Settlement 1 2

7/21/2019 Settlement 1 2

1/16

Soil SettlementBy

Kamal Tawfiq, Ph.D., P.E., F.ASCE

Fall 2010


2/16

Soil Settlement:Total Soil Settlement = Elati! Settlement " Conoli#ation Settlement

Stotal= Se" S!

$oa# Ty%e &'i(i#) Fle*i+le

Elati! Settlement o- mme#iate Settlement #e%en# on

Settlement $o!ation &Cente- o- Co-ne-

/ Theo-y of Elati!ity

Elati! Settlement

Time De%en#e# Elati! Settlement &S!hme-tman a-tman etho# &1345/By: Kamal Tawfiq, Ph.D., P.E.

Elati! ettlement o!!6- in an#y, ilty, an# !layey oil.


3/16


4/16

Elati! Settlement

Se= &1 > ?2

2

&!o-ne- of the fle*i+le fo6n#ation

Se= &1 > ?2

&!ente- of the fle*i+le fo6n#ation

By: Kamal Tawfiq, Ph.D., P.E.


5/16


.0

2.

2.0

1.

1.0

L / B

.02 5 4 1031

,av,r

??a8

?-

Fo- !i-!6la- fo6n#ation? = 1?a8= 0.5

?-= 0.55

9al6e of ?, ?a8, an# ?-

Bqo &1 > ?

ESe =


6/16


Elastic Settlement of o!ndation on Sat!rated Clay

Gan+6, BHe--6m, an# KHae-nli &13 %-o%oe# an eq6ation fo- e8al6ation of thea8e-a(e elati! ettlement of fle*i+le fo6n#ation on at6-ate# !lay oil &PoionI-atio, >= 0.. 'efe--in( to Fi(6-e 1 fo- notation, thi eq6ation !an +e w-itten a

Se= A1A2qoBE

whe-e A1i a f6n!tion B an# $B, an# i a f6n!tion of D fB.Ch-itian an# Ca--ie- &1345 ha8e mo#ifie# the 8al6e of A1an# A2to ome e*tent, an# thee a-e%-eente# in Fi(6-e 2.

1.0

0.5

0.3

0

DfB

20110

A2

L/B =

Sq6a-e

L/B = 10

Ci-!le

2

2.0

1.

010

0.

1.0

10.1 100 1000

H /B

A1

9al6e of A1 an# A2 fo- elati! ettlement !al!6lation &afte- Ch-itian an# Ca--ie-, 1345


7/16

Elastic Settlement "sin# t$e Strain %nfl!ence actor: @S!hme-tman a-tman etho# &1345J

E*am%le:B x L

EsDf Iz

De%th,

q= L Df&'1

q

&'2

&'

&'

s3

Is3

A8e-a(e A8e-a(e E

The 8a-iation of the t-ain infl6en!e fa!to- with #e%th+elow the fo6n#ation i hown in Fi(6-e 1.ote that, fo- q6a-e o- !i-!6la- fo6n#ation,

= 0.1 at = 0= 0. at = 0.B

= 0 at = 2B

Simila-ly, fo- fo6n#ation with $B M 10

= 0.2 at = 0= 0. at = B= 0 at = B

Se = C1C2& q q N & E ;

whe-e= t-ain infl6en!e fa!to-C1= a !o--e!tion fa!to- fo- the #e%th of fo6n#ation em+e#ment

= 1 0. @q &q qJ

C2= a !o--e!tion fa!to- to a!!o6nt fo- !-ee% in oil = 1 " 0.2 lo( &time in yea- 0.1q = t-e at the le8el of the fo6n#ationq = o8e-+6-#en %-e6-e = L Df


8/16

Elati! Pa-amete- of 9a-io6 Soil

Oo6n(I o#6l6, E

Ty%e of Soil Bm2 $+Bin2 PoionI 'atio,

$ooe an# 10.C 2.1 1,00 C,00 0.20 0.0e#i6m #ene an# 14.2 24.0 2,00 ,000 0.2 0.0Dene an# C.0 .20 ,000 5,000 0.C0 0.Silty an# 10.C 14.2 1,00 2,00 0.20 0.0San# an# -a8el 3.00 142.0 10,0002,000 0.1 0.CSoft !lay 2.04 .15 C00 40e#i6m !lay .15 10.C 40 1,00 0.20 0.0Stiff !lay 10.C 2.1 1,00 C,00

E&QBm2 = 4E= 2q!

whe-e = tan#a-# %enet-ation n6m+e-q!= tati! !one %enet-ation -eitan!e

ote: Any !onitent et of 6nit !an +e 6e#

The Oo6n(I mo#6l6 of no-mally !onolia#ate# !lay !an +e etimate# a

E= 20! to 00!

Fo- o8e-!onoli#ate# !lay

E= 40! to 1000!

whe-e ! = 6n#-aine# !oheion of !layey oil


9/16

E*am%le:

2

12,000 20,000

De%th, &m

5

,000

B x L = 3 m x 3m

Es (k/m!"1.# m

q = 1$0 k/m!

%&'al

0.!

2 1.

Iz= 0.5

0.)

00.1 0.$

%*+a-+

Iz

= 14.5 Qm

De%th &m R &m E&Q:Bm2 A8e-a(e &BE. K &mBQ:

0 1 1 5,000 0.2 0.231 * 10

1.0 1. 0. 10,000 0. 0.214 * 10

1. 2. 10,000 0.F1 0.30 * 10

.0 F 2 1F,000 0.111 0.13 * 10

= 1.0 * 10

C1= 1 0. &q B q q

= 1 0. @ 14.F5 * 1. B 1F0 &14.5 * 1.J

C2= 1 " 0.2 lo( &B0.1 = 1.

en!e

S! = C1. C2&q q &BE K

= &0.3&1.@1F0&14.5*1.J&1.*10

= 23.2*10m 2.3 mm

0

2B

Tim+ = # y+as


10/16

! !2

St-ee# Rone

Conoli#ation Settlement

Conoli#ation Settlement &P-ima-y Conoli#ation = S!= &C!1"eo !. lo( @&Po" PPoJ

#ei(n= Col6mn $oa#

OverburdenPressure

o


San#

San#

aly

B

*

*

StressDistribution

o-mallyConoli#ate#Clay


11/16

2

1

p

p

Hsand

Hclay

/2 Hclay

Cc

Log PPo

Void Ratio

Log P

P

Void Ratio

Po Po + P

Cc H log po+pSultimate= H =Po1 + eo

( )

Log P

P

Void Ratio

Po Po +

P

2

1

p

Hsand

Hclay

/2 Hclay

Loading Unloading

Po= sand Hsand+ ( clay! "ate#) Hclay/2

$o#mallyConsolidated Soil

Clay

Sand

Sand

eo


Consolidation Settlement

Sand

Sand

Sand

Sand

=CS H

1 + eO P0

Po + Plog( )

% %

% %

%%


12/16

Cs H PcSultimate= H =Po 1 + eo

( ) logCc H

+1 + eo

logPc

( )Po + P2

Log P

P

Void Ratio

Po Po + P=Pc

2

1

p2

p2

Hsand

Hclay

/2 Hclay

2

1

p

Hsand

Hclay/2 Hclay

Log P

Void Ratio

Po Pc

P2

Cs

Cs

Po + P2

%&e soil 'ecomeoe#consolidated

soil

eo

Re loading"it& Heay Load


%%

%2

%2%2

%%

= log ( ) +CS H

1 + eO

PCPo

C C H

1 + eO PC

Po + Plog( )


13/16

Cs H PcSultimate= H =Po

( )1 + eo

log

Log P

P

Void Ratio

Po Pc

2

1

p2

p2

H sand

Hclay/2 H clay

2

1

p

H sand

H clay/2 H clay

Log P

Void Ratio

Po Pc

P 2

C s

Po + P2%&e soil 'ecomeoe#consolidated

soil

eo

Re loading"it& lig&t Load


%

%2%2

%2

%2

= logCS H

1 + eO Po

Po + P ( )2


14/16

Log P

Void Ratio

CR = Pc/PoCR = 1CR * 1CR *

o-mally Conoli#ate#

ea8ily 8e- Conoli#ate#

8e- Conoli#ate#

Pc

,ete#mining %&e P#econsolidation P#essu#e (Pc)

1

-

2

.


Po

0

Caa(-an#e -a%hi!al etho#


15/16

#ei(n= Col6mn $oa#

"o

*++2P+ss+

=Ex&+ss P+ 4a'+ P+ss+

=Ex&+ss P+ 4a'+ P+ss+

o

Hdr = Hc

5'+ss Dis'i'i2!: 1 m+'h

6!= $aye- Thi!Qne


Rate o Consolidation

Settlement at any time = Stime

Stime= Sultimate U3 S6ltimate= &C!1"eo !. lo( @&Po" PPoJ

U3 = (%)

%= (c)

%=(Hd#)

2

c t

San#

San#

Caly


16/16

Rate o Consolidation

Settlement at any time = Stime

Stime= Sultimate U3

U3 = (%)

%=

%= %ime 4acto#

t = time (mont&5 day5 o# yea#)(H

d#)2= ,#ainage Pat&

Hd#= H o# H/2

%= (c)

(Hd#)2

c t

C= Coeicient o Consolidation

Cv is obtained from laboratory testing

Clay

Sand

Sand

Clay

Roc6

Sand

%"o "ay d#ainageHd#= Hclay/2

ne "ay d#ainageHd#= Hclay

From Tables


Settlement 1 2

Documents

Transcript of Settlement 1 2