Mechanics of Unsaturated Geomaterials

Lyesse Laloui

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN:
  9781848212664
• eBook ISBN:
  9781118616765
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

This book provides a sound basis in the challenging area of the mechanics of unsaturated geomaterials. The objective is to supply the reader with an exhaustive overview starting from the basics and covering the most recent theories and applications (i.e. natural disasters, nuclear waste disposal, oil and agriculture productions). The presentation of the fundamental concepts is based on an interdisciplinary approach, in the areas of soil, rock and cement-based material mechanics.

PART I

Fundamental Concepts

Chapter 1

Basic Concepts in the Mechanics and Hydraulics of Unsaturated Geomaterials ¹

Unsaturated geomaterials are geomaterials with void spaces partially filled with liquid and partially with gas. The liquid (wetting) phase is an aqueous solution, generically referred to as water, whereas, the gaseous (non-wetting) phase is a mixture of air and water vapor, generically referred to as air. The mutual interaction between these two phases and their interaction with the solid phase plays a key role in the mechanical and hydraulic response of unsaturated geomaterials. The basic mechanisms and thermodynamics of the interaction between the liquid, gaseous, and solid phases are not commonly covered in undergraduate and graduate courses. As a result, students and engineers with geotechnical background may find it difficult to approach the mechanics and hydraulics of unsaturated soils. The purpose of this chapter is to fill this gap and to illustrate the basic elementary mechanisms behind water retention, water flow, and mechanical behavior of unsaturated geomaterials. Special emphasis has been given to capillary mechanisms arising from surface tension at the air-water interface and from the angle formed by the air-water interface at the solid-liquid-gas junction (contact angle). Capillary actions play a major role in the response of unsaturated geomaterials and can conveniently serve as a basis to introduce the most distinctive features of the hydraulic and mechanical response of unsaturated geomaterials.

1.1. Water retention mechanisms in capillary systems

1.1.1. Surface tension, contact angle, and water tension

Liquid surfaces act as if they are in tension as a result of an imbalance between intermolecular attractions at a surface. In bulk liquid, the forces acting on a molecule are effectively equal in all directions and the molecule feels no net force. As a molecule moves to the surface, it loses some nearest neighbors, thus leaving it with unbalanced attractive forces with a downward resultant force (Figure 1.1(a)). For a molecule to stay in the surface region, it must gain excess energy (and entropy) over those in the bulk liquid. This excess energy (surface free energy) is the surface tension and causes the surface to act like a membrane in tension. When in contact with a solid surface, the interface will curve near that surface to form a meniscus. If adhesive forces between solid and liquid prevail on cohesive forces in the liquid, the interface will curve up and will form an angle lower than 90° with the solid surface (Figure 1.1(b)). Contact angles, which are measured through the liquid, lower than 90° are typical for soil water on soil minerals.

Figure 1.1. (a) Development of surface tension at the gas-liquid interface and (b) curvature of the gas-liquid interface in proximity of a solid surface

Menisci concave on the air side generate water pressures lower than the air pressure. Let us consider a meniscus in a capillary tube of diameter d (Figure 1.2). The water pressure at the back of the meniscus can be calculated by considering the vertical force equilibrium of the air-water interface:

[1.1]

where u_w is the water pressure at the back of the meniscus, u_a the air pressure, T the surface tension, θ the contact angle, and R the radius of curvature of the interface. If the contact angle is lower than 90°, the gauge water pressure u_w-u_a becomes negative.

Using equation [1.1], it is instructive to calculate the gauge and the absolute water pressure for capillary tubes having diameters of the same order of magnitude as the size of pores in clay, silt, and sand. For the sake of simplicity, let us assume that pore size is about 1/10 of the grain size and contact angle is θ = 0. As shown in Table 1.1, if the pore size is sufficiently small, as in the case of clays, absolute water pressure may be negative. Water can, therefore, be held in tension (i.e. it is being stretched) in unsaturated geomaterials.

Figure 1.2. Negative water pressure generated by meniscus concave on the air side

Water can indeed sustain high tensile stresses as recognized earlier by Berthelot [BER 50] and confirmed by several experiments carried out using metal and glass Berthelot-type systems (see [MAR 95]). The magnitude of negative pressure and the duration over which the negative pressure can be sustained is limited by the phase relationships of the pore fluid and the phenomenon of heterogenous cavitation [MAR 08]. Heterogenous cavitation of water typically occurs at negative gauge pressures close to −100 kPa, but this pressure should not be mistaken for the tensile strength of water.

Table 1.1. Minimum sustainable gauge and absolute water pressure and hydraulic conductivity in capillary tubes having diameters representative of typical geomaterial pore size (θ = 0°, T = 0.072 N/m, u_a = 100 kPa, η = 10⁻⁶ m²/s)

1.1.2. Hysteresis of contact angle

Gibbs [GIB 48] showed that only one stable contact angle exists for a given system of smooth, homogenous, and non-deformable solids. In practice, however, this is rarely, if ever, the situation. If these assumptions are removed, within the framework of classical thermodynamics it can be shown that many different stable angles exist for a given system, i.e. the contact angle shows hysteresis [JOH 69].

The concept of contact angle hysteresis can perhaps be best explained by considering a drop of water placed on a surface. The water drop contact angle attains an equilibrium value θ_c when the surface is horizontal (Figure 1.3(a)). If the surface is progressively tilted, the contact angles at the leading and trailing edge of the drop will increase and decrease, respectively, to prevent the drop periphery from moving. In this way, the tangential component of the drop weight can be equilibrated by the tangential component of the surface tension forces T acting at the drop periphery. This will continue until a limiting condition is attained when these angles become the advancing and receding angles, θ_a and θ_r,, respectively, at which point the drop will roll off the plate (Figure 1.3(b)). Thus, a number of macroscopic stable contact angles exist for a given system in the range from θ_r to θ_a. The hysteresis of the contact angle can be produced by surface roughness and surface heterogeneity [JOH 69].

Figure 1.3. Hysteresis of the contact angle: (a) water drop on horizontal surface and (b) water drop on a tilted surface

1.1.3. Evaporation from capillary systems and geomaterials

Unsaturated geomaterials are found in earth structures and in the upper zone of the ground above the water table. The main mechanisms of desaturation consist of evaporation from the surface and lowering of the water table. These mechanisms can conveniently be illustrated by considering systems of capillary tubes, which mimic the network of capillaries across the pore space in geomaterials. The evaporation of water from a capillary tube is shown in Figure 1.4. At Stage 1, let us assume that the air-water interface is flat and that the gauge water pressure is therefore zero in the tube. If evaporation occurs, water is initially removed without displacement of the gas-liquid-solid junction of the men...

Table of contents

• Cover
• Title Page
• Dedication
• Copyright
• Preface
• PART I: Fundamental Concepts
• PART II: Experimental Characterization
• PART III: Theoretical Developments
• PART IV: Engineering Applications
• List of Authors
• Index