Else ie Edi o ial Sys em( m) o Composi es Pa B
Manusc ip D a
Manusc ip Numbe :
Ti le: NON-LINEAR ANALYTICAL MODEL OF COMPOSITES BASED ON BASALT TEXTILE REINFORCED
MORTAR UNDER UNIAXIAL TENSION
A icle Type: Full Leng h A icle
Keywo ds: A. Fab ics/ ex iles; B. Mechanical p ope ies; C. Analy ical modelling; D. Mechanical es ing
Co esponding Au ho : D . Pello La inaga Alonso, Ph. D.
Co esponding Au ho 's Ins i u ion: TECNALIA Resea ch & Inno a ion
Fi s Au ho : Pello La inaga Alonso, Ph. D.
O de o Au ho s: Pello La inaga Alonso, Ph. D.; Ca los Chas e, Assis an P o esso ; José Tomás San-
José, Assis an P o esso ; Lei e Ga mendia, PhD Indus ial Enginee
Abs ac : The ecen de elopmen o ino ganic based composi es as low-cos ma e ials in ein o ced
conc e e s uc u al s eng hening and p ecas hin-walled componen s, equi es he c ea ion o models
ha p edic he mechanical beha iou o hese ma e ials.
Tex ile Rein o ced Mo a (TRM) shows complex s ess-s ain beha iou in ension de i ed om he
he e ogenei y o i s cons i uen ma e ials. This complexi y is mainly caused by he o ma ion o se e al
c acks in he ino ganic ma ix. The mul iple c acking leads o a dec ease in s uc u al s i ness. Due o
he se e e condi ions o he se iceabili y limi s a e in s uc u al elemen s, he p edic ion o he
s ess-s ain cu e is essen ial o design and calcula ion pu poses. A e checking o he models, a
nonlinea app oach, which is based on he c ack con ol exp ession included in he Eu ocode 2, is
p oposed in his pape .
Following his scope, his pape p esen s an expe imen al campaign ocused on hi y one TRM
specimens ein o ced wi h ou di e en ein o cing a ios. The esul s a e analysed and sa is ac o ily
con as ed wi h he p esen ed non-linea app oach.
Sugges ed Re iewe s: Ami Si La bi
Claude Be na d Uni e si y o Lyon 1, F ance
ami .si-la bi@uni -lyon1.
D . Si La bi has b oad expe ience in he ield o ib e-cemen i ious composi es, especially wi h Tex ile
Rein o ced Conc e e (TRC), a composi e e y simila o he one included in his pape . Due o his
esea ch ac i i y D . Si La bi has o deal wi h he analysis o TRC uniaxial ensile beha iou . Hence, I
conside D . Si La bi a sui able e iso o his pape .
Heidi Cuype s PhD Ci il Enginee
V ije Uni e si ei B ussel
heidi.cuype s@ ub.ac.be
D . Cuype s has b oad expe ience in he ield o ino ganic based composi es, especially he s udy o
ma ix c acking and i s du abili y. Thus, I conside D . Cuype s a sui able e iso o he p esen ed
a icle.
This is he accep manusc ip o he ollowing a icle ha appea ed in inal o m in
Composi es Pa B: Enginee ing 55: 518-527 (2013),which has been published in inal o m a
h ps://doi.o g/10.1016/j.composi esb.2013.06.043.Copy igh © 2013 Else ie L d. unde CC BY-NC-ND
licence (h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
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NON-LINEAR ANALYTICAL MODEL OF COMPOSITES BASED ON
BASALT TEXTILE REINFORCED MORTAR UNDER UNIAXIAL TENSION
Pello La inaga a, * , Ca los Chas e b, José T. San-José c, Lei e Ga mendia a
a TECNALIA. c/Geldo, Ed. 700, Pa que Tecnológico de Bizkaia, 48160, De io, Spain
b UNIC, Faculdade de Ciências e Tecnologia, Uni e sidade No a de Lisboa, 2829-516 Capa ica – Po ugal
c UPV/EHU, Depa men o Enginee ing o Ma e ials. c/Alameda U quijo s/n, 48013 Bilbao, Spain
Abs ac
The ecen de elopmen o ino ganic based composi es as low-cos ma e ials in
ein o ced conc e e s uc u al s eng hening and p ecas hin-walled componen s,
equi es he c ea ion o models ha p edic he mechanical beha iou o hese ma e ials.
Tex ile Rein o ced Mo a (TRM) shows complex s ess-s ain beha iou in ension
de i ed om he he e ogenei y o i s cons i uen ma e ials. This complexi y is mainly
caused by he o ma ion o se e al c acks in he ino ganic ma ix. The mul iple c acking
leads o a dec ease in s uc u al s i ness. Due o he se e e condi ions o he
se iceabili y limi s a e in s uc u al elemen s, he p edic ion o he s ess-s ain cu e
is essen ial o design and calcula ion pu poses. A e checking o he models, a
nonlinea app oach, which is based on he c ack con ol exp ession included in he
Eu ocode 2, is p oposed in his pape .
Following his scope, his pape p esen s an expe imen al campaign ocused on hi y
one TRM specimens ein o ced wi h ou di e en ein o cing a ios. The esul s a e
analysed and sa is ac o ily con as ed wi h he p esen ed non-linea app oach.
Keywo ds: A. Fab ics/ ex iles; B. Mechanical p ope ies; C. Analy ical modelling; D.
Mechanical es ing;
1. In oduc ion
By means o se e al esea ch p ojec s, he mechanical possibili ies and ad an ages o
Tex ile Rein o ced Mo a ha e been p o en, bo h as s eng hening ma e ial and as
p ecas ma e ial (in his ield his composi e is also called Tex ile Rein o ced Conc e e)
[1-5]. Howe e , i s implemen a ion as a egula echnique is s ill a . One impo an s ep
o each his objec i e is modelling he mechanical beha iou o TRM o u u e
applica ions in eal si ua ions. As TRM usually bea s ensile loads, i is e y ele an o
* Co esponding au ho . Tel: +34 667 178 992/946 430 850; ax: +34 946 460 900
E-mail add ess: p[email p o ec ed]m
*Manusc ip
Click he e o iew linked Re e ences
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model he beha iou o his ma e ial unde pu e ensile loads, i.e. o de ine i s s ess-
s ain ela ionship.
In he bibliog aphy, he e is b oad in o ma ion e e ed o nume ical o analy ical TRM
models which show excellen esul s [6-9]. Ne e heless, mos o hese analyses equi e
he use o speci ic so wa es [9] o a e cos ly in e ms o ime. Mo eo e , in some cases
addi ional in o ma ion is equi ed, which in ol es he de elopmen o addi ional es s
[7,8].
Fo hese easons, i is con enien o p oduce simple and easy- o-implemen models.
S ess-s ain ma hema ical exp essions a e usually p oposed o model he ma e ials,
bo h o linea and non-linea analysis. These exp essions a e based on expe imen al
da a and can be used as cons i u i e equa ions in simple nume ical models. Conc e e
and s eel a e ob ious examples o s ess modelling by means o ma hema ical
exp essions, in ac , bo h ma e ials a e modelled in design codes as he Eu ocode 2.
A nonlinea app oach is p esen ed in his pape o de ine he s ess-s ain ela ionship o
Basal Tex ile Rein o ced Mo a (BTRM) unde uniaxial ensile loads. The model is
based on he conc e e c ack con ol exp ession included in he Eu ocode 2 [10]. The
de eloped exp ession is calib a ed empi ically wi h expe imen al da a included in he
a icle, he esul s o hi y one TRM specimens subjec ed o uniaxial ensile loads.
2. Ma e ials. Basal ex ile and mo a cha ac e iza ion.
Basal appea s o be a ma e ial which can o e in e es ing oppo uni ies in he u u e o
he cons uc ion indus y [11]. Recen s udies ha e included basal ab ics as
ein o cemen in FRP composi es [11,12] and basal ex ile as TRM in e nal co e
[13,14].
The basal ex ile used in his s udy consis s o o ings wo en in he wo p incipal
di ec ions, i.e. a bidi ec ional mesh which geome y is de ailed in Table 1. Basal
o ings a e co e ed by a bi umen coa in o de o imp o e he bond be ween he mo a
ma ix and he ex ile. In addi ion, he coa imp o es he ex ile pe o mance due o i s
capaci y o ans e load di ec ly o mo e o ing ilamen s [15,16].
Table 1
Basal ex ile geome y
Acco ding o se e al p e ious s udies, he e is a conside able gap be ween he main
mechanical p ope ies - ensile s eng h, ul ima e s ain and Young’s modulus - o a
single ib e o ilamen and hose o he ex ile mesh [17]. Fo his eason, he
mechanical cha ac e is ics o he ex ile we e expe imen ally de e mined in ensile es s
on specimens which leng h was 600mm.
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ASTM D 5034 [18] s anda d, used as a e e ence, sugges s a s ain a e o 300mm/min.
Howe e , in o de o ca y ou a sui able da a acquisi ion, a speed o 1mm/min was
selec ed o he p esen es . In o al, se en ex ile specimens o ou o ings we e
es ed. The esul s a e summa ised in Table 2.
Table 2
A e age esul s o basal ex ile unde pu e ensile load
The di e ence be ween he da a gi en by he manu ac u e and he expe imen al esul s
is caused by se e al ac o s, mainly he load ans e be ween ilamen s and he
di icul y o exe an iden ical ini ial leng h and s ain o all he s ands o he
specimens [13,17]. Hence, i was impossible o achie e a simul aneous up u e o all he
o ings, so he expe imen al alues o ul ima e ensile s eng h and ul ima e ensile
s ain can no be conside ed as e e ence da a. Howe e , as he es ed ex ile p esen s
linea beha iou un il up u e, he ensile Young’s modulus alues ob ained in his es
can be easily calcula ed [14] and i will be conside ed o he model p esen ed in his
pape . Mo eo e , despi e he di icul ies de i ed in his kind o es s, he ob ained
esul s p esen ed low sca e ing.
A non-comme cial cemen -based mo a was used as TRM ma ix. The pe o mance o
any ex e nally bonded s eng hening sys em is clea ly in luenced by he in e ac ion
be ween he ma ix and he inne ein o cemen and he capaci y o he composi e-
subs a e in e ace [15]. The maximum g ain size o he sand used in he mo a was
0.6mm. This ac o enhances he wo kabili y o he esh mix u e and acili a es i s
in e ac ion wi h he ex ile mesh. The amoun o edispe sable esins was lowe han
5%, in o de o achie e a i e-p oo mo a . As can be obse ed in Table 3, he e a e no
inno a i e p oduc s in he mo a composi ion because he idea is o p esen he TRM as
a compe i i e ma e ial. Howe e , special a en ion was paid o i s composi ion so as o
achie e app op ia e wo kabili y, cu ing ime and i e esis ance.
Table 3
Mo a dosage by weigh (%)
Ma ix mo a was mechanically cha ac e ized acco ding o. A e 28-day cu ing,
40x40x160mm p isms we e es ed o de e mine mo a mechanical p ope ies acco ding
o UNE-EN 1015.11:1999 [19]. Comp essi e s eng h is 19.8MPa while ensile lexu al
s eng h is 7.2MPa.
3. Uniaxial ensile es
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The expe imen al campaign included in his pape is o med by hi y one uniaxial
ensile specimens. Fou se ies, om one o ou ex ile laye s, o se en specimens each
one we e de ined. The e ec o ein o cing a io was he e o e analysed. Specimens
we e agged as TBX, whe e he X ep esen s he numbe o in e nal ein o cemen
laye s, i.e. in his pape om TB1 o TB4. Besides, h ee addi ional specimens we e also
manu ac u ed wi hou ein o cing ma e ial.
3.1.Specimens geome y and manu ac u ing p ocess
TRM has a ac ed a en ion o he las en yea s. The e has been a conside able
inc ease in esea ch p ojec s and publica ions ela ed o his inno a i e composi e.
Howe e , no s anda d cha ac e iza ion es s a e a ailable in he bibliog aphy. Thus,
se e al es p oposals ha e al eady been made [6,15,20,21] by di e en au ho s. They
di e p ima ily in: he shape and geome y o he specimens, he connec ion wi h he
es machine clamps, he s ain a e and he ins umen a ion.
Fig. 1. Uniaxial ensile TRM specimen geome y.
The ec angula pa allelepiped specimen is easy o manu ac u e and implemen . Fo he
p esen s udy i was decided o manu ac u e specimens wi h a 100x10mm c oss-
sec ional a ea and 600mm in leng h. Samples we e p epa ed in plywood o mwo ks. In
o de o p omo e he ailu e o he specimen in i s middle hi d po ion, bo h ends o
each specimen we e ex a- ein o ced wi h wo laye s o 200x100mm ex ile (Figu e 1).
The in e nal ein o cemen o co e laye s (800x100mm) we e always uni o mly
posi ioned wi hin he c oss sec ion. In he pa icula case o he un ein o ced specimens,
only he addi ional ein o cemen was ins alled a bo h ends.
(a) (b)
Fig. 2. Two s eps o he TRM ensile specimens manu ac u ing.
Specimens we e cu ed in a sa u a ed a mosphe e o se en days, and, hen, hey we e
s o ed o 21 days a oom empe a u e (18ºC and 60%RH). Tes s we e ca ied ou
be ween 28 and 34 days a e he specimens we e manu ac u ed.
3.2.Tes Se up
TRM ensile specimens we e es ed in a Schenk 100kN p ess which was p og ammed o
exe a de o ma ion a e o 0.5mm/min [15]. Tensile o ce was applied wi h specially
designed me allic clamps, in o de o a oid any s ess concen a ion poin , which would
cause p ema u e b i le ailu e wi hou eaching he ul ima e ensile load.
Fig. 3. Uniaxial ensile o he es se up.
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As he o ma ion o c acks is p omo ed in he specimen cen al hi d pa , wo
displacemen ansduce s (LVDTs) we e placed on each side o he specimen o
measu e he elonga ion o ha a ea. The measu ed e e ence leng h, as can be obse ed
in Figu e 3, was 210mm. All he da a was compiled by a da a logge a a equency o
5Hz.
3.3.Expe imen al esul s
The pu pose o es ing un ein o ced specimens was o cha ac e ize he beha iou o he
mo a unde pu e ensile loads. As i was expec ed, only one c ack was o med in he
un ein o ced specimens. The a e age esul s o he h ee specimens a e displayed in
Table 4.
Table 4
A e age esul s o un ein o ced specimens
The load-s ain cu es o 28 TRM es s wi h 1-4 laye s a e shown g aphically in Figu e
4. The esul s show good epea abili y in con as wi h he cha ac e is ic sca e ing o
his kind o ma e ials. Th ee s ages a e clea ly di e enced in each cu e. This beha iou
is ypical in ino ganic composi es subjec ed o uniaxial ensile load [22], ein o ced
abo e he c i ical olume ac ion. These s ages a e:
- S age I. P e-c acking s a e.
- S age II. Mul ic acking p ocess.
- S age III. S abilized c ack pa e n. Only he ib es ca y load.
Fig. 4. Load-s ain cu es o TRM specimens.
Table 5 includes he a e age main alues o each se ies: ul ima e ensile o ce and
s ess, he Young’s modulus o s age III, and he inal s ain a each s age. The ensile
s ess o he specimens is calcula ed di iding measu ed load by he a ea o in e nal
ein o cemen : b· ·n; whe e b is he wid h o he specimen (100mm), is he design
hickness (0.0349mm) and n is he numbe o ex ile laye s ins alled as in e nal
ein o cemen .
Table 5
A e age esul s o each TRM se ies
The analysis o he esul s p oduces in e es ing in e p e a ions. Acco ding o he
bibliog aphy, he s i ness o he hi d s age E ,III is sligh ly lowe han he Young’s
modulus o he ex ile ein o cemen E (see Table 2). In h ee o he ou se ies E ,III
emained close o 60GPa, while he basal ex ile Young’s modulus is 67GPa, i.e. 9%
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highe . This educ ion has been quan i ied (10-30%) by o he au ho s [22,23]. Likewise,
he e was good co ela ion in se ies TB2, TB3 and TB4 in e ms o ensile s eng h and
ul ima e s ain. The main di e ence be ween hese h ee se ies is he leng h o he S age
II (see Table 5). The mul iple c acking s ain ε ,II was educed wi h a highe numbe o
ein o cemen laye s [24].
Ne e heless, se ies TB1 showed a signi ican disc epancy when compa ed wi h he
o he esul s. The a e age alue o E ,III was equal o 43GPa. The low amoun o
in e nal ein o cemen in se ies TB1 can explain his disc epancy; one laye may no be
enough o achie e a monoli hic ma e ial which could be conside ed as a composi e.
Acco ding o Peled and Ben ou [16] he c i ical olume con en o ib es in cemen
composi e is abou 1-3%. A a ios abo e his le el he beha iou load is cha ac e ized
by mul iple c acking and he TRM is able o ca y he addi ional load applied a e he
ma ix has c acked. Howe e , Se ies TB2 p esen s a olume con en o 0.7% and he
specimens showed mul iple c acking and beha ed as he es o he se ies wi h highe
ib e con en .
These s a emen s can be con as ed wi h he s ess-s ain esul s included in Figu e 5.
While se ies TB2, TB3 and TB4 p esen ed simila beha iou a e mul iple-c acking,
se ies TB1 de eloped a di e en slope a hi d s age.
Fig. 5. Di ec compa ison be ween specimens o di e en se ies.
The analysis o he c ack pa e n also p o ides in e es ing in o ma ion. Fi s ly, i is
no iceable how he numbe o c acks ises when he numbe o ex ile laye s inc eases
(see Figu e 6). Mo eo e , he dis ance be ween c acks is educed when mo e in e nal
ein o cemen is used. A se ies TB1 only one o h ee c acks we e o med, being an
e idence o i s incapabili y o de eloping mul iple c acking and beha e as an ino ganic
based composi e. Finally, as he ib e con en inc eases, he c ack pa e n ends o
s anda dize.
(a) (b)
(c) (d)
Fig. 6. C ack pa e n de elopmen . F om up-le o down igh : TB1, TB2, TB3 and TB4.
In he ollowing sec ion a non-linea analy ical model is p esen ed. The ob ained
expe imen al esul s will be compa ed wi h hose ob ained in he model in o de o
check i s alidi y.
4. TRM modelling
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The p oposed model is based on he c ack con ol exp ession included in he “Eu ocode
2: Design o conc e e s uc u es. Pa 1-1” and he A es on-Coope -Kelly heo y. This
well-known heo y was he i s sa is ac o y explana ion o mul iple c acking. Fo his
eason, he au ho s would like o e ise he ACK heo y and compa e i s esul s wi h he
expe imen al da a.
4.1. ACK-Theo y
This heo y de ines a heo e ical i-linea s ess-s ain beha iou o a composi e wi h a
b i le ma ix, in which i is assumed ha he ib es a e held in he ma ix solely by he
p esence o ic ion, and ha axial sliding along a ib e-ma ix in e ace would occu
unde a c i ical, limi ing alue o longi udinal shea s ess [25,26]. The ib e debonding
deg ee and c ack spacing a e closely linked o he maximum shea s ess a he ib e-
ma ix in e ace.
Se e al models o b i le ma ix composi es ha e al eady been modelled conside ing
he ACK heo y, e.g. [27,28]. Basic assump ions, employed in i s de elopmen , a e [24]:
- The ib es a e only capable o ca ying load along hei longi udinal axis.
- The ma ix- ib e bond is weak.
- Once he ma ix and he ib e a e debonded, a pu e ic ional shea s ess η
eplaces he p e iously exis ing adhesion shea s ess ηa. This ic ional in e ace
shea s ess η is cons an along he debonded in e ace.
- Poisson e ec s o he ib e and ma ix a e neglec ed.
- Global load sha ing is assumed o he ib es.
- No mal ma ix s esses, ans e sal o he loading di ec ion, a e uni o m in a
c oss sec ion.
As i has been expe imen ally s a ed, TRM ensile beha iou could be di ided in h ee
di e en , bu complemen a y, s ages. The ACK heo y consis s on h ee s aigh lines
which supe imposes he expe imen al s ess-s ain cu e (see Figu e 7).
Fig. 7. Typical s ess-s ain cu e o TRM in ension (in black) and ACK linea iza ion (in do ed g ey)
Acco ding o ACK heo y, a he i s s age, he composi e obeys he law o mix u es:
mm c VEVEE
1
(1)
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whe e Ec1 is he composi e s i ness, E ep esen s he ensile Young’s modulus o he
ib es, Em is he ma ix one, and V and Vm a e he olume ic ac ion o ib es and
ma ix, espec i ely. A he i s s age, he ma ix- ib e in e ace shea beha iou is
assumed o be elas ic.
S age I inishes when he ma ix eaches i s ensile ailu e s ess ζmc. Ma ix ensile
ailu e s ess, ζmu, (and i s co esponding s ain εmu) has a di ec in luence on ζmc:
m
muc
mc E
E
1
(2)
A his alue, he composi e p esen s mul iple c acking, i.e. successi e c acks a e
o med as he composi e s ain inc eases.
As has been s a ed, when a c ack appea s in he ma ix and eaches a ib e, debonding o
he ma ix- ib e in e ace occu s due o weakness o he bond. Then, a cons an
ic ional in e ace shea s ess η is conside ed. This shea s ess p o ides no mal s ess
ans e om ib es o he ino ganic ma ix. The leng h o he debonded in e ace δ can
be w i en by exp essing he o ce equilib ium along he loading (longi udinal) axis o
he ib es [25]:
2
mum
V
V
(3)
whe e, is he ib e adius and η ep esen s he ic ional shea s ess a he ma ix- ib e
in e ace. A he mul iple c acking s age, dis ances be ween c acks a e no smalle han δ
and no la ge han 2δ. The spa ial in oduc ion o c acks occu s andomly un il no space
emains o new c acks, in a simila way o he geome ical ca pa king p oblem.
Widom [29] de e mined ha he a e age dis ance be ween c acks equals X=1.337δ. By
means o his alue i is possible o de e mine he composi e s ain (εmc) when he
mul iple c acking s ops:
m
mu
emc E
)666.01(
(4)
whe e:
mm
eVE
VE
(5)
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o in e nal ein o cemen and gene a es a cu e ha shows conside able di e ences wi h
he expe imen al ones (se ies TB1).
The p oposed simula ion p esen s op imum esul s o he mul iple c acking s ain εmc,
so he e a e no signi ican disc epancies be ween he analy ical and expe imen al da a
on his key poin . The beha iou o he model a s age III is sa is ac o y due o he
in oduced non-linea i y which imp o es he model’s pe o mance a he end o his
s age.
The C acking Model has been success ully p o en by he au ho s wi h o he ein o cing
ma e ials such as glass, ca bon and s eel wi e [14]. This ac enhances he e sa ili y o
he C acking Model o ma e ials ha could be used as TRM ein o cing co e. Mo eo e ,
his model has al eady been employed as a cons i u i e equa ion in nume ical models
de eloped o simula e he beha iou o ein o ced conc e e beams s eng hened in
lexu e using Tex ile Rein o ced Mo a [14].
5. Conclusions
Bo h as new cons uc ion ma e ial o as s uc u al s eng hening solu ion, ino ganic-
based composi es, mainly TRM and TRC, ha e inc eased hei ele ance wi hin he
cons uc ion a ea and a e cu en ly ocusing he e o s o se e al esea ch g oups.
Fo his eason, i is impo an o s anda dize he use o he TRM. Cha ac e iza ion es ,
manu ac u ing and applica ion guides o analy ical models a e among he aspec s ha
should be no malized. The e a e s udies ha ha e de eloped analy ical and nume ical
models wi h sa is ac o y esul s. Howe e , mos o hem a e e y sophis ica ed and hei
applica ion could be expensi e in e ms o ime and budge . The e o e, i is necessa y o
de elop models easy- o-apply.
TRM, as s eng hening ma e ial, usually wo ks unde ensile loads which a e ans e ed
by adhe ence om he s eng hened elemen . I is essen ial o s udy he ensile
beha iou o TRM o de ine i s possibili ies and ailu e modes. Especially a e s a ing
ha hese ailu e modes ha e di e en na u e compa ed o hose obse ed in o he
ex e nally bonded s eng hening sys ems.
Tex ile Rein o ced Mo a is a composi e wi h a e y complex ma e ial beha iou . In
addi ion, i s s uc u al ele ance asks o accu a e model wi h no signi ican
disc epancies wi h he eal beha iou .
A non-linea model is p esen ed in his pape o desc ibe he s ess-s ain beha iou o
TRM unde uniaxial ensile loading. The model is based on he RC c ack con ol
exp ession included in he Eu ocode 2, bu akes in o accoun he na u e o he
composi e cons i uen ma e ials. The goal o his s udy is o e i y he simula ion, called
C acking Model, con as ing i s esul s wi h hose ob ained in an expe imen al
campaign also included in his pape . In addi ion, a well-known model as ACK heo y is
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also discusses in his documen and i s simula ions compa ed wi h he expe imen al
esul s.
Due o he good i be ween he calcula ed and he expe imen al alues, he C acking
Model migh be employed in nume ical models as TRM cons i u i e equa ions.
Ne e heless, due o he na u e and he ho oughness o he s uc u al calculus wi hin
cons uc ion sec o , i is necessa y o suppo his model by means o mo e expe imen al
da a. Fu u e esea ch lines a e ocused on es ing new ein o cing ma e ials, mo e
e ec i e ma ices and di e en ein o cing a es.
Acknowledgmen s
This esea ch wo k was unded h ough he esea ch p ojec s DFB 7-12-TK-2009-10
and BIA2010-20789-C04-03/04; and he schola ship p og amme o he Iñaki Goenaga
Founda ion.
Re e ences
[1] Omb es L. Flexu al analysis o ein o ced conc e e beams s eng hened wi h a cemen based high
s eng h composi e ma e ials. Composi e S uc u es, 94, pp. 143-155. 2011.
[2] Si La bi A, Con amine R, Hamelin P. TRC and hyb id solu ions o epai ing and/o s eng hening
ein o ced conc e e beams. Enginee ing S uc u es, 45, pp.12-20. 2012.
[3] La inaga P, San-José JT, Ga cía D, Ga mendia L, Díez J. Expe imen al s udy o he lexu al
beha iou o low pe o mance c beams s eng hened wi h Tex ile Rein o ced Mo a . P oceedings o he
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2010.
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[5] Bou nas D, Lon ou P, Papanicolau CG, T ian a illou TC. Tex ile-Rein o ced Mo a (TRM) e sus
FRP con inemen in ein o ced conc e e columns. ACI S uc u al Jou nal, 104(6), pp. 740-748. 2007.
[6] Haüßle -Combe U, Ha ig J. Bond and ailu e mechanism o Tex ile Rein o ced Conc e e (TRC) unde
uniaxial ensile loading. Cemen & Conc e e Composi es, 29, pp. 279-289. 2007.
[7] Ri che M, Zas au BW. On he nonlinea elas ic p ope ies o ex ile ein o ced conc e e unde
ensile loading including damage and c acking. Ma e ials Science and Enginee ing A, 422, pp. 278-284.
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on Tex ile Rein o ced S uc u es, CTRS4, D esden, Ge many. pp. 87-98. 2006.
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S anda disa ion, Cen al Sec e a ia , B ussels. 2004.
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Composi es: Pa B, 42, Issue 4, pp.717-723. 2011.
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Compa ible Ad anced Composi e Ma e ial. Cons uc ion and Building Ma e ials, Volume 25, Issue 12,
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Table 1
Basal ex ile geome y
Design hickness,
0.0349 mm
Opening size
25x25 mm
Weigh o he d y shee
233 g/m2
Densi y
2.75 g/cm3
Table 2
A e age esul s o basal ex ile unde pu e ensile load
Filamen - Gi en by
he manu ac u e
Tex ile –
Expe imen al*
Ul ima e ensile s eng h, σ u [MPa]
2100
1160 (0.025)
Young’s Modulus, E [GPa]
89
67 (0.054)
Ul ima e ensile s ain, ε [%]
3.14
1.82 (0.054)
*COV be ween b acke s
Table 3
Mo a dosage by weigh (%)
W/C a io
0.2
Sand (g ain size < 0.6mm)
60-70
G ey cemen ype II 42.5R
30-40
Polyme ic chopped ib es
3-5
Redispe sable esins
1-3
Table 4
A e age esul s o un ein o ced specimens
Fmu [N]
σmu 1 [MPa]
εmu [%]
Em [GPa]
2480
2.48
0.03
8.25
1 σmu = Fmu / (10·100)
Table 5
A e age esul s o each TRM se ies
Se ies
F (N)
σ 1 (MPa)
E ,III (GPa)
ε ,I (%)
ε ,II (%)
ε ,III (%)
TB1
3797
1088
43
0.034
0.40
2.15
TB2
8772
1256
59
0.041
0.29
1.96
TB3
12515
1195
57
0.028
0.21
2.10
TB4
16679
1194
61
0.028
0.15
2.07
1 σ = F / (0.0349·100·n)
Table
Table 6
ACK Theo y esul s
Se ies
Vm
[-]
V
[-]
Ec1
[GPa]
σmc
[MPa]
εmc
[%]
TB1
0.9965
0.0035
8.46
2.54
0.734
TB2
0.9930
0.0070
8.66
2.60
0.381
TB3
0.9895
0.0105
8.87
2.67
0.263
TB4
0.9860
0.0140
9.07
2.73
0.204
Table 7
C acking Model da a and esul s
Se ies
Vm
[-]
V
[-]
Ec1
[GPa]
σmc
[MPa]
εmc
[%]
TB1
0.9965
0.0035
8.46
2.54
0.896
TB2
0.9930
0.0070
8.66
2.60
0.473
TB3
0.9895
0.0105
8.87
2.67
0.332
TB4
0.9860
0.0140
9.07
2.73
0.261
Figu e1
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Figu e2a
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Figu e2b
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Figu e3
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Figu e7
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Figu e8
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Figu e9
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Figu e10
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Figu e11
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Figu e12a
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Figu e12b
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Figu e13
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Figu e14
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Figu e15
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Figu e22
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