Estimation of the modulus of elasticity for dam concrete
Abstract
The modulus of elasticity of dam concrete is difficult to determine directly from tests due to the necessity for large specimens and testing machines. In order to study the applicability of simple elastic models for predicting the modulus from standard size specimens, tests were conducted on prisms of 45×45×90 cm fabricated with dam concrete (maximum aggregate of 120 mm). The tests on standard 15×30 cm cylinders were made with the mortar and wet-screened components of this concrete. It is seen that the use of the data from these components together with estimated values of the modulus of the aggregates gives reasonable predictions of the moduli of the dam concrete. This has been verified for a range of ages, from 7 to 180 days.
Full text
ESTIMATION OF THE MODULUS OF ELASTICITY FOR DAM CONCRETE
J. Vila dell, A. Aguado, L. Agulló and R. Ge u
Uni e si a Poli ècnica de Ca alunya, Depa men o Cons uc ion Enginee ing,
ETSECCPB-UPC, Edi icio C-1, G an Capi án s/n, 08034 Ba celona, Spain.
ABSTRACT
The modulus o elas ici y o dam conc e e is di icul o de e mine di ec ly om
es s due o he necessi y o la ge specimens and es ing machines. In o de o
s udy he applicabili y o simple elas ic models o p edic ing he modulus om
s anda d size specimens, es s we e conduc ed on p isms o 45×45×90 cm
ab ica ed wi h dam conc e e (maximum agg ega e o 120 mm). The es s on
s anda d 15×30 cm cylinde s we e made wi h he mo a and we -sc eened
componen s o his conc e e. I is seen ha he use o he da a om hese
componen s oge he wi h es ima ed alues o he modulus o he agg ega es
gi es easonable p edic ions o he moduli o he dam conc e e. This has been
e i ied o a ange o ages, om 7 o 180 days.
In oduc ion
The modulus o elas ici y o conc e e is a pa ame e necessa y in s uc u al analysis o he
de e mina ion o he s ain dis ibu ions and displacemen s, especially when he design o
he s uc u e is based on elas ici y conside a ions. This p ope y is con en ionally
measu ed using s anda dized es s based on small specimens subjec ed o uniaxial
comp ession loading. The specimen dimensions a e aken o be a leas h ee imes he
maximum agg ega e size o he conc e e. Fu he mo e, empi ical exp essions de eloped
om expe imen al s udies a e a ailable o es ima e he modulus o elas ici y om he
comp essi e s eng h, which is a s anda d measu e o cha ac e izing conc e e.
The conc e e used in he cons uc ion o dams is o en composed o a binde con aining
cemen and a high amoun o ly ash, and agg ega es wi h a maximum size anging om 80
o 200 mm. The comp essi e s eng h o hese conc e es has o be measu ed wi h la ge
specimens, o example cylinde s o 45×90 cm (1). Due o p ac ical di icul ies in pe o ming
such es s, dam conc e e is usually we -sc eened, emo ing agg ega es la ge han abou
40 mm, and s anda d cylinde s o 15×30 cm a e cas and es ed in comp ession (2).
Howe e , his p ocedu e can esul in he o e es ima ion o he comp essi e s eng h (3);
Tu hill e al. (1) sugges ha he s eng h o he dam conc e e be aken as 85% o he we -
sc eened conc e e, when speci ic es da a a e lacking.
A p ocedu e simila o ha o he comp essi e s eng h has a imes been adop ed o he
expe imen al de e mina ion o he modulus o elas ici y, whe e es s a e pe o med on
con en ional-size specimens made om we -sc eened conc e e (4). Mo e o en, he
empi ical exp essions o con en ional conc e e a e used o es ima e he modulus o
elas ici y om he comp essi e s eng h. Such app oaches neglec he e ec o agg ega e
and specimen size on he modulus, which can be signi ican and a y wi h he age o he
dam conc e e (5).
In he p esen wo k, es s on p isms o 45×45×90 cm made wi h dam conc e e (maximum
agg ega e size = 120 mm), and on cylinde s made wi h he we -sc eened conc e e
(maximum agg ega e size = 40 mm) and he mo a o he dam conc e e (maximum
agg ega e size = 5 mm) we e pe o med. The objec i e was o s udy he ela ions be ween
he moduli o elas ici y de e mined om he di e en specimens, and o e alua e he
possibili y o using an elas ic wo-phase composi e model o es ima e he modulus o he
dam conc e e.
Expe imen al de ails and esul s
The conc e e used in he s udy co esponds o ha used in he cons uc ion o he Llosa del
Ca all double a ch dam on he Ri e Ca dene in Ca alunya, Spain. The nominal
composi ion o he dam conc e e had he ollowing p opo ions, pe cubic me e : Spanish
ype I 45A (CEN Class I 42.5R): 130 kg, ly ash: 89 kg, ine sand (0-1.25 mm): 398 kg,
coa se sand (1.25-5 mm): 234 kg, ine g a el (5-20 mm): 392 kg, medium g a el (20-60
mm): 646 kg, coa se g a el (60-120 mm): 558 kg, plas icize : 0.55 li e s, and wa e : 45 kg.
The agg ega es used we e ob ained along he Ri e Seg e nea he loca ion o he dam,
and we e iden i ied o be mainly limes one. In addi ion o he dam conc e e, he mo a
co esponding o his conc e e was ab ica ed wi h he componen s up o he g ain size o 5
mm (i.e., excluding he g a els). The dam conc e e was also sie ed o emo e g a el o
size la ge han 40 mm, and is deno ed as we -sc eened conc e e. The mo a and he
conc e es we e ab ica ed in a plan a he si e o he dam.
S anda d cylinde s o 15×30 cm we e cas in s eel molds o he mo a and he we -
sc eened conc e e. Such cylinde s could no be cas o he dam conc e e since he
diame e o he cylinde was almos he same as he maximum agg ega e size o 120 mm.
The e o e, la ge p isma ic specimens o 45×45×90 cm we e cas om he dam conc e e
using lamina ed plywood molds. No e ha he heigh /wid h a io was equal o 2 in bo h he
specimen geome ies.
The specimens we e loaded in uniaxial comp ession in a 4.5 MN se ohyd aulic
c ushing machine wi h an MTS 458 closed-loop con olle . The cylinde s we e loaded a he
pis on displacemen a e o 0.004 mm/s and he p isms a a a e o 0.012 mm/s, p oducing
he same nominal axial s ain a e. The a es co esponded o ha needed o each ailu e
in he cylinde s a e abou 4 minu es. In he cylinde es s, he loading was s opped a
in e als co esponding o 10% o he ailu e s ess in o de o eco d he de o ma ions. In
he p isms, he loading was s opped a in e als o 10% o he ailu e s ess ob ained in he
we -sc eened cylinde s, in he 7-day es s, and a in e als o app oxima ely 500 kN, in he
o he s. The es s we e pe o med a 7, 28, 90 and 180 days a e cas ing.
The de o ma ion o each cylinde was measu ed h ough 3 s ain gauges placed in
he middle along he axis. The leng hs o he s ain gages we e 30 mm and 120 mm o he
mo a and we -sc eened conc e e, espec i ely. Fo he p isms, e e ence discs we e
glued on wo opposi e e ical aces as shown in Fig. 1, and a DEMEC- ype mechanical
ex ensome e , o 15 cm gage leng h, was used o manually ob ain he displacemen
be ween adjacen discs. The de o ma ions o he s ain gages we e made h ough a
compu e -based da a acquisi ion
sys em.
FIG. 1
The con igu a ion o e e ence discs o de o ma ion measu emen
Typical s ess-s ain cu es o he h ee ma e ials a di e en ages a e p esen ed in
Fig. 2 a-c. The cu es a e plo ed almos un il ailu e in he case o he cylinde s, and un il a
load o 2 MN o he p isms (Fig. 2c; no e he di e en scales). I can be seen ha un il he
s esses o a leas 30% o he maximum, he cu es a e p ac ically linea . The e o e, he
modulus o elas ici y was aken as he a e age slope o he cu es be ween 10% and 30%
o he maximum s ess.
FIG. 2 a-c
S ess-s ain cu es o (a) mo a , (b) we -sc eened conc e e
and (c) dam conc e e, a di e en ages
The a e age alues o he modulus ob ained o each ma e ial, along wi h he coe icien o
a ia ion in pa en heses, a e gi en in Table 1. I can be seen ha he alues o E inc ease
wi h age in each ma e ial. Mo eo e , he modulus o he dam conc e e (Edc) is highe han
ha o he we -sc eened conc e e (Ewsc), which is highe han ha o he mo a (Emo ); i.e.,
Edc>Ewsc>Emo . Also, he modulus inc eases wi h a dec ease in he pas e con en , as
expec ed. The a iabili y o he esul s in he case o he mo a (de e mined wi h s anda d
cylinde s) is small, while he a ia ion o he dam conc e e esul s (de e mined wi h p isms)
is much highe . The comp essi e s eng hs ob ained om he 15×30 cm cylinde s a e
p esen ed in he same able, along wi h he coe icien s o a ia ion. The p isms could no
be loaded o ailu e since he capaci y o he machine was exceeded in some cases.
TABLE 1. Tes Resul s
Modulus o elas ici y
(GPa)
Comp essi e s eng h
(MPa)
Age
(days
)
Mo a We -
sc eened
conc e e
Dam
conc e e
Mo a We -
sc eened
conc e e
7 19.6
(1.9 %)
24.8
(20.4 %)
30.3
(18.2 %)
22.8
(0.2 %)
23.7
(0.9 %)
28 23.8
(2.9 %)
34.5
(4.2 %)
37.3
(14.2 %)
41.4
(4.2 %)
45.0
(4.2 %)
90 28.2
(4.6 %)
35.1
(1.2 %)
43.0
(16.1 %)
52.6
(1.1 %)
50.7
(2.3 %)
180 30.7
(3.1 %)
37.2
(5.0 %)
42.2
(11.0 %)
60.8
(1.8 %)
56.9
(2.3 %)
P edic ion o he Elas ic Modulus o he Dam Conc e e
Since i is p ac ically cumbe some o es la ge specimens, i is p oposed he e ha he
elas ic modulus ob ained om con en ional specimens (15×30 cm cylinde s) o mo a
and/o we -sc eened conc e e, along wi h he modulus o he g a el, be used o es ima e
he modulus o elas ici y o he dam conc e e. A simple composi e model is used o his
pu pose.
Mos composi e models o desc ibing he elas ic beha io o wo phase ma e ials a e
basically combina ions o pa allel and se ies phase a angemen s, as shown in Fig. 3 o
he models o Hi sch and Coun o (6). Fo applying hese models, he basic assump ions
a e ha (a) conc e e is a h ee-dimensional combina ion o wo homogeneous and iso opic
phases: he ma ix phase and he coa se agg ega es; and (b) each phase beha es linea ly
in he linea elas ic egime o he conc e e. Also, i is necessa y o know he mix p opo ions
o he conc e e, he uni weigh s o he agg ega es o hei olume ac ions, and he
modulus o elas ici y o each phase.
FIG. 3
Mul iphase models o Hi sch and Coun o
The modulus o elas ici y o he conc e e is gi en by he exp essions in Equa ions 1 and 2
o he Hi sch and Coun o models (Fig. 3), espec i ely (6). The Hi sch model is con igu ed
wi h he ela i e p opo ions o he pa allel (uni o m s ain model) and se ies (uni o m s ess
model) componen s as x:(1-x).
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
E
V
+
E
V
x)-(1 +
E
V
+
E
V
1
x =
)
E
,
E
,
V
,
V
(
E
1am
ama
a
m
m
am
am
c
E
+
E
V
V
1
1
+
E
V
1
1
= )
E
,
E
,
V
(
E
am
a
a
m
a
am
a
c
whe e Ec, Em and Ea a e he elas ic moduli o he composi e, ma ix and agg ega e,
espec i ely, and Vm and Va a e he olume ac ions o he ma ix and agg ega e. In he
calcula ions ha ollow, a alue o x = 0.5 was used in he Hi sch model, ollowing o he
wo ks (6,7), which co esponds o an equal dis ibu ion o he pa allel and se ies phases.
As explained ea lie , he moduli o he mo a and he we -sc eened conc e e ha e been
ob ained expe imen ally using s anda d size specimens. Since he i e g a els we e mixes
o di e en mine alogies, p edominan ly limes one, a ange o modulus o elas ici y alues
is possible; he ange used he e o he p edic ions is 35-65 GPa (8). Wi h hese alues, he
moduli o he dam conc e e is calcula ed and compa ed wi h he expe imen al da a.
By aking he ma ix phase as he mo a and he agg ega e phase as he g a el o
5-40 mm, he p edic ion o he we -sc eened conc e e modulus, deno ed as WS(M), can be
ob ained om he models. Simila ly, wi h he ma ix phase as he mo a and he agg ega e
phase as he g a el o 5-120 mm, he p edic ion can be made o he dam conc e e,
deno ed as D(M). Al e na i ely, he we -sc eened conc e e can be conside ed as he ma ix
phase and he g a el o 40-120 mm as he agg ega e phase o p edic he modulus o he
dam conc e e, deno ed D(WS). The esul s o hese h ee simula ions a e gi en in Table 2
o he age o 90 days, which is a usual e e ence age o dam conc e es. The alues in
pa en heses a e he e o s wi h espec o he expe imen ally ob ained da a gi en in Table
1. No e ha he e o is calcula ed as he di e ence be ween he p edic ion and he
expe imen al da a, exp essed as a pe cen age o he la e (whe e a posi i e sign indica es
ha he p edic ed alue is lowe han he ac ual alue).
TABLE 2. Ec P edic ions (in GPa) o he Two Models o Di e en Agg ega e Moduli, a 90
days