Unit 2 Effective Stress & Permeability

1. Department of Civil
Engineering
20CE402
GEOTECHNICAL ENGINEERING I
SOIL WATER AND WATER FLOW
Prepared by
D.MYTHILI AP CIVIL
EXCEL ENGINEERING COLLEGE

2. Department of Civil
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SOIL WATER
 Water present in the void spaces of a soil mass is called
‘Soil Water’
 The sub-surface water which occupies the voids in the soil
above the ground water table.
 Movement of water into soil - Infiltration
 Downward movement of water within the soil - Percolation,
Permeability or Hydraulic conductivity
SOIL WATER
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3. FORMS OF SOIL WATER
There are mainly two forms of soil
water.
Gravitational water
Free water
Ground water
Capillary water
Held water
Adsorbed water
Capillary water
Structural water
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SOIL WATER
Fig. 1 Soil water
Source: Fig. 1 - https://www.tutorvista.com/biology/types-of-soil-conservation

4. Gravitational water
 The water in the soil due to the movement of water under
gravitational forces.
Free water :
 Similar properties as that of liquid water
 Moves under the influence of gravity, or due to difference in
hydrostatic pressure head.
 Sources - precipitation, run-off, floodwater, melting snow,
water from certain hydraulic operations.
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SOIL WATER

5. Ground water :
 Fills up the voids in the soil up to the ground water table
and translocates through them.
 Fills coherently and completely all voids which makes the
soil completely saturated.
 Ground water subjected to atmospheric pressure - Ground
water table
 Elevation of the ground water table at a given point -
Ground water level
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SOIL WATER

6. Capillary water :
 Water in a suspended condition, held by the forces of
surface tension within the interstices and pores of capillary
size in the soil.
 Retained as minute bodies of water filling part of the pore
space between particles.
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SOIL WATER

7. Held water
 Water held in soil pores or void spaces because of certain
forces of attraction.
Adsorbed water :
 Strongly attracted to soil mineral surfaces by electrostatic
forces especially clays.
 Dry soil mass adsorb water from atmosphere even at low
relative humidity known as hygroscopic water content.
 Water lost from an air-dry soil when heated to 105ºC.
 Neither affected by gravity nor by capillary forces and would
not move in the liquid form. 7
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SOIL WATER

8. Structural water :
 Chemically combined as a part of the crystal structure of the
mineral of the soil grains
 Cannot be separated/removed when subjected to loading
conditions or oven drying to 105ºC - 110ºC
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SOIL WATER

9. STRESSES IN SOIL
 Stresses (Total Stress) within a soil mass caused by external loads
applied to the soil and also self-weight of the soil.
 Total stress increases with depth (Z) and with unit weight of soil
(ɣ).
 At any point inside a soil mass, resisted by the soil grains and
water present in the pores or voids (saturated soil).
Vertical total stress at depth Z, σv = ɣ.Z
Fig. 2 Stress in soil mass
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STRESSES IN SOIL
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Source: Fig. 2
http://environment.uwe.ac.uk/geocal/SoilMech/stresses/stresses.htm

10.  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.
σv = ɣ.Z + ɣw.Zw
Fig. 3 Stress in submerged soil mass
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STRESSES IN SOIL
Source: Fig. 3
http://environment.uwe.ac.uk/geocal/SoilMech/stresses/stresses.htm

11. Pore Pressure/Neutral stress
 Pore water pressure (u) - Pressure of groundwater held within a
soil or rock, in gaps between particles (pores).
 Pore water pressures below the phreatic level of the
groundwater are measured with piezometers.
 Magnitude of the pore water pressure at water table - zero.
 Below the water table, pore water pressure - positive.
u = Ɣw . h
Ɣw – Unit weight of water
Fig 4. Pore water pressure in soil mass
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STRESSES IN SOIL
Source: Fig.4
http://environment.uwe.ac.uk/geocal/SoilMech/stresses/stresses.htm

12. Effective Stress / Inter-granular Pressure
• Effective stress - Pressure transmitted through grain to grain at
the contact points through a soil mass causing displacements.
• Compression and Shear strength of the soil depends on effective
stress.
• Effective stress (σ') acting on a soil is calculated from two
parameters, total stress (σ) and pore water pressure (u)
according to:
σ‘ = σ – u
Fig. 5 Total stress, Effective stress and Pore water pressure
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STRESSES IN SOIL
Source: Fig. 5 – Schofield and Wroth, “Critical State Soil Mechanics”

13. STRESSES IN SOIL
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STRESSES IN SOIL
Fig. 6 Schematic representation of Total stress, Effective stress and Pore water
pressure
Source: Fig. 6
http://environment.uwe.ac.uk/geocal/SoilMech/stresses/stresses.htm

14. Example 1
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For the soil deposit shown below, draw the total stress, pore water
pressure and effective stress diagrams. The water table is at ground
level.
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STRESSES IN SOIL

15. Solution:
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Total stress
At - 4m, σ = 1.92 x 4 = 7.68 T/m2
At -11m, σ = 7.68 + 2.1 x 7 = 22.38 T/m2
Pore water pressure
At - 4 m, u = 1 x 4 = 4 T/m2
At -11 m, u = 1 x 11 = 11 T/m2
Effective stress
At - 4 m , σ‘ = 7.68 - 4 = 3.68 T/m2
At -11m , σ‘ = 22.38 - 11 = 11.38 T/m2
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STRESSES IN SOIL

16. Example 2
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Determine the neutral and effective stress at a depth of 16 m below the
ground level for the following conditions: Water table is 3 m below
ground level ; G = 2.68; e = 0.72; average water content of the soil above
water table is 8%.
Solution:
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STRESSES IN SOIL

17. Department of Civil
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STRESSES IN SOIL
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18. Department of Civil
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STRESSES IN SOIL
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19. PERMEA BILITY OF SOIL
 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 soil (cm/sec)
i – hydraulic gradient (Δh/L)
Δh - difference in total heads
L – Length of soil mass
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SOIL PERMEABILITY
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Fig. 7 Flow of water in soil
Source: Fig. 7 - NPTEL

20. What is permeability of soil?
 Permeability is defined as the property of a porous material which
permits the passage or seepage of water through its interconnecting
voids.
 Rate of permeability varies based on void spaces between the
grains (irregular shape of the individual particles)
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SOIL PERMEABILITY
Fig. 8 Comparison of Permeability of different soil
Source: Fig.8 - https://www.pinterest.com/jvonstorch/muro-contenci/

21. PERMEABILITY FOR DIFFERENT SOILS
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For different soil types as per grain size, the orders of magnitude for
permeability are as follows:
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SOIL PERMEABILITY

22. FACTORS AFFECTING SOIL PERMEABILITY
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SOIL PERMEABILITY

23. DETERMINATION OF CO-EFFICIENT OF PERMEABILITY
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SOIL PERMEABILITY

24. CONSTANT HEAD PERMEABILITY TEST
 Quantity of water (Q) that flows under a given hydraulic
gradient through a soil sample of known length & cross
sectional area in a given time (t).
 Water is allowed to flow through the cylindrical sample of soil
under a constant head.
For testing of pervious, coarse grained soils
k = Coefficient of permeability
Q = total quantity of water
t = time
L = Length of the coarse soil
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SOIL PERMEABILITY

25. CONSTANT HEAD PERMEABILITY TEST SETUP
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SOIL PERMEABILITY
Fig. 9 Constant Head Permeability test setup
Source: Fig. 9 - Venkatramaiah, C., “Geotechnical Engineering”

26. FALLING HEAD PERMEABILITY TEST
 Relatively for less permeable soils
 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.
t = time
L = Length of the fine soil
A = cross section area of soil
a= cross section area of tube
k = Coefficient of permeability
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SOIL PERMEABILITY

27. FALLING HEAD PERMEABILITY TEST SETUP
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SOIL PERMEABILITY
Fig. 10 Falling Head Permeability test setup
Source: Fig. 10 - Venkatramaiah, C., “Geotechnical Engineering”

28. Example 3
A sample in a variable head permeameter is 8 cm in diameter and 10 cm
high. The permeability of the sample is estimated to be 10 × 10–4cm/s. If
it is desired that the head in the stand pipe should fall from 24 cm to 12
cm in 3 min., determine the size of the standpipe which should be used?
Solution:
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SOIL PERMEABILITY

29. Department of Civil
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SOIL PERMEABILITY
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30. Example 4
The discharge of water collected from a constant head
permeameter in a period of 15 minutes is 500 ml. The internal
diameter of the permeameter is 5 cm and the measured
difference in head between two gauging points 15 cm vertically
apart is 40 cm. Calculate the coefficient of permeability.
Solution:
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SOIL PERMEABILITY

31. PERMEABILITY – STRATIFIED SOIL DEPOSITS
 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 kV and kH respectively.
 Consider a stratified soil having horizontal layers of
thickness H1, H2, H3, etc. with coefficients of
permeability k1, k2, k3, etc.
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SOIL PERMEABILITY
Fig. 11 Permeability of stratified soil deposits
Source: Fig. 11 - NPTEL

32. For vertical flow
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For horizontal flow
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SOIL PERMEABILITY

33. Example 5
A horizontal stratified soil deposit consists of three layers each
uniform in itself. The permeabilities of these layers are 8 × 10–4
cm/s, 52 × 10–4 cm/s, and 6 × 10–4 cm/s, and their thicknesses
are 7, 3 and 10 m respectively. Find the effective average
permeability of the deposit in the horizontal and vertical
directions.
Solution:
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SOIL PERMEABILITY

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SOIL PERMEABILITY

35. QUICK SAND CONDITION
Quicksand forms in saturated loose sand when suddenly agitated.
When water in the sand cannot escape, it creates a liquefied soil
that loses strength and cannot support weight.
In the case of upwards flowing water, seepage forces oppose the
force of gravity and suspend the soil particles causing lose of
strength.
The cushioning of water gives quicksand, and other liquefied
sediments, a spongy, fluid-like texture.
Objects in liquefied sand sink to the level at which the weight of
the object is equal to the weight of the displaced soil/water mix
and the submerged object floats due to its buoyancy.
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SOIL LIQUEFACTION
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36. MECHANISM
 An upward flow opposes the force of gravity and cause to
counteract completely the contact forces.
 Effective stress is reduced to zero and the soil behaves like a
very viscous liquid - Quick sand condition.
 This condition occurs in coarse silt or fine sand subject to
artesian conditions.
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SOIL LIQUEFACTION
Fig. 12 Quick sand condition - Mechanism
Video link : https://www.youtube.com/watch?v=eImtYyuQCZ8
Source: Fig.12 - NPTEL

37. Contd….
At the bottom of the soil column,
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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.
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SOIL LIQUEFACTION

38. SOIL LIQUEFACTION
 Liquefaction is a special case of quicksand.
 In this case, sudden earthquake forces immediately increase
the pore pressure of shallow groundwater.
 The saturated liquefied soil loses strength, causing buildings
or other objects on that surface to sink.
Video link : https://www.youtube.com/watch?v=ZMWKTuRgJjY
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SOIL LIQUEFACTION

39. REFERENCES
 Arora K R., “Soil Mechanics and Foundation Engineering”,
Standard Publishers, 2011.
 Venkatramaiah, C., “Geotechnical Engineering”, New Age
International Publishers, New Delhi,6th edition, 2018.
 https://nptel.ac.in/courses.php
 https://en.wikipedia.org/
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