Ma e iales de Cons uCCión
Vol. 65, Issue 320, Oc obe –Decembe 2015, e072
ISSN-L: 0465-2746
h p://dx.doi.o g/10.3989/mc.2015.01115
Acous ic p ope ies o po ous conc e e made om
a li e and e miculi e ligh weigh agg ega es
J. Ca bajoa*, T.V. Esque do-Llo e b, J. Ramisa, A.V. Nadal-Gisbe c, F.D. Deniad
a. Depa men o Physics, Sys ems Enginee ing and Signal Theo y, Uni e si y o Alican e (Alican e, Spain)
b. Ins i u o de Diseño pa a la Fab icación y P oducción Au oma izada, Uni e si a Poli ècnica de Valencia (Valencia, Spain)
c. Ins i u o de Tecnología de Ma e iales, Uni e si a Poli ècnica de Valencia (Valencia, Spain)
d. Cen o de In es igación en Ingenie ía Mecánica, Uni e si a Poli ècnica de Valencia (Valencia, Spain)
*jesus[email p o ec ed]
Recei ed 9 Feb ua y 2015
Accep ed 11 May 2015
A ailable on line 12 No embe 2015
ABSTRACT: The use o sus ainable ma e ials is becoming a common p ac ice o noise aba emen in building
and ci il enginee ing indus ies. In his con ex , many applica ions ha e been ound o po ous conc e e made
om ligh weigh agg ega es. This wo k in es iga es he acous ic p ope ies o po ous conc e e made om a li e
and e miculi e ligh weigh agg ega es. These na u al esou ces can s ill be ega ded as sus ainable since hey
can be ecycled and do no gene a e en i onmen ally haza dous was e. The expe imen al basis used consis s o
di e en ype specimens whose acous ic pe o mance is assessed in an impedance ube. Addi ionally, a simple
heo e ical model o g anula po ous media, based on pa ame e s measu able wi h basic expe imen al p oce-
du es, is adop ed o p edic he acous ic p ope ies o he p epa ed mixes. The heo e ical p edic ions compa e
well wi h he abso p ion measu emen s. P elimina y esul s show he good abso p ion capabili y o hese ma e-
ials, making hem a p omising al e na i e o adi ional po ous conc e e solu ions.
KEYWORDS: Acous ic impedance; Abso p ion coe icien ; Po ous conc e e; Ligh weigh agg ega es
Ci a ion/Ci a como: Ca bajo, J.; Esque do-Llo e , T.V.; Ramis, J.; Nadal-Gisbe , A.V.; Denia, F.D. (2015) Acous ic
p ope ies o po ous conc e e made om a li e and e miculi e ligh weigh agg ega es. Ma e . Cons ucc. 65 [320], e072
h p://dx.doi.o g/10.3989/mc.2015.01115.
RESUMEN: P opiedades acús icas del ho migón po oso a base de á idos lige os de a li a y e miculi a. El uso
de ma e iales sos enibles se es á con i iendo en una p ác ica común pa a la educción de uido en las indus-
ias de la edi icación e ingenie ía ci il. Es e abajo in es iga las p opiedades acús icas de ho migón po oso
ab icado a pa i de á idos lige os de a li a y e miculi a. Es os ecu sos na u ales oda ía pueden consi-
de a se sos enibles ya que pueden se eciclados y no gene an esiduos pelig osos pa a el medio ambien e.
La base expe imen al u ilizada se compone de especímenes de di e en e ipo cuyas p es aciones acús icas se
e alúan en un ubo de impedancia. Adicionalmen e, se ha adop ado un modelo eó ico simple pa a medios
po osos g anula es, basado en pa áme os medibles con p ocedimien os expe imen ales básicos, con obje o de
p edeci las p opiedades acús icas de las mezclas p epa adas. Las p edicciones eó icas mues an una buena
conco dancia con las medidas de abso ción. Los esul ados p elimina es demues an la buena capacidad
abso ben e de es os ma e iales, haciendo de ellos una al e na i a p ome edo a a las soluciones de ho migón
po oso adicionales.
PALABRAS CLAVE: Impedancia acús ica; Coe icien e de abso ción; Ho migón po oso; Ag egados lige os
Copy igh : © 2015 CSIC. This is an open-access a icle dis ibu ed unde he e ms o he C ea i e Commons
A ibu ion-Non Comme cial (by-nc) Spain 3.0 License.
2 • J. Ca bajo e al.
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
1. INTRODUCTION
Po ous conc e e manu ac u ed om ligh weigh
agg ega es is each passing day mo e commonly used
o passi e noise educ ion in he building indus y
(1, 2). Conc e e ma e ials, unlike o dina y oams and
ib ous abso be s, mee po en ial p ope ies when
used o s uc u al pu poses (du abili y, s uc u al
s eng h, s i ness, e c.) along wi h a good acous-
ic pe o mance i p ope ly designed. These con-
solida ed g anula ma e ials a e also widely used in
nume ous ou doo noise con ol applica ions such
as noise ba ie s (3, 4) and in g ound su aces (5–9).
In his con ex , he need o educe CO2 emissions
while limi ing a ic noise (10, 11) has p omp ed he
ci il enginee ing indus y o ocus e o s on de el-
opmen o new en i onmen ally iendly g anula
ma e ials while p o iding simila sound abso bing
cha ac e is ics.
Some esea ch has been de o ed o s udy sus-
ainable conc e e-based ma e ials, which a e usu-
ally made om na u al o ecycled ma e ials. The
o me , which can be made om ege able pa icles,
a e o g ea in e es inasmuch as hey a e enew-
able (12) and o en p esen good sound abso p ion
capabili ies (13). O he ma e ials, also called “g een
ma e ials”, come om ecycling p ocesses; some o
hem use esidues coming om cons uc ion and
demoli ion was es (14, 15), c umb ubbe (16) o
plas ic was e om ecycling o elec ic wi es (17).
Besides, hese new kinds o ma e ials a e expec ed
o sa is y he mal, acous ical and inc easingly s uc-
u al demands. A e iew o sus ainable ma e ials o
acous ic applica ions, ei he na u al o made om
ecycled ma e ials, can be ound in (18). Among
hese, expanded ce amic ma e ials ob ained by ex o-
lia ion, as in he case o a li e and e miculi e, can
s ill be ega ded as sus ainable (19) since hey can be
ecycled and do no gene a e en i onmen ally haz-
a dous was e.
The expanded ma e ials consis o e y ligh d y
clay and a e ob ained om open-pi mining. The
i gin ock c ushed is placed in an o en a 1200°C o
gene a e he mal shock. Combus ion gases gene a e
clay expansion, hus inc easing a li e and e miculi e
pa icles 5 and 15 imes he o iginal size, espec i ely.
The g ains o a li e acqui e a da k g ey colou and
a a iable size be ween 2 and 20mm, while o e -
miculi e a yellowish laye ed s uc u e is gene a ed
and pa icles a y be ween 0.1 and 15mm. They
a e ma ke ed in bags o 50 o 100li e s o bulk.
Fu he mo e, no only do hey o e a ai du abili y,
bu also a low manu ac u ing cos and good he mal
insula ion (20). Conc e e p oduced om his ype
o clays and de i a i es p esen s low densi y alues
app op ia e o ligh weigh applica ions (21–23).
The ma e ial he e conside ed can be c ushed and
eused in he p epa a ion o new ligh ened conc e e.
A li e and e miculi e can be used as subs i u es o
o he a ids usually employed, e.g., sand and g a el,
and also p esen in e es ing p ope ies such as non-
oxici y and insolubili y in wa e and o he o ganic
sol en s. They a e also ha mless, odo less, ine and
s e ile. In addi ion, hey exhibi s abili y and insen-
si i i y o a mosphe ic agen s, hese p ope ies being
kep o e ime. Raw ma e ials a e a na u al agg e-
ga e, being he use o non- enewable ene gy in he
manu ac u ing p ocess he main sou ce o en i on-
men al pollu ion. Conce ning hei use wi h acous i-
cal pu poses, p o i om hei mic opo osi y looks
p omising and makes hem become an in e es ing
al e na i e o ypically used solu ions. Consequen ly,
an expe imen al and heo e ical cha ac e iza ion
p ocess is equi ed so as o e alua e hei acous ical
beha iou . The eby, he use o p edic i e impedance
models o analize g anula po ous media is o g ea
in e es and may help on he choice o an op imal
mix composi ion p o iding he maximum a e age
abso p ion wi hin a p esc ibed equency band.
Nume ous wo ks ha e been dedica ed o de i e
o mula ions o he acous ic impedance o g anu-
la po ous media (24–27). Mos o hem assume
he ma e ial o be composed o s acked disc e e ele-
men s and include empi ical shape ac o s whose
alues a e equen ly i ed o expe imen al da a
(28). Ea ly wo ks (29) lead o he asse ion ha he
acous ic p ope ies o consolida ed ma e ials, as in
he case o po ous conc e e, a e la gely in luenced
by heconsolida ion p ocess. Fo hese cases, a s ill
simple and p ac ical heo e ical al e na i e was p o-
posed by Ho oshenko and Swi (30), who success-
ully es ed he me hod on a ep esen a i e selec ion
o consolida ed and non-consolida ed po ous g anu-
la ma e ials. This model was based on ou measu -
able non-acous ic pa ame e s (po osi y, o uosi y,
low esis i i y and s anda d de ia ion o he po e
size) assuming a gi en po e geome y and a po e
size dis ibu ion close o log-no mal, which is o en
ound in g anula ma e ials. The p edic ion me hod
was subsequen ly shown o be in good ag eemen
wi h he expe imen al da a o o he consolida ed
g anula mixes o conc e e using aluminous agg e-
ga e (31) and expanded clay g anula es (32). This
leads o he choice o his model o he s udy o
po ous conc e e made om ligh weigh ma e ials as
hose o he a o emen ioned ype.
The p esen wo k aims o explo e he e ec o
a li e and e miculi e ligh weigh agg ega es o di -
e en sizes and ypes on he acous ic pe o mance
o po ous conc e e. Fo his pu pose, i e se s o
consolida ed g anula mixes a e p epa ed and he e-
om es specimens a e manu ac u ed. The no -
malized su ace impedance and sound abso p ion
coe icien unde no mal incidence o hese samples
a e de e mined by means o an impedance ube.
The expe imen al esul s a e compa ed o he p e-
dic ions o he Ho oshenko and Swi model (30),
which uses as inpu he measu ed da a o po osi y,
Acous ic p ope ies o po ous conc e e made om a li e and e miculi e ligh weigh agg ega es • 3
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
o uosi y, low esis i i y and s anda d de ia ion
o he po e size. The heo e ical model shows a ea-
sonable good ag eemen wi h he measu emen s and
can hus be used in di e en a eas o cons uc ion
enginee ing o acous ically design conc e e made
om ligh weigh a li e and e miculi e agg ega es.
The s uc u e o he pape is as ollows. Sec ion
2 in oduces he heo e ical backg ound o s udy
he acous ic p ope ies o g anula po ous media
and e iews he well-es ablished Ho oshenko and
Swi model. In sec ion 3, he samples p epa a ion
p ocess is explained in de ail and he expe imen al
se up used o de e mine he inpu pa ame e s o he
model and o alida e i is b ie ly desc ibed. In addi-
ion, an op imiza ion p ocess is p esen ed o de i e
hese pa ame e s when some measu emen di icul-
ies a ise. In sec ion 4, impedance ube measu emen
esul s a e analysed and compa ed o hose ob ained
in he p edic ions o some o he manu ac u ed
mixes. A discussion on he de i ed physical pa am-
e e s and he applicabili y o he heo e ical model
a e p esen ed oge he . Finally, sec ion 5 desc ibes
he main conclusions o his wo k.
2. THEORETICAL BACKGROUND
2.1. Acous ic modeling o g anula po ous media
Sound p opaga ion in g anula po ous media
is di icul o s udy on a mic oscopic scale because
o he complex geome y o he ame. Ins ead, a
mac oscopic o mula ion unde igid ame app ox-
ima ion is commonly employed. As he ame is
assumed o be mo ionless, a simpli ied equi alen
luid app oach can be used o de i e equency-
dependen exp essions o i s ele an acous ic p op-
e ies, namely cha ac e is ic impedance, Z (
w
), and
complex wa e numbe , k (
w
):
ωρ
ωω
() ()
()
=
ZC
, [1]
ωωρω ω
() ()
()
=
kC
, [2]
whe e
w
is he angula equency,
ρ
(
w
) is he
equi alen luid densi y and C (
w
) is he comp essibil-
i y o he luid. These quan i ies accoun o he is-
cous ic ion and he mal loss mechanisms a he po e
walls, and a e linked o he size o he po es and he
p opo ion o open po es h ough
ρ
(
w
) and C (
w
).
The su ace impedance Zs and sound abso p-
ion coe icien
α
o a ha d-backed g anula laye
o hickness h o he case o no mal incidence a e
calcula ed using he ollowing exp essions:
ZS=Z co h (−jkh), [3]
α
ρ
ρ
=− −
+
Zc
Zc
1,
S
S
00
00
2
[4]
whe e
ρ
0 and c0 a e he densi y and he sound
p opaga ion eloci y in ai , espec i ely. The su ace
impedance is also usually exp essed no malized o
ρ
0 c0.
Al hough basic equa ions [1] o [4] a e gene ic o
s udy he acous ic p ope ies o po ous media, hey
cons i u e he undamen als o mos o he exis ing
heo e ical app oaches and will se e o he model
adop ed he e.
2.2. Ho oshenko and Swi model
Ho oshenko and Swi (30) de i ed equa ions
o he p e ious p ope ies o igid ame g anu-
la media wi h a log-no mal po e size dis ibu ion.
These exp essions can be w i en in he ollowing
o m [5, 6]:
R
jF,
0
~
ρω α
φρφ
ωα ω
() ()
=−





∞
∞
[5]
CPN
1,
p
0
0
ωφ
γγρα γ
φρ ω
()
()
()
=− −





∞ [6]
whe e
α
∞
is he o uosi y,
φ
is he po osi y, R is he
low esis i i y,
γ
is he a io o speci ic hea s, P0 is he
a mosphe ic p essu e and Np is he P and l numbe .
F
˜ is he iscosi y co ec ion unc ion, which can be
p esen ed in he o m o a Padé app oxima ion as [7]:
Faa
b
1
1,
~
12
2
1
ω
εε
ε
()
≅++
+ [7]
wi h a1=
θ
1
/θ
2, a2=
θ
1 and b1=a1, being
θ
1=4e4
x
/3−1
and
θ
2=e3
x/
2/
2
o he ci cula po e geome y
assump ion, whe e
x=
(
σ
ln 2)2 and
σ
is he s an-
da d de ia ion in he log-no mally dis ibu ed po e
size, and
εω
ρα φ
()
=− ∞
jR
0 is a dimensionless
pa ame e .
The p esen ed model is used in his wo k o p edic
he acous ic p ope ies o a ious consolida ed g an-
ula samples made om a li e and e miculi e agg e-
ga es using a cemen i ious binde . The co esponding
ma e ial p epa a ion is desc ibed nex .
3. METHODOLOGY
3.1. Sample p epa a ion
The acous ical and non-acous ical p ope ies o
i e se s o consolida ed g anula mixes made om
ligh weigh agg ega es using cemen i ious binde a e
o be in es iga ed expe imen ally. Each se comp ises
six samples ha ing he same dimensions and he
i e se s consis o small and la ge g ain a li e, small
and la ge g ain e miculi e ype 2 and la ge g ain
4 • J. Ca bajo e al.
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
e miculi e ype 3. This numbe o samples was con-
side ed ep esen a i e enough o compa ison be ween
se s. Figu e 1 shows he mo phology o he h ee ypes
o ligh weigh agg ega es used in his s udy.
Fi s , since he s a ing a li e and e miculi e
g ains ha e a ious sizes, a apping sie e analysis
was ca ied ou o assess he g ada ion o he agg e-
ga es. I was pe o med using he digi al mechani-
cal shake CISA model RP09 wi h pe o a ed pla e
sie es ollowing he UNE-EN 933-2 s anda d (33).
The es esul s showed ha he a li e g ains ange
mainly om 2 o 8 mm in diame e , whe eas he
e miculi e ype 2 g ains ange om 0.25 o 2 mm
and he e miculi e ype 3 om 0.5 o 4 mm. As
men ioned p e iously, wo di e en pa icle size
anges we e ex ac ed o he a li e and e miculi e
ype 2 se s.
In a ollowing s ep, and in o de o p oduce a
i m consolida ed po ous s uc u e om he loose
g anula ma e ial, a kneading p ocess was unde -
aken by means o a cemen i ious binde . In his
wo k, he samples we e made by dissol ing high
s eng h whi e Po land cemen BL I 52.5 R in wa e
un il ha ing a homogeneous mix u e and hen add-
ing he agg ega es while using a mechanical au o-
cla e ype o bi al BOMANN model CB 332 a
69 .p.m (le el3) o abou 10–15 minu es ollowing
he UNE EN 196-1 s anda d (34). No plas icize s
o ex a admix u es we e added. The esul ing mixes
we e a anged in 72mm diame e and 50 mm hick
moulds o 48hou s be o e being ex ac ed o he
comple e cu ing o he samples o a pe iod 30 days
a 23 °C and 34% ela i e humidi y a ambien con-
di ions and weighing he eo . I should be no ed ha
his consolida ion p ocess may ha e a subs an ial
in luence on he acous ic p ope ies o he samples,
i.e., he binde quan i y used has a c i ical e ec on
he size and dis ibu ion o he po es in he inal
mix. In ou case, p elimina y ial and e o es s
we e necessa y o choose adequa e binde quan i-
ies o ensu e enough cohesion o subsequen han-
dling and su icien p opo ion o open po es. This
wo k phase led o he use o a lowe agg ega e-
binde a io o he case o la ge g ain e miculi e
ype 2, ob aining a mo phology simila o ha o
he consolida ed mix o la ge g ain a li e bu much
Figu e 1. Mo phology o he h ee ypes o ligh weigh agg ega es used: (a) a li e; (b) e miculi e ype 2 and (c) e miculi e ype 3.
Acous ic p ope ies o po ous conc e e made om a li e and e miculi e ligh weigh agg ega es • 5
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
lessdense. Special a en ion was paid o he ac
ha he e miculi e o e s a highe wa e abso b-
ing capaci y when compa ed o a li e. Fu he mo e,
each g ain o he inal consolida ed mix may con-
ain se e al pa icles o agg ega e.
The g anula mixes p epa a ion da a o he i e
se s is gi en in Table 1. He eina e , each mix will be
deno ed using he ollowing abb e ia ions: A (a li e);
V2 ( e miculi e ype 2) and V3 ( e miculi e ype 3),
dis inguishing wo g ain sizes (small and la ge) o
he wo i s mix ypes. The desc ip ion o he cha ac-
e is ics o he es ed samples is p o ided in Table2.
Pho og aphs o h ee consolida ed specimens co e-
sponding o he se s o la ge g ain A, la ge g ain V2
and V3 a e shown in Figu e 2. I is wo h ecalling
he ela i ely simila mo phology o he wo i s
cases in spi e o ha ing a signi ican densi y educ-
ion in he case o la ge g ain V2. A mo e de ailed
iew o hese samples is also gi en in he images cap-
u ed using a pho o came a a ached o a magni ying
glass sys em and imming he esul ing image o a
ci cula diame e o 22 mm using an image edi o . In
hese images, he p e iously men ioned bonding di -
icul ies o he case o e miculi e s and ou .
3.2. Expe imen al se up
The heo e ical model desc ibed in Sec ion 2.2 is
based on ou measu able physical p ope ies: po os-
i y, o uosi y, low esis i i y and s anda d de ia ion
o he po e size. The co esponding alues can be
de e mined using basic expe imen al p ocedu es.
The po osi y measu es he emp y space in a ma e-
ial and is calcula ed om
φ
=V »V , whe e V is he
olume o luid-space and V he o al olume o he
ma e ial sample. In he case o consolida ed po ous
conc e e, he d y samples olume is measu ed be o e
imme sing hem in wa e o 24hou s o be mois-
u ized. The ea e , he samples a e placed in a es-
sel and wa e is pou ed on i un il po e s uc u e
is sa u a ed. Then, he illing liquid is emo ed o
a lask and he olume o e ic ed wa e measu ed.
This p ocedu e has been shown o p o ide simila
esul s o hose used in o he p e iously e e ed
wo ks (4, 6, 32). Consolida ed ma e ials ha e mo e
complex po e ne wo ks ha include closed po es
(o non-connec ed ca i ies), ne e heless hey may
be neglec ed as conside ed inaccessible o ai low.
The o uosi y is a p ope y ha gi es a mea-
su e o he geome ic complexi y o a po ous ma e-
ial as he a io o he eal dis ance be ween bo h
ex emes and ha o a s aigh line. Tha is o say,
i indica es he ease o an acous ic wa e o p opa-
ga e inside he ma e ial. Gi en he inhe en pseudo-
des uc i e ea u es in using any o he commonly
adop ed chemical me hods (35) ha equi e he use
o an elec oly e, an in e se me hodology desc ibed
la e was used ins ead o de e mine his p ope y.
The low esis i i y measu es he esis ance ha
a po ous s uc u e o e s o he ai low and hence
gi es an idea o he ene gy loss occu ing inside
he ma e ial. E en hough s anda dized labo a o y
p ocedu es o measu e his pa ame e exis (36), a
simple al e na i e acous ic me hod de eloped by
Inga d and Dea (37) was used. This me hod is based
on acous ic measu emen s in an impedance ube
wi h a pai o mic ophones, he e conduc ed in an
imp o ed way using a digi al analyse ha gene a es
a andom signal. The esis i i y i sel is he eupon
ob ained as he o dina e alue om a linea i o he
low esis i i y alues a audible equencies whe e
he sample- igid e mina ion dis ance is an odd
numbe o qua e wa eleng hs, being he hickness
o he sample unde es necessa ily much smalle
han he wa eleng h in ol ed. This me hod can be
ega ded as indi ec inasmuch as i es ima es he
ze o equency low esis i i y om highe equency
alues measu ed.
Table 1. G anula mixes p epa a ion da a
G anula mix
G ain size
(mm)
A/C/W*
(%)
D y densi y
(kg/m3)
A li e (A) ≤4 50/33/17 650
>4 50/33/17 700
Ve miculi e ype 2 (V2) ≤1 11/55/34 640
>1 12/49/39 560
Ve miculi e ype 3 (V3) 0.5–4 11/56/33 690
* A/C/W indica es he Agg ega e, Cemen and Wa e p opo ions
o each mix, espec i ely.
Table 2. Cha ac e is ics o he p epa ed samples
G anula mix
E ec i e
hickness (mm), h
D y
weigh (g)
A li e (A) ≤4 mm 51.0 (0.5) 135 (8)
>4 mm 50.7 (1.0) 143 (3)
Ve miculi e ype 2 (V2) ≤1 mm 50.6 (1.0) 135 (7)
>1 mm 50.5 (1.5) 115 (6)
Ve miculi e ype 3 (V3) 0.5–4 mm 50.9 (0.4) 144 (7)
The alues in pa en hesis indica e he maximum de ia ion om he a e aged alue.

6 • J. Ca bajo e al.
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
The mean po e size and i s s anda d de ia ion a e
o he impo an pa ame e s when s udying acous ic
po ous ma e ials, he la e being an inpu o he
model used in his wo k. This pa ame e measu es
he dispe sion om he a e age po e size and gi es
an idea o he dis ibu ion o po es. The s anda d
de ia ion can be de e mined h ough heo e ically
i ing he cumula i e po e size dis ibu ion mea-
su ed using he wa e suc ion me hod (38) o he
in eg a ion o a log-no mal s a is ical dis ibu ion
wi h he p obabili y densi y unc ion [8]:
ϕσπ
()
=
ϕϕ σ
()
()
−−
PD
Fe
1
2,
2
22
[8]
wi h s being he po e size in s anda d uni s de e -
mined om he expe imen ,
ϕ
is de ined as
ϕ =
−log2s
and he median alue is calcula ed as
ϕ
=−
slog2.
In a second s ep, and so as o alida e he applica-
ion o he heo e ical model o his ype o mixes,
he sound abso p ion coe icien unde no mal inci-
dence o he p epa ed samples was measu ed ollow-
ing he s anda dized impedance ube me hod (39) in
he equency ange 200–2200 Hz. Bo h impedance
ube me hods, ha o Inga d and Dea (37) and ha
jus men ioned, we e pe o med a anging he sam-
ples so ha he incoming acous ic wa e impinges
on he oughe su ace o he sample. This se up
consis s o wo cus om-made ubes: one o he
loudspeake sec ion and he o he o he igid e -
mina ion, coupled by a sample holde as indica ed
in he schema ic o Figu e 3. The specimen is placed
in his sample holde and his in u n a ached o he
ubes using adjus able sc ews on h eaded ba s. An
addi ional igid piece is placed behind he sample o
he abso p ion measu emen s whe eas i is emo ed
o he low esis i i y expe imen s. In his manne ,
bo h me hods can be pe o med in a e sa ile way
using a unique expe imen al ig. The ubes ha e ci -
cula c oss-sec ion wi h a hickness o 6 mm and a
cu -o equency a ound 2500 Hz. All he elemen s
a e made om s ainless s eel. A andom exci a ion is
p o ided o he loudspeake om he analyse (OR34
Compac Analyse ) and he co esponding p essu e
ans e unc ions a e measu ed subsequen ly using
wo 1/2 in. p essu e mic ophones (B&K Type 4188)
moun ed lush wi h he inne su ace o he ubes
a hei espec i e loca ions (1, 2: abso p ion; 3, 4:
low esis i i y). Acquisi ion da a was pos -p ocessed
in Ma lab. Since he acous ic analysis o he p es-
en s udy is based upon linea models, he inciden
sound p essu e le el in he impedance ube has been
kep below 90 dB. The equency ange o analysis
Figu e 2. (Le ) Pho og aphs and (Righ ) immed zoomed image o es specimens o
po ous conc e e made om: (a) la ge g ain A; (b) la ge g ain V2 and (c) V3.
Figu e 3. Schema ic o he impedance ube used o bo h
abso p ion and low esis i i y measu emen s (dimensions
a e in mm). h is he sample hickness and (i=1…4)
a e he mic ophone posi ions.
Acous ic p ope ies o po ous conc e e made om a li e and e miculi e ligh weigh agg ega es • 7
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
was chosen o ensu e plane wa e p opaga ion and
a oid exci a ions o highe o de modes. The esul-
an sound abso p ion coe icien and low esis i i y
o he abso ben ma e ials can hus be ob ained.
3.3. In e se nume ical me hod
To a oid some o he limi a ions discussed abo e,
i is common o use some op imiza ion me hod o
de e mine indi ec ly he inpu pa ame e s ha le he
acous ic model ob ain he bes i o he impedance
ube measu emen s (40, 41). This p ocedu e is also
ecu en ly used when any o he p e ious physical
pa ame e s a e di icul o measu e o canno be
p ope ly de e mined, as i was in he cu en in es-
iga ion o he o uosi y. The Nelde -Mead di ec
sea ch op imiza ion me hod (42) is a echnique ha
minimizes an objec i e unc ion o one o se e al
a iables om an ini ial es ima e and se ial i e a-
ions un il he speci ied ole ance is achie ed, hough
i can some imes p esen discon inui ies o no con-
e gence p oblems. Hence, o hese cases whe e he
equi ed adjus men is wi hin he expe imen al ole -
ance alues, his in e se nume ical me hod is p o en
o be a use ul ool o accu a ely es ima e he physical
p ope ies o g anula mixes in a simple manne .
Fo his pu pose, he ollowing objec i e unc ion
is de ined [9]:
OF (
α
∞)=
i
N
1
∑
=
α
( i)−
αˆ
( i,
α
∞) , [9]
whe e α( i) and αˆ( i) co espond o he measu ed
and he es ima ed sound abso p ion coe icien unde
no mal incidence o each equency o in e es i,
espec i ely. He eby, he design a iable pa ame e
( o uosi y
α
∞ in ou case) ha bes i s he expe i-
men al da a o he heo e ical model is ob ained.
4. RESULTS AND DISCUSSION
4.1. Physical pa ame e s
Table 3 summa izes he physical p ope ies o
he i e g anula mixes es ed. These a e ob ained
by a e aging he alues measu ed in each o he six
samples o hei espec i e se s. The p edic ion o
he acous ic p ope ies was ca ied ou using hese
alues as inpu da a in he heo e ical model.
Po osi y measu emen s o he p epa ed mixes
indica e simila alues o a ound 39% o his ma e-
ial p ope y. As s a ed abo e, e miculi e high wa e
abso bing capaci y can esul in e y misleading al-
ues o po osi y i no ca e ully measu ed, bu a e s ill
accep able o p ac ical pu poses. To uosi y alues
indica e ha o he same mix ype he g ain size has
a sligh in luence on hem. Ne e heless, i should be
ecalled ha his p ope y has been ob ained h ough
an in e se me hod and he e o e i is wo h no ing
ha u he expe imen al wo k is equi ed o con-
i m his. Flow esis i i y alues show o be in e sely
p opo ional o he g ain pa icle size o he samples,
as he sound p opaga ion damping inc eases wi h
he educed g ain size. This asse ion is no ue o
excessi ely high alues o low esis i i y, as i would
in ol e oo high cha ac e is ic impedance alues and
he e o e wo sen ai -g anula mix impedance cou-
pling, yielding less sound abso p ion. Wi h his in
mind, lowe g ain sizes a ain highe low esis i i y
alues o he cases examined.
Figu e 4 displays he a e age cumula i e po e
size dis ibu ion ob ained expe imen ally and he
heo e ical i ed cu e using equa ion [8] o each
g anula mix se . The a e age s anda d de ia ion i -
ed alues a e in he ange 0.17–0.24. The esul ing
da a e i ies ha he po e size dis ibu ion is log-
no mal o hese g anula ma e ials. The e miculi e
ype 3 mixes exhibi smalle po es and highes alue
o s anda d de ia ion o po e size, somewha due o
he ela i ely b oades g ain size ange.
4.2. Acous ic p ope ies
Figu e 5 shows he a e age measu ed sound ab -
so p ion coe icien o he se s o g anula mixes
es ed. The acous ic beha iou o hese ma e ials is
go e ned by hei dimensions, he po osi y, he po e
shape and size along wi h hei dis ibu ion. Indeed,
he dimensions and he po osi y a e o he same
o de o all he samples so ha maximum abso p-
ion equency ange 1000–1400 Hz is alike, being
he di e ences o he sound abso p ion coe icien
Table 3. A e age measu ed physical p ope ies o he g anula mixes used in he heo e ical model
G anula mix Po osi y,
φ
To uosi y,
`
∞
*Flow esis i i y
(Pa·s·m−2), R
S anda d
de ia ion,
A li e (A) ≤4 mm 0.39 1.82 2176 0.21
>4 mm 0.38 1.87 1839 0.16
Ve miculi e ype 2 (V2) ≤1 mm 0.39 1.70 2230 0.17
>1 mm 0.37 1.73 1424 0.17
Ve miculi e ype 3 (V3) 0.5–4 mm 0.40 1.70 1720 0.24
* To uosi y alues we e ob ained wi h he in e se nume ical me hod desc ibed in Sec ion 3.3.
8 • J. Ca bajo e al.
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
ampli ude pa icula ly due o he wo la e pa am-
e e s. This bandwid h depends on he design pa am-
e e s o he g anula mix (g ain size, binde , A/C/W
p opo ions,…), whose modi ica ion could e en
lead o di e en abso p ion p ope ies. The imped-
ance ube expe imen s sugges ha he smalle g ain
mixes show highe sound abso p ion and a b oade
equency ange han hose made om la ge g ains.
This is pa ly due o hei ela i ely highe low
esis i i y, whils he enhanced sound a enua ion in
he high equency ange may be a ibu ed o he
majo impo ance o isco he mal loss mechanisms
h ough he na owe po ous s uc u e. Mo eo e ,
he peak equency shi owa ds lowe equencies
as he g ain size is educed migh be also linked o a
highe alue o low esis i i y, which is associa ed
wi h he highe a enua ion o he acous ic wa es
in he g anula ma e ial. No ice ha o he ana-
lysed cases a sligh po osi y educ ion esul s in a
poo e acous ic pe o mance, somehow due o he
binde e ec s on he g ain disposi ion and inal po e
s uc u e.
The SEM images on a cu la su ace o esidual
g ains o he la ge g ain A and he V3 mixes illus-
a e some di e ences be ween a li e and e micu-
li e agg ega es (Figu e 6). While a li e e idences he
expansion p ocess in he o m o an in e nal mac o-
po ous p oduc , e miculi e p o ides a la and well
de ined lamella s uc u e su ounded by cemen on
i s bounda ies. In bo h cases, a ai ly good adhe-
sion wi h a con inuous in e ace agg ega e-cemen is
obse ed.
Figu e 7 depic s he a e age eal and imagina y
pa s o he no malized su ace impedance o he
la ge g ain A mix, he small g ain V2 mix and he
V3 mix. Fo he la ge g ain mix, he eal and imagi-
na y pa s o he su ace impedance inc ease in
ampli ude a low equencies and abo e 1800 Hz,
while o he o he mixes his occu s a lowe alues.
As a consequence, he wid h o he equency ange
Figu e 4. Cumula i e po e size dis ibu ion o he g anula
mix se s analyzed. The ma ke s deno e expe imen al
da a and he do ed lines he heo e ical i .
Figu e 5. Sound abso p ion coe icien o
he di e en se s o g anula mixes.
Figu e 6. SEM image o es samples o po ous conc e e made om: (a) la ge g ain A and (b) V3.
Acous ic p ope ies o po ous conc e e made om a li e and e miculi e ligh weigh agg ega es • 9
Ma e iales de Cons ucción 65 (320), Oc obe –Decembe 2015, e072. ISSN-L: 0465-2746. doi: h p://dx.doi.o g/10.3989/mc.2015.01115
a which sound abso p ion is e ec i e becomes
educed o he la ge g ain mix. This aise in he
su ace impedance also yields lowe abso p ion al-
ues o his mix ype and explains he wo s imped-
ance ma ch in he ai -g anula mix in e ac ion
egion. On he o he hand, he equency associa ed
wi h he ze o alue o he su ace eac ance (imagi-
na y pa o he su ace impedance) is obse ed o
be nea ly unchanged om his mix se o he o he s.
A equency shi o he sound abso p ion peak
o wa ds lowe equencies is mo e p onounced o
he small g ain wi h espec o he la ge g ain o he
same agg ega e ype, as i was p io app ecia ed in
Figu e 5.
In addi ion, he expe imen al esul s o he sound
abso p ion coe icien ha e been compa ed o hose
p edic ed by he heo e ical model using he mea-
su ed physical pa ame e s o some o he manu ac-
u ed mixes. In Figu e 8 a good ag eemen be ween
he p edic ions and he impedance ube es s is e i-
ied h oughou he equency ange 500–1800 Hz,
showing some disc epancies a equencies abo e
1800 Hz and in he low equency ange. A closes
ma ch is ound o he case o la ge g ain A whe eas
he heo e ical model is less accu a e in he case o
la ge g ain V2 and V3, likely due o he lowe eli-
abili y o he expe imen s in ol ing wa e in his
ype o samples and/o o he measu emen e o s.
These di e ences may be a esul o bo h on su -
ace oughness and no low occu ing h ough dead-
end po es (po es connec ed o he ex e io a only
one end o he sample). Fu he mo e, he ci cula
po e shape assump ion may no be as close o man-
u ac u ed samples. Al e na i ely, o he po e geom-
e ies could be used o he p edic ions, hough his
is usually unknown o no easy o de ine.
5. CONCLUSIONS
This wo k p esen s and analyses he acous ic
p ope ies o po ous conc e e made om ligh -
weigh a li e and e miculi e agg ega es o di e en
sizes and ypes. Fo his pu pose, se e al mixes we e
p epa ed and impedance ube measu emen s we e
pe o med on manu ac u ed specimens. The esul s
indica e ha hese consolida ed ma e ials yield a
ela i e high sound abso p ion and can hus become
a sus ainable al e na i e o o he commonly used
solu ions in p ac ical applica ions. Addi ionally,
p edic ions a e ob ained o he sound abso p ion
coe icien based upon a gene al heo e ical model
whose inpu pa ame e s (po osi y, o uosi y, low
esis i i y and s anda d de ia ion o he po e size)
ha e been easily de e mined h ough basic expe i-
men al p ocedu es. In gene al, measu ed and es i-
ma ed alues showed a ela i e good ag eemen and
con i m ha he model can be success ully used o
he design o po ous conc e e made om a li e and
e miculi e agg ega es.
Summa izing, hese ma e ials (a li e and e mic-
uli e) ha e adequa e s uc u al s eng h o manu ac-
u ing and manipula ion pu poses. The inal conc e e
p oduc is a achable o exis ing elemen s such as
plas e boa d, plas e and alse ceilings, and can be
used as isible o hidden cons uc ion solu ions. A
numbe o di e en cha ac e is ics can be ob ained,
including ex u e, oughness, a bi a y shape and
hickness. In he case o sound walls, hese can be
manu ac u ed wi h special shapes like undula ions
o p ojec ions. In addi ion, hese ma e ials allow
aes he ic applica ions and can include pe o a ions.
Figu e 7. No malized su ace esis ance (con inuous line)
and eac ance (do ed line) o he la ge g ain
A, small g ain V2 and V3 mixes.
Figu e 8. Measu emen (ma ke s) and p edic ion (do ed line) esul s o sound abso p ion
coe icien o : (le ) la ge g ain A, (cen e ) la ge g ain V2 and ( igh ) V3.