1. Clays, Clay Minerals and Soil Shrink/Swell Behavior
Hillel, pp
Clays, Clay Minerals and Soil Shrink/Swell Behavior

2. Introduction
Volume and pore space of swelling clayey soils vary with hydration state.
Shrink-swell phenomena affect many mechanical and engineering properties of soils and clay liners.
Constitutive transport properties for swelling soils are complicated by hydration-dependent soil attributes (pore space, strength, etc).
As many of you are aware, dealing with swelling soil has always been a challenge to soil physicists, chemists and engineers.
The primary reason is the often large change in volume and in pore space with changes in hydration state of the soil.
These changes present a challenge to development of predictive models for soil hydraulic functions needed for prediction of transport processes in these soils.
The primary cause of soil shrink-swell behavior is interactions between adjacent diffuse double layers associated with the lamellar structure of soil clay whose distance vary with potential.
A small but important component of swelling is associated with the first few molecular layers of water and is termed crystalline swelling whereas DDL swelling is called osmotic swelling
The solids that make up the soil clay fabric are organized in a complex fashion resulting in a hierarchy of structures and pores that affect retention of water and volume changes.
Finally, shrink-swell phenomena is of interest to many disciplines other than hydrology and soil physics as it affect many importance mechanical and rheological soil properties.

3. Clay shrink/swell damage to structures & roads
Changes in soil water content or solution chemistry of clayey soils induce swelling pressures sufficiently large to fracture and damage structures and roads.
Estimated damage in excess of $7 billion/yr in the US.
As many of you are aware, dealing with swelling soil has always been a challenge to soil physicists, chemists and engineers.
The primary reason is the often large change in volume and in pore space with changes in hydration state of the soil.
These changes present a challenge to development of predictive models for soil hydraulic functions needed for prediction of transport processes in these soils.
The primary cause of soil shrink-swell behavior is interactions between adjacent diffuse double layers associated with the lamellar structure of soil clay whose distance vary with potential.
A small but important component of swelling is associated with the first few molecular layers of water and is termed crystalline swelling whereas DDL swelling is called osmotic swelling
The solids that make up the soil clay fabric are organized in a complex fashion resulting in a hierarchy of structures and pores that affect retention of water and volume changes.
Finally, shrink-swell phenomena is of interest to many disciplines other than hydrology and soil physics as it affect many importance mechanical and rheological soil properties.

4. Clay Minerals – building blocks
Distinguish between “clay” size <2mm and clay minerals
Basic building blocks of clay minerals:
Silica centered tetrahedra
Al3+ (+ other cations Mg2+ ) centered octahedra

5. Formation of Silica and Alumina Sheets
The tetrahedra are joined (share oxygen) at their basal corners in a hexagonal pattern forming flat sheets ~ nm thick.
The octahedra join along their edge to form triangular array nm thick.
Stacked sheets form lamellae.

6. Isomorphic substitution
The space occupied by silica in a tetrahedron can accommodate atoms <~0.4 times O2 radius (Si4+ & Al3+).
Octahedra times O2 radius (accommodates iron, magnesium, aluminum, manganese, titanium, sodium, calcium)
Substitution of central atoms with valence < +4 (tetrahedron) or <+3 (octahedron) during crystallization is known as isomorphic substitution and results in net negative charge that must be balanced externally by adsorption of cations.
These cations are not permanent and can exchanged by other cations in soil solution.

7. Cation Exchange Capacity
The cation exchange capacity (CEC) describes the amount of exchangeable cations per unit soil mass: CEC = cmol of positive charge/kg
CEC values range from 2-15 cmol+/kg for Kaolinite; illite, and for montmorillonite.

8. Formation of a Diffuse Double Layer (DDL)
Some of the exchangeable cations are bounded to surfaces whereas others may be dispersed in the aqueous solution – hence a “double layer”…
The distribution of cations (and associated anions) in solution reflect a balance between electrical and thermal forces resulting a diffuse “cloud” of cations with concentration diminishing with distance from clay surface.
The extent of this diffuse layer is not constant and varies with solution concentration, clay hydration, cation valence and clay type.

9. Different Clay Minerals
Distinguished by number and order of layering of basic tetra & octahedral sheets
Amount of isomorphic substitutions.
Types and amounts of cations bound to surfaces.

10. Montmorillonite
2:1 - one octahedral sheet sandwiched between two tetrahedral sheets
Many isomorphic substitutions: Mg+2, Fe+2, & Fe+3 for Al+3 in octa
High surface area ( m2/g)
Large CEC
Very active shrink/swell behavior
Exchangeable cation

11. Kaolinite 1:1 alternating octa/ tetrahedral sheets.
Few isomorphic substitutions
Thicker and stable stacks
Relatively low surface area: 5-30 m2/g
Not much swelling

12. Swelling and changes in lamellar Spacing- +
H2O osmosis from bulk soil solution due to DDL cations
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.

13. Swelling and Lamellar Spacing
Clay lamellar spacing increases with increasing potential (less negative/ wetter) resulting in swelling.
Interacting diffuse double layers (DDL) dominate swelling behavior.
Reasonable agreement exists between measured lamellae spacing and DLVO-theory: approaching DDLs develop a repulsive force proportional to excess ions relative to bulk (giving rise to osmotic pressure).
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.
Low [1980]; Warkentin et al. [ 1957]

14. Interacting DDL and swelling pressure
When two DDLs approach each other they develop a repulsive force that is proportional to excess ions relative to bulk (giving rise to osmotic pressure).
A convenient point for evaluation is midplane where dy/dx=0 (due to symmetry for equal surfaces).
Langmuir [1938] calculated the swelling pressure as: which simply van’t Hoff relations.
For short separation distances Langmuir obtained:
h = separation distance [m]
c0 = bulk electrolyte concentration [mol m-3]
e = electron elementary charge [ x10-19 C]
k = the Boltzmann constant [ x10-23 J K-1]
R = universal gas constant [ J mol-1K-1]
y1= y(h/2) mid-plane electric potential [V]
z = signed ion valence.
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.
Scale electric potential
The “trick” is how to determine the mid-plane electric potential y1 ?

15. Measurement of swelling pressure
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.

16. Large spacing weak interaction approximation
A very useful approximation for swelling pressure at large spacing and weak interactions was developed by Derjaguin [1987]:
Note that this expression is dependent on surface potential 0 (and not on mid-plane 1)
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.
Low [1980]; Warkentin et al. [ 1957]

17. Calculation of swelling pressure - Example
Consider two DDLs separated by a distance of h=5 nm with bulk monovalent electrolyte concentration of [NaCl]=0.001 M; surface potential y0 =55 mV. Find the swelling potential.
Using the approximation:
Simplified as:
Approximating k:
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.
We find that Pe(5 nm)=22.5 kPa
Changing the concentration to 0.01 M, we obtainPe(5 nm)=73.2 kPa
Changing the distance to 1 nm ([NaCl]=0.01) Pe(1 nm)=273 kPa

18. Lamellar swelling – the disjoining pressure
A more general treatment considers the various interactions between charged clay surfaces and aqueous solutions using the disjoining pressure formalism (P), or the so-called DLVO theory.
The equilibrium potential (m) as function of water film thickness (h =half lamellar spacing) is comprised of three primary components:
Where:
As indicated earlier the “engine” behind shrink-swell phenomenon are changes in interlamellar spacing with changes in potential, electrolyte charge density, etc.
The theoretical basis for modeling interactions between charged surfaces in the presence of electrolyte is provided by the DLVO theory using the disjoining pressure as the basic thermodynamic property (or changes in free energy per unit surface area per film thickness -----clarify here!!!)
In equilibrium the chemical potential is composed of three components – the primary source is due to electrostatic repulsion between adjacent DDLs, there are two other short-range forces the van der Waals attractive force and the so-called hydration force that prevents collapse of the DDL at short separation distances (a repulsive force)
The details of the calculations to find the film or half-separation distance that satisfy all component is often tedious – in subsequent discussion we will show results based the electrostatic repulsive component only (due to its dominance in the clay system of interest here).
The magnitude of this component is a function of clay surface charge density, electrolyte valence and concentration, and potential.
= van der Waals forces (attractive, “short” range)
= hydration force (short range, repulsive)
= electrostatic force (long range, repulsive)

19. The disjoining pressure at equilibrium
van der Waals forces (attractive)
hydration force (repulsive)
As indicated earlier the “engine” behind shrink-swell phenomenon are changes in interlamellar spacing with changes in potential, electrolyte charge density, etc.
The theoretical basis for modeling interactions between charged surfaces in the presence of electrolyte is provided by the DLVO theory using the disjoining pressure as the basic thermodynamic property (or changes in free energy per unit surface area per film thickness -----clarify here!!!)
In equilibrium the chemical potential is composed of three components – the primary source is due to electrostatic repulsion between adjacent DDLs, there are two other short-range forces the van der Waals attractive force and the so-called hydration force that prevents collapse of the DDL at short separation distances (a repulsive force)
The details of the calculations to find the film or half-separation distance that satisfy all component is often tedious – in subsequent discussion we will show results based the electrostatic repulsive component only (due to its dominance in the clay system of interest here).
The magnitude of this component is a function of clay surface charge density, electrolyte valence and concentration, and potential.
electrostatic force (repulsive)

20. Mesopores and their role in volume change
Lamellar swelling alone cannot explain volume changes and water retention in clay fabric.
SEM images show a lamellar network with micropores separating tactoids (quasi- crystalline stacks of lamellas).
Important for modeling clay fabric response.

21. Hydration effects on clay fabric geometry
0.03 bar
SEM images support bulk volume measurements and reveal a lamellar network with micropores between quasi-crystalline stacks of lamellae.
The SEM images show simultaneous evolution of microstructure and bulk volume of Greek Na+ montmorillonite during first drying [Tessier, 1990].
A strong orientation of lamellar structure and micropores (1-2 mm) occurs during drying  anisotropy.
1.0 bar
A Clay mineralogy is very important in determining the activity (in terms of shrink-swell behavior) as well as microstructure; we focus on behavior of smectites or monmorillonite (2:1 layer clays) that are quite abundant and represent an active clay fraction (more than illites and kaolinites)
SEM images reveal a rich three-dimensional arrangement of quasi-crystalline stacks of lamellae (tactoids) forming a network of micropores (1-2 um)
Upon drying of an initially saturated clay sample, the shrinkage in volume is accompanied by strong orientation or the lamellar structure and preferential closure of the micropores.
10 bars

22. Interacting DDL different electrolytes
Ion distribution between two clay surfaces – different electrolytes.
To motivate the construction of a geometrical model for clay fabric we need to understand the basic processes causing swelling.
Observations show that clay lamellar spacing increases with increasing chemical potential (less negative)
The core of the swelling phenomenon and the dominating process is the interactions of DDL – other interactions play a secondary role in clays…
This slide shows that there is reasonable agreement between measurements of lamellae spacing and calculations based on the DDL model that considers electrostatic repulsion.
However, lamellar swelling alone cannot explain observed volume changes and the amount of water retained in clay fabric – evidence show that clay fabric can arrange itself in an open micropore structure due to face-to-edge bonds.

23. Electrolyte effects on microstructure
SEM images (+ scheme) for influences of Ca2+ and Na+ montmorillonite microstructure prepared with dilute solutions [Tessier, 1990].
Electrolyte type and concentration affects:
Arrangement and spacing between layers (smaller for Ca2+), between ordered stacks, and between tactoids.
Number of layers and apparent length of quasi-crystals (tactoids) - more lamellae for Ca2+ (dilute) solutions.
In addition to effects of drying, the type of electrolyte (and concentration) has a strong impact on the extent (width) of the DDL and thus affects clay fabric microstructure.
SEM observations show that the average distance between individual layers is much smaller in Ca2+ montmorillonite relative to Na+ (as expected from DDL behavior).
The number of layers per stack is larger in Ca2+ montmorillonite (55 at bar; 225 at 10 bars; and 400 at 1000 bars) – this is a result of increased face-to-face bonding.
Additionally, because the plates in Ca2+ montmorillonite seem to be more disposed to face-to-face bonding (collapse of the DDL), the stacks that form micropore walls are relatively longer than those that develop in Na+ montomorillonite.

24. Evolution of clay fabric - mesopore formation
Images of uniform Glass beads (40 um):
mixed with 10% dry Na+ Bentonite.
wetting resulted in complete filling of skeletal pore space by jell-like clay fabric.
upon subsequent drying, mesopores are formed between glass beads.
The mixing and distribution of clay domains among other soil textural components remains an open question.
Silt-clay
Mesopores
Sand-clay
An important pore space feature at this microscopic scale is formation of “mesopores” – these are are voids that form between sand or silt grains, they are larger than either interlamellar spaces or typical micropore size in a network of tactoids.
These mesopores form the backbone of the so-called textural pore size of soils.
The example shown here illustrate their formation between uniform glass beads (40um) mixed with 10% bentonite.
The size of these mesopores is proportional to the sand grain size.
[Fies and Bruand, 1998]

25. Clay barriers for waste isolation

26. Clay Liners Clay layers (Bentonite) to prevent leaching
Geotextile layers for mechanical stability

27. Clay Liners
Geotextiles are permeable fabrics (polypropylene, polyesters, etc.) which, when used in association with soil, have the ability to separate, filter, reinforce, protect or drain. Geomembranes are impermeable membranes used widely as cut-offs and liners.

28. Clay Liners

29. Effect of shrink-swell on soil pore volume

30. Shrink-swell affects soil pores at all scales
Microscale
(clay fabric)
Macroscale
(cracks)
Mesoscale (texture)

31. Effect of clay content on porosity & permeability
The critical clay content that completely fills sand-silt skeletal porosity is about 35-40% (and minimum overall porosity).
For more realistic modeling even at the sub-sample scale, we need to consider the presence and influence of other textural classes coexisting in an elementary volume.
In particular, we need to consider effects of different clay contents on overall mixture porosity and on permeability.
Data from geophysical surveys for the petroleum industry show a clear trend of reduction in porosity of the mix towards a critical clay content where the void space formed by the coarse texture is completely filled by the clay fabric. Subsequent increase in the clay content increases the distance between adjacent sand grains that “float” in matrix of clay.
The saturated hydraulic conductivity decreases with increased clay content to critical value, and then rebounds to the value of clay fabric saturated hydraulic conductivity.

32. Modeling clay fabric geometry
Development of an idealized clay fabric representation:
(a) SEM of montmorillonite; (b) approximated clay fabric structure; and (c) idealized clay fabric representation applied in the model
After introduction of the theoretical basis for shrink-swell phenomenon – the second step is to assemble a mathematically tractable geometrical representation of the soil clay fabric.
How do we harness the behavior at the lamellar scale to prediction of changes at the sample scale?
The choices we made in this preliminary study were based on abstraction of direct SEM observations.
For example, in this figure on the right we see an SEM image of motmorillonite from Tessier [1990] and geometrical simplification of the micropore structure
The basic element in the abstraction is the clay fabric unit cell and the potential changes in its geometry with changes in potential.
SEM observations and bulk clay behavior are used to derive and constrain parameter values for the idealized clay fabric.