P oceedings 2018, 2, 399; doi:10.3390/ICEM18-05236 www.mdpi.com/jou nal/p oceedings
P oceedings
Compa ison o F ac u e Resis ance o he No mal and
High S eng h Conc e e E alua ed by B azilian Disc
Tes †
Pe Mia ka 1,*, S anisla Sei l 1,2 and Vlas imil Bílek 3
1 Facul y o Ci il Enginee ing, B no Uni e si y o Technology, B no 602 00, Czech Republic; [email p o ec ed]
2 Ins i u e o Physics o Ma e ials, Academy o Science o he Czech Republic, B no 616 62, Czech Republic
3 Facul y o Ci il Enginee ing, VSB-Technical Uni e si y o Os a a, Os a a 708 33, Czech Republic;
las imil.b[email p o ec ed]
* Co espondence: pe .mia k[email p o ec ed]; Tel.: +004-20-54-114-7116
† P esen ed a he 18 h In e na ional Con e ence on Expe imen al Mechanics, B ussels, Belgium,
1–5 July 2018.
Published: 19 May 2018
Abs ac : Nowadays, high pe o mance conc e e is used mo e equen ly because o he many
ad an ages compa ed o adi ional conc e e. The highe mechanical p ope ies (e.g., comp essi e
s eng h, lexu al s eng h, and Young’s modulus) allow o la ge spans and slende c oss-sec ions.
Despi e he use o ad anced ma e ial, s anda ds o s uc u al design do no ully use ma e ials’
po en ial. This can be minimized by using ac u e mechanical p ope ies in s uc u al analysis. The
ac u e mechanical p ope ies help o pe o m ad anced s uc u al analysis, especially when some
o he s uc u al elemen s ha e a c ack. The load p esence on he s uc u e can be di ided in o
ensile—mode I, shea —mode II, and combina ion o ension and shea —mixed mode I/II load.
The e o e, i is necessa y o pe o m es , which co e s mixed mode loading condi ions. One o he
es s usually used o he e alua ion o ac u e esis ance o conc e e is B azilian disc es . This
con ibu ion compa es ac u e esis ance o wo ypes o s uc u al conc e e (no mal and high
s eng h) unde he mixed mode I/II. The gene alized maximum angen ial s ess (GMTS) c i e ion
was used o he e alua ion o he ac u e esis ance.
Keywo ds: B azilian disc es ; ac u e mechanics; GMTS; high s eng h conc e e; mixed mode
1. In oduc ion
The design o conc e e s uc u al elemen s used in ci il enginee ing is op imized o educe
ma e ial consump ion and o imp o e s uc u al beha io . Howe e , he adi ional conc e e does
no sa is y inc easing demands on he s uc u al and ma e ial pe o mance. The e o e, new ma e ials
a e de eloped wi h ocus on mechanical pe o mance such as comp essi e s eng h, lexu al s eng h,
and Young’s modulus. The use o conc e e wi h high comp essi e s eng h (HSC) [1] in s uc u al
design can p o ide slende e c oss-sec ion, which leads in o educing o al ma e ial consump ion
wi h e aining simila mechanical pe o mance o he s uc u e.
The ad anced s uc u al analysis uses ac u e mechanical p ope ies as an inpu pa ame e o
p edic o al s uc u al se ice li e ime and ac u e esis ance. The s uc u al elemen s a e ce ain
ime can show mino su ace damage o sh inkage can c ea e mic o-c acks. These de ec s a e zones
o weakness, whe e he c ack can ini ia e. The load p esence on he s uc u al elemen can be
cha ac e ized by ensile mode I and shea mode II. In eali y, some c acks a e loaded by combina ion
o ension and shea —mixed mode I/II load. Hence, i is necessa y o es ma e ial unde he mixed
P oceedings 2018, 2, 399 2 o 6
mode loading condi ions [2–4]. One o he es s usually used o e alua ion o ac u e esis ance o
conc e e is B azilian disc [5,6].
The aim o his con ibu ion is o e alua e and compa e he ac u e esis ance o wo conc e e
ypes used o p ecas s uc u al elemen s unde he mixed mode load. The i s one is adi ional
conc e e wi h g ade C 50/60 and he second ype is HSC conc e e wi h comp essi e s eng h a ound
100 MPa. The assessmen o he ac u e esis ance o bo h s udied ma e ials, is e alua ed om he
expe imen al esul s by employing ac u e esis ance cu e calcula ed om he gene alized
maximum angen ial s ess (GMTS) c i e ion, which is based on wo-pa ame e linea elas ic ac u e
mechanics. The esul s a e compa ed and discussed.
2. Theo e ical Backg ound
This con ibu ion is based on a linea elas ic ac u e mechanics. The linea elas ic ac u e
mechanics concep uses he s ess ield in he close icini y o he c ack ip desc ibed by Williams
expansion [7]. This expansion is an in ini e powe se ies o iginally de i ed o a homogenous elas ic
iso opic c acked body. The s ess ield o mode I and mode II can be desc ibed by a ollowing
equa ion:
, =
√

,
()+
√

,
()++,(,), (1)
whe e σij ep esen s he s ess enso componen s, KI, KII a e he s ess in ensi y ac o s (SIF) o mode
I and mode II, espec i ely, ,
(), ,
(), a e known shape unc ions o mode I and mode II usually
w i en as YI and YII, T (o T-s ess) ep esen s he second e m independen on , Oij ep esen s highe
o de e ms, and , θ a e he pola coo dina es (wi h o igin a he c ack ip; c ack aces lie along he
x-axis).
2.1. B azilian Disc Tes
B azilian disc es wi h a cen al no ch (BDC) is specimen wi h ci cula c oss sec ion, made om
he cylinde wi h a no ch in he middle o specimen (see Figu e 1a) [8–10]. The es pe o med on he
BDC specimen is ca ied ou unde ela i ely simple expe imen al condi ions (see Figu e 1b), using
only he es ing p ess wi h su icien load capaci y. The e alua ion o he ac u e pa ame e s o
modes I, II and mixed mode I/II is done by inclining he no ch by angle α agains he load posi ion.
(a) (b)
Figu e 1. B azilian disc wi h cen al no ch—p inciple o es ing (a) and ac ual es se up (b).
The SIF o a ini e specimen in shape o B azilian disc and he pola angle θ = 0° can be calcula ed
by ollowing equa ions [11,12]:
=√
√


(/,), (2)
P oceedings 2018, 2, 399 3 o 6
 =√
√


(/,), (3)
whe e P is comp essi e load, a is a c ack leng h, R is adius o he disc (D/2), B is disc hickness, α is
inclina ion angle and YI(a/R, α), YII(a/R, α) a e dimensionless shape unc ions o mode I and mode II,
espec i ely. Geome y unc ions YI and YII used in Equa ions (2) and (3) can be ound in [8,9].
To calcula e T-s ess, a di ec ex apola ion me hod [13] is used, o pola angle θ = 0° he
ollowing equa ion is used:
T=
→ −, (4)
whe e σxx and σyy a e he s ess componen s in on o he c ack ip in di ec ion o θ = 0°.
2.2. GMTS C i e ion
The e a e se e al c i e ia o p edic ing he onse o mixed mode ac u e o b i le ma e ials. The
c i e ia which can be used on he BDC specimen he maximum angen ial s ess (MTS) c i e ion [14]
and he minimum s ain ene gy densi y (SED) c i e ion [15]. Howe e , hese c i e ia a e no able o
accu a ely p edic onse o mix mode ac u e. These disad an ages lead o he de elopmen o he
gene alized maximum angen ial s ess (GMTS) c i e ion [16]. The GMTS c i e ion has been ecen ly
used o he ac u e esis ance o he BDC specimen by Aliha e al. [17] o PMMA and Hou e al. [18]
o mo a and conc e e. All s udies displayed an accu a e p edic ion o ac u e esis ance.
Acco ding o he i s hypo hesis o he GMTS c i e ion, he onse o ac u e is he angle o
maximum angen ial s ess θ0 and can be de e mined om:

 |=0
and 
<0, (5)
Assump ion men ioned in Equa ion (5) leads in o:
󰇟+(3−1)󰇠−


2
=0, (6)
C ack ini ia ion angle θ0 is hen used o e alua ion o beginning o mixed mode I/II on BDC
specimen.
Applica ion o he GMTS on B azilian Disc Specimen
Pu e mode I ac u e ini ia ion appea s when KI = KIC, KII = 0 and θ0 = 0°, his assump ion leads
in o Equa ion (7):
 =
󰇣
−
󰇤+

2, (7)
whe e KIC is ma e ials’ ac u e oughness. F ac u e esis ance o bo h modes is exp essed by a io
KI/KIC and KII/KIC. This a io is ob ained om Equa ion (7) by di iding he whole exp ession by KI, KII,
espec i ely.
Equa ion (6) shows ha he angle θ0 o any combina ion o modes I and II depends on KI, KII, T,
and C. C i ical dis ance C can be e alua ed om Equa ions (8) and (9) o plane s ess and plane
s ain espec i ely [11].
=1
2
 (8)
=
󰇡
󰇢. (9)
3. Ma e ials
3.1. No mal S eng h Conc e e
P oceedings 2018, 2, 399 4 o 6
The C 50/60 conc e e ype was chosen o he s udy because i is ypically used o he p e-
s essed p ecas elemen s which a e p oduced nowadays. The s udied conc e e con ains 450 kg o
CEM I 42.5 R, he wa e o cemen a io c/w is 0.40. Fine agg ega e was na u al sand 0/4 mm and
c ushed agg ega es 4/8 mm and 8/16 mm om high quali y g ani e was used as well as d inking
wa e . The conc e e was mixed in a olume o 1 m3 and pou ed immedia ely in o molds. A
polyca boxyla es-based supe plas icize was used o each good wo kabili y [10].
3.2. High S eng h Conc e e
High s eng h conc e e was designed wi h in en o p oduce sub le elemen s. The maximum size
o agg ega e was chosen 8 mm. The agg ega es we e composed om na u al sand 0/4 mm and
c ushed high quali y g ani e 4/8 mm. Po land cemen CEM I 42.5 R was used wi h h ee mine al
admix u es. The i s , was me akaolin, wi h s ong pozzolanic p ope ies. The second and hi d
admix u e we e chosen o each syne gy in e na y binde s [19] based on expe imen s, see o
example [20]. Gene ally, binde consis 81% o CEM I 42.5 R, 9.5% o me akaolin, 7.5% o GBFS and
2.5% o limes one. Wa e /binde a io was 0.22. A polyca boxyla e based supe plas icize was
selec ed based on i s compa ibili y wi h cemen . The conc e e was mixed in olume 0.7 m3 and pou ed
in o molds.
4. Expe imen al Measu emen
The machine o es s has a maximum loading capaci y 200 kN, he speed o he induced
displacemen o he uppe suppo was equal o 0.025 mm/s. BDC specimens wi h ela i e no ch
leng h a/R = 0.4 we e inclined agains loading posi ions unde he selec ed angles. Tables 1 and 2 gi e
o e iew o he mean alues o he specimen dimensions o C 50/60 and HSC, espec i ely.
Table 1. Dimensions o BDC specimens made om C 50/60.
Specimen
nm .
Inclina ion Angle
α [°]
Diame e D
[mm]
Thickness B
[mm]
No ch Leng h 2a
[mm]
a
/
R
[-]
6_03 0 149.200 31.380 60.210 0.404
6_09 0 149.182 29.927 60.170 0.403
6_01 0 149.155 31.440 60.920 0.408
6_01 5 149.162 31.440 60.920 0.408
6_05 10 149.143 30.580 60.140 0.403
6_04 10 149.162 30.973 60.040 0.403
6_04 15 149.208 30.970 60.040 0.402
6_06 15 149.214 32.390 60.150 0.403
6_02 25.2 149.180 30.770 60.110 0.403
6_07 25.2 149.205 31.173 59.940 0.402
Table 2. Dimensions o BDC specimens made om HSC.
Specimen
nm .
Inclina ion Angle
α [°]
Diame e D
[mm]
Thickness B
[mm]
No ch Leng h 2a
[mm]
a
/
R
[-]
6_2_02 0 149.09 29.43 59.70 0.400
6_2_01 0 149.15 29.99 59.44 0.399
6_2_05 5 149.23 28.35 59.91 0.401
6_2_10 10 149.32 28.48 59.27 0.396
6_2_11 10 149.01 27.57 60.13 0.403
6_2_08 15 149.18 28.09 60.06 0.403
6_2_09 15 149.28 28.70 59.96 0.402
6_2_06 20 149.21 28.33 60.01 0.402
6_2_07 20 149.12 28.45 60.03 0.403
6_2_03 25.2 149.18 28.45 59.81 0.400
6_2_04 25.2 149.23 28.96 59.93 0.402
P oceedings 2018, 2, 399 5 o 6
5. Resul s and Discussion
F ac u e mechanical p ope ies (SIFs) o in es iga ed ma e ials we e e alua ed by using
Equa ions (2) and (3). F om Figu e 2a i can be seen, ha he ac u e o HSC ma e ial is done unde
highe ac u e o ce han o he C 50/60 ma e ial. The Figu e 2b show ac u e esis ance o s udied
ma e ials.
(a) (b)
Figu e 2. Compa ison o measu ed o ces (a) and alues o SIFs (b) o C 50/60 and HSC.
The compa ison o expe imen al esul s is done by ac u e esis ance cu es. F ac u e esis ance
cu es we e calcula ed using Equa ion (7) o each ma e ial and i s c i ical dis ance
C
. F om Figu e 3
i can be no ed, ha he MTS c i e ion is e y conse a i e o bo h ma e ials. The GMTS c i e ion
p edic ac u e esis ance wi h g ea ag eemen especially o plane s ain bounda y condi ions.
(a) (b)
Figu e 3. Mixed mode ac u e oughness diag am o C 50/60 (a) and HSC (b) ma e ials, using
a ious c i ical dis ances
C
.
6. Conclusions
In his pape a ac u e esis ance o wo conc e e ypes C 50/60 and HSC was expe imen ally
in es iga ed by using B azilian disc es . The mixed mode ac u e esis ance is e alua ed by
employing GMTS c i e ion. The ollowing conclusions we e ound:
• The ac u e oughness measu ed on he HSC ma e ial is highe in all in es iga ed cases han o
he adi ional C 50/60 ma e ial.
• The expe imen al esul s done on he HSC ma e ial showed highe ac u e esis ance in mixed
mode I/II han he adi ional C 50/60 ma e ial.
• The ac u e esis ance o he C 50/60 ma e ial is cha ac e ized bes by
C
o plain s ain, ye o
HSC, i is be e o use alue o
C
o ine agg ega e.

P oceedings 2018, 2, 399 6 o 6
Au ho Con ibu ions: P.M. and S.S. pe o med he expe imen s and analyzed he expe imen al da a om BDC
specimen; V.B. p o ides ma e ial’s composi ion.
Acknowledgmen s: This pape has been w i en wi h inancial suppo om he FAST-J-18-5164 suppo ed by
he Minis y o Educa ion, You h and Spo s o he Czech Republic and B no Uni e si y o Technology. The i s
au ho is B no Ph.D. Talen Schola ship Holde —Funded by he B no Ci y Municipali y.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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