lec 2+3 settlement analysis

8/17/2019 lec 2+3 Settlement Analysis

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FOUNDATION ENGINEERING -I

Settlement Analysis

Course Instructor : Syed Zisan Asi!

Lecture 05Au"ust #$%&

Mirpur University of Science & Technology MirpurAJK


2/38

What is a Settlement?

2

Definition

The total vertical deformation at the surface resulting from :

1. External Load

2. Dewatering

Settlement om!onents1. "mmediate Settlement # Se elastic

2. $rimar% onsolidation Settlement # Sc

&. Secondar% Settlement 'ree!( # Ss

sce S S S S ++=


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De"ne# as settlement $hich occurre##irectly after the application of a loa#%$ithout a change in the moisture content

ause# 'y soil elasticity 'ehavior

The magnitu#e of the contact settlement$ill #epen# on the (e)i'ility of thefoun#ation an# the type of material on$hich it is resting

*or clay% the imme#iate settlementgenerally very small comparing to theconsoli#ation settlement% therefore thisimme#iate settlement mostly ignore#

Usually consi#ere# at san# or san#y soil

IMMEDIATE SETTLEMENT


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IMMEDIATE SETTLEMENT

General Equation (Harr, 1966)

General Equation (Bowles, 1982)


5/38

General Equation (Harr, 1966)

1. Flexile Foun!ation

At "orner

At "enter

A#era$e

%. &i$i! Foun!ation Es ) Elasticit% modulus of soil

* ) +oundation width

L ) +oundation Length

; ; , ) ∞

( ) 21. 2 α

µ s s

o

e E

q B

S −=

( )α µ 21. s s

oe

E

q BS −=

( ) r s s

oe

E

q BS α µ 21

.−=

−+

+++

−+

++=

11

11ln.

1

1ln

1

2

2

2

2

m

mm

mm

mm

π α

( ) av s s

oe

E

q BS α µ 21

.−=

L

Bm =


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I''e!iate Settle'ent


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General Equation (ole*, 19+%)

Es ) Elasticit% modulus of soil

, ) Effective thic-ness of soil la%er e.g. 2 to /* under foundation

0t the center and +1 is multi!lied % /

0t the corner and +1 is multi!lied % 1

%

(( =

1*

%

*

oe F.E

1

.(.qS

µ

=

π 1NMM

N11MMln

1NM1M

NM1M1ln.M

1F

%%

%%

%%

%%%

1

(

LM

(

HN

%

LL =

(( =LL =


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8

Saturated la%

I''e!iate Settle'ent

*

o

%1eE

.qA.AS


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Young’s Modulus

Foundation with L/B ≥ 10

z = 0 Iz = 0.2

z = z1 = B Iz = 0.5

z = z2 = 4B Iz = 0.0

I''e!iate Settle'ent (La-ere! Soil)

Circular Foundation or

L/B =1z = 0 Iz = 0.1

z = z1 = 0.5 B Iz = 0.5

z = z2 = 2B Iz = 0.0


10/38

Exam!le


11/38

Depth

(m)

∆z(m)

Es

(kN/m2)

Iz

(average) (m3/kN)

0.0 – 1.0 1.0 8000 0.233 0.291 x 10-4

1.0 – 1. 0. 10000 0.433 0.21! x 10-4

1. – 4.0 2. 10000 0.3"1 0.903 x 10-4

4.0 – ".0 2.0 1"000 0.111 0.139 x 10-4

Σ 1. x 10-4

( ).3

4.15.16173

4.15.164.314.311 =

−

−=

−

−= x

x

qq

qC &/.1

1.3

4log.2.31

1.3log.2.312 =

+=

+=

t C

( )

mmS

x xS

z E I qqC C S

e

e

B

s

z e

5.2/

(1344.1('4.15.16173('&/.1('.3'

...

/

2

3

21

=

−=

∆−=

−

∑


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When the stress on a saturated cla% la%er in the field isincreased the !ore water !ressure in the cla% willincrease.

*ecause the coefficients of !ermeailit% of cla%s arever% low it will ta-e some time for the excess !ore

water !ressure to dissi!ate and the stress increase to etransferred to the soil s-eleton graduall%.

onsolidation is the !rocess of dissi!ation of excess !ore water !ressure in a row of time.

8ote:Dissi!ation of !ore water !ressure occurs simultaneousl% with the s9ueeingout of the !ore water. Therefore the consolidation time de!end on:

1. The distance of !ore water to e s9ueeed out

2. The coefficient of !ermeailit% of soft soil

onsoli#ation Settlement


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onsoli#ation +hilosophy

S ! , - D A . /

S ! T TL ! M ! - T 0 S s 1

2 / D . , S TA T 3

+ . ! S S U . !

3M M ! D 3 A T!S ! T TL ! M ! - T 0 S i1

+ . 3M A . / , . , - S , L 3 D A T 3, -S ! T T L ! M ! - T 0S c 1

L , 4 T 3M !

S

!

T

T

L

!

M

!

-

T

S ! TTL ! M ! - T U . 5 !

3 D ! A L 3S A S 3

S p r in g0 s o i l p a r tic le s 1

5 a lv e0 so il 6s p e rm e a ' i li t y 1

7 a t e r " lle # c h a m ' e r0 $ a t e r s a t u r a t e # s o i l6 s p o r e s 1

a o

2

o

a i

a o

U - D . A 3 - ! D

0 2

o

8

S

i 1

S i

+ r e s s u r e i s ' o r n e' y p o r e $ a t e r

L a te ra l # e f o r m a t io n

0 2

o

8

S

i

8

S

c

1

S c

a i

a c

S p ri n g c o m p r e s s e #

7 a t e r p re s s u r e r e # u c e #

, - S , L 3 D A T 3, -

7 a t e r i s e ) p e ll e #

L

,

A

D

D . A 3 - ! D . ! ! +

- o $ a t e r ( o $

a c a

s

S s

0 2

o

8

S

i

8

S

c

8

S

s

1

A l l lo a # is ' o rn e ' y s p r in g

2 y # ro s ta t i c p re s s u re0 9 e r o e ) c e s s p o re $ a t e r p re s s u r e 1


14/38

+irst time suggested % Teraghi '123;12/( withseveral assum!tion :1 dimensionalSaturation is com!leteom!ressiilit% of water is negligileom!ressiilit% of soil grains is negligile 'ut soil grains

rearrange(Darc%


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1. 8ormal onsolidation

2. =ver consolidation

OR

OR

po + ∆p < pc

po < pc < po+∆p

o" ≈ 1

o

"≈

o

o

""

lo$.H.

eo1

/"S

∆

o" 1

o

"

o

occ

p

p p H

eo

Cr S

∆++

= log..1

c

oc

o

ccc

p p p H

eoCc

p p H

eoCr S ∆++++=

log..1

log..1


16/38

onsoli#ation +arameters


17/38

0ro"e!ure*

1. Deter'ine t2e oint 3 on t2e e4lo "ur#e

t2at 2a* t2e *2are*t "ur#ature (t2at i*, t2e

*'alle*t ra!iu* o5 "ur#ature)

%. Dra a 2oriontal line 3A

7. Dra a line 3 t2at i* tan$ent to t2e e4lo$ "ur#e at 3

8. Dra a line 3/ t2at i*e"t* t2e an$le A3

. 0ro!u"e t2e *trai$2t line ortion o5 t2e e4lo$

"ur#e a":ar! to inter*e"t 3/. T2i* i*

oint D. T2e re**ure t2at "orre*on!* to

t2e oint i* t2e re4"on*oli!ation re**ure,

".

Deter'ination o5 /on*oli!ation 0roertie*


18/38

Deter'ination o5 /on*oli!ation 0roertie*


19/38

Deter'ination o5 /o're**i#e 0ara'eter*


20/38:ina -usantara

Where :

mv ) om!ression "ndex

,c ) Thic-ness of soft soil la%er

∆ ! ) The stress increment due to the external

load

/on*oli!ation Settle'ent

.H.'S "#" ∆

o

##

1

%

%1#

e1

a'

eea

=


21/38

/on*oli!ation Ti'e

Where :

t ) consolidation time

Tv ) consolidation factor de!ended on consolidation degree '>(

> ) consolidation degree in !ercent descri!t as ratio of design settlement to total settlement

v ) coefficient of consolidation get from consolidation test

= 0 ! "0#

$ "0#

/#

H.Tt

%

#

;+1,1T#

;1==xS

S<

"

i,"

%

#1==

;<

8T


22/38

/on*oli!ation Settle'ent

Hc

0orou* La-er

0orou* La-er

Hc

0orou* La-er

I'er'eale

la-er

Where :

, ) length of water !ath

% = %c % = 0.5%c

/#H.Tt

%

#=


23/38

/on*oli!ation Ti'e o5 La-ere! Soil*

,c1

,c2

,c&

v1

v2

v&

) 4.2 %ears

) &./ %ears

) 7.1 %ears

t ? 6.1 De*i$n

1

%

1,"#

1/#

%H.Tt =

%

%%,"#

%/#

%H.Tt

7

%

7,"#

7/#

H.Tt


24/38

/on*oli!ation Ti'e o5 La-ere! Soil*

- Deter'ine t2e equi#alent o5 H" o5 ea"2 la-er

4Deter'ine t2e *u' o5 equi#alent H"

4Deter'ine t2e "on*oli!ation ti'e

4Deter'ine t2e equi#alent o5 /#

,c1

,c2

,c&

v1

v2

v&

ref

iicic

Cv

Cv H H

? =

e:

%

"

/#

H.T#t ∑

( )

( )

2

2?

.

∑

∑=c

cref ek

H

H CvCv


25/38

E@AM0LE

Determine the total consolidation time of & la%er of cla% which

have different value of coefficient of consolidation and thic-ness for

3@ degree of consolidation.

1st La%er : thic-ness 4 m v ) 4 x 13;& cm2As

2nd La%er : thic-ness & m v ) 7 x 13 ;& cm2As

&rd La%er : thic-ness 5 m v ) 6 x 13;& cm2As


26/38

La%er Thic-ness

',c(

v

'm2

As(

E9uivalent

Thic-ness',c


27/38

E@AM0LE

0 laorator% consolidation test on a normall% cla% showed the following result :

Load ! '-8Am2( Boid ratio at the end of consolidation e

1/3 3.2

212 3.57

The s!ecimen thic-ness was 24./ mm and drained on oth sides. The time re9uiredfor the s!ecimen to reach 43@ consolidation was /.4 min.

0 similar cla% la%er in the field 2.5 m thic- and drained on oth sides is suCectedto similar average !ressure increase that is !o ) 1/3 -8Am

2 and !o∆ ! ) 212 -8Am2.Determine the following :

1. The ex!ected maximum consolidation settlement in the field

2. The length of time it will ta-e for the total settlement in the field to reach /3 mm&. e!eated no.2 !rolem in case of drained on one side


28/38

E@AM0LE

&equire'ent 1

−=

1

2

21

log p

peeCc &&&.3

1/3

212log

57.32.3 =

−=

Cc

o

o

""

lo$.H.

eo1

/"S ∆

mmS c 4.561/3

212log.5.2.231

&&&.3 =+

=


29/38

E@AM0LE

&equire'ent %

Determine field consolidation coefficient

alculate consolidation time

Where :

> ) /4.6@

Tv ) πA/ '>2( ) 3.17/ '> ) /4.6@(

, ) ,cA2 ) 1./ m ) 1/33 mm

v ) 6.371 mm2Amin

We got

? 8%7 'in ? 71.6 !a-*

/#

H.Tt%

#

371.6

1/3317/.3 2

xt =

@6./[email protected]

/3@133

=== x xS

S U

c

ic


30/38

E@AM0LE

&equire'ent 7

alculate consolidation time

Where:

> ) /4.6@

Tv ) πA/ '>2( ) 3.17/ '> ) /4.6@(

, ) ,c ) 2.5 m ) 2533 mm

v ) 6.371 mm2Amin

,ence

? 1+%=97 'in ? 1%6. !a-*

/#

H.Tt

%

#=

371.6

253317/.3 2 xt =


31/38

In5luen"e o5 0ore ater 0re**ure

Two influences of !ore water !ressure to the

settlement are :

i. "nitial average overurden !ressure '!o( should

e in effective condition '!o


32/38

Se"on!ar- /on*oli!ation (/ree)

i. =ccur after !rimar% consolidation !rocess finished

ii. Defined as an adCustment of soil s-eleton after theexcess !ore water dissi!ated.

iii. De!end on time and will e occurred in a longtime

iv. Difficult to e evaluated


33/38

Se"on!ar- /on*oli!ation (/ree)

Time Min1

5 o i #

. a t

i o


34/38

Exa'le

A laorator- te*tin$ o5 "on*oli!ation 5or *e"i'en t2i":ne** %.8 '' i* "arrie! out to !eter'ine t2e

*e"on!ar- *ettle'ent, it2 t2e re*ult a* *2on in t2e 5olloin$ tale


35/38

Exa'le

Assume te tic'ness o( te

com)ressi*le layer is %$ m and teconsolidation settlement is +$ cm ,icoccurs a(ter #& years Te initial .oidratio eo is #/&&0 and te initial dial

readin" is %#1$$ mm

Re!uired :

Com)ute te amount o( secondarycom)ression tat ,ould occur (rom #&to &$ years a(ter construction Assumete time rate o( de(ormation (or te load

ran"e in te test a))ro2imates tat


36/38

Exa'le


37/38

Exa'le

S* ? 8.6 "'

"

*t

ttlo$.H.

e1

/S

∆

α

+= 2443log.13.

&62.21342.3 sS


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Thank you for

listening

lec 2+3 settlement analysis

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