An equation of state for unsaturated soils

2002 ◽  
Vol 39 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Edward J Murray
Keyword(s):  
Equation Of State ◽  
Effective Stress ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Deformation Behaviour ◽  
Water Volume ◽  
State Variables ◽  
Stress Equation ◽  
Stress Regime ◽  
Soil System

The enthalpy within a soil system under equilibrium conditions is investigated theoretically. Terzaghi's effective stress equation for a saturated soil is first examined and the approach extended to determine the enthalpy associated with the air, water, and solid phases, and the interactions between the phases, in an unsaturated soil. An equation of state is developed which links the stress state variables (p – ua) and (ua – uw) to the specific volume (v) and specific water volume (vw) and thus to the volumes of the phases. The equation is shown to provide a logical interpretation of the average volumetric "coupling" stress p'c within unsaturated soils which highlights the significance of the dual stress regime and bimodal structure. The new equation is compared with previously reported experimental data on kaolin and a lateritic gravel. The agreement is good and it provides insight into unsaturated soil strength and deformation behaviour and clarifies various previously identified anomalies.Key words: partial saturation, unsaturated soils, thermodynamics, effective stress, equation of state, critical state.

scholarly journals Relative performance of two unsaturated soil models using different constitutive variables

2014 ◽  
Vol 51 (12) ◽  
pp. 1423-1437 ◽  
Author(s):  
Martí Lloret-Cabot ◽  
Simon J. Wheeler ◽  
Jubert A. Pineda ◽  
Daichao Sheng ◽  
Antonio Gens
Keyword(s):  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Water Retention ◽  
Experimental Tests ◽  
Experimental Results ◽  
Degree Of Saturation ◽  
State Variables ◽  
Retention Behaviour ◽  
Model Predictions ◽  
Water Retention Behaviour

Mechanical and water retention behaviour of unsaturated soils is investigated in the context of two well established coupled constitutive models, each of which is formulated in terms of a different set of stress state variables or constitutive variables. Incremental relationships describing the volume change and variation of the degree of saturation are derived for each model. These incremental relationships are used to simulate a set of experimental tests on compacted Speswhite kaolin previously reported in the literature. Six individual tests, involving isotropic compression and various forms of shearing, are analyzed in the context of the incremental forms developed, and the model predictions are then compared against experimental results. The results show that, although each constitutive model uses a different set of constitutive variables and a different scheme for coupling mechanical and water retention behaviour, the two sets of model predictions are similar and both sets provide a reasonable match to the experimental results, suggesting that both models are able to capture the relevant features of unsaturated soil behaviour, despite expressing the constitutive laws in different ways.

Constitutive relations for volume change in unsaturated soils

1976 ◽  
Vol 13 (3) ◽  
pp. 261-276 ◽  
Author(s):  
D. G. Fredlund ◽  
N. R. Morgenstern
Keyword(s):  
Volume Change ◽  
Unsaturated Soils ◽  
Soil Structure ◽  
Constitutive Relations ◽  
Water Volume ◽  
Engineering Practice ◽  
State Variables ◽  
Volume Changes ◽  
Stress Changes ◽  
Measured Volume

Volume change constitutive relations for unsaturated soils are proposed from a semi-empirical standpoint. One equation describes the deformation of the soil structure and a second equation defines the volume of water present in the element. Each equation can be viewed as a three-dimensional surface with two independent stress state variables forming the abscissas.Uniqueness is tested by measuring volume changes resulting from stress changes in two orthogonal directions and comparing predicted and measured volume changes resulting from a stress change in a third direction. Samples of undisturbed Regina Clay and compacted kaolin showed good agreement between the predicted and measured volume changes for monotonic deformation of the soil structure. The agreement was not as close for the water phase. The variation was attributed to difficulties in measuring water volume changes over a long period of time. The laboratory results indicate that the proposed constitutive equations are of the appropriate form for use in engineering practice.

scholarly journals The, K.M. A Study on the Relationship Between Matric Suction and the Void Ratio and Moisture Content of a Compacted Unsaturated Soil

2018 ◽  
Author(s):  
Minh The Kieu ◽  
András Mahler
Keyword(s):  
Moisture Content ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Void Ratio ◽  
Clayey Soil ◽  
Matric Suction ◽  
Moisture Ratio ◽  
Distinct Advantage ◽  
State Variables ◽  
Test Procedures

The volumetric behaviour of compacted unsaturated soils is particularly complex due to the co-existence of three different phases: solid, liquid and air. Matric suction has been perceived as a significant influence on the volumetric behaviour of unsaturated soils and has been used as one of the constitutive variables for most the constitutive models of unsaturated soils in the literature. However, suction-controlled works are complex in practice since they generally require special test procedures and advanced equipment, and usually are very time-consuming. Thus, some researchers have tried to seek alternative frameworks that use the traditional choice of state variables to simulate the behaviour of unsaturated soils. Recently, Kodikara [1] proposed the MPK framework to interpret the behaviour of compacted unsaturated soil in the void ratio (e) – net stress (p) – moisture ratio (ew ) space. The distinct advantage of the model is that it is based on traditional constant moisture content compaction testing which is more common and simple than constant suction loading. The MPK framework has been shown to be capable of presenting the volumetric behaviour of compacted unsaturated soils. However, this framework is expected to use not only for compacted soil but for the behaviour of unsaturated soil in general. The incorporation of soil suction within the MPK framework can be helpful for creating a correlation with previous models which used matric suction as a constitutive variable. This paper presents the development of LWSBS for one clayey soil in Hungary within the MPK framework and then suction is incorporated, which is related to void ratio and moisture ratio through SWCC.

The shear strength of unsaturated soils

1978 ◽  
Vol 15 (3) ◽  
pp. 313-321 ◽  
Author(s):  
D. G. Fredlund ◽  
N. R. Morgenstern ◽  
R. A. Widger
Keyword(s):  
Shear Strength ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Research Literature ◽  
Test Results ◽  
State Variables ◽  
Limited Data ◽  
Laboratory Test Results

The shear strength of an unsaturated soil is written in terms of two independent stress state variables. One form of the shear strength equation is[Formula: see text]The transition from a saturated soil to an unsaturated soil is readily visible. A second form of the shear strength equation is[Formula: see text]Here the independent roles of changes in total stress σ and changes in pore-water pressure uw are easily visualized.Published research literature provides limited data. However, the data substantiate that the shear strength can be described by a planar surface of the forms proposed. A procedure is also outlined to evaluate the pertinent shear strength parameters from laboratory test results.

scholarly journals A Unified Elastoplastic Model of Unsaturated Soils Considering Capillary Hysteresis

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Tiantian Ma ◽  
Changfu Wei ◽  
Pan Chen ◽  
Huihui Tian ◽  
De'an Sun
Keyword(s):  
Soil Water ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Mechanical Response ◽  
Internal State ◽  
Degree Of Saturation ◽  
State Variables ◽  
Soil Behavior ◽  
Capillary Hysteresis ◽  
Modified Cam Clay

Unlike its saturated counterparts, the mechanical behavior of an unsaturated soil depends not only upon its stress history but also upon its hydraulic history. In this paper, a soil-water characteristic relationship which is capable of describing the effect of capillary hysteresis is introduced to characterize the influence of hydraulic history on the skeletal deformation. The capillary hysteresis is viewed as a phenomenon associated with the internal structural rearrangements in unsaturated soils, which can be characterized by using a set of internal state variables. It is shown that both capillary hysteresis and plastic deformation can be consistently addressed in a unified theoretical framework. Within this context, a constitutive model of unsaturated soils is developed by generalizing the modified Cam-Clay model. A hardening function is introduced, in which both the matric suction and the degree of saturation are explicitly included as hardening variables, so that the effect of hydraulic history on the mechanical response can be properly addressed. The proposed model is capable of capturing the main features of the unsaturated soil behavior. The new model has a hierarchical structure, and, depending upon application, it can describe the stress-strain relation and the soil-water characteristics in a coupled or uncoupled manner.

A u-p Formulation for Fully Coupled Dynamic Analysis of Flow and Deformation in Unsaturated Soils

2016 ◽  
Vol 846 ◽  
pp. 378-384 ◽  
Author(s):  
Babak Shahbodagh ◽  
Nasser Khalili
Keyword(s):  
Effective Stress ◽  
Unsaturated Soils ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Deformation Behaviour ◽  
Time Integration ◽  
Mixture Theory ◽  
Coupled Dynamic Analysis ◽  
Effective Stress Parameter ◽  
Fully Coupled

A u-p formulation based on the mixture theory is presented for describing the dynamic flow and deformation behaviour of unsaturated soils. In the formulation proposed, the solid displacement, pore water pressure, and pore gas pressure are considered as primary variables. The spatial discretization of the governing equations is achieved using finite element method, whereas the time integration is conducted using the Newmark technique. The coupling between solid and fluid phases is enforced according to the effective stress principle taking suction dependency of the effective stress parameter into account. Numerical examples and comparisons with known analytical solutions are presented, demonstrating the performance of the proposed approach.

ON PRESSURE DISTRIBUTION AND EFFECTIVE STRESS IN UNSATURATED SOILS

1981 ◽  
Vol 61 (2) ◽  
pp. 431-443 ◽  
Author(s):  
P. H. GROENEVELT ◽  
B. D. KAY
Keyword(s):  
Pressure Distribution ◽  
Effective Stress ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Clay Soil ◽  
Thermodynamic Models ◽  
Liquid Pressure ◽  
Load Pressure ◽  
Integral Relations

A theory is presented for the distribution of load pressures over the different phases in an unsaturated soil. It provides differential and integral relations between the equilibrium liquid pressure, the equilibrium solid pressure and the load pressure. Mechanical and thermodynamic models are presented by which the effective stress in unsaturated soils is defined. The value of the effective stress is then calculated for a certain state of a clay soil.

Soil Strength Reduction Method Induced by Variation of Water Content

2012 ◽  
Vol 170-173 ◽  
pp. 847-852
Author(s):  
Peng Ming Jiang ◽  
Zhong Lei Yan ◽  
Peng Li
Keyword(s):  
Slope Stability ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Characteristic Curve ◽  
Strength Reduction ◽  
Actual State ◽  
Soil Slope ◽  
Simple Method ◽  
The Common ◽  
The Stability

As the complexity of unsaturated soil theory, and it must have a long test period when we study the unsaturated soils, so the conventional design analysis software does not provide such analysis, so we can imagine that such a slope stability analysis does not accurately reflect the actual state of the slope. Based on the known soil moisture content，this paper use the soil water characteristic curve and strength theory of unsaturated soil to calculate the strength reduction parameters of soil which can calculate the stability of the soil slope when using the common calculation method. It is noticeable that this method can be extended and applied if we establish regional databases for this simple method, and these databases can improve the accuracy of the calculation of slope stability.

Discussion of “Unified Effective Stress Equation for Soil” by Chao Zhang and Ning Lu

2021 ◽  
Vol 147 (2) ◽  
pp. 07020003
Author(s):  
Sakineh Fazli Ghiyasabadi ◽  
Ehsan Nikooee ◽  
Ghassem Habibagahi
Keyword(s):  
Effective Stress ◽  
Stress Equation
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