KHOA HQC - CONG NGHE
NGHIEN CUfU XAC DINH HE SO NHQlT NEN DlTfllNG 0 TO BANG THlTC NGHIEM
• •
Tom tit: V$t liiu dit ndi chung vi dit nin dtfdng d td ndi riing cd tinh din nhdt (biin dang chim pha so vdi tii trpng tic dpng). Khi tinh toin kit ciu mit dtfdng vdi tii trpng tfnh ho$c gii tfnh tinh chit niy thtfdng chtfa dupc ki din (coi r^n Ii vit lidu din hii).
Tuy nhidn, trong cic bii toin ding, tinh chit din nhdt cOa dit nin cin phii dupc xit din di md ti sit thtfc hdn phin tfng cda nin mdng dUdng dUdi tic dtfng cda tii trpng d0ng binh xe. Trong bii bio niy, cic tic gii trinh biy cP sd ly thuyit vi trinh ttf xic djnh hi si nhdt nin dtfdng d td tfng xtf theo md hinh Kelvin - Voight tfng dpng cdng nghi "Phin tich phi sing bS mit • Spectral analysis surface wave - SASW"lim cin ctf Itfa chpn thdng si diu vio khi tinh toin kit du io dtfdng d td vi sin tmy chiu tii trpng ddng ctfa phtfdng tiin khai thic.
I . D i t v i n d l
Mdt trong nhUng ylu td quan trpng inh hUdng din ttnh chfnh xic cda b i i toin tUdng t i c glda k i t clu vdl mdi trudng I i su phd hpp cda cic thdng s6 dlu vio, trong dd eic die trung cd ly cda mdi trudng ddng vai trd rlt quan trpng nhlt I i khi k i t c l u chju t i i trpng d$ng. d Viit Nam hiin nay, cic nghiin cdu xic djnh cic die trung cd hpc ddng eua d i t (hi s l nhdt, mddun d i n h6i...) chua dUpc quan t i m diy dd m i phin Idn phii tham khio cic k i t q u i thgc nghidm cda nude ngoii nin chua thit phu hpp vdl dllu ki$n cg t h l cda nudc ta. Do dd, v i n d l nghidn cdu thgc nghiim nhim xie dinh cic die trung co hpc ddng cCia cic logi d i t xiy dgng ndi chung va d i t nln dudng ndi riing I i rlt cin thilt. Bii bio trinh biy k i t qui nghiin cdu thgc nghiim xic djnh mddun din hdi v i h i s6 nhdt cua dit nln dUdng d td.
2. Cd sd khoa hpc
D l md t i cic phin dng phg thudc thdi gian cCia nln dit khi kit clu mit dudng chju t i i trpng ddng, cin phii bilt cic chl tidu md t i tinh chit ddng Itfc hpc cda nln.
Nhilu thuc nghl$m da chdng td ring, nln dit dudi i o dudng d td I i vit liiu d i n nhdt - biln dgng cOa n l n chim so vdi pha eiia p t i i trpng tie dgng. Hiin | nay cd nhilu md hinh md
t i tfnh d i n nhdt ciia v i t liiu: md hinh Maxwell, md hinh Kelvin, md hinh Berger... Trong dd, md hinh Kelvin thudng dupe chpn trong tfnh toin k i t c l u i o
NCS. TRAN THI THU TRANG PGS.TS. PHf M CAO THANG TS. NGUYEN Tl/ONG LAI Hgc viin Ky thuit Quin stf ddng vi nd ddn giin trong tfnh toin ma v i n cd t h l md t i t i t die tfnh biln dgng "trS" eda v i t liiu. Hai tham s l CP bin cda md hinh n l n Kelvin I i h i sd dd cdng 0 v i h$ sd nhdt cda d i t (hinh 1). Khi n l n din nhdt Kelvin dao ddng tu do, phUdng trinh vi phin dao ddng cda nln cd dgng:
mx-\-Tjx+Cx = 0 0) Vdl x v i m lin lupt I i chuyin vj v i khil lupng dao
d$ng cda nln.
Nghiim cda (1) cd dgng:
X = Ae""' sin {Q)J + ^ ) (2) Trong dd:
a I i h i s l glim biin dd hay dd c i n dao d$ng
cda h i , xic djnh theo [6]; « - — (3a) cofj la t i n s l dao ddng tu do cd ein eda h i ,
Q)d=i^-a^ (3b) vdi ^0 I i t i n s l dao d$ng rldng ciia h i ,
9 I i gdc pha dao ddng cda h i ,
Dd thj cOa (2) cd dgng nhu trong hinh 2, vdl sU tit dao ddng cda h i dupe djnh lupng qua t$' s l glda hai
^
biin dd Ilin tilp: (4)
vdl S l i dd glim Idga biin d$ dao ddng cCia h§.
H i s l nhdt cOa mdt trUdng thf nghl|m xic djnh
nhd h§ thdc, [6]: S = ^'^'^'' (5) E
x(0) = i „ vi i(0) = v.
Hinh 2. Dao ding ttf do ci cin: diiu klin diu Jc(0) = Jr„ v i i ( 0 ) = v„
Trin cd sd thdng tin v i sU tit dao ddng thu dUdc tu tip sS liiu ghi bdi cic thlit bi nhin, tU thuc nghiim dudng d td chiu t i l trong/flnft /. Md hinh nin Kelvin hiin trudng, cd t h i xic dinh duoc dd glim idga v i
Tgp chl GTVT 3/2012
t i n s l dao d$ng tg do ciia nln thuc. Bllt md dun dan hdi E, thdng qua (5) hoin toin cd t h l xic djnh dupc h i s l nhdt cda nln nhd cdng thdc;
S.E , „ , rj= (6)
rr.0}^
vdi md dun d i n hdi E cda nln, xac dinh thdng qua md dun trupt v i h$ s l Polsson fi theo hd thUc:
IT g
2(1 + //) *"
trong mdi trudng ddng nhlt v i ding hudng, mddun trupt, G, dupe xic djnh bing cdng ttidc:
G=pyl (8)
vdl p, Vs iln lupt l i mit dd khii v i vin toe truyin sdng c i t trong n l n , xic djnh bing thuc nghiim.
3. Xic d)nh mo dun dan hdi cda n l n b i n g thi nghl$m p h i n tfch phS sdng b l mgt
3.1. Cdsdl^ thuyit
Trong mdt b i n khdng gian hai ldp gim: Mdt Idp hdu hgn trin m$t mdi trudng bin vd hgn, cic cdng thde giil tfch cda sU truyin sdng Rayleigh r l t phUe tgp. Tuy nhiin, cic tinh chit din hii cda Idp trin cd t h l x i c djnh td dd liiu cDa t i n s l cao (budc sdng ngin), cdn cic tfnh chit din hii cua mdi trudng b i n dUdl Igi nhin dUpc td dO ll$u t i n s l thlp (budc sdng dii) - tfnh chit t i n sic, [2].
Trong mil trUdng ding nhlt v i dSng hudng, vin tic truyin sdng b l mit l i hing s l . Do dd, nlu sdng b l m$t truyin trong bin khdng gian phin ldp theo phUdng dUng thl d l thj tin sic eCia sdng sd cd dgng nhu hinh 3. Chd y ring cic phgm vi cd vin t i c sdng hiu nhu khdng d l i md t i hiin tupng sdng truyin trong c i c ldp khic nhau. Chilu siu cda b l mit chuyin tilp glda cic ldp dd dUpc xem gin dung bing 1/2 chilu d i i sdng tgi vj trf chuyin tilp eda g i i trj vin tic sdng trin d l thj t i n sic [5]. Sd dTcd t h l lly gin diing nhu viy l i vl tfn hllu thu dupe la tr$i nhlt khi Ung vdl mdt dfnh sdng cOa t i n s l ed budc sdng dai nhit trong Idp m i sdng truyin qua nhu hinh 3.
v^ fp^
Hinh 3. Stf tin sic sdng bi mit trong bin khdng gian phin Idp
MUC nUde ngim trong dit dgng hgt tgo thinh md*
mit chuyin tilp d l i vdi sdng ndn, nhung cic sdng Rayleigh bj t i e ddng khdng nhilu bdi mUc nude ngim, bdi vl nudc Id rdng khdng truyin sU trUdt.
NghTa ta nUdc id rdng trong dit khdng lam i n h hudng tdl k i t qui thf nghiim khio s i t sdng be mit.
3.2. Thf nghi$m phin tich phasing tti mit PhUdng phip phin tfch phi sdng be mit dupc sd dgng nhu l i mdt phUdng phap thf nghidm khdng phi hdy d l xic dinh hd sd (profile) v l md dun dan hdi cho nln dit phan ldp. De tlln hinh thf nghiem nay, m$t nguon nhieu dpng dupc d i t trin b l mat nen (biin cda b i n khong gian) d l tgo ra sdng Ung suit m i hlu h i t la truyen dudl dgng sdng b l mat vdi cac bgdc sdng khac nhau. Cic sdng niy dupc hien thj v i thu thip thdng qua mdt h i thing thu dd lieu sdng tgi hiln trudng (nhu hinh 4). Cac phan tich tfn hieu v i phin tfch phi sdng b l m§t dUpe thUe hidn d l xiy dung m^t dd thj -tan sac (md t i stf biln thlin ciia v i n tie pha theo chieu d i i sdng hoic theo tan so).
P o r t a b I * Micro Cocnputw
I T t k t r o n i x Fourtor I Analyzttr
Hinh 4. Sd di m^ch lip dit thlit bl thi nghiim SASW
3.2.1. Trinh ttf thl nghidm vi thu th$p dtf liiu hidn trudng
Di tlln hanh hoin chlnh mdt thf nghidm SASW cln qua 3 bude cd bin nhU sau:
- Thu thip dd lllu hiin trudng;
- Xd ly dd ll|u thd d l xiy dUng d l thj tan sic;
- Xic djnh vin tic tnjyIn sdng cda cic ldp khic nhau trong nln nhd dd thj tin sic.
Theo trinh tg trin, mdt nguin nhlSu ddng dupc giy ra trin mit dit d l tgo ra t i p hpp cic sdng b l mit cd tan so khic nhau trong nln. Hal hoic nhilu thilt bj thu sdng (receiver) dupc b l tri trdn mit d i t d nhdng khoing cich cich dlu nhau td dudng tam cda ngudn nhiSu. Nguin nhilu dupe chpn nin l i nguin tgo ra nhilu sdng Rayleigh truyin trin b l m i t [3]
n l n . Bda IUc l i mdt trong nhdng thilt bj g i y nhilu hay dupe sd dgng trong cac thf nghl|m SASW do dip Ung dupc yiu clu tren, Igi d l sd dgng, gpn ging d l v i n chuyin trong qua trinh thf nghiim tgi hiin tnidng.
So do bd trf thilt bj eo t h l dupc b l trf theo mdt trong hai cich nhu bilu dlln trong hinh 5, d l ning cao chit lupng dudng cong t i n xg thUe nghidm v i thuin lpi cho qui trinh tg d|ng hda xd ly s l lidu sau niy [3,4].
Mli mdt khoing cich b l trf thilt bj, tiln hanh g i y xung ddng trdn mit nln r l i thu thap va ghi dd liiu d l dung cho budc xd ly tilp theo.
3.2.2. XCe 19 si liiu thl nghiim vi kit qui thu dupc a. Xiy dtfng dd thj tin sic thtfc nghiim
Nhu da gldl thilu d trin, dU lj$u hidn trudng cung
KHOA HQC - CdNG NGHE
^ ^
^ z E i : X
Dol vdi m5l mdt t i n s l f. pha (*, dUpe lly tU phi ning lupng chio. Phi chdo la mgt tham s6 ed gli tr|
phUc. Do dd, gdc pha dupe tfnh theo cdng thUe; -
Hinh 5. Sd di bi tri thiit bi do t^i hiin trudng thf nghiim SASW
c l p cic thdng tin v l pha cda p h i ning lUpng chio v i cic him tUdng quan tU cic t i p dd li^u gN d cic khoing cich b l trf thilt bj nhin khic nhau.
Pho ning lupng chio v i him tUdng quan gida eic b i n ghi td hai d i u do dUpe tinh toan d l ddng trong eic thuit toin xd ly tfn hiiu [4].
Gpi r-f (t) v i r-| (t) l i cae bin ghi phg thuQc thdi gian thu thip tU hai d i u do dit each nhau mdt khoing D.
Phi chio glda hai tfn hiiu do xic djnh tiieo edng thde:
KrSf) = •^Z{[«.(A]-[«2'(/),]} (9)
trong dd:
^]{f) ^if) lln lupt la biln doi Fourier rdi rgc ciia r-| (t) v i r2(t). G l i sd cd tip dO li$u rdi rgc r^
(n = 1, 2, ..., N), khai thin Fourier rdi rgc cda t i p rp xic djnh theo cdng thUe:
R,(f) = f,r„.cxp^-2m^'^ (10) vdl k = 1, 2 N v i N l i s l dilm ciia tip dU ll^u r(t);
Ky hiiu ggch ngang bin trdn p h i chio 5"^.^, ( / ) l i ai ChT g l i trj trung binh phg thudc t i n s l cda mdt v i i bin ghi tUPng tg;
Tham s l n l i s l bin ghi dUpc ddng d l xic djnh gli trj trung binh. Dlu * d phfa trdn /?2(/) chl phin i o cda dgl lupng tfnh toin.
Khi dd, him tuong quan, y^{f) dupe xie djnh theo cdng thdc:
2(^)^3iM_ (11)
^,(/H(/)
trong dd ^ , ( / ) va A-2 \f> tUdng dng la cic gla tri trung binh cda mit dd phi tU cic thilt bj nhin 1 v i 2, xic djnh theo edng thdc:
4(/)=-Z{[«(/).]-[«'(/),]}
(12)4.00
^ 2.00
— ooo S -2 0 0 0 * 0 -
-4.00
• " i / ^ ^
Thdi gian (a) Hinh 6: DQ li^u tfiu ao 1 adt c&ch nauin chin tfdna 1ft
^- tan'
3S,„,(/)
(13)trong dd: til sd va miu s6 lin iUdt i i phin i o v i phin thuc cOa phd chio.
TO thdng tin v i pha, thdi gian tdl dUdc tinh theo cdng thUc:
( = — ^ (14) 360./
V i vin tde pha cd t h l nhin dUdc tU cdng thUc:
(15) vdi D l i khoing each giUa cic thiit bi nhin.
Chiiu d i i sdng (budc sdng) quan h i vdi vin tde pha v i t i n s5 qua cdng thilc:
Nhu viy, nlu b i l l pha v i tan s l , cd the tfnh dUpc v i n tic pha ddng cic edng thdc (14) v i (15).
T i p hpp dU liiu hien trudng bj trQn bdi cic tfn hiiu nhlSu. Do dd cln phil xie djnh dU liiu pha da dUpc c i t bdt trong d i i t i n s l cda tfn hi|u nhilu d l xiy dgng d l thj t i n sic. Him tUdng quan, y, dupe dClng cho mgc dfch niy. Ham tudng quan cd g i i trj td 0 - 1 trong d i i t i n s l khio sit. G i i trj 1 eh? sU tudng quan ly tudng glda eic tfn hiiu ghi dupe, cdn gii trj 0 cfia ham niy t h l hiin su khdng tUdng ding gtUa cic tfn hiiu dd. DU lidu pha ed t^dng quan thlp dUpe logi b6 khdi vi^c xiy dgng d l thj t i n sic.
b. Si liiu khio sit vi kit qui thu dupc - Dja diim: Sin v i n ddng khu 361 -Hpc viin KTQS - Hoing QuIe Vlit - C l u Glly - H i Ndi;
- Logi d i t n l n : Dat i sdt, dd I m tU nhiin chUa xac djnh;
- Thilt bj thf nghiim: Bing 1 s x r
1 2 3 4 5
I j O i ^ l T H l E l T B I Miiy d o d^ng da nSng NI
scja-iax)E>c Bli a h/c P C B 086C42 Bflu do eia tde PCB 353B33
M^v linh xdch tav Lenovo FtiSn mSm thu vii xfl- ly Ifn
l i e u L.abview3.0 s6 IAS0NG
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5 -ZOO-'— ' TttHi gian (•) Hinh T: DO ll^u aiu do 2 a$t c6ch aiu ao thCr nhUt 1ft Bang 1. Thing ki thlit bi thl nghiim - Sd do thi nghiim: nhu hinh 5a;
- S l lieu thf nghiim do dgc tgl hiin trudng vdl khoing cich b l trf thilt bj l i 1ft (0,3048 m) t h l hiin trong hinh 6 va 7.
T9P chl GTVT 3/2012
M i t dd phi ning lupng cda hai tfn hiiu thu dupc td hai d i u do xic djnh theo cic cdng thdc (9) v i (10) bilu diln d bilu d l hinh 8.
S 01
- as 1 at
a n
_ 1 - ^ ^ " ' • - — - • • • « ^ * - . . Ldp1 2
XI 0J26 0,174
XI
0.IJ7 0,08!
omega-D (nd/>) 209,J1J 204,60
XI/X2
2 J 7 % 2,0471
m
g u m log!
0.8669 0,7164
Nhdl I P l s l 3 J 7 E « 5 4J7E-H)!
to 5) BO ISO
Jin a6 (Hz)
Hinh 8: Pho ning lupng cOa tin hi$u ttf diu dol va2 Thdng tin v l pha v i him tUdng quan glUa hai t i p dd ll|u phg thgdc t i n s l dao ddng xic djnh thdng qua cic bilu thdc (11), (12) v i (13) bilu dlln qua d l thi hinh 9 v i 10. Trin cd sd dd, tlln hinh logi bd cic dij liiu cd gli trj tUdng quan thip.
^ng 3. Kit qui xic dinh h$ si nhdt c&a nin Ket lugn - Kiln nghj
- Thf nghidm SASW cho phep xac djnh mddun trupt G va mddun din hii E cda nln thdng qua viic x i c djnh toe do truyin sdng c i t trong n l n va khii lupng riing cua d i t nln;
- Td thdng tin v l dao ddng tg do tat din cda nln thu dupe thdng qua cac thiet bj thu dia chin, cd t h l xic dinh he s l nhdt cda nln lim cd sd xic djnh thdng s l d i u v i o cho bii toin tUdng tie k i t c i u vdi n l n d i n nhdt Kelvin;
- Tiln hinh thf nghiim theo trinh tu nhu bii bio
r&n a6 (Hz]
Hinh 9: Pha gitfa hai tfn hl$u phg thuic tin si DUdng cong t i n sic thgc nghidm xiy dgng td hai tip dO li|u do cd dgng nhu d l thj hinh 11.
" ' * ^ ' * - ^ l ^ . . 1
J 1 1
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i
V p h (ft/s>
Hinh 11: Dudng cong tin sdc sdng bi mit ttf hai tin Miu dolviZ
TU dudng cong t i n s i c thgc nghidm, theo cdng thdc (7) v i (8) ta nh^n dupe k i t qui md dun trupt va md dun d i n h i l eua nln nhu trong bing 2.
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Bing 2. Kit qui tic di truyin sing cit trong nin ttf thf nghiim SASW
k
Trin cd sd thdng tin v l sU giirn biin dd dao ddng do c6 c i n tU hai t i p dd liiu, nhin dupc k i t q u i h i jihdt cda d i t n l n tfnh theo cdng thdc (6) t h l hiin l i bing 3.r6n 86 (Hz)
Hinh 10: Gid trf hdm cocherence gitfa hai tin hipu md t i , cd t h l xie djnh h i s l nhdt cda d i t n l n dudng lim cd sd tfnh toin nln va mdng trong k i t c i u i o dudng d td v i sin bay chju t i l trpng ddng.
- Theo kit qui da cdng b l ciia tac gii Barcan (1959) [1], h$ s l nhdt rung eiia d i t phg thudc r l t nhilu vie dd Im ciia dit: gii trj nhd nhlt cda h i s l nhdt dupc quan trie khi d i t khd hoic hoin toin no nudc (0,1-0,2 MPa.s - d l i vdl c i t hgt nhd) v i d mdt g l i trj dd I m nio dd dit cd dd nhdt cgc dgl (12-14 MPa.s - dli vdl c i t hgt nhd). Do dd, d l tlm ra qui luit trin d l i vdi eic logi dit ddl hdi thf nghiim d nhilu dQ am khic nhau cua d i t G
TAI U | U THAM KHAO
[1]. Xdt- td - vfeh, Co hpc dit. Bin djch tiing Nga, MatscPva, 1983.
[2]. Braja.M.Das, "Fundamentals of soil dynamics", The University of Texas at El Paso, Elsevier Science Publishing Co., Inc, 1983.
13]. Ronald J.Ebelhar, Vincent P.Drnevlch, Bruce LKutter, "Dynamic geoteehnlcai testing 11", ASTM STP 1213 USA, 1994.
[4]. Soheil Nazarlan, Ph.D., P.E., Deren Yuan, Ph.D., Mark R. Baker, Ph.D., "Rapid Detenninatlon of Pavement Moduli with Spectral Analysis of Surface Waves Method", The Center for Geoteehnlcai and Highway Materials Research, The University of Texas at el Paso, November 1995.
[5]. K.R. Saxena, V.M. Sharma, "In - Situ Charac- terization of Soil", Swets and Zeltllnger, 2003.
1 6 ] , H . fl. KpaCHMKOB, "flHHaMMMeCKMe CBOCiCTBa rpyHTOB M MeTOflW MX onpefleneHHfl", /IcHMHrpafl M3AaTenbCTB0 nmepaTypw no crpoMrenbCTBy, 1970.
