Week 5 - Consolidation

8/18/2019 Week 5 - Consolidation

1/24

Last Updated:April 22, 2016 © LMS SEGi education group 1

SOIL MECHANICS II

WEEK

!"#S"L$%A&$"#

PowerPoint ® Slides

by Mr Mohamad Shakri


2/24


Chapter Overview

' !(apter 1 introduced )ou *it( t(e process o+

consolidation using spring analog)

' Application o+ &er-ag(i.s t(eor) o+ one/

diensional consolidation *ill e introduced


3/24

Learnin Ob!e"tives

' &o proide understanding on t(e terinolog) o+

t(e consolidation

' &o introduce t(e students *it( t(e consolidation

process *it( using spring analog)' &o introduce students *it( t(e &er-ag(i.s t(eor)

o+ t(e one/diensional priar) consolidation



4/24

Learnin O#t"omes

' 4e ale to understand t(e process o+ t(e

consolidation

' Ale to understand and appl) &er-ag(i.s t(eor)

o+ one/diensional priar) consolidation



5/24

THE OEDOMETER TEST

s f f

f

Ge ω

ω

==

=

swellingafterratioVoid

swellingaftercontentwaterFinal

AMethod

( )

1ely,Alternativ

stage,aof startatratioVoid

1ratio,in voidchange(10.1);eqn.From

ssin thicne!hange

andstageaof endandstartat"hicness

stageaof endat theratioVoid

readings.thicnessandcontentwaterfinal

thefrom #acwards #y woringo#tained #emay

stageincrementloadeachof startat theratiovoid"he

0

10

1

1

1

1

−=

∆+=

+∆

=∆

−=∆=

=

=

s

o

o

o

f

H

H e

eee

e H

H e

H H H

H H

e

1swellingafterratioVoid

$articlessolidof thicness%q&ivalent

sam$letestof Area $eriodswellingafterthicnessFinal

swellingaftermass'ry

(Method

−=−

==

==

==

=

s

f

s

s f

f

w s

d s

f

d

H

H

H

H H e

AG

M H

A H

M

ρ

ooo e

e

H

H

V

V

+

∆

=

∆

=

∆

1


6/24

6

THE OEDOMETER TEST - Result Interpretation

Plotting compression curves

The data collected from the oedometer test

enables changes in void ratio to be related tochanges in effective stress.

The amount of consolidation settlement canthen be obtained using the e/σ ’ curve. Figure 10.7 shows void ratio/effective stress curve (e/σ ’ ).

onsolidation of settlement then is given b!"

Fig. 10.# swelling $ recompression path.

The shape of e/σ

’ curve depends on theconsolidation histor!. %f the soil was initiall!normally consolidated the compression path &'moves along .

&fter unloading from point ' it follows theswelling line (*+) to , reloading would cause

recompression to - and further loading normalcompression from - onword.

0

0

10

11 H

e

ee H

e

e H

o +

−=

+

∆=∆

ooo e

e

H

H

V

V

+

∆=

∆=

∆

1


7/24


-etermination of coefficient of volumecompressibilit! (mv )

The coefficient of volume compressibility (mv )represents the amount of change in unit volume

due a unit increase in effective stress.

The value mv is not constant for a given soil but

varies with the level of effective stress.

From euation 10. mv is given b!"

c&rve)theof slo$ee

where

1

1therefore

1(&t

*

*

0

*

0

*

σ σ

σ

σ

e

e

em

e

e

H

H

H

H m

v

v

=∆∆

+⋅

∆∆=

+∆

=∆∆∆

=

ooo e

e

H

H

V

V

+

∆=

∆=

∆

1


8/247


-etermination of the compression inde (Cc )

%f the test data are plotted as e against log σ ’

the found to be a straightl! line Figure 10.2 The initial curved part is representative the

preconsolidation , the greater the length of thiscurve the greater amount of overconsolidation.

The compression index (Cc) is slope of the

( portion of a straight line) and is measuredfrom the plot"

Thus the change in void ratio for a give in

effective stress is "

The compression index (Cc) ma! be ta3en asa constant in settlement computations providing σ ’ the lies within the limit of the i.e. it is actingas normall! consolidated cla!.

onsolidation settlement is given b!"

( ) *0

*

1

10

*

0

*

1

10

*loglog)loglog σ σ σ σ σ −

−=

−=

∆∆

= eeeee

C c

( )*0*110 )log σ σ cC ee =−

0*0

*

1

0log1 H e

C

s

c

s ×

×+= σ σ


9/248

Compression Index

1

+

1+

logσ

σ

′′−=

eeC c

Recompression Index

1

+

1+

logσ

σ

′′

−=

eeC r

(d) Void ratio versus eective stress(lo! scale)(a"ter Holt# $ %ovacs& '')


10/2410

*i!ure +, S.ellin! andrecompression

(a"ter /0itlo.& 122')


11/2411

Ta3le +,1 Correlation e4uations "or soil compressi3ilit56consolidation(a"ter 7o.les& '8)


12/2412

$%$%& Pre"onsolidation Press#re' Soils (ae a 9eor) o+ t(e stress and ot(er c(anges t(at (ae occurred

during t(eir (istor)

' &(e a;iu stress e;perienced ) t(e soil in t(eir (istor) is B 1, Under !onsolidatedvo

pOCR

σ

σ

′

′=


13/2413

'etermination o( Pre"onsolidation Press#re

)sin Casarande Constr#"tion

' !(oose ) e)e t(e point o+iniu radius =or a;iucurature? on t(e consolidationcure =indicated ) point a?

' %ra* a (ori-ontal line +ro point

a' %ra* a line tangent to t(e cure

at point a' 4isect t(e angle ade ) steps 2

and 3' E;tend t(e straig(t line portion o+

t(e irgin copression cure upto *(ere it eets t(e isectorline otained in step 5 &(e pre/consolidation pressure σ′p is t(eintersect point et*een t(e t*o=indicated ) point + ?

*i!ure +,8 Casa!rande construction


14/24

Worked Example 10.4

T0e "ollo.in! readin!s .ere o3tained "rom an oedometer test on a specimeno" saturated cla5, T0e load 3ein! 0eld constant "or 19 0our 3e"ore t0e

addition o" t0e next increment,

Applied stress

(kPa) 0 25 50 100 200 400 800

Thickness

(mm) 19.60 19.25 18.98 18.61 18.14 17.68 17.24

:t t0e end o" t0e last load period& t0e load .as removed and t0e sampleallo.ed to expand "or 19 0our& at t0e end o" .0ic0 time its t0ic;ness .as'8,1mm and its .ater content "ound to 3e +', percent, T0e speci? curve and "rom it determine t0e compressi3ilit5 index (CC)

and t0e preconsolidation pressure(>?pc),

(c) =lot a mv6> curve "or t0e soil,

(d) @sed t0e data o3tained in (a)& (3)& and A to o3tain and compare t0evalues "or consolidation settlement "or 9m t0ic; la5er o" cla5 .0en t0e


15/24

SOLUTION

*irstl5& determine t0e


16/24

T0e rest o" t0e results and calculations are ta3ulated 3elo.

σ(kPa) !σ (kPa) h (mm) !h (mm) e !e l"# σ (!e$!σ)%10&' m (m2 $*)

0 19.60 1.014

25 &0.'5 &0.0'6 1.440 0.715

25 19.25 0.978 1.40

25 &0.27 &0.028 1.120 0.566

50 18.98 0.950 1.70

50 &0.'7 &0.0'8 1.760 0.'90

100 18.61 0.912 2.00

100 &0.47 &0.048 0.480 0.251

200 18.14 0.864 2.'0

200 &0.46 &0.047 0.2'5 0.126

400 17.68 0.817 2.60

400 &0.44 &0.045 0.11' 0.062

800 17.24 0.772 2.90

0.68 0.070

0 17.92 0.842


17/24

σ’

(a) *i!ure 3elo. s0o.s t0e e vs, >? curve

e' B

2,1

e2 B

2,

> ? 2 B

1 1 2

> ? ' B

+ - 2

e


18/24

*rom t0e curve "or >J2 B 112& e B 2,"or >J' B +2& e B 2,1

Fe B (2, -2,1) '2+ B 2,2++ '2+

F>? B +2 K 112 B '92

' G e2 B ' G 2, B ',

Volume compressi3ilit5& mV B (Fe6F>?)('6'Ge2)

B Fe6LF>?('Ge2) B (2,2++ '2+)6 ('92 ',) B 0.127 m2/MN


19/24

log σ’

e

> ? B + I

(3) T0e e6lo! >? curve is s0o.n 3elo.

T

T

=

R

N


20/24

Compressi3ilit5 index CC B slope o" strai!0t portion

B (2,9 K 2,881) 6 (lo! 22 K lo! 122)

B 0.153

*rom Casa!rande met0od& lo! >? B ',

T0us& t0e preconsolidation met0od& >?p B 35 kPa


21/24

*#estion%%

+able below shows a res#lt o( one dimensional"onsolidation test on a sat#rated sample ornormally "onsolidated "lay%

,inal heiht o( sample whi"h was meas#red a(ter-. ho#rs o( the #nloadin pro"ess is /0%0&mm%+he sample was (#lly sat#rated with water"ontent and spe"i(i" ravity respe"tively o( -1%&2and -%3&

Press#re

45N6m-

78 &8 /88 -88 .88 8

+hi"kness o(sample4mm7

/1%&8 /1%8- /0%13 /0%$& /0%-- /0%0&


22/24

GienC

Water content, * 27D

Speci+ic grait), SG 26

a?

!alculate oid ratio at t(e end o+ eac(pressure stage

? lot t(e oid ratio against log F. cureand deterine t(e alue +or

reconsolidation stress


23/24

Sol#tion%%

Applied Chane in

+hi"kness9

h ∆ h :oid ;atio lo


24/24

;e(eren"e

' %as, 4M =1880? rinciples o+ Geotec(nical

Engineering, t( ed, &(oson Learning, $nc,

USA

Last Updated:April 22 2016 © LMS SEGi education group 25

Week 5 - Consolidation

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