Okay, here are the steps to solve this: 1) Given: Specific gravity (Gs) = 2.65 Void ratio (e) = 0.5 2) Critical hydraulic gradient (icr) is given by the equation: icr = Gs - 1/(1+e) 3) Substitute the values: icr = 2.65 - 1/(1+0.5) = 2.65 - 1/1.5 = 2.65 - 0.667 = 1.983 So the critical hydraulic gradient for this sand deposit is 1.983.

1. Unit No: 2
Permeability and Seepage

2. • Soil Water: Water present in the void spaces of a soil mass
is called ‘Soil water’
• Soil water may be in the forms of ‘free water’ or
‘gravitational water’ and ‘held water
• The first type is free to move through the pore space of the
soil mass under the influence of gravity; the second type is
that which is held in the proximity of the surface of the soil
grains by certain forces of attraction.
• Capillary water. Water which is in a suspended condition,
held by the forces of surface tension within the interstices
and pores of capillary size in the soil, is called ‘capillary
water’

3. Held Water
‘Held water’ is that water which is held in soil pores or void spaces
because of certain forces ofattraction.
It can be further classified as (a) Structural water and (b) Absorbed
water.
Structural water.
Water that is chemically combined as a part of the crystal structure
of the mineral of the soil grains is called ‘Structural water’
Adsorbed water: This comprises, (i) hygroscopic moisture and (ii) film
moisture.Hygroscopic moisture. Soils which appear quite dry contain,
nevertheless, very thin films of moisture around the mineral grains,
called ‘hygroscopic moisture’, which is also termed ‘contact moisture’
or ‘surface bound moisture

4. Permeability: Definition
• Seepage: The passage of water through porous material is
called seepage.
• Permeable material: The material with continuous voids is
called as permeable material.
• Hence permeability is a property of porous material which
permits passage of fluids through inter connecting voids.
• Permeability is defined as the rate of flow of water under
laminar flow conditions through a unit cross sectional area
perpendicular to the direction of flow through porous medium
under unit hydraulic gradient and under standard temperature
conditions.

5. What is permeability?
• Property of a soil which permits the flow of water
• Permeability is defined as the property of a porous
material which permits the passage or seepage of water
through its interconnecting voids.
• It is a very important Engineering property
gravels highly permeable
stiff clay least permeable

7. Necessity of Study:
(a) The rate at which water flows throughsoil (for example,
the determination of rate of leakage through an earth dam)
(b) Compression (for example, the determination of the rate
of settlement of a foundation
(c) Strength (for example, the evaluation of factors of safety
of an embankment). The emphasis in this discussion is on
the influence of the fluid on the soil through which it is
flowing ; in particular on the effective stress.

8. Permeability through soil is important for the
following engineering problems:
• Calculation of uplift pressure under hydraulic structure and
their safety against piping
• Ground water flow towards wells and drainage of soil
• Calculation of seepage through the body of earth dams and
stability of slopes
• Determination of rate of settlement of a saturated
compressible soil layer

9. Flow of water through soils may either be a
laminar flow or a turbulent flow
Each fluid particle travel
along a definite path
which never crosses
the path of any other
particle
Paths are irregular and
twisting, crossing at
random

10. Coefficient Of
Permeability
Depends not only on the
properties of soil but also
on the properties of water
Absolute permeability
Independent of the properties
of water
It depends only on the
characteristics of soil
The absolute permeability only
depends on the geometry of the
pore-channel system.
Relative permeability is the ratio of
effective permeability of a particular fluid to its
absolute permeability.

11. • factors affecting permeability :
• Particle size
• Structure of soil mass
• Shape of particles
• Void ratio
• Properties of pore fluid
• Degree of saturation
• Adsorbed water
• Impurities in water
• Laboratory Measurement of Permeability
1. Constant head permeameter
2. Falling or variable head permeameter
Field determine permeability methods
1. Pumping out of wells
2. Pumping into wells

14. DARCY’S LAW
The law of flow of water through soil was first studied by Darcy in 1856.
The Darcy’s law is,
“For laminar flow through saturated soil mass, the discharge per unit
time is proportional to the hydraulic gradient”.
q = k.i.A
= k.i q/A= v
v = k.i ……. Darcy’s Law
Where, q = Discharge per unit time (rate of flow)
A = Total c/s area of soil
mass i = Hydraulic
gradient = h/L
k = Darcy’s coefficient of
Permeability v = Velocity of flow
(discharge velocity)

15. Darcy’s Law:
Darcy in 1856 derived an empirical formula for the behavior of flow
through saturated soils.
He found that the quantity of water q per sec flowing through a cross-
sectional area of soil under hydraulic gradient / can be expressed by
the formula
q = kiA
k- coefficient of permeability
or the velocity of flow can be written as
A - cross-sectional area of soil
v=
𝒒
𝑨
=ki
q- rate of flow of water

16. ASSUMPTIONS OF DARCY’S LAW :-
• The following assumptions are made in
Darcy’s law.
 The soil is saturated.
 The flow through soil is laminar.
 The flow is continuous and steady.
 The total cross sectional area of soil mass is
considered.
 The temperature at the time of testing is 270C.

17. VALIDITY OF DARCY’S LAW
1.Darcy’s law is valid if the flow through soils is laminar :
 The flow of water through soils depends upon the dimension of particles.
In fine grained soils the dimensions of the interstices (voids) are very small
and flow is necessarily laminar.
 In course- grained soil, the flow is also laminar. However, in very coarse
grained soils, such as
gravels, the flow may be turbulent.
 For flow through soils, the flow is laminar if the Reynolds number is less
than unity.
1. As per Allen Hazen, the maximum diameter of the particle for the flow to be laminaris
about 0.50 mm.
2. It is valid for flow in clays, slits and fine sands. In coarse sands, gravels and boulders, the
flow may be turbulent and Darcy’s law may not be applicable.
4. For Darcy’s law to be valid, the relationship between velocity (v) and hydraulic gradient
(i) should be linear.
5. In extremely fine-grained soils, such as collodial clay, the interstices are very small.The
velocity is therefore very small. In such soils, the Darcy’s law is not valid.

18.  If a soil sample of length L, and cross- sectional area A, is
subjected to differential head of water ( h1 – h2), the hydraulic
gradient (i) will be equal to,
 We know that v = k.i
 If hydraulic gradient (i) is equal to unity,
v = k
1 2
. .
h h
q k A
L


𝒊 =
𝒉
𝑳
=
𝒉𝟏 − 𝒉𝟐
𝑳
𝒒 = 𝒌.
𝒉𝟏 − 𝒉𝟐
𝑳
. 𝑨

19. Seepage Pressure
The pressure that is exerted on the soil due to the seepage of water is
called the seepage pressure
Quick Sand Phenomenon
quicksand conditions occur more commonly in fine sands with low
permeability. In case of gravels with high permeability, much higher velocity
of flow will be required to cause the‘‘quick sand condition’’.
Critical Hydraulic Gradient:
We can determine the hydraulic gradient that brings a soil mass (essentially,
coarse-grained soils) to static liquefaction. Solving for i in Equation we get
icr = G-1/1+e
where icr is called the critical hydraulic gradient, Gs is specific gravity, and e
is the void ratio. Since Gs is constant, the critical hydraulic gradient is solely
a function of the void ratio of the soil. In designing structures that are
subjected to steady-state seepage, it is absolutely essential to ensure that
the critical hydraulic gradient cannot develop.

20. • Flow Net
• A flow net for an isometric medium is a network of flow lines and
equipotential lines intersecting at right angles to each other. The
path which a particle of water follows in its course of seepage
through a saturated soil mass is called a flow line.
• Equipotential lines are lines that intersect the flow lines at right
angles
Example :What is the critical gradient of sand deposits os specific gravity= 2.65 &
void ratio=0.5