Numerical Initial Value Problems in Ordinary Differential Equations

Keywords: Mecanique des sols ; Drainage ; Ecoulement souterrain Reference Record created on 2004-09-07, modified on 2016-08-08

Applications of soil physics.

[1] We propose that the recently conceptualized suction stress characteristic curve represents the effective stress for the shear strength behavior of unsaturated soil. Mechanically, suction stress is the interparticle stress called tensile stress. The working hypothesis is that the change in the energy of soil water from its free water state is mostly consumed in suction stress. We demonstrate that the suction stress lies well within the framework of continuum mechanics where free energy is the basis for any thermodynamic formulation. Available experimental data on soil water characteristic curves and suction stress characteristic curves are used to test the hypothesis, thus validating a closed-form equation for effective stress in unsaturated soil. The proposed closed-form equation is intrinsically related to the soil water characteristic curve by two pore parameters: the air entry pressure and pore size spectrum number. Both semiquantitative and quantitative validations show that the proposed closed-form equation well represents effective stress for a variety of earth materials ranging from sands to clays. Of important practical implications are (1) the elimination of the need for any new shear strength criterion for unsaturated soil, (2) the elimination of the need for determining the Bishop's effective stress parameter χ because the new form of effective stress is solely a function of soil suction, and (3) the ready extension of all classical soil mechanics work on limit equilibrium analysis to unsaturated soil conditions.

/pdf/a-closed-form-equation-for-effective-stress-in-unsaturated-uw4ohcr7fm.pdf

A closed‐form equation for effective stress in unsaturated soil

Extensions to the land surface scheme (LSS) in the National Centers for Environmental Prediction, regional, coupled, land-atmosphere weather prediction model, known as the mesoscale Eta model, are proposed and tested off-line in uncoupled mode to account for seasonal freezing and thawing of soils and snow-accumulation-ablation processes. An original model assumption that there is no significant heat transfer during redistribution of liquid water was relaxed by including a source/sink term in the heat transfer equation to account for latent heat during phase transitions of soil moisture. The parameterization uses the layer-integrated form of heat and water diffusion equations adopted by the original Eta-LSS. Therefore it simulates the total ice content of each selected soil layer. Infiltration reduction under frozen ground conditions was estimated by probabilistic averaging of spatially variable ice content of the soil profile. Off-line uncoupled tests of the new and original Eta-LSS were performed using experimental data from Rosemount, Minnesota. Simulated soil temperature and unfrozen water content matched observed data reasonably well. Neglecting frozen ground processes leads to significant underestimation/overestimation of soil temperature during soil freezing/thawing periods and underestimates total soil moisture content after extensive periods of soil freezing.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JD900232

A parameterization of snowpack and frozen ground intended for NCEP weather and climate models

The effective stress principle, conventionally applied in saturated soils, is reviewed for constitutive modelling purposes. The assumptions for the applicability of Terzaghi’s single effective stress are recalled and its advantages are inventoried. The possible stress frameworks applicable to unsaturated soil modelling are reassessed in a comparative manner, specifically the Bishop’s single effective stress, the independent stress variables approach and the generalized stress framework. The latter considerations lead to the definition of a unified stress context, suitable for modelling soils under different saturation states. In order to qualify the implications brought by the proposed stress framework, several experimental data sets are re-examined in the light of the generalized effective stress. The critical state lines (CSLs) at different saturation states tend to converge remarkably towards a unique saturated line in the deviatoric stress versus mean effective stress plane. The effective stress interpretation is also applied to isotropic paths and compared with conventional net stress conception. The accent is finally laid on a second key feature for constitutive frameworks based on a unified stress, namely the sufficiency of a unique mechanical yield surface besides the unique CSL.

/pdf/effective-stress-concept-in-unsaturated-soils-clarification-13p0rtmfd7.pdf

Effective stress concept in unsaturated soils: Clarification and validation of a unified framework

Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used is a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non‐linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr‐Coulomb, modified Cam clay and generalised Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non‐linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress‐strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.

Refined explicit integration of elastoplastic models with automatic error control

This paper first presents a complete formulation of a constitutive model that deals with the irreversible behaviour of unsaturated soils under various loading and drying/wetting conditions. A standard form of incremental stress-strain relations is derived. The constitutive model is then cast into the thermodynamical theories and verified using the thermomechanical principles. It is shown that hydraulic hysteresis does not contribute to the plastic dissipation, though it contributes to the plastic work. All plastic work associated with a plastic increment of the degree of saturation is stored and can be recovered in a reversed plastic increment of saturation. The incremental constitutive equations are also reformulated for implementation in finite element codes where displacements and pore pressures are primary unknowns. Qualitative predictions of the constitutive model show that incorporating two suction related yield surfaces and non-associated flow rules into the Barcelona Basic Model opens a full range of possibilities in modelling unsaturated soil behaviour.

A constitutive model for unsaturated soils: thermomechanical and computational aspects

In this paper, some practical aspects of the finite element implementation of critical state models are discussed. Improved automatic algorithms for stress integration and load and time stepping are presented. The implementation of two generalized critical state soil models, with one described first in this paper and the other recently published elsewhere, is discussed. The robustness and correctness of the proposed numerical algorithms are illustrated through both coupled and uncoupled analyses of geotechnical problems.

Aspects of finite element implementation of critical state models

The paper presents a review of constitutive modelling of unsaturated soils. After a brief historical perspective, a number of existing constitutive models are classified and discussed according to the type of stress variables adopted in their formulation. Afterwards, attention is given to recent developments in the proposal of coupled hydraulic-mechanical models and the possibility of casting them in a sound thermodynamical framework. Finally, a double structure model for expansive soils is described. The incorporation of microstructural considerations and its use as a platform for incorporating the influence of new variables are highlighted.

Daichao Sheng

Papers

Refined explicit integration of elastoplastic models with automatic error control

A constitutive model for unsaturated soils: thermomechanical and computational aspects

Aspects of finite element implementation of critical state models

On constitutive modelling of unsaturated soils

Review of fundamental principles in modelling unsaturated soil behaviour