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Geostatistics For Environmental Scientists

SUMMARY

The presence of fluid in the pores of a solid imposes a volume constraint on the deformation of the solid. Finite changes in the pore volume alter the degree of saturation of a porous material, impacting its fluid flow and water retention properties. This intricate interdependence between the hydromechanical properties related to solid deformation and fluid flow is amplified when the deformation of the solid matrix is large. In this paper, we present a mathematical framework for coupled solid-deformation/fluid-diffusion in unsaturated porous material considering geometric nonlinearity in the solid matrix. The framework relies on the continuum principle of thermodynamics to identify an effective or constitutive stress for the solid matrix, and a water-retention law that highlights the interdependence of the degree of saturation, suction, and porosity of the material. Porous materials are typically heterogeneous, making them susceptible to localized deformation. In this work, we consider random heterogeneities in density and degree of saturation as triggers of localized deformation in a porous material. Copyright © 2013 John Wiley & Sons, Ltd.

Mathematical framework for unsaturated flow in the finite deformation range

Coupled hydro-mechanical analysis of two unstable unsaturated slopes subject to rainfall infiltration

The water retention behaviour of compacted bentonites is strongly affected by multi-physical and multi-scale processes taking place in these materials. Experimental data have evidenced major effects of the material dry density, the imposed volume constraints, and the soil fabric. This paper presents a new water retention model accounting for proper retention mechanisms in each structural level of compacted bentonites, namely adsorption in the intra-aggregate pores and capillarity in the inter-aggregate ones. The model is calibrated and validated against experimental data on different bentonite-based materials, showing good capabilities in capturing the main features of the behaviour. The model is able to reproduce experimental data on compacted bentonites over a wide range of suction values, within a unified framework, and using a limited number of parameters. Some of the parameters introduced are shown to take approximately the same value for several bentonites, providing a significant basis for prelimin...

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Water retention model for compacted bentonites

The first law of thermodynamics suggests an energy-conjugate relationship among degree of saturation, suction stress, and density of an unsaturated porous material. Experimental evidence affirms that this constitutive relationship exists and that the water retention curves are dependent on the specific volume or density of the material. This constitutive feature must be incorporated into the mathematical formulation of boundary-value problems involving finite deformation. We present a fully coupled hydromechanical formulation in the finite deformation range that incorporates the variation of degree of saturation with the Kirchhoff suction stress and the Jacobian determinant of the solid-phase motion. A numerical simulation of solid deformation–fluid flow in unsaturated soil with randomly distributed density and degree of saturation demonstrates an intricate but well-established coupling of the hydromechanical processes. As deformation localizes into a persistent shear band, we show that bifurcation of the hydromechanical response manifests itself not only in the form of a softening behavior but also through bifurcation of the state paths on the water-retention surface.

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Finite Deformation and Fluid Flow in Unsaturated Soils with Random Heterogeneity

A porous model to simulate the evolution of the soil–water characteristic curve with volumetric strains

This paper presents the modeling of the phenomenon of collapse upon wetting using the effective stress approach. To this purpose, Bishop’s effective stress equation is applied in addition to an elastoplastic framework for the volumetric behavior of unsaturated soils. Bishop’s parameter χ is obtained from a porous-solid model that is able to simulate the soil-water retention curves during wetting-drying cycles. The proposed framework includes the hysteresis of the retention curve and to some extent the hydro-mechanical coupling of unsaturated soils. This model is able to reproduce quite precisely the phenomenon of collapse upon wetting using a single valued compressibility index. It also represents a unifying framework for saturated and unsaturated soils.

Use of Effective Stresses to Model the Collapse upon Wetting in Unsaturated Soils

SUMMARY

This paper describes a random solid-porous model capable of simulating the structure of porous materials. To this purpose, the grain and pore size distributions as well as the void ratio of the material are required. Solids and pores are distributed at random in the model's space according to a size strategy. Herein, the model is used to simulate the retention curves of soils. The Laplace equation is used to determine the size of the pores able to saturate or dry during a wetting or drying process, respectively. The continuous path principle is used to define those elements that effectively saturate or dry during these processes. With this procedure, it is possible to simulate the main retention curves as well as the scanning curves during wetting–drying cycles. Some experimental results reported in the international literature have been used to test the model. This model can be enhanced to study the mechanical behavior of unsaturated soils. Copyright © 2012 John Wiley & Sons, Ltd.

A random solid‐porous model to simulate the retention curves of soils

Simulation of the shear strength for unsaturated soils

This work presents the physical-chemical, geotechnical and mechanical characterization of a sample of mine tailings from the state of Zacatecas, Mexico with the objective of evaluating their possible use as a construction material for pavement support layers or as an aggregate of a hydraulic concrete. The material analyzed was classified as a poorly graded silty sand (SP-SM) according to the USCS classification and is composed mainly of quartz and calcite. The analyzed sample satisfies the necessary requirements, according to current Mexican regulations, to be used as i) a subgrade layer in a pavement, without the addition of virgin aggregates, or ii) as fine aggregates in the production of hydraulic concrete, previously sieved to correct its grain-size distribution. The mining residues studied do not require stabilization because the material transported in the leaching process is below the permissible limits for heavy metals according to Mexican regulations; this may be caused by the neutral pH of the sample, demonstrating a high adsorption of the heavy metals that avoids potential leaching. However, the sample was stabilized with Portland cement with 3 and 5 % respectively to corroborate the decrease in heavy metal transport based on the consulted bibliography; the concentrations of the analyzed elements decreased except for chrome due to its presence in the stabilizing material and an increase in the pH value was observed.

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María de la Luz Pérez-Rea

Papers

A porous model to simulate the evolution of the soil–water characteristic curve with volumetric strains

Use of Effective Stresses to Model the Collapse upon Wetting in Unsaturated Soils

A random solid‐porous model to simulate the retention curves of soils

Simulation of the shear strength for unsaturated soils

Characterization of mine tailings in their natural state and stabilized with cement, focused on construction