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

The concept of pore pressure parameters has been found convenient to visualize the pore pressure response of saturated soils for various applied stress changes. This paper derives pore pressure par...

Pore pressure parameters for unsaturated soils

An Introduction to Unsaturated Soil Mechanics

There are significant advantages in using indirect pedo-transfer functions, (PTFs) for the estimation of unsaturated soil properties. The pedo-transfer functions can be used for the estimation of the soil–water characteristic curve (SWCC) which in turn is used for the estimation of other unsaturated soil properties. The accuracy of the indirect pedo-transfer function method for the estimation of the SWCC depends on the PTF and the equation used to best-fit the particle-size distribution (PSD) data. The objectives of this study are to: (1) evaluate the performance of the Fredlund et al. (Can Geotech J 37:817–827, 2000) equation for best-fitting the particle-size distribution, (PSD) data, and, (2) compare the predictions made by two of the commonly used PTFs; namely, Arya and Paris (Soil Sci Soc Am J 45:1023–1030, 1981) and Fredlund et al. (Can Geotech J 39:1103–1117, 2002), for estimating the SWCC from the PSD. The authors used 258 measured PSDs and SWCC datasets from the Loess Plateau, China, for this study. The dataset consisted of 187 silt–loam soils, 41 loam soils, 11 silt–clay–loam soils, 10 sand–loam soils, 6 silt–clay soils, and 3 loam–sand soils. The SWCC and PSD datasets were measured using a Pressure Plate apparatus and the pipette method, respectively. The comparison between the estimated and measured particle-size distribution curves showed that the Fredlund et al. (Can Geotech J 37:817–827, 2000) equation closely prepresented the PSD for all soils in the Loess Plateau, with a lower root mean square error (RMSE) of 0.869%. The comparison between the estimated and measured water contents at the same suction showed that the Fredlund et al. (Can Geotech J 39:1103–1117, 2002) PTF performed somewhat better than the Arya and Paris (Soil Sci Soc Am J 45:1023–1030, 1981) function. The Fredlund et al. method had RMSE value of 0.039 cm3 cm−3 as opposed to 0.046 cm3 cm−3 for the Arya and Paris (Soil Sci Soc Am J 45:1023–1030, 1981) method. The Fredlund et al. (Can Geotech J 39:1103–1117, 2002) PTF produced the closest predictions for sand–loam, loam–sand, and loam soils, with a lower RMSE for gravimetric water content ranging from 0.006 to 0.036 cm3 cm−3. There were consistent over-estimations observed for silt–loam, silt–clay–loam, and slit–clay soils with RMSE values for gravimetric water content ranging from 0.037 to 0.043 cm3 cm−3. The measured and estimated air-entry values were closest when using the Fredlund et al. (Can Geotech J 39:1103–1117, 2002) PTF. The measured and estimated maximum slopes on the SWCC were closest when using the Arya and Paris (Soil Sci Soc Am J 45:1023–1030, 1981) PTF.

Comparison of Measured and PTF Predictions of SWCCs for Loess Soils in China

Volume change behavior of unsaturated soils

A common occurrence in cuts or fills of swelling soils is their reduction in strength with time. At the time of compaction, the clay generally has a high matrix suction. Correspondingly, it has a high strength and will stand at relatively steep side slopes. With time, the soil generally tends towards saturation and the matrix suction reduces towards zero. There is a reduction in total strength and if the gravitational forces are too large, the slope fails.During the past several years, numerous cut and fill slopes have been observed in the Regina area of Saskatchewan. Many of these slopes have remained stable for 4–6 years and then failed. There has been a 20 year history of observations on the Belle Plaine overpass west of Regina. Field and laboratory investigations have been conducted.With a knowledge of the geometry of the slope and failure plane, the simplified Bishop method of stability analysis was used to perform a 'back-analysis' to assess the shear strength parameters. The shear strength paramete...

Delwyn G. Fredlund

Papers

Pore pressure parameters for unsaturated soils

An Introduction to Unsaturated Soil Mechanics

Comparison of Measured and PTF Predictions of SWCCs for Loess Soils in China

Volume change behavior of unsaturated soils

Stability of swelling clay embankments