Deformation Of Unsaturated Soils Research Articles

Modeling pore fluid pressure and deformation in unsaturated soils under gravitational compaction and cyclic loading

Cyclic loading of fluid-bearing soils often induces excess pore water pressure, leading to accumulation of strain in the solid matrix. Additionally, variations in material density and volumetric fraction due to gravitational effects generate momentum forces, which subsequently cause deformation in the soil. In this paper, we present a mathematical framework of poroelasticity that generalizes the simultaneous action of gravitational body forces and cyclic loading to analyze solid deformation and fluid pressure dissipation in partially-saturated porous media. To account for the effect of gravity, the gradient of the vertical displacement needs to be treated as an additional dependent variable alongside pore air and water pressures.We numerically solve a mixed strain-controlled and pressure-prescribed boundary-value problem using a finite difference scheme as a representative example to quantify the impact of gravitational forces. Our results show that gravitational compaction affects both total settlement and excess pore water pressure, with its influence being particularly significant at lower water saturations, regardless of excitation frequency, soil depth, or type. The effect of gravity is more pronounced in soils with higher compressibility but appears insensitive to excitation frequency. Notably, the gravitational effect correlates linearly with the depth of the soil deposit and, therefore, should be well integrated into the consolidation theory of poroelasticity.

Updated Lagrangian unsaturated periporomechanics for extreme large deformation in unsaturated porous media

Unsaturated periporomechanics is a strong nonlocal poromechanics based on peridynamic state and effective force state concept. In the previous periporomechnics the total Lagrangian formulation is adopted for the solid skeleton of porous media. In this article as a new contribution we formulate and implement an updated Lagrangian unsaturated periporomechanics framework for modeling extreme large deformation in unsaturated soils under drained conditions. In this new framework the so-called bond-associated sub-horizon concept is utilized to enhance the stability and accuracy at extreme large deformation of the solid skeleton. The stabilized nonlocal velocity gradient in the deformed configuration is used to update the effective force state from a critical state based visco-plastic constitutive model for unsaturated soils. The updated Lagrangian periporomechanics paradigm is numerically implemented through an explicit Newmark scheme for high-performance computing. Numerical examples are presented to demonstrate the stability of the computational updated Lagrangian periporomechanics paradigm and its efficacy and robustness in modeling extreme large deformation in porous media under drained conditions.

Study on the coupled heat-water-vapor-mechanics process of unsaturated soils

Freezing of unsaturated soils jointly involves heat transfer, water-vapor migration, water-ice and water-vapor phase changes and deformation. To understand this freezing, we conducted a series of one-dimensional freezing tests to study the influences of the initial water content and cooling temperature on the water-vapor migration and deformation of unsaturated soils. Results show that the initial water content determines the water and vapor migration intensity and deformation of unsaturated soils. Vapor migrates prominently and frost heave develops slowly when the initial water content is lower than a critical value. Above this value, the liquid water migration dominates, and frost heave develops rapidly. It is also found that the cooling temperature dominates water and vapor fluxes in such a manner that a higher cooling temperature leads to faster migrations of water and vapor in unsaturated soil. We further analyzed the coupled heat-water-vapor-mechanics process of unsaturated soils and proposed a coupled heat-water-vapor-mechanics model. The simulated temperatures, volumetric water content, and displacement agree well with those measured data, validating that the model can describe effectively the coupled heat-water-vapor-mechanics process in freezing unsaturated soils.

Explicit approximate analytical solutions of seepage‐deformation in unsaturated soils

SummaryAn approximate analytical solution is presented for the coupled seepage and deformation problem of unsaturated soils. Because of the matric suction dependence of both saturation and permeability coefficient, the coupled governing equations are strongly nonlinear. To obtain an analytical solution, these coupled governing equations are linearized and analytically solved for a specified saturation using the eigenfunction method. Then, the obtained analytical solutions are extended to the entire saturation range. Comparison between the current solution and the previous theoretical solution indicates that the proposed solution yields excellent results. Due to its analytical nature, the proposed procedure can be effectively used to obtain the solution of the coupled seepage and deformation of unsaturated soils.

Incorporating hydro-mechanical coupling in an analysis of the effects of rainfall patterns on unsaturated soil slope stability

Rainfall-induced landslides can cause loss of life and damage to property, infrastructure, and the environment. Rainfall patterns affect the pore-water pressure of unsaturated soil slopes, and are related to the slopes’ stability. Four rainfall patterns were chosen to represent natural rainfall patterns for an examination of rainfall infiltration into soil slopes using numerical models incorporating coupled water infiltration and deformation in unsaturated soils. Our analysis showed that rainfall patterns play a significant role in the distribution of the pore-water pressure in soil slopes, and influence the slope stability. The pore-water pressure profile of soil slopes and the factor of safety are affected by the ratio of rainfall intensity and the coefficient of permeability. The depth and shape of the shallow sliding plane of the landslide is closely related to the rainfall pattern; moreover, the results showed a correlation between the factor of safety of the slope and the rainfall intensity. This relationship can be described by a dimensionless rainfall intensity. The nonlinear relationship can be used to estimate the slope stability resulting from rainfall infiltration when the hydro-mechanical coupling in unsaturated soil slopes is considered.

Detection of water infiltration and deformation of unsaturated soils by elastic wave velocity

Intense rainfall is the most important landslide trigger. In many mountainous environments of the world, heavy rainfall has caused many landslides and slope failures in a matter of seconds without warning. Therefore, an early warning system can be an effective measure to reduce the damage caused by landslides and slope failures by facilitating the timely evacuation of people from landslide-prone areas. In this study, we propose an idea to correlate soil moisture changes and deformations in slope surface by means of elastic wave propagation in soil. Constant shear stress drained triaxial tests where water was infiltrated from the bottom of specimen until failure, and slope model tests under artificial rainfall were performed to investigate the response of elastic wave velocities during pre-failure phases of rainwater infiltration and deformation. Analysis of the results has established that the elastic wave velocity continuously decreases in response of moisture content and deformation, and there was a distinct surge in the decrease rate of wave velocity when failure was initiated. Possible mechanisms were interpreted based on the test results. It is proposed that a warning be issued at switch of wave velocity decrease rate. This approach can thus serve as the basis of an early warning system for landslides and slope failure considering both moisture content and deformation.

Transient bifurcation condition of partially saturated porous media at finite strain

SummaryBifurcation of unsaturated soils into a localized shear band is a ubiquitous failure mode of partially saturated soils. The density and degree of saturation have major impacts on the inception of localized deformations in unsaturated soils. Unsaturated fluid flow may dramatically change the density and degree of fluid saturation of unsaturated soils. Therefore, the unsaturated fluid flow is a potential trigger for shear banding in such materials. In this paper, we derive a simplified bifurcation condition of localized deformation in unsaturated soils under the local transient condition at finite strain. This transient bifurcation condition is implemented into a nonlinear finite element code to study the inception of localized deformation in unsaturated soil specimens. Numerical simulations are conducted to study the impact of soil fabrics of density, a ‘bonding’ variable, and intrinsic permeability on the inception of localized failures via the transient bifurcation criterion. Mesh sensitivity analysis is performed to demonstrate the viscosity effect of unsaturated fluid flow on the localized deformation. Numerical simulations demonstrate that the transient bifurcation condition can detect the localized deformation triggered by the internal unsaturated fluid flow process in unsaturated soils. Copyright © 2016 John Wiley & Sons, Ltd.

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

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.

A finite strain elastoplastic constitutive model for unsaturated soils incorporating mechanisms of compaction and hydraulic collapse

Although the deformation of unsaturated soils has usually been described based on simple infinitesimal theory, simulation methods based on the rational framework of finite strain theory are attracting attention especially when solving geotechnical problems such as slope failure induced by heavy rain in which large a deformation is expected. The purpose of this study is to reformulate an existing constitutive model for unsaturated soils (Kikumoto et al., 2010) on the basis of finite strain theory. The proposed model is based on a critical state soil model, modified Cam-clay, implementing a hyperelastic model and a bilogarithmic lnv -lnP ’ (v , specific volume; P ’, effective mean Kirchhoff stress) relation for a finite strain. The model is incorporated with a soil water characteristic curve based on the van Genuchten model (1990) modified to be able to consider the effect of deformation of solid matrices. The key points of this model in describing the characteristics of unsaturated soils are as follows: (1) the movement of the normal consolidation line in lnv -lnP ’ resulted from the degree of saturation (Q , deviatoric Kirchhoff stress), and (2) the effect of specific volume on a water retention curve. Applicability of the model is shown through element simulations of compaction and successive soaking behavior.

One-Dimensional Coupled Infiltration and Deformation in Unsaturated Soils Subjected to Varying Rainfall

AbstractAssuming that the water content and hydraulic conductivity of unsaturated soil are exponential functions of the pressure head, Green’s function is used to obtain analytical solutions to one-dimensional coupled rainfall infiltration and deformation in unsaturated soils under varying surface rainfall flux. The analytical solution considers varying flux and pressure head at the top boundary and arbitrary initial conditions. In particular, nonlinearly increasing rainfall intensity at the surface boundary is considered. The result indicates that the coupling of seepage and deformation has a significant effect on the pressure-head profiles for the transient unsaturated seepage. The coupling effect is closely related to the boundary conditions. The coupling effect almost disappears if ponding at the ground surface occurs. The ponding time is different under the coupled and uncoupled conditions. There is a quick change in the pressure-head profiles near the time of ponding or peak or discontinuous rain in...

Analytical Solutions to the One-Dimensional Coupled Seepage and Deformation of Unsaturated Soils with Arbitrary Nonhomogeneous Boundary Conditions

In one-dimensional coupled seepage and deformation problems, permeability coefficients are a function of matric suctions in unsaturated soils. Due to the presence of permeability coefficient and the coupling effect in one dimension, coupled equations are nonlinear. Additionally, different boundary conditions can also make coupled seepage and deformation difficult to get its analytical solution. This study presents solutions in the one-dimensional coupled seepage and deformation of unsaturated soils with arbitrary nonhomogeneous boundary conditions. Analytical solutions were derived for a finite thickness and confined lateral directions in unsaturated soils. Furthermore, the coupled seepage and deformation equation in one dimension was derived from the mass conservation principle integrated with Dakshanamurthy’s constitutive relationships, in which the water and air flows follow Darcy’s law in unsaturated soils. To linearize a governing equation, an exponential transform and several dimensionless variables were selected. Solutions were obtained by applying a Laplace integral transform to a dimensionless linear equation under arbitrary initial and boundary conditions. After performing inverse Laplace transforms and using the residue theorem, analytical solutions were obtained in the time domain. Finally, three typical examples of nonhomogeneous boundary conditions were considered as case studies. It can be noted that the analytical solutions are consistent with the numerical results by a finite difference method. The result also indicates that the boundary conditions and the coupling effect have a significant influence on the seepage in unsaturated soils.

Numerical analysis of seepage–deformation in unsaturated soils

A coupled elastic–plastic finite element analysis based on simplified consolidation theory for unsaturated soils is used to investigate the coupling processes of water infiltration and deformation. By introducing a reduced suction and an elastic–plastic constitutive equation for the soil skeleton, the simplified consolidation theory for unsaturated soils is incorporated into an in-house finite element code. Using the proposed numerical method, the generation of pore water pressure and development of deformation can be simulated under evaporation or rainfall infiltration conditions. Through a parametric study and comparison with the test results, the proposed method is found to describe well the characteristics during water evaporation/infiltration into unsaturated soils. Finally, an unsaturated soil slope with water infiltration is analyzed in detail to investigate the development of the displacement and generation of pore water pressure.

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.

An Improved Elasto-Plastic Model for Unsaturated Soils

The strength and deformation behaviors of unsaturated soil can be approximately described by elasto-plastic constitutive model that was proved by abundance academic and test researches. The Barcelona elastic-plastic model is an excellent model that can simulate the strength and deformation of unsaturated soil. But their calculated result of shear strength is low. So an improved Barcelona model is settled by using drop-shaped shear yield surface and hardening theory of dual stress. The results show that the improved model can more accurately predict the strength and deformation behaviors of unsaturated soil under suction-controlled triaxial compression stress states.

Work and energy equations and the principle of generalized effective stress for unsaturated soils

AbstractThe effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single‐effective‐stress variable theory and two‐effective‐stress‐variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single‐stress variable or the two‐stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils. Copyright © 2009 John Wiley & Sons, Ltd.

Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils

AbstractAn analytical solution to 1D coupled water infiltration and deformation is derived using a Fourier integral transform. Exponential functional forms are used to represent the hydraulic conductivity–pore‐water pressure relationship and the soil‐water characteristic curve. Fredlund's incremental‐linear constitutive model for unsaturated soils is adopted. The analytical solution considers arbitrary initial pore‐water pressure distributions and flux and pressure boundary conditions. The corresponding analytical solutions to coupled steady‐state problems are also obtained. The analytical solutions demonstrate that the coupling of seepage and deformation plays an important role in water infiltration in unsaturated soils. In the early stages of infiltration, the difference between uncoupled and coupled conditions becomes marked over time, and in late stages, the difference caused by the coupling effects diminishes toward the steady state. The difference between the uncoupled and coupled conditions increases with decreasing desaturation coefficient (α). Pore‐water pressure or deformation changes caused by the coupling effects are mainly controlled by the degree of soil volume change due to a change in soil suction (H). The smaller the absolute value of H, the greater the effect of coupling on the infiltration and deformation. The ratio of rainfall intensity to saturated permeability (q/ks) also has a strong influence on the coupled seepage and deformation. Copyright © 2008 John Wiley & Sons, Ltd.