consolidation

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CE 353 Geotechnical Engineering

Lecture Outlines:

1. Introduction

2. Elastic Settlement3. Consolidation Settlement

4. One-Dimensional Laboratory Consolidation Test

5. Void Ratio – Pressure Plots

6. Normally Consolidated and Overconsolidated Soils

7. Calculation of Settlement from 1-D Primary Consolidation

8. Secondary Consolidation

9. Time Rate of Consolidation

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7 th

E. ( Chapter 11).

Compressibility of Soil 11

Dr M. Touahmia

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Introduction

•

Structures are built on soils. They transfer loads to the subsoil through thefoundations. The effect of the loads is felt by the soil normally up to a depth of about

four times the width of the foundation. The soil within this depth gets compressed

due to the imposed stresses. The compression of the soil mass leads to the decrease in

the volume of the mass which results in the settlement of the structure.

• The settlement is defined as the compression of a soil layer due to the loading

applied at or near its top surface.

• The total settlement of a soil layer consists of three parts:

1. Immediate or Elastic Settlement (Se): caused by the elastic deformation of dry

soil and of moist and saturated soils without change in the moisture content.

2. Primary Consolidation Settlement (Sc): volume change in saturated cohesivesoils as a result of expulsion of the water that occupies the void spaces.

3. Secondary Consolidation Settlement (Ss): volume change due to the plastic

adjustment of soil fabrics under a constant effective stress (creep).

sceT S S S S



3

Elastic Settlement

Defined as settlement which occurred directly after theapplication of a load (weight of the foundation), without achange in the moisture content. This is why the elasticsettlement is also called immediate settlement.

The magnitude of the contact settlement will depend onthe flexibility of the foundation and the type of soil.

For perfectly flexible foundation:

For rigid foundation:

• = net applied pressure

•

At center: = 4, B' = B/2 • At corner: = 1 , B' = B

• μs = Poisson’s ratio of soil

• E s = average modulus of elasticity

measured from z = 0 to about z = 4 B

• I s = shape factor (Steinbrenner, 1934)

F 1 & F 2: given in Table 1 & Table 2

for center: m’ = L/B, n’ = H/(B/2)

for corner: m’ = L/B, n’ = H/B

• I f = depth factor (Fox, 19482), Table 3.

21

1

21 F F

s

s

f s

s

s

e I I E BS

2

1

center ,flexiblerigid 93.0

ee S S

z z E E i si s



4

Elastic SettlementTable 1: Variation of F 1 with m’ and n’



5

Elastic SettlementTable 1: Variation of F 2 with m’ and n’



6

Elastic Settlement

Table 4: Representative Values of

Poisson’s Ratio of soil

Table 3: Variation of I f with L/B and D f /B

Table 5: Representative Values of the

Modulus of Elasticity of Soil



Consolidation Settlement

• Consolidation settlement is the vertical displacement of the surfacecorresponding to the volume change in saturated cohesive soils as a result ofexpulsion of the water that occupies the void spaces.

• Consolidation settlement will result, for example, if a structure is built over alayer of saturated clay or if the water table is lowered permanently in a stratumoverlying a clay layer.

•

When a saturated clay is loaded externally, the pore water pressure in the clay willincrease. Because the coefficients of permeability of clays are very low, it willtake some time for the excess pore water pressure to dissipate and the stressincrease to be transferred to the soil skeleton gradually.

• Consolidation is the time-dependent settlement of soils resultingfrom the expulsion of water from the soil pores. The rate of escape of water

depends on the permeability of the soil.




Consolidation of sand

• Permeability of sand is high

• Drainage occurs almost instantaneously – The settlement is IMMEDIATE.

• Elastic and consolidation processes cannot be isolated.

• Primary Consolidation is incorporated in the elastic parameters.

• Coarse-grained soils DO NOT undergo consolidation settlement due to relativelyhigh hydraulic conductivity compared to clayey soils. Instead, coarse-grained soilsundergo IMMEDIATE settlement.




Consolidation of clay

• Permeability of clay is low

• Drainage occurs slowly – therefore, the settlement is DELAYED.

• Settlement can be separated (elastic, primary and secondary consolidation).

•

Clayey soils undergo consolidation settlement not only under the action of “external” loads (surcharge loads) but also under its own weight or weight of soils that existabove the clay (geostatic loads).

• Clayey soils also undergo settlement when dewatered (e.g., ground water pumping) – because the effective stress on the clay increases.




• The time-dependent deformation of saturated clayey soil best can be understood byconsidering a simple model that consists of a cylinder with a spring at its center:

During consolidation, pore water or

the water in the voids of saturated

clayey soils gets squeezed out –

reducing the volume of the soil –

hence causing settlement called as

consolidation settlement.

(Undrained

clay in short

term)

(drained sand

in short term)




•

Variation of total stress, pore water pressure, and effective stress in a clay layerdrained at top and bottom as the result of an added stress, :

(b) At time = 0

(d) At time = (c) At time 0 t

(a) + u

• During consolidation , remains the same, u decreases (due to drainage) while ’

increases, transferring the load from water to the soil.



One-Dimensional Laboratory Consolidation Test

•

The characteristics of a soil during one-dimensional consolidation or swelling can bedetermined by means of the oedometer test.

• The main purpose of consolidation tests is to obtain soil data which is used in

predicting the rate and amount of settlement of structures founded on clay.

1. Place sample in ring

2. Apply load

3. Measure height change

4. Repeat for new load.

Before After

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•

Oedometer Test

• The oedometer test is used to investigate the 1-D consolidation behaviour of fine-

grained soils.• An undisturbed soil sample 20 mm in height and 75 mm in diameter is confined in a

steel confining ring and immersed in a water bath.

• It is subjected to a compressive stress by applying a vertical load, which is assumed to

act uniformly over the area of the soil sample.

• Several increments of vertical stress are applied usually by doubling the previous

increment.

• Two-way drainage is permitted through porous disks at the top and bottom.

• The vertical compression of the soil sample is recorded using highly accurate dial

gauges.

• For each increment, the final settlement of the soil sample as well as the time taken to

reach the final settlement is recorded.




•

The compression of soil is possible only when there is an increase in effective stresswhich in turn requires that the void ratio of the soil be reduced by the expulsion of

pore water.

• After a few seconds, the pore water begins to flow out of the voids.

• This results in a decrease in pore water pressure and void ratio of the soil sample and

an increase in effective stress.

• As a result, the soil sample settles as shown in the figure:

+ u




•

The main purpose of consolidation test is to obtain soil properties which are used in predicting the rate and amount of consolidation settlement of structures founded on

clay.

• The most important soil properties determined by a consolidation test are:

– The pre-consolidation stress ( c’ ), This is the maximum stress that the soil has

been subjected in the past.

– The compression index (C c), which indicates the compressibility of a normally-

consolidated soil.

– The swelling index (C s), (recompression index, C r ), which indicates the

compressibility of an over-consolidated soil.

– The coefficient of consolidation (C v), which indicates the rate of compression

under a load increment.




•

The general shape of the plot of deformation of the specimen against time for a givenload increment is shown below. From the plot, we can observe three distinct stages:

Occur after complete dissipation of the excess pore

water pressure, this is caused by the plastic adjustment

of soil fabric

Mostly caused by preloading

Excess pore water pressure is gradually transferred into

effective stress by the expulsion of pore water



Void Ratio – Pressure Plots

•

The step-by-step procedure for getting the void ratio-pressure relationship is asfollows:

• Step 1: Calculate the height of solids, H s from:

• Step 2: Calculate the initial height of voids as:

• Step 3: Calculate the initial void ratio, eo:

• Step 4: For the first incremental loading 1

calculate the change in the void ratio as:

• Step 5: Calculate the new void ratio after consolidation:

For the next loading, 2, the void ratio at the end of consolidation:

At this time, 2 = 2’ .

Void

Solid

Specimen

area = A



Void Ratio – Pressure Plots

• The effective stress ’ and the corresponding void ratios e at the end of consolidation

are plotted on semi-logarithmic graph:

In the initial phase, relatively greatchange in pressure only results in less

change in void ratio e. The reason is

part of the pressure got to compensate

the expansion when the soil specimen

was sampled. In the following phase e

changes at a great rate



Normally Consolidated and Overconsolidated Soils

• Normally Consolidated Soil: A soil that has never experienced a vertical effective

stress that was greater than its present vertical effective stress is called a normally

consolidated (NC) soil.

• Overconsolidated Soil: A soil that has experienced a vertical effective stress that was

greater than its present vertical effective stress is called an overconsolidated (OC)

soil.

When the effective pressure on the specimen

becomes greater than the maximum effective past

pressure, the change in the void ratio is much

larger, and the e – log ’ relationship is practically

linear with a steeper slope (b to c) or ( f to g ).

This relationship can be verified in the laboratory

by loading the specimen to exceed the maximum

effective overburden pressure, and then unloading

and reloading again (c – d – f – g ).




• Preconsolidation pressure: the maximum effective past pressure, which can be

determined as follow (Casagrande , 1936):

• The overconsolidation ratio :

1. Establish point a, at which the e – log ’ plot has a

minimum radius of curvature.

2. Draw a horizontal line ab.

3. Draw the line ac tangent at a.4. Draw the line ad, which is the bisector of the angle bac.

5. Project the straight-line portion gh of the e – log ’ plot

back to intersect line ad at f . The abscissa of point f is

the preconsolidation pressure, c ’.

c’ = preconsolidation pressure

’ = effective vertical pressure

• The OCR for an OC soil is greater than 1.

• Most OC soils have fairly high shear strength.

• The OCR cannot have a value less than 1.

cOCR




Consolidation characteristics of overconsolidated

clay of low to medium sensitivityConsolidation characteristics of of normally

consolidated clay of low to medium sensitivity



Calculation of Settlement from One-Dimensional

Primary Consolidation

• Because of an increase of effective pressure, s, let the primary settlement be Sc. Thus,

the change in volume can be given by:

• For normally consolidated clays, that exhibit a linear

e – log ’ relationship:Solid

Void

Soil



23

Calculation of Settlement from One-Dimensional

Primary Consolidation

• For normally consolidated clays:

• For overconsolidated consolidated clays:

If then:

If then:

c

c

Compression index C c = slope of the e – log ’ plot

Skempton (1944) suggested: C c = 0.009( LL-10)

Swell index C s = slope of the rebound curve

cc s C C C

5

1 to

10

1



24

Secondary Consolidation

• It is the settlement due to plastic compression arising out of readjustment of soil

particles at constant effective stress. It occurs after primary consolidation settlement.

• the secondary compression index can be defined as:

• The magnitude of the secondary consolidation can be calculated as:



25

Time Rate of Consolidation

• Terzaghi(1925) derived the time rate of consolidation based on the following

assumptions: 1. homogeneous clay-water system;

2. complete saturation;

3. zero compressibility for water;

4. zero compressibility for solid grains;

5. One-D flow;

6. Darcy’s law is valid



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• Variation of U z with T

v and z / H

dr :



27


• Variation of average degree of consolidation U with time factor, T v (u

o constant with

depth):



28


• Table 6: Variation of T v

with U :



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• Coefficient of consolidation (C v

)

Log-of-Time Method (Cassagrande)

1. Extend the straight line portion of primary and

secondary consolidation curve to intersect at

A. A is d 100, the deformation at the end of

consolidation.

2. Select times t 1 and t 2 on the curve such that t 2

= 4t 1. Let the difference is equal to x.

3. Draw a horizontal line (DE) such that the

vertical distance BD is equal to x. The

deformation of DE is equal to d 0.

4. The ordinate of point F represents thedeformation at 50% primary consolidation,

and it abscissa represents t 50.

5. For 50% average degree of consolidation, T v

= 0.197 (see Table 6), so:

or

50

2

dr 197.0

t

H C

v 2

dr

50

50

H

t C T v




• Coefficient of consolidation (C v

)

Square-Root-of-Time Method (Taylor)

1. Draw a line AB through the early portion of the

curve.

2. Draw a line AC such that OC = 1.15 OB. Theabscissa of D which is the. intersection of AC

and the consolidation curve, gives the square-

root-of-time for 90% consolidation.

3. For 90% consolidation, T 90 = 0.848 (see Table

6), so:

or

90

2

dr 848.0

t

H C

v 2

dr

90

90 848.0

H

t C T v

consolidation

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