PIEN DAN KHOA HOC CONG NGHl
THIET KE TOI UU MAlBl/CiNG BE TONG XI M A N G
BANG THUAT TOAN TIEN HOA VI PHAN
OPTIMAL DESIGN OF CEMENT CONCRETE PAVEMENT BY THE DIFFERENTIAL EVOLUTION ALGORITHM TS. BUI D Q C N A N G Hoc vl#n Ky thuat quan sii
T6m tit: Thiet 1(1 cdu tao mat diffing (ciJng ho|c m^m) thifdng thi/c hi^n theo phi/dng phip "thiJ - sai". Mac id ift phi/ong phdp 6on giSn, de ap dyng nhimg rit khd iJ^t diffjc mpt phiWng an tli IAJ V^ chilu day cho tat cS cac Wp. Tren cfli;
sd Vi du tlii^t k^ ddn gian la mat di/Ong cilng be tdng xi mang, bai bao trinh bay mdt each tilp can mdi kht thi^t l(^ chiSu day cac !()p sao cho chi ph( thdp nhk ThuSt toan toi i/u diwc siJ dung la thuat toan tiln hda vi phSn (Differential Evolution - DE). Day la mot trong nhdng thuat toSn tii lAi iJi/dc (janh gia la tin c§y, co t8c (36 hpi tu nhanh va cd kha nang gi3i bii toan tdi liU toan cue b^ng phuong phap sd.
Tfif kh6a: mat iJifdng b6 tdng xi mang, t6i Uu, tien hda vi phSn
Abstract: Usually design of pavement sb-ucture (hard or soft) are performed by the method of "trial - error". Although the method is simple, easy to apply but very difficult to achieve an optimal schemes of thickness for all grades. Through a simple example is the design of cement concrete pavement, the paper presents a n&N approach to the design thickness of the layer so that the lowest cost. The differential evolution algorithm (DE) selected for use. This is one of the opfimlzation algorithm is considered reliable, fast convergence speed and has the ability to solve global optimization problems by numerical meUtods.
Keywords: Cement concrete pavement. Optimization, Differential Evolution
L M d d l u
Nhu cdu xdy di^g nhung cdng trinh dudng, sdn bay cd dd tin cdy cao, tidt kidm id mOt ddi hdi trong qud trinh phdt then. Vipc Idm hdi hda hai tidu chf ndy chi cd thi dupc gidi quydt khi si> ly ddng thdi trong qud trinh tfnh todn thidt kd. Bdi toan thidt kd mdt dudng Cling thuc chdt Id xdc dinh chidu day Idp mat dufimg bd tdng xi mdng khdng hodc cd edt thdp. Cdc tinh todn chu ydu ehl thuc hidn vdi Idp mat, chidu day tijng Idp mdng thudng khdng tinh toan md chpn theo kinh nghidm da cho trong cdc tieu chuin hodc tai lieu hudrig ddn thldt kd. Mac dij iy thuydt da chi ra mdi
quan he mat thidt giQa chidu day Idp be tdng vd Ccic Idp mong song de cd mdt td hpp chidu day tdi lAi cDa cdc Idp chua thdy tdi lidu ndo dd cap mpt cdch chi ti^,
Vide t'lm mdt to hop chidu ddy cua cdc Idp m^
dudng sao cho ddm bdo edc ydu cdu thidt kd viSi chi phf nhd nhdt Id muc tidu cua nghien ciJru ndy Npi dung bdi bdo se trinh bdy tdm tdt cd sd IJ thuylt xay di^g hdm mgc tieu, cac didu kidn rdng budc va thu$t to^
tdi uu kdt cdu mat dudng vdi chi phf vat lieu Id tdi thifti theo cdc tidu chuan thidt kd mat ducmg cufng. Qui trinh tdi uu duoc thuc hidn bdng thudt todn tidn h6avi phdn (DE), ddy la mdt trong nhiJng thudt todn t6i lAi
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Tflm M tflng )d mflng pote larq)
^ ^ ' TBhJyduOnadto [ThoUnjOcng&n f i d hop)
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Hinh 1. Ciu tao dien hinh cua mit dUSng cOng bi tdng xi mang Ididng c6 dai phan cich NGUOI XAY DUNG SO THANG 5 & 6 - 2015
THIJT KE TOI Ou MAT DlfdNG BE T 6 N G XI MANG...
todn cue tin cay, cd tdc dp hdi tu cao thupc ldp cdc thudt todn tdi uu tidn hda.
2. Xay di/ng bai todn tdi i/u thilt kd mat du'dng bg tdng xi mang (BTXIUI)
£)e ddn gian cho tinh toan nhung khdng giam tinh t6ng qudt ta xet kdt cdu mat dudng BTXM cd chidu ddi Id a, chidu r^ng Id b ddt tu do trdn ndn hai Idp mdng ddn hdi. Nhodd bidt, ldp chju Igc chfnh Id ldp bd tdng mat dudng, tuy nhien khd nang ndy phu thude nhidu vdo chidu ddy vd tfnh chdt eo ly cCia cac Idp mdng. Ky hidu:
h,E,^l- Ldn lupt Id chidu ddy, modun dan hdi, he sd poisson cua Idp be tdng.
Hi, Ei, ^1 - Ld chidu day, mddun dan hdi, he s6 poisson cua Idp mdng trdn.
Ha, Eg, fia - Ld chidu day, mddun dan hoi, he s6 poisson cua Idp mdng dudi.
En, ^n - Ld modun ddn hdi, hd s6 poisson cua tdp ddt ndn.
c, c,, Ca - Ld chi phf de thi cdng 1 don vj dien tich mdi Idp cd chidu ddy 1 don vj ddi (ddng/m^). Chi phf ndy bao gom chi phf vdt lidu, mdy, nhan cdng vd mpi khodn chi khde.
Nhu vdy tong chi phf d^ hodn thdnh mdt don vj didn tfch mdt dodng se Id:
T^ = ch + c,h, + Czhs (1) Trong tnjftmg hpp ndy bdi todn tdi uu eo th^ sir
dyng bilu thtirc (1) Idm hdm muc tidu, ed nghTa la cdn ,,ehpn chidu ddy mdi Idp sao cho tdng chi phi la nhd j,nh^t vdi edc didu kidn rdng budc vd hinh hpe vd co
- Dieu kidn rang budc vd hlnh hoc: Chieu day mdi i. Idp phdi nam trong gidi han cho phep theo ydu chxx icua cdc tieu chuan thidt kd hidn hdnh:
I hu<h,£hsi (2) hy - Gidi h^n dudi cOa chidu ddy Idp thiJr i
hei - Gidi h^n trdn ciJa chidu ddy Idp thur i.
- Didu kidn rdng budc ve co hoc: Tong ung sudt cue
"•^d^i sinh ra do tai trpng khai thdc vd cdc ydu td khde khdng vuot qud gia tri cho phdp:
^ o < [ o ] (3) Di dam bdo dieu ki^n rdng budc vd dp bdn (3) ta
phdi tfnh gid trj cua edc thanh ph^n Cing sudt sinh ra t^i ede di^m nguy hiem cua tdm be tdng khi chiu tdi :rpng.
3. CO sd tmh todn iPng suat tdm be tdng tren i^n dan h6i
J, 3.1. Tinh theo chi tidu ifng suit keo uon cua Westergaad [4]
- Tdi trpng ddt d tdm tdm, dng sudt keo udn sinh ra y ddy tdm:
' -, =0.275(1..)^ J ^
m
- TSi trong dat d cgnh tSm (bi§n tir do), ijmg suit \dn
nhit xuit hien d day tdm ngay dudi vj tri dat tai
<7„=0.529(l + 0.54/i)^lg -0.71
(5) E, - Modun dan h6i, he so poisson cua t§m b§tong
CM - He s6 nhn tucfng ducfng cua m6ng v^ n^n b - tham s6 duoc tfnh theo cong thut
b = ^l.6r^ + h^-0.615h khir<\.12Ah
Uii r>l.724h
(6)r - V^t banh xe quy ddi xac djnh theo tSi trgng banh xe ti^u chuin:
Di^u l<ign b§n ddi vcri mat du£mg be tong:
MaxfCT,, <T,i) < [o] (7) 3.2. Xac djnh he so nen Ufang dif ang
Khi sCf dung mo hinh mot he s6 n§n, vdi n4n hai Idp c4n x^c dinh he s6 n4n tucmg ducmg ta sir dung bieu thiic sau:
_C,+C,a,+C,a,
C1, C2, C3 - Hd s6 ndn cua Idp thur nhdt, thu- 2 vd Idp ndn tu nhidn
h^\\.6D^~(h,-¥Q.5h^)']
0.5[l.6D^-(h^+h,)f
(9)
(10) D, - Dudng kfnh dudng tron quy udc dien tieh truydn tai xudng ndn, vdi ndn dudng d td thudng D, = 2,2m.
4. Thuat toan tidn hda vi phan vd i^ng dung giai bai toan thilt ke toi u'u mait durdng BTXIUI
4.1. Thuat toin toi i/u tien hda
Thuat todn tdi uu tidn hda dude xay dung tren md phong mdt s6 qud trinh phdt trien tu nhidn md trudc tidn Id quy ludt tiln hda. Kdt hop vdi khd nang cCia cac thd he mdy tfnh hien dai md Idp thudt toan tdi uu ndy phat trien khong ngCmg va chung td Id nhOng thudt toan du kha nang tim dUdc nghiem tdi uu toan cue cua nhung bdi todn khd vupt qua khd ndng giai ci!ia cdc phuong phdp gidi tfch. Hai khai nidm cdn duoc lam rd trong cdc thudt todn tdi uu tidn hda Id:
- Cd thi: Ld mdt phuong an nghidm thoa mdn tdt ca cdc didu kidn rdng bude vdi gid trj ham muc tidu f(xj) ndo dd.
- Qudn thd: Ld mdt tap hpp cdc cd thi vdi mdt sd luong nhdt djnh.
Qud trinh tim nghiem tdi uu cua thudt toan tidn hda thudng thuc hidn cdc todn tir co bdn: Lai ghdp, dot NGUOI XAY DIMG SO THANG 5 & 6 - 2015
THIJT KE T 6 I lAJ MAT eUClNG BE TONG XI MANG
bidn, lua chpn, tdi sinh. Ld duong nhidn cdc todn t d nay thyc hien trong mot hodc mpt vai qudn the xdc djnh. Chfnh didu nay tao ra s y khac bidt Idn giiia thudt toan tidn hda vdi cac thuat todn tdi uu truydn thdng.
Cho ddn nay ed the ke ddn mdt sd thudt todn da dupc cac tac gid trong nude sir dung de gldi bdi toan tdi uu trong ky thudt: Thuat toan GA (Genetic Angorithm), thuat todn tidn hoa vi phdn DE (Differential Evolution), thudt todn tdi uu dam hat PSO (Partieal Sw/arm Optimization)...
4.2. Ngi dung thuit toin tdi t/u tien hda viphin DE (Differential Evoiutlon)[3J
Tren co sd y tudng cua thuat toan GA, ndm 1995, Rainer Storn va Kenneth Price dd dd xudt mdt thudt todn mdi vdi tdn goi Id Differential Evolusion - DE. Mdc dCi thudt todn vdn bao gdm edc toan tCr eo ban nhu GA nhung ndi dung eua mdi todn tis da duoc thay ddi.
Thudt todn DE khong xCr ly tisng hit trdn chudi 'GEN' nhu GA, d l ed ca the mdi DE sir dung thdng tin cua nhidu cd the duoc chpn ngdu nhidn. Didu khde bidt nQa cCia DE Id Idm viee ddng thdi tren hai qudn the do dd nd khde phuc dupc nhidu nhupc diem cua GA vd tao ra mOt thudt todn mdi tin edy vdi tde dd hOi tu cao hdn. Phien ban ddu tidn thudt todn DE dUdc trinh bay (DE/rand/1/bin) cd ndi dung nho sau:
' Xiy dung quan the ban diu. [X]g_i duoc xdy dung ngdu nhidn trong midn cho phdp cua cdc bidn dpc ldp theo cdng thuc (11)
x„ = rand{0,1) "(bu, - d y + bl, (11) X,, - 1 ^ bidn j cua ed t h i i thupc qudn t h i [X] vdi i
= 1 , 2 np; np - T o n g sd cdc cd the; j = 1, 2,..., nx;
(nx - Tdng sd cae bidn); rand (0,1) - Sd ngdu nhidn
phdn bd ddu trong khoang (0,1); bUj vd bij - Gidi hgn trdn va gidi han dudi cua bidn thijf j .
' Dot bidn: Todn t i l ddt bidn se tao ra qudn t h i (Vt tL/[X]g theo cdng thiic (12):
v„ = x^,-i-F'(x,,i-x^J _ (12) Vdi F - h e sd td hop sai sd F = (0,1.0) va i ?; rj, * r,
^ ^2, i - Chi sd xac dfnh cd the thur i trong qudn ttie ma [V]g; fo, r,, r^ - Chi sd cua ba ca the duoc chgn ngju nhien trong qudn the [X]g;
• Lai ghep: Trdn co s d hai qudn t h i [X]g vd [V]g ti^r hdnh lai ghep theo cdng thute (13) ta dupc qudn thi mdi [U]g:
_ifrand(0,l)<C^
r j = rand{nx) ,; otherwise
{13}
Vdi C, = (0,1) id xdc sudt lai ghdp; rand(nx) - Sfl ngdu nhien phdn bd ddu trong tap [ 1 , nx].
* Chon loc: Trdn co s d hai qudn the [X\ va [U]g tiSn hdnh chpn Ipe (cho bdi toan tim c i ^ tieu) theo cflng thijfc (11) ta duoc qudn the [Y]g bao gdm cac ca the c6 gid trj ham nhd hdn.
u,uf nu,j)<nx„)
X,,; otherwise
(14)
' Tii sinh: Thgc hidn phdp gdn [X]g^, = [Y]g ta 6\S(fa thd he he mdi. Qud trinh tidn hda sd lap lai tis b\S(K 1 cho ddn khi c^du kien dimg thda mdn.
Cho ddn nay ndi dung eua thudt todn DE theo 5
Hinh 2. Sd dd mieu ti hoat ddng cua thuit toin DE
N G U O I XAY D U N G SO T H A N G 5 & 6 - 2 0 1 5
THIET KE T 6 | U U MAT flUClNG BE TONG XI MANG...
budc trdn la thuat todn co s d cho mpi cai tidn khac vd dupc xem Id DE tidu chu^n (DE Standar).
* DiSu Iden ddng : Qud trinh tim nghidm tdi uu se kdt thuc khi thda man didu kidn:
/(-•L Z/(-), <£; (15)
Cdng thiic trdn cd nghTa tdt cd ede ed the (np) cua qudn the da hdi t u , mite dp hpi tu ttiy thudc vdo gia tn ( t h u d n g = 10"*-^ 10-").
4.3. lfng dung giai bai toan thiet ki tdi i/u mat dif dng BTXh/l
Bdi todn (1) vdi cdc didu kien rdng buoc (2), (3) cd the gidi bdng thudt todn DE. T h i r t y eac budc nhu sau:
Budc 1: Xdy dyng qudn the ban ddu, chpn ngdu nhien chidu ddy tdm bd tdng vd cdc idp mdng trong gidi han cho phdp. K i l m tra gid trj img sudt theo cdng thuc (4) & (5). Ndu nhd hon gid tri cho phep ta cd mdt phuong dn thidt kd. Tfnh gid trj hdm theo cdng thiic (1). Budc 1 k i t thiie khi da 6ii sd cd the cdn thidt.
Thudng sd cd t h i np > 6.nx - vdi nx Id s6 bidn thidt kd.
Sau budc 1 ta cd qudn the ban dku [X].
SutSe 2 ; Sif dung bieu thiic (12) thuc hien qua trinh dot bien qudn the [X] de dupc qudn the mdi [V]. Cae ca the cua qudn the [V] cung sd dupc k i l m tra xem cd thda man cdc didu kidn rdng budc hay khdng. Ndu khdng thda mdn qud trinh dot bidn sd thyc hidn lai.
Budc 3: Qua trinh lai ghdp giiia qudn the [X] & [V]
dUPC thuc hidn theo cdng thiJic (13). Khi lai ghdp gia tn cdc bidn thay ddi ndn cung cdn k i l m tra cac didu kien rdng budc cho mdi phuong an. Ndu khong thoa man, qud trinh lai ghdp phai thyc hidn l^i. Sau lai ghep ta duoc qudn t h i [U].
Budc 4: Chpn Ipc, chpn trong hai qudn the [X] & [U]
nhiing cd the tdt hdn de tao ra qudn the mdi [Y].
Budc 5: Tai sinh, kiem tra didu kien dyng theo b i l u thiJC (14) ddi vdi qudn the [Y]. N l u thda mdn qud trinh tim k i l m k i t thiic, ndu khdng eho [X]=(Y] va ldp lai t y budc 2.
Trdn c d s d nam budc tfnh todn trinh bdy tren vd eac edng thiic giai tfch tfnh toan bdn cho tdm be tdng, nhdm nghidn CUTJ da tidn hdnh ldp trinh d l tfnh todn.
Chuong trinh tfnh ed tdn Opt_Pavement dope vidt trdn ngdn n g y c + + .
5. Vl du s o
5.1. Cic so lieu ban dau
T h i l t kd tdi uu tdm BTXM mdc M300/40 (cudng dp kdo udn tfnh todn tuong iing Id 20 daN/cmO; Kfch thudc tdm 4,75m x 3,5m; Md dun ddn hdi E, = 275000 daN/cm^; He sd Poisson ^ i , = 0.15; canh tdm Id c^nh t y d o .
- Ldp 1: Cdp phdi dd dam lo^i I gia c6 vifrt xi mdng, mddun ddn hdi E j =48000 daN/cm^ He sd Poisson ^ i .
= 0,15.
- Ldp 2: Cdp p h l i da dam loai II, mddun ddn hdi Eg
= 1000 daN/cm^ Hd sd Poisson fia = 0.''5- - Ldp ndn cd mddun ddn hdi E3 = 400 daN/cm^; Hd sd Poisson ^3 = 0,25.
- Tdi trpng true xe tfnh todn, P = 10000 daN.
- Oudng kfnh vet banh xe tfnh todn, D = 33em.
Cac thanh phdn chi phf:
- Odl vdl ldp be tdng mat e = 1.200.000 d/m';
- Ddi vdi Idp mong trdn c, = 650.000 d/m^
- Ddi vdi Idp mong dudi Cg = 350.000 d/m^
5.2. Kit qua tfnh
Vdi cdc thdng sd ban ddu nhu tren da sir dung chuong trinh Opt_Pavement de tim chidu day cua cdc Idp vdi chi phf thdp nhdt. Sd ca the cua qudn t h i Id 25, hd sd td hdp F=0,85 vd xdc sudt lai ghdp la 0,25. Vdi d i l u kidn dCmg Id 0,005 cua tdng chi phf nhd nhdt, qud trinh tim kidm se dimg sau khoang 50 ldn tidn hda.
Phuong an eudi cung cd cdc thdng sd nhu sau:
- Chidu ddy Idp bd tong mat: 22cm - Chidu ddy Idp mdng trdn: 15em - C h i l u ddy Idp mdng dudi: 35em - T o n g chi phf: 496.818 6/rrP
- Qng suat kdo udn cyc dai: 16,708 daN/cm^
Kdt qud trdn tuc^g duong vdi kdt qud tfnh theo tdi lidu [2] khi k i t cdu mat dudng BTXIVI M350/45 chi cd ldp mdng tren day 15cm (Dudng Hd Chf Minh doan Km305 -e- Km357+800), ifng sudt cUC dai tai tdm tdm Id 17,52 daN/cm^
6. Ket luan
Bdng each dua thudt todn tdi uu vao qud trinh thidt kd trong thdi gian ngdn tdc gid dd chi ra duoc mpt td hop chidu ddy eae Idp mdt dudng bd tdng xi mdng dam bao d i l u kidn b i n vdi chi phf tdi thieu. Tren co s d k i t qua nay cd t h i bd sung nhijng phUdng phdp tfnh todn vdi dd chfnh xdc cao hon vd phdt t r i l n d l thidt kd mdt dudng m i m vd mat dudng cirng theo tidu e h u i n dd tin cdy.Q
Tai lieu Iham khdo:
1. BO Giao thflng Van xii (1998), Tieu chuin thik ke io dddng cdng dddng d td 22TCN223-95. NXB, Giao thflng vSn tai. Hi Nfli.
2. Nguyin Ho^ng Long (2011), Nghidn cdu mdt s6 van de ve dd tin ciy cua mit du&ng 6 to vi sin bay, Luan in Ti^n sl ky thuat, Hpe vi6n laos.
3. Bill DtJc NSng. I>lguyln Quin Thang (2012), 'Tinh toan tdidu kit cau khung bi tdng cot thip cho cong trinh khu vdc bien B6ng • hii dao CO ke dSn tic ddng cua mdi tnidng", Tuyen tap cong trinh khoa tioc Hpi nghi cd hgc to^n qu6c iSn thil 9, TSp 2. Cp hoc vat ran bi^n d a n g - P h ^ n II, tr. 472-751,
4. Pham Cao ThSng (2014), Tinh toin thiet k^ cic kit ciu mit dddng. NXB xay dung, Ha Noi.
5. T S. Willlian (1990), Analysis ol Plate on Elastic Foundations, Dissertation Doctor of Philosophy in Civil Engineering, Taxas Tech University.
N G U d i X A Y D U N G s 6 T H A N G 5 & 6 • 2 0 1 5