Lecture 4 permeability

Concept of effective stress
Permeability
Shear characteristics of soils
Coulomb’s equation for shear strength
Determination of shear strengths of soils
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Lecture
4
Elias A.

Permeability
 Definition of hydraulic conductivity and its magnitude in various soils
 Laboratory determination of hydraulic conductivity
 Empirical relationship to estimate hydraulic conductivity
 Equivalent hydraulic conductivity in stratified soil based on the direction of
the flow of water
 Hydraulic conductivity determination from field tests
In this section, you will able to know the following:
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Soil Permeability
Permeability is defined as a capacity of soil to allow water
passes through it i.e. quantity of flowing for a unit of soil
surface under a pressure of 1 unit hydraulic gradient.
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Soil Permeability
 One of the major physical parameters of a soil that controls the rate of seepage
through it is hydraulic conductivity, otherwise known as the coefficient of
permeability
 Soils are permeable due to the existence of interconnected
voids through which water flow from points of high energy
to points of low energy.
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A soil is highly pervious when water can flow through it
easily. (Gravels)
In an impervious soil, the permeability is very low and
water cannot easily flow through it. (Clays)
Rocks are impermeable
The study of the flow of water through permeable soil
media is important in soil mechanics.
Soil Permeability
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Importance of Permeability
The following applicationsillustrate theimportanceof permeabilityin
geotechnical design:
● Permeabilityinfluencestherateof settlement of a saturatedsoil
under load.
● The design ofearth dams is very muchbaseduponthepermeability of
thesoils used.
● The stability ofslopesand retaining structurescanbe greatly affectedby the
permeability ofthesoils involved.
● Filters made ofsoilsaredesignedbasedupontheir permeability.

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1. Particle size
The Permeability varies approximately as
the square of grain size. It depends onthe
effective diameter of the grain size (D10)
2. Void ratio
Increasein the void ratio increasesthe area
available for flow hencepermeability
increasesfor critical conditions.
Factors Affecting Permeability of Soils

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3. Properties of pore fluid.
Porefluids arefluids that occupyporespaces
in a soil or rock.Permeability is directly
proportional to the unit weight of pore
fluid and inversely proportional to viscosity
of pore fluid.
FactorsAffecting Permeability of Soils

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4. Shape of particles
Permeability is inversely proportional to specific
surfacee.g.asangular soil have morespecific
surfaceareacomparedto the round soil
therefore,the soil with angular particles is less
permeable thansoil of rounded particles.

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5. Structure of soil mass
For samevoid ratio the permeability is more
for flocculentstructure ascomparedto the
dispended structure

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6. Degree of saturation
The permeability of partially saturated soil is
less thanthat of fully saturated soil.
Permeability

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7. Adsorbed Water
Adsorbed Water meansa thin microscopic
film of water surrounding individual soil
grains. This water is not freeto moveand
hencereducesthe effective porespacean thus
decreases coefficient of permeability.

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8. Entrapped air and organic impurities
The organic impurities and entrapped air
obstruct the flow and coefficient of
permeability is reducedueto their presence.

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9. Temperature
As the viscosity of the porefluid decreasewith the
temperature,permeability increaseswith
temperature, asunit weight of porefluid does
not changemuchwith changein temperature.

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10. Stratification of soil
Stratified soilsarethosesoilswhich areformed
by layer uponlayer of the earth or dust
depositedoneach other. If the flow is parallel
to the layers of stratification ,the permeability
is max. while the flow in Perpendicular
direction occurwith min.permeability.

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Water Flow
The water flow isdivided into two
categories:
1)Laminar flow
2)Turbulent flow

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Water Flow
Laminar flow indicates that eachwater particle
follows a definite path and never crosses the
path of another particle.

the total head will be the sum of pressure head and
elevation head
h : head (m)
uw: pore pressure (Pa)
ϒw: unit weight of water
Z : elevation head
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Pressure head = pore water pressure/ϒw
Elevation head = height above the selected datum
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Flow of an ideal fluid (incompressible and non viscous)
The head remain constant between two points on the flow line
- Water is a viscous fluid and when it flows through a saturated soil
mass there is
dissipation or loss of energy
loss of head between two points on the flow line
Water flows from points of high to low =TOTAL head
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Hydraulic gradient
 As the water flows from A to B, there is an energy loss which is
represented by the difference in the total heads h1 - h2 (hA - hB)
 The loss of head of Dh units is effected as the water flows from A to B.
• The loss of head per unit length of flow may be expressed as
Where i is called the hydraulic gradient
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Henry Darcy (1803-1858), Hydraulic Engineer. His
law is a foundation stonefor several fields of study
Darcy’sLaw demonstrated experimentally
that for laminar flow conditions in a
saturated soil, the rateof flow or the
dischargeperunit time is proportional to the
hydraulic gradient
Darcy’s Law

Darcy’s Law
Darcy(1856) stated that the flow of water through porous media is
directly proportional to the head loss and inversely proportional to the
length of flow path. This may be written as:
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Hydraulic Conductivity
Permeability is also known as hydraulic
conductivity.
Hydraulic conductivity, marked as K, values,
is one of the principal and most important soil
hydrology (hydraulic) characteristic
(parameter) and it is an important factor in
water transport in the soil and is used in all
equations for groundwater (subsurface water)
flow.
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 The value of hydraulic conductivity varies widely for
different soils.
 The hydraulic conductivity of unsaturated soils is lower
and increases rapidly with the degree of saturation.
Hydraulic Conductivity
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The determination of permeability
 The permeability of a soil can be measured in either the
laboratory or the field;
•Laboratory methods are much easier than field methods.
•Field determinations of permeability is important
–k is a function of both micro- and macro
structure
–difficulty of getting representative soil samples
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Methods of determination of hydraulic conductivity of soils
Laboratory methods: 1. Constant head permeability method
2. Falling head permeability method
How good is the sample ?
•Field methods: 1. Pumping tests
2. Borehole infiltration tests
Need to know soil profile (inc. water table) & boundary
conditions?
•Indirect Method:
Empirical correlations (relating grain size and void ratio to
hydraulic conductivity)
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Determination of Coefficient of Permeability
Constant – Head Test
The permeability test is a measure of the rateof the
flow of water through soil.
In this test, water is forcedbya known constant pressure
through a soil specimen of known dimensions and the
rate of flow is determined.
This test is usedprimarily to determine the suitability
of sands and gravels for drainage purposes,and is
made only onremolded samples

More suited for coarse grained soils such as gravelly
sand, coarse and medium sand ; k > 10 -5 m/s
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Example
• L = 30 cm
• A =area of the specimen = 177 cm2
• Constant-head difference, h =50 cm
• Water collected in a period of 5 min = 350 cm3
Calculate the hydraulic conductivity in cm/sec.
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Falling – Head Test
● Relatively for lesspermeablesoils
● Water flows through the sample from a standpipe
attached to the top of the cylinder.
● The head of water (h) changes with time as flow
occurs through the soil. At different times the head of
water is recorded.

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Falling – Head Test
A typical arrangement of the falling-head
permeability test is shown in figure in the next slid.
Water from a standpipe flows through the soil ,the
initial headdifference h1 at time t=0 is recorded
and water is allowed to flow through the soil
specimensuchthat the final headdifference at time t
= t2 is h2.

Field Tests for K
Field tests are generally more reliable than laboratory tests
for determining soil permeability , the main reason being
that field tests are performed on the undisturbed soil
exactly as it occurs in situ at the test location.
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In stratified soils, average horizontal permeability is
greater than average vertical permeability .
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Seepage and flow nets
In this section, we will discuss the following:
 Procedure to construct flow nets and calculation of
seepage in isotropic and anisotropic soils
 Seepage through earth dams
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Seepage
In many instances, the flow of water through soil is not in one direction only, nor is it
uniform over the entire area perpendicular to the flow.
In such cases, the groundwater flow is generally calculated by the use of graphs
referred to as flow nets.
The concept of the flow net is based on Laplace’s equation of continuity, which
governs the steady flow condition for a given point in the soil mass.
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A flow line is a line along which a water particle will travel from
upstream to the downstream side in the permeable soil medium.
An equipotential line is a line along which the potential head at all
points is equal.
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Properties of a Flow Net
1. Flow and equipotential lines are smooth curves
2. Flow lines and equipotential lines meet at right angles
to each other
3. No two flow lines cross each other.
4. No two flow or equipotential lines start from the same
point.
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Flownet construction
Rules for drawing flownets
1. All impervious boundaries are flow lines.
2. All permeable boundaries are equipotential
3. Phreatic surface - pressure is atmospheric, i.e. excess pressure is zero.
4. All parts of the flow net must have the same geometric proportions
(e.g. square or similarly shaped rectangles).
5. Good approximations can be obtained with 4 - 6 flow channels
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Procedure for drawing flow nets
 Mark all boundary conditions
 Draw a coarse net which is consistent with the boundary
conditions and which has orthogonal equipotentials and
flow lines. (It is usually easier to visualise the pattern of
flow so start by drawing the flow lines).
 Modify the mesh so that it meets the conditions outlined
above and so that rectangles between adjacent flow lines
and equipotentials are square.
 Refine the flow net by repeating the previous step.
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The geometrical conditions
are plotted to scale
The boundary flow lines and
equipotentials are drawn
A few additional flow lines are then
plotted, perpendicular to the known
boundary equipotentials
The equipotential lines necessary to obtain
curvilinear squares are then plotted so that both
sets of curves are perpendicular to each other.
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Determination of quantity of seepage
The quantity of seepage q is calculated per unit length of the section.
Flow is assumed to be two dimensional so a unit width of the cross-section is considered.
The total flow around the structure will then depend on its overall length.
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Example: If k = 10 -7 m/sec, what would be the flow per day
over a 100m length of wall?
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Lecture 4 permeability

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