geotechnical enginnering

1. PERMEABILITY

2. PERMEABILITY
• Permeability is the ability of porous medium to permit the flow of
fluid through its interconnecting voids. It is expressed by K which is
called coefficient of permeability or hydraulic conductivity. It is
defined by darcy.

3. soil K(cm/sec)
Gravel >1
sand 1 to 10^-3
Silt 10^-3 to 10^-7
Clay <10^-7

4. Darcy’s Law
• According to this law for laminar
conditions through a saturated
soil mass the discharge velocity
is directly proportional to
hydraulic gradient.
• V directly proportional to i
• V=Ki (K=is darcy’s
constant )

5. • If the soil is homogeneous then hydraulic gradient is constant. But if soil is
non homogeneous then hydraulic gradient line will be curved and will not
be constant.
• Let the A is the area of cross section of soil.
• Then discharge through the saturated soil mass is
• Q=KiA=VA

6. Assumptions of Darcy’s Law
• The soil mass is homogeneous
• The soil mass is saturated (s=1)
• The flow through the soil is laminar( it means the Reynold number ≤1
• Note- for laminar flow in open channel re ≤500
• For laminar flow through pipe re ≤2000
• For laminar flow around spherical bodies re ≤1
• Note-2- Generally flow through gravels is turbulent hence Darcy’s law
is not valid.

7. • Note-3- the discharge velocity (v=q/a) is fictitious/apparent which is
not true velocity. Because total area of cross section of soil (a) is not
available for flow. Because flow occurs only through area of voids.
• If the area of void is considered then the actual velocity or true
velocity/ seepage velocity can be computed. Which will be more than
discharge velocity.
• Seepage velocity Vs=q/Av
• (Av= area of voids)

9. If tracer is introduced in the water it will flow through soil having velocity equal to seepage velocity

10. Factors affecting permeability:-
• Particle Size:- k is directly proportional to D10
• If the void ratio is same then the coarse grained soils have more
permeability then fine grained soils.
• K gravel> K sand> K silt> K clay
• Void ratio:- k directly proportional to e /(1+e) , (k1/k2)=e1 /e2
for purpose of computation k directly proportional to e
If the particle size is same then k is more for loose soil than the dense
soil.
2
2
3 2 2

11. Factors affecting permeability:-
• Particle Shape :- the effect of size & shape is expressed in terms of
specific surface area.
• Specific surface area- is surface area per unit volume.
• Degree of Saturation:-the presence of voids create air lock and reduce
the velocity of flow.
• K is less in partially saturated soil & increases with the degree of
saturation.

12. • Impurities present in water:- Due to presence of entrapped gases or
due to organic and inorganic impurities voids are blocked. Therefore
permeability is reduced.
• Structure of Soil:- if soil is layered or stratified then k is more in the
direction parallel to bedding planes and less in the direction
perpendicular to bedding planes.
• Kx>Kz
• Properties of water/Fluid:- k directly proportional unit weight of
water/dynamic viscosity.
• It means permeability depends upon temperature
• K directly proportional to temperature
Kz
Kx

13. • Adsorbed water( film water/ hygroscopic water):-the fine soils have
good capacity to adsorb water. The adsorbed water is strongly
attached to the soil. Which offers more viscosity. Hence k is reduced.
• K is more for distilled water and less for sea water.
• Methods to determine permeability (Hydraulic Conductivity k)
• Laboratory methods
• Constant head permeability test( suitable for coarse soils)
• Falling head permeability (variable head) (suitable for fine soils)
• Capillary permeability test (applied for partially saturated soils also)

14. • Indirect Methods :-Using empirical equations permeability can be
computed by relative soil properties & permeability.
• Kozney karman Equations
• Lloudens equations
• Allen hazen equations
• Terzaghis equations
• Consolidation equations
• Field method
• Pumping out test:- it is suitable when area of influence is large use
dupit theory or thiems theory
• Pumping in test:- these are suitable when area of influence is
small/less. It includes open end test and packers test.

15. Constant Head permeability Test
The flow takes place under constant head
difference HL it means H1 and H2 are kept
constant.
Let V is the volume of water collected in
graduated in time t

16. Falling Head/Variable Head Permeability

17. • Let at the beginning of test the head difference between upstream &
downstream level is h1 after time t head difference become h2.
• Let at any intermediate stage head difference is h
• Which falls by dh in time dt
• Since hydraulic gradient changes with the time therefore discharge
will change.
• Q=KiA
• =kAh/L
• h= head difference at any intermediate time when discharge is q

18. Note :- if the variable head
test is performed in two
stages at same interval
that is in first stage head
difference changes from h1
and h2 in time t. in second
stage in same soil head
difference changes from h2
to h3 is same time t then
relation between h1 ,h2,h3
is that

19. Capillary permeability test:-
• This method is also Known as horizontal capillary test.
• It can be used to find permeability of soil as well as capillary head in the
soil.
• The previous two methods are applicable for only saturated soils where as
this method can applied for partially saturated soils also.
• In this method partially saturated soil sample is placed in a cylindrical glass
tube of dia 4 cm and length 35 cm through which water is allowed to flow
under constant head applied at inlet.
• The outlet or other end of the tube is kept open to the atmosphere in
order to permit, escape of air present in the voids.
• The test is performed in two stages at constant head ho1, ho2 and the
distance of travel of water is noted in both stages.

30. Seepage forces
• The seepage forces are sometimes converted into forces by
multiplying them by total cross-sectional area of the soil sample. The
seepage force is applied by following water to the soil skeleton
through frictional drag. In an isotropic soil, the seepage force always
acts in the direction of flow.
• Seepage force is usually expressed as force per unit volume of soil.
Thus,
• J=seepage force/volume of soil=(seepage pressure x area)/volume
• =

31. Quick Sand condition
• It is clear from equation that by increasing the total head difference h, it is
possible to reach a condition when effective stresses in soil become equal
to zero that is.
• The condition occurs when hydraulic gradient.
•
• Icr is called the critical hydraulic gradient. When upward flow takes place at
the critical hydraulic gradient, a soil such as small loses all its shearing
strength and it can not support any load. The soil is said to have become
quick or alive and boiling will occur. The popular name for this
phenomenon is quick sand.