ON DINH DOC MAT OU'CTNG BE

^aaaa KHOA HQC - CONG NGH?

Tom tit: Xu hw&ng sir dung mat dw&ng bd tdng xi ming cot thep lien tuc (BTCTLT) trong twang lai phit triin manh, die bidt a Vi$t Nam.

Nhung kit qua nghien cu'u ve mit dw&ng BTCTLT ChO yiu di/a tren thi/c nghidm, mdi nw&e CO cic qui dinh khic nhau phy thuOc vio diiu kidn khi hgu cOa nwac minh. Cf Viet Nam, trong khoing 10 nim gin day da cd mgt sd cdng trinh khoa hgc nghien ciru vd mit dwang BTCTLT theo hw&ng tht/c nghidm, vi dd thu dwoc mgt so kit qua nhdt dmh. Tuy nhien, vin de 6n dinh dgc cOa mSt dw&ng chwa dwoc quan tim, nghien cCru. Bdo cdo khoa hgc di I sdu vio md hinh bii toin /j? thuyit ve Sn dinh dgc, khio sdt trgng thii mat Sn dfnh dgc cOa . m$t dw&ng BTCTLT trong diiu kidn khi hau ,

Vigt Nam. .^

Tir khoa: Be tdng cit thep lidn tuc; Sn djnh dgc.

Abstract: Trends of using continously reinforced concrete pavement (CRCP) is growing strongly in the future, particularly in ^ Vietnam. The results of studies on the pa vement CRCP are mainly based on field experiment, each country has different regulations ^ depending on the climatic conditions of their countries. In the Vietnam, over the past 10 years there were a number of scientific research projects on the road surface in the direction of empirical CRCP, and has obtained a certain number of results. However, stability | issues along the pavement are not taken care of and researched. Scientitic reports are going into model theory of stable longitudinal survey destabilized state of the road surface along CRCP in Vietnam climatic conditions.

Keywords: CRCP, stability issues along the pavement.

I . D A T V A N D E

Mat dudng BTCTLT d u p c xay d y n g dau tidn d Hoa Ky vdo nam 1930. Hi^n nay, mgt dudng BTCTLT dupe dp dung khd pho b i l n d nhleu nude. Cl Vigt Nam trong khoang 10 nam gan ddy, mgt dudng BTCTLT mdi d u y c nghien cuu dp dung. Do efi it khe ngang so vdl mat d u d n g BTXM thfing thudng, nen xe chgy dm thudn, gtam on, giam h u hong mgt dudng, mfing vd n i n dudng on djnh nhd hgn e h l dupe nude mat t h i m xuong, v.v... nhung vdn phdt huy d u o c uu d i l m eiia mat dudng BTXM.

ON DINH DOC MAT OU'CTNG BE TONG XI MANG COT THEP

LIEN TUC

N G d HA SOU Hpc vipn Ky thuat Quan si;

MOt so nude tien tien trdn the gidi, nhu: Hoa Ky, Australia, Tnjng Q u i c , v.v... da nghien cuu dng dung mat dudng BTCTLT, vd da ed duoc mpt s6 thanh cfing nhat djnh, dae bifit trong nghidn cuu thuc nghiem. Tuy nhien, khi ung dung logt mat dudng nay vao Vidt Nam cfin gap n h i l u kho khan do thieu co s d 1^ t h u y l t tinh todn thiet k l , dgc bigt la on djnh dgc mat d u d n g .

2. T 6 N G Q U A N MAT DU'ONG BTCTLT Mat dudng BTCTLT cfi c l t thep dpc dupe b l trf Hen tue s u i t ehilu dai d u d n g , song song vdi tim dudng, c l t thep dpc chi de han e h l viee phat sinh s l luang khe nut, va b l r i n g khe ndt. Cot thep ngang b6 trf theo e l u tgo. C l t thep dpc va cot thep ngang dupc dgt d vj trf khodng tCr 1/3 -^ 1/2 chleu ddy phia trdn eiia Idp BTXM mat d u d n g . Bo ldp each li vdi lap mfing [1],

Theo AASHTO qui djnh [4]: hdm lupng cot thep doc t u 0,5% -^ 0,7% dien tich t i l t dien ngang mgt dudng BTXM; khoang cdch giua eae khe nut ngang tir 1,0

* 2.5 m; dp rfing khe nCrt khfing d u p e qud 1 mm. H?

d i m ngang diing de neo eot thep dpc b l trf tgi khe dan, g i m t u 3 -E- 5 dam ngang hinh chu nhgt bang bd tfing c l t thep. Khoang edeh ldn n h i t giii'a cac dam ngang 200 -^ 240 m, hay h i l u each khac ddy chfnh la chieu ddi ldn n h i t cua t i m BTCTLT.

Cae tdi lieu nghien euu ve mat d u d n g BTCTLT hidn cd, khfing thay de cap d i n co s d khoa hpc eho glal phap e l u tgo. Trong dd, khoang cdch giua 2 khe gidn len d i n 240 m, tuc Id dai gap 4 l l n so vdi c l u tgo mgt dudng BTXM phdn t i m thfing thudng. Do vdy, vtec nghien cuu on djnh dpc mat d u d n g BTCTLT khi ung dung vao d i l u kign khf hdu Viet Nam Id can thilt.

3. B A I T O A N 6 N O I N H D p c MAT DU'ONG BTCTLT C o ehe lam vigc eua mgt d u d n g BTCTLT, dudi tac dpng ciia thay d l i nhigt do deu: khi nhidt dp 6h\i trong t i m giam, tam co v l tdm hinh hpe eua t i m . Kht nhidt dp deu trong t i m tdng, t i m gian, tdm gian triing vdl tdm hinh hpc cua t i m .

Khi tinh khe eo, lay chenh leeh nhigt dO thay db\

deu eiia t i m g i u a thdi d i l m xet v d i thdi d i l m do

So 9 nam 2017 I

KHOA HOC - C6NG NGHE aaaaa be tfing, cfi k l d i n hidn t u o n g co do mat n u d c

eua be tfing t u o n g u n g gtam khoang 15''C. Khi tfnh khe g i a n , t h u d n g xet d i n s y thay dot nhidt dO trung binh theo m u a trong nam, cu t h l : chenh tdch nhlOt dO trung binh thdng ndng n h i t v d i nhlOt dp trung binh thang nhd n h i t eiia khfing khi va cfi k l d i n dnh h u d n g eua b d e xa mat t r d i . Kht nhigt dp d i u trong t i m tang, trong tam x u l t hign d n g s u i t nen va hinh thanh l y e nen dpc. L y e ndn dpc tang d i n mOt gtd tri ndo d d , se gay phd hogt b i n hoac mat on dlnh d p c mat d u d n g va day chinh la ea s d ly t h u y l t d l xdc djnh khoang each giO'a 2 khe d a n .

Bdi todn I n djnh dpc eua mat d u d n g d u p e xem xdt d u d i bai todn on djnh dpc cua thanh, v d i gta t h i l t thanh d trgng thai t h i n g chju l y c nen P dung tdm.

Bdi todn Euler la bdi toan thanh bj nen doe trye, khi lye nen dgt tdi gta trj t d i hgn thanh bj eong vd mat on djnh. S o d l tinh xem hinh 1 .

lidn k i t 2 d i u khdp ed c h i l u ddy xde djnh, ti lg nghjch vdl blnh phuang chieu dai cua thanh.

Vdn dyng mfi hinh bdi todn I n djnh ciia thanh cho t i m BTCTLT, ta nhgn thay 2 dau t i m hgn c h l gian, khfing hgn che xoay, do vgy hodn todn cd t h l mfi phdng g l l t y a (khdp); l y c dpc x u l t hidn trong t i m Id l y c ndn khi nhiet dO trung blnh trong tam tdng, md t i m lal khfing efi khd nang gian. Do vdy, mfi hinh xet on djnh eiia tam BTCTLT sat v d l mfi hinh on djnh dpc cua thanh da neu d tren. T i m mat on djnh khi xuat hten hign t u o n g t i m tdch khfii be mgt mfing.

Ket qua tfnh u n g s u i t tdi hgn va ung s u i t eho phdp khi xdt I n djnh t i m BTCTLT theo efing thde (2), v d i hd s l an todn ve on cTinh n ^ = 1,1 d u p c cho trong bang 1 va the hign tren hinh 2.

Bing 1. Kit qui tinh toin ung suit t&i han ath vd Crng suit cho phep

M = 1

Hinh 1. Sa do bii toan Sn dinh dgc cOa thanh Vdi [1 la hg so tfnh doi chieu dai thanh.

Khi ndy, lye tdi hgn cua thanh bj nen dpc true:

p _ " ' £ ! ,

^ I h . 2

Trong dd: E - mfi dun ddn hoi cua vgt ligu thanh; J^ - mfi men qudn tfnh theo phuang mat I n djnh trfin t i l t didn ngang cua thanh; 1 - chieu dai thanh.

O'ng s u i t tdi hgn trong thanh d u p e xdc djnh theo cfing thdc:

AY (2) Thanh on djnh khi:

(3) Trong dd: a - u n g s u i t nen dpc true trong thanh; P - lye ndn dung tam; F - didn tfch ttet dign ngang cua thanh; n ^ - hg s l an toan v l on djnh; [ a ] ^ - ung s u i t cho phdp khi tinh on djnh.

Cong thirc (2) cho t h i y u n g s u i t tdl hgn trong thgnh

1 S6 9 nam 2017

L(m) cr,^ (i(G/cm=) [cr] (IsG/cm')

75 7,82 6,52

100 4,40 3,67

150 1,96 1,63

200 1.10 0,92

240 0,76 0,64

(1)

60,00

"l 50,00 e . 40,00

,°~

•S. 30,00 Q

. 1 20,00

^ 10,00

0,00

0 100 200

Chieu dai thanh (m)

Hinb 2. Di thj bieu didn mil quan hd giOa wng suit

cho phep nen dgc true vdi chidu dii tim V i n d l t i l p theo Id xde djnh lyc dpc Idn n h i t trong t i m . Bdl todn xde djnh u n g s u i t nhidt trong t i m BTCTLT cd k l d i n ma sat day t i m vdi b l mat mfing, khi nhigt dO trung blnh trong tam tang la c o s d d l xde djnh l y c doe Idn nhat cua tam.

S o do tinh: xem hinh 3.

p ^

AT,b>0

<-

_{T T}

->

Hinh 3. So' do tinh img suat nhiet trong m$t dw&ng iihi nhiet do dSu trong tam tang

^\m\m,

l l l l l KHOA HOC - CONG NGHE

Xet dieu ki$n can bSng ptian to: xem hinh 4.

P+dP AT,b>0

thay doi nhiet dp trung binh, thi u'ng s u i t lan nh^to tam tam;

K-

ciT= Tdx dx

M

Hinh 4. Sa do xdt dieu kien cdn bing phin td Dya tren dieu kien can bang phdn to, ta cfi phuang trinh vl phdn t h l hign lien he giua b i l n dgng mat dudng vdl s y thay d l i nhifit dp trung binh vd lyc dpc cua t i m :

du

d x ' a^T^ ^ ^ (4)

d'u

E..h

^{^ u = 0} Gial phuang trinh vl phan (7), ta dupe, C h u y i n vi Idn nhat d eanh t i m :

th

=

aAT,

c7:r=(^,-o7 01)

Trong d d ; a ^ - d n g s u i t Idn n h i t d tam tam;

o^ - ung s u i t trong tam khi b i l n dgng trong tim bj can trd hoan toan, vd d u y c xdc djnh theo cong thirc:

(7, =

oAT,

E., ₍₁₂₎

(5) Trong dfi: AJ^ - gtd trj thay d l i nhigt dp trung binh cCia t i m ; P - tyc dpc trung binh trong t i l t didn ngang CLia tam; u - chuyen djch ngang cua tam; T - lyc ma sat phan bo tren mfit dan vi chieu dai giua day t i m vdi be mat mdng; T - lye ma sdt giua ddy t i m vdi b l mat mfing; E^, - mfi dun ddn hoi cua BTXM.

Gia thieV tyc ma sat phdn bo theo qui ludt ty 1^ thudn vdt c h u y i n djeh ngang d mat ddy tam (mfi hinh Med- nhl-elp), ta cfi:

T = k u (6) Trong dfi: k - md dun can trupt, kG/cm^.

Dgo ham 2 v l phuang trinh vt phdn (4) theo x vd thay gtd trj cua T theo cdng thdc (6) vdo, ta d u y c :

k ( i - r )

cr^ - ung s u i t Idn n h i t d tdm t i m khi b i l n dang ngang cua t i m bj can t r d mOt p h i n , vd dupc xdc djnh theo cfing thdc (9); o^ - luang ehuyen vj dupc qui d l i ra ung s u i t d tam t i m khi egnh t i m chuyin vj vd k l d i n b l rpng cua khe nut ngang b, khd nang co Igi d u p e ciia khe gian e, vd dupe xdc djnh ttieo cfing thde:

th nL

4s^^^

⁽¹³⁾

Trong dfi, b i l u thdc t h u n h i t trong ngodc vufing la chuyen vj Idn nhat d cgnh t i m , tuong ung vdi ifng s u i t Idn n h i t d tdm tam, b i l u thuc thd hai trong ngogc vudng la tong be rfing khe nut ciia t i m ; va cia khd ndng eo Igi d u p c cua khe gian. Thay efing thifc (9), (12), (13) vdo efing thuc (11), ta dupc:

= a A T ^ E ^ - a A T ,

^E«

1 - ^ '

1 1

. h 5 t I 2 j

(7)

^ V b + c

(14)

Tu'ang O'ng v&t Crng suat ian n h i t & tam t i m :

T r o n g d o : a - he so dan n a nhiet cOa BTXM;

^^' ^"^ib' 9'^ tri thay doi nhiet do trung binh cQa tam;

E^j - mo dun dan hoi cija BTXIVI; j i - he so Poatxfing cua BTXM; b, - chieu rdng l<he niit thif I cOa m|t duang BTCTLT; c - kha nang co lai du'gc cua lihe gian; n - he so d u a c xac dinh theo c6ng thiic (10);

(9) L - chiAu dai tSm BTCTLT

C6ng thiic (14) chi cho b i i t gia tri ling suat ft vi Iri day tam tai mgt c i t giua t i m , c h i i khSng cho biet phan bo l i n g suat theo c h i i u day tam. Neu biit plian (10) bo l i n g s u i t theo chieu day t i m , ta c6 the xac ainli

dup'c gia tri luc nen P.

Ap dung mo hinh trSn cho bai toSn tam BTCTLT chju Trong t^i ii^u [3], khi xet den lu'c ma sat giua day tam

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KHCA HOC - CONG NGH^ aaaaa

vdi nen theo md hinh ma sat Coulomb thi ung s u i t d tam t i m phan bo theo chieu ddy t i m Id d u d n g bde 2 T nhat. Gia tri dng suat kdo d be mat tren Id: o=

' Bh

, . 4T

vd gid trj u n g suat nen d be mgt ddy t i m la: c r ^ = —

B h tdc la gid tri ung suat nen d b l mat ddy t i m g l p 2 lan gia trj dng s u i t keo d be mgt tren eiia t i m . Trong dd: T - l y e ma sat giu'a ddy t i m vdl n i n ; B - chleu rOng t i m ; h - c h i l u ddy t i m

D y a vdo phan b l ung s u i t theo chleu day t i m d mo hinh ma sat Coulomb, ta cd t h l dp dung eho md hinh ma sat Med-nhl-cop. Khi ndy, ung s u i t keo nam d 1/3 chleu day t i m d phia tren vd ung s u i t ndn nam d 2/3 chleu day t i m d phfa d u d i . Gia trj luc ndn P d u p c xdc ffinh theo eong thdc:

1 "B.^h^io 3 3

"Bh (15)

N l u l l y B Id 1 don vl chieu rpng mgt d u d n g thl l y e nen P d u o e xae djnh theo efing thue:

1

(16)

Phdn tieh cong thuc (14), ta t h i y : b i l u thuc dau tien cua v l phai, Id dgi lupng ung s u i t trong t i m , khi b i l n dgng cua tam bj hgn c h l hodn todn; b i l u thuc thu 3, Id dgi l u o n g ung s u i t trong t i m , khi coi khdng efi v l t nirt va eanh t i m khdng c h u y i n dich. Do vdy, gid trj irng s u i t tiep x u l t hidn tgt b l mat day tam vdi be mgt mong d u p c xde djnh theo efing thuc:

T-oAT^E^ !(i). (17)

T u cfing thuc (14), (16) vd (17), tde xde dlnh d u p e lyc nen doe P theo cdng thice:

(18)

Khi nay, dng s u i t trung binh trong t i m do lye dpc t i m gdy ra va d i l u kign d l tam I n djnh dpc dwqic xae djnh theo cong t h d c (19):

.^ -^2b.c

Trong d f i : F - dign tieh t i l t didn ngang cua t i m ; 0,^ - dng s u i t tdl hgn I n djnh eua t i m , d u p c xde djnh theo cfing thdc (2); n ^ - hg so an todn ve on djnh, vdi mat d u d n g BTCTLT, n ^ = 1,2; eae ky hieu khde d u y c gldl thich d cac cdng thuc tren.

Dya vdo cfing thdc (19) ta efi t h l khdo sat trang thdi ung s u i t vd I n djnh dpc cOa mat d u d n g BTCTLT.

4. K H A O S A T TRANG T H A I I > N G S U A T , 6 N OINH D p c MAT Dlf^fNG BTCTLT

Muc tidu khdo sat trgng that ung s u i t vd I n djnh dpc cua mat d u d n g BTCTLT nham tim moi quan hd giua ung s u i t vdi trgng thai mat on djnh dpc cua mat d u d n g trong dieu kien khf hgu Viet Nam.

a. So Iidu dau vao

K i t c l u : tam BTCTLT dgt tren Idp mfing dd dam.

BTXM cfi: E „ = 3,1.10*^ kG/cm^; ^ = 0,15; y = 2,4.10-^

kG/cm^ a = 1.10='mm/mm.°C.

T i m BTCTLT ed: h = 24 cm; b = 0,1 em; e = 1 em.

Mdng: hg so nen C = 12 kG/cm^

Nhigt dp trung binh t i m tang AT^ = 20°C [2], xdt thay d l i nhifit dp trung blnh theo mua trong nam cua tam.

b. Cdc triFdng hap khao sat trang thai ^ng suat va on dmh doc cua t i m

Trw&ng hap 1: thay dol c h i l u dai tam L, n h l m tim moi quan he giua c h i l u ddi t i m L vdi on dfnh dpc eua tam. Trong trudng hpp ndy ehpn gia tri mfi dun can truot k = 2 kG/em'.

Trw&ng hap 2: thay doi gia tri md dun can truot k, nham tim mot quan hg giira mfi dun can t r u y f k vdi dng s u i t vd I n djnh dpc cua t i m , Trong trudng hpp nay, ehpn chleu ddi t i m Id 240 m.

Trw&ng hop 3: thay d l i bten dp dao dpng nhigt dO trung binh cua t i m AT^^, nham tim m i l quan he giua AT,^ vdi ung s u i t va on dinh dgc eiia t i m . Trong trudng hap ndy, ehpn e h i l u dai tam Id 240 m, gid tri mfi dun can truyt k = 2 kG/cm^

c. K i t qua tinh

Trw&ng hap 1: xem bdng 2 va hinh 5.

Bang 2. Kit qud tinh Ong suit nen dgc trye trung binh trong tam khi thay dii chiiu ddi tim

3^(19)

L(m) a (kG/cm^)

50 0,27

75 0,41

100 0,54

150 0,75

200 0,89

240 0,93

I S6 9 ndm 2017

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l l l l l KHOA H(?C - CONG N G H f

-J»,6 5 0,5 S0,4 ^E

.

J £.

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^ ^

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= = - ; .-

trang that m l t I n dlnh dgc cua t i m . Day Id d i l u khi b i t n g d d l i vdi nhfim tae gia.

Trw&ng hgp 3: K i t qua tinh xem bang 4 vd hinh 7, fiang 4. Kit qui tinh ung suit nen dgc true tmng binh trong tam khi thay doi bidn do dao dgng nhi$t

dg trung blnh

t^o,i

25 125 225 Chieu dat lim (m)

Hinh 5. Do thj biiu diin mii quan hg giu'a Ong suit nen dgc true trung binh vol ehiiu dii tim Nhdn xet: ehilu ddi t i m edng ldn, ung s u i t nen dpc true trung binh cdng tang. D i l u nay phii hpp vdi thye t l Id d u d i tde dfing eua nhiet dp tnjng binh trong tdm tang thi tam edng dai, ung s u i t nen dpc true trung blnh cdng ldn; Kht chilu dat tam nho han 100 m, quan he giua ung suat nen dpc true tnjng binh vdi chieu dai tam gan nhu t u y i n tinh, ham quan he y

= 0,0056x - 0,015 vdl hg so tuang quan R^ = 0,999.

Trong do: y - ung s u i t nen dpc true trung binh trong t i m (kG/cm^); x - chieu dai t i m (m). Khi chieu dai tam Idn hon 100 m, quan he giua u n g suat nen dpc true trung btnh vdi chieu ddi tam Id phi t u y i n va gan nhu tiem can vdi dudng ung s u i t nen dpc trye co gtd trj bang 1. Khi ndy, chieu dat tam tang nhung gia trj ung suat ndn dpc trye khdng tang nhieu; Tam m l t I n dinh dpc, khi chieu dai tam dgt den gia trj gan 240 m. Tde Id, khi ndy ung s u i t nen dpc trye trung binh eOa t i m xap xi gid trj dng s u i t cho phep kht xet d i n on djnh dpc. Nhung nghien cuu thyc nghiem eua mOt so nude, n h u : Trung Quoc, Australia, Hoa K;y, v.v... eung cho k i t qud la chieu dai ldn n h i t eua t i m Id 240 m. D i l u ndy, eung dgt cho n i i m tin v l eo s d ly t h u y l t dua ra la tin cay.

Trw&ng hgp 2: K i t qua tinh xem bdng 3 vd hinh 6.

Bang 3. Kit qud tinh ung suat ndn dgc true trung binh trong tam khi thay doi md dun cin trwgt

|k (kG/cm») ]a (kG/cm')

0,75 0,89

1,00 0,90

1.50 0,90

2,00 0,92

3,00 0,92

4.22 0,93 1 n'!**

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Hinh 6. DS thi biiu didn mdi quan he giu'au'ng suit ndn dgc true trung binh vai mo dun cin trwgt Nhgn xet: quan h§ giua u n g s u i t nen dpc trye trung binh vdl mo dun can trupt k g i n n h u khfing doi, cfi nghta la mfi dun can trupt k khfing anh hudng d i n

A T . f C ) a (kG/cm')

15 0,74

20 0,91

25 1,07

30 1 35 1,24 j 1,42

40 1.61 Nhgn xet: quan he giua d n g s u i t nen dpc tRjc tmng blnh vdl bidn dp dao dOng nhigt dfi trung binh c6 dgng t u y i n tfnh, ham quan h§ y = 0,0341x + 0,2279 vdl hg so t u o n g quan R^ = 0,9992. Trong dfi: y - dng s u i t nen dpc trye trung binh (kG/cm^); x - bidn dg dao dOng nhidt dp trung binh cua t i m BTCTLT ("C);

t i m BTCTLT on djnh dpc khi bidn dO dao dfing nhi^t dp trung blnh AT,,, < 20°C v d i chieu ddi t i m la 240 m.

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Cac trudng hop khdo sdt trgng thai ung s u i t vd 6n djnh dpc cCia tam la sat vdi d i l u kidn ldm vlfc thyc eiia mat d u d n g BTCTLT; T i m mat on djnh dpc, khi chleu dat t i m dgt d i n gid tri gan 240 m;

Trong mat d u d n g BTCTLT thl ehilu ddi t i m va thay doi eiia nhigt dp trung blnh tam la 2 dgi luyng Hen quan chinh den on djnh doe cua t i m ; Mfi dun can truot h l u n h u khdng anh hudng d i n trgng thdi m^t on dlnh dpc ciia t i m BTCTLT •

TAl L i e u THAM K H A O

1, Nguyln XuSn D i o (2001). Bao c^o ting kit a l tSi:

"Nghi&n cdu dng dyng cbng ngh# m0t du^ng BTXM it m6i noi, xSy dyng du'dng d p cao d Vi§t Nam". Vi^n Khoa hpc Cong ngh$ GTVT, H6 NOi.

2, NgS H i Son (8/2015). Cfng dyng mat du&ng bfi t6ng xi m^ng c l t thfip lifin tyc trong dt^u ki§n khf h^u Vifit Nam. Hgi ngh| Co' hpc toan quoc \kn thd IX. HS Nfii, 8-9/12/2012. ISBN 978-604-911-431-1.

3. r M. rnytuKOB, B, * . ba6K0B, !\. M. ropeumii, A. C.

CMMPHOB; noa peA T, V\. HnyiuKOBa (1981}, MsbicKaHHfl M npoeiaiipoBaHMe aapoApowoB. M.: TpaHcnopi.

4. AASHTO (1993), AASHTO Guide for Design of Pavement Stmcture. Washington D.C.

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