Chapter 3 compaction and consolidation

Shivaji University
TE Civil
GEotechnical ENgineering -I
unit3 notes

1. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 1 of 16

Compaction
Q: Differentiate between compaction and consolidation
Sr. Compaction Consolidation
1 Mechanical process carried out to reduce
the volume of sub-soil below the structure
It is unwanted process of reduction in volume
of sub-soil below the structure
2 Compaction is carried out before
construction of structure.
Consolidation starts after construction of
structure
3 Soil experiences dynamic loading for volume
reduction
Soil experiences static loading (self weight of
structure) for volume reduction
4 It is very fast process It is very slow process
5 Expulsion of air voids, causes reduction in
volume
Expulsion of water voids, causes reduction in
volume
6 For proper compaction process water
content should be at OMC level.
For consolidation process soil should be
saturated.
7 It does not go indefinitely It goes on indefinitely
8 Reduces settlement of structure Responsible for settlement of structure
Q: Explain dry density and water content relationship for soil
Q: Explain compaction process and compaction curve.
 Mechanical process carried out to reduce the volume of sub-soil through expulsion of air voids
below the structure in order to increase the dry density of soil.
 The increase in dry density ensures the increase in resistance (bearing capacity) of soil.
 Compaction is carried out before construction of structure.

dry density and water content relationship-compaction curve
OMC- optimum moisture content at which dry density is maximum for soil,
MDD – maximum dry density ZERO AIR VOIDS LINE
MODIFIED
PROCTOR TEST
STANDARD
PROCTOR TEST
MDD-1
MDD-2
OMC-1 OMC-2
Water Content (%)
Dry Density

2. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 2 of 16

 Explanation of graph:
o Optimum Moisture Content (OMC) is the moisture content at which the maximum
possible dry density is achieved for a particular compaction energy or compaction
method.
o The corresponding dry density is called Maximum Dry Density (MDD).
o Water is added to lubricate the contact surfaces of soil particles and improve the
compressibility of the soil matrix.
o It should be noted that increase in water content increases the dry density inmost soils
up to one stage (Dry side).
o Water acts as lubrication.
o Beyond this level, any further increase in water (Wet side)will only add more void space,
there by reducing the dry density.
o Hence OMC indicates the boundary between the dry side and wet side.
o Hence the compaction curve as shown in figure indicates the initial upward trend up to
OMC and the down ward trend.
 Effect of Compaction process: 1) Increases density 2) Increases strength characteristics 3)
Increases load-bearing capacity 4) Decreases undesirable settlement 5) Increases stability of
slopes and embankments 6) Decreases permeability 7) Reduces water seepage 8) Reduces
Swelling & Shrinkage 9) Reduces frost damage 10) Reduces erosion damage 11) Develops high
negative pore pressures (suctions) increasing effective stress
Q: Explain Standard Proctor test/ Modified Proctor test.
Q: differentiate between Standard Proctor test & Modified Proctor test.
Sr. Standard Proctor Test Modified Proctor Test
1 Mould capacity 1000 cc or 2250 cc Mould capacity 1000 cc or 2250 cc
2 Rammer used- 2.6 kg
Drop height =31cm
Rammer used- 4.89 kg
Drop height = 45cm
3 Three layers for soil compaction Five layers for soil compaction
4 Number of blows:
If 1000cc mould used = 25 for each layer
If 2250cc mould used = 56 for each layer
Number of blows:
If 1000cc mould used = 25 for each layer
If 2250cc mould used = 56 for each layer
5 MDD is low compared to Modified test
OMC is high compared to Modified test
MDD is high compared to Standard test
OMC is low compared to Standard test
Procedure:
1. About 3 kg of dry soil, passing through 4.75 mm sieve.
2. Add approx.5-8% of water for the first trial. (Less -Corse grained & more -Fine grained soil)
3. Find dimensions and weight of mould. Note it down separately.
4. The inner surfaces of mould, base plate and collar are greased.

3. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 3 of 16

5. Soil is placed in mould and compacted in 3 uniform layers for SPT/ 5 layers for MPT , with 25
blows in each layer of standard rammer (Rammer used- 2.6 kg wt. & drop height =31cm for
SPT/4.89 kg wt. & drop height =45cm for SPT for MPT)
6. After final layer remove excess soil/ trim top surface
7. Weigh the mould and soil. Take some sample of soil for determination of water content.
8. The procedure is repeated with increasing water content.
9. The number of trials shall be at least 6 with a few after the decreasing trend of bulk density.
10. Plot the graph of dry density vs water content.

Q: Explain compaction methods and its suitability
 Rammers:
o Rammers are used for compacting small areas by providing impact load to the soil. This
equipment is light and can be hand or machine operated.
o For machine operated rammers, the usual weight varies from 30kg to 10 tonnes.
o These hammers with 2- 3 tonnes weights are allowed to free fall from a height of 1m to
2m on the soil for the compaction of rock fragments.
o Rammers are suitable for compacting cohesive soils as well as other soils.
o This machine used in areas with difficulty in access.
 Vibrating Plate Compactors:
o Vibrating plate compactors are used for compaction of coarse soils
o These equipments are used for small areas.
 Vibro Tampers:
o Vibro tampers is used for compaction of small areas in confined space.
o This machine is suitable for compaction of all types of soil by
 Smooth Wheeled Rollers:
o Smooth wheeled rollers are of two types: Static smooth wheeled rollers & Vibrating
smooth wheeled rollers
o The most suitable soils for these roller type are well graded sand, gravel, crushed rock,
asphalt etc. where crushing is required.
o These are used on soils which does not require great pressure for compaction. ZERO AIR VOIDS LINE
MODIFIED
PROCTOR TEST
STANDARD
PROCTOR TEST
MDD-1
MDD-2
OMC-1 OMC-2
Water Content (%)
Dry Density

4. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 4 of 16

o These rollers are generally used for finishing the upper surface of the soil.
o These roller are not used for compaction of uniform sands.
o The performance of smooth wheeled rollers depend on load per cm width it transfers to
the soil and diameter of the drum.
o The smooth wheeled rollers consists of one large steel drum in front and two steel
drums on the rear. The gross weight of these rollers is in the range of 8-10 tonnes.
o The other type of smooth wheel roller is called Tandem Roller, which weighs between 6-
8 tonne.
o The performance of these rollers can be increased by increasing the increasing the
weight of the drum by ballasting the inside of drums with wet sand or water.
o In case of vibrating smooth wheeled rollers, the drums are made to vibrate by employing
rotating or reciprocating mass.
o These rollers are helpful from several considerations like:- (i) Higher compaction level
can be achieved with maximum work (ii) Compaction can be done up to greater depths
(iii) Output is many times more than conventional rollers
o Although these rollers are expensive but in the long term the cost becomes economical
due to their higher outputs and improved performance.
o The latest work specifications for excavation recommends the use of vibratory rollers
due to their advantage over static smooth wheeled rollers.
 Sheepsfoot roller Roller:
o Sheepsfoot rollers are used for compacting fine grained soils such as heavy clays and
silty clays.
o Sheepsfoot rollers are used for compaction of soils in dams, embankments, subgrade
layers in pavements and rail road construction projects.
o Sheepsfoot rollers are of static and vibratory types.
o Vibratory types rollers are used for compaction of all fine grained soils and also soil with
sand-gravel mixes.
o Generally this roller is used for compaction of subgrade layers in road and rail projects.
o The weight of drums can be increased as in the case of smooth wheeled rollers by
ballasting with water, wet sand or by mounting steel sections.
o The efficiency of sheepsfoot rollers compaction can be achieved when lugs are gradual
walkout of the roller lugs with successive coverage. The efficiency is affected by the
pressure on the foot and coverage of ground obtained per pass. For required pressure
and coverage of ground, the parameters such as gross weight of the roller, the area of
each foot, the number of lugs in contact with the ground at any time and total number
of feet per drum are considered.
o The compaction of soil is mainly due to foots penetrating and exerting pressure on the
soil. The pressure is maximum when a foot is vertical.
 Pneumatic Tyred Rollers:
o Pneumatic tyred rollers are also called as rubber tyred rollers.
o These rollers are used for compaction of coarse grained soils with some fines.
o These rollers are least suitable for uniform coarse soils and rocks.
o Generally pneumatic tyred rollers are used in pavement subgrade works both earthwork
and bituminous works.

5. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 5 of 16

o Pneumatic rollers have wheels on both axles. These wheels are staggered for
compaction of soil layers with uniform pressure throughout the width of the roller.
o The factor which affects the degree of compaction is tyre inflation pressure and the area
of the contact.
 Grid Rollers:
o Grid rollers are used for compaction of weathered rocks, well graded coarse soils.
o These rollers are not suitable for clayey soils, silty clays and uniform soils.
o The main use of these rollers are in subgrade and sub-base in road constructions.
o As the name suggests, these rollers have a cylindrical heavy steel surface consisting of a
network of steel bars forming a grid with squire holes.
o The weight of this roller can be increased by ballasting with concrete blocks.
o Typical weights vary between 5.5 tonnes net and 15 tonnes ballasted.
o Grid rollers provide high contact pressure but little kneading action and are suitable for
compacting most coarse grained soils.
 Pad Foot / Tamping Rollers:
o These rollers are similar to sheep foot rollers with lugs of larger area than sheep foot
rollers.
o The static pad foot rollers also called tamping rollers have static weights in the range of
15 to 40 tonnes and their static linear drum loads are between 30 and 80 kg/cm.
o These rollers are more preferable than sheep foot roller due to their high production
capacity, and they are replacing sheep foot rollers.
o The degree of compaction achieved is more than sheep foot rollers.
o The density of soil achieved after compaction with this roller is more uniform.
o These rollers operate at high speeds, and are capable to breaking large lumps.
o These rollers also consists of leveling blades to spread the material.
o Pad foot or tamping rollers are best suitable for compacting cohesive soils.
Q: Explain compaction Field control of compaction methods and its suitability
Q: Explain field compaction control
Objective of Field Compaction Control:
The following are the important objectives of field compaction control:
1. To determine the in-situ dry density and water content immediately after the compaction
2. To check and ensure that the soils from the prescribed borrow area, having the desired
properties, are used for compaction.
3. To check and ensure that the required compaction energy is used in compacting the soil. This
consists of ensuring that the required type of roller suitable to the soils being compacted is used
as well as that the roller is of required capacity.
4. Certain minimum number of tests are to be done in the field when the compaction is in progress
Determination of In-Situ Density:
The determination of relative compaction requires the following finding:
 In-situ bulk density.
 Field moisture content.
The in-situ density can be computed by following methods:
 Core cutter method.
 Sand replacement method.

6. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 6 of 16

 Rubber balloon method.
Determination of water content of compacted soil can be done by following methods:
 Calcium carbide method
 Proctor’s Needle Method:
 Nuclear Method
Proctor Needle Test
Principle: The basic principle of Proctor’s needle method is to determine the water content of
compacted soil indirectly without drying the sample based on the resistance offered by the
compacted soil to the penetration of Proctor’s needle.
About Test:
 The Proctor’s needle consists of a needle attached to a spring-
loaded plunger.
 The needle consists of a needle point attached to the bottom of a
needle shank, as shown in Fig.
 The needle can be pushed into the compacted soil by pressing the
loading plunger.
 The needle shank has graduations to read the penetration of the
needle into the compacted soil.
 The stem of the loading plunger has graduations to show the
resistance offered by the compacted soil to the penetration of the
needle.
 The loading plunger is calibrated to indicate the penetration
resistance of the compacted soil based on the deformation of the
spring, which depends on the load applied and the spring constant.
 Needle points of different cross-sectional areas are supplied along
with the equipment such as 0.25, 0.5, 1.0, and 2.5 cm
2
to use in
compacted soils of increasing penetration resistance.

Determination of In-Situ Moisture Content and Dry Density:
 The soil used for compaction in the field, mixed with placement water content, is compacted into
the compaction mould using the same compaction energy.
 The Proctor’s needle with the same needle point as used for preparation of calibration chart is
forced into the compacted soil in the mould and the penetration resistance is determined.
 The water content and dry density of the compacted soil are then read from the calibration chart
corresponding to the penetration resistance.

7. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 7 of 16

Consolidation
Q: Explain Terzaghi’s spring-mass analogy
Q: Explain Terzaghi’s consolidation theory
 Consolidation is process of reduction in volume due to expulsion of water particle with the
application of static load for long duration

Terzaghi’s Spring Mass Analogy
Assumptions:
 The soil medium is completely saturated
 The soil medium is isotropic and homogeneous
 Darcy’s law is valid for flow of water
 Flow is one dimensional in the vertical direction
 The coefficient of permeability is constant
 The coefficient of volume compressibility is constant
 The increase in stress on the compressible soil deposit is constant (∆σ´ = constant)
 Soil particles and water are incompressible
One dimensional theory is based on the following hypothesis
1. The change in volume of soil is equal to volume of pore water expelled.
2. The volume of pore water expelled is equal to change in volume of voids.
3. Since compression is in one direction the change in volume is equal to change in height.

 T=0
 σ = u and σ´=0
 Soil=Spring
 Water= Water Void
 After application of load -
primary consolidation Start
 No reduction in volume
 0<T<∞
 σ = u + σ´
 All load is resisted by water
 flow is upward
 reduction in volume
 spring & water share load
 T = ∞
 All the load is resisted by
spring
 Water doesn’t carry any load
 Soil solids carry external
pressure
 Excess pore water pressure is
zero
 End of primary consolidation

8. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 8 of 16

Theory
 Terzaghi’s model consists of a vessel with a piston attached to spring as shown.
 The space below piston is filled with water. The piston has outlet to allow for passage of
water.
 Piezometers can be inserted to measure the excess pore water pressure.
 Terzaghi has correlated the spring mass compression process with the consolidation of
saturated clay subjected to external load σ.
 The springs and the surrounding water represent the saturated soil.
 The springs represent the soil skeleton networks of soil grains and water in the vessels
represents the water in the voids.
 In this arrangement the compression is one dimensional and flow will be in the vertical
direction.
 When pressure σ is applied this will be borne by water surrounding the spring
σ = u and σ´=0 at time t =0
where, u is called excess hydrostatic pressure and there will be no volume change.
 After sometime ‘t’ there will be flow of water through outlet.
 Since the flow is in upward direction/segment there will be reduction in volume.
 Due to this spring get compressed and being to carry a portion of the applied load.
 This signifies a reduction in excess pore water pressure and increase in effective stress.
σ = u + σ´ load shared by both water and spring
 At time t = ∞ when no more pore water flows out the excess hydrostatic pressure will be
and the entire load is carried by spring.
σ = σ’ and u=0 at time t =∞
Q: Explain laboratory consolidation test
The test is conducted to determine the settlement due to primary consolidation. To determine :
 Rate of consolidation under normal load.
 Degree of consolidation at any time.
 Pressure-void ratio relationship.
 Coefficient of consolidation at various pressures.
 Compression index.
From the above information it will be possible for us to predict the time rate and extent of
settlement of structures founded on fine-grained soils. It is also helpful in analyzing the stress history
of soil. Since the settlement analysis of the foundation depends mainly on the values determined by
the test, this test is very important for foundation design.

Principal Involved

9. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 9 of 16

When a compressive load is applied to soil mass, a decrease in its volume takes place, the
decrease in volume of soil mass under stress is known as compression and the property of soil mass
pertaining to its tendency to decrease in volume under pressure is known as compressibility. In a
saturated soil mass having its void filled with incompressible water, decrease in volume or
compression can take place when water is expelled out of the voids. Such a compression resulting
from a long time static load and the consequent escape of pore water is termed as consolidation.
Procedure
1] Saturate two porous stones by keeping them submerged in the distilled water for 4 to 8 hrs.
Wipe away excess water.
2] Assemble the consolidometer, with the soil specimen and porous stones at top and bottom of
specimen, providing a filter paper between the soil specimen and porous stone. Position the
pressure pad centrally on the top porous stone.
3] Mount the mould assembly on the loading frame, and center it such that the load applied is
axial.
4] Position the dial gauge to measure the vertical compression of the specimen. The dial gauge
holder should be set so that the dial gauge is in the begging of its releases run, allowing
sufficient margin for the swelling of the soil, if any.
5] Connect the mould assembly to the water reservoir and the sample is allowed to saturate. The
level of the water in the reservoir should be at about the same level as the soil specimen.
6] Apply an initial load to the assembly. The magnitude of this load should be chosen by trial, such
that there is no swelling.
7] The load should be allowed to stand until there is no change in dial gauge readings for two
consecutive hours or for a maximum of 24 hours.
8] Note the final dial reading under the initial load. Apply first load of intensity 0.1 kg/cm2 start the
stop watch simultaneously. Record the dial gauge readings at various time intervals. The dial
gauge readings are taken until 90% consolidation is reached. Primary consolidation is gradually
reached within 24 hrs.
9] At the end of the period, specified above take the dial reading and time reading. Double the load
intensity and take the dial readings at various time intervals. Repeat this procedure for
successive load increments. The usual loading intensity are as follows :
a. 0.1, 0.2, 0.5, 1, 2, 4 and 8 kg/cm2.
10] After the last loading is completed, reduce the load to half of the value of the last load and allow
it to stand for 24 hrs. Reduce the load further in steps of half the previous intensity till an
intensity of 0.1 kg/cm2 is reached. Take the final reading of the dial gauge.
11] Reduce the load to the initial load, keep it for 24 hrs and note the final readings of the dial
gauge.
12] Quickly dismantle the specimen assembly and remove the excess water on the soil specimen in
oven, note the dry weight of it.
Analysis:
(1) Calculate the initial water content and specific gravity of the soil.
(2) For each pressure increment, construct a semi-log plot of the consolidation dial readings versus
the log time (in minutes). Determine the coefficient of consolidation (cv).
(3) Calculate the void ratio at the end of primary consolidation for each pressure increment. Plot log
pressure versus void ratio. Based on this plot, calculate compression index, recompression index
and preconsolidation pressure (maximum past pressure).

10. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 10 of 16

Q: Explain Log – time curve fitting method to find coefficient of consolidation (Cv)
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 P and Q on the upper portion of the consolidation curve (say compression line)
corresponding to time t1 and t2 such that t 2 =4t 1
iii. Let x be the difference in dial reading between P and Q. locate R at a vertical distance x above
point P
iv. Draw a horizontal line RS the dial reading corresponding to this line is d 0 which corresponds
with 0% consolidation.
v. Project the straight line portion of primary and secondary consolidation to intersect at point T.
The dial reading corresponding to T is d 100 and this corresponds to 100% consolidation.
vi. Determine the point V on the consolidation curve which corresponds to the dial reading of
d 50 = (d 0 +d 100)/2 . The time corresponding to point V is t 50 i.e time for 50% consolidation.


Log – time curve fitting method

11. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 11 of 16

Q: Explain Square root of time method to find coefficient of consolidation (Cv)
i. Plot the dial reading and the corresponding square-root-of-time &#3627408481; as shown in Figure
ii. Draw the tangent PQ to the early portion of the plot.
iii. Draw a line PR such that OR = (1.15)(OQ).
iv. The abscissa of the point S (i.e., the intersection of PR and the consolidation curve) will give
√&#3627408481;90 ( i.e., the square-root-of-time for 90% consolidation).
v. The value of ???????????? for Uav = 90% ??????&#3627408480; 0.848. so,


Square root of time method
Q: Explain soil compressibility characteristics
Q: Explain normally consolidated, over and under consolidated soil
 A laboratory soil specimen of dia 60mm and height 20mm is extracted from the undisturbed soil
sample obtained from the field.
 This sample is subjected to 1D consolidation in the lad under various pressure increments.
 Each pressure increment is maintained for 24 hrs and equilibrium void ratio is recorded before
the application of the next pressure increment.
 Then a plot of void ratio versus effective stress is made as shown in Fig.
 When the sample is recompressed from point D it follows DE and beyond C it merges along BCF
and it compresses as it moves along BCF
 During the initial stages (at low effective stress) sample follows recompression path (portion AB)
and undergoes less compression.
 Beyond this is the virgin compression line (portion BC) also called the normal compression line
and the sample undergoes large compression.
1. BC – Virgin compression curve also called normal consolidation line

12. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 12 of 16

2. From ‘C’ when the sample is unloaded, sample expands and traces path CD (expansion curve
unloading)
3. Sample undergoes Permanent strain due to irreversible soil structure and there is a small elastic
recovery.
4. The deformation recovered is due to elastic rebound
5. When the sample is reloaded-reloading curve lies above the rebound curve and makes an
hysteresis loop between expansion and reloading curves.
6. The reloaded soils shows less compression.
7. Loading beyond ‘C’ makes the curve to merge smoothly into portion EF as if the soil is not
unloaded.

Soil Compressibility

13. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 13 of 16

It is the maximum effective stress experienced by a soil in its stress history (past existence)

 For the soil loaded along the recompression curve AB the effective stress close to point B will
be the preconsolidation pressure.
 If the soil is compressed along BC and unloaded along CD and then reloaded along DC the
effective stress close to point C will be the new preconsolidation pressure.
Effect of Stress History
It is based on the stress history (preconsolidation pressure) soils are classified as
1. Normally Consolidated Soils
2. Over Consolidated Soils
3. Under Consolidated Soils
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.

14. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 14 of 16

Over Consolidated Soils It is a soil deposit that has been subjected to vertical effective stress greater
than the present vertical effective stress.
Q: how to determine pre-consolidation pressure ?
Determination of Preconsolidation Pressure (Yield Stress)
Step 1. Conduct an oedometer test on the undisturbed soil sample obtained from the field.
Step 2. Plot e - log σ´ plot as shown. The equilibrium void ratio at the end of each of the pressure
increments are used in obtaining e - log σ´ plot.
Step 3. Select the point of maximum curvature (Point A) on the e - log σ´ curve
Step 4. Draw a tangent at the point of maximum curvature (Point A)
Step 5. Draw a horizontal line AC
Step 6. Draw the bisector line AD between the tangent and horizontal line
Step 7. Extend the normally consolidated line to intersect the bisector line at ‘O’
Step 8. The vertical effective stress corresponding to point of intersection (O) is the
preconsolidation pressure (σ´pc)

Q: Explain compressibility characteristics mv, av,Cc
Compressibility Characteristics
The compressibility of soils under one-dimensional compression can be described from the decrease
in the volume of voids with the increase of effective stress. This relation of void ratio and effective
stress can be depicted either as an arithmetic plot or a semi-log plot.
It can be said that the compressibility of a soil decreases as the effective stress increases.
This can be represented by the slope of the void ratio – effective stress relation, which is called the
coefficient of compressibility, av.
??????
??????=
&#3627408466;
1− &#3627408466;
2
??????
2
′
− ??????
1
′

O

15. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 15 of 16

Co-efficient of volume compressibility (mv) It is the ratio of change in volume of a soil per unit initial
volume due to unit increase in effective stress and is given by ??????
??????=
??????
&#3627408483;
1+ &#3627408466;
??????



Coefficient of compression/compression index (Cc):It is the slope of the normal consolidation line in
a plot of void ratio-logarithm of effective stress (e - logσ´). It is given by

Empirical correlations
Cc = 0.009 (LL-10) Undisturbed clays
Cc = 0.007 (LL-10) Remoulded soil sample
Cc = 1.15 (e0-0.30) Upper bound values
Cc = 0.30 (e0-0.27) Lower bound values
The value of Cc is constant for a given soil. The compression index is used to determine primary
consolidation settlement of normally consolidated soils. A high value of Cc indicates high
compressibility and higher consolidation settlement.

16. Compaction & Consolidation
Prof. P.P. Prabhu-GTE Notes Page 16 of 16

Formulae in Consolidation chapter:
 Compression index
 It is a slope of pressure-voids ratio curve when plotted on logarithmic graph
 &#3627408464;
??????=
&#3627408466;0− &#3627408466;
log10
(
??????′
??????0
′
)

 Coefficient of compressibility
 It is a slope of pressure-voids ratio curve when plotted on natural graph
 ??????
??????=
&#3627408466;0− &#3627408466;
??????
′
− ??????0
′

 Coefficient of volume change
 ??????
??????=
??????&#3627408483;
1 + &#3627408466;0

 Where, e0 is initial voids ratios when pressure = ??????
0
′
, e is voids ratio when pressure
change to ??????
′

 Consolidation settlement
 ??????
&#3627408467;= ??????
?????? ?????? ∆??????′
 H = soil thickness, ∆??????′= pressure increment
 Coefficient of Consolidation
 &#3627408464;
??????=
??????
??????&#3627408483; ??????&#3627408484;

 Where, k is coefficient of permeability
 From consolidation test data
o &#3627408464;
??????=
&#3627408455;&#3627408483;
??????
&#3627408465;
2

o ??????
??????=
??????
4
(
&#3627408456;
100
)
2
….when degree of consolidation =U < 60%
o ??????
??????= −0.9332 log
10(1−
&#3627408456;
100
)− 0.0851….when degree of consolidation =U > 60%
o Where, Tv is time factor, t is time required for consolidation, d is drainage path
o d = soil thickness when soil has single drainage
o d = (soil thickness/2) when soil has double drainage