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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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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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1
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
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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
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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
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propert' as the Houng mo%ulus (Es) an% the
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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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%
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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
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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
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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%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
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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": ,
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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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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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
,
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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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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218 S" mana%eh et al" # Engineering Structures 71 (2014) 212–221
$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
variabilit' o& soil mo%ulus
(Section ;"1) an% &or the
continuous sprea% &ooting
(2) !e consi%er that there
is a lo! sti&&ness one o&
cla'e' soil" $or this one
the values o& soil mo%ulus
an% soil reaction mo%ulus
are respectivel' e@ual to
1";4 ,
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$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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,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"
$or the overall
structure %esign* all o&
the sprea% &ootings
are a&&ecte% b' almost
the same spatial
variabilit' o& soil
mo%ulus
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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$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
variabilit' o& soil mo%ulus
an% a geological anomal'
&or the continuous sprea%
&ooting (2)"
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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220 S" mana%eh et al" # Engineering Structures 71 (2014) 212–221
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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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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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
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8/21/2019 1. Foundation and Overall iStructure Designs of Continuous Spread Footings
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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*