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.     

NaCl溶液对土体持水特性影响的试验研究

分别采用不同浓度的NaCl溶液对低塑性黏土进行饱和,然后进行压力板和蒸汽平衡法试验,获得整个吸力范围内的土-水特征曲线（SWCC）。分析不同浓度的孔隙溶液对SWCC的影响规律,结果表明：盐分对基质吸力的影响较小,对总吸力影响较大,这主要是因为盐溶液引起的渗透吸力所致。在蒸汽平衡法试验中,随着含水率的降低,孔隙浓度增大,渗透吸力增大。然而,基质吸力随着含水率的减小迅速增大,使得渗透吸力所占的比例逐渐减小。在非饱和土中,总吸力包括基质吸力和渗透吸力;基质吸力包括毛细部分和吸附部分,当土体中含水率较低时,主要是吸附效应在起作用;渗透吸力与溶液浓度有关。根据试验结果深入分析了吸附水膜和土颗粒之间的相互作用,得出由于溶质的存在对分子间吸附力的影响规律。根据表面化学原理,建立了分子间作用力和吸附水膜厚度之间的关系,以描述处于吸附状态的土-水特征曲线。     

不同类型黏土的强度特性及其预测

强度特性是非饱和土力学中基础性的研究内容。目前对广吸力范围内非饱和黏土强度的预测研究相对较少。本文首先基于文献中粉质黏土、Madrid黏土和南阳弱膨胀土的非饱和强度特性进行了对比与分析。将不同类型非饱和黏土的强度特性大致分为3种类型:（1）在某一吸力范围试样出现强度峰值,并随着吸力值的进一步增大而降低;（2）达到某一吸力值后其强度几乎维持不变,不受吸力值的影响;（3）其强度随着吸力值的增大而增大。此外,基于现有考虑吸附水膜和毛细水作用的方法拟合广吸力范围内不同类型土的土水特征曲线,并将土水特征曲线分离成吸附土水特征曲线和毛细土水特征曲线。在非饱和土的抗剪强度公式中,认为吸力引起的非饱和强度增强部分主要由毛细水作用决定的,故将非饱和抗剪强度公式中吸力引起非饱和增强项的有效应力系数（即饱和度或有效饱和度）用毛细水对应的饱和度替代。最后,利用修正后的非饱和抗剪强度公式对3种较广吸力范围内非饱和土的强度进行了预测。预测结果表明过渡区段内的强度预测效果较好,但高吸力段非饱和强度的预测还有待进一步研究。     

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.     

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。     

全吸力范围生物炭−黏土混合土的土−水特性

土−水特征曲线在研究非饱和土的水力与力学特性中发挥着重要的作用。生物炭具有多孔结构、高比表面积和强吸附的特性。将生物炭改性土应用于垃圾填埋场上覆盖层,因受自然环境因素的影响会使其水力特性发生改变。为了研究全吸力范围内生物炭掺量对生物炭−黏土混合土保水特性的影响,利用蒸汽平衡法（吸力范围 3～368 MPa）、滤纸法（吸力范围 0 ～40 MPa）和压力板法（吸力范围 0～1.5 MPa）控制土样的吸力,测定吸力平衡后土样的含水率和饱和度,得到全吸力范围内生物炭−黏土混合土的土−水特征曲线。试验结果表明：（1）3种吸力测试方法很好地表达了生物炭−黏土混合土全吸力范围内的土−水特征曲线。（2）生物炭能够影响黏土的保水性,但在一定的吸力范围内,生物炭−黏土混合土的保水性还与孔隙结构和孔隙中水的形态相关。（3）通过压力板法测得,试样的进气值随着生物炭掺量的增加而减小。当吸力值小于进气值时,曲线出现水平段,土样始终处于饱和状态,生物炭掺量越大,试样的保水性越好。（4）由生物炭−黏土混合土微观孔隙结构以及生物炭在黏土中的分布形态来解释生物炭改性黏土的保水能力随生物炭掺量的变化关系。     

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...     

击实黄土孔隙结构对土水特征的影响分析

土水特征曲线是非饱和土的基本土物理-力学关系,即将含水率这一物理参数转化为土粒间力的作用,土水特征曲线受土的结构控制。为了探讨击实黄土孔隙结构对土水特征曲线的影响,本文在3种不同的初始含水率（小于最优含水率8%、最优含水率17%和大于最优含水率19%）下制备不同结构的击实黄土试样,分别用压汞试验测其孔隙分布曲线,用滤纸法测其土水特征曲线,并用扫面电镜获得其微观结构图像。对以上测试结果的分析表明,3种击实土样的孔隙分布曲线在相应的大孔径范围内相差较大,在小孔径范围内趋于一致;土水特征曲线在低吸力区差异较大,小于最优含水率的击实黄土土水特征曲线最陡;在高吸力区,3种击实土样的土水特征曲线趋于一致,这与孔隙分布特征一致。对比孔隙密度分布曲线与土水特征区曲线发现,土的土水特征受孔隙分布的控制,孔隙密度越大,土水特征曲线的斜率越陡。SEM图像也显示出3种击实土样的结构特点,小于最优含水率的土样有较多架空孔隙,优势孔径最大;高于最优含水率的土样,大孔隙减少,小孔隙增多,优势孔径最小。而最优含水率的击实黄土的孔隙分布较均匀,优势孔径覆盖范围大。     

考虑吸力效应的非饱和黏土回弹模量预估模型

回弹模量是反映路基弹性支撑能力的重要指标,并受运营期间基质吸力变化的显著影响。通过3种压实黏土试样的土-水特征曲线试验和重复动三轴试验,研究了回弹模量与基质吸力的相关性,并基于非饱和土有效应力原理,提出了考虑吸力效应的回弹模量预估模型。结果表明：基质吸力与回弹模量之间具有较强的非线性相关性,可采用指数形式进行两者的拟合;含水率由最佳含水率-4%提升至最佳含水率+4%时,受基质吸力减小的影响,回弹模量降幅达到29.1%～39.0%;在 土-水特征曲线过渡区,采用以饱和度表征的有效应力参数,可较好地反映基质吸力对于回弹模量的贡献,预估效果优于采用残余含水率或进气值相关的有效应力参数;在相同饱和度的情况下,黏粒含量越多、塑性指数越高,基质吸力对有效应力的贡献比例越小。     

A water retention model accounting for void ratio changes in double porosity clays

This paper presents a constitutive model that predicts the water retention behaviour of compacted clays with evolving bimodal pore size distributions. In line with previous research, the model differentiates between the water present inside the saturated pores of the clay aggregates (the microstructure) and the water present inside the pores between clay aggregates (the macrostructure). A new formulation is then introduced to account for the effect of the macrostructural porosity changes on the retention behaviour of the soil, which results in a consistent evolution of the air-entry value of suction with volumetric deformations. Data from wetting tests on three different active clays (i.e. MX-80 bentonite, FEBEX bentonite, and Boom clay), subjected to distinct mechanical restraints, were used to formulate, calibrate, and validate the proposed model. Results from free swelling tests were also modelled by using both the proposed double porosity model and a published single porosity model, which confirmed the improvement in the predictions of degree of saturation by the present approach. The proposed retention model might be applied, for example, to the simulation of the hydromechanical behaviour of engineered bentonite barriers in underground nuclear waste repositories, where compacted active clays are subjected to changes of both suction and porosity structure under restrained volume conditions.

     

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。     

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.

     

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。     

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.     

基于微结构失稳假说及广义吸力理论的黄土体变模型

针对原状非饱和及饱和黄土的体积变形问题,提出了一个复合体计算模型。该模型将黄土看作由各自均匀分布于土中的原状部分和扰动部分组成的,这两部分土体的体积比率,可由黄土结构的微观几何模型、孔隙率密度曲线及考虑广义吸力的微结构失稳条件计算得出。假设原状部分仅发生弹性变形,扰动部分符合重塑土的变形规律。复合体的应变增量包括原状部分的弹性、重塑土的塑性及结构崩塌3部分;其中：结构崩塌变形特指微结构失稳时原状土体的孔隙率突然变为重塑土的孔隙率;重塑土的体积应变形采用广义吸力理论计算。采用不同的初始饱和度的黄土结构强度计算出非饱和土微观结构刚度与饱和度的函数,从而获得非饱和土黄土微观结构失稳的判别条件。分别计算了低含水天然非饱和及饱和黄土的压缩曲线,并与试验结果对比说明了模型的合理性。     

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。     

层状土毛细水上升过程中Lucas-Washburn模型评价及修正

受界面效应影响,毛细水在层状土中运移规律还难以用描述均质土中水分运移规律的Lucas-Washburn（LW）渗吸模型进行描述。基于此,本文设计了层状土室内模型试验,采用分布式的主动加热光纤法（简称AHFO）监测毛细水上升过程。根据AHFO测试结果,进一步对LW模型进行了修正,提出了适用于描述层状土中毛细水上升规律的ILW模型,并对ILW模型进行了试验验证。试验结果表明:（1）当毛细水湿润锋抵达“黏土（下部）-砂土（上部）”界面时,会产生“毛细屏障作用”,从而导致上部砂土中毛细水含水率急剧下降;（2）“毛细屏障作用”由砂土和黏土中的基质吸力不均衡造成,基质吸力大小由含水率决定;（3）当毛细水湿润锋抵达“砂土（下部）-黏土（上部）”界面时,在界面处出现“反毛细屏障作用”,从而导致上部黏土层中的含水率比相邻下部砂土层含水率更高;（4）虽然常见的LW模型可准确预测均质土中毛细水上升高度及速率,但受“毛细屏障作用”和“反毛细屏障作用”影响,LW模型在层状土中失效;（5）相比LW模型,ILW模型精度更高,能够更加准确地描述层状土中毛细水上升规律。     

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.     

Irreducible water distribution in sandstone rock: Two phase flow simulations in CT-based pore network

A simple cutoff approach based on the capillary bundle model has become an industrial standard method to quickly obtain the irreducible water saturation from NMR T₂ distribution. However this approach is not always valid. To overcome the shortcoming of the capillary bundle model that ignores pore-pore connectivity, we have conducted a two-phase flow simulation in a CT-based pore network. The CT -based pore network is a representation of a real rock pore structure that is described by a binary X-ray tomographic data set. Simulation on such network mimics a process of the porous plate measurement. The generated capillary curve is quite reasonable. The oil accession distributions at different water saturations plotted as a function of pore size provide an insight for the immiscible displacement process in the real rock pore structure. Water is trapped not only in dead ends but also in the well-connected pores due to a pore level by-pass mechanism. At the capillary end point pressure, a plot of the trapped water distribution as a function of pore size has the same lognormal distribution as the pore size distribution, which is much different from what the simple capillary bundle model suggests.     

基于孔径分布的全风化泥岩持水曲线推算

采用压力板法、滤纸法和饱和盐溶液蒸气平衡法,分别对取自广西岑溪滑坡现场的全风化泥岩原状样进行了持水特性试验,得到全吸力范围内的持水曲线;用压汞试验测试经受不同吸力原状样的孔径分布,并用此分布曲线推算持水曲线。试验结果表明：全风化泥岩原状样的进气值为110 kPa,用3种方法可测得全风化泥岩的全吸力范围内的持水曲线。全风化泥岩原状样的孔隙大小分布可认为单峰结构,其孔隙的孔径主要分布在10～1 000 nm,但也有孔径在50～300 ?m范围内的小部分孔隙存在,主要因为原状样中存在少量的原生裂隙。利用3个经受过不同吸力土样的孔径分布分别推算其持水曲线,3条曲线组合与实测值比较表明,用一次压汞试验结果（孔径大小分布曲线）预测全吸力范围内的持水曲线精度较低,而选取各自吸力范围段的预测曲线组合而成全吸力范围持水曲线,与试验数据更为接近。