙体积控制;压实黄土存在一个临界孔径,而残余含水率主要受孔径小于临界孔径的孔隙体积控制,并且提出了求取残余体积含水率的经验方法。与传统方法相比,所提出的方法可以在确定SWCC时节省大量时间。     

双孔结构非饱和压实土微观结构演化模型

在最优含水率干侧压实的黏土一般具有明显的双孔结构,其集聚体间孔隙（又称宏观孔隙）和集聚体内孔隙（又称微观孔隙）对土体宏观水力和力学特性影响差异显著,同时,水-力耦合作用下两种孔隙的演化规律也存在明显不同。双孔结构非饱和土对应的孔径分布函数为双峰孔径分布形式,该分布函数可通过叠加宏观孔隙和微观孔隙的单峰孔径分布曲线得到,并通过平移量、缩放量和分散度3个演化参数对双孔结构土的孔隙演化规律进行描述。通过构建在力学及水力加、卸载过程中演化参数与孔隙比之间的关系,提出了适用于描述变吸力下非饱和压实土的微观结构演化模型。分别基于所开展的桂林红黏土压汞试验数据和文献中的米尼亚卢博瓦膨胀土试验数据,对所建立的微观结构演化模型进行参数标定,并通过模型预测结果与试验结果的对比,验证了所建立模型的适用性。     

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.     

考虑孔隙水微观赋存形态的非饱和粉土有效应力方程及其验证

有效应力参数的合理确定是非饱和土有效应力研究的重要内容。然而,现有的有效应力参数未能较好地考虑孔隙水的微观赋存形态对有效应力的影响。为此,分析了孔隙水的微观赋存形态,明确了孔隙水可分为收缩膜、吸附水和毛细水,建立了非饱和粉土的扩展三相孔隙介质模型,即孔隙气、毛细水和广义土骨架。基于该模型,采用分相平衡分析法,推导了非饱...     

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.     

非饱和土壤水力参数预测的分形模型

综述了利用分形几何理论,可在土壤水力性质,包括土壤水分特征曲线及水力传导系数与土壤结构分维之间建立起一定的函数关系式.这些函数关系式大多与Campbell定律具有相同或相似的幂定律形式,一方面揭示了Campbell定律的物理实质,另一方面可用于土壤持水量及水力传导系数的预测.     

基于细观模拟的软土导热系数数值预测模型

热环境控制是城市地下空间安全运行的有力保障,科学预测地下围岩的导热性能是地下空间环控系统热负荷评估的基础。软土是地下空间开发中一类常见土体,现有模型主要适合于预测中低含水率范围内土体导热系数的变化,而对于高含水率软土,合适的导热系数预测模型较少。基于细观模拟,本文提出了一种能有效预测软土导热系数的数值模型。该模型除了能够反映含水率、干密度等常规因素影响外,还可考虑矿物组成以及粒径分布等的影响。最后,通过与苏通GIL管廊工程中20个软土样的实测导热系数进行对比以验证数值模型的可靠性。首先借助激光粒度分析仪和X射线衍射分析测试了矿物组成和粒度分布,代入模型进行数字建模并通过细观导热模拟得到导热系数预测值。导热系数模拟预测值与实测值对比结果显示:模拟预测值基本在实测值±20%范围内,验证了本文模型的可靠性,表明了该模型在预测高含水率软土导热系数方面的潜力。此外,该模型还可以直观地展示土内各处局部热流的分布特征,这为深入认识土体导热行为的机理奠定了基础。本文研究可为软土以及土体导热系数的预测评价提供新的思路和方法。     

毛细水作用下非饱和土压缩过程的微观非连续变形数值分析

研究非饱和土微结构的动态演化规律对认识非饱和土宏观物理力学行为的本质有重要意义。然而目前岩土学界对此尚不清楚。文章提出利用毛细水算法进行非饱和土压缩数值试验,研究其宏观变形过程中土水作用与孔隙的演变规律。首先参考黄土骨架颗粒的形态和优势颗粒的大小,建立了540 μm×400 μm理想的非饱和土微观结构模型;其次利用毛细...     

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...     

非饱和土粒间毛细作用的微观不连续变形分析

非饱和土粒间毛细水作用是其基质吸力的主要来源。本文基于二维非连续变形分析算法(DDA),建立了一种能够模拟不同饱和度下毛细水分布状态及计算土水特征曲线的扩展DDA算法。该算法首先通过反复迭代的方式来计算出不同饱和度下毛细水弯液面的半径,并利用圆心轨迹交汇法确定粒间毛细水弯液面与颗粒的搭接位置,从而确定各个颗粒表面被毛细水浸湿的区域。而后利用Young-Laplace方程计算出各个浸湿区域毛细负压的大小,并将其与表面张力添加到传统DDA算法控制方程中。为验证该算法,参照真实黄土中含量最多的粗颗粒建立一理想黄土微观土骨架模型,模拟了不同饱和度下土体中的毛细水分布状态,并获得了土水特征曲线。将模拟结果与实测的土水特征曲线进行对比分析,结果显示预测值和实测值基本一致,该方法能够从微观上揭示非饱和土粒间吸力作用的本质。