Nasser Khalili

A three-phase model for unsaturated soils

A comprehensive framework to define the constitutive behaviour of unsaturated soils is developed within the theory of mixtures applied to three-phase porous media. Each of the three phases is endowed with its own strain and stress. Elastic and elastic–plastic constitutive equations are developed. Particular emphasis is laid on the interactions between the phases both in the elastic and plastic regimes. Nevertheless, the clear structure of the constitutive equations requires a minimal number of material parameters. Their identification is provided: in particular, it incorporates directly the soil–water characteristic curve. Crucial to the formulation is an appropriate definition of the effective stress. The coupled influence of this effective stress and of suction makes it possible to describe qualitatively many of the characteristic features observed in experiments, e.g. for normally consolidated soils, a plastic behaviour up to air entry followed by an elastic behaviour at increasing suctions, and, on the way back, an elastic behaviour, unless compression is applied in which case plastic collapse occurs. Copyright

An effective stress elastic–plastic model for unsaturated porous media

Abstract Within a three-phase framework, an extension of elastic–plastic models of saturated soils to unsaturated states has been presented in [Int. J. Numer. Anal. Meth. Geomech. 24 (2000) 893–927]. Here, the main concern is on the behaviour of the solid skeleton. A simple, yet effective, model for the elastic–plastic behaviour of unsaturated soils is described, requiring minimal number of material parameters to define the effect of desaturation. These material parameters are identified and the application of the model is demonstrated using a comprehensive set of data reported by Wheeler and Sivakumar [Geotechnique 45 (1) (1995) 35–53], that includes first wetting, followed by consolidation and finally triaxial compression tests. The model is also applied to describe qualitatively two characteristic features observed in experiments, e.g., plastic volumetric contractancy followed by an elastic response observed in normally consolidated soils subject to increasing values of suction, and elastic rebound upon wetting, unless compression is applied in which case collapse may occur.

An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media : Formulation

A rigorous and unified treatment of the theory of non-isothermal flow and deformation in unsaturated porous media is presented. The governing equations based on the equations of equilibrium, the effective stress concept, Darcys law, Fouriers law and the conservation equations of mass and energy are derived using a systematic macroscopic approach. The thermo-hydro-mechanical coupling processes taken into account include: thermal expansion, thermal convection by moving fluid, fluid flux due to temperature gradient (Soret effect), phase exchange (vaporisation, condensation), heat exchange between the phases, heat of wetting, and heat due to phase compression. Both elastic and elasto-plastic constitutive equations are developed. All model coefficients are identified in terms of measurable parameters. The governing equations derived are general in nature, embodying all previously presented formulations in the field. For example, when the heat of wetting, and that heat due to phase compression are neglected, and it is assumed that the vapour is at the saturated liquid pressure, with all phases in thermal equilibrium, and that the forced convection is negligible, the theory of heat and mass transfer presented by Thomas and his coworkers is obtained. Also when the pore air volume reduces to zero and the thermal equilibrium is assumed, the thermo-elastic model for fluid saturated media presented by McTigue [J. Geophys. Res. 91 (B9) (1986) 9533] is recovered.

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

Abstract In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.

Non‐linear seismic behaviour of concrete gravity dams using coupled finite element–boundary element technique

In this paper, the seismic response of concrete gravity dams is presented using the concept of Continuum Damage Mechanics (CDM) and adopting the hybrid Finite Element–Boundary Element technique (FE–BE). The finite element method is used for discretization of the near field and the boundary element method is employed to model the semi-infinite far field. Because of the non-linear nature of the discretizied equations of motion modified Newton–Raphson approach has been used at each time step to linearize them. Damage evolution based on tensile principal strain using mesh-dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation in gravity dams. Other important features considered in the analysis are: (1) realistic damage modelling for concrete that allows isotropic as well as anisotropic damage state and exhibits stiffness recovery upon load reversals. (2) softening initiation and strain softening criteria for concrete, and (3) proper modelling of semi-infinite foundation using FE–BE method that allows to consider dam–foundation interaction analysis. As an application of the proposed formulation a gravity dam has been analysed and the results are compared with different foundation stiffnesses. The results of the analysis indicate the importance of including rock foundation in the seismic analysis of dams. Copyright

Seismic analysis of arch dams—a continuum damage mechanics approach

In this paper, the non-linear seismic response of arch dams is presented using the concept of Continuum Damage Mechanics (CDM). The analysis is performed using the finite element technique and appropriate non-linear material and damage models in conjunction with the α-algorithm for time marching. Because of the non-linear nature of the discretizied equations of motion, modified Newton–Raphson approach has been used at each time step. Damage evolution based on tensile principal strain using mesh-dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation. As an application of the proposed formulation, a double curvature arch dam has been analysed and the results are compared with the solutions from linear analysis and it is shown that the structural response of arch dams varies significantly in terms of damage evolution. Copyright

Effective stress in double porous media with two immiscible fluids

Note: Sols Reference LMS-ARTICLE-2005-006doi:10.1029/2005GL023766View record in Web of Science Record created on 2006-11-09, modified on 2016-08-08

Wave propagation analysis of two-phase saturated porous media using coupled finite-infinite element method

Abstract A fully coupled two-dimensional infinite element for frequency domain analysis of wave propagation problems in unbounded saturated porous media is presented. The decay function of the element is derived based on the analytical solution of Biot (Theory of propagation of elastic waves in fluid-saturated porous solid. 1. Low-frequency range. Journal of the Acoustical Society of America 1956;28(2):168–78) formulation for a one-dimensional configuration. After a detailed description of the element formulation, the effectiveness and the accuracy of the present infinite element in simulating unbounded domains are demonstrated through two numerical examples. Extremely good agreements are obtained between the results from a very large mesh and those from the coupled finite–infinite element method. It is shown that the accuracy of the solutions deteriorate significantly when the infinite elements are removed and fixed to free displacement boundary conditions are introduced at the truncated boundaries.

Mixed solid/dispersed phase particles in multiphase fluidised beds, Part I: Free energy of stability due to interfacial tension

Abstract A theoretical analysis is conducted of the retention of a dispersed phase fluid within a (multiphase) fluidised bed, in terms of the behaviour of mixed phase particles , or composite particles of the solid and dispersed fluid phases. By analysis of the thermodynamic stability of such particles due to interfacial tension — in the general case considering an “ n -plet” ( n solid grains surrounding a dispersed phase droplet) — solutions are obtained for the Gibbs free energy of several detachment processes as sets of dimensionless equations which are solved numerically. The analysis indicates that all geometrically possible mixed particles require energy for their rupture, of which the minimum energy rupture process (for a preferentially nonwetting dispersed phase) is isolated solid particle detachment. Thus, if sufficient energy is available, an n -plet will shed solid particles in successive rupture processes, such that if these reach the point at which the n -plet is either buoyant or elutriable, it will be released from the bed. The analysis determines the energy required for mixed-phase particle rupture and the limits of retention of such particles in any given fluidised bed. The derived energy functions are compared to the energy available for mixed particle rupture in Part II (Niven, Khalili & Hibbert, 2000).

EARTHQUAKE ANALYSIS OF GRAVITY DAMS BASED ON DAMAGE MECHANICS CONCEPT

In this paper, the seismic response analysis of concrete gravity dams is presented using the concept of Continuum Damage Mechanics. The analysis is performed using the finite element technique and a proper material degradation/damage model. The damage criterion used here is a second order tensor model based on elastic-brittle characterization and on a power function of the principal tensile stress. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and propagation. Other important features considered in the analysis are: (1) dam-foundation interaction (2) appropriate modelling of joined rock mass using continuum damage mechanics, and (3) proper modelling of unbounded domain of foundation rock. The infinite media representation of the foundation material has been achieved by using doubly asymptotic approximation. The results of the analysis indicate that the seismic response of a damaged concrete dam could be significantly different from that of an undamaged one. In particular, the analysis shows that during a seismic event, the microstructure of a damaged zone can significantly change due to growth and propagation of microcracks.