Osnovne preporuke za dozimetriju X-zračenja 40kv - 40MV, ##-zračenja ##Co i ###Cs i elektrona 4- 40 MeV

VOJNO-MEDICINSKA AKADEMIJA, BEOGRAD
SREDIŠNJI INSTITUT ZA TUMORE I SL. BOLESTI, ZAGREB
ONKOLOŠKI INŠTITUT, LJUBLJANA
SAVEZNI ZAVOD ZA MERE I DRAGOCENE METALE, BEOGRAD
INSTITUT ZA RADIOLOGIJU, BEOGRAD
OSNOVNE PREPORUKE ZA DOZIMETRIJU X-ZRAČENJA 40 kV-40 MV, y-ZRAČENJA
6°Co i 137Cs I ELEKTRONA 4
-40 MeV*
BASIC RECOMMENDATIONS FOR THE DOSIMETRY OF 40 kV - 40 MV X-RAYS, 6°Co
AND 137Cs y-RAYS AND 4- 40 MeV ELECTRONS
Andric S, Bistrovic M, Cevc P, Spasic V, Vujnic V
Abastract- The equipment and procedures are recommended tor obtaining an accuracy of ±3,5 o/o
(1
o-) while determining the absorbed dose in radiotherapy. Recommendations touch the following
points: the calibration of the dosemeter, the experimental arrangement, the correction and conversion
factors, the definition and determination of the beam quality. The conditions of the quality assurance
are summarized.
UDC: 615.849.5
Key words: radiotherapy, X-rays, dosimetry
Profess paper
Radiol lugosl 1989; 23: 403-9
Uvod - Pridržavajuci se preporuka koje
slede, bit ce, u svim našim radioterapijskim cen
trima, ostvareni preduslovi odredivanja apsor
bovane doze ( u daljem tekstu - doze) mernom
nesigurnosti ±
3,5
% (1
a). U ovim preporukama
predlaže se:
[kg]
[u]
- kilogram vazduha
- proizvoljne jedinice očitanja na
dozimetru
Ostale oznake:
C [J c-1]
- konverzioni faktori za komoru
1. Rečnik oznaka i mernih parametara
2. Izbor i kalibracija dozimetra
3. Odredivanje jačine ekspozicije
4. Specifikacija
i
odredivanje
kvaliteta
datu u tabeli 1 i izračunati u tabeli
4; primena u izrazu (6); Cx - za
X-zračenje 40-300 kV; Cy-za
y-zračen1e; Cx - za X-zračenje
zračenja
.
?= 1 MV; Ce - za elektrone
.
D(d) [Gy r1J- jačina doze na dubini d, na osi
5. Dokumentacija
zračenje
provera
uredaJa
za
snopa u vodi; računa se izrazom
D.
[G ·-1]
(?)
k .
1
. ..
d
o·
1. Rečnik oznaka i mernih parametara
m
y J
- ma sima na Jacma
oze:
m =
=
D(dm); računa se izrazom (6)
d [cm]
Posebne merne jedinice:
dm [cm]
- dubma na osi snopa u fantomu;
sa brojnim indeksom, npr. dso,
podrazumeva dubinu na kojoj je
PDD (d)=50%
- dubina d smeštaja komore, na
kojoj X ima maksimum u odnosu
[j]
- sekund minut ili čas kod rend-
na ostale dubine duž ose snopa;
k.h'
·
·
.
dm =
d100·
dm(137Cs)
=
O 12 cm·
gens I
uredaJa I uredaJa za
dm(eoco) ¨ o 5 cm
'
'
y-zračenje: monitorski impuls
dm, P [cm]
- dm u PMMA- fantomu; dm, P =
kod akceleratora
= 0,88 dm, v
* Predočeni tekst pri
premila je tokom 1986-1988. godi
ne Radna grupa Komisije za kliničku dozime
triju pri Saveznom zavodu za mere i dragocene 'Tletale. Komisiji i Radnoj grupi predsedavao je dr. P.
Cevc.
Received: September 1
O, 1989 - Accepted: September 13, 1989
403
AndriC Set al. Osnovne preporuke za dozimetriju X-zračenja 40 kV-40 MV, y-zračenja 6°Co i 137Cs i elektrona 4-40 MeV
dm, v [cm]
dp [cm]
d,et [cm]
Eo [MeV]
Ed [MeV]
F [cm]
FFD [cm]
FKD [cm]
FPR
FPV
[mmAI]
ili[mm Cu]
fa
fp, t
f,
404
- dm u vodenom fantomu
- praktični domet elektrona u vodi;
vidi definiciju na slici 2
referentna dubina u vodi, na osi
snopa y- i X-zračenja; vidi defini
ciju u tabeli 2
- srednja energija upadnih elek
trona na površini vodenog fan
toma; računa se izrazom (4)
- srednja energija elektrona na
dubini d u vodenom fantomu;
računa se izrazom (5)
- rastojanje od tačke Pet komore
do fokusa, duž ose snopa
- rastojanje od površine fantoma
do fokusa, duž ose snopa
- fokusno-kožna distanca; rasto
janje od površine kože bolesnika
do fokusa, duž ose snopa
- faktor povratnog rasejanja; dat je
u tabeli 3 radi pri
mene u izrazima
(3a) i (3b)
- filtarska poluvrednost X-zrače-
nja;
debljina
aluminijskog
(¾ 100 kV)
ili
bakarnog
(100-300 kV) atenuatora (ap
sorbera) koja jačinu ekspozicije
uskog snopa u vazduhu uma
njuje na 50 % vrednosti u tački
udaljenoj od atenuatora
- faktor atenuacije u zidu cilin
drične komore; pri
menjuje se kod
X-zračenja 40-100 kV, a u su
protnom se stavlja fa =
1; vred
nosti fa mere sa uporedivanjem s
tankozidnom komoram; vred
nosti fa za komoru predvidenu
ovim preporukama date su u ta
beli 1; ako je fa > 1,05, komora
nije pogodna za merenje u datom
snopu
- faktor korekcije na vazdušni pri
tisak p [mbar] i temperaturu t [0 C]
mernog ambijenta; izračunava se
izrazom
273,
16 +
t 1013
fp, 1 =
293,16
-p-
- faktor rekombinacije; primenjuje
se kod merenja vrlo velikih
1ja9ina
ekspozicije(> 0,003 C kg- s- ) i u
akceleratorskom snopu, ako do
zimetar ima mogucnost pramene
radnog napona U; u suprotnom
se stavlja f, =
1; račµna. se po
mocu parametra w = M.;/
Mu;2 -1,
gde su Mu i Mu;2 - očitanja kod
napona U, odnosno U/2; u snopu
X-zračenja
40-300 kV
i
y-
zračenja: f, = 1 + w
/3, a u akcele
ratorskim snopovima: f, = 1 +
w;
ako je f, > 1,05, komora nije po
godna za merenje u datom snopu
ni je racini napon U prenizak
k [C kg-1
u-1]- kalibracioni
faktor
komore,
odredu
je se izrazom (1)
M [u r1J
- prirast očitanja po jedinici [ j ]  na
dozimetru; sa indeksom, npr. M1 0
podrazumeva M sa komoram
smeštenom na dubinu d =
1
O cm
u vodi
Mkor [u r1J - M korigovano: Mkor = M fp, t fa f,
NAP [MV] - nominalni akceleracioni potenci
jal; definicija NAP putem TFOf8
data je u tabeli 4
PDD(d) [%] - procenat dubinske doze na du
bini d u vodi; PDD(dm) = 100 %;
graf ove funkcije je - kriva PDD;
tabelarni prikaz funkcije su - ta
bele PDD
Pet
PMMA
R [mm]
TFOf8
- efektivna merna tačka cilindrične
komore; u snopu X-zračenja
40-300 kV, Pet je u centru ko
more, na njenoj uzdužnoj osi,
okomitoj na osu snopa; u snopu
y-zračenja, X-zračenja 1-40 MV
i elektrona, Pet je od ose komore
pomaknut za R/2 u smeru fokusa
- polimetil-metakrilat,
perspeks,
lucit, pleksigals
- spoljašnji radijus komore
- tkivno-fantomni
odnos, para-
metar
kvaliteta
X-zračenja
1-40 MV; sa nepromenjenim po
ložajem k?more, F = konst., meri
se M10 i M20; dubina d =
10cm i
d = 20 cm postiže se pomica
njem vodenog fantoma na FFD =
= F-1
O cm i FFD = F-2O cm·
veličina polja je 10 X 10 cm2 n¿
distanci F od fokusa; računa se
izrazom TFOf8 = M20/
M1 0
X [C kg-1 f1]- jačina ekspozicije u mernoj tački;
odreduje se izrazom (2)
Xm [C kg-1 f1l- maksimalna vrednost jačine eks
pozicije duž ose snopa, na dubini
dm; odreduje se izrazima (3)
Odgovarajuce engleske kratice i termini
FFD
FKD
FPR
FPV
PDD
NAP
TFOf8
FPD: focus-phantom distance
FSD: focus-skin distance
BSF: back-scatter factor
HVL: half-value layer
PDD: percent-depth dose
NAP: nominal accelerating poten
tial
TPRf8: tissue-phanatom ratio
Radiol lugosl 1989; 23: 399-402
Andric Set al. Osnovne preporuke za dozimetriju X-zračenja 40 kV-40 MV, y-zračenja 60Co i 137Cs i elektrona 4-40 MeV
2. Izbor i kalibracija dozimetra - Osnovni
merni instrument za odredivanje ekspozicije je
dozimetar koji se sastoji od
- vazdušne jonizacione komore (dalje: ko-
more),
- elektrometra i
- etalonskog radioaktivnog izvora.
Za merenje ekspozicije primenjuju se tan
kozidne komore u snopovima X-zračenja
40-100 kV (8), plan
paralelne komore u snopo
vima elektrona 4 - 15 MeV (1, 8, 11) i cilindrične
komore (naprstak-komore) u snotovima X
-zračenja 40 kV-40 MV, y-zračenja
0co i
137 Cs
i elektrona 4-40 MeV (1, 5, 6, 8, 1
O). Cilindrična
komora predvidena za merenja opisana u ovim
preporukama mora udovoljavati propisima (13,
14) a njene karakteristike (2, 12) date su u tabeli
1.
Elektrometar je instrument za merenje količine
naboja disociranog jonizacijom u efektivnoj za
premini komore. Elektrometar treba zasebno ka
li
brisati u slučajevima kada je komora kalibri
sana odvajeno od elektrometra.
Etalonski radioaktivni izvor (obično 90Sr) pri
menjuje se za proveru vremenske stabilnosti do
zimetra, tako da očitanje za datu referentnu eks
poziciju varira u granicama ne večim od 0,5 %
tokom jedne godine.
Spoljašnja dužina
Spoljašnji dijametar (2R)
Unutrašnja dužina
Unutrašnji dijametar
Merni volumen
Zid komore
Debljina zida
Bildap-kapa
Debljina bildap-kape
Maksimalni radni napon
Sadržaj komore
25,8mm
7,0mm
24,1
mm
6,3mm
0,63cm3
čisti grafit
0,065g cm-2
PMMA
0,465
g cm-2
400V
vazduh pod
atmosferskim pritiskom ,
vlažnosti 30-70%
faktor atenuacije
fa
FPV [mmAI]
fa
1,0
1,052
1,5
1,035
2,0
1,026
4,0
1,013
5,0
1,010
10,0
1,000
Tabela 1 - Karakteristike cilindrične jonizacione ko
more (2, 12)
U radioterapiji se jačina ekspozicije X
odreduje samo kalibrisanim dozimetrom. Kali
bracija je postupak odredivanja kalibracionog
faktora dozimetra i vrši se neposrednim uporedi
vanjem dozimetra sa etalonom koji može biti
Radiol lugosl 1989; 23: 403-9
primaran (uporeduje se u primarnoj etalonskoj
laboratoriji), sekundaran (uporeduje se u sekun
darnoj etalonskoj laboratoriji) ili radni (upo
reduje se u radioterapijskom centru) (7). Radni
etalon je dozimetar, kalibrisan pomoču sekun
darnog etalona, a njime se kalibrišu ostali kli
nički dozimetri. Radni etalon treba da bude kali
brisan svake dve godine (13), a ostali klinički
dozimetri češče.
Kalibracioni faktor nekog kliničkog dozimetra
odreduje se izrazom
k=u,
(1)
Mkor
gde je Xe jačina ekspozicije u mernoj tački
odredena radnim etalonom. Dozimetar se kali
briše prema vrsti zračenja koje če nji
me biti me
reno:
- za merenje X-zračenja 40-300
kV kali
briše se u vazduhu,
- za merenje y-zračenja
6°Co i 137Cs, X-
-zračenja 1-40 MV i elektrona 4-40 MeV kali-
briše se u vazduhu, a ako se dijametri
komora ne
razlikuju za više od 15 % može se kali brisati u
vodi ili PMMA
Kalibracioni faktori se sa sekundarnog eta
lona na radni etalon moraju preneti mernom ne
sigurnosti od 1 % (1
er), a na ostale dozimetre
mernom nesigurnosti od 2 % (1
er).
3. Odredivanje jačine ekspozicije - Pre me
renja dozimetrom treba da prode izvesno vreme
da bi instrument i merni fantom dostigli termičku
ravnotežu sa mernim ambijentom. Merni (vodeni
ili PMMA) fantom treba da bude dovoljno velik,
da izvan polja zračenja i iza komore uvek bude
još 5 cm fantomnog m_edijuma.
Jačina ekspozicije u maksimumu X uvek se
odreduje u nekoj mernoj tački u vazduhu,
vodi ili PMMA, u koju treba smestiti komoru to
kom merenja. Komora u toku merenja treba da
bude smeštena tako da Pet komore bude u mer
noj tački. Jačina ekspozicije X u mernoj tački,
kada se komora ukloni, odreduje se izrazom
X=k ?or
(2)
Maksimalna jačina ekspozicije Xm, odreduje
se na sledeči način. Najpre če se odrediti X u
mernoj tački definisanoj standardnom geometri
jam, zavisno o tipu i kvalitetu zračenja, a potom
če se izračunati Xm ovako:
A)
z a  X-zračenje 40-300kV odredi X
prema tabeli 2 (slučaj a) i slici 1
a i izračunaj
Xm =
X FPR [(FKD + R/2)/
FKD]2,
(3a)
405
Andric Set al. Osnovne preporuke za dozimetriju X-zračenja 40 kV-40 MV, y-zračenja G-OCo i 13
7Cs i elektrona 4-40 MeV
gde su vrednosti FPR date u tabeli 3, a kvadratni
izraz predstavlja korekciju
zbog nezanemarljivih
dimenzija komore;
B) za y -zračenje, X - zračenj
e 1-40 MV i
elektrone:
- ako se Xodreduje u mernoj tački u vazduhu
prema tabeli 2 (slučaj b) i slici 1
b, tada izračunaj
Xm = X FPR,
(3b)
gde su vrednosti FPR date u tabeli 3;
Tip zračenja
vazduh
a) X-zračenje
F=FKD+R/2
40-300kV
(slika 1a)
b) y-zračenje i
F =FKD+dm
X-zračenje
(slika 1b)
1-3MV
-
-
-
c) X-zračenje
3-10MV
d) X-zračenje
10-40MW
e) elektroni
4-20MeV
f) elektroni
20-40MeV
- ako je X od
reden na dubini d,e1 u vodenom
fantomu prema tabeli 2 (slučaj b, c i d) i slici 1
c,
tada izračunaj:
100
Xm =
X POD (Dret)'
(3c)
- ako je X odreden na dubini dm u vodenom ili
PMMA-fantomu prema tabeli 2 (slučaju d, e i f) i
slici 1
d i 1
e, tada je
Xm =X
Medijum
voda
d,.1 = 5cm
(slika 1
c)
d,., = 7
cm
(slika 1
c)
d,e1 = 10
cm (slika 1
c)
ili
dm, v (slika 1
d)
dm, v
(slika 1
d)
dm, v
(slika 1
d)
(3d)
PMMA
dm, p = 0,88
dm, v
FFD = FKD +0,12dm, v
(slika 1
e)
dm, p = 0,88
dm, v
FFD =FKD
(slika 1
e)
dm, p = 0,88
dm, v
FFD= FKD+0,12dm, v
(slika 1
e)
Tabela 2 - Smeštaj komore kod standardne geometrije merenja
Kvalitet snopa
FPV [mm AI]
0,5
1,0
1,5
2,0
3,0
4,0
FPV [mmCu]
0,25
0,5
1,0
2,0
3,0
4,0
131cs
soco i X-zračenje
1-3MV
3cm
1,06
1,10
1,12
1,14
1,16
1,17
1,17
1,19
1,15
1,12
1,1
O
1,08
1,02
1,01
5cm
1,07
1,13
1,16
1,19
1,22
1,23
1,23
1,24
1,20
1,16
1,13
1,1
O
1,02
1,02
Dijametar kružnog polja
10cm
20cm
1,08
1,17
1,16
1,18
1,20
1,25
1,24
1,30
1,29
1,36
1,33
1,41
1,33
1,41
1,36
1,46
1,34
1,46
1,27
1,39
1,22
1,32
1,18
1,26
1,04
1,06
1,03
1,06
30cm
1,08
1,08
Tabela 3 -Faktor povratnog rasejanja , FPR,
za razne kvalitete zračenja. Tabela izradena na osnovu (3, 4, 8, 9)
406
Radiol lugosl 1989; 23: 403-9
AndriC Set al. Osnovne preporuke za dozimetriju X-zračenja 40 kV-40 MV, y-zračenja 6°Co i 137Cs i elektrona 4-40 MeV
fokus
fokus
,-
--:------r-:J- ---r
F
I
FKD
F
j
J_
	 _ J
_
_
!
____
1 l
-1
.
: ---I
d
R
I vazduh
vazduh
b1/dap-
m
kapa
fokus
-rrT-
fokus
__
r 1
_

-=:=:::,
M
rA,12 dm,v
fokus
d 1
1
d'
. -v-; m,J..
_1e
-
-
-\- _L
---

"'
/
1 iodCt
voda
I
zašt,tna
Pt1t1A cev
F
ln d'I?
-- -0- - \
PMMA 1
Slika 1 - Standardna geometrija. Križicem (x) je oz
načena tačka P., - efektivna merna tačka komore. a)
X-zračenje 40-300 kV; komora u vazduhu, tik do tu
busa. b) y-zračenje i X-zračenje 1-3 MV; komora sa
bildap-kapom namenjenom za mereni tip zračenja. c)
y-zračenje i X-zračenje 1-40 MV; komora je na dubini
d,e, u vodi i u zaštitnoj PMMA-cevi. d) X-zračenje
10-40 MV i elektroni 4-40 MeV; komora je na dubini
dm u vodi i zašticena PMMA-cevi. e) X-zračenje
10-40 MV i elektroni 4-40 MeV; kad je dm, v >
2
cm
treba izvršiti korekciju na elektonsku gustinu PMMA,
dm, 0 =
0,88 dm, v, kod čega F zadržava istu vrednost
kao kod merenja u vodi (uporedi sa slikom d); zbog
toga je FFD =
FKD + 0,12
dm, V•
4. Specifikacija
i
odredivanje
kvaliteta
zračenja
-
Kvalitet
snopa
X-zračenja
40-300 kV specifikuje se (8) naponom na rend
genskoj cevi, sveukupnom filtracijom i prvom
filtarskom poluvrednosti (FPV).
Kvalitet snopa y-zračenja specifikuje se ime
nom radionuklida. 137Cs emitira fotone energije
0,662 MeV, a 6°Co fotone srednje energije
1,25 MeV.
Kvalitet snopa X-zračenja 1-40 MV specifikuje
se (1, 8) parametrom tkivno-fantomnog odnosa
TFOf8 i nominalnim akceleracionim potencija
lom NAP. Meduzavisnost ova dva parametra
data je u tabeli 4.
Kvalitet elektronskog snopa specifikuje se (1,
8) vrednostima srednje energije elektrona duž
ose snopa u vodi. Srednje energije elektrona
Rac;ol lugosl 1989; 23: 403-9
izračunavaju se pomocu grafički definisanih pa
rametara funkcije POD (d) (slika 2). Srednja en
ergija upadnih elektrona je
Eo= 2,33d50
(4)
a srednja energija elektrona na dubini d u vodi
Ed = Eo(1-d/dp)
POD
700% 1--
50%1
-
- - - j- - - - - - - .
1
,,
1.,
dm
d50 dp
d[cm]
(5)
Slika 2- Grafički prikaz funkcije PDD(d)-kriva POD.
Definicija parametara dm, dso i d0.
5. Odredivanje jačine doze u vodi - jačina
doze u maksimumu Dm računa se izrazom
Dm= X m C
(6)
Konverzioni faktor C, sem kvaliteta zračenja,
uračunava i perturbaciju usled prisustva komore
i odreduje se pomocu tabele 4, zavisno o medi
jumu u kome se nalazi merna tačka: Cx, Cx i C
prema specifikovanom kvalitetu snopa, a C.,
prema srednjoj energiji elektrona u mernoj tački.
Jačina doze duž ose snopa D(d) data je izra
zom
D(d) = Dm POD (dret)
100
(7)
Funkcija PDD(d) može da se odredi merenjem
u vodenem fantomu ili se koriste tabele POD
date u priručnicima (3, 4, 9).
6.
Dokumentacija i provera uredaja za
zračenje - Za radioterapisku primenu, po
trebno je na osnovu mernih podataka pripremiti
kliničku dokumentaciju uredaja: tabele vred
nosti Dm (ili Dm-1 [j Gy-1]) i tabele POD za izvestan
broj klinički primenjivanih snopova. Tabelarni
prikaz mora omoguciti da se podaci za ostale
snopove mogu tačno izračunati interpolacijom.
Tabele POD dobivaju se merenjem, ili se, za X-
407
Andric Set al. Osnovne preporuke za dozimetriju X-zračenja 40 kV-40 MV, y-zračenja 6°Co i 137Cs i elektrona 4-40 MeV
X-zračenje (kV)
Cx (voda)
FPV
0,5mmAI
34,5
1 mmAI
34,1
2 mmAI
33,7
4 mmAI
33,7
0,3mmCu
34,1
-0,5mmCu
34,5
1 mmCu
35,3
1,5mmCu
36,1
2 mmCu
36,4
3 mmCu
36,8
4 mmCu
37,2
y-zračenje
TFO§g
Cy (voda)
Sy (PMMA)
131cs
-
37,5
37,5
soco
0,53
37,4
37,4
X-zračenje (MV)
TFO§g
Cx (voda)
Cy (PMMA)
NAP
4MV
0,65
37,3
37,3
6MV
0,70
37,2
37,2
8MV
0,73
37,0
37,1
10MV
0,75
36,9
37,0
15MV
0,77
36,6
36,9
20MV
0,80
36,2
36,6
25MV
0,82
36,0
36,5
35MV
0,83
35,8
36,5
45MV
0,84
35,6
36,4
elek troni
Cx (voda)
Cy(PMM
A)
Ed
2 MeV
34,2
34,1
2,5
MeV
34,1
34,0
3 MeV
33,9
33,8
4 MeV
33,7
33,5
5 MeV
33,3
33,2
6 MeV
33,1
32,8
8 MeV
32,8
32,6
10 MeV
32,7
32,5
12 MeV
32,5
32,4
16 MeV
32,1
32,0
20 MeV
31,8
31,7
25 MeV
31,6
31,5
30 MeV
31,2
31,1
35 MeV
31,0
30,9
Tabela 4-Vrednosti
C-fak tora
[J
C-1],
za komoru datu tabelam 1,
izračunate na
os
novu (1, 5),
a vrednosti TFO§g
i
NAP odredene prema (1)
-zračenje 40-300 kV i y-zračenje, mogu upo-
Poprečna raspodela doze može se proveriti bilo
trebiti prethodno proverene tabele iz priručnika
merenjem ekspozicije u ravni maksimuma doze,
(3, 4, 9).
bilo denzitometriranjem prethodno eksponova-
Radi obezbedenja zahtevane merne ne-
nog filma. Film se eksponuje u PMMA-fantomu,
sigurnosti, potrebno je povremeno proveravati
u ravni maksimuma doze. Kod snopova X-
ravnomernost poprečne raspodele doze Ued-
-zračenja 1-40 MV i y-zračenja, uglovi svet-
[)Om mesečno) i vremensku stabilnost vrednosti
losne simulacije snopa se markiraju proba-
Dm te kvaliteta zračenja Uednom sedmično) u
danjem filma ili drugačije. Doza se proverava u
nekoliko referentnih snopova. Kod 6°Co i 13 Cs
dva okomita smera, od kojih je jedan paralelan
uredaja proverava se samo poprečna raspodela
osi rotacije uredaja. U terapiski primenjivanom
doze Uednom godišnje) uz uslov da se tabele
delu snopa, doza prema rubovima snopa ne sme
vrednosti Dm koriguju na radioaktivni raspad u
da padne za više od 5 % u odnosu na dozu u osi,
vremenskim razmacima od cca 0,01 T112
a u tačkama simetričnim obzirom na osu snopa
(T,12(6°Co) =
5,26 g; T,12(137 Cs) =
30 g). Merenja
ne smeju se razlikovati za više od 3 %. U snopo-
prilikom provera beleže se u dnevnik radi lakšeg
vima X-zračenja 1-40 MV i y-zračenja, doza na
uočavanja pramena rada uredaja, a vrše se na
rubovima svetlosne simulacije mora biti 50 ± 5 %
sledeci način.
one na osi snopa.
408
Radiol lugosl 1989; 23: 403-9
Andric Set al. Osnovne preporuke za dozimetriju X-zračenja 40 kV-40 MV, y-zračenja '°Co i "'Cs i elektrona 4-40 MeV
Stabilnost vrednosti Dm i kvaliteta snopa može
se proveriti u PMMA-fantomu, merenjem na osi
Dnopa _u dve dubine dA), dm i ds >
dA tako da je
D(ds)/D(dA) :S0,75.
Merene jačine ekspozicija uporeduju se sa
onima koje su dobijene prilikom kalibracije
uredaja pod potpuno identičnim uslovima, a ods
tupanje ne sme biti vece od 2 %.
Pokažu li se odstupanja vecim od dopuštenih,
potrebno je tehnički proveriti i doterati uredaj, a
potom izvršiti novu kalibraciju i obnoviti kliničku
dokumentaciju.
Sažetak
Preporučeni su oprema i postupci radi postizanja
merne nesigurnosti od± 3,5 % kod odredivanja apsor
bovane doze u radioterapiji. Preporuke dotiču sledeča
pitanja: kalibracija dozimetra, eksperimentalni razmeš
taj, korekcioni i konverzioni faktori, definicija i odredi
vanje kvaliteta snopa. Ukratko su pobrojani uvjeti za
obezbedenje kvaliteta radioterapije.
Reference
1. AAPM (1983): A protocol for the determination of
absorbed dose from high-energy photon and electron
beams. Med. Phys. 10: 741-771.
Radio! lugosl 1989; 23: 403-9
2. Aird EG i Farmer FT (1972): The design of a thimble
chamber for the Farmer 1dosemeter. Phys. Med. Biol.
17: 169-17
4.
3. British Jou
rnal of Radiology (1972): Central axis
depth dose data tor use in radiotherapy, Supplement
11.
4. British Journal of Radiology (1983): Depth dose
tables for use in radiotherapy, Supplement 17.
5. HPA (1983): Revised code of practice tor the dosi
metry of 2 to 35 MV X-ray, and Caesium-137 and Co
balt-60 gamma-ray beams. Phys. Med. Biol. 28:
1097-1104.
6. HPA (1985): Gode of practice tor electron beam
dosimetry in radiotherapy. Phys. Med. Biol. 30:
1169-1194.
7. IAEA (1979): Calibration of dose meters used in
radiotherapy, TRS No. 185, Vienna.
8. IAEA (1987): Absorbed dose determination in pho
ton and electron beams. An international code of pra
ctice. TRS No. 277, Vienna.
9. Johns HE i Cunningham JR (1983): The physics of
radiology. Charles Thomas Publishers.
1
O. NACP (1980): Procedures in external radiation
therapy dosimetry with electron and photon beams
with maximum energies between 1 and 50 MeV. Acta
Radiol. Oncol. 19: 56-79.
11. NACP (1981
): Electron beams with mean energies
at the phanton surface below 15 MeV. Acta Radio. On
col. 20: 401-415.
12. Nuclear Enterprises Ud. (1975): lnstruction ma
nual tor Farmer dosemeter type 2502/3.
13. Savezni zavod za mere i dragocene metale (1984):
Naredba o rokovima za periodične preglede etalona i
merila. Službeni list SFRJ, br. 26: 734-739.
14. Savezni zavod za standardizaciju (1986): Pravil
nik o tehničkim normativima za jonizacione komore
koje se upotrebljavaju u radioterapijskoj dozimetriji.
Službeni list SFRJ, br. 36: 1104-1108.
.409


Medved, Samo Peter;Žlender, Bojan;Lenart, Stanislav

Građevinar 6/2018
497
GRAĐEVINAR 70 (2018) 6, 497-508
DOI: https://doi.org/10.14256/JCE.2038.2017
Parametric study of geocell
reinforced pavement
Primljen / Received: 11.3.2017.
Ispravljen / Corrected: 23.2.2018.
Prihvaćen / Accepted: 4.3.2018.
Dostupno online / Available online: 10.7.2018.
Authors:
Samo Peter Medved, PhD. CE
LINEAL, Slovenia
samo.medved@lineal.si
Assoc. Prof. Bojan Žlender, PhD. CE
University of Maribor
Faculty of Civil Engineering
bojan.zlender@um.si
Assist.Prof. Stanislav Lenart, PhD. CE
Slovenian National Building and
Civil Engineering Institute
stanislav.lenart@zag.si
Preliminary report
Samo Peter Medved, Bojan Žlender, Stanislav Lenart
Parametric study of geocell reinforced pavement
Parametric study of geocell reinforced pavement is presented in this paper. The FEM
analysis models include unreinforced pavement structures and geocell-reinforced
pavements with various geocell positions, thicknesses and strengths. The model output
includes the expected life of the pavement. Parametric study results are consistent
with the results of analytical solutions, laboratory tests, and field-test experiments. The
results reveal a significant improvement in capacity, reduction in asphalt-layer thickness,
and an increase in life expectancy of the geocell-reinforced pavement structure.
Key words:
flexible pavement, geocell, geosynthetic, reinforced soil, numerical modelling
Prethodno priopćenje
Samo Peter Medved, Bojan Žlender, Stanislav Lenart
Parametarska studija kolničke konstrukcije ojačane geoćelijama
U radu je prikazano parametarsko ispitivanje kolničke konstrukcije ojačane geoćelijama.
Analiza temeljena na metodi konačnih elemenata uključuje model neojačane kolničke
konstrukcije te model kolničke konstrukcije ojačane geoćelijama, pri čemu se analiziraju
razni položaji, debljine i čvrstoća geoćelija. U okviru modela određen je i očekivani
vijek trajanja kolničke konstrukcije. Rezultati parametarskog proučavanja u skladu
su s rezultatima analitičkih rješenja, laboratorijskih i terenskih ispitivanja. Dobiveni
rezultati upućuju na bitno poboljšanje nosivosti, smanjenje debljine asfaltnih slojeva
i povećanje trajnosti kolničke konstrukcije kada je ona ojačana geoćelijama.
Ključne riječi:
savitljivi kolnik, geoćelija, geosintetik, ojačano tlo, numeričko modeliranje
Vorherige Mitteilung
Samo Peter Medved, Bojan Žlender, Stanislav Lenart
Parameteruntersuchung der durch Geozellen verstärkten Fahrbahnkonstruktion
In der Abhandlung wird die Parameteruntersuchung der die sich auf den Ergebnissen
der FEM begründen. Die auf der FEM begründete Analyse umfasst das Modell der
nicht verstärkten Fahrbahnkonstruktion sowie das Modell der durch Geozellen
verstärkten Fahrbahnkonstruktion, wobei verschiedene Positionen, Stärken und
Festigkeiten der Geozellen analysiert werden. Im Rahmen der Modelle wurde auch
eine erwartete Nutzungsdauer der Fahrbahnkonstruktion festgelegt. Die Ergebnisse
der Parameterstudie stimmen mit den Ergebnissen der analytischen Lösungen, der
Labor- und Felduntersuchungen überein. Die erhaltenen Ergebnisse weisen auf
eine wesentliche Verbesserung der Tragfähigkeit, die Verringerung der Stärke der
Asphaltschichten sowie die Erhöhung der Haltbarkeit der Fahrbahnkonstruktion hin.
Schlüsselwörter:
flexible Fahrbahn, Geozellen, Geosynthetik, verstärkter Boden, nummerische Modellierung
Građevinar 6/2018
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GRAĐEVINAR 70 (2018) 6, 497-508
Samo Peter Medved, Bojan Žlender, Stanislav Lenart
1. Introduction
Pavement structures are an important element of any road.
They represent at least 40% of the total investment costs of
roads and about 70% of the maintenance management costs.
According to the Road Statistics Yearbook, 2016 [1], the EU has
over 4.8 million km of paved roads. To achieve an appropriate
quality of roads, at least 6% of the length of the entire network
must be built or restored each year. This involves considerable
quantities of built-in material, high energy consumption, and
significant costs. Therefore, finding alternative ways to design
pavement structures is a permanent engineering challenge, and
has been the subject of numerous studies.
This paper focuses on geocell reinforced flexible pavements.
An investigation of the effects of geocell reinforcement
on pavements was carried out. The basic purpose of the
investigation was to find the capacity, durability and cost-
optimized solution for such a project, while attempts were
simultaneously made to try to minimize consumption of
materials and energy.
In recent years, several researchers, such as Cowland and
Wong, Dash et al., and Yang et al. [2-5], have focused on
studying geocell soil reinforcement and the improvement
of soil bearing capacity of embankments in which geocells
are used. They found that an appropriate geometry of
geocells is effective for improving load capacity. Some other
researchers, such as Bathurst and Karpurapu [6], Rajagopal
et al. [7], Mengelt et al. [8], Wasseloo et al. [9], and Pokharel
et al. [10], have studied the effect of geocells on deformed
ground, and the impact on soil modulus under static and
dynamic load. The results of their research have shown that
the capacity of the base material can be improved by using
geocells, which depends on the load, geocell type and type of
load. Mengelt et al. [8] investigated the ways in which the use
of geocells increases elastic modulus of pavement layers.
The above-mentioned studies were specifically focused on
testing single geocells structures. Rajagopal et al. [7] and
Wasseloo, et al. [9] carried out research on the deformation
characteristics of pavements reinforced with several geocell
layers. They mostly used geocells 100 mm and 200 mm in
thickness. The results show that the use of geocells reduces
the occurrence of rutting in road surfaces. Al-Qadi and
Hughes [11] studied the effect of non-woven geosynthetic
geocells, with heights of 100 mm. An analysis using the
Falling Weight Deflectometer (FWD) showed that the elastic
modulus increased by a factor of 2 over a three-year period
in the pavements reinforced with geocells. Latha et al. [12]
conducted a field study of geocells on unpaved roads, using
geocells from various types of geosynthetics. Pokharel,
et al. [10] examined the use of Neoloy polymer geocells as
reinforcement on low traffic unpaved roads, constructed over
a subgrade with a CBR lower than 3. This study shows that
the use of thinner and more rigid geocells can be even more
effective.
A parametric study of geocell reinforced pavement using
the Finite Element Method (FEM) is presented in this paper.
The method is implemented by installing geocells in the
base layer to prevent excessive horizontal deformation.
This increases the overall capacity of the pavement. For
this purpose, an extensive research work was conducted,
involving analytical solutions, numerical analyses with
parametric studies, experimental analyses with laboratory
experimental tests, and a field-test experiment. The research
was based on previous laboratory TLS tests [13] conducted
using a new testing device, and referred to as the Traffic Load
Simulator (TLS). This device was constructed at the Slovenian
National Building and Civil Engineering Institute (ZAG). The
aim of this experimental campaign was to perform laboratory
tests on full-scale pavement structures subjected to traffic
load. The mathematical model for the multi-layer system
was derived from a geocell-reinforced pavement analysis.
The model combines known empirical relationships with
a representation of the physics and mechanics behind the
flexible pavement behaviour. The mathematical model is a
useful indicator for the effectiveness of pavement structure.

The use of the model is presented via the TLS test results
[14]. Experimental and theoretical analyses show significant
improvement in capacity and reduction of deformation
when geocells are used. By using geocells, the bearing
capacity and the elastic area of the unbound bearing layer
are increased, while permanent deformation to pavement
structure is decreased. This method has been tested in the
field on geocell reinforced pavement structures, which were
compared to unreinforced pavements structures. The geocell
efficiency was also confirmed by field experiments [14, 15].
Initial results show that geocells embedded in unbound
bearing layers provide pavement structures with flexibility
and sufficient capacity. The investigations will continue in the
future, with the focus on the time-effect of geocell reinforced
pavements.
This paper presents only the results of a parametric study
conducted on an investigated pavement structure using the
Finite Element Method (FEM). Other laboratory experiment and
field test results are presented elsewhere [13-15].
2. Concept of geocell reinforced pavement
Pavement structures are reinforced by installing geocells
in the base layer (Figure 1). This is intended to prevent
excessive horizontal deflection of unbound supporting
layers of the pavement structure and to simultaneously
increase capacity of the entire pavement structure. As
the use of geocells limits movements in the horizontal
direction, it also enables additional horizontal confinement
of the base layer.
The construction of geocell pavement structures is simple.
Geocells are placed in a base layer and filled with gravel
material. The material in the cells is first vibrated into
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Parametric study of geocell reinforced pavement
place using a compactor plate. The dynamic and static
compacting with a heavier compactor is then conducted
at the pre-prepared base. Medved et al. [14] tested this
type of installation technology. The field test in this area
showed that the installation technology is fully effective and
unproblematic.
Figure 1.
Geocell reinforced flexible pavement concept: layers (upper
left), installation of geocells (upper right), geocells with
compacted crushed stone material (bottom left) and final
pavement structure (bottom right)
Mechanisms of the effect of reinforcing pavement structures
with geocells have been explored in detail by several authors
[16-18]. In principle, there are three main mechanisms by
which geocells can have an increasing effect on the capacity
of reinforced layers: the mechanism of lateral resistance
(cell-effects), the mechanism of stress dispersion, and the
membrane effect mechanism.
The mechanism of lateral resistance results from friction
between the geosynthetic reinforcement and the soil. In this
case, the shear stress is efficiently transmitted from the soil, by
friction to the tension in the geosynthetic reinforcement. Figure
2 shows a cross-sectional view and the unitary pocket shear
force.
Figure 2. Mechanism of lateral resistance, Ling [17]
The confinement effect improvement is the sum of the unitary
pocket shear forces under load, obtained by multiplying the
number of cells under load by the unitary pocket shear force
[18].

(1)
where: ΔFt is the sum of unitary pocket shear forces under load
(confinement effect improvement), h/d is the geocell aspect
ratio, k0 is the lateral earth pressure at rest (k0 = 1-sinφ’), B and
L are the load width and load length, δ is the interface friction
angle between the filling soil and the geocell wall, and p is the
load at the top of the geocell mattress.
Figures 3 and 4 show the bearing capacity mechanism and
the force vectors by using the membrane effect mechanism.
The second improvement effect is the stress distribution
mechanism [16]. The stress in the upper level of the geocells is
reduced at the lower level from p to p’.

(2)
where: p is the stress on the upper level of the geocell, p’ is
the stress on the basis of the geocells, B is the load width, hCEL
is the thickness of the geocells, and α is the angle of stress
distribution.
Figure 3. Stress distribution capacity increase mechanism
The third improvement effect is the membrane mechanism [17],
which occurs when the reinforced soil has already developed a
certain deformation. The increase in capacity is calculated from
the tensile force in geocells, eq (3):

(3)
The tension force is given by equation (4):
T = ECEL · eCEL · hCEL
(4)
where: Dp is the bearing capacity increment, B is the width of the
uniform load, ECEL is the tensile elasticity modulus of the geocell;
εCEL is the tensile strain of the geocell layer, hCEL is the thickness
of the geocells and α is the horizontal angle of the tensional
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3.3. Base and sub-base layers
The modulus of elasticity of base layer may be constant
throughout the layer, or it can be expressed as a function of
stress. In the analysis presented in this paper, the modulus
of elasticity is expressed as a function of stress. Witczak and
Uzan [19] modified the model by including the octahedral shear
stress in the model instead of the deviator stress.

(5)
where: k1, k2, and k3 are regression analysis constants evaluated
by the multiple regression analysis of experimental data. At the
same time, the Austroroads theory [20] was considered.
Quality criteria and procedures for the investigation of stone
grain mixtures, which are intended for unbound base and
subbase, were provided by European standards [21-25].
4. Loading conditions
A simplified measure of traffic for pavement design ESAL
(Equivalent Single Axle Load) was used. In the presented
analyses, an ESAL is defined as a 100 kN dual tire axle with a
tire pressure of 690 kPa.
4.1. Criteria
4.1.1. Single loading cycle
An analysis that considers the following criteria must be
satisfied during each cycle of load. The tensile strain of the
asphalt layer εt,A and the tensile strain of the geocell layers εt,CEL,
both increased by the safety factor SF, should be less than their
permissible strain εt,lim [16, 17].
SF · et,A ≤ et,A,lim
(6)
SF · et,CEL ≤ et,CEL,lim
(7)
The stress-strain in the base and subbase layers (if they exist),
and also in the subgrade, must be within the failure lines of the
p - q stress space (Hornych et al [26]):
SF · sd,B ≤ qf,B
(8)
where: σd,B is the deviator stress in the base layer, SF is the safety
factor and qf,B is the maximum stress, defined from material
failure lines in the  p - q stress space (based on laboratory tests).
A similar relation is used for the sub-base layer and the subgrade
SF · sd,SB ≤ qf,SB
(9)
SF · sd,SG ≤ qf,SG
(10)
force T. Figure 4 shows the bearing capacity mechanism by
membrane effect and the force vectors.
Figure 4. Membrane mechanism
3. Material properties
3.1. Geocells
Geocells are made up of vertically-oriented strip-form cells
that can assume rectangular, square or hexagonal forms
(Figure 5). Stone material is laid into the cells and compacted
up to an optimum value. The cells are of an appropriate size:
the spacing between the bands is greater than three times the
maximum grain, and no smaller than the thickness of the layers
(i.e. than the geocell layer thickness). Geocells range from 5 to
20 cm in thickness. Most previous researchers tested geocells
varying from 10 to 20 cm in thickness. Geocells can assume two
extreme positions in the base layer of the pavement structure:
the extreme position in contact with ground, and the extreme
position in contact with asphalt.
Geocells have been recognized as a suitable geosynthetic
reinforcement of granular soils for supporting static and moving
wheel loads on roadways. The analysis considers the stiffness
of geocells with the elastic modulus ECEL ranging from 200 MPa
to 3000 MPa.
Figure 5. Geocells in pavement structure before asphalt laying
3.2. Asphalt layers
The asphalt layer was treated in the analysis as an elastic
material with a modulus of elasticity of EAC and a Poisson ratio
of νAC. The fatigue of the asphalt due to repeated loads is given
by the maximum number of cyclical repetitions of load, specified
as a function of deformation.
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Parametric study of geocell reinforced pavement
The vertical strain of the base layer and both subbase and
subgrade must be lower than the permissible value εv,lim
SF · ev,B ≤ ev,B,lim
(11)
SF · ev,SB ≤ ev,SB,lim
(12)
SF · ev,SG ≤ ev,SG,lim
(13)
4.2.1. Repeated loading
The expected life of the pavement is calculated by simulating
traffic load strains, and by using an empirical transfer function
to determine Allowed Repetitions for each load. If the applied
load repetitions exceed the allowed repetitions, the pavement
is assumed to have failed. Various correlations can be used to
determine the maximum number of cyclic repetitions of traffic
load. The correlation [27] is used to determine the tensile
deformation of asphalt and the maximum number of cyclical
repetitions of traffic loads NF, according to equation (7):

(14)
where: EA is the dynamic elasticity modulus of asphalt (psi), εt,A is
the lateral deformation of asphalt, CF is the correction factor and
KF1, KF2, KF3 are constants.
The following Tseng and Lytton relationships [28] were used in
the prediction of permanent strain in pavement structure:

(15)
where εv,B,max is the maximum permanent strain at a very high
number of loading cycles, and ρ and β are the parameters. The
parameters εv,B,max, ρ and β were defined by laboratory tests
using the repeated load triaxial apparatus and the Tseng and
Lytton procedures [28].
Considering the thickness of base layer h, the permanent
vertical deformation of the layer is:

(16)
where: εv,B,rx is the resilient strain in the single loading cycle,
computed from the FEM analysis.
By criterion of subgrade rutting [27], the maximum number of
cyclical repetition of traffic loads NR is

(17)
where CR is the correction factor and KR1, KR2 are constants.
5. FEM analyses
The analysis of stress and strain in pavement structure, based
on the Finite Element Method (FEM), was conducted using the
FEM program Everstress  [29]. The purpose of the analysis was to
examine the effect the reinforcement has on the pavement. Control
calculations were implemented using the FEM program Plaxis
[30]. Comparison of both results shows good correlation between
displacements and stresses. Two distinct models were made:
-
-
the basic model, without reinforcement
-
-
the model in which the base layer is reinforced with geocells.
In the second model, the position of geocells in the base layer
varied from bottom to top. The traffic axle load of F = 100
kN and the wheel pressure of p = 690 kPa was applied in the
analysis. The analysis of the results focused on three criteria:
tensile strain in asphalt, vertical strain in the base layer and
vertical strain in the subgrade (Eq. 6, 9, 10).
5.1 Unreinforced pavement structure
The basic numerical model consisted of the asphalt layer, with
thickness dA; the base layer, with thickness dB; and the subgrade,
with a constant depth of dSG = 150 cm. The analysis was
performed on variable thicknesses of asphalt layer dA, and for the
thickness of the base layer dB, while the depth of the subgrade
was constant and amounted to dSG =150 cm. A variable value ESG
was applied in the calculations, while the stiffness of asphalt EA
and base layer EB was constant. The properties of layers were:
-
-
Asphalt layer (EA = 3 GPa, νA = 0.40, dA = 10, 20, 30 cm)
-
-
Base layer (k1 = 200 MPa, k2 = 0.5, k3 = 0, νB = 0.3, dB = 20,
40, 60 cm)
-
-
Subgrade layer  (ESG = 9; 14.7; 20.3 MPa, νSG = 0.45, dSG = 150 cm).
Figure 6 shows the symmetric FEM model frame disposition. The
results of the FEM analysis of the unreinforced pavement structure
with properties of layers dA, dB, ESG are: tensile strain in the asphalt
et,A, vertical strain in the base layer ev,B, vertical strain in the subgrade
layer ev,SG, number of repeating traffic loads NF and NR.
Figure 6. Numerical model without geocell
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5.1.1. Tensile strain in asphalt
The correlation between the tensile strain in asphalt et,A and the
asphalt layer thickness dA is shown in Figure 7.a for different
values of base layer thickness dB and subgrade stiffness ESG. The
results show that the asphalt layer thickness dA has a high impact
on the tensile strain in asphalt et,A. The correlation between the
tensile strain in asphalt et,A and the thickness of  base layer dB,
at different values of asphalt layer thickness dA and subgrade
stiffness ESG, is shown in Figure 7.b. The results show that the
thickness of base layer dB has a high impact on the tensile strain
in asphalt et,A only in case of large deformations (settlements) of
pavement structure. The correlation between the tensile strain in
asphalt et,A and subgrade stiffness ESG, at various values of asphalt
layer thickness dA and base layer thickness dB, is shown in Figure
7.c. The results confirm that the stiffness of the subgrade ESG has
a low impact on tensile strain in asphalt layer et,A if the pavement
structure is sufficiently dimensioned (low settlements).
Comparison of results for tensile strain in asphalt et,A, between
the unreinforced pavement structure and the geocell reinforced
pavement beneath the asphalt, shows that a thin asphalt layer and
an adequate stiffness of cells can have the same effect on tensile
strain in asphalt et,A as an increase in asphalt layer thickness.
5.1.2. Vertical strain in base layer
The correlation between the vertical strain in base layer ev,B
and asphalt layer thickness dA, at various values of base layer
thickness dB and subgrade stiffness ESG. is shown in Figure 8.a.
The results show that the thickness of asphalt layers dA has a
high impact on vertical strain in base layer ev,B. The correlation
between the vertical strain in base layer ev,B  and the thickness
of base layer dB, at different values of asphalt layer thickness dA
and subgrade stiffness ESG, is shown in Figure 8.b. The results
confirm that the thickness of base layer dB has a significant
impact on vertical strain in base layer ev,B . The correlation
between the vertical strain in base layer ev,B  and the stiffness of
subgrade ESG, at various values of asphalt layer thickness dA and
base layer thickness dB, is shown in Figure 8.c. The results show
that the stiffness of subgrade ESG has a low impact on vertical
strain in base layer ev,B if pavement structure is sufficiently
dimensioned (low settlements). The comparison of results for
the vertical strain in base layer ev,B, between the unreinforced
pavement structure and the geocell reinforced pavement
beneath the asphalt, shows that a thin layer of asphalt and
an adequate stiffness of geocells can reduce vertical strain in
base layer ev,B but cannot produce the same effect as when the
asphalt layer thickness is increased.
5.1.3. Vertical strain in subgrade layer
The correlation between the vertical strain in subgrade layer ev,SG
and the thickness of asphalt layers dA at different values of base
layer thickness dB and subgrade stiffness ESG, is shown in Figure
9a.  The results show that the thickness of the asphalt layers dA
has a high impact on the vertical strain in subgrade layer ev,SG.
Figure 7.
Tensile strain in asphalt et,A vs: a) asphalt layer thickness dB at different values of base layer thickness dB and subgrade stiffness ESG;
b) base layer thickness dB at different values of asphalt layer thickness dB and subgrade stiffness ESG; c) subgrade stiffness ESG at
different values of asphalt layer thickness dA and base layer thickness dB
Figure 8.
Vertical strain in base layer ev,B vs: a) asphalt layer thickness dA at various values of base layer thickness dB and subgrade stiffness ESG;
b) base layer thickness dB at various values of asphalt layer thickness dA and subgrade stiffness ESG; c) subgrade stiffness ESG at various
values of asphalt layer thickness dA and base layer thickness dB
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Parametric study of geocell reinforced pavement
-
-
Geocells (ECEL = 200 - 3000 MPa, ν = 0.20, dCEL = 5, 10, 15 cm)
-
-
Lower base layer (k1 = 200 MPa, k2 = 0.5, k3 = 0, νB = 0.3, dB =
0 to 40 cm - dCEL)
-
-
Subgrade layer (ESG = 9; 14.7; 20.3 MPa, νSG = 0.45, dSG = 150 cm).
Generally, three models of reinforced pavement structures
were analyzed: with geocells on top of the base layer, with
geocells inside the base layer, and with geocells directly under
the asphalt layer.
The results of the FEM analysis of the reinforced pavement
structure with properties of layers dA, dB, dCEL, EA, ECEL, EB, ESG,
were expressed as: tensile strain in asphalt et,A, tensile strain
in geocells eCEL, vertical strain in base layer ev,B, vertical strain in
subgrade layer ev,SG, number of repeating traffic loads NF and Nr.
5.2.1. Tensile strain in asphalt
Figure 10.a shows the correlation between the tensile strain
in asphalt et,A and the stiffness of geocells ESG, with a geocell
thicnkness of dCEL = 10 cm and a subgrade stiffness of ESG =
20.3 MPa, for the geocells directly under the asphalt layer. The
results show that the geocell stiffness ESG has a high impact
on the tensile strain in asphalt et,A. The geocells thickness dCEL
also has a significant impact on the tensile strain in asphalt et,A.
Figure 10.b shows the correlation between the tensile strain
in asphalt et,A and the geocell stiffness ECEL at various values of
geocell thickness dCEL and subgrade stiffness ESG – geocells are
in contact with subgrade. The results show that geocells do not
exert a significant impact on the tensile strain in asphalt et,A.
The correlation between the vertical strain in subgrade layer ev,SG
and the thickness of base layer dB, at various values of asphalt
layer thickness dA and subgrade stiffness ESG, is shown in Figure
9.b. The results confirm that the thickness of base layer dB has
a significant impact on the vertical strain in subgrade ev,B . The
correlation between the vertical strain in subgrade ev,SG and
the stiffness of subgrade ESG at various values of asphalt layer
thickness dA and base layer thickness dB. is shown in Figure
9c. The results show that the stiffness of subgrade ESG has an
impact on vertical strain in subgrade ev,SG  if pavement structure
is not sufficiently dimensioned.
5.2. Reinforced pavement structure
The numerical model of the reinforced pavement structure,
with geocells in its base layer, consists of an asphalt layer with
thickness dA, an upper base layer with thickness dB,UP, a layer of
geocells with thickness dCEL, a lower base layer with thickness
dB,L, and a subgrade with a constant depth of dSG = 150 cm. The
analyses were performed with the constant thickness of the
asphalt layer dA and base layer dB, while the geocells thickness
dCEL was a variable. The variable value ESG was applied to the
calculations of subgrade. The stiffness value of geocells was
also variable, while the stiffness values of asphalt EA and base
layer EB were constant. Layer properties can be summarized as
follows:
-
-
Asphalt layer (EA = 3 GPa, νA = 0.40, dA = 10 cm)
-
-
Upper base layer (k1 = 200 MPa, k2 = 0.5, k3 = 0, νB = 0.3, dB =
0 to 40 cm - dCEL)
Figure 9.
Vertical strain in subgrade layer ev,SG vs: a) asphalt layer thickness dA at different values of base layer thickness dB and subgrade stiffness
ESG; b) base layer thickness dB at various values of asphalt layer thickness dA and subgrade stiffness ESG; c) subgrade stiffness ESG at
various values of asphalt layer thickness dA and base layer thickness dB
Figure 10.
Typical tensile strain in asphalt et,A vs: a)geocells stiffness ESG, for geocells directly under asphalt layer; b) geocell stiffness ECEL at
various geocell thicknesses dCE, geocells are in contact with subgrade; c) distance between geocells and asphalt Dh
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The distance of geocells from asphalt Dh was analysed. Figure
10c shows the correlation between the tensile strain in asphalt
et,A and the distance of geocells from asphalt for specific geocell
characteristics (ECEL = 2000 MPa, dCEL = 5 cm) and ground
conditions (ESG = 9-20.3 MPa). The results show that the tensile
strain in asphalt et,A is the lowest when geocells are in contact or
at very slight distance from the asphalt.  There is a significant
increase of tensile strain in asphalt when the distance between
geocells and asphalt exceeds 1 cm. When the distance is beyond
2 cm, the tensile strain in asphalt increases constantly with an
increase in distance, but at lower rate.
Based on this analysis, it can be concluded that the placement
of geocells has a significant impact on the transverse tension
in asphalt, and that the location of geocells just below asphalt
is advantageous and contributes significantly to the reduction
of deformation. The significance of using geocells decreases
rapidly with an increase in installation depth.
5.2.2. Vertical strain in base layer
Figure 11.a shows the correlation between the vertical strain
in base layer ev,B and geocell stiffness ECEL, the geocells being
directly under the asphalt layer, at different values for geocell
thickness dCEL and subgrade stiffness ESG. The results show
that geocell stiffness ECEL and geocell thickness dCEL have a high
impact on the vertical strain in base layer ev,B. Figure 11.b shows
the correlation between the vertical strain in base layer ev,B and
geocell stiffness ECEL (geocells are in contact with subgrade), at
different geocell thicknesses dCEL. The results show that geocell
stiffness ECEL has a high impact on the vertical strain in base layer
ev,B, while geocell thickness dCEL has no significant  impact on the
vertical strain in base layer ev,B. Results for geocells inside the
base layer range between extreme values shown in Figure 11.a
and Figure 11.b and depend on the distance between geocells
and asphalt.
5.2.3. Vertical strain in subgrade
Figure 12.a shows the correlation between the vertical strain
in subgrade layer ev,SG and the stiffness of geocells ECEL, for the
geocells directly under the asphalt layer, at different geocell
thicknesses dCEL and subgrade stiffness ESG. The results show
that the stiffness of the geocells ECEL has no important influence
on the vertical strain in subgrade layer ev,SG. However, the
thickness of geocells dCEL has a significant  impact on the vertical
strain in subgrade layer ev,SG. Figure 12.b shows the correlation
between the vertical strain in subgrade layer evSG and geocell
stiffness ECEL, for geocells in contact with subgrade, at various
values of geocell thickness dCEL. The results show that the
stiffness of geocells ECEL has an influence on the vertical strain in
Figure 11.
Vertical strain in base layer ev,B vs. geocell stiffness ECEL at various geocell thicknesses dCEL a) the geocells are positioned directly under
the asphalt layer; b) the geocells are in contact with subgrade
Figure 12.
Vertical strain in subgrade layer ev,SG vs. geocell stiffness ECEL at various geocell thicknesses dCEL:  a) for geocells directly under the
asphalt layer; b) for geocells in contact with the subgrade
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Parametric study of geocell reinforced pavement
subgrade layer ev,SG. Results for geocells inside the base layer are
between the extreme values shown in Figure 12.a and Figure
12.b, which is dependent on the distance between geocells and
asphalt. The results show that vertical strain in subgrade layer
ev,SG is smaller when geocells are deeper in base layer.
5.3. The effect of reinforcement
Tensile strain in asphalt et,A is highly important for the life cycle
of pavement structures. Figure 13.a shows the correlation
between the maximum number of repeated loadings NF and
asphalt layer thickness et,A (Eq. 7). For unreinforced pavement,
the results of FEM Analysis are similar to the results of the
empirical method [31], which did not take into account the
conditions of the subgrade; the number of passes depended
only on the dimensions of the asphalt. The number of repeated
loads significantly increases when the pavement is reinforced
on top of the base layer with geocells only 5 cm in thickness
(depending on the stiffness of the geocells). Similarly, the
correlation between the maximum number of repeated loadings
NF and base layer thickness dB (Figure 13.b) is presented, as
well as the correlation between the maximum number of
repeated loadings NF and subgrade stiffness ESG (Figure 13.c).
The vertical strain in subgrade layer ev,SG is highly important
Figure 13.
a) Number of repeated loadings NF in life cycle vs. asphalt layer thickness dA for unreinforced pavement (FEM and empirical), compared
to the increasing number of repeating loadings NF in life cycle for asphalt layer with constant thickness and an increasing stiffness of
geocells; b) Number of repeated loadings NF in life cycle vs. base layer thickness dB; c) Number of repeated loadings NF in life cycle vs.
subgrade stiffness ESG
Figure 14.
a) Number of repeated loadings NR in life cycle vs asphalt layer thickness dA; b) dB (dA =10 cm) compared to an increasing number of
repeating loadings NR in life cycle for constant asphalt layer thickness and an increasing stiffness of geocells; c) Number of repeated
loadings NR vs. subgrade stiffness ESG
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for the life cycle of pavement structures. Figure 14.a shows
the correlation between the maximum number of repeated
loadings NR and asphalt layer thickness dA (eq. 10) for different
thicknesses of base layer dB and different subgrade stiffness
values ESG. Similarly, the correlation between the maximum
number of repeated loadings NR and base layer thickness dB
(Figure 14.b) is presented, as well as the correlation between
the maximum number of repeated loadings NR and subgrade
stiffness ESG (Figure 14.d). Figure 14.c shows the correlation
between the maximum number of repeated loadings NR and
base layer thickness dB (eq. 10) for an unreinforced pavement
and pavement that has been reinforced at the bottom of the
base layer with geocells 5 cm in thickness.
The results show that the geocells installed directly under the
asphalt have a high impact on the number of repeated loadings
NF in life cycle (tensile strain of asphalt layer), see Figure 15.a,
and a low impact on the number of repeated loadings NR in life
cycle (vertical strain of subgrade), see Figure 15.b.
The situation is quite the opposite for geocells in contact with
subgrade: they have a low impact on the number of repeated
loadings NF in life cycle (tensile strain of asphalt layer), see
Figure 16.a, and a high impact on the number of repeated
loadings NR in life cycle (vertical strain of subgrade), see Figure
16.b.
Figure 15.
a) Number of repeated loadings NF in life cycle vs. subgrade stiffness ESG (geocells placed directly under asphalt); b) Number of
repeated loadings NR in life cycle vs. subgrade stiffness ESG (geocells placed directly under asphalt)
Figure 16.
a) Number of repeated loadings NR in life cycle vs. subgrade stiffness ESG geocells in contact with subgrade; b) geocells in contact with
subgrade
6. Conclusion
Both an investigation and a parametric study were conducted
to analyse an innovative approach to the design of geocell-
reinforced flexible pavements. Extensive research conducted
to this effect involved: analytical solutions, numerical analyses,
a parametric study, experimental analyses, experimental
laboratory tests, and field experiments. The parametric study
is presented in the paper. The results are consistent with other
above-mentioned analyses.
The parametric study was conducted based on the results
obtained by FEM analysis. The FEM analysis included
unreinforced and geocell-reinforced pavements with various
positions of geocells and various stiffness and thickness values
of geocells. The following findings were obtained in the scope of
the parametric study:
-
-
Geocells significantly increase the capacity of the asphalt
layers of pavement structures, and reduce permanent
deformation in asphalt. Therefore, the use of geocells could
significantly reduce the asphalt-layer thickness and/or
increase life time of pavement structures.
-
-
The results show that the stress - strain state in pavement
layers mostly depends on the location of geocells in the
base layer and the stiffness of geocells. When geocells
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Parametric study of geocell reinforced pavement
are positioned directly under the asphalt, the stiffness of
geocells has a high impact on the tensile strain of asphalt.
-
-
The stiffness and thickness of geocells also have a high
impact on vertical strain in base layer, while they have no
important influence on vertical strain in subgrade layer.
-
-
The thickness of geocells also has a significant impact on the
tensile strain of asphalt.
-
-
When geocells are positioned on top of the subgrade, the
stiffness and thickness of the geocells have an impact on
vertical strain in base layer and on vertical strain in subgrade.
They have no significant impact on tensile strain in asphalt.
This effect is reduced significantly when the distance
between geocells and asphalt exceeds 1 cm.
-
-
The geocells installed at the bottom of base layer improve
the capacity of subgrade and reduce the permanent vertical
deformation of base layer. Geocells affect the reduction of
shear deformation in the base layer directly at the position
of the reinforcement.
The conclusion of the parametric study is: geocells have an
effect on tensile strain of asphalt only when they are placed in
contact with asphalt, or just beneath the asphalt. When they
are placed lower in the base layer, the effect on asphalt reduces
significantly. Geocells installed deeper or at the bottom of the
base layer improve the capacity of subgrade and reduce the
permanent vertical deformation of the base layer.
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