UNIT I.

BASIC CONCEPTS

I.1 Definitions

Soil mechanics.- Is the science of equilibrium and motion of soils. It is based on the principles
of mechanics and hydraulics to solve engineering problems related to masses of soil.
Soil.- Is a group of particles of different shapes and sizes that can be
disaggregated with the strength of one hand when wet. These particles constitute the
solid phase of the soil and vary over a wide range of sizes, shapes, and constitutive
minerals. They are produced by the mechanical breakdown and chemical decomposition
of rocks.
Rocks are the most abundant material on the Earth’s surface and are divided into
three main categories, igneous, metamorphic, and sedimentary.
Igneous rocks.- They are formed by the cooling and solidification of magma
that emerges or is close enough to the surface. The different types of igneous rocks
depend on the chemical composition of the magma and its rate of cooling.
Sedimentary rocks.- They are formed by compaction, cementation or
crystallization of large deposits of weathered rocks and/with organic matter, through
large periods of time.
Metamorphic rocks.- They are formed by the effect of heat and pressure. This
effect generates a change in the composition and texture of rocks but without melting
the rock into magma. New minerals are formed in these conditions, while existing ones
form the leaf-like texture of rocks.

I.2 Origin and Formation

The process in which rocks are broken down into smaller particles is called weathering. This
phenomenon is produced mainly by the weathering agents such as temperature, ice, rain, wind,
waves, water flow and gravity.
 Mechanical degradation.- It is produced by mechanical agents such as waves,
gravity, water flow, temperature or living organisms that do not affect the chemical
bonds of the structure of the particles. Each weathered particle is a small version of the
parent rock. Mechanical degradation produces gravel, sand and silt.
Chemical degradation.- It appears when the minerals of the parent rock are
affected by chemical reactions, generating new minerals. The main chemical reactions
are oxidation, carbonation and hydration. These reactions occur between minerals, salts,
acids and water. The minerals resulting from the chemical transformation of feldspars,
ferromagnesians and micas are extremely small particles called clays. These particles
show flat shapes and important electrical forces at their surfaces resulting in plastic and
viscoplastic phenomena.
Also, topography and climate influence the type of soil that can be formed in a
certain location. Soils can show homogeneous or heterogeneous particle sizes. A
homogeneous soil shows particles of about the same size. A heterogeneous soil shows
particles of very different sizes.

I.3 Types of Soils

Residual soils.- They are found in the same place where they have been generated. Residual
soils show inherited structures from the parent rock such as exfoliations, joints and fissures. An
important characteristic of residual soils is the weathering profile, which shows a proportional
grading of particle size with depth; the finest grained soil can be commonly found on the surface.
Then, the size of particles increases with depth. Sharp boulders and rocks can be found at greater
depths. Finally, the undisturbed parent rock can be found at the bottom.
Transported soils.- They have been transported to different locations from the
parent rock by air, water, ice or by the force of gravity. These soils are named according
to their location: glacial, moraine, alluvial, fluvial, lacustrine, aeolian and marine.
Types of Transported Soil Deposits
Glacial.- They are formed mainly by the effects of ice and gravity on the parent rock. These
soils are in loose state, usually very heterogeneous, showing high strength and low
compressibility. Big rocks are mixed with coarse gravel and sand.
Moraine.- These soils are formed mainly by the action of avalanches, ice flow,
water flow, rockslides or landslides. These phenomena bring down and deposit material
at the bottom of hills or mountains. The soils are usually heterogeneous, in a loose state,
showing high strength and low compressibility.
Alluvial soils.- They are transported by water and deposited on large planes.
These soils are homogeneously formed by mixtures of sands, silts and clay. They have
medium strength and medium compressibility.

Figure 1.1 Profile showing different types of soils

according to their origin.

Fluvial.- They are transported by rivers and show different sizes of particles depending on their
location with respect to the central line of the river. During flooding the river can carry large
boulders and gravels which are deposited at the banks. During the dry season the velocity of
flow reduces; sand, silt and clay are deposited along the edges of the river depending on the
velocity of flow. The higher the velocity of flow the smaller the size of transported particles. So,
silt and clay are deposited mainly at the center of the river when the flow rate reduces and the
velocity of flow is low.
Lacustrine.- These soils are formed by particles deposited in lakes. They are
homogeneous, formed by mixtures of silt and clay, they show very large compressibility, and low
resistance. The structure of clay aggregates is usually flocculated when deposited in water.
Aeolian.- They are transported by wind. There are two main types: loess, and
dunes. Loess soils are a uniform, cohesive, wind-blown, usually light brown sediment.
 Cohesion in these soils is caused mainly by the presence of calcareous binders or clay
minerals. The loess type has the ability to stand on nearly vertical slopes. Dunes are
mounds of fine sand formed by the wind. They are very common in deserts and
coastlines. This soil is mainly formed by quartz sands showing low compressibility and
high resistance.
Marine.- They are transported by ocean waves and tides, and are mainly
homogeneous, stratified and of medium compressibility and resistance. This material is
stratified by layers of sand, silt and clay.
Organic.- They are top soils formed by solid particles of different sizes mixt
with plant roots, microfossils, animal carcasses and soot. Generally, these soils are dark
in color, have a characteristic smell and present gaseous by product. They show low
permeability, very high compressibility and very low strength.

I.4 Constitutive Minerals

A mineral is defined as an inorganic material, showing a unique internal structure. Its chemical
composition is very stable, and its mechanical properties are constant. The most important
physical properties are color, crystalline shape, relative density, hardness, luster, tenacity, fracture
shape, disposition plane and the capacity to allow radiation to pass through.
Soil classification.- The predominant size of particles that form the soil is
considered to define the type of soil. The three main classifications are gravel, sand, silt
and clay. Several organizations have developed classification systems based on the size
of particles. One of the most used and accepted is the USCS (Unified Soil Classification
System). Table 1.1 shows the particle size ranges for the classification of soils.
Coarse-grained soils (gravel and sand).- The mechanical and hydraulic
behavior of coarse-grained soils depend mainly on the structure and orientation of their
particles. Their particle size varies from 75 mm to 0.075 mm. The more important
constitutive minerals in coarse soils are:
a) silicates, such as feldspars, micas and olivine;
b) oxides, such as quartz (SiO2), siltstone and magnetite;
c) carbonates, such as calcite and dolomite and
d) sulfates, such as gypsum, anhydrates.
Fine-grained soils.- The mechanical behavior of silts and clays, unlike coarse
soils, is strongly influenced by their particular mineral composition.
Clays are mainly composed of complex aluminum silicates, which present two
basic units: silica tetrahedron and alumina octahedron. A tetrahedral silica unit consists
of four oxygen atoms surrounding a silicon atom, as shown in Figure 1.2a. The
octahedral alumina unit consists of six hydroxyls surrounding an aluminum atom as
shown in Figure 1.2b.
The combination of tetrahedral silica units gives a silica sheet, and the
combination of octahedral alumina hydroxyl units gives an octahedral sheet, also called
gibbsite sheet.
The specific piling of silica and alumina sheets generates the different clay
minerals.

Table 1.1 Unified Soil Classification System, particle size ranges and symbols.

Soil fraction or
Symbol Size Range
component

Boulders None Greater than 300 mm

Cobbles None 75 mm to 300 mm
(1) Coarse soils:
Gravel Coarse 75 mm to 19 mm
G
Fine 19 mm to No. 4 sieve (4.75 mm)
Sand Coarse No. 4 (4.75 mm) to No. 10 (2.0 mm)
Medium No. 10 (2.0 mm) to No. 40 (0.425 mm)
Fine Less than No. 200 sieve (0.075 mm)
(2) Fine soils:
Silt M (No specific grain size - Atterberg limits)
Clay C (No specific grain size - Atterberg limits)
(3) Organic soils: O (No specific grain size)
(4) Peat: Pt (No specific grain size)
 a) Silica Tetrahedron b) Alumina Octahedron (Gibbsite)
Figure 1.2 Main constituents of clays.

Primary Bonds
a) Ionic bonds.- In this case, electrons are transferred from one atom to another (Na+ Cl-
) to reach the required number of electrons in their last orbit to become stable;
b) Covalent bonds.- Here, electrons are shared by two different atoms (H2O) in order to
complete their last orbit;
c) Hydrogen bonds.- In this case, one atom of hydrogen can be combined with oxygen,
flour or nitrogen, where the hydrogen transfers its single electron to the other atom.
These links are weaker than the ionic and covalent bonds and can be found between the
octahedral and tetrahedral sheets of clay.
Secondary Bonds
a) Van der Waals electrical forces (Water dipole, H2O).- They can be found between
different basic units of clays that form a single particle. In such a case, the number of
layers of molecules of water can increase between the platelets of basic units, producing
the expansion of clays.

Types of Clay
 Kaolinite.- It is formed by the piling of a silica with a gibbsite sheet. The layers are held
together by hydrogen bonding. Among the three main clay minerals described here, kaolinite is
the most stable.
Illite.- It consists of a gibbsite sheet between two silica sheets. It is also called clay mica.
Illite layers are bonded by potassium ions. Some siliceous atoms substitute aluminum atoms in
the tetrahedral sheets. Illite tends to form lumps and shows low expansion when saturated.
Montmorillonite.- It has the same structure as illite: a gibbsite between two silica sheets.
Some atoms of aluminum are substituted by magnesium and iron in the octahedral sheets.
Potassium is not present; however, a large amount of water is attracted into the interlayer spaces.
Because of this, montmorillonite exhibits large expansion when saturated. Bentonite is a type
of montmorillonite produced by chemical breakdown of volcanic ashes. As montmorillonite, it
shows large expansion.

Figure 1.3 Atomic structure of kaolinite.

 Figure 1.4 Atomic structure of illite.

Figure 1.5 Atomic structure of montmorillonite.

I.5 Molecular Structure

The most important characteristic of clays is their mineralogical composition. Clays are primarily
differentiated from silts because of the size and shape of their particles. Clays are formed by
particles smaller than 0.002 mm. These particles show a flat shape: small thickness compared
with the other two dimensions. Because of the presence of oxygen atoms on top and at the
bottom of clay particles, they show important electrical negative charges on their surface, while
on the edges it has positive charges. In that sense, gravity forces are negligible when compared
with electrical forces. In clay particles, the influence of electrical forces is predominant over
gravity forces.
Specific Surface.- From the combination of alumina and silica sheets, the
different clay minerals such as kaolinite, illite, montmorillonite, halloysite, bentonite, etc.
are formed showing mainly negative surface charges. Thickness of different minerals
may vary from 0.001 to 0.01 mm and their lateral dimensions from 0.1 to 2 m. The
specific surface is defined as the surface area of soil particles by unit mass. Common
values of specific surface for different soils are presented in Table 1.2.
 Table 1.2 Specific surface for different soils.
Mineral Se (m2/g)
Sand ** 0.2
Halloysite + 35 to 70
Montmorillonite + Up to 800
Kaolinite + 5 to 15
Illite + 80
+ Secondary consolidation is more important than primary
** Secondary consolidation is negligible

Cation Exchange Capacity (CEC).- It is a quantitative measure of the negative charges in the
soil. The larger the CEC, the larger the quantity of cations that the soil can hold. CEC represents
the quantity of positive ions (cations) that a clay mineral accommodates on its negatively charged
surface. It is measured in miliequivalent per gram (meq/gr). One equivalent is the atomic weight
of the element divided by its electrical charge.

Table 1.3 Cation Exchange Capacity of Principal Clay Minerals.

Mineral Cation Exchange Capacity

(meq/g)
Kaolinite 0.03-0.1
Illite 0.2-0.3
Chlorite 0.2-0.3
Attapulgite 0.2-0.35
Hydrated halloysite 0.4-0.5
Montmorillonite 0.8-1.2

Due to the negative electrical charges on their particle surface, water is strongly attracted by clay
minerals. Water molecules are electrical dipoles, meaning that they have both positive and
negative electrical charges. Therefore, water molecules can intrude between the van der Waals
links. In general, water will be found attached to all clay particles in the form of adsorbed water
layers. On the surface of the particle, some molecules of water can be found in dense state due
to the strong attraction forces between water and clay particles. Pressures in adsorbed water
layers can reach values of about 1000 MPa, generating a viscous water layer with a maximum
thickness of 0.1 m. Farther away from the particle surface, free water can be found. The
adsorbed viscous water layer generates the phenomena of plasticity and secondary consolidation
in clays. CEC greatly depends on the pH of the soil. Neutral soils have larger CEC than acid
soils.
Plasticity.- It is the ability of a soil to retain water and deform without fissuring
or cracking. This parameter is an indirect measure of the amount of fines present in the
soil. Clays show plasticity because of the presence of adsorbed water layers and the large
electrical forces on their surface. Sands, unlike clays, show no plasticity due to the
absence of adsorbed water
When clays are unsaturated, their strength is produced by two phenomena:
friction and cohesion.
Cohesion is the effect of water menisci on the strength of soils. These menisci
appear mainly at the contact between solid particles. Clays show large cohesive forces
while sands exhibit low cohesion.
The strength of sands is due mainly to friction forces with a small contribution
of cohesion when unsaturated. Their structure is generated as a result of loading and the
corresponding relative displacement between particles. When loose sands are subjected
to high loads and vibration or water flow occurs, their structure breaks down and large
volumetric strains occur. This phenomenon is called soil liquefaction.
Flocculation.- The flat particles of clay repel each other when they meet face to
face if no positive ions are in between to generate electrical attraction. These positive
ions diluted in the adsorbed water layer form the so called diffuse double layer. The
density of positive ions reduces as the distance from the particle surface increases.
Therefore, at some distance from the surface of the particle, the attraction forces tend
to disappear. Instead, particles will be held together by electrostatic forces when they
meet edge to face. This is so because the positively charged edges are attracted by the
negatively charged faces, as gravity forces are negligible. This phenomenon is called
flocculation, and packages of flocculated particles are called flocs, peds or aggregates.
When the flocs become large enough in the presence of water, they settle by gravity
forming layers of clay.
 However, it is very difficult to find a natural deposit of pure clay. In general,
grains of sand and silt with clay particles form a mixture that is named according to the
largest percentage of material found in the sample. So, when the largest percent of
material is represented by particles with sizes smaller than 0.002 mm it is called clay.
Ordinary clays.- They have, as it is presented here, a flocculated or aggregated
structure because of the electrochemical attraction forces between particles.
Dispersive clays.- These materials show repulsive electrochemical forces in the
presence of water, tending to destroy the aggregates and form single particle-structures.
This behavior is explained in Figure 1.6.

Figure 1.6 Attraction and repulsion forces for different soils.

I.6 Methods for Identification of Clay Minerals
X-Ray diffraction.- First, the soil is hardened by introducing a resin into its pores. Then, it is
cut in thin slices. Subsequently, X-Rays are shot against these thin slices of soil. Later, the angle
of refraction of these rays is measured when they cross the soil sample. And finally, a graph
showing the frequency of refracted rays against the angle of diffraction allows identifying the
types of minerals present in the soil sample.
Chemical analysis.- In this method, different active chemical products are
added to the clay sample. The effects of these products on specific minerals are already
known. Therefore, this reaction allows identifying different minerals present in the soil.
Thermo-gravimetric analysis.- This method consists on measuring the
physical and chemical changes produced in a soil sample when subjected to an increase
 in temperature. The interpretation of the response of the soil permits the identification
of its minerals.
Differential Thermal Analysis (DTA).- It is a method in which the sample
and an inert reference material are heated up to 1 000 °C over a period of time. Then,
the difference in temperature between these two materials with the temperature in the
oven leads to the identification of minerals present in the soil.

I.7 Shapes of Soil Particles

As previously mentioned, the shape of particles influences the mechanical behavior of soils.
Coarse-grained soils.- For sands and gravels, the shape of grains has influence on its
void ratio, structure, internal friction angle and permeability, among other properties.
Gravel.- It commonly consists of hard rock fragments composed of one or more
minerals. These fragments may be angular, subangular, rounded or subrounded. They may be
freshly exposed or show signs of considerable weathering therefore, they can be stiff or crumbly.
Sands.- They are made of small particles of rock where quartz is one of their main
constituents. The individual grains may be angular, subangular or rounded. Some sands contain
a fairly high percentage of mica flakes that make them very elastic or springy.
Angular shapes are mostly formed by mechanical breakdown of large boulders and rocks.
Depending on the time of exposition and intensity of the weathering agents, subangular and
rounded shapes can be produced over time. Residual and marine sands as well as volcanic ashes
present typically angular mineral shapes. Eolic sands tend to have finer and more rounded shape
particles. In general, the strength and stiffness of soils reduces with grain size.
Fine-grained soils.- In the fine fraction, where solids range from 0.07 mm to about 0.1
μm (1μm=0.001 mm), a single particle usually consists of a single mineral. The particles may be
flake-shaped or tubular. Rounded particles, however, are conspicuously absent.
Clay minerals.- They are mostly laminar, mening that two dimensions of the particle
are much greater than the other. Angular shape is also present but far more rare, this shape
consists of one dimension much bigger than the other two. Exceptionally, the fine fraction
contains a high percentage of porous fossils, such as diatoms, that are a major group of
microalgae. These algae is the most common type of phytoplankton or radiolarian and is defined
as marine protozoan, having rigid siliceous skeletons and spicules. These characteristics produce
abnormal mechanical properties in fine soils.
Table 1.4 Specific gravity of some common minerals.
Mineral Specific gravity, Gs
Quartz 2.65
Kaolinite 2.6
Illite 2.8
Montmorillonite 2.65-2.80
Halloysite 2.0-2.55
Potassium feldspar 2.57
Sodium and calcium feldspar 2.62-2.76
Chlorite 2.6-2.9
Biotite 2.8-3.2
Muscovite 2.76-3.1
Homblende 3.0-3.47
Limonite 3.6-4.0
Olivine 3.27-3.7

Specific gravity of solids.- It is defined as the ratio of the volumetric weight of a given material
to the volumetric weight of water. The specific gravity of soil is needed for the determination of
their volumetric and gravimetric parameters.
The specific gravity of solids of light-colored sand, which is mostly made of quartz, may
be estimated to be about 2.65. Soils with plenty of iron may present values of 3; for clayey and
silty soils, it may vary from 2.6 to 2.9. Volcanic clays as the ones present in the Mexico City
Valley have values between 2.2 and 2.6.

I.8 Soil Structure

Soil structure is the particular geometric arrangement of solid particles in the material. The
shape, size and mineralogical composition of soil particles, as well as the chemical composition
of trapped water, among others factors, affect the structure of the soil. In general, soils can be
divided in two large groups: cohesionless and cohesive.
Structures of Cohesionless Soils
The structure generally found in cohesionless soils can be divided into two major groups: single-
grained and honeycombed.
Single-grained structures.- In this case, soil particles are in stable positions, with each
particle in contact with the surrounding ones. The shape and grain size distribution of the soil
as well as their relative arrangement influence the density of the material. Thus, a wide range of
void ratios is possible for the same grain size distribution. These materials may show a loose or
dense structure.

Figure 1.7 Loose and dense structure for sand.

Honeycombed structures.- In this case, relatively fine sand and/or silt form small rings with
chains of particles. In the contacts between particles, carbonates, electrical forces and water
menisci give the stiffness required for this arrangement. Soils exhibiting a honeycombed
structure have large void ratios, and they can carry low static loads. However, under heavy loads,
or when subjected to dynamic loading, the structure breaks down, resulting in large settlements.

Figure 1.8 Honeycombed structure.

Structure of Cohesive Soils

When clay particles are initially suspended in pure water, they repel each other because of the
absence of positive ions. This repulsion occurs because of the negatively charged surfaces of clay
particles (van der Waals forces). The force of gravity on these particles is negligible. Thus, in the
presence of water, the individual particles settle at a slow rate. In some cases they remain in
suspension during a long time, undergoing Brownian motion (a random zigzag motion of
colloidal particles in suspension).
When sediment formed in water by the settling of the individual particles, it shows a
dispersed structure. In such a case, all particles are oriented more or less parallel to one another.
This arrangement is presented in Figure 1.9 (a).
If clay particles, initially dispersed in water, come close to another during random
motion, they might aggregate into visible flocs with edge-to-face contact. At this moment,
particles are held together by electrostatic attraction between positively charged edges with
negatively charged faces. This aggregation is known as flocculation. When the flocs become
large, they settle under the force of gravity. The sediment formed in this way has a flocculent
structure as shown in Figure 1.9 (b).
Flocculated clays are lightweight and show high void ratios. Clay deposits formed in the
seas are highly flocculated. Most of the sediment deposits formed in freshwater possess an
intermediate structure between dispersed and flocculated.

Figure 1.9 Types of structure for clays, a) dispersive, b) flocculated without salt and c)
flocculated in presence of salt.

There is yet another structure for clays when salt is present. Salt ions tend to depress the double
layer around the particles, this phenomenon reduces the interparticle repulsion forces allowing
particles to attract each other and form aggregates. Finally, these aggregates settle with time. This
structure shows a high degree of parallelism as shown in Figure 1.9(c).
Scans with electron microscope have shown that clay particles tend to be
flocculate in submicroscopic units called domains. These domains group together to
form clusters which then regroup again to form aggregates or peds. Peds can be seen
without a microscope. Batches of peds have macrostructural features such as cracks and
fissures. Arrangement of peds, domains and clusters are shown in Figure 1.10.
 Figure 1.10 Macro and microstructure of soils.

I.9 Thixotropy and Sensitivity

Thixotropy is defined as an isothermal, reversible, and time-dependent process occurring under
constant volumetric conditions and water composition. This phenomenon occurs because clays
stiffen at rest because electrical links increase. These links can be broken by remolding the soil.
Montmorillonitic clays show this property most frequently, as they lose significant strength when
remolding but recover it with time.
The remolding of thixotropic clays causes an abrupt drop in pore water tension (increase
in pore water pressure) followed by slow regain during periods at rest. A way to determine the
degree of thixotropy of a clay is by determining its remolded liquid limit first and then once again
some minutes later. If this clay presents thixotropy, the second liquid limit shows higher avlues
than the first one.
Terzaghi measured thixotropy through clay sensitivity. Sensitivity (St) is defined as the
ratio of the peak undisturbed strength of the soil versus the remolded strength, as determined by
an unconfined compression test.
Most clays sensitivity values range from 1 to 8. Some highly flocculent marine clay
deposits, or previously glaciated zones have sensitivity values ranging from 10 to 80.

𝑞𝑢(𝑢𝑛𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑒𝑑)
𝑆𝑡 = …………………………………………….(1.1)
𝑞𝑢(𝑟𝑒𝑚𝑜𝑙𝑑𝑒𝑑)
Figure 1.11 Clay behavior through time of a thixotropic material.

Table 1.5 Values of sensitivity

Type of Soil Sensitivity (St)
Insensitive clays ~ 1
Slightly sensitive clays 1–2
Medium sensitive
clays 2–4
Very sensitive clays 4–8
Slightly quick clays 8 – 16
Medium quick clays 16 – 32
Very quick clays 32 – 64
Extra quick clays > 64