Review of fundamental principles in modelling unsaturated soil behaviour

An unsaturated soil is a state of the soil. All soils can be partially saturated with water. Therefore, constitutive models for soils should ideally represent the soil behaviour over entire ranges of possible pore pressure and stress values and allow arbitrary stress and hydraulic paths within these ranges. The last two decades or so have seen significant advances in modelling unsaturated soil behaviour. This paper presents a review of constitutive models for unsaturated soils. In particular, it focuses on the fundamental principles that govern the volume change, shear strength, yield stress, water retention and hydro-mechanical coupling. Alternative forms of these principles are critically examined in terms of their predictive capacity for experimental data, the consistency between these principles and the continuity between saturated and unsaturated states.     

Measurement of Matric Suction Using Tensiometric and Axis Translation Techniques

Experimental equipment for the measurement of matric suction in unsaturated soils using hydraulic tensiometers and the axis translation technique share a common working principle; that is, the measurement of a pressure differential across a high air entry porous ceramic. In this paper, the current state of the art in these two suction measurement techniques is presented and discussed together with the underlying physics thereby giving the reader the necessary basis to use and interpret the results obtained from those two techniques.     

A constitutive model for unsaturated soils with consideration of inter-particle bonding

The paper presents a physically-based constitutive model for unsaturated soils that considers the bonding effect of water menisci at inter-particle contacts. A bonding factor has been used to represent the magnitude of the equivalent bonding stress, defined as the bonding force per unit cross-sectional area. The average skeleton stress is employed to represent the effect of average fluid pressures within soil pores. Based on an empirical relationship between the bonding factor ζ and the ratio e/e_s (where e and e_s are void ratios at unsaturated and saturated states, respectively, at the same average skeleton stress), we propose an elasto-plastic constitutive model for isotropic stress states, and then extend this model to triaxial stress states within the framework of critical state soil mechanics. Because only one yield surface is needed in the proposed model, a relatively small number of parameters are required. Comparisons between experimental data and model results show that, in most cases, the proposed model can reasonably capture the important features of unsaturated soil behavior.     

土壤水分特性曲线的分形模拟

应用Menger海绵结构模型,推导出包含有分形维数的土壤水分特征曲线的解析模型,该模型与Brook Corey (1964)及Campbell (1974)经验模型的结构相似。通过对不同地区所采集的10种土壤样本利用压力薄膜仪实测得到水分特性曲线资料反求得到相应的分形维数,分析了分形维数与土壤质地、结构之间的关系,结果表明分形维数随土壤粘粒含量的增大而增大,随砂粒含量的增大而减小。同时对土壤水分特性曲线模型的分形维数与基于质量的土壤颗粒分布分形维数进行了比较,结果表明,两者十分接近,而且具有良好的线性相关关系。根据上述关系,利用易测得的土壤粒径分形维数结合所推导的解析模型,对土壤水分特性曲线进行了预测,预测值与实测值具有良好的一致性。     

Modelling water retention and volume change behaviours of unsaturated soils in non-isothermal conditions

This study presents a simple approach to modelling the effect of temperature on the soil–water retention curves (SWRCs) of deformable soils and takes into consideration the following two aspects: (1) the effect of temperature on the liquid–gas interfacial tension and (2) temperature-induced deformation of the soil skeleton. The first aspect, the temperature effect, can be modelled using an equation proposed by Grant and Salehzadeh [18], but the second aspect is generally neglected in the literature. To quantify the thermo-hydro-mechanical (THM) deformation of unsaturated soils (i.e., the second aspect mentioned above), a simple volume change equation, referred to as the non-isothermal SFG volumetric equation, is proposed on the basis of the original SFG framework [37]. A three-dimensional THM yield surface in the space of net mean stress, suction and temperature is presented here. The proposed volume change equation is integrated into the non-isothermal SWRC by means of a simple hydro-mechanical coupling law [38]. The performance of the non-isothermal SFG volumetric equation and the non-isothermal SWRC equation is investigated through several numerical examples. A number of experimental results reported in the literature are employed to confirm the validity of the proposed non-isothermal SFG volume change equation and the non-isothermal SWRC equation.     

A simple model for preliminary evaluation of rainfall-induced slope instability

Slope failures in the tropical regions, particularly Malaysia are commonly triggered by frequent rainfall. The tropical rainfall can be characterized as short and intense throughout the year, and prolonged and less intense during monsoon seasons. Under such circumstances, various rainfall patterns should be included in the analysis of rainfall-induced slope failure in the tropical regions. This paper is aimed to demonstrate a simple model for preliminary evaluation of rainfall-induced slope failure. The critical rainfall patterns for four typical types of soil were first determined. Seepage finite element analyses were conducted using the extreme rainfall of ten-year return period for Johor Bahru, Malaysia. The results showed that the ratio of rainfall intensity to soil saturated permeability (i.e., I/k_sat) plays an important role in determining the critical rainfall pattern. Two critical combinations of antecedent rainfall and major rainfall, 1-day, 2-day, 3-day, 5-day, 7-day, 14-day, and 30-day antecedent rainfalls and the redistribution of the critical combination of antecedent rainfall and 1-day major rainfall were responsible for the formation of suction envelope in soil. The suction envelope, representing the worst suction distribution in soil, was used for the computation of factor of safety of soil slope through the modified infinite-slope–limit-equilibrium method. A model, PERISI, was developed based on the findings from numerical simulation. The suction envelope and factor of safety computed from the PERISI model showed good agreements with the results obtained from Seep/W and Slope/W computer programs and the results derived from the model of Rahardjo et al. developed in 1995.     

A multi-gene genetic programming model for estimating stress-dependent soil water retention curves

Soil water retention curve (SWRC) is an important parameter required for seepage modelling in unsaturated soil and is used for analysing rainfall-induced slope failures, design of waste contaminant liners and cover, etc. The influence of stress, which is one of constitutive variables that governs unsaturated soil behaviour on the SWRC, has been well recognised by researchers. Stress is essential for study as it drastically alters the soil fabric which includes macropores, minipores and micropores and thus affects the ability of soil to retain water. Various computational modelling techniques that formulate models based on existing databases such as UNSODA, ISRIC and HYPRES for the estimation of SWRC do not take into account the stress influence on soil behaviour. In the present work, three artificial intelligence (AI) methods of support vector regression, artificial neural network and multi-gene genetic programming (MGGP) have been applied to formulate the mathematical relationship between the water content and input variables such as stress and suction (i.e. stress-dependent soil water characteristic curves (SDSWRCs)). The results indicate that the MGGP model outperforms the other two models and is able to extrapolate the water content values satisfactorily along the stress value of 800 kPa. This MGGP model can then be deployed by experts for the estimation of SDSWRCs, thus eliminating the need for conducting costly and time-consuming experiments.     

Model suggested for an important part of the hydro-mechanical behaviour of a water unsaturated bentonite

The hydro-mechanical behaviour of a clay-based buffer material for nuclear waste disposal has been investigated in a laboratory program. In this program, the main focus was on the influence of confinement on water uptake and swelling pressure during suction decrease. The laboratory program and some of the results are presented by Dueck [Dueck, A., 2006. Laboratory results from hydro-mechanical tests on a water unsaturated bentonite. submitted for publication.].

The results from the laboratory tests were used to find a relationship between water content, void ratio, swelling pressure and suction. Two equations for swelling pressure represent the outline of the model.

In the first equation, the swelling pressure developed during water uptake is normalised by a pressure corresponding to the swelling pressure at saturation. This is done in order to be independent of void ratio. A relationship between the normalised swelling pressure and the degree of saturation is suggested.

The second equation describes a relationship between the swelling pressure, the water content and the actual suction (or relative humidity). The equation is based on a thermodynamic relationship and includes the retention curve (i.e. water content vs. suction under free swelling conditions).

The model can be used for a state where two of the four variables; water content, void ratio, swelling pressure and suction are known and can thus be useful to evaluate field measurements and model late stages of the wetting process. An example of an application is given. The equations are mainly based on results from tests with increasing degrees of saturation under constant void ratio but are also suggested for use with increasing void ratio.     

土壤水分特征曲线模型模拟性能评价

土壤水分特征曲线模型作为实验测定土壤水分特征数据的一种替代方法,因其具有计算方便快捷和便于嵌入数值模拟程序的优点,开始受到越来越广泛的关注。虽然文献中存在众多的土壤水分特征曲线模型,但是这些模型的适用范围及拟合性能尚不明确。为了获得更加准确适用的土壤水分特征曲线,在实际应用中通常需要花费大量时间和精力去测试各种模型。为了解决上述问题,在国内外研究成果的基础上收集整理了12种典型的土壤水分特征曲线模型,并利用包含不同质地、有机质含量及容重的8种土壤的实测土壤水分特征数据来评估比较这些模型的模拟性能。模型性能通过均方根误差（RMSE）、平均偏差（AD）、AIC准则（Akaike Information Criterion）和纳什效率系数（NSE）4个指标评估。研究结果表明：大部分的模型能够提供比较接近于实际的拟合结果,评价指标值也比较相近。其中,KCGS2006（包含3个参数）和K1999模型（包含2个参数）拟合效果最好,而Gregson1987（包含1个参数）的拟合效果最差。该研究可以深入了解各种土壤水分特征曲线模型的适用性与局限性,更好地为生态环境建设和农业可持续发展研究中土壤水力参数的选取提供依据和参考。     

紫色土水分特征曲线室内测定方法的对比

为探寻全吸力范围内土壤水分特征曲线的可靠测定方法,采用沙箱排水法、Hyprop仪蒸发法、压力膜仪排水法和露点水势仪蒸发法分吸力段测定盐亭紫色土耕地表层2~7 cm和亚表层7~12 cm土壤的水分特征曲线,对比测定结果的方法间差异,并分析其原因。结果表明:对于表层和亚表层土壤,低吸力段(h >-100 cm)水分特征曲线的沙箱法和Hyprop仪法的均方根误差E_RMS (θ)均较小,在0.026~0.082 cm3/cm3范围内,确定系数R2均大于0.962,说明这两种方法测定结果之间差异不大。高吸力段(h <-330 cm)的压力膜仪法与露点仪法测定结果之间的差异较大,E_RMS (θ)为0.062~0.097 cm3/cm3,R2较低,为0.775~0.952。因此,全吸力范围内水分特征曲线测定方法的选择与组合应考虑土壤孔径分布特征和研究目的。     

非饱和膨胀土的土-水特征曲线研究

在干旱和半干旱地区 ,土体中含水量的变化常会引发各种工程问题。研究表明 ,非饱和土的工程性质不仅取决于土的组成、结构和应力状态 ,还与土中的吸力密切相关。非饱和土的土 -水特征曲线表达了土体中含水量与吸力的关系 ,是非饱和土研究的重要内容之一。     

A modified permeameter for determination of unsaturated coefficient of permeability

The design details of a modified permeameter used for determining the unsaturated coefficient of permeability of tailings are presented in this Paper. This permeameter can accommodate a large tailings specimen, 200 × 200 × 400 mm high, and uses the Instantaneous Profile Method (IPM) to determine the variation of unsaturated coefficient of permeability with respect to soil suction using a single specimen. The soil-water characteristic curve data can also be simultaneously determined from the modified permeameter. The key design features in comparison to a conventional permeameter include the provision of adjustable sensors that move along with the tailings as it settles due to desaturation during the testing period. The advantages of using a modified permeameter in the determination of the coefficient of permeability of unsaturated tailings are also discussed in this paper. Tests were carried out by providing suction using hanging column technique in the suction range of 0–10 kPa. Such an apparatus can easily be modified to accommodate higher suction values.     

尾矿坝非饱和带滞水曲线模型的建立及应用

本研究的目的是建立一种简单实用的上游式尾矿坝非饱和带滞水曲线的数学模型。研究方法采用拟合法。在揭示了硬岩尾矿砂的沉积距离与含水率、孔隙比等之间关系的基础上,建立了一种arctanx的函数,用来表征含水率与基质吸力的关系。将本模型应用于降雨入渗条件下饱和-非饱和渗流场分析,结果表明,数学模型与实验数据,具有明显的一致性。研究表明:该数学模型函数简单,适用于上游式尾矿坝。     

A constitutive model for unsaturated soil interfaces

A constitutive model based on the disturbed state concept is presented to describe the behavior of interfaces in unsaturated soil. The model is an extension of an existing model developed for a sand–steel interface. As opposed to the original model, the modified model incorporates two independent stress variables, which are the net normal stress and matric suction. The saturated and dry state of the interface can be modeled as a special case using the constitutive model presented in this paper. The modified model is capable of capturing the main features of unsaturated interfaces observed during laboratory testing, including increasing shear strength and strain softening with increasing suction and net normal stress and increasing dilatancy with increasing suction. Laboratory tests were carried out on unsaturated interfaces in a modified direct shear test apparatus. The observed behavior of interfaces between unsaturated soil and steel plates (rough and smooth) is presented in comparison with model predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

Seasonal water uptake near trees: a numerical and experimental study

Issues related to the numerical simulation of moisture migration patterns in the unsaturated zone and in the vicinity of mature trees are explored in this paper. The research is based on the use of Richard's equation for unsaturated moisture flow incorporating a sink term. A numerical solution has been achieved via the finite-element method for spatial discretization along with a finite-difference time-marching scheme. An axisymmetric solution is developed to represent water uptake near an established tree. The approach adopted utilizes radial symmetry and assumes a linear distribution of water extraction rates with both depth and radius. The model has been validated by direct comparison with field measurements recorded (by others) for a mature lime tree located on a boulder clay subsoil. Non-linear hydraulic properties have been obtained from independent published data. A good correlation between field data and simulated results has been achieved. The simulation covers a full annual cycle starting from field capacity in winter, extending through a full spring–summer drying period and subsequent autumn recharge. It is believed that this is the first attempt to simulate the behaviour of an established tree over such a time-scale. This relatively straightforward approach is thought to be suitable for development and application to a range of geo-engineering problems (e.g. slope stability, shrinkage/heave prediction, etc).     

Research of soil–water characteristics and shear strength features of Nanyang expansive soil

Nanyang expansive soil is investigated in its unsaturated state in this paper. The wetting–drying cycle tests of soil–water characteristics of Nanyang expansive soil have been performed in the laboratory. The test results show that the soil–water characteristic curve of the pre-load specimen can well reflect the soil property function of expansive soil. The strength features of the different suction states of the unsaturated expansive soil are also investigated. The hyperbolic model of the suction strength is presented and the parameters of this model are easily determined by tri-axial tests of unsaturated soils. The hyperbolic model is conveniently applied to predict suction strength of an unsaturated soil.     

Correlation of unsaturated soil and dielectric property for monitoring of subsurface characteristics: development of unsaturated dielectric mixing models and its application

The behavior due to rainfall infiltrating the ground plays a role in landslides, groundwater recharge and various other ground responses. Most of these geotechnical behaviors have a correlation between soil pore space and soil volumetric water content in the unsaturated and saturated soil porous media. Therefore, the soil porosity associated with soil pores and the distribution of volumetric water content are significantly important hydrological characteristics. In the case of shallow slope failure such as landslide, the infiltration activity due to the connectivity of soil pore spaces in a porous media is induced. Slope failure may be attributed to the effect of a wetting front with the slope due to liquid infiltration, which changes the volumetric water content, soil matric suction and shear strength of the slope. This study was performed with an unsaturated injection test using a frequency domain reflectometry (FDR) dielectric device which measures the dielectric constant of unsaturated soil and the study then proposed the unsaturated dielectric mixing models to calculate soil porosity and effective porosity of unsaturated soils. From the experimental results the ratio of effective porosity to porosity of soils are measured in a range of 70–85%. These experimental results show a decrease of about 5–10% for unsaturated soil compared to the ratio of effective porosity to porosity of saturated soil. The infiltration passages of tracer material are restricted within the pore connectivity in the unsaturated soil which is caused by dead-pores in the soil. Using the FDR device and the unsaturated dielectric mixing models, we can consider the acquisition of physical properties to detect the infiltration activity, the response of the dielectric constant along with the injected tracer and hydrological parameters for the unsaturated soil porous media.