This document discusses the consolidation of soil. It defines important terms like compression, compressibility, and consolidation. It outlines the differences between compaction and consolidation. The importance of consolidation theory is that it provides information on total settlement, time for settlement, and types of settlement. Terzaghi's spring analogy is described to explain the consolidation process. A one-dimensional consolidation test procedure is outlined. Important definitions related to consolidation like compression index, swelling index, and coefficients are provided. The document also discusses normally, under, and over consolidated soils and how to determine preconsolidation pressure. Terzaghi's one-dimensional consolidation theory and solution are presented. Methods to determine degree of consolidation and coefficient of consolidation from laboratory test data are

1. CONSOLIDATION
OF SOIL
Prepared by:
Arbaz M. Kazi
Asst. Professor,
VCET, Vasai (W)

2. Contents:
1. Important Terminologies
2. Difference between Compaction & Consolidation
3. Importance of consolidation theory
4. Terzaghi’s Spring Analogy
5. One Dimensional Consolidation Test
6. Important Definitions
7. Normally, Under & Over Consolidated Soil
8. Determination of Pre-consolidation Pressure
9. Terzaghi’s One Dimensional Consolidation Theory
10.Solution to 1-D Consolidation.
11.Determination of Co-efficient of Consolidation
12.Computation of Consolidation Settlement

3.  Compression:
The change in the volume of a soil mass under stress is
known as compression.
 Compressibility:
The property of soil mass pertaining to its susceptibility to
decrease in volume under pressure is called compressibility.
 Consolidation:
According to Terzaghi “every process involving a decrease
in water content of a saturated soil without replacement of water by air
is called consolidation”
 Swelling:
The process of increase in water content due to increase in volume
of voids is called as swelling.
IMPORTANT TERMINOLOGIES

4. Sr.
No
COMPACTION CONSOLIDATION
1 Expulsion of pore air Expulsion of pore water
2 Soil involved is partially saturated Fully saturated soil
3
Applies to cohesive as well as
cohesionless soils
Applies to cohesive soils only
4
Brought about by artificial or
human agency
Brought about by application of load
or by natural agencies
5
Dynamic loading is commonly
applied
Static loading is commonly applied
6 Relatively quick process Relatively slow process
7
Relatively complex phenomenon
involving expulsion, compression,
and dissolution of pore air-in water
Relatively simple phenomenon
8
Useful primarily in embankments
and earth dams
Useful as a means of improving the
properties of foundation soil
DIFFERENCE BETWEEN COMPACTION &
CONSOLIDATION

5. IMPORTANCE OF CONSOLIDATION STUDY
The study of consolidation helps to provide answers
for:
1. Total settlement (volume change).
2. Time required for the settlement of compressible
layer. The total settlement consists of three
components.

6. Elastic Settlement or Immediate Settlement
This settlement occurs immediately after the load is applied. This is due to distortion
(change in shape) of soil mass. There is negligible flow of water in less pervious soils.
In case of pervious soils, the flow of water is quick at constant volume. This is
determined by elastic theory (E & μ are used).
Primary Consolidation Settlement
It occurs due to expulsion of pore water from the voids of a saturated soil. In case of
saturated fine-grained soils, the deformation is due to squeezing of water from the
pores leading to rearrangement of soil particles. The movement of pore water depends
on the permeability and dissipation of pore water pressure.
Secondary Consolidation Settlement
This is also called Secondary compression (Creep). “It is the change in volume of a
fine-grained soil due to rearrangement of soil particles (fabric) at constant effective
stress”. The rate of secondary consolidation is very slow when compared with primary
consolidation.
Types of Settlement

7. Terzaghi’s Spring Analogy

8.  Fig. a shows piston and spring arrangement where piston is of 10 units
and length of spring is Zo.
 Fig. b shows compression of the spring due to addition of 2 units
surcharge above piston which compresses length of spring to Z1.
 More load application will cause spring to further decrease in length and
within elastic limit the load deflection curve may be assumed to be
straight.
 Fig. c shows piston and spring arrangement kept in a cylinder in which
water is filled till bottom of piston and valve is kept open.
 Fig. d shows surcharge of 2 units added above piston and valve is kept
closed, but additional load doesn’t causes spring to compress (this is so
because water is incompressible hence entire 2 units load is being
borne by water alone only).

9.  Fig. e shows valve is partially open and water is allowed to escape, the
piston moves down, there slight exchange of pressure from water to
spring.
 Fig. f shows valve being completely open, hence water escaped out the
cylinder and length of spring compressed to Z1 this is because entire
transfer of pressure from water to spring.
 Hence we can say when there is pressure increment it is first borne by the
water. As water escapes the system, load transfer takes place from water
to spring until full compression of spring takes place.
 This analogy can also be applied to the consolidation process of soil mass
comprising of soil-water system in which spring represents grain
structure, cylinder represents voids filled with water and valve opening
represents permeability of a soil sample.

10. One Dimensional Consolidation Test
• This test is also called as ‘Oedometer Test”
• This test is performed to determine the magnitude and rate of volume
decrease that a laterally confined soil specimen undergoes when
subjected to different vertical pressures.
• From the measured data, the consolidation curve (pressure-void ratio
relationship) can be plotted.
• This data is useful in determining the compression index Cc, the
recompression index Cr and the Preconsolidation pressure (or
maximum past pressure) of the soil.
• In addition, the data obtained can also be used to determine the
coefficient of consolidation Cv and the coefficient of secondary
compression mv of the soil.

11. Equipment:
 Consolidation device (including ring, porous stones, water reservoir, and load
plate).
 Dial gauge (0.001 mm = 1.0 on dial).
 Sample trimming device, glass plate, Metal straight edge, Clock, Moisture can,
Filter paper.
Test Procedure:
• Weighing the empty consolidation
ring together with glass plate.
• Measuring the height (h) of the ring
and its inside diameter (d).
• Extruding the soil sample from the
sampler, generally thin-walled Shelby
tube.

12. • Cutting approximately a three-inch long sample. Being careful throughout
the trimming process to insure that there is no void space between the
sample and the ring.
• Turning the ring over carefully and removing the portion of the soil
protruding above the ring. Using the metal straight edge, cutting the soil
surface flush with the surface of the ring.
• Place the previously weighed Saran-covered glass plate on the freshly cut
surface, turn the ring over again, and carefully cut the other end in a similar
manner.
• Weigh the specimen plus ring plus glass plate.
• Adjust the dial gauge to a zero reading set the pressure gauge dial (based
on calibration curve) to result in an applied pressure of 0.2 kg/sq.m
• Record the consolidation dial readings at the elapsed times given on the
data sheet etc.

15. • After 24hrs increase the
applied pressure to 0.5 kg/sq.m
and continue this till applied
pressure of 8kg/sq.m in a time
interval of 24 hrs.
• After final settlement is
observed note it down and start
unloading the weights.
• Remove weight one by one
• Tabulate the readings as
shown.

19. The straight-line portion of virgin compressive curve is expressed by the equation
given by Terzaghi.
𝑒 = 𝑒0 − 𝐶𝑐 . 𝑙𝑜𝑔10
𝜎′
𝜎0′
Where, e0 = initial void ratio coressponding to initial pressure σ0′
e = void ratio coressponding to increased pressure σ′
Cc = compression index
Hence the above equation can be rewritten as
𝐶𝑐 =
𝑒0 − 𝑒
𝑙𝑜𝑔10
𝜎′
𝜎0′
=
∆ 𝑒
𝑙𝑜𝑔10∆ 𝜎′
IMPORTANT DEFINITIONS
1. Compression Index:

20. The expansion curve is also a straight line and is expressed by;
𝑒0 = 𝑒 + 𝐶𝑠 . 𝑙𝑜𝑔10
𝜎′
𝜎0′
Where, Cs = swelling index
Different equation given for compression index by different researchers are:
Cc = 0.007(𝑤 𝐿 − 10%)
Cc = 0.009(𝑤 𝐿 − 10%)
Cc = 0.3(𝑒0 − 0.27)
2. Swelling Index:

21. 3. Co-efficient of compressibility (𝑎 𝑣): It is defined as the decrease in the void
ratio per unit increase in pressure.
𝑎 𝑣 =
−∆𝑒
∆𝜎′
=
𝑒0 − 𝑒
𝜎′ − 𝜎0′
4. Co-efficient of volume change (𝑚 𝑣): It is defined as change in volume of a
soil per unit initial volume due to given unit increase in pressure.
𝑚 𝑣 =
∆𝑒
1 + 𝑒0
.
1
∆𝜎′
=
𝑎 𝑣
1 + 𝑒0
When soil is laterally confined the change in volume is proportional to
change in thickness (ΔH) and initial volume is proportional to initial
thickness (𝐻0)
𝑚 𝑣 =
−∆𝐻
𝐻0
.
1
∆𝜎′
=
𝑎 𝑣
1 + 𝑒0
Therefore, ΔH = −𝑚 𝑣 . 𝐻0 . ∆𝜎′

22. Normally Consolidated Soils
It is a soil deposit that has never subjected to a vertical effective stress greater
than the present vertical stress.
Under Consolidated Soils
A soil deposit that has not consolidated under the present overburden pressure
(effective stress) is called Under Consolidated Soil. These soils are
susceptible to larger deformation and cause distress in buildings built on these
deposits.
Over Consolidated Soils
It is a soil deposit that has been subjected to vertical effective stress greater
than the present vertical effective stress.

23. Determination of Preconsolidation Pressure:
The earliest and the most widely used
method was the one proposed by
Casagrande (1936).The method involves
locating the point of maximum
curvature, on the laboratory e-log p
curve of an undisturbed sample as shown
in Fig. Below From B, a tangent is
drawn to the curve and a horizontal line
is also constructed. The angle between
these two lines is then bisected. The
abscissa of the point of intersection of
this bisector with the upward extension
of the inclined straight part corresponds
to the preconsolidation pressure.

24. Assumptions:
The following are the assumptions of one-dimensional consolidation theory;
a) The soil is homogeneous and fully saturated.
b) Soil particles and water are incompressible.
c) Darcy’s law for the velocity of flow of water through soil is perfectly
valid.
d) Coefficient of permeability(k) is constant during the process.
e) Soil is laterally confined so that the compression is one dimensional.
f) Excess pore water drains out only in a vertical direction.
g) Linear relationship between effective pressure and void ratio exist are
constant for every stage of consolidation.
h) The time log of consolidation is due entirely to the low permeability of
soil, and thus the secondary consolidation is disregarded.
Terzaghi’s 1D Consolidation Theory:

25. t
V
dxdyvdxdydz
z
v
v z
z
z











t
V
dxdydz
z
vz





rate of water outflow] - [rate of water inflow] = [rate of change of volume]

26. Darcy's law gives
z
u
k
z
h
kkivz





 since hu w
combining gives
t
V
dxdydzz
uk
w 






1
2
2
during settlement
 
t
e
e
dxdydz
t
eVV
t
V
t
V
o
SSv












1
, since 0


t
VS
and
oo
S
e
dxdydz
e
V
V




11 t
e
ez
uk
ow 







1
1
2
2
assume that the decrease in void ratio is proportional to the increase in effective stress (or the
decrease in pore pressure)
uae v
,

27. Where, 𝑎 𝑣 = coefficient of compressibility
Also, coefficient. of volume compressibility is,
o
v
v
e
a
m


1
t
u
m
z
uk
v
w 





 2
2
But coefficient. of consolidation
vw
v
m
k
c

 
t
u
c
z
u
v





2
2
,
The above basic differential equation of consolidation which relates the rate of change of
excess hydrostatic pressure to the rate of expulsion of excess pore water from a unit volume of
soil during same interval.
Solution of 1D Consolidation:
The solution of variation of excess pore water pressure with depth and time can be obtained for
various initial conditions.
Uniform excess pore water pressure with depth
1. Single Drainage (Drainage at top and bottom impervious)
2. Double Drainage (Drainage at top and bottom)

28. Single Drainage (drainage at top and bottom impervious)
Double Drainage

29. Boundary Conditions are
i) At t = 0 Δu = Δσ and Δσ’ = 0
ii) At the top z = 0 Δu =0 Δσ = Δσ’
iii) At the bottom z = 2Hdr Δu =0 Δσ = Δσ’
A solution of equation (1) for the above boundary conditions using Fourier seriesis given by
∆ 𝑢(𝑧,𝑡)
=
2∆ 𝑢0
𝑀
∞
𝑚=0
. sin
𝑀𝑍
𝐻𝑑𝑟
. 𝑒−𝑀2.𝑇𝑣
𝑀 =
𝜋
2
. (2𝑚 + 1)
𝑇𝑣 =
𝐶𝑣 . 𝑡
𝐻𝑑𝑟
2
Solution of 1D Consolidation:

30. Degree of Consolidation (U):
(a) Section of clay layer, (b) Excess pore pressure distribution
The degree of consolidation at any depth is given by
𝑈𝑧 = 1 −
2
𝑀
∞
𝑚=0
. sin
𝑀𝑍
𝐻
. 𝑒−𝑀2.𝑇𝑣
Where, Uz = degree of consoildation.

31. Average Degree of Consolidation (U):
The average degree of consolidation for the whole soil deposit at any time isgiven by
U =
Area of the diagram of excess pore water pressure dissipated at any time
Area of the diagram of initial excess pore water pressure
U =
Area shaded
Area of abcd
As per Taylor (1948) solution, the following approximation is possible
when U ≤ 60 %𝑇𝑣 =
𝜋
4
. 𝑈2
when U ≥ 60 %𝑇𝑣 = 1.781 − 0.933. log⁡(100 − 𝑈%)
U = 50% Tv = 0.197
U = 60% Tv = 0.287
U = 90% Tv = 0.848
Typical values of Tv

32. Determination of coefficient of consolidation (Cv) from laboratory data
The coefficient of two graphical procedure are used
1. Logarithm of time method
2. Square root of time method
Log – time curve fitting method
The basis for this method is the theoretical
(Uz) versus log Tv curve and
experimental dial gauge reading and log t
curves are similar.
Steps
I. Plot the dial reading of compression for a given pressure increment versus time to log
scale as shown in figure.
II. Plot two points B and C on the upper portion of the consolidation curve (say
compression line) corresponding to time t1 and t2 such that t2= 4.t1

33. III. Let x be the difference in dial reading between B and C. locate D at a vertical
distance x above point B
IV. Draw a horizontal line DE the dial reading corresponding to this line is d0which
corresponds with 0% consolidation.
V. Project the straight-line portion of primary and secondary consolidation to
intersect at point A. The dial reading corresponding to A is d100 and this
corresponds to 100% consolidation.
VI. Determine the point F on the consolidation curve which corresponds to the dial
reading of
𝑑0+ 𝑑100
2
= 𝑑50. The time corresponding to point F is t50 i.e. time for
50% consolidation.
VII.Determine Cvfrom
𝐶 𝑣 =
𝑇𝑣 . 𝐻2
𝑡
=
0.197 . 𝐻2
𝑡
For Uz = 50%, Tv = 0.197

34. Square-root – time curve fitting method:
Steps:
I. Plot the dial reading and square root of time
i.e. 𝑡for a pressure increment as shown in fig.
II. Draw a tangent AB to the initial portion of the plot
as shown in fig.
III. Draw a line AC such that OB=1.15*OC.
IV. The intersection of the line AC with the second
portion of the curve i.e. point D is marked.
V. The time corresponding to point S represent 𝑡90
(Square root of time for90% consolidation).
𝐶 𝑣 =
𝑇𝑣 . 𝐻2
𝑡
=
0.848 . 𝐻2
𝑡
For Uz > 60%, 𝑇𝑣 = 1.781 − 0.933. log(100 −

35. Computation of Consolidation Settlement:
Consolidation settlement can e computed by two methods:
a. Using Co-efficient of Volume change(𝑚 𝑣)
The consolidation settlement (ρf) when the soil stratum of thickness H has fully consolidated
under a pressure increment Δσ’ is given by equation;
𝜌 𝑓 = 𝑚 𝑣 . H . Δσ’
b. Using void ratio.
The final settlement can be computed using following relation;
𝜌 𝑓 = ∆H =
𝑒0 − 𝑒
1 + 𝑒0
. H
For normally consolidated clay:
𝜌 𝑓 = H .
𝐶𝑐
1 + 𝑒0
. 𝑙𝑜𝑔10
𝜎′
𝜎0′
For Preconsolidated soil:
𝜌 𝑓 = H .
𝐶𝑠
1 + 𝑒0
. 𝑙𝑜𝑔10
𝜎′
𝜎0′