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
Ci a ion: Láza o, J.; Pe ei a, M.;
Cos a, P.A.; Godinho, L. Pe o mance
o Low-Heigh Railway Noise
Ba ie s wi h Po ous Ma e ials. Appl.
Sci. 2022,12, 2960. h ps://doi.o g/
10.3390/app12062960
Academic Edi o : Massimo Ga ai
Recei ed: 4 Feb ua y 2022
Accep ed: 3 Ma ch 2022
Published: 14 Ma ch 2022
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Copy igh : © 2022 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
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A ibu ion (CC BY) license (h ps://
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4.0/).
applied
sciences
A icle
Pe o mance o Low-Heigh Railway Noise Ba ie s wi h
Po ous Ma e ials
João Láza o 1,*,† , Ma heus Pe ei a 1,† , Ped o Al es Cos a 1,† and Luís Godinho 2,†
1CONSTRUCT, Facul y o Enginee ing (FEUP), Uni e si y o Po o, Rua D . Robe o F ias,
4200-465 Po o, Po ugal; [email p o ec ed] (M.P.); [email p o ec ed] (P.A.C.)
2ISISE, Depa men o Ci il Enginee ing, Uni e si y o Coimb a, Pólo II, Rua Luís Reis San os,
3030-788 Coimb a, Po ugal; [email p o ec ed]
*Co espondence: jlaza [email p o ec ed]
† These au ho s con ibu ed equally o his wo k.
Abs ac :
Rail anspo is he mos sus ainable anspo a ion mode, wi h he lowes ene gy con-
sump ion and ca bon oo p in . Howe e , he noise induced by ailway a ic in u ban egions is
a signi ican d awback and se e al epo s poin ou he isks and he amoun o people su e ing
om di ec exposu e o ailway noise. One o he mos used mi iga ion measu es o ailway noise
is he implemen a ion o noise ba ie s. Al hough hey o e a signi ican educ ion in noise le els,
hei heigh makes people eel enclosed. The e o e, in he case o ailway in as uc u e, he solu-
ion o he p oblem may lie in he use o ba ie s wi h a lowe heigh placed close o he ailway
ack. As he noise- o ming mechanisms a e mainly loca ed a he ack le el, placing he ba ie
in a posi ion close o he ack allows mi iga ing ail noise wi hou causing he p oblems iden i ied
abo e o he popula ion in he icini y. The pu pose o his pape is o illus a e he de elopmen
o a ba ie solu ion o be used in a ailway con ex h ough nume ical modelling wi h he Bounda y
Elemen Me hod (BEM). The solu ions de eloped we e placed close o he ack and ha e a low
heigh . The geome y was de ined so as o di ec he ene gy back o he ack o ake ad an age
o he acous ic p ope ies o he ballas . The addi ion o a po ous g anula ma e ial on he inne ace
o he ba ie allows he con ol o e lec ions be ween he ehicle body and he ba ie , inc easing
i s acous ic e iciency. Finally, conside ing he mos e icien solu ion, he inse ion loss in a ne wo k
o ecei e s loca ed 10 m away om he ack is analysed in o de o s udy he noise educ ion le els
in a place whe e human ecei e s a e usually loca ed.
Keywo ds: ailway noise; low heigh noise ba ie s; acous ic e iciency; noise mi iga ion
1. In oduc ion
Railway anspo is he mos sus ainable mode o anspo , wi h he lowes ene gy
consump ion and ca bon oo p in compa ed o any o he mode o anspo .
Howe e , a epo by he Eu opean En i onmen Agency (EEA) [
1
] om 2019 on his
subjec s a es ha a he Eu opean le el, ail noise is he second mos dominan sou ce, wi h
an es ima ed 22 million people exposed o a leas 55 dB du ing he day and nigh pe iods.
On he same subjec , howe e , wi h a di e en ime ho izon, he epo by he Eu opean
En i onmen Agency [
2
], whose aim is o p ojec scena ios o he decade 2020 o 2030,
s a es ha he si ua ion o he popula ion’s exposu e o en i onmen al noise le el in Eu ope
will wo sen in p ac ically all a eas esponsible o cu en exposu e le els. The p ojec ions
sugges ha in 10 yea s mo e han one million people will be exposed o excessi e ail noise,
bo h in u ban cen es and ou side hese agglome a ions. In ligh o he abo e, a epo
o he Wo ld Heal h O ganisa ion (WHO) Regional O ice o Eu ope [
3
] is p esen ed. This
documen highligh s he e ec s o noise and inco po a es a numbe o indica ions o ce -
ain policies ha mus be implemen ed in o de o ensu e heal h and well-being o people
li ing wi h he mos di e se o ms o en i onmen al noise. The WHO wo king g oup s a e
Appl. Sci. 2022,12, 2960. h ps://doi.o g/10.3390/app12062960 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2022,12, 2960 2 o 18
ha , o he day ime pe iod, noise le els should be below 54 dB, and o he nigh - ime
pe iod, hey should no exceed 44 dB. Finally, i s esses ha in e en ions o educe noise
le els and o comply wi h he limi s indica ed should ocus on in e en ions a he ack
le el, he imp o emen o olling s ock and he implemen a ion o small noise ba ie s.
Rail noise mi iga ion measu es can be applied in h ee di e en loca ions and acco ding
o he en i onmen and he le el o noise p essu e educ ion ha one wan s o achie e [
4
].
Usually, he mos widely deployed solu ions a e hose ha ac a he le el o he p op-
aga ion pa h o a he le el o he ecei e s. In places whe e housing densi y is high,
he solu ions ha ac on he pa h o p opaga ion a e mo e ad an ageous in economic
e ms [
4
]. Acous ic ba ie s a e usually a i icial and solid elemen s made o di e en
ypes o ma e ial and placed in di e en posi ions, depending on he place o be p o ec ed.
This noise mi iga ion solu ion has been widely adop ed in he con ex o oad noise mi iga-
ion, and he e a e se e al me hods o designing hese solu ions. Acous ic ba ie s can
ha e di e en ope a ing p inciples depending on he ma e ial hey a e made o ; i.e., hey
can wo k by e lec ing acous ic wa es and/o abso bing hem. In gene al, he ba ie s a e
e ical elemen s be ween 3 m and 4 m high posi ioned along he oad o ailway.
Howe e , despi e he inhe en bene i s o educing noise and imp o ing he quali y o li e
o he popula ion li ing nea by, his ype o solu ion aces he eluc ance o he popula ions
li ing nea he ailway in as uc u e. This si ua ion is ela ed o he size o he ba ie , a ec ing
he ield o ision, causing a sense o imp isonmen , loss o na u al ligh o a ec ing ai ci cula-
ion. F om ano he pe spec i e, o hose who a el on ains, complain s a e also egis e ed
o simila easons [
5
–
7
]. In o de o ackle some o he nega i e poin s iden i ied o he highe
acous ic ba ie s, namely, being obs acles o one’s ield o ision, he na u al e olu ion o hink-
ing has led o he c ea ion o solu ions whose wo king p inciple is simila o he one in ended
o be applied in he wo k p esen ed in his documen . The inhe en ad an age o low-heigh
solu ions is ela ed o he posi ioning o his elemen . As he mechanisms o noise gene a ion
a e mos ly a he le el o he ail [
8
], he placemen o he ba ie in a posi ion close o he ack
allows he p opaga ion o sound wa es o be in e up ed close o he sou ce. The educed
heigh o hese elemen s hus allows his posi ioning close o he sou ce wi hou cons i u ing an
obs acle o he ield o ision o passenge s and passe s-by.
Bea ing his in mind, se e al au ho s ha e wo ked on his issue in o de o de elop a so-
lu ion o mi iga e he noise le els associa ed wi h ail a ic. The s udies om he li e a u e
p esen solu ions o he design o he ba ie s and o a mo e e ec i e nume ical modelling.
Koussa [
9
] s udied, bo h nume ically and expe imen ally, he use o gabion walls as a o m
o mi iga ion. The esul s indica e ha his solu ion can achie e up o
8 dB(A)
o inse ion
loss. Jilibois [
10
] p esen s a ull-scale model o an L-shaped ba ie buil wi h wooden
panels and inside wi h abso ben ib ous ma e ial. Tes s ca ied ou by he expe imen al
au ho e ealed an a enua ion o 10 dB(A). Nieuwenhuizen [
11
] showed ha he Du ch cal-
cula ion scheme o con en ional ba ie s is easonably applicable o low-heigh solu ions.
Finally, Kasess [
12
] p oposes co ec i e unc ions ha allow one o e icien ly calcula e com-
plex geome ies using BEM, in o de o apply mo e complex geome ies in noise mapping
p og ams. To con ol he e lec ions be ween he ca body and he noise ba ie , an abso p-
i e ea men is equi ed. Fibe s and oams a e commonly used in passi e noise con ol;
howe e , o ex e nal applica ions, hese ma e ials equi e p o ec ion agains en i onmen al
agen s and s uc u al ein o cemen . Because o hese equi emen s, he in e es in sound
abso p i e solu ions, such as po ous conc e e, made using consolida ed ligh weigh and
sus ainable g anula ma e ials ha e inc eased o e ecen decades [
13
–
21
]. The in es iga-
ion o he luid-equi alen ep esen a ion o po ous conc e e made wi h expanded clay
has been shown o be ele an in he scien i ic communi y.
Ca bajo e al. [22]
s udied pe o-
a ed conc e e and highligh ed he highe du abili y and he excellen s eng h- o-weigh
a io o his solu ion. Pe ei a e al. [
23
] s udied he in luence o he wa e –cemen a io,
he expanded clay g ain size, and he sample hickness in he sound abso p ion beha iou ,
while Zolan a i [
24
] s udied he luid-equi alen ep esen a ion o po ous conc e e using
di e en agg ega es.
Appl. Sci. 2022,12, 2960 3 o 18
The modelling o he ailway scena io has, o he easons gi en, an impo an
ole o play in o ecas ing and c ea ing measu es o mi iga e ail a ic-induced noise.
The Bounda y Elemen Me hod (BEM) is widely used o sol e acous ic p oblems [
7
,
25
],
and can be an excellen op ion o model he e ec o mi iga ion measu es. The e sa ili y
o his nume ical me hod allows he c ea ion o simply e lec i e acous ic ba ie s and/o
he inclusion o po ous ma e ial which ac s as a sound abso p ion elemen , allowing he im-
p o emen o he pe o mance on he ba ie , mi iga ing he ene gy e lec ed be ween
he ehicle and he ba ie . In his a icle, he BEM will be used o sol e an ex e nal acous ic
p oblem, essen ially o es he geome y o he ba ie s. In addi ion, a BEM o mula ion
conside ing mul iple ma e ial egions is implemen ed o allow he modelling o he e ec
o possible abso p i e ma e ials coupled o he noise ba ie . Using his model, i becomes
possible o model he abso p i e ma e ials using equi alen luid heo ies, leading o a
ealis ic ep esen a ion o such media. To assess he capaci y o he ba ie , he inse ion
loss was used, i.e., he di e ence be ween he scena io wi h and wi hou he ba ie . Using
he inse ion loss allows he ba ie o be assessed as a noise con ol measu e placed in a lo-
ca ion wi h speci ic cha ac e is ics. In his way, he IL calcula ion p esen s he ac ual losses
o e a wide ange o equencies, o any se o ecei e s, ega dless o he scena io o be
e alua ed and mainly ega dless o he ype o ma e ial and geome y o he p o o ype.
This pape ’s s uc u e is as ollows: Sec ion 2shows he expe imen al ailway noise
cha ac e isa ion. Sec ion 3p esen s he expe imen al p ocedu e used o cha ac e ise
po ous conc e e samples, allowing he luid-equi alen heo y ep esen a ion. Sec ion 4
p esen s he nume ical o mula ion o he BEM used o model he desc ibed p oblem.
Sec ion 5p esen s he s a egy used o de ine he ba ie ’s geome y and he pa ame ic
s udy o di e en noise ba ie con igu a ions. Then, Sec ion 6shows he sound p essu e
le els p edic ed a ound he noise ba ie , in he p esence o he ain, and he inse ion loss
esul s. Finally, Sec ion 7summa ises he main conclusions o his wo k.
2. Railway Noise Cha ac e isa ion
Noise induced by ail a ic has se e al sou ces wi h di e en cha ac e is ics. Despi e
he a ious componen s o ailway noise, he noise gene a ed by he wheel- ail in e ac ion
plays he mos impo an ole in noise gene a ion. The a iable ha mos condi ions
he sound p essu e le els and he o igin o he noise is he unning speed o he ehicles
as illus a ed in Figu e 1, whe e he main noise sou ces a e de ined acco ding o he
ain speed.
10 20 50 100 200 300 400
Speed [km/h]
70
80
90
100
110
120
130
Sound P essu e Le el [db(A)]
T ac ion noise
Rolling noise
Ae odynamic noise
To al
Figu e 1.
E olu ion o he con ibu ion o he di e en sou ces acco ding o he speed o ci cula ion
(adap ed om [26]).
The comple e s udy o he ailway noise p oblem in ol es examining se e al dimen-
sions, namely gene a ion, p opaga ion and ecep ion. The e o e, he de ini ion o measu es
Appl. Sci. 2022,12, 2960 4 o 18
aimed a i s mi iga ion equi es a clea unde s anding o hese dimensions. Consequen ly, i
can be concluded ha only he cha ac e isa ion o noise in di e en ypes o scena ios, wi h
di e en unning speeds, ehicle ypes, ack ypes and u ban meshes allows a clea e iew
o he noise le els in ol ed and especially which a ia ions a e associa ed wi h he di e en
a ic condi ions men ioned abo e.
In his con ex , he main objec i e o he expe imen al cha ac e isa ion is o cla i y he noise
le els associa ed wi h he a ic unde analysis. The sys ema isa ion o maximum noise le els,
as well as he equency con en in ol ed, ela ing hem o speci ic condi ions, makes i possible
o be e de ine mi iga ion measu es o deal wi h he noise con en iden i ied.
In his wo k, a cha ac e isa ion campaign has been pe o med, in which he acquisi ion
o he signal was made using ou mic ophones Beh inge ype ECM 8000, connec ed
o a Focus i e Scla e 4P e USB o he signal acquisi ion, as is shown in Figu e 2. Pos -
p ocessing o he da a was pe o med in Ma lab using he ITA-Toolbox unc ions [
27
].
Figu e 2.
Expe imen al se up o he acous ic signal acquisi ion; (
1
) Beh inge ECM 8000 mic ophone,
(2) compu e , (3) Focus i e Scla e 4P e USB acquisi ion uni .
The placemen o he mic ophones was de ined o allow acqui ing he noise in he clos-
es possible place o he sou ce, and a successi ely la ge dis ances om he sou ce, hus
allowing o s udy in a comple e way he p opaga ion o he sound wa es. Figu e 3shows
he se up used o he measu emen , wi h he dis ance be ween mic ophones and posi ion
ela i e o he ack. Figu e 4shows pho os aken a he measu emen si e, in scena ios wi h
and wi hou ehicle, espec i ely. As can be seen om he illus a ions, he mic ophone
called M1 is e y close o he sou ce, while he o he s, M2, M3 and M4, occupy a ela i e
posi ion in acco dance wi h places whe e pedes ians ci cula e. Be o e each measu emen
campaign, e i ica ion was pe o med making use o a BK 4231 mic ophone calib a o .
Since some o he mic ophones a e posi ioned close o he ailway, some in luence o po-
en ial ai - low gene a ed by he ain passage will ine i ably be included in he egis e ed
esponses. Howe e , he egis e ed acous ic signals a e s ill ele an o be e unde s and
he acous ic esponses a posi ions close o he ailway, since sound p essu e le els a
such posi ions g ea ly helps o de ine e ec i e mi iga ion measu es o ackle he exposu e
o pedes ians and sensible ecei e s.
Figu e 3. Expe imen al se up con igu a ion.
Appl. Sci. 2022,12, 2960 5 o 18
(a)
Appl. Sci. 2022,1, 0 5 o 19
(a) (b)
Figu e 4.
Pho og aphs o he in si u expe imen al cha ac e isa ion. (
a
) Pho og aph o he mic ophones
on si e. (b) Pho og aph o he measu emen se up in he p esence o he ehicle.
The sound p essu e le els (SPL) collec ed in a ballas ack con ex in each o he ou
a ailable mic ophones a e shown below, in Figu e 5. F om he expe imen al cha ac e isa ion
i was possible o collec da a om nume ous passages wi h di e en unning speeds.
In o de o summa ise he da a collec ed, he noise le els co esponding o he wo eco ded
speed ( espec i ely, 84 km/h and 78 km/h) eco ded a e p esen ed. The da a a e p esen ed
in one- hi d oc a e bands and i is in ended o highligh om among he a ious ecei e s
he mos signi ican spec al con en ha will se e as a basis o he nume ical simula ions
explained in he p e ious sec ions.
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 1 (M1)
V=84km/h V=72km/h
(a)
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 2 (M2)
V=84km/h V=72km/h
(b)
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 3 (M3)
V=84km/h V=72km/h
(c)
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 4 (M4)
V=84km/h V=72km/h
(d)
Figu e 5.
Reco ds o measu ed sound p essu e le els; in blue a ehicle ope a ing a 84 km/h; in yellow
a ehicle ope a ing a 72 km/h. (
a
) Fi s mic ophone; (
b
) Second mic ophone; (
c
) Thi d mic ophone;
(d) Fou h mic ophone.
Sound p essu e le els (SPL), p esen ed in Figu e 5a e il e ed o ake in o accoun
he esponse o he human ea , and hus a e p esen ed in dB(A). By analysing he one-
hi d oc a e bands p esen ed, i is concluded ha he mos p e alen equency con en
esponsible o he highes noise le els is be ween 200 Hz and 4000 Hz, i.e. he equency
in e al be ween he wo discon inuous black lines in each o he hi d oc a e bands. This
in o ma ion has been he basis o he nume ical modelling p esen ed la e in his pape ,
(b)
Figu e 4.
Pho og aphs o he in si u expe imen al cha ac e isa ion. (
a
) Pho og aph o he mic ophones
on si e. (b) Pho og aph o he measu emen se up in he p esence o he ehicle.
The sound p essu e le els (SPL) collec ed in a ballas ack con ex in each o he ou
a ailable mic ophones a e shown below, in Figu e 5. F om he expe imen al cha ac e isa ion
i was possible o collec da a om nume ous passages wi h di e en unning speeds.
In o de o summa ise he da a collec ed, he noise le els co esponding o he wo eco ded
speed ( espec i ely, 84 km/h and 78 km/h) eco ded a e p esen ed. The da a a e p esen ed
in one- hi d oc a e bands and i is in ended o highligh om among he a ious ecei e s
he mos signi ican spec al con en ha will se e as a basis o he nume ical simula ions
explained in he p e ious sec ions.
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 1 (M1)
V=84km/h V=72km/h
(a)
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 2 (M2)
V=84km/h V=72km/h
(b)
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 3 (M3)
V=84km/h V=72km/h
(c)
20 40 60 100 200 400 1k 2k 4k 6k 10k 20k
F equency [Hz]
0
10
20
30
40
50
60
70
80
90
100
Sound P essu e Le el [dBA]
Mic ophone 4 (M4)
V=84km/h V=72km/h
(d)
Figu e 5.
Reco ds o measu ed sound p essu e le els; in blue a ehicle ope a ing a 84 km/h; in yellow
a ehicle ope a ing a 72 km/h. (
a
) Fi s mic ophone; (
b
) Second mic ophone; (
c
) Thi d mic ophone;
(d) Fou h mic ophone.
Sound p essu e le els (SPL), p esen ed in Figu e 5a e il e ed o ake in o accoun
he esponse o he human ea , and hus a e p esen ed in dB(A). By analysing he one-
hi d oc a e bands p esen ed, i is concluded ha he mos p e alen equency con en
esponsible o he highes noise le els is be ween 200 Hz and 4000 Hz, i.e., he equency
in e al be ween he wo discon inuous black lines in each o he hi d oc a e bands. This
in o ma ion has been he basis o he nume ical modelling p esen ed la e in his pape ,

Appl. Sci. 2022,12, 2960 6 o 18
allowing he de ini ion o he equency ange and con en ha needs o be mi iga ed by
he noise ba ie .
3. Expe imen al Cha ac e isa ion o Po ous Conc e e
In he po ous conc e e ma e ial, g anules a e usually dis ibu ed di e en ly om
he wha is obse ed in ib ous ma e ials by ollowing a log-no mal po e dis ibu ion,
esul ing in smalle po osi y and highe o uosi y. The abso p ion coe icien o hese
ma e ials depends on he size o he po es, he po osi y, he o uosi y and he hickness
o he ma e ial sample.
Six samples o po ous conc e e we e p oduced using expanded clay agg ega es, wi h
g ain size o 0–2 mm. All samples we e p epa ed wi h 10.1 cm o diame e and hickness
o 4, 6 and 8 cm, being hese p ocedu e p e iously p esen ed in [
23
]. The sample p opo ions
in weigh (kg) a e p esen ed in Table 1.
Table 1. Ma e ials p opo ions in weigh (kg) o he p oduced samples.
G ain Size (mm) Agg ega e (%) Cemen (%) Wa e (%)
0–2 43.96 37.36 18.68
Se e al app oaches can be used o cha ac e ise acous ic abso bing ma e ials, such as hose
desc ibed o example in Ciabu o e al. [
28
], A enas e al. [
29
] o del Rey e al. [
30
]. He e,
an expe imen al expe imen al p ocedu e based on he use o an impedance ube was used
o cha ac e ise he no mal incidence acous ic p ope ies o he po ous conc e e samples. As
desc ibed in ISO 10534-2 [
31
], hese p ope ies can be ob ained om he ans e unc ion
be ween wo mic ophones. To ob ain he in insic acous ic p ope ies o he po ous conc e e
samples, he Two-Ca i y Me hod p oposed by U suno e al. [32] was used.
The impedance ube used has a ci cula c oss-sec ion o 10.1 cm diame e , he cu -o
equency being app oxima ely 1600 Hz o he chosen mic ophone spacing. A whi e
noise signal was used o exci e he speake om he analyse , OR 34 Compac Analyze ,
he sound p essu e was measu ed using wo mic ophones B&K Type 4188 1/2
00
, posi ioned
a 16 cm and 10 cm om he sample su ace, and he p essu e da a we e pos -p ocessed
in Ma lab, o ob ain bo h he su ace impedance and he sound abso p ion. A schema ic
ep esen a ion o he expe imen al se up is p esen ed in Figu e 6, whe e he e m
d1
is
he sample hickness, and D is he ai ca i y hickness.
Figu e 6. Schema ical ep esen a ion o he expe imen al wo-ca i y me hod ( e ie ed om [23]).
The wo-ca i y me hod is based on wo measu emen s o he same sample h ough
he ISO 10534-2 p ocedu e. Each measu emen uses a di e en ai ca i y dep h, D, be ween
he sample and he igid e mina ion. The complex cha ac e is ic impedance,
˜
Zc
, and
he complex wa e numbe ,
˜
kc
, can be de e mined, espec i ely, by he ollowing equa ions,
˜
Zc=s˜
Zs1˜
Zs2Z1−Z0
1−Z1Z0
1˜
Zs1˜
Zs2
Z1−Z0
1−˜
Zs1˜
Zs2, (1)
Appl. Sci. 2022,12, 2960 7 o 18
˜
kc=j
2d1
ln˜
Zs1+˜
Zc
˜
Zs1−˜
Zc
˜
Zs2+˜
Zc, (2)
whe e
d1
is he sample hickness,
˜
Zs1
is he complex su ace impedance measu ed wi h
he i s ai ca i y dep h D, and
˜
Zs2
is he complex su ace impedance measu ed wi h
he second ai ca i y dep h D
0
.
Z1
and
Z0
1
deno e he acous ic impedance o each ai ca i y,
Z1=−jρ0c0co (k0D), (3)
Z0
1=−jρ0c0co k0D0. (4)
The measu emen s we e pe o med o a igid e mina ion and an ai ca i y dep h
D
=
2 cm. This op ion p ese es he me hod’s alidi y and allows minimising he numbe
o measu emen s o each sample o de e mine bo h i s sound abso p ion coe icien and
i s in insic acous ic p ope ies. Figu e 7shows he po ous conc e e samples and sound
abso p ion cu es be ween samples wi h di e en hicknesses. Each cu e co esponds
o he a e age be ween he wo samples o same hickness, espec i ely, 4, 6 and 8 cm. I
was obse ed ha he inc ease in he hickness p oduces a shi in he sound abso p ion
coe icien cu e owa ds low equencies.
(a) (b)
Figu e 7.
Sound abso p ion beha iou o po ous conc e e. (
a
) Po ous conc e e buil samples.
(
b
) A e age o he sound abso p ion coe icien o h ee di e en hicknesses: 4, 6, and 8 cm.
( e ie ed om [23]).
To p edic he acous ic beha iou o po ous conc e e wi h di e en hicknesses and
o ep esen hese ma e ials as he luid-equi alen heo y, he Ho oshenko and Swi
model was used [33]. This model was de i ed assuming igid ame g anula media wi h
a log-no mal po e size dis ibu ion o p edic he he cha ac e is ic impedance,
˜
Zc
, and
he wa e numbe ,
˜
kc
, o po ous conc e e samples. I conside s ou mac oscopic pa ame e s
o de e mine he acous ic beha iou : ai low esis i i y,
σ
, open po osi y,
φ
, o uosi y,
τ
,
and he s anda d de ia ion o he po e size, σp.
The in e se echnique was pe o med using a gene ic algo i hm in which he objec i e
unc ion was based on he quad a ic sum o e o s be ween he analy ical and expe imen al
da a, along a equency ange wi h n disc e e equency alues,
OF(ω) =
n
∑
i=1αana −αexp, (5)
whe e
αana
is he abso p ion coe icien ob ained om he Ho oshenko and Swi
model [
33
], and
αexp
is he expe imen al abso p ion coe icien . These ou mac oscopic
pa ame e s we e p e iously ob ained in [
23
], and a e p esen ed in Table 2. The open
Appl. Sci. 2022,12, 2960 8 o 18
po osi y was he only mac oscopic pa ame e expe imen ally de e mined, using he wa e
sa u a ion me hod.
Table 2. Mac ospic pa ame e s ob ained o he po ous conc e e s udied samples.
Ai low Resis i i y σ
[Ns/m4]Open Po osi y φ[-] To uosi y α∞[-]
S anda d De ia ion
o he Po e Size σp
[-]
3896.06 0.46 1.89 0.25
Figu e 8shows a compa ison be ween he complex p ope ies using he p esen ed
mac oscopic pa ame e s and hose expe imen ally ob ained h ough he wo-ca i y me hod
o a sample wi h 4 cm. As obse ed in [
34
], an excellen ag eemen can be obse ed
be ween he expe imen al da a and he semi-phenomenological p edic ion, allowing us
o ep esen and p edic he po ous conc e e beha iou o di e en samples hicknesses
and geome ies.
200 400 600 800 1k 1.2k 1.4k 1.6k
F equency [Hz]
- 1000
- 500
0
500
1000
1500
2000
Cha ac e is ic impedance [Pa.s/m]
Real Two-Ca i y Me hod
Imag. Two-Ca i y Me hod
Real Ho oshenko -Swi Model
Imag. Ho oshenko -Swi Model
(a)
200 400 600 800 1k 1.2k 1.4k 1.6k
F equency [Hz]
- 20
0
20
40
60
80
Wa enumbe [ ad/m]
Real Two-Ca i y Me hod
Imag. Two-Ca i y Me hod
Real Ho oshenko -Swi Model
Imag. Ho oshenko -Swi Model
(b)
Figu e 8.
Compa ison be ween he expe imen al cha ac e isa ion and he semi-phenomenological
ep esen a ion n. (a) Cha ac e is ic impedance, ˜
Zc. (b) Wa e numbe , ˜
kc( e ie ed om [34]).
4. Nume ical Modelling
The Bounda y Elemen Me hod, BEM, was used o model he acous ic p oblem since
i allows analysing complex geome ies wi hou he need o desc ibe he whole p opaga ion
medium, and allows us o sol e p oblems wi h bo h in ini e o limi ed domains [6].
In he equency domain, he p oblem is go e ned by he Helmhol z equa ion,
∇2p+k2p=δ( 1− 0). (6)
whe e pis he acous ic p essu e and k is he wa e numbe .
The de elopmen o Equa ion (6) yields Equa ion (7), which allows he acous ic p ob-
lem o be sol ed by in eg a ion along he de ined bounda ies. Thus, sol ing Equa ion (7)
can be de ined as app oxima ing he solu ions o each bounda y elemen j.
N
∑
j=1
(x,~
n)ZΓiρωG(x,x0)dΓj+
N
∑
j=1
p(x)ZΓH(x,x0,~
n)dΓj+cpp(x0)=pinc x0,x (7)
Usually, he ma ix o mula ion is used as he p e e ed means o ca y ou he Bound-
a y Elemen Me hod [35,36],
Cp−Hp=iρ0ωG +pinc. (8)
Appl. Sci. 2022,12, 2960 9 o 18
whe e pand a e he acous ic quan i ies o be calcula ed— he p essu e and eloci y
o pa icles acco ding o he su ace—and
pinc
is he acous ic p essu e in he ee ield due
o a sou ce loca ed on he domain. The
G
and
H
ma ices a e ully popula ed ma ices.
Finally, Cis a diagonal a ay whose alues depend on he colloca ion poin . I is common
o add he ma ix Cand H, w i ing he p e ious equa ion in i s mos simpli ied o m,
Hp=iρ0ωG +pinc. (9)
The o mula ion p esen ed up o his poin only allows he s udy o he in e ac-
ion o he bounda ies wi h a single ex e nal medium, in his case, he acous ic medium.
In o de o ep esen he po ous ma e ials ha a e o be placed on he ba ie and ha will
be s udied in his documen , i is necessa y o ex end he me hod o include he simula ion
o po ous ma e ials as luid-equi alen s. In o he wo ds, i is necessa y o simula e mo e
han one p opaga ion medium, wi h di e en p ope ies.
The e o e, i is necessa y o de ine each o he media and ensu e ha in he in e aces
be ween hem he e is coupling be ween he p essu es and no mal eloci y.
The sys ema isa ion o his p oblem in ol es he de ini ion o he equa ions p esen ed
in Equa ion (7) o each p opaga ion domain and he bounda ies alid o bo h he ex e nal,
Ωex e io and in e nal domain, Ωi, as illus a ed in Figu e 9.
Figu e 9. Rep esen a ion o he coupled in e io /ex e io p oblem.
The coupling be ween domains is achie ed by ensu ing equilib ium and con inui y
condi ions a he sha ed bounda ies o he domains [37].
pΩex =pΩin (10)
1
iωρΩex
∂pΩex
∂n=−1
iωρΩn
∂pΩin
∂n(11)
The calcula ion p ocess in ol es sol ing a sys em o equa ions aking in o accoun
he equa ions de ined o he wo mediums unde conside a ion (Equa ion (7)). The sys em
o equa ions can be exp essed as
(iωρΩex GΩex {˜
}+HΩex {ˆ
p}={¯
pinc}, o ai
−iω˜
ρΩjGΩj{¯
}+HΩj{¯
p}=0, o po ous ma e ial (12)
Once he acous ic a iables a he de ined bounda ies a e known, he acous ic p essu e
a he ex e nal ecei e s is equal o he sum o he inciden acous ic p essu e and he acous-
ic p essu e esul ing om he in e ac ion o he bounda ies wi h he acous ic medium,
as shown in Equa ion (13).
pT=pinc +pS(13)
Appl. Sci. 2022,12, 2960 16 o 18
Figu e 20.
Inse ion loss maps o he cu ed noise ba ie wi h abso p i e laye o equencies
315 Hz, 400 Hz, 500 Hz, 630 Hz, 800 Hz and 1000 Hz (
a
–
), wi h he p esence o he ecei e s (black
do s) used o calcula e mean IL (Figu e 18).
Figu e 21.
Inse ion loss maps o he cu ed noise ba ie wi h abso p i e laye o equencies
1250 Hz, 1600 Hz, 2000 Hz, 2500 Hz, 3150 Hz and 4000 Hz (
a
–
), wi h he p esence o he ecei e s
(black do s) used o calcula e mean IL (Figu e 18).
7. Conclusions
This pape p esen s he de elopmen o a low-heigh acous ic ba ie o be used close
o he noise sou ce in a ailway en i onmen . The de elopmen o he solu ion is composed
by wo dis inc phases, namely he op imisa ion o he ba ie geome y and he in eg a-
ion o a po ous ma e ial in o de o inc ease he acous ic pe o mance o he solu ion.
Taking ad an age o sound p essu e le el eco ds acqui ed in he ailway en i onmen
in he me opoli an a ea o Po o, i was possible o de ine he mos impo an equency
con en and hus design a solu ion whose pe o mance was supe io in ha equency
ange. The nume ical modelling and s udy o he a ious solu ions we e ca ied ou by
applying a BEM o mula ion wi h mul iple egions, simula ing he po ous ma e ial as an
equi alen luid and hus inco po a ing i s acous ic abso p ion p ope ies. The pa ame ic
s udy p esen s he me hodology o sizing he cu ed ba ie . Th ough he simula ion
o a sound wa e, he inne ace o he ba ie was cons uc ed so ha i coincides wi h
he shape o he inciden wa e on coming om he sou ce. Thus, he e lec ion no mal
o he p opaga ion di ec ion is a ou ed and, as such, mo e ene gy is sen in he di ec ion
o he noise sou ce and he ailway. In his way, an in eg a ed solu ion was buil aking

Appl. Sci. 2022,12, 2960 17 o 18
ad an age o he acous ic abso p ion capaci y o he ack o abso b he ene gy sen back.
In a complemen a y manne , a po ous conc e e laye was added, which on he one hand
has a good acous ic abso p ion capaci y and on he o he hand gua an ees he du abili y
equi ed o solu ions used ou doo s. The main pu pose o he po ous ma e ial is o abso b
pa o he ene gy a ising om he e lec ions be ween he ba ie and he ehicle, ensu ing
ha he ene gy ha is no sen back o he ack can be sen in he di ec ion o he ex e nal
ecei e s. The esul s p esen ed show he clea imp o emen achie ed by using po ous ma-
e ial as a means o abso bing pa o he ene gy in de imen o pu ely e lec i e solu ions.
The cu ed solu ion wi h po ous ma e ial p esen s an IL in he de ined ecei e s highe han
10 dB in all he calcula ed equency ange; o some equencies he IL alue is e en highe
han 15 dB, wi h he maximum egis e ed in he equency 3150 Hz whe e he IL alue
is highe han 25 dB. In his way, he p esen ed solu ion appea s o be an use ul elemen
o he educ ion in ain-induced noise, gua an eeing an e ec i e mi iga ion. In addi ion,
due o i s low-heigh , his solu ion does no ep esen a isual obs acle, as is usual o noise
ba ie s, bu i s ill e ec i ely educes noise le els a he ecei e s o in e es .
Au ho Con ibu ions:
Concep ualisa ion, J.L., M.P., P.A.C. and L.G.; me hodology, J.L., M.P., P.A.C.
and L.G.; so wa e, J.L., M.P. and L.G.; alida ion, J.L., M.P., P.A.C. and L.G.; o mal analysis, J.L., M.P.,
P.A.C. and L.G.; in es iga ion, J.L. and M.P.; esou ces, J.L., M.P., P.A.C. and L.G.; da a cu a ion, J.L.
and M.P.; w i ing—o iginal d a p epa a ion, J.L. and M.P.; w i ing— e iew and edi ing, P.A.C. and
L.G.; isualisa ion, J.L., M.P., P.A.C. and L.G.; supe ision, P.A.C. and L.G.; p ojec adminis a ion,
P.A.C. and L.G.; unding acquisi ion, J.L., P.A.C. and L.G. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding:
This esea ch was unded by Base Funding—UIDB/04708/2020 and P og amma ic
Funding—UIDP/04708/2020 o he CONSTRUCT—Ins i u o de I&D em Es u u as e Cons uções—
unded by na ional unds h ough he FCT/MCTES (PIDDAC); Base Funding—UIDB/04029/2020—
o ISISE (Ins i u e o Sus ainabili y and Inno a ion in S uc u al Enginee ing) unded by na ional
unds h ough he FCT/MCTES (PIDDAC); P ojec POCI-01-0247-FEDER-033990 unded by FEDER
unds h ough COMPETE2020—P og ama Ope acional Compe i i idade e In e nacionalização
(POCI); Na ional unds (PIDDAC) h ough FCT/MCTES; Indi idual G an : SFRH/BD/148367/2019.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Re e ences
1.
EEA (Eu opean En i onmen Agency). En i onmen al Noise in Eu ope—2020; Technical Repo ; EEA (Eu opean En i onmen
Agency): Copenhagen, Denma k, 2020; ISBN 9789294802057.
2.
Blanes, N.; Ma in, A.; Ramos, U.M.J. Noise Exposu e Scena ios in 2020 and 2030 Ou looks o EU 28; Technical Repo ; Eu opean Topic
Cen e on Ai Pollu ion, T anspo , Noise and Indus ial Pollu ion—No wegian Ins i u e o Ai Resea ch: Kjelle , No way, 2019.
3.
Wo ld Heal h O ganiza ion. En i onmen al Noise Guidelines o he Eu opean Region; Wo ld Heal h O ganiza ion: Copenhagen,
Denma k, 2018.
4. De Vos, P. Railway Noise in Eu ope. S a e o he A Repo ; In e na ional Union o Railways (UIC): Pa is, F ance, 2016.
5.
Ma ei, L.; Masullo, M.; Ale a, F. In luence o he design o ailway noise ba ie s on soundscape pe cep ion. In P oceedings
o he INTER-NOISE and NOISE-CON Cong ess and Con e ence P oceedings. Ins i u e o Noise Con ol Enginee ing, Lexing on,
KY, USA, 13–15 June 2012; Volume 2012, pp. 1966–1972.
6.
Eu opean Comission. Hosanna—Holis ic and Sus ainable Aba emen o Noise by Op imized Combina ions o Na u al and A i icial
Means; Eu opean Comission: B ussels, Belgium, 2009.
7. C ocke , M.J. Handbook o Noise and Vib a ion Con ol; John Wiley & Sons: Hoboken, NJ, USA, 2007.
8.
Thompson, D. Railway Noise and Vib a ion: Mechanisms, Modelling and Means o Con ol; Else ie : Ams e dam, The Ne he -
lands, 2008.
9.
Koussa, F.; De ance, J.; Jean, P.; Blanc-Benon, P. Acous ic pe o mance o gabions noise ba ie s: Nume ical and expe imen al
app oaches. Appl. Acous . 2013,74, 189–197. [C ossRe ]
10.
Jolibois, A.; De ance, J.; Ko ene , H.; Jean, P.; Duhamel, D.; Spa ow, V.W. In si u measu emen o he acous ic pe o mance
o a ull scale amway low heigh noise ba ie p o o ype. Appl. Acous . 2015,94, 57–68. [C ossRe ]
11.
Nieuwenhuizen, E.; Yn ema, N. The e ec o close p oximi y, low heigh ba ie s on ailway noise. In P oceedings o he
Eu onoise, He aklion, G eece, 27–31 May 2018; pp. 1375–1380.
12.
Kasess, C.H.; K euze , W.; Waubke, H. De i ing co ec ion unc ions o model he e iciency o noise ba ie s wi h complex
shapes using bounda y elemen simula ions. Appl. Acous . 2016,102, 88–99. [C ossRe ]
Appl. Sci. 2022,12, 2960 18 o 18
13.
K ezel, Z.A.; McManus, K. Recycled agg ega e conc e e sound ba ie s o u ban eeways. In Was e Managemen Se ies;
Else ie : Ha oga e, UK, 2000; Volume 1, pp. 884–892.
14.
Mag ini, U.; Riccia di, P. Su ace sound acous ical abso p ion p ope ies o mul ilaye panels. In P oceedings o he INTER-NOISE
and NOISE-CON Cong ess and Con e ence P oceedings, Nice, F ance, 27–31 Augus 2000; Ins i u e o Noise Con ol Enginee ing:
Res on, VA, USA, 2000; Volume 2000, pp. 2953–2959.
15. Asd ubali, F.; Ho oshenko , K. The acous ic p ope ies o expanded clay g anula es. Build. Acous . 2002,9, 85–98. [C ossRe ]
16.
Vašina, M.; Hughes, D.; Ho oshenko , K.; Lapˇcík, L., J . The acous ical p ope ies o consolida ed expanded clay g anula es.
Appl. Acous . 2006,67, 787–796. [C ossRe ]
17.
Ba olini, R.; Filippozzi, S.; P inci, E.; Schenone, C.; Vicini, S. Acous ic and mechanical p ope ies o expanded clay g anula es
consolida ed by epoxy esin. Appl. Clay Sci. 2010,48, 460–465. [C ossRe ]
18.
Kim, H.K.; Lee, H.K. In luence o cemen low and agg ega e ype on he mechanical and acous ic cha ac e is ics o po ous
conc e e. Appl. Acous . 2010,71, 607–615. [C ossRe ]
19.
San Ma ín, J.C.; Esque do-Llo e , T.V.; Ramis-So iano, J.; Nadal-Gisbe , A.V.; Denia, F.D. 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. Cons. Supe . In es ig. Cien . 2015,65, e072.
20.
Tie, T.S.; Mo, K.H.; Pu a, A.; Loo, S.C.; Alenga am, U.J.; Ling, T.C. Sound abso p ion pe o mance o modi ied conc e e: A e iew.
J. Build. Eng. 2020,30, 101219. [C ossRe ]
21.
Pe ei a, A.; Godinho, L.; Mo ais, L. The acous ic beha io o conc e e esona o s inco po a ing abso bing ma e ials. Noise Con ol.
Eng. J. 2010,58, 27–34. [C ossRe ]
22.
Ca bajo, J.; Esque do-Llo e , T.V.; Ramis, J.; Nadal-Gisbe , A.V.; Denia, F.D. Acous ic modeling o pe o a ed conc e e using
he dual po osi y heo y. Appl. Acous . 2017,115, 150–157. [C ossRe ]
23.
Pe ei a, M.; Ca bajo San Ma ín, J.; Godinho, L.; Amado-Mendes, P.; Ma eus, D.; Ramis-So iano, J. Acous ic beha io o po ous
conc e e. Cha ac e iza ion by expe imen al and in e sion me hods. Ins . Cienc. Cons . Edua do To oja
2019
,69, e202. [C ossRe ]
24.
Zolan a i, S.M.H. Nume ical Modeling and Ma e ial De elopmen o a Conc e e-Based Acous ic Abso be ; F aunho e Ve lag: S u ga ,
Ge many, 2019.
25.
Ki kup, S.M. The Bounda y Elemen Me hod in Acous ics; In eg a ed Sound So wa e; Uni e si y o Cen al Lancashi e:
P es on, UK, 2007.
26.
Hemswo h, B. En i onmen al noise di ec i e de elopmen o ac ion plans o ailways. In UIC Noise Expe Ne wo k: In e na ional
Union o Railways (UIC); Union In e na ionale des Chemins de e (UIC): Pa is, F ance, 2008.
27.
Be zbo n, M.; Bomha d , R.; Klein, J.; Rich e , J.G.; Vo lände , M. The ITA-Toolbox: An open sou ce MATLAB oolbox o acous ic
measu emen s and signal p ocessing. In P oceedings o he 43 h Annual Ge man Cong ess on Acous ics, Kiel, Ge many,
6–9 Ma ch 2017; Volume 2017, pp. 6–9.
28.
Ciabu o, G.; Iannace, G.; Ali, M.; Alabdulka em, A.; Nuhai , A. An a i icial neu al ne wo k app oach o modelling abso ben
asphal s acous ic p ope ies. J. King Saud-Uni . Eng. Sci. 2021,33, 213–220. [C ossRe ]
29.
A enas, J.P.; Rebolledo, J. Acous ic cha ac e iza ion o loose- ill cellulose c umbs ob ained om wood ibe s o sound ab-
so p ion. In P oceedings o he INTER-NOISE and NOISE-CON Cong ess and Con e ence P oceedings, Innsb uck, Aus ia,
15–18 Sep embe 2013;
Aus ian Noise Aba emen Associa ion Aus ian Noise Aba emen Associa ion: Vienna, Aus ia; Ins i u e
o Noise Con ol Enginee ing: Res on, VA, USA, 2013; Volume 247, pp. 1734–1739.
30.
del Rey, R.; Be ó, L.; Alba, J.; A enas, J.P. Acous ic cha ac e iza ion o ecycled ex ile ma e ials used as co e elemen s in noise
ba ie s. Noise Con ol. Eng. J. 2015,63, 439–447. [C ossRe ]
31.
ISO. Acous ics—De e mina ion o Sound Abso p ion Coe icien and Impedance in Impedance Tubes—Pa 2: T ans e -Func ion Me hod;
Technical Repo ; In e na ional O ganiza ion o S anda diza ion: Gene a, Swi ze land, 1998.
32.
U suno, H.; Tanaka, T.; Fujikawa, T.; Seybe , A. T ans e unc ion me hod o measu ing cha ac e is ic impedance and
p opaga ion cons an o po ous ma e ials. J. Acous . Soc. Am. 1989,86, 637–643. [C ossRe ]
33.
Ho oshenko , K.V.; Swi , M. The acous ic p ope ies o g anula ma e ials wi h po e size dis ibu ion close o log-no mal. J.
Acous . Soc. Am. 2001,110, 2371–2378. [C ossRe ] [PubMed]
34.
Pe ei a, M.; Ca bajo, J.; Godinho, L.; Ramis, J.; Amado-Mendes, P. Imp o ing he sound abso p ion beha iou o po ous conc e e
using embedded esonan s uc u es. J. Build. Eng. 2020,35, 102015. [C ossRe ]
35.
Ma bu g, S.; Nol e, B. Compu a ional Acous ics o Noise P opaga ion in Fluids: Fini e and Bounda y Elemen Me hods;
Sp inge : Be lin/Heidelbe g, Ge many, 2008; Volume 578.
36.
Chandle -Wilde, S.; Langdon, S. Bounda y Elemen Me hods o Acous ics; Lec u e No es; Depa men o Ma hema ics, Uni e si y
o Reading: Be kshi e, UK, 2007.
37.
Seybe , A.; Cheng, C.; Wu, T. The solu ion o coupled in e io /ex e io acous ic p oblems using he bounda y elemen me hod. J.
Acous . Soc. Am. 1990,88, 1612–1618. [C ossRe ]
38.
B oadben , R.; Thompson, D.; Jones, C. The acous ic p ope ies o ailway ballas . In P oceedings o he Eu onoise 2009,
Edinbu gh, UK, 26–28 Oc obe 2009.