1. foundation and overall istructure designs of continuous spread footings

8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings

1/19

Engineering Structures 71 (2014) 212–221

Contents lists available at ScienceDirect

Engineering Structures

journal homepage !!! " elsevier " com#locate#engstruct

$oun%ation an% overall structure %esigns o& continuous sprea% &ootings

along !ith soil spatial variabilit' an% geological anomal'

S" mana%eh* +" Denis* +" ,arache⇑

-niversit. %e /or%eau* CS* -, 32352,* 6CE Department* /t" /18* +ll.e 6eo&&ro' St 9ilaire* CS 3002:* ::;13 umar

et al" stu%ie% the

sources o& these

natural variabilit'

an% the

⇑ Correspon%ing

author" Ael" :: 3

40 00 88 27 &a

:: 3 40 00 :1 1:"

E5mail a%%resses

s"imana%ehi2m"

u5bor%eau1"&r (S"

mana%eh)* alain"

%enisu5bor%eau"&r

(+" Denis)* antoine"maracheu5bor%eau"&r ( +"

,arache)"

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http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://www.sciencedirect.com/science/journal/01410296http://www.elsevier.com/locate/engstructhttp://www.elsevier.com/locate/engstructmailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://www.sciencedirect.com/science/journal/01410296http://www.elsevier.com/locate/engstructmailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019


2/19

0"101;#j"engs

truct"2014"04"

01 01415

02;# 2014

Elsevier ?t%"

+ll rights

reserve%"

prese

nce o&

a

geolo

gical

anom

al' in

&oun%

ation

%esign

param

eters

F1G"

a'ch

o!%hu

r' et

al"

stu%ie

% the

shallo

!

&oun%

ation response variabilit'

%ue to parameter

uncertaint' F2G"

n &oun%ation %esign* a

lo! !eight buil%ing is

simpl' mo%ele% !ith a

one5%imensional mo%eling

o& a continuous sprea%

&ooting !ith a loa%ing F:G"

9o!ever* in overall

structure %esign* this lo!

!eight buil%ing is

mo%ele% !ith a t!o or

three %imensional

mo%eling o& its continuous

sprea% &ootings along !ith

buil%ing elements such as

columns* beams* !alls

an% slabs F4G"

n these conventional

%esigns an% %imensioning

computations* continuous

sprea% &ootings are o&ten

%esigne% on the

basis o& the

%eterministic

approaches !here

natural variabilit' o&

soil an% uncertaint'

relate% to imper&ect

Bno!le%ge o& the

presence o& a

geological anomal'o& soil * in their

longitu%inal

%irections are usu5

all' not consi%ere%"

Ahese e&&ects an%

the soil–shallo!

&oun%ation

interaction along

the longitu%inal

%irection o&

continuous sprea%

&ootings nee% to be

taBen into account

an% stu%ie% in

or%er to per&orm an

accurate anal'sis

lea%ing to correct

%esigns"

n this research

!orB* t!o

approaches are

use% &or the %esign

o& continuous

sprea% &ootingsthe &irst approach

!ith a &oun%ation

%esign using a

one5%imensional

&inite element

mo%eling (1D) an%

the secon%

approach !ith an

overall structure

%esign using a

three5%imensional

&inite element

mo%eling (:D)"

Ahese approaches

http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://dx.doi.org/10.1016/j.engstruct.2014.04.019http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10http://var/www/apps/conversion/tmp/scratch_5/HYPERLINK%23page10


3/19

S" mana%eh et al" # Engineering Structures 71 (2014) 212–221 21:

are compare% &or t!o cases the &irst case* taBing

into account the spatial variabilit' o& soil mo%ulus

(Es) an% the secon% case* taBing into consi%eration

the spatial variabilit' o& soil mo%ulus accompa5nie%

b' the presence o& a geological anomal' as a lens

o& cla'e' soil o& !eaB mechanical properties"

Ahrough these both approaches an% cases* thesoil–shallo! &oun%ation interaction along the longi5

tu%inal %irection o& continuous sprea% &ootings is

then stu%ie% in or%er to better un%erstan% the

in&luence o& the spatial variabilit' o& Es an% a

geological anomal' on the maimum settlement*

ma5imum %i&&erential settlement an% maimum

ben%ing moment"

n or%er to achieve this goal* geological

con%itions o& the stu%ie% construction site an%

available %ata &rom the geoph'sical an% geo5

technical investigations are presente%" Aherea&ter*

the appropriate geostatistical metho%s (collocate%

or%inar' coBriging an% con%i5tional simulations

F3*;G) are use% to mo%el the spatial variabilit' o&

HoungIs soil mo%ulus (Es) on a construction site"

Ahis spatial var5iabilit' are then use% through the

&inite element mo%eling o& the JinBler soil–

&oun%ation interaction mo%el in the longitu%inal

%irection F7–14G along !ith an% !ithout the

presence o& a geolog5ical anomal' &or both

geotechnical an% structural %esigns o& continuous

sprea% &ootings" $rom these numerical mo%els* the

maimum settlements* maimum %i&&erential

settlements* maimum ben%ing moments an% their

uncertainties are obtaine% in or%er to per&orm a

statistical anal'sis that %escribes the longitu5%inal

behavior o& continuous sprea% &ootings in 1D an%

:D mo%els" $inall'* a comparison bet!een theobtaine% results &rom &oun%a5tion an% overall

structure %esigns is %one to stu%' &irstl'* the in&lu5

ence o& the spatial variabilit' o& soil mo%ulus an%

secon%l'* the in&luence o& this spatial variabilit'

couple% !ith the presence o& a geological anomal'

on the behavior o& continuous sprea% &ootings"

2" Soil–shallo! &oun%ation interaction mo%el

n the conventional calculations o& the shallo!

&oun%ations %esign* the behavior is onl' stu%ie% in

a cross section to represent the transverse

behavior o& the &oun%ation elements" n the case o& a continuous sprea% &ooting an% particularl' !hen

a %i&&erential set5tlement ma' appear* the

longitu%inal behavior o& sprea% &ooting shoul% be

taBen into consi%eration"

n the past* man' researchers have !orBe% on

the soil–structure interaction !hich is re&erre% to as

beams an% plates on elastic &oun%ations" ,ost o&

the previous !orB began !ith JinBlerIs !ell Bno!n

mo%el !ith one parameter F13G* !hich !as

originall' %evelope% &or the anal'sis o& railroa%

tracBs" Ahis mo%el is epresse% b' the &ollo!ing

e@uation (E@" (1))

pKL M Bs b !KL K1L

!here Bs is the coe&&icient o&

subgra%e reaction* !() is the

%e&lec5tion* b is a !i%th o& the

&oun%ation an% p() is the reactive

pressure o& the &oun%ation"

JinBlerIs i%ealiation consi%ers the

soil as being a s'stem o& i%entical

but mutuall' in%epen%ent* closel'space%* %is5crete* linearl' elastic

springs" +ccor%ing to this

i%ealiation* %e&or5mation o&

&oun%ation %ue to applie% loa% is

con&ine% to loa%e% regions onl'"

$urthermore this mo%el cannot

transmit the shear stresses !hich

are %erive% &rom the lacB o& spring

coupling F1;*17G" Nlassov an%

?eontiev F18G* recogniing the

%i&&icult' to %etermine values o& Bs

&or soils* postulate% a t!o5

parameter mo%el" Ahe continuit' in

this mo%el is characterie% b' the

consi%eration o& the shear la'er"

>err F1G attempte% to maBe

JinBlerIs mo%el more realistic b'

assuming some &orms o&

interaction among the spring

elements that represent the soil

continuum even though it re@uires

more parameters (three5parameter

mathematical mo%el)"

JinBlerIs mo%el* %ue to its

simplicit'* has been etensivel'

use% to solve man' soil–

&oun%ation interaction problems

an% has given satis&actor' results

&or man' practical problems"

$urther5

more* this mo%el seems* &rom a

practical point o& vie!* to be

appropriate &or light!eight

structures such as a lo! !eight

buil%ing"

Ahe %i&&erential e@uation

governing the %e&lection* !()* o& ahomogeneous elastic ben%ing

beam !ith constant ben%ing

sti&&ness resting on JinBlerIs

mo%el an% subjecte% to a vertical

continuous loa%* @()* can be

!ritten as F20G

Ec (%

4!K0L

O Bs b !KL M @KL4%

!here Ec is the constant ben%ing

sti&&ness o& the beam (Ec an% are

respectivel' HoungIs mo%ulus o&

concrete an% the moment o& inertiao& the cross section o& the

&oun%ation)" Jhen the %e&lection

!() is Bno!n* the ben%ing

moment an% shear &orce can be

%etermine%"

umerous epressions or semi5

empirical mo%els are available to

%etermine the soil reaction

mo%ulus (Bs) as a &unction o& the

stu%ie% applications F*21–24G"

Ahe Nesic semi5empirical mo%el

(Nesic F23G)* commonl' use% in

the %esign o& continuous sprea%&ootings* is consi%ere% in this stu%'

in or%er to obtain a value o& the soil

reaction mo%ulus (E@" (:))"

Bs0;3 12 12Esb

:Es

:

M b sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m2

Ec h s

!here Es is the HoungIs soil

mo%ulus* ms the


4/19

propert' as the Houng mo%ulus (Es) an% the


5/19

214 S" mana%eh et al" # Engineering Structures 71 (2014) 212–221

buil%ings a !i%th o& 0"3 m an% a heighto& 0": m" HoungIs mo%ulus o& the

&oun%ation (Ec) an%


6/19

anal5'sis an% the t!o consi%ere%

geostatistical metho%s together !ith the

application o& these metho%s using real

%ata in or%er to mo%el the spatial

variabilit' o& soil mo%ulus" Ahis mo%ulus

can be assesse% &rom pressuremeter

mo%ulus* using common relation E


7/19

S" mana%eh et al" # Engineering Structures 71 (2014) 212–221

$ig" :" ?ocaliation o& the N?$ point measurements* !ells an% pressuremeter tests inthe stu%ie% area"

Aable 1

+verage values &or the %e&ormation mo%ulus E


8/19

%e&ormation mo%ulus an% resistivit'" Ahus* it is

assume% that %e&ormation mo%ulus is in%irectl'

linBe% to soil resistivit' %erive% &rom geoph'sical

metho%s F:*27*:2G" + linear relationship !ith a

correlation o& 0"; !as obtaine% bet!een the

%e&ormation mo%ulus an% resistivit' values"

Ahe %ataset in this stu%' is constitute% o& a

&e! set o& pressure5meter boreholes !ith the

%e&ormation mo%ulus E


9/19

21; S" mana%eh et al" # Engineering Structures 71 (2014) 212–221

!hich is also represente% b' a re% line

in $ig" 4" Ahe bivariate mo%el is

%e%uce% &rom this mo%el an% &rom the

coe&&icient o& correlation an% variance

ratio bet!een both variables"

h 831

e0p:h

h lag m:7cK L M

Ahe collocate% coBriging map o& soil

mo%ulus (Es) (mean an% its coe&&icient

o& variation e@ual to 8": ,


10/19

construction site is %epicte% in $ig" ;"

Ahe soil parameters* the loa%* concrete

columns* beams* &loor slab* the

mechanical propert' an% the

geometrical %imensions o&

these sprea% &ootings are

i%entical to those

previousl' presente% in

this paper (see Section

:)" $or this location o&

sprea% &ootings* the values

o& HoungIs soil mo%ulus

are obtaine% at each no%e

o& a

$ig" 4"Eperimental

(blacB line) an% mo%ele% (re% line) isotropicvariograms o& the

soil resistivit'" ($or interpretation o& there&erences to color in this &igure legen%* the

$ig" ;" $our sprea% &ootings o& a

lo! !eight buil%ing !ith lengths o& 10 m an%; m

rea%er is re&erre% to the !eb version o& this

article") on the construction site"

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11/19

S" mana%eh et al" # Engineering Structures 71 (2014) 212–221 217

gri% (ever' 0"3 m) &rom the 1000

con%itional simulations results" $rom

these values o& Es* the values o&

subgra%e reaction mo%ulus (Bs) &or the

Nesic mo%el are obtaine% b' E@" (:)*

representing ;4*000 values o& Bs" Ahesevalues o& subgra%e reaction mo%ulus

are then intro%uce% in the &inite element

mo%el to obtain the ma5imum

settlement* maimum %i&&erential

settlement an% maimum ben%ing

moment &or each sprea% &ooting o& the

buil%ing &or each simulation" Ahen the

1000 results &or the maimum

settlement* maimum %i&&erential

settlement an% maimum ben%ing

moment &or each continuous sprea%

&ooting can be trans&orme% in the &orm

o& cumulative %istribution &unction"

$ig" 7 %epicts the %ata %istributiono& Es &or the &our sprea% &ootings taBing

into account the spatial variabilit' o& Eson the con5struction site" $or the soilmo%ulus probabilit' bet!een 1V an%

V* the interval o& soil mo%ulus values&or the sprea% &ootings (1)* (2)* (:) an%

(4) are respectivel' F7"2*8"2;G*

F7"23*"2G* F7"3*":7G an% F7":*8":;G

,


12/19

upper parts o& the sprea% &ootings (&or

the cross sectional area 0"3 0": m2)"

Ahese negative ben%ing moments can

impose the installation o& longitu%inal

steel rein&orcements in the upper part o&

the &oun%ation &ootings F27G"

Ahe 1000 results obtaine% &or the

maimum sett lement* maimum

%i&&erential settlement an% maimum

ben%ing moment &or each o& these t!o%esigns* are trans&orme% in the &orm o&

cumu5lative %istribution &unction ( $ig")"

$or the &oun%ation %esign o& this

continuous sprea% &ooting the intervals

o& the maimum settlement* maimum

%i&&erential set5tlement an% maimum

ben%ing moment ranging bet!een 1V

an% V o& cumulative probabilit' are

respectivel' F7";* 8"4G mm* F0"2;* :G mm

an% F0"14* 2"21G B m" Ahe latter

intervals &or the overall structure %esign

o& this continuous sprea%

&ooting are respectivel'

F7":* 8"1G mm* F0"2* 2"1G

mm an% F0"3;* :"8;G B m

( $ig" )" $rom theseresults !e obtain &or each

%esign the means (EFDG*

EFD%G* EF,G)* variances

(NarFDG* NarFD%G* NarF,G)

an% then the coe&&icients o& variation (CNFDG* CNFD%G*

CNF,G) o& the mai5mum

settlement (D)* maimum

%i&&erential settlement (D%)

an% maimum ben%ing

moment (,) ( Aables 2an% :)"

;"2" AaBing into

consi%eration the spatial

variabilit' o& soil mo%ulus

an% the presence o& a

geological anomal' in

&oun%ation an% overall

structure %esigns o&

continuous sprea%

&ootings

Wnl' one geological

anomal' (a lens o& cla'e'soil !ith lo! sti&&5ness) has

been encountere% %uring

site investigation but !e

h'pothesie that other

lenses can eist on the

construction site" Ahe

reason &or taBing this

h'pothesis is that the soil

resistivit' measurement

points are %istribute% over

uni&orm pro&iles !ith

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13/19


$ig" " Cumulative %istribution &unction o& the (a)maimum settlement* (b) maimum %i&&erential

settlement an% (c) maimum ben%ing moment&or the Nesic mo%el taBing into account the

spatial variabilit' o& Es &or the continuous sprea%

&ooting (2)"

mean spacing o& 10 m

bet!een measurement

points an% a lo! sti&&ness

ones o& soil such as !eaB

pocBets or lenses o& cla'

in a san% la'er !ith a

length o& 2 m an% a %epth

o& 2–4 m is %i&&icult to

%etect b' geoph'sical an%

geotechnical surve'

campaign" n the &ollo!ing*

&or the same spatial


(Section ;"1) an% &or the

continuous sprea% &ooting

(2) !e consi%er that there

is a lo! sti&&ness one o&

cla'e' soil" $or this one

the values o& soil mo%ulus

an% soil reaction mo%ulus

are respectivel' e@ual to

1";4 ,


14/19

$ig" a an% b)" Aheir associ5ate%

uncertainties @uanti& ie% b' the

coe&&icient o& variation are

also

Aable 2

Statistical parameters o& themaimum settlement*maimum %i&&erentialsettlement an% maimumben%ing moment &or the&oun%ation %esign o&continuous sprea% &ooting (2)

!ith taBing into account thespatial variabilit' o& Es"

Statistical parameters(&oun%ation %esign* 1D)

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15/19

,aimum settlement (D) ,aimum %i&&erential settlement (D%) ,aimum ben%ing moment (,)

EFDG (mm) 8"00; EFD%G (mm) 1"472 EF,G (B m) 0"7340

NarFDG (mm)2

0"0204 NarFD%G (mm)2

0"2;2 NarF,G (B m)2

0"1827

CNFDG 0"017 CNFD%G 0":324 CNF,G 0"3;70

S" mana%eh et al" # Engineering Structures 71 (2014) 212–221

Aable :

Statistical parameters o& the maimum settlement* maimum %i&&erential settlement an% maimum ben%ing moment &or the

overall structure %esign o& continuous sprea% &ooting (2) !ith taBing into account the spatial variabilit' o& Es"

Statistical parameters (overall structure %esign* :D)

,aimum settlement (D) ,aimum %i&&erential settlement (D%) ,aimum ben%ing moment (,)

EFDG (mm) 7"730 EFD%G (mm) 1"04 EF,G (B m) 1"87;

NarFDG (mm)2

0"0::2 NarFD%G (mm)2

0"1271 NarF,G (B m)2

0"43;2

CNFDG 0"02:3 CNFD%G 0":237 CNF,G 0":;01

$ig" 10" Schematic vie! o& the &inite element mo%eling o& the

spatial variabilit' o& soil mo%ulus an% the presence o& a

geological anomal' &or the continuous sprea% &ooting (2)"

$ig" 11" /en%ing moment along the sprea% &ootings o& thelo! !eight buil%ing &or both &oun%ation an% overall structure

%esigns in the presence o& the spatial variabilit' o& Es an% a

geological anomal' &or one simulation"

close together ( Aables 2 an% :)" n this case* aone %imensional &inite element mo%eling

(&oun%ation s'stem) is su&&icientl' a%e5@uate &or

the %esign o& sprea% &ootings" t shoul% be note%

that this result is vali% &or the i%entical charges on

each o& the sprea% &ootings"

9o!ever* there is a %i&&erence bet!een the

values o& maimum ben%ing moments obtaine%

&rom these both %esigns" Ahe obtaine% values o&

the maimum ben%ing moments &rom 1D

mo%eling (&oun5%ation s'stem) are smaller than

those obtaine% &rom :D mo%eling (overall

structure s'stem*

$ig" c) an% then the

same interpretation

&or the mean o& the

maimum ben%ing

moments ( Aables 2an% :)" ote that* the

values o& the

maimum ben%ing

moments remain lo!

compare% to the

value o& the maimum

elastic ben%ing

moment e@ual to :7"3

B m &or such

structural elements"

Ahe uncertaint' o& the

maimum ben%ing

moment &rom 1D

mo%eling is greater

than that one

obtaine% &rom :D

mo%eling ( Aables 2

an% 3)" Ahis sho!sthat* although the

mean value o& the

maimum ben%ing

moment obtaine%

&rom the overall

structure %esign is 2"3

times greater than

that one obtaine%

&rom the &oun%ation

%esign* the

uncertaint' o& the

maimum ben%ing

moment &or the

overal l structure

%esign is less than

the same uncertaint'

&or the geotechnical

%esign"

$or the overall

structure %esign* all o&

the sprea% &ootings

are a&&ecte% b' almost

the same spatial

variabilit' o& soil

mo%ulus

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16/19

$ig" 12" Cumulative %istribution &unction o& the (a) maimum

settlement* (b) maimum %i&&erential settlement an% (c)

maimum ben%ing moment

&or the Nesic mo%el taBing

into account the spatial


an% a geological anomal'

&or the continuous sprea%

&ooting (2)"


17/19


Aable 4

Statistical parameters o& the maimum settlement* maimum %i&&erential settlement an% maimum ben%ing moment &or the &oun%ation %esign o& continuous sprea% &ooting (2) !ith

taBing into account the spatial variabilit' o& soil mo%ulus an% the presence o& a geological anomal'"

Statistical parameters (&oun%ation %esign* 1D)

,aimum settlement (D +) ,aimum %i&&erential settlement (D%+) ,aimum ben%ing moment (, +)

EFD +G (mm) 11"78: EFD%+G (mm) 4"::2 EF, +G (B m) 27"337

NarFD +G (mm)2

0"082; NarFD%+G (mm)2

0"1483 NarF, +G (B m)2

0"1:;4

CNFD +G 0"0244 CNFD%+G 0"080 CNF, +G 0"01:4

Aable 3

Statistical parameters o& the maimum settlement* maimum %i&&erential settlement an% maimum ben%ing moment &or the overall structure %esign o& continuous sprea% &ooting (2)

!ith taBing into account the spatial variabilit' o& soil mo%ulus an% the presence o& a geological anomal'"

Statistical parameters (overall structure %esign* :D)

,aimum settlement (D +) ,aimum %i&&erential settlement (D%+) ,aimum ben%ing moment (, +)

EFD +G (mm) "281 EFD%+G (mm) 1"421 EF, +G (B m) 17"702

NarFD +G (mm)2

0"0480 NarFD%+G (mm)2

0"07;8 NarF, +G (B m)2

0"1127

CNFD +G 0"02:; CNFD%+G 0*130 CNF, +G 0"010

(isotropic spatial variabilit')" Ahe in&luences o& continuous sprea% &ootings(1)* (:)* (4) in the overall structure %esign* an% more generall'* its global

structure rigi%it' ( $ig" ;) are the reasons &or %i&&erences bet!een theresulting sprea% &ooting (2) o& this %esign an% those o& &oun%ation %esign"

n this case* !e can conclu%e that the &oun%ation %esign is a

signi&icantl' simpli&ie% approach compare% to the overall structure %esign

&or an estimation o& ben%ing moment !hen spatial variabil5it' o& soil

mo%ulus is consi%ere%"

Ahe values o& the maimum settlements* maimum %i&&erential

settlements an% maimum ben%ing moments obtaine% &rom the

&oun%ation an% overall structure %esigns* taBing into account both the

spatial variabilit' o& soil mo%ulus an% the presence o& a geolog5ical

anomal'* are ver' %i&&erent &rom each other ( $ig" 12)" Ahe latter valuesobtaine% &rom &oun%ation %esign are signi&icantl' greater than those

obtaine% &rom overall structure %esign but their associ5ate% uncertainties

obtaine% &rom the both %esigns are almost the same ( Aables 4 an% 3)"Ahe &oun%ation %esign in this case* appears more on sa&et' si%e respect

to the overall structure %esign an% the maimum angular %istortion o& the

sprea% &ooting (2) (1#;00) remains smaller than the limit angular

%istortion %e&ine% &or a lo! !eight buil%ing (1#300 F:;G)"

Ahese results sho! that taBing into consi%eration a geological

anomal' in a%%ition* increases signi&icantl'* &or the both &oun%a5tion an%

overall structure %esigns* the values o& maimum settle5ments* maimum

%i&&erential settlements an% maimum ben%ing moments ( $igs" an%12)" t also %ecreases the uncertainties on the estimations o& the

maimum %i&&erential settlement an% ma5imum ben%ing moment

compare% to those obtaine% !hen onl' %ealing !ith the spatial variabilit'(CNFD%G* CNF,G* CNFD%+G* CNF, +G* Aables 2–3)"

n &act* in the overall structure %esign* the presence o& a geolog5ical

anomal' lea%s to an anisotropic spatial variabilit' o& soil mo%ulus on the

beneath the sprea% &ootings !hich lea%s to signi&5icant impacts on their

settlements an% their ben%ing moments" Ahis is illustrate% &or the ben%ing

moment as previousl' presente% in $ig" 11 onl' &or one simulation" Ahe

values o& the ben%ing moment &or the sprea% &ootings (1)* (:) an% (4) are

bet!een 4": to 3"7 B m ( $ig" 11)* !hich are i%entical to some etent tothose obtaine% !ithout taBing into account the geological anomal' ( $ig"8)" 9o!ever* !e observe a consi%erabl' %i&&erent %istribution o& these

values along their lengths !hich is %ue to an e&&ect o& loa% re%istribution

in the structure F21G" Ahe values o& the ben%ing moment &or the sprea%

&ooting (2) are smaller than those obtaine% &rom the &oun%ation %esign ($ig" 11)" Ahe loa% re%istribution e&&ect

re%uces the value o& the ben%ing

moment to 17"4 B m but itcannot completel' absorb it" Ahe

overall structure %esign in this

case* appears closer to realit'

than a &oun%ation %esign in !hich

the e&&ect o& this loa%

re%istribution cannot be

consi%ere%"

7" Conclusions

Ahe main aim o& this stu%'

!as to %esign the continuoussprea% &ootings* &or lo! !eight

buil%ings !ith relativel' lightl'

loa%e% !alls (using the JinBler

soil–&oun%ation interaction

mo%el)* &rom t!o approaches the

&irst approach !ith a &oun%ation

%esign using a one5%imensional

&inite element mo%eling (1D) an%

the secon% approach !ith an

overall structure %esign using a

three5%imen5sional &inite element

mo%eling (:D)" Ahese approaches

!ere com5pare% &or t!o %i&&erent

cases the &irst case %ealing !ith

the spatial variabilit' o& HoungPs

soil mo%ulus (Es) an% the secon%

case !ith the spatial variabilit' o&

Es couple% !ith the presence o& a

geolog5ical anomal' as a lens o&

cla'e' soil o& !eaB mechanical

properties"

Ahe values o& the maimum

settlements* maimum %i&&erential

settlements an% their associate%

uncertainties obtaine% &rom the

both &oun%ation an% overall

structure %esigns o& the

continuous sprea% &ooting taBing

into account onl' the spatial

variabilit' o& Es (&irst case) are

nearl' close together" n this case*

the &oun%ation %esign o& a

continuous sprea% &ooting is

su&&icientl' a%e@uate &or the

estimations o& the maimum

settlements* maimum %i&&eren5

tial settlements an% their

associate% uncertainties"

$or the consi%ere% &irst case*

the obtaine% value o& the

maimum ben%ing moment &or

the overall structure %esign is

greater than the maimum

ben%ing moment value &or the

&oun%a5tion %esign" Ahen* in this

case the overall structure %esign

o& a con5tinuous sprea% &ooting is

appropriate &or the estimations o&

the maimum ben%ing momentsan% their associate%

uncertainties"

Consi%ering the spatial

variabilit' o& soil mo%ulus an% a

geolog5ical anomal' as a lens o&

cla'e' soil o& !eaB mechanical

properties (secon% case !here a

geological anomal' is presente%

in the mi%5%le o& a sprea% &ooting)

increase signi&icantl'* &or both

&oun%ation an% overall structure

%esigns* the values o& maimum

settlements* maimum %i&&erential

settlements an% maimumben%ing moments but the'

%ecrease the uncertainties on the

estimations o& the maimum

%i&&erential settlement an%

maimum ben%ing moment" Ahen

in this secon% case* the results

obtaine% &rom the overal l

structure %esign appear the more

appropriate approach compare%

to the &oun%ation %esign %ue to

the loa% re%istribution

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18/19

S" mana%eh et al" # Engineering Structures 71 (2014) 212–221 221

e&&ects in the structure !hich cannot be consi%ere% in the

&oun%a5tion %esign"

$inall'* the results obtaine% here sho! &or continuous

sprea% &ootings* the importance o& the longitu%inal

behavior o& these structures !hen the spatial variabilit'

an% a geological anomal' o& soil properties can be present"

n the case o& the spatial variabil5it' o& soil properties on aconstruction site* the &oun%ation %esign (1D) can be

per&orme% onl' in this case to estimate the settlement an%

%i&&erential settlement but in the other cases* an%

particularl' in the case o& a construction site !ith a strong

probabilit' o& the issue o& a geological anomal' (one o&

lo! sti&&ness) the overall structure %esign (:D) appears the

more appropriate approach in the %esign o& continuous

sprea% &ootings"

e&erences

[1] >umar * Chou%hur' D* /hargava >" ecent %evelopmentin mo%eling* anal'sis* an% %esign o& &oun%ation s'stems subjecte%

to blast loa%ing consi%ering uncertainties" n astner " $ull5scale eperiment

%etermination o& concrete pipe joint behavior an% its mo%eling" =

n&rastruct S'st 200814(:)"

[13] /uco =* Emeriault $* ?e 6au&&re astner " Statistical an% :D numerical

i%enti& ication o& pipe an% be%%ing

characteristics responsible &or longitu%inal

behaviour o& burie% pipes" n +SCE

con&erence pipelines 200;* Chicago* -S+"

[14] /uco =* Emeriault $* >astner " :Dnumerical anal'ses o& the soil variabilit'

impact on longitu%inal behavior o& burie%

pipes" n 12th +C,+6* 6oa* n%ia* 1–;

Wctober 2008" p" :827–:4"

[15] JinBler E" Die lehre von %er elasticitaet un% &estigBeit" " /en%ing o& beams on three5parameter elastic

&oun%ation" nt = Sol Struct 200;4:(2):37–

73"

[18] Nlassov NR* ?eontiev " /eams*plates* an% shells on elastic &oun%ations"

Aranslate% &rom ussian* srael err +D" + stu%' o& a ne! &oun%ationmo%el" +cta ,ech 1;3(2)1:3–47"

[20] 9eten'i ," /eams on elastic&oun%ations" Scienti&ic series N" Chicago

Ahe -niversit' o& ,ichigan


19/19

measurements application to an urban tunnel site" = +ppl 6eoph's

200230(:);–81 "

[31] Cassan ," ?es essais in situ en m.cani@ue %e sol" Aome *E%itions E'rolles*

1. foundation and overall istructure designs of continuous spread footings

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