Effective Stress In Unsaturated Soils Research Articles

Physical meaning and mechanical effects of the neutral stress and effective stress in unsaturated soils

Physical meaning and mechanical effects of the neutral stress and effective stress in unsaturated soils

Contribution of capillary pressure to effective stress for unsaturated soils: Role of wet area fraction and water retention curve

Estimating the contribution of capillary pressure to the effective stress is critical for studying the mechanical and hydraulic behavior of unsaturated soils. Based on experimental evidence, we clarify that the degree of saturation (Sr) rather than matric suction (s) is more suitable as a variable for modeling Bishop's effective stress parameter (χ). The wet area fraction, defined as the ratio of the wet external area of soil particles to the total surface area, is then introduced as an alternative to the parameter χ. Because the contact area between soil particles and pore water is affected by both hydraulic (matric suction) and mechanical (volumetric deformation) states, the soil water retention curve (SWRC) is embedded in the proposed model to simulate the influences of pore size distribution and hydraulic hysteresis on shear strength. The proposed model requires only the material parameters of soils in the reference state and then can be used to predict the strength characteristics in other mechanical or hydraulic states. The shear strength data under different test conditions and the corresponding SWRC data are adopted to validate the new model. The results reveal that the wet area fraction could well predict the contribution of capillary pressure to the shear strength of unsaturated soils.

Effective stress in unsaturated soils: Lessons from capillarity in regular sphere arrangements

In this paper, capillary stresses and water retention of regular arrangements of rough spherical particles are analysed to shed light on the effective stress in unsaturated soils. These arrangements can be used to model soils with uniformly graded round particles such as sand as they are simpler to analyse due to their symmetries. Capillary stress determines the effective stress in unsaturated sphere arrangements and is highly dependent on the morphology of the soil voids.In general, it is shown that capillary stress and water retention dependence on suction and degree of saturation in regular arrangements of spheres is more complex than usually assumed with relevant implications for unsaturated soil mechanics and its effective stress. It is also shown that: (i) sphere roughness explains the observed disappearance of capillary stresses in sand with drying; (ii) the capillary stress evolution with suction (or RH) is non monotonic; (iii) it is possible to have significant capillary stresses at zero suction in regular and irregular sphere arrangements, and the Bishop’s effective stress cannot represent this or even the capillary stresses in regular arrangements; (iv) the water in the pores can assume diverse and complex configurations besides the simpler isolated menisci that prevail at larger suctions, and the alternative configurations for the same suction or degree of saturation support hysteretic response.

Support pressure assessment of tunnels in the vicinity of leaking pipeline using unified upper bound limit analysis

Pipeline leakage is a common phenomenon encountered in subway construction, which can happen before tunneling or may be induced by tunnel advancement. The strength deterioration of the surrounding soils and the downward seepage force caused by the infiltrated water will reduce the factors of safety of the tunnel. In the present work, a unified three-dimensional upper bound finite element method is established for support pressure assessment of tunnels around leaking pipelines. With the incorporation of suction stress-based effective stress of unsaturated soils, saturated and unsaturated soils could be simulated consistently. Two- and three-dimensional parameter analysis is conducted to study the evolution of limit support pressures and collapse mechanisms with the process of leakage. The effect of leaking location, ground water level, hydraulic properties, water pressure and axial length of leakage on the stability of surrounding tunnels is discussed in detail. It is shown that, the limit support pressure of the tunnel can increase rapidly after the occurrence of pipeline leakage, and a close correlation is found between the limit support pressure and the pore water pressure at the head of the tunnel.

Generalized Terzaghi’s Effective Stress Equation for Unsaturated Soil: An Independent Phase Balance Approach That Considers a Pore Water Content Gradient

The effective stress equation for unsaturated soil is the most important equation in unsaturated soil mechanics. It has been derived by many scholars using different methods. However, none of them considered the gradient of the pore water content, which results in unreasonable force balance equations for different constituent phases in unsaturated soil. To introduce the gradient, we propose an extended three-phase physical model that includes capillary water, air, and generalized soil skeletons. Based on this model, three balance equations for these three constituent phases are separately formulated by considering the gradient of the pore water content. Comparing the result of the superposition of these three balance equations with the total balance equation, we derive a generalized Terzaghi’s effective stress equation. This equation states that the effective stress is equal to the total stress minus the neutral stress. In comparison with the classical Bishop’s equation, the generalized Terzaghi’s equation ensures a smooth and continuous transition from unsaturated to saturated conditions not only in mathematical expression but also in physical meaning. Furthermore, the different pressure effects of capillary water and adsorbed water, their volumetric (or areal) effects, and the transformation between them can be considered by adopting the effective saturation of the capillary water as the effective stress parameter. Therefore, the generalized Terzaghi’s equation can provide a better choice for estimating the effective stress in unsaturated soils.

Compressional wave velocity and effective stress in unsaturated soil: Potential application for monitoring moisture conditions in vadose zone sediments

AbstractCompressional seismic (P‐wave) velocities were measured experimentally at different matric suctions and confining pressure states using a variety of sediments collected from the USDOE Hanford Site in southeastern Washington State. The P‐wave velocity was measured in variably saturated sediments using ultrasonic piezoelectric transducers, and matric suction was measured with a heat dissipation sensor. Desaturation of the samples occurred by means of evaporative drying. We propose a model to relate changes in P‐wave velocity to soil stress conditions using an effective stress formulation that includes capillary stress as well as adsorptive stress. We show that compressional wave velocities can be related to matric suction and confining stress using a model with five fitted parameters. A single set of parameters describing the relationship between effective stress and P‐wave velocity provide an excellent fit to data acquired on Hanford Formation samples. The results presented here suggest the utility of seismic methods for establishing low matric suction and flow conditions within variably saturated Hanford formation sediments, which could be applied at the field scale for evaluating the performance of environmental remediation efforts, such as soil desiccation and surface infiltration barriers.

Determining Bishop's parameter χ based on pore size distribution

Extension of the effective stress concept to unsaturated soils has been a major concern for decades. Recent studies significantly contributed to the understanding of the fundamentals behind Bishop's parameter χ, which is generally used to define the effective stress for unsaturated soils. An examination of the recently proposed methods showed that the contribution of suction to effective stress was often overestimated, especially in high suction range. In this study, considering that soil pores with different sizes contribute differently to the overall hydro-mechanical behaviour, a new method to determine Bishop's parameter χ is proposed. The key variable used in this method is the ratio of the change in water volume to the change in macropore void volume due to loading at constant suction. Shear strength data for a weakly expansive clay were used for validation. A good agreement was obtained between prediction and measurement, indicating the validity of the proposed method.

Shakedown Analysis of Unsaturated Soils Considering the Variation of Hydraulic States

Long-term stability evaluation of unsaturated earth structures has always been one of the most important issues in geotechnical engineering. Most available methods are appropriate for calculating the maximum loads that the structures can resist when the hydraulic state is fixed, and the external loads are monotonically increased. In practical engineering, however, the hydraulic condition is ever changing, and so are the matric suction and the shearing strength of unsaturated soils. In this situation, the obtained minimized collapse loads can no longer be used as reference for the design criterion, which may greatly overestimate the stability of the structures. Classical shakedown analysis is a more appropriate method, which can only consider the variation of the loads but not the variation of hydraulic states. This paper presents a novel formulation for shakedown analysis of unsaturated soils considering both the variation of external loads and the variation of the shearing strength caused by drying–wetting cycles. By using the suction stress-based effective stress of unsaturated soils, the three-phased mixture is dealt with as a single-phased material. The suction-stress equivalent forces are established, and the variation of the hydraulic state is dealt with as the variation of equivalent forces. Numerical formulations are then developed by the combination of the finite-element method and the second-order cone programming. Some shakedown problems are solved, and the effect of hydraulic state variation on the shakedown limits of foundations, pavements, and slopes is studied in detail. It is shown that the neglection of moisture content variation would greatly overestimate the safety of earth structures, and the produced errors become more significant with the increase of the suction-stress increment and the decrease of the shearing strength. The shakedown limit reaches the smallest when both external loads and suction stress are varying. When the variation of equivalent forces is complicated, the loading domain can be approximated by a polyhedron using a uniform distribution of sampling points, and the shakedown factor of safety converges to the true value with the increase of the number of sampling points. Shakedown analysis is necessary in engineering designs when several wetting and drying cycles happen.

A theory of loosening earth pressure above a shallow tunnel in unsaturated ground

SummaryA theory is proposed to evaluate the loosening earth pressure (vertical earth pressure after excavation) acting on a shallow tunnel in unsaturated ground with an arbitrary groundwater level. The theory is developed based on the limit equilibrium theory, combining soil–water characteristic curves, Mohr–Coulomb failure criteria, and effective stress for unsaturated soils. The proposed theory is applied to predict the vertical distribution of loosening earth pressure in unsaturated ground, which shows a significant difference from that in saturated ground. In unsaturated ground, suction contributes to the increase in effective loosening earth pressure and shear resistance. The remarkable effects of groundwater depth, soil type, and scale of overburden height and trapdoor width on loosening earth pressure are also revealed. Based on the soil–water characteristic curve, the degree of saturation decreases, which causes wet density to decrease and the total and effective loosening earth pressures to have contrary tendencies. Moreover, effective loosening earth pressures vary with soil type as the degree of saturation varies. The total loosening earth pressures are, however, very similar regardless of soil type, because wet density and shear resistance have similar tendencies. The proposed theory provides a valid model for loosening earth pressure in unsaturated ground that will be useful for shallow tunnel excavations.

Closed-Form Models for Nonisothermal Effective Stress of Unsaturated Soils

AbstractEffective stress is a critical factor controlling the mechanical behavior of unsaturated soils. There has been an increasing interest toward fundamental and applied research on emerging app...

Critical state behaviour of an unsaturated clayey sand along constant water content direct shear and triaxial loading conditions

This article examines the critical state behaviour of an unsaturated clayey sand with respect to the principle of effective stress in unsaturated soils. This was experimentally achieved through a series of constant water content triaxial and direct shear tests in a range of matrix suction and net confining stress. The general trends observed are discussed and compared in relation to some available data in the literature. It is shown that the slope of critical state line in q−p′ space in unsaturated condition appeared to be close but not equal to saturated state. Accordingly, it is observed that an equation of state also exist in v−ln p′ space for unsaturated condition that is identical to the equation used for saturated state with the difference that their coefficients were dependent to the variation of degree of saturation and their corresponding values in complete saturation condition. The above-mentioned trends were identical throughout the results attained from both triaxial and direct shear tests.

Structural behaviour of unstabilized rammed earth constructions submitted to hygroscopic conditions

Rammed earth constructions exhibit strength and deformation properties that evolve as a function of the relative humidity of the air in contact with the walls. This effect must be considered in the structural design of the construction. This work studies, through finite element simulation, the impact of the hygroscopic transfers through the wall on the structural response of a classical two-storey rammed earth building. The coupling between the mechanical and the hygroscopic behaviour is considered by the concept of effective stress for unsaturated soils, in order to reproduce the effect of suction on the strength, the stiffness and the volumetric variations of the rammed earth. The simulations show classical deformation of the structure due to distributed load on the floors while the hygroscopic changes in the rammed earth (essentially drying) induce additional displacements of the walls that remain in a very acceptable range. Finally, an extreme case is envisaged in which the loads on the floors are increased excessively in order to study the plastic response of the wall.

Cyclic Direct Simple Shear Test to Measure Strain-Dependent Dynamic Properties of Unsaturated Sand

The dynamic properties of a clean sand under different degrees of saturation were investigated using a modified custom built Direct Simple Shear (DSS) apparatus at the University of New Hampshire. The specific characteristics of the DSS were presented, and the testing procedures were discussed. The device used the axis translation and tensiometric techniques to control the matric suction in the soil specimen. The investigation on F75 Ottawa Sand showed a decrease in shear modulus and an increase in damping by increasing the shear strain over the tested range of strains for various degrees of saturation: dry, saturated, and partially saturated. The modulus reduction in the applied range of medium shear strains regardless of the degree of saturation demonstrated the capability of the DSS in consistently capturing the changes of dynamic properties. Experimental results indicated that the matric suction can have a substantial effect on the stiffness of the soil. However, the extent of this effect may depend on the induced strain level of the effective stress in unsaturated soil. In addition, partially saturated specimens resulted in lower dynamic compression.

Simulation of liquefaction of unsaturated soil using critical state soil model

SummarySeveral researchers have reported that the mean effective stress of unsaturated soils having a relatively high degree of saturation gradually decreases under fully undrained cyclic loading conditions, and such soils can be finally liquefied like saturated soils. This paper describes a series of simulations of fully undrained cyclic loading on unsaturated soils, conducted using an elastoplastic model for unsaturated soils. This model is a critical state soil model formulated using effective stress tensor for unsaturated soils, which incorporates the following concepts: (a) the volumetric movement of the state boundary surface containing the critical state line owing to the variation in the degree of saturation; (b) the soil water characteristic curve considering the effects of specific volume and hydraulic hysteresis; and (c) the subloading surface concept for considering the effect of density. Void air is assumed to be an ideal gas obeying Boyle's law. The proposed model is validated through comparisons with past results. The simulation results show that the proposed model properly describes the fully undrained cyclic behavior of unsaturated soils, such as liquefaction, compression, and an increase in the degree of saturation. Finally, the effects of the degree of saturation, void ratio, and confining pressure on the cyclic strength of unsaturated soils are described by the simulation results. The liquefaction resistance of unsaturated soils increases as the degree of saturation and the void ratio decrease, and as the confining pressure increases. Furthermore, the degree of saturation has a greater effect on the liquefaction resistance than the confining pressure and void ratio. Copyright © 2017 John Wiley & Sons, Ltd.

A procedure for the direct determination of Bishop's χ parameter from changes in pore size distribution

Most of the recent works relating to the concept of effective stress in unsaturated soils focus on the proposal by Bishop, and, more particularly, on the search for suitable relationships between Bishop's χ parameter and the main controlling variables. These relationships are generally formulated by theoretical derivations and back-analyses of the dependency of mechanical parameters on hydraulic variables such as suction or saturation. In this note, a new procedure is proposed to evaluate directly, and without any a priori assumptions, values for Bishop's χ parameter. In the first part, a general derivation based on the definition of work conjugated variables allows the χ parameter to be defined as the ratio of the change of water volume over the change in pore volume during a process at constant suction. This definition is further exploited to evaluate Bishop's parameter from the changes suffered by material pore size distribution during loading. The method is applied to data obtained by mercury intrusion porosimetry tests on low-plasticity silt (Jossigny silt), low-plasticity sandy clay (lean clay) and highly plastic clay (Febex clay). Values obtained for these materials show that the χ parameter is close to the effective degree of saturation rather than the total degree of saturation.

Average Soil Skeleton Stress for Unsaturated Soils and Discussion on Effective Stress

AbstractThe principle of effective stress is the most fundamental and important principle in soil mechanics. It serves as the foundation of modern soil mechanics. This paper starts with a discussion of effective stress expressions for unsaturated soils. The relationship between the total stress and stress of each phase in unsaturated soils is developed based on three-phase equilibrium equations of a representative element volume (REV). The expression of average soil skeleton stress, defined as effective stress, for unsaturated soils is then derived. This expression is consistent with the effective stress equation in unsaturated soils derived based on deformation work in the energy conservation equation. The general philosophy for the definition of effective stress in unsaturated soils is pointed out, followed by the discussion of some fundamental problems of unsaturated soils, including effective stress, choice of stress state, capillary phenomenon, and so on. The limitations and application scope of the ...

On the theory of Brutsaert about elastic wave speeds in unsaturated soils

Recently a theoretical model for elastic wave speeds in partially-saturated soils proposed by Brutsaert (and Luthin) in 1964 has been used to investigate the relationship between the elastic wave speeds and the moisture content in soils. It has been suggested that there was a ‘typing error’ in the formula for the composite fluid bulk modulus of the partially-saturated medium which has been modified accordingly. However we argue that the problem appears to be more of an inconsistency in the definition of the composite bulk modulus than a typing error: we have not been able to reproduce some numerical figures reported by Brutsaert and Luthin with the formulae therein. Moreover we point out that an assumption in the original theory of a saturation-independent Poisson's ratio has bigger implications for the more recent works as result (a) of not being realised and (b) of not being supported by experimental evidence. We comment also on the use of effective stress in unsaturated soils and the difficulty in deducing the moisture content from measurements of elastic wave speeds, due probably to the predominance of water potential rather than water content on the wave speed of shallow soils.

Effective Stress Principle for Partially Saturated Rock Fractures

Soils and rocks are commonly characterized as a porous or fractured medium, with liquid and gaseous fluids occupying and moving in the void space. The presence of water in the void space remarkably influences the deformation behaviors, mechanical properties and stress states of soils and rocks. It has been well recognized that the induced volume change, deformation and shear strength decrease of soils and rocks do not depend on the total stress applied, but on the effective stress defined at the saturated state due to the difference between the total stress and the fluid pressure in the pore space. The deformation of soils and rocks further alters the pore or fracture network and induces a nonnegligible variation in hydraulic properties (Kirby 1991; Chen et al. 2007; Li et al. 2014a). Therefore, the concept of effective stress plays a dominant role in understanding the coupled hydromechanical behaviors of soils and fractured rocks. Von Terzaghi (1923) pioneered the principle of effective stress for saturated soils, in which the effective stress was defined as the difference between the total stress and the pore water pressure: r0 1⁄4 r uw ð1Þ where r denotes the total stress, uw the pore water pressure, and r0 the effective stress. The pores and voids of an unsaturated soil, however, are only partially occupied by water, with the rest being occupied by air, which leads to a different stress state in the soils. A modification of Terzaghi’s effective stress principle is therefore required for unsaturated soils. Bishop (1959) proposed the principle of effective stress for unsaturated soils by introducing an effective stress parameter into Eq. (1): r0 1⁄4 r ua ð Þ v uw ua ð Þ ð2Þ

Fractal Representation for Effective Stress of Unsaturated Soils

AbstractBishop’s effective stress equation for unsaturated soils was abandoned for some time because of the difficulties in estimating the value of parameter χ. Only recently has it been recognized that the use of Bishop’s stress equation can lead to simpler and more realistic constitutive models for unsaturated soils. Based on the analysis of the equilibrium of solid particles, it was possible to establish an analytical expression for Bishop’s parameter χ from soil pore structure. It is shown that quantitative predictions of shear strength and volume change in unsaturated soils can be made using the effective stress concept.

Modeling the dependency of Suction Stress Characteristic Curve on void ratio in unsaturated soils

Geotechnical problems associated with unsaturated soils are common in semi-arid climates, where the upper soil layers are naturally unsaturated. Once a soil becomes unsaturated, its mechanical properties become different from its saturated counterpart. The main part of effective stress in unsaturated soils resulting from the soil moisture can be defined by the Suction Stress Characteristic Curve (SSCC). Although, the suction stress characteristic curve is determined from shear strength tests, but recent works show that the SSCC can be connected to the Soil Water Characteristic Curve (SWCC). This paper presents a simple and novel approach to model the effect of void ratio changes on SSCC in unsaturated soils. The proposed approach can be easily utilized with existing Soil Water Characteristic Curve (SWCC) equations to model any changes in suction stress for unsaturated soils. The main advantage of the suggested method is in fact its dependency to just one parameter, simply calibrated by the conventional water retention tests. This characteristic is so applicable in hydro mechanical constitutive models of unsaturated soils. Finally, the efficiently predicting of the experimental results implicitly demonstrates the applicability of effective stress principle using the concept of Suction Stress Characteristic Curve (SSCC) for unsaturated soils.