Introduction to Soil Mechanics
The term "soil" can have different meanings, depending upon the field in
which it is considered. To a geologist, it is the material in the relative thin
zone of the Earth's surface within which roots occur, and which are formed as
the products of past surface processes. The rest of the crust is grouped under
the term "rock".
To a pedologist, it is the substance existing on the surface, which supports
plant life. To an engineer, it is a material that can be: built
on: foundations of buildings, bridges
built in: basements, culverts, tunnels
built with: embankments, roads, dams
supported: retaining walls
Soil Mechanics is a discipline of Civil Engineering involving the study of
soil, its behaviour and application as an engineering material. Soil Mechanics
is the application of laws of mechanics and hydraulics to engineering problems
dealing with sediments and other unconsolidated accumulations of solid
particles, which are produced by the mechanical and chemical disintegration of
rocks, regardless of whether or not they contain an admixture of organic
constituents.
Soil consists of a multiphase aggregation of solid particles, water, and
air. This fundamental composition gives rise to unique engineering properties,
and the description of its mechanical behavior requires some of the most classic
principles of engineering mechanics.
Engineers are concerned with soil's mechanical properties: permeability,
stiffness, and strength. These depend primarily on the nature of the soil
grains, the current stress, the water content and unit weight.
Formation of Soils: In the Earth's surface, rocks extend upto as much as 20 km
depth. The major rock types are categorized as igneous, sedimentary, and
metamorphic.
Igneous rocks: formed from crystalline bodies of cooled magma.
Sedimentary rocks: formed from layers of cemented sediments.
Metamorphic rocks: formed by the alteration of existing rocks due to heat
from igneous intrusions or pressure due to crustal movement.
Soils are formed from materials that have resulted from the disintegration
of rocks by various processes of physical and chemical weathering. The nature
and structure of a given soil depends on the processes and conditions that
formed it:
Breakdown of parent rock: weathering, decomposition, erosion.
Transportation to site of final deposition: gravity, flowing water, ice, wind.
Environment of final deposition: flood plain, river terrace, glacial moraine,
lacustrine or marine.
Subsequent conditions of loading and drainage:
little or no surcharge, heavy surcharge due to ice or overlying deposits, change
from saline to freshwater, leaching, contamination.
All soils originate, directly or indirectly, from different rock types.
Physical weathering reduces the size of the parent rock material,
without any change in the original composition of the parent rock. Physical or
mechanical processes taking place on the earth's surface include the actions of
water, frost, temperature changes, wind and ice. They cause disintegration and
the products are mainly coarse soils.
The main processes involved are exfoliation, unloading, erosion, freezing,
and thawing. The principal cause is climatic change. In exfoliation, the outer
shell separates from the main rock. Heavy rain and wind cause erosion of the
rock surface. Adverse temperarture changes produce fragments due to different
thermal coefficients of rock minerals. The effect is more for freeze-thaw
cycles.
Chemical weathering not only breaks up the material into smaller particles
but alters the nature of the original parent rock itself. The main processes
responsible are hydration, oxidation, and carbonation. New compounds are formed
due to the chemical alterations.
Rain water that comes in contact with the rock surface reacts to form
hydrated oxides, carbonates and sulphates. If there is a volume increase, the
disintegration continues. Due to leaching, water-soluble materials are washed
away and rocks lose their cementing properties.
Chemical weathering occurs in wet and warm conditions and consists of
degradation by decomposition and/or alteration. The results of chemical

weathering are generally fine soils with altered mineral grains.
The effects of weathering and transportation mainly determine the
basic nature of the soil (size, shape, composition and distribution of the
particles).
The environment into which deposition takes place, and the subsequent
geological events that take place there, determine the state of the soil
(density, moisture content) and the structure or fabric of the soil (bedding,
stratification, occurrence of joints or fissures)
Transportation agencies can be combinations of gravity, flowing water or
air, and moving ice. In water or air, the grains become sub-rounded or rounded,
and the grain sizes get sorted so as to form poorly-graded deposits. In moving
ice, grinding and crushing occur, size distribution becomes wider forming wellgraded deposits.
In running water, soil can be transported in the form of suspended
particles, or by rolling and sliding along the bottom. Coarser particles settle
when a decrease in velocity occurs, whereas finer particles are deposited
further downstream. In still water, horizontal layers of successive sediments
are formed, which may change with time, even seasonally or daily.
Wind can erode, transport and deposit fine-grained soils. Wind-blown soil is
generally uniformly-graded.
A glacier moves slowly but scours the bedrock surface over which it
passes.
Gravity transports materials along slopes without causing much
alteration.
Soil Types: Soils as they are found in different regions can be classified into
two broad categories:
(1) Residual soils
(2) Transported soils
Residual Soils: Residual soils are found at the same location where they have
been formed. Generally, the depth of residual soils varies from 5 to 20 m.
Chemical weathering rate is greater in warm, humid regions than in cold,
dry regions causing a faster breakdown of rocks. Accumulation of residual soils
takes place as the rate of rock decomposition exceeds the rate of erosion or
transportation of the weathered material. In humid regions, the presence of
surface vegetation reduces the possibility of soil transportation.
As leaching action due to percolating surface water decreases with
depth, there is a corresponding decrease in the degree of chemical weathering
from the ground surface downwards. This results in a gradual reduction of
residual soil formation with depth, until unaltered rock is found.
Residual soils comprise of a wide range of particle sizes, shapes and
composition.
Transported Soils: Weathered rock materials can be moved from their
original site to new locations by one or more of the transportation agencies to
form transported soils. Tranported soils are classified based on the mode of
transportation and the finaldeposition environment.
(a) Soils that are carried and deposited by rivers are called alluvial deposits.
(b) Soils that are deposited by flowing water or surface runoff while entering a
lake are called lacustrine deposits.Atlernate layers are formed in different
seasons depending on flow rate.
(c) If the deposits are made by rivers in sea water, they are
called marine deposits. Marine deposits contain both particulate material
brought from the shore as well as organic remnants of marine life forms.
(d) Melting of a glacier causes the deposition of all the materials scoured by
it leading to formation of glacial deposits.
(e) Soil particles carried by wind and subsequently deposited are known
as aeolian deposits.
Phase Relations of Soils: Soil is not a coherent solid material like steel and
concrete, but is a particulate material. Soils, as they exist in nature, consist
of solid particles (mineral grains, rock fragments) with water and air in the
voids between the particles. The water and air contents are readily changed by
changes in ambient conditions and location.
As the relative proportions of the three phases vary in any soil deposit,
it is useful to consider a soil model which will represent these phases
distinctly and properly quantify the amount of each phase. A schematic diagram
of the three-phase system is shown in terms of weight and volume symbols

respectively for soil solids, water, and air. The weight of air can be
neglected.
The soil model is given dimensional values for the solid, water and air
components.
Total volume, V = Vs + Vw + Vv
Three-phase System:
Soils can be partially saturated (with both air and water
present), or be fully saturated (no air content) or be perfectly dry (no water
content).
In a saturated soil or a dry soil, the three-phase system thus reduces to
two phases only, as shown.
For the purpose of engineering analysis and design, it is necessary to
express relations between the weights and the volumes of the three phases.
The various relations can be grouped into:
Volume relations
Weight relations
Inter-relations
Volume Relations
As the amounts of both water and air are variable, the volume of solids is taken
as the reference quantity. Thus, several relational volumetric quantities may be
defined. The following are the basic volume relations:
1. Void ratio (e) is the ratio of the volume of voids (Vv) to the volume of soil
solids (Vs), and is expressed as a decimal.
2. Porosity (n) is the ratio of the volume of voids to the total
volume of soil (V ), and is expressed as a percentage.
Void ratio and porosity are inter-related to each other as follows:
and
3. The volume of water (Vw) in a soil can vary between zero (i.e. a dry soil)
and the volume of voids. This can be expressed as the degree of saturation
(S) in percentage.
For a dry soil, S = 0%, and for a fully saturated soil, S = 100%.
4. Air content (ac) is the ratio of the volume of air (Va) to the volume of
voids.
5. Percentage air voids (na) is the ratio of the volume of air to the total
volume.
Weight Relations:
Density is a measure of the quantity of mass in a unit
volume of material. Unit weight is a measure of the weight of a unit volume of
material. Both can be used interchangeably. The units of density are ton/m³,
kg/m³ or g/cm³. The following are the basic weight relations:
1. The ratio of the mass of water present to the mass of solid particles is
called the water content (w), or sometimes the moisture content.
Its value is 0% for dry soil and its magnitude can exceed 100%.
2. The mass of solid particles is usually expressed in terms of their particle
unit weight or specific gravity (Gs) of the soil grain solids .
where = Unit weight of water
For most inorganic soils, the value of Gs lies between 2.60 and 2.80. The
presence of organic material reduces the value of Gs.
3. Dry unit weight is a measure of the amount of solid particles per unit
volume.
4. Bulk unit weight is a measure of the amount of solid particles plus water per
unit volume.
5. Saturated unit weight is equal to the bulk density when the total voids is
filled up with water.
6. Buoyant unit weightor submerged unit weight is the effective mass per unit
volume when the soil is submerged below standing water or below the ground water
table.
Inter-Relations: It is important to quantify the state of a soil
immediately after receiving in the laboratory and prior to commencing other
tests. The water content and unit weight are particularly important, since they
may change during transportation and storage.
Some physical state properties are calculated following the practical

measurement of others. For example, dry unit weight can be determined from bulk
unit weight and water content. The following are some inter-relations:
Worked Examples
Example 1: A soil has void ratio = 0.72, moisture content = 12% and Gs= 2.72.
Determine its
(a) Dry unit weight (b) Moist unit weight, and the
(c) Amount of water to be
added per m3 to make it saturated.
Solution:
Soil Classification
It is necessary to adopt a formal system of soil description and
classification in order to describe the various materials found in ground
investigation. Such a system must be meaningful and concise in an engineering
context, so that engineers will be able to understand and interpret.
It is important to distinguish between description and classification:
Description of soil is a statement that describes the physical nature and state
of the soil. It can be a description of a sample, or a soil in situ. It is
arrived at by using visual examination, simple tests, observation of site
conditions, geological history, etc.
Classification of soil is the separation of soil into classes or groups each
having similar characteristics and potentially similar behaviour. A
classification for engineering purposes should be based mainly on mechanical
properties: permeability, stiffness, strength. The class to which a soil belongs
can be used in its description.
The aim of a classification system is to establish a set of conditions which
will allow useful comparisons to be made between different soils. The system
must be simple. The relevant criteria for classifying soils are the size
distributionof particles and the plasticity of the soil.
Particle Size Distribution:
For measuring the distribution of particle
sizes in a soil sample, it is necessary to conduct different particle-size
tests.
Wet sieving is carried out for separating fine grains from coarse grains
by washing the soil specimen on a 75 micron sieve mesh.
Dry sieve analysis is carried out on particles coarser than 75 micron.
Samples (with fines removed) are dried and shaken through a set of sieves of
descending size. The weight retained in each sieve is measured. The cumulative
percentage quantities finer than the sieve sizes (passing each given sieve size)
are then determined.
The resulting data is presented as a distribution curve with grain size along xaxis (log scale) and percentage passing along y-axis (arithmetic scale).
Sedimentation analysis is used only for the soil fraction finer than 75
microns. Soil particles are allowed to settle from a suspension. The decreasing
density of the suspension is measured at various time intervals. The procedure
is based on the principle that in a suspension, the terminal velocity of a
spherical particle is governed by the diameter of the particle and the
properties of the suspension.
In this method, the soil is placed as a suspension in a jar filled with
distilled water to which a deflocculating agent is added. The soil particles are
then allowed to settle down. The concentration of particles remaining in the
suspension at a particular level can be determined by using a hydrometer.
Specific gravity readings of the solution at that same level at different time
intervals provide information about the size of particles that have settled down
and the mass of soil remaining in solution.
The results are then plotted between % finer (passing) and log size.
Grain-Size Distribution Curve: The size distribution curves, as
obtained from coarse and fine grained portions, can be combined to form one
completegrain-size distribution curve (also known as grading curve). A typical
grading curve is shown.
From the complete grain-size distribution curve, useful information can be
obtained such as:
1. Grading characteristics, which indicate the uniformity and range in
grain-size distribution.
2. Percentages (or fractions) of gravel, sand, silt and clay-size.

Grading Characteristics: A grading curve is a useful aid to soil description.
The geometric properties of a grading curve are called grading characteristics.
To obtain the grading characteristics, three points are located first on the
grading curve.
D60 = size at 60% finer by weight ; D30 = size at 30% finer by weight
D10 =
size at 10% finer by weight
The grading characteristics are then determined as follows:
1. Effective size = D10; 2. Uniformity coefficient,
3. Curvature
coefficient, Both Cuand Cc will be 1 for a single-sized soil.
Cu >
5 indicates a well-graded soil, i.e. a soil which has a distribution of
particles over a wide size range.
Cc between 1 and 3 also indicates a wellgraded soil.
Cu < 3 indicates a uniform soil, i.e. a soil which has a very
narrow particle size range.
Consistency of Soils:
The consistency of a fine-grained soil refers to its
firmness, and it varies with the water content of the soil. A gradual increase
in water content causes the soil to change from solid to semisolid to plastic to liquid states. The water contents at which the consistency
changes from one state to the other are called consistency limits (orAtterberg
limits).
The three limits are known as the shrinkage limit (WS), plastic limit (WP),
and liquid limit (WL) as shown. The values of these limits can be obtained from
laboratory tests.
Two of these are utilised in the classification of fine soils:
Liquid limit (WL) - change of consistency from plastic to liquid state
Plastic limit (WP) - change of consistency from brittle/crumbly to plastic state
The difference between the liquid limit and the plastic limit is known as
the plasticity index (IP), and it is in this range of water content that the
soil has a plastic consistency. The consistency of most soils in the field will
be plastic or semi-solid.
Indian Standard Soil Classification System
Classification Based on Grain Size: The range of particle sizes encountered in
soils is very large: from boulders with dimension of over 300 mm down to clay
particles that are less than 0.002 mm. Some clays contain particles less than
0.001 mm in size which behave as colloids, i.e. do not settle in water.
In the Indian Standard Soil Classification System (ISSCS), soils are classified
into groups according to size, and the groups are further divided into coarse,
medium and fine sub-groups.
The grain-size range is used as the basis for grouping soil particles into
boulder, cobble, gravel, sand, silt or clay.
Very coarse soils Boulder size > 300 mm Cobble size 80 - 300 mm Coarse soils
Gravel size (G) Coarse 20 - 80 mm Fine 4.75 - 20 mm Sand size (S) Coarse 2 4.75 mm
Medium 0.425 - 2 mm Fine 0.075 - 0.425 mm
Fine soils Silt size (M) 0.002 0.075 mm Clay size (C) < 0.002 mm
Gravel, sand, silt, and clay are
represented by group symbols G, S, M, and C respectively.
Physical weathering produces very coarse and coarse soils. Chemical
weathering produce generally fine soils.
Coarse-grained soils are those for which more than 50% of the soil
material by weight has particle sizes greater than 0.075 mm. They are basically
divided into either gravels (G) or sands (S).
According to gradation, they are further grouped as well-graded (W) or poorly
graded (P). If fine soils are present, they are grouped as containing silt fines
(M) or as containing clay fines (C).
For example, the combined symbol SW refers to well-graded sand with no fines.
Both the position and the shape of the grading curve for a soil can aid in
establishing its identity and description. Some typical grading curves are
shown.

Curve A - a poorly-graded medium SAND
Curve B - a well-graded GRAVEL-SAND (i.e. having equal amounts of gravel and
sand)
Curve C - a gap-graded COBBLES-SAND
Curve D - a sandy SILT
Curve E - a silty CLAY (i.e. having little amount of sand)
Fine-grained soils are those for which more than 50% of the material has
particle sizes less than 0.075 mm. Clay particles have a flaky shape to which
water adheres, thus imparting the property of plasticity.
A plasticity chart , based on the values of liquid limit (WL) and
plasticity index (IP), is provided in ISSCS to aid classification. The 'A'
line in this chart is expressed as IP = 0.73 (WL - 20).
Depending on the point in the chart, fine soils are divided into clays
(C), silts (M), or organic soils (O). The organic content is expressed as a
percentage of the mass of organic matter in a given mass of soil to the mass of
the dry soil solids.Three divisions of plasticity are also defined as follows.
Low plasticity WL< 35%
Intermediate plasticity 35% < WL< 50%
High
plasticity WL> 50%
The 'A' line and vertical lines at WL equal to 35% and 50% separate the
soils into various classes. For example, the combined symbol CH refers to clay
of high plasticity.
Soil classification using group symbols is as follows:
Group Symbol Classification
Coarse soils GW: Well-graded GRAVEL GP ; Poorly-graded GRAVEL GM; Silty GRAVEL
GC:
Clayey GRAVEL SW: Well-graded SAND SP:
poorly-graded SAND SM : Silty
SAND SC: Clayey SAND Fine soils ML SILT of low plasticity MI: SILT of
intermediate plasticity MH: SILT of high plasticity
CL CLAY of low
plasticity: CI CLAY of intermediate plasticity CH; CLAY of high plasticity OL
Organic soil of low plasticity OI: organic soil of intermediate plasticity OH:
organic soil of high plasticity
Pt Peat
Activity: "Clayey soils" necessarily do not consist of 100% clay size
particles. The proportion of clay mineral flakes (< 0.002 mm size) in a fine
soil increases its tendency to swell and shrink with changes in water content.
This is called the activity of the clayey soil, and it represents the degree of
plasticity related to the clay content.
Activity = (PIasticity index) /(%
clay particles by weight)
Classification as per activity is:
Activity Classification <
0.75 Inactive 0.75 - 1.25 Normal > 1.25 Active
Liquidity Index: In fine soils, especially with clay size
content, the existing state is dependent on the current water content (w) with
respect to the consistency limits (or Atterberg limits). The liquidity index
(LI) provides a quantitative measure of the present state.
Classification as per liquidity index is:
Liquidity index Classification
> 1 Liquid 0.75 - 1.00 Very soft 0.50 - 0.75
Soft 0.25 - 0. 50 Medium stiff 0 - 0.25 Stiff < 0 Semi-solid
Visual Classification: Soils possess a number of physical characteristics which
can be used as aids to identification in the field. A handful of soil rubbed
through the fingers can yield the following:
SAND (and coarser) particles are visible to the naked eye.
SILT particles become dusty when dry and are easily brushed off hands.
CLAY particles are sticky when wet and hard when dry, and have to be
scraped or washed off hands.
Worked Example
The following test results were obtained for a fine-grained soil:
WL=
48% ; WP = 26%
Clay content = 55%
Silt content = 35%
Sand content
= 10%
In situ moisture content = 39% = w
Classify the soil, and
determine its activity and liquidity index
Solution:
Plasticity index, IP = WL– WP = 48 – 26 = 22%
Liquid limit lies between 35%
and 50%.
According to the Plasticity Chart, the soil is classified as CI, i.e. clay

of intermediate plasticity.
Liquidity index , = = 0.59
The clay is of normal activity and is of soft consistency.
Formation of Clay Minerals: A soil particle may be a mineral or a rock fragment.
A mineral is a chemical compound formed in nature during a geological process,
whereas a rock fragment has a combination of one or more minerals. Based on the
nature of atoms, minerals are classified as silicates, aluminates, oxides,
carbonates and phosphates.
Out of these, silicate minerals are the most
important as they influence the properties of clay soils. Different arrangements
of atoms in the silicate minerals give rise to different silicate structures.
Basic Structural Units: Soil minerals are formed from two basic structural
units: tetrahedral and octahedral. Considering the valencies of the atoms
forming the units, it is clear that the units are not electrically neutral and
as such do not exist as single units.
The basic units combine to form sheets in which the oxygen or hydroxyl ions are
shared among adjacent units. Three types of sheets are thus formed,
namely silica sheet, gibbsite sheet and brucite sheet.
Isomorphous substitution is the replacement of the central atom of the
tetrahedral or octahedral unit by another atom during the formation of the
sheets.
The sheets then combine to form various two-layer or three-layer
sheet minerals. As the basic units of clay minerals are sheet-like structures,
the particle formed from stacking of the basic units is also plate-like. As a
result, the surface area per unit mass becomes very large.
Structure of Clay Minerals:
A tetrahedral unit consists of a central silicon
atom that is surrounded by four oxygen atoms located at the corners of a
tetrahedron. A combination of tetrahedrons forms a silica sheet.
An octahedral unit consists of a central ion, either aluminium or
magnesium, that is surrounded by six hydroxyl ions located at the corners of an
octahedron. A combination of aluminium-hydroxyl octahedrons forms a gibbsite
sheet, whereas a combination of magnesium-hydroxyl octahedrons forms a brucite
sheet.
Two-layer Sheet Minerals:
Kaolinite and halloysite clay minerals are
the most common.
Kaolinite Mineral
The basic kaolinite unit is a two-layer unit that is
formed by stacking a gibbsite sheet on a silica sheet. These basic units are
then stacked one on top of the other to form a lattice of the mineral. The units
are held together by hydrogen bonds. The strong bonding does not permit water to
enter the lattice. Thus, kaolinite minerals are stable and do not expand under
saturation.
Kaolinite is the most abundant constituent of residual clay
deposits.
Halloysite Mineral : The basic unit is also a two-layer sheet similar to that of
kaolinite except for the presence of water between the sheets.
Three-layer Sheet Minerals: Montmorillonite and illite clay minerals are
the most common. A basic three-layer sheet unit is formed by keeping one silica
sheet each on the top and at the bottom of a gibbsite sheet. These units are
stacked to form a lattice as shown.
Montmorillonite Mineral
The bonding between the three-layer units is by van der Waals forces. This
bonding is very weak and water can enter easily. Thus, this mineral can imbibe a
large quantity of water causing swelling. During dry weather, there will be
shrinkage.
Illite Mineral : Illite consists of the basic montmorillonite units but
are bonded by secondary valence forces and potassium ions, as shown. There is
about 20% replacement of aluminium with silicon in the gibbsite sheet due
to isomorphous substitution. This mineral is very stable and does not swell or
shrink.
Fine Soil Fabric:
Natural soils are rarely the same from one point in the
ground to another. The content and nature of grains varies, but more
importantly, so does the arrangement of these. The arrangement and organisation
of particles and other features within a soil mass is termed its fabric.

CLAY particles are flaky. Their thickness is very small relative to
their length & breadth, in some cases as thin as 1/100th of the length. They
therefore have high specific surface values. These surfaces carry negative
electrical charge, which attracts positive ions present in the pore water. Thus
a lot of water may be held as adsorbed water within a clay mass.
Stresses in the Ground:
Total Stress: When a load is applied to soil, it is carried by the solid
grains and the water in the pores. The total vertical stress acting at a point
below the ground surface is due to the weight of everything that lies above,
including soil, water, and surface loading. Total stress thus increases with
depth and with unit weight. Vertical total stress at depth z, v = .Z
Below a water body, the total stress is the sum of the weight of the soil
up to the surface and the weight of water above this. v = .Z + w.Zw
The total stress may also be denoted by z or just . It varies with
changes in water level and with excavation.
Pore Water Pressure
The pressure of water in the pores of the soil is called pore water pressure
(u). The magnitude of pore water pressure depends on:
the depth below the
water table. the conditions of seepage flow.
Under hydrostatic conditions, no water flow takes place, and the pore
pressure at a given point is given by
u = w.h
where h = depth below water table or overlying water surface
It is convenient to think of pore water pressure as the pressure exerted by a
column of water in an imaginary standpipe inserted at the given point.
The natural level of ground water is called the water table or
the phreatic surface. Under conditions of no seepage flow, the water table is
horizontal. The magnitude of the pore water pressure at the water table is zero.
Below the water table, pore water pressures are positive.
Principle of Effective Stress:
The principle of effective stress was
enunciated by Karl Terzaghi in the year 1936. This principle is valid only for
saturated soils, and consists of two parts:
1. At any point in a soil mass, the effective stress (represented by or ' ) is
related to total stress () and pore water pressure (u) as
=  - u
Both the total stress and pore water pressure can be measured at any point.
2. All measurable effects of a change of stress, such as compression and
a change of shearing resistance, are exclusively due to changes in effective
stress.
Compression =
Shear Strength =
In a saturated soil system, as the voids are completely filled with water,
the pore water pressure acts equally in all directions.
The effective stress is not the exact contact stress between particles but the
distribution of load carried by the soil particles over the area considered. It
cannot be measured and can only be computed.
If the total stress is increased due to additional load applied to the
soil, the pore water pressure initially increases to counteract the additional
stress. This increase in pressure within the pores might cause water to drain
out of the soil mass, and the load is transferred to the solid grains. This will
lead to the increase of effective stress.
Effective Stress in Unsaturated Zone:
Above the water table, when
the soil is saturated, pore pressure will be negative (less than atmospheric).
The height above the water table to which the soil is saturated is called
the capillary rise, and this depends on the grain size and the size of pores. In
coarse soils, the capillary rise is very small.
Between the top of the saturated zone and the ground surface, the soil is
partially saturated, with a consequent reduction in unit weight . The pore
pressure in a partially saturated soil consists of two components: Pore water
pressure = uw
Pore air pressure = ua
Water is incompressible, whereas air is compressible. The combined
effect is a complex relationship involving partial pressures and the degree of
saturation of the soil.

Effective Stress Under Hydrodynamic Conditions
There is a change in pore water pressure in conditions of seepage
flow within the ground. Consider seepage occurring between two points P and Q.
The potential driving the water flow is the hydraulic gradient between the two
points, which is equal to the head drop per unit length. In steady state
seepage, the gradient remains constant.
Hydraulic gradient from P to Q, i = h/s
As water percolates through soil, it exerts a drag on soil particles it comes in
contact with. Depending on the flow direction, either downward of upward, the
drag either increases or decreases inter-particle contact forces.
A downward flow increases effective stress. In contrast, an upward flow opposes
the force of gravity and can even cause to counteract completely the contact
forces. In such a situation, effective stress is reduced to zero and the soil
behaves like a very viscous liquid. Such a state is known as quick sand
condition. In nature, this condition is usually observed in coarse silt or fine
sand subject to artesian conditions.
At the bottom of the soil column,
During quick sand condition, the effective stress is reduced to zero.
where icr = critical hydraulic gradient
This shows that when water flows upward under a hydraulic gradient of about 1,
it completely neutralizes the force on account of the weight of particles, and
thus leaves the particles suspended in water.
The Importance of Effective Stress: At any point within the soil mass, the
magitudes of both total stress and pore water pressure are dependent on the
ground water position. With a shift in the water table due to seasonal
fluctuations, there is a resulting change in the distribution in pore water
pressure with depth.
Changes in water level below ground result in changes in effective
stresses below the water table. A rise increases the pore water pressure at all
elevations thus causing a decrease in effective stress. In contrast, a fall in
the water table produces an increase in the effective stress.
Changes in water level above ground do not cause changes in effective
stresses in the ground below. A rise above ground surface increases both the
total stress and the pore water pressure by the same amount, and consequently
effective stress is not altered.
In some analyses it is better to work with the changes of quantity, rather than
in absolute quantities. The effective stress expression then becomes:
´ =  - u
If both total stress and pore water pressure change by the same amount, the
effective stress remains constant.
Total and effective stresses must be distinguishable in all calculations.Ground
movements and instabilities can be caused by changes in total stress, such as
caused by loading by foundations and unloading due to excavations. They can also
be caused by changes in pore water pressures, such as failure of slopes after
rainfall.
Worked Examples
Example 1: For the soil deposit shown below, draw the total stress, pore water
pressure and effective stress diagrams.The water table is at ground level.
Solution:
Example 2: An excavation was made in a clay stratum having = 2 T/m3. When
the depth was 7.5 m, the bottom of the excavation cracked and the pit was filled
by a mixture of sand and water. The thickness of the clay layer was
10.5 m, and below it was a layer of pervious water-bearing sand. How much was
the artesian pressure in the
sand layer?
Permeability of Soils:
pressure, Elevation and Total Heads
In soils, the interconnected pores provide passage for water. A large
number of such flow paths act together, and the average rate of flow is termed
the coefficient of permeability, or just permeability. It is a measure of the
ease that the soil provides to the flow of water through its pores.

At point A, the pore water pressure (u) can be measured from the height of water
in a standpipe located at that point.
The height of the water column is the pressure head (hw).
hw = u/w
To identify any difference in pore water pressure at different points, it is
necessary to eliminate the effect of the points of measurement. With this in
view, a datum is required from which locations are measured.
The elevation head (hz) of any point is its height above the datum line. The
height of water level in the standpipe above the datum is the piezometric
head (h).
h = hz + hw
Total head consists of three components: elevation head, pressure head, and
velocity head. As seepage velocity in soils is normally low, velocity head is
ignored, and total head becomes equal to the piezometric head. Due to the low
seepage velocity and small size of pores, the flow of water in the pores is
steady and laminar in most cases. Water flow takes place between two points in
soil due to the difference in total heads.
Darcy's Law:
Darcy's law states that there is a linear relationship between
flow velocity (v) and hydraulic gradient (i) for any given saturated soil under
steady laminar flow conditions.
If the rate of flow is q (volume/time) through cross-sectional area (A)
of the soil mass, Darcy's Law can be expressed as v = q/A = k.i
where k = permeability of the soil
i = h/L
h = difference in total heads
L = length of the soil
mass
The flow velocity (v) is also called the Darcian velocity or the superficial
velocity. It is different from the actual velocity inside the soil pores, which
is known as the seepage velocity, vS. At the particulate level, the water
follows a tortuous path through the pores. Seepage velocity is always greater
than the superficial velocity, and it is expressed as:
where AV = Area of voids on a cross section normal to the direction of flow
n = porosity of the soil
Permeability of Different Soils
Permeability (k) is an engineering property of soils and is a function
of the soil type. Its value depends on the average size of the pores and is
related to the distribution of particle sizes, particle shape and soil
structure. The ratio of permeabilities of typical sands/gravels to those of
typical clays is of the order of 106. A small proportion of fine material in a
coarse-grained soil can lead to a significant reduction in permeability.
For different soil types as per grain size, the orders of magnitude for
permeability are as follows:
Soil k (cm/sec) Gravel 100 Coarse sand 100 to 10-1 Medium sand 10-1 to 10-2 Fine
sand 10-2 to 10-3 Silty sand 10-3 to 10-4 Silt 1 x 10-5
Clay 10-7 to 10-9
Factors affecting Permeability:
In soils, the permeant or pore fluid is mostly
water whose variation in property is generally very less. Permeability of all
soils is strongly influenced by the density of packing of the soil particles,
which can be represented by void ratio (e) or porosity (n).
For Sands: In sands, permeability can be empirically related to the square of
some representative grain size from its grain-size distribution. For filter
sands, Allen Hazen in 1911 found that k  100 (D10)2 cm/s where D10= effective
grain size in cm.
Different relationships have been attempted relating void ratio and
permeability, such as k  e3/(1+e), and k e2. They have been obtained from
the Kozeny-Carman equation for laminar flow in saturated soils.
where ko and kT are factors depending on the shape and tortuosity of the pores
respectively, SS is the surface area of the solid particles per unit volume of

solid material, andw and are unit weight and viscosity of the pore water.
The equation can be reduced to a simpler form as
For Silts and Clays: For silts and clays, the Kozeny-Carman equation does not
work well, and log k versus e plot has been found to indicate a linear
relationship.
For clays, it is typically found that
where Ckis the permeability change index and ek is a reference void ratio.
Laboratory Measurement of Permeability
Constant Head Flow: Constant head permeameter is recommended for coarsegrained soils only since for such soils, flow rate is measurable with adequate
precision. As water flows through a sample of cross-section area A, steady total
head drop h is measured across length L.
Permeability k is obtained from:
Falling Head Flow
Falling head permeameter is recommended for fine-grained soils.
Total head h in standpipe of area a is allowed to fall. Hydraulic gradient
varies with time. Heads h1 and h2 are measured at times t1 and t2. At any
time t, flow through the soil sample of cross-sectional area A is
--------------------- (1)
Flow in unit time through the standpipe of cross-sectional area a is
= ----------------- (2)
Equating (1) and (2) , or Integrating between the limits,
Field Tests for Permeability
Field or in-situ measurement of permeability avoids the difficulties involved in
obtaining and setting up undisturbed samples in a permeameter. It also provides
information about bulk permeability, rather than merely the permeability of a
small sample.
A field permeability test consists of pumping out water from a main well
and observing the resulting drawdown surface of the original horizontal water
table from at least two observation wells. When a steady state of flow is
reached, the flow quantity and the levels in the observation wells are noted.
Two important field tests for determining permeability are: Unconfined flow
pumping test, and confined flow pumping test.
Unconfined Flow Pumping Test: In this test, the pumping causes a drawdown in an
unconfined (i.e. open surface) soil stratum, and generates a radial flow of
water towards the pumping well. The steady-state heads h1 and h2 in observation
wells at radii r1 and r2 are monitored till the flow rate q becomes steady.
The rate of radial flow through any cylindrical surface around the pumping
well is equal to the amount of water pumped out. Consider such a surface having
radius r, thickness dr and height h. The hydraulic gradient is
Area of flow, From Darcy's Law, Arranging and integrating,
Field Tests for Permeability
Confined Flow Pumping Test:
Artesian conditions can exist in a aquifer of
thickness D confined both above and below by impermeable strata. In this, the
drawdown water table is above the upper surface of the aquifer.
For a cylindrical surface at radius r,
Integrating,
Permeability of Stratified Deposits: When a soil deposit consists of a number of
horizontal layers having different permeabilities, the average value of
permeability can be obtained separately for both vertical flow and horizontal
flow, as kVand kH respectively.
Consider a stratified soil having horizontal layers of thickness H1, H2, H3,
etc. with coefficients of permeability k1, k2,k3, etc.
For vertical flow, The flow rate q through each layer per unit area is the same.
Let i be the equivalent hydraulic gradient over the total thickness H and let
the hydraulic gradients in the layers be i1, i2, i3, etc. respectively.

where kV = Average vertical permeability
The total head drop h across the layers is
Horizontal flow: When the flow is horizontal, the hydraulic gradient is the same
in each layer, but the quantity of flow is different in each layer.
The total flow is
Considering unit width normal to the cross-section plane,
Worked Examples
Example 1: Determine the following:
a) Equivalent coefficient of vertical
permeability of the three layers
(b) The rate of flow per m2 of plan area
(c) The total head loss in the three layers
Example 2: For a field pumping test, a well was sunk through a horizontal
stratum of sand 14.5 thick and underlain by a clay stratum.Two observation wells
were sunk at horizontal distances of 16 m and 34 m respectively from the pumping
well.The initial position of the water table was 2.2 m below ground level.
At a steady-state pumping rate of 1850 litres/min, the drawdowns in the
observation wells were found to be 2.45 m and 1.20 m respectively. Calculate the
coefficient of permeability of the sand.
A rectangular soil element is shown with dimensions dx and dz in the plane, and
thickness dy perpendicuar to this plane. Consider planar flow into the
rectangular soil element.
In the x-direction, the net amount of the water entering and leaving the element
is
Similarly in the z-direction, the difference between the water inflow and
outflow is
For a two-dimensional steady flow of pore water, any imbalance in flows into and
out of an element in the z-direction must be compensated by a corresponding
opposite imbalance in the x-direction. Combining the above, and dividing
bydx.dy.dz , the continuity equation is expressed as
From Darcy's law, ,, where h is the head causing flow.
When the continuity equation is combined with Darcy's law, the equation for flow
is expressed as:
For an isotropic material in which the permeability is the same in all
directions (i.e. k x= k z), the flow equation is
This is the Laplace equation governing two-dimensional steady state flow. It can
be solved graphically, analytically, numerically, or analogically.
For the more general situation involving three-dimensional steady flow, Laplace
equation becomes:
One-dimensional Flow
For this, the Laplace Equation is
Integrating twice, a general solution is obtained.
The values of constants can be determined from the specific boundary conditions.
As shown, at x = 0, h = H , and at x = L, h = 0
Substituting and solving,
c2 = H ,
The specific solution for flow in the above permeameter is
which states that head is dissipated in a linearly uniform manner over the
entire length of the permeameter.
Two-dimensional Flow
Flow Nets : Graphical form of solutions to Laplace equation for two-dimensional

seepage can be presented as flow nets. Two orthogonal sets of curves form a flow
net:
Equipotential lines connecting points of equal total head h
Flow lines indicating the direction of seepage down a hydraulic gradient
Two flow lines can never meet and similarly, two equipotential lines can never
meet. The space between two adjacent flow lines is known as a flow channel, and
the figure formed on the flownet between any two adjacent flow lines and two
adjacent equipotential lines is referred to as a field. Seepage through an
embankment dam is shown.
Calculation of flow in a channel : If standpipe piezometers were inserted into
the ground with their tips on a single equipotential line, then the water would
rise to the same level in each standpipe. The pore pressures would be different
because of their different elevations.There can be no flow along an
equipotential line as there is no hydraulic gradient.
Consider a field of length L within a flow channel. There is a fall of total
head h. The average hydraulic gradient is
As the flow lines are b apart and considering unit length perpendicuar to field,
the flow rate is
There is an advantage in sketching flow nets in the form of curvilinear
'squares' so that a circle can be insrcibed within each four-sided figure
bounded by two equipotential lines and two flow lines.
In such a square, b = L , and the flow rate is obtained as q = k.h
Thus the flow rate through such a flow channel is the permeability k multiplied
by the uniform interval h between adjacent equipotential lines.
Calculation of total flow
For a complete problem, the flow net can be drawn with the overall head
drop h divided into Nd so that h = h / Nd.
If Nf is the no. of flow channels, then the total flow rate is
Procedure for Drawing Flow Nets: At every point (x,z) where there is flow, there
will be a value of head h(x,z). In order to represent these values, contours of
equal head are drawn.
A flow net is to be drawn by trial and error. For a given set of boundary
conditions, the flow net will remain the same even if the direction of flow is
reversed. Flow nets are constructed such that the head lost between
successiveequipotential lines is the same, say h. It is useful in visualising
the flow in a soil to plot the flow lines, as these are lines that are
tangential to the flow at any given point. The steps of construction are:
1. Mark all boundary conditions, and draw the flow cross section to some
convenient scale.
2. Draw a coarse net which is consistent with the boundary conditions and which
has orthogonal equipotential and flow lines. As it is usually easier to
visualise the pattern of flow, start by drawing the flow lines first.
3. Modify the mesh such that it meets the conditions outlined above and the
fields between adjacent flow lines and equipotential lines are 'square'.
4. Refine the flow net by repeating step 3.
The most common boundary conditions are:
(a) A submerged permeable soil boundary is an equipotential line. This could
have been determined by considering imaginary standpipes placed at the soil
boundary, as for every point the water level in the standpipe would be the same
as the water level. (Such a boundary is marked as CD and EF in the following
figure.)
(b) The boundary between permeable and impermeable soil materials is a flow line
(This is marked as AB in the same figure).
(c) Equipotential lines intersecting a phreatic surface do so at equal vertical
intervals.
Uses of Flow Nets

The graphical properties of a flow net can be used in obtaining solutions for
many seepage problems such as:
1. Estimation of seepage losses from reservoirs: It is possible to use the flow
net in the transformed space to calculate the flow underneath the dam.
2. Determination of uplift pressures below dams: From the flow net, the pressure
head at any point at the base of the dam can be determined. The uplift pressure
distribution along the base can be drawn and then summed up.
3. Checking the possibility of piping beneath dams: At the toe of a dam when the
upward exit hydraulic gradient approaches unity, boiling condition can occur
leading to erosion in soil and consequent piping. Many dams on soil foundations
have failed because of a sudden formation of a piped shaped discharge channel.
As the stored water rushes out, the channel widens and catastrophic failure
results. This is also often referred to as piping failure.