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