The soil-water characteristic curve can be used to estimate various parameters used to describe unsaturated soil behaviour. A general equation for the soil-water characteristic curve is proposed. A nonlinear, least-squares computer program is used to determine the best-fit parameters for experimental data presented in the literature. The equation is based on the assumption that the shape of the soil-water characteristic curve is dependent upon the pore-size distribution of the soil (i.e., the desaturation is a function of the pore-size distribution). The equation has the form of an integrated frequency distribution curve. The equation provides a good fit for sand, silt, and clay soils over the entire suction range from 0 to 106 kPa. Key words : soil-water characteristic curve, pore-size distribution, nonlinear curve fitting, soil suction, water content.

Equations for the soil-water characteristic curve

The Paper presents a constitutive model for describing the stress-strain behaviour of partially saturated soils. The model is formulated within the framework of hardening plasticity using two iodependent sets of stress variables: the excess of total stress over air pressure and the suction. The mode1 is able to represent, in a consistent and unified manner, many of the fundamental features of the behaviour of partially saturated soils which had been treated separately by previously proposed models. On reaching saturation, the mode1 becomes a conventional critical state model. Because experimental evidence is still limited, the model has been kept as simple as possible in order to provide a basic framework from which extensions are possible. Tbe mode1 is intended for partially saturated soils which are slightly or moderately expansive. After formulating the model for isotropic and biaxial stress states, typical predictions are described and compared, in a qualitative way, with characteristic trends of the behaviour of partially saturated soils. Afterwards, the results of a number of suction-controlled laboratory tests on compacted kaolin and a sandy clay are used to evaluate the ability of the model to reproduce, quantitatively, observed behaviour. The agreement between observed and computed results is considered satisfactory and confirms the possibilities of reproducing the most important features of partially saturated soil behaviour using a simple general framework.

A constitutive model for partially saturated soils

The Paper presents a constitutive model for describing the stress-strain behaviour of partially saturated soils. The model is formulated within the framework of hardening plasticity using two independent sets of stress variables: the excess of total stress over air pressure and the suction. The model is able to represent, in a consistent and unified manner, many of the fundamental features of the behaviour of partially saturated soils which had been treated separately by previously proposed models. On reaching saturation, the model becomes a conventional critical state model. Because experimental evidence is still limited, the model has been kept as simple as possible in order to provide a basic framework from which extensions are possible. The model is intended for partially saturated soils which are slightly or moderately expansive. After formulating the model for isotropic and triaxial stress states, typical predictions are described and compared, in a qualitative way, with characteristic trends of the...

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A Constitutive Model for Partially Saturated Soils

Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

Soil Behaviour and Critical State Soil Mechanics

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Water content of soil matrix during lateral water flow through cracked soil

During the past decade, the theory for heave prediction has developed within the context of unsaturated soil behavior and has become a valuable tool for geotechnical practice. The laboratory procedures for testing expansive soils have also been essentially standardized. The heave prediction theory is briefly reviewed in this paper, and the importance of sampling disturbance is emphasized. Closed-form solutions are presented for several possible situations that can be applied to engineering practice. In all cases, the soil deposit is assumed to be homogeneous, and the swelling pressure is assumed to be constant with depth. The closed-form solutions are presented for the calculation of total heave when: (1) A portion or the entire "active depth" is wetted; (2) a portion of the expansive soil is excavated; and (3) the excavated portion is backfilled with a nonexpansive soil.

Closed-form heave solutions for expansive soils

This paper presents a synthesis of mechanisms related to structure development of surficial heavy clay soils. These clay soils develop specific structural features due to wet/dry cycles and desiccation cracking they undergo during soil 'ripening'. There is substantial field and laboratory evidence to indicate that clay soils generally develop stable structures with stable material properties when they ripen under repeated wet/dry cycles of climatic change. This development occurs as a result of the re-arrangement of the soil particles to minimise the potential or free energy. Available evidence indicates that under field climatic conditions, swelling/shrinkage of clay soils occur predominantly due to water loss from inter-particle and inter-aggregation pores. Vertisols or heavy clay surficial soils can develop special geomorphological features such as gilgai. Mechanisms of gilgai formation are also analysed, and their origin is related to the initial pattern of soil desiccation cracking. The process of shrinkage cracking and associated volume change in soils is explained on the basis of unsaturated soil mechanics theory. Crack patterns are divided into orthogonal and non-orthogonal patterns, and the conditions that lead to the development of these crack patterns are highlighted. Finally, a conceptual approach for modelling of the desiccation cracking process is presented.

Structure Development in Surficial Heavy Clay Soils: A Synthesis of Mechanisms

Soil desiccation cracking is important for a range of engineering applications, but the theoretical advancement of this process is less than satisfactory. In particular, it is not well understood how the crack spacing-to-depth ratio depends on soil material behaviour. In the past, two approaches, namely stress relief and energy balance, have been used to predict the crack spacing-to-depth ratio. The current paper utilises these two approaches to predict the approximate spacing-to-depth ratio of parallel cracks that form in long desiccating soil layers subjected to uniform tensile stress (or suction profile) while resting on a hard base. The theoretical developments have examined the formation of simultaneous and sequential crack patterns and have identified an important relationship between the stress relief and energy approaches. In agreement with experimental observations, it was shown that the spacing-to-depth ratio decreases with layer depth, and crack spacing generally increases with layer depth. The influence of the stiffness at the base interface indicated that decreasing the basal interface stiffness makes the crack spacing to increase in sequential crack formation. The experimental observations also show a decrease in cracking water content with the decrease in layer thickness, and this behaviour was explained on the basis of a critical depth concept.

Theoretical analysis of desiccation crack spacing of a thin, long soil layer

The soil stress state is innucnced by the number of phases Apart from the three independent phases, namely solid. water. and air, usually ascribed to soil, a rourth phase has been postulated as being of importance in understanding thc behaviour or an unsaturated soil. This additional phase is described as the air-water inlcrphase (i.e., contractile skin) and provides a normal stress due to the pore-water pressure (Fredlund and Rahardjo 1993a). While a sa'ura'ed soil possesses positive pore-water pressure, an unsaturated soil is charactcrized by negative pore-water pressure which exerts a tensile pull at all air-water interfaces in (he soil profile (Fig. I). The surface tension on the contractile skin pulls the particles together providing additional strength to an unsaturated soil compared to a saturated soil where, in contrast, the positive pore-water pressure reduces the strength. At the air~water interface of an unsaturated soil, the pore air pressure I/a is greater than the pore water pressure, If\\\\'. The difference in these two indcpendent pressures (Ua-lfl\\\") is referred 10 as the soil mat ric suction. There is increasing acceptancc ror applying mat ric suction as an independcnt stress state variable in describing (he behaviour of an unsaturated soil.

Delwyn G. Fredlund

Papers

Water content of soil matrix during lateral water flow through cracked soil

Closed-form heave solutions for expansive soils

Structure Development in Surficial Heavy Clay Soils: A Synthesis of Mechanisms

Theoretical analysis of desiccation crack spacing of a thin, long soil layer

Application of unsaturated soil mechanics for agricultural conditions