46...prof. b v s viswanadham, department of civil engineering, iit bombay effect of sample...

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

46


Module 3:

Lecture - 8 on Compressibility and Consolidation


Stresses in soil from surface loads; Terzaghi’s 1-D consolidation theory; Application in different boundary conditions; Ramp loading; Determination of Coefficient of consolidation; Normally and Over-consolidated soils; Compression curves; Secondary consolidation; Radial consolidation; Settlement of compressible soil layers and Methods for accelerating consolidation settlements.

Contents


Effect of sample disturbance on e-logσ′ curvesNC ClayCurve I: e – log σ′ variation for

an undisturbed normallyconsolidated clay in the field.Curve II: e – log σ′ variationobtained from consolidation teston a carefully recoveredspecimen.Curve III: e – log σ′ variationobtained from consolidation teston a remoulded specimen.

e – log σ′ curves intersect at 0.4e0(Terzaghi and Peck, 1967)


Effect of sample disturbance on e-logσ′ curves

Curve I: e – log σ′ variation foran undisturbed over consolidatedclay in the field.Curve II: e – log σ′ curve onlaboratory specimen.Schmertmann (1953) concluded thatthe field recompression branch (ab)has approximately the same slope asthe laboratory unloading branch, cf.

e – log σ′ curves intersect at 0.4e0(Terzaghi and Peck, 1967)

OC Clay

Cr ≈ Cc/5 - Cc/10


Effect of load incrementsStandard 1D Consolidation tests are conducted with asoil specimen having a thickness of 25.4 mm in whichthe load on the specimen is doubled every 24 hours.

This means that

What will be the effect of any deviation from thestandard procedure?

Striking changes in the shape of the compression-timecurves for 1D consolidation tests are noticed if themagnitude of

1=′

∆σσ

25.0<′

∆σσ


After Leonards and Altschaeffl (1964)

Effect of load incrementsLeonards and Altschaeffl (1964) conducted several testson Mexico city clay with different load increment ratiosand with the variation of excess PWP measurement withtime.

For , the positionof end of primaryconsolidation issomewhat difficult toresolve and also Cα/Ccincreases with thedecrease of load-increment ratio.

25.0<′

∆σσ


1=′

∆σσ

1>′

∆σσ

1<′

∆σσ

Void

ratio

, e

Log σ′

Effect of load increments

When , the ability ofindividual particles toreadjust to theirpositions is small, whichresults in a smallercompression comparedto

1<′

∆σσ

1≥′

∆σσ


Effect of load durationIn conventional consolidation test, in which a soil specimen leftunder given load for about a day, a certain amount of secondaryconsolidation takes place before the next load increment is added.

Load duration justsufficient for primaryconsolidation

Increasing load duration

Volume change due to secondary compression

Shape of curves become less distinctwith longer period/duration and it ismore difficult to determine σ′c

For soils that display secondarycompression vol. changes occurafter the end of primaryconsolidation (if each loadincrement is in place for a longerperiod). Most common for NC andlightly OC soils. Heavily OC soilsare less prone for secondarycompression.


For similar load increment ratios proportion ofsecondary to primary compression increases with adecrease in sample thickness.

Also, the ratio of secondary to primary compressionincreases with decrease of load settlement ratio.

Effect of sample thickness


Effect of secondary consolidationThe continued secondaryconsolidation of a natural claydeposit has some influence onthe preconsolidation pressure σ′c.

A clay that has recently beendeposited and comes to equilibriumby its own weight can be called a“young, normally consolidated clay.”

Curve a is for young NC clayσ′c = σ′0 at e0.

If the same clay is allowed to remain undisturbed for 10,000 yrs, for example,under the same effective overburden pressure σ′0, there will be creep orsecondary consolidation. This will reduce the void ratio to e1. The clay maynow be called an aged NC clay.


If the clay at e1 and effective overburden pressure σ′0, then curvelooks like ‘b’. The preconsolidation pressure, when determinedby standard procedure, will be σ′1.

Now, σ′c = σ′1 > σ′0. This is sometimes referred to as a quasipreconsolidation effect (More pronounced in plastic clays)

Effect of secondary consolidation

Bjerrum (1972) gave an estimate ofthe relation between the plasticityindex and the ratio of quasi-preconsolidation pressure to effectiveoverburden pressure σ′c /σ′0 for lateglacial and postglacial clays.


Terzaghi’s equilibrium states

If a series of load-increments is applied to specimenwhich is initially very wet, the resulting equilibriumstates will appear, as shown below.


The outermost curve connecting the points when thespecimen is in the looses possible states is referred asthe virgin compression line, because it is strictly theline connecting equilibrium states whereasconsolidation is a term used only for the timedependent process between any pair of equilibriumstates.Equation of virgin compression line:


Equation of virgin compression line will also bedenoted by the equation:

And equation for swelling and recompression loop willbe represented by a single straight line of the form;

Where λ and κ are characteristic constants for the soil.Virgin compression λ - line represents an irreversibleprocess, whereas the swelling and recompression κ-linesrepresent reversible processes.


1D compression and swelling

NCL

e

A

O

C

σ′zσ′o

DB

σ′y

e

A

O

, C

logσ′zσ′= 1 kPa

DB

σ′0

e0

eκ

Slope -Cc

Slope -Cs

σ′y

Equation for normal compression line OACD is given by:e = e0 – Cc logσ′z

• Equation for swelling and recompression line ABC is given by:e = eκ – Cs logσ′z


1D compression and swelling

Since δv = δe and log10x = 0.43lnx, we get Cc = 2.3λ and Cs = 2.3κ

For OC soil at a point such as B the yield stress ratio Y0is given by: Y0 = σ′y/σ′0; where is the current stress andis the yield point which lies at the intersection of theswelling line through B with normal compression line.


Deposition

Erosion

σ′z

σ′h

za

zb

zc

wA

BC

wa

wc

logσ′σ′aσ′c σ′b

1D consolidation and swellingof soil in the ground due todeposition and erosion

B

A

σh′

σz′

σ′z = σ′hK0 = 1

Erosion


1D consolidation and swelling of soil in the ground dueto deposition and erosion


Variation of water content inthe ground in NC and OC soils

σ′a

σ′b

za

zb

zc

A

B

σ′c

σ′d

zc

C

D

Consider variation of watercontent with depth for a depositwhich is lightly eroded (i.e.depth of erosion Zc is small) orheavily eroded (i.e. depth oferosion is large)


Variation of water content inthe ground in NC and OC soils

w

z

w

AB

C

σ′zσ′a σ′b

D

A

B

C

D

σ′a

σ′b

For the lightly eroded soil the difference between thewater contents at A and B is relatively large, while forheavily eroded soil the difference between the watercontents at C and D is much smaller.

Low water contentsat C and D attributedto the very large paststress.


ExampleAn oedometer test was performed on a clay sample 30mm thick, drained on both sides, and taken from mid-stratum shown below. Seventy percent consolidationwas attained in 6.67 minutes. Find:

a) The time required to attain 70% consolidate of theclay stratum

b) The magnitude of that settlement in that time


Example


Solution


ExampleAn oedometer test is performed on a 100 mm thickspecimen, drained on top and bottom. It was observedthat 45% consolidation (Tv = 0.15) was attained in 78hours. Determine the time required to attain 70%consolidation (Tv = 0.40) in a job site where the claystratum is shown in the figure.


Solution

In such situations, if the significant amountconsolidation settlements can occur in the designedlife of a structure, there is a need for acceleratingconsolidation of soils…

46...prof. b v s viswanadham, department of civil engineering, iit bombay effect of sample...

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