thi nghiem ba

(1)

He so bien dang ngang cua dat xac djnh bang thi nghiem ba true

Coefficient of horizontal deformation ofthe soils determined by triaxial experiments

Ngay nhan bai: 27/10/2014 Ngay sij-a bai: 25/12/2014 Ngay chap nhan dang: 11/2/2015

T r a n t h u ' t f n g B i n h

T C M

TAT:

Bien dang ngang cua dat la thong so quan trong trong tinh toan dia ky thuat, gia tri ciia no phu thuoc vao nhieu yeu t6 dSt nen, nhiing khi tinh toan thiet ke

nin mong va ho dao thiidng lay theo gia t n tra bang.

Mac du, nhieu phong thi nghiem d Viet Nam da trang hi thiet bi thi nghiem ba true hi6n dai, nhiing chi xac dinh dilgfc he so bien dang ngang cho mot so tnidng hop dac bi^t don gian ma nguyen nhan la can tao thiet bi va quy trinh thi nghiem khong phii hop.

Thong qua phSn tich ly thuyet, bai bao trinh bay cac giai phdp di sii dung cac thiet bi hien co trong viec xac dinh he so bien dang ngang cho moi doi tilcfng dat nen va sij lila chon khai thac cac thong tin tif ket qua thi nghiem.

Khoa tfi: Thi nghiSm ba true ho dao ABSTRACT

Horizontal deformation of the soils is an important parameter in geotechnical calculations, its value depends on many factors of the ground, but when calculating the design foundation and excavation usually taken by the table value. Although many laboratones in Vietnam has equipped m o d e m laboratory triaxial, but only determine the coefficient of horizontal deformation for some simple special cases where the cause is composed of equiments and experimental procedures are not appropriate. Through theoretical analysis, the paper presents the solution to use the existing equipment in the determination of deformation for all subjects across the ground and the selection of information extraction from experimental results experience.

Keyword: Triaxial experiments Tran thilcfng Binh Dai hpc Kien tnic Ha Npi

1. D a t v a n cte

Boussmesq (1885) difa tren nguyen ly Saint- Venant da giSi bai toan t i m trang thai ling suat tai m o t ctiem trong ban khong gian v o han, dong nhat, dan h6i tuyen tinh du6l tac dung cila tSi trong tSp trung.Theo do, m o t diem trong ban khong gian chiu lUc trung P co cac thanh phan utig suat duac biiu diin bdfi cac bieu thu'c sau-

, (1-2v) <"(2r + z) r2(r-.z)2 "

3Pxyz P xy(z-i-2r E(1-2v)

^ ' ^ ^ 27cr^ " ' 2 ^ r 3 ( r + 2 ) ^ 4 v + E{(1-2v)

Bieu thu'c (1) cho thay cacthanh phan Ong suat phap theo phuong ngang du'c'i nen chiu tal trong tap trung c6 g i i tri phu thuoc vao he so bi^n dang ngang v

Nam 1924giao sungudi Nga Kipitrevda co I6i giSi dtJn gian tir bieu thiJtc Boussinesq tuong ling v6i v=O.S khi do bieu thilc xac dinh u n g suat chinh va thanh ph^n ung suat t h i n g diJng o^

3dPcosB BdPcos^B 3dPz^

a,= - C v a c T ^ = r ^ — " T f2) 2 7 t r 2jtr'^ 27ir^

Nam 1934 Frohlich bang nghien cilu thuc nghiem ve mfii quan he giu'a bien doi modul dan hoi theo do sau va he so poisson da du'a ra bieu thij'c xac dinh sU phan bo ling, trong do ilng suat phu thuoc vao he sd Poisson v cua dat va dua ra I6i giSi t6ng quat ve sU phu thuoc cua Ong suat a^ vdi he so Poisson v, k^t qua cua 161 giai t h e hien 6 cong thOc t 6 n g quat

(v+1) dP (cosp) V , (3)

03 bleu thO-c (1) va (3) se co dang bi^u thOc 6an gi3n cCia Co the nhan thay.

Kip It rev 3dPcosp

Trong do p - goe hop bcii dufjng t h i n g qua diem dat luc va diem dang xet v6l t r u c z Nhu vay, bieu thOc (3) cOa Frohlich (1934) la sU m515 t 6 n g quat nhit vi trang thA\

ling suat cila dat nen duOi t^i trong tSp t m n g , n h u n g khi giSi phUOng trinh vi p h i n 6i t i m Ong s u i t dudl cac dien chiu tai se rat phu'c tap.Tlieo d6, sd d u n g ldi giai tronq tfnh toan cang phUc tap. Chfnh vi the, cac bi^u thOc tfnh toan ilng suat bien dang Is he quA cCia bieu thUc dan gi^n da mac nhien coi v = 03.€)6i vdi t n f d n g h o p Ong xif n is 'at nen khi c h i t tal t h i sis dung cac bleu thilc don g i i n , trong tfnh t o^ n t h i l t ke la lu , ' hon tin

130EVniCHHX 4.2015

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d y ve dp 6n djnh vi v l thi, cd t h ^ c h i p n h | n . Nhifng vdi t i n h toan cd yfiu c l u chfnh xAc vi ket qui ddnh g i l Ong xOcOa nin d i t n h u t i m hieu n g i i y ^ nhan cOa d c cdng trinh cd sued v^ nen mong hoac I n h hu'dng cua h d d i o sau vdl mdi tnffrng dat d l x u n g quanh th) khd c h i p n h i n , vi k ^ q u l d i n h g i l khdng cd y nghla, ddl khi dua ra nhiing k ^ l u ^ n sal lam.

Trong c i c b i l u thUc li^n h^ cac h i n g sd dan hoi, nhieu bleu thilc cd mdl lien he vdi h^ sd bien dang ngang nhU:

, _ i t L , _ 2 ^ ^ ^ , E = 2[1.-v)M,

2e3^

AV

{5)

1 - (l + v ) { 1 - 2 v )

2(1+v) 3(1-2v) Trong dd, X, p- Hal hSng sd Lame G- Modul b i i n dang truot K- Modul bien dang the tich E- Modul bien dang doc true (modul dan hdi young)

Ve nguyen t i c , dUa vko c i c mdi quan he niy cd the x i c djnh hi sd b i l n ngang, t h d n g qua xac dmh c i c h^ sd k h i c Nhung, d i t cd dac tinh b i l n d^ng rl4ng vdi d i e trUng Ong xO bien dang ldn, nfen c i c t h d n g sd la hSng sd khd c6 t h i chip nhan. Xac dinh b i l n d^ng ngang b i n g thuc nghifem cd the t h i nghidm ngoai hien trudng va thi nghidm trong phdng.

Thi nghidm hifen t r u d n g x i c dinh cac dac tri/ng bien dang cOa nfen p h l i ke d i n I I n^n nd hfing trong Id khoan, nd cho b i l t modul b i l n tf?ng ngang. D d I I sd lifeu r i t c i n t h i l t trong t h i l t k l h d d i o vdi y nghla p h l n Snh trung thyc trang thai Ong s u i t b i l n dang d khu vUc d d m l c i c t h i nghifem trong phdng khdng t h i cd duoc. Xong, cOng nhu h i u h i t t h i nghifem hiin trudng. k i t qui thf nghifem ludn chiu I n h hudng cOa n h l l u ylu t6 khic, nfen gia tri cOa k i t q u i khdng dac trUng cho mot loai dat cd thanh phan cau trOc va tfnh chat co 1;/ x i c dinh.

Thf nghifem trong phdng, x i c dmh b i l n dang ngang cho dat cilng v l d i t b l o hda h o i n toan co t h i t i l n h l n h tren t h i l t bi ba true. Trong dd, d i t bao hda h o i n t o i n , b i l n dang ngang duoc x i c dinh thdng qua b i l n dang doc v l t h i tich mau Hit.

NhUv^y, vdt d i t khdng bao hda chua cd g i l l phap d l x i c ^ n h b i l n d ^ n g ngang cda mau trong phdng thf nghiem.

2.Bieu thOrc x<ic d i n h b i l n d a n g n g a n g cua flat

2.1 Biiu thdc Kerisel vd Quatre's Theo Skempton v^ Bjiraim (1957) khi t i m hilu b i l n dang cua dat bao hda nudc d l xay di;ng b i l u thOc tinh b i l n dang lun cho d i t nen, d c flng da cho r i n g b i l n dang doc ciia m l u a i t ludn cd 51/ tham gia ciia b i l n dgng t h i tich.

Khi t i m h i l u b i l n dang d i t trfin t h i nghiem ba tn^c d l xay d u n g b i l u thOc tfnh b i l n dang lun, Kerisel v l Quatre's (1968) da x i c lap mdi quan he gliJfa b i l n dang ngang vdi bifen dang doc v l bien dang t h i tfch, m d i quan h | duoc b i l u dien bdi b i l o '

Theo bleu thilc nay, vi nudc khdng chju nen, nfen mau bao hoa hoan toan va khdng thoat nudc, dudi t i c d u n g ben ngoai se khdng c6 sU bien ddl t h e tich V=const nen he sd bien dang ngang v = 0,5

Bieu thiJc (5)dUoc xay d u n g doa tren each dat v l n d e va gial q u y l t nhU sau:

Xet m d t phan t d dat la dang hinh hdp ehU nhat vdi 3 mat dai dien cho ba phUcmg, d trang thai thuy t i n h , b l l n dang the tfch cOa phan t d cd kieh t h u d c abc duoc xac djnh theo bleu thOre:

V _ a b c - [ ( l - e i ) ( ( l - e 2 ) ( l - e 3 ) ] a b c AV ~ abc De t h e hifen k i t q u i don gian xet trudng hop

— = l - ( 1 - e i ) ( l - 2 e 2 + e^) =

= 2 e 2 - e ^ + e i - 2 e 2 e , - e i e ^ N l u b d qua nhQng vd ciing be trong b i l u thOc, nhU: e2'"2e2e];ei€^thi bleu thUc xac dinh b i l n dang the tich cd t h e v i l t g o n

V ., AV ^ ^

Trong do AV - gia tri b i l n dang t h i tfch cOa phan t o e d t h e tich V

Nhu vay, quan he cua cac thanh phan bien dang e, .e^, e, trong bleu thUc la quan he gan dOng,sesailfeeheang Idn, khi bien dang doc truc Idn. trong khi bien dang doc cOa mau dat cd the Idn hon 10%vdie,=0,125

2.2 Bieu thifc xdc dinh bien dang ngang cho mau dat trong thinghiem ba truc

5a 66 tac d u n g ba true cd cac thdng sd sau:

o , H 3 j ^ - Oj = Ao>0 va e^=e^

Vdi Ao la Ong suat lech, cdn lai la cac thanh Ong suat p h i p theo phUOng thang dOng va nam ngang a^,a^.a^ va eae bien dang e,,ej,ej theo eac phuong.

De sang t d mdi quan hien giUa cac thanh phan b i l n dang e^.e^ trong dieu kien xac djnh cua cac thanh phan ung suat 0^,0,. DUa vao nguyen ly bao toan v i t chat, duoc phat bieu nhU sau: 'vat chat khdng tU nhien sinh ra va khdng t u nhifen mat di chung chi chuyen td dang nay sang dang khic". Theo do, sU chuyen hda vat c h i t trong mau dat dudi dieu kien nen ep t h o n g t h u d n g cua t h i nghiem ehi I I sU thay ddi vj tri t u o n g ddl giOfa hat ran, dan d i n sit thay ddi mat d d v l hinh dang di d i m bao khdi lUOng khong ddi. D i l u dd ehi ra rang vdi:

Mau bao hda hoan toan va khdng thoat nude, dudi tac d u n g ben ngoai, n l u mau khdng ed sU bien ddi the tich, thi bien dang nen d phuong nay se p h l i ehuyen thanh bien dang nd d phuong khac sao cho htnh dang m i u cd ndi lUc c i n b i n g vdi luc tac d u n g theo cac phUOng

Mau bao hda h o i n toan va cd thoat nUde, dudi tac d u n g Ong s u i t lech bien ddi t h i tich mau Id the tfch nudc thoat ra khdi mau.

ri e , Hinh IS0 do tac dung lu tnic

Trong dd sUthay ddi the tieh nUde lien quan d i n q u i trinh tham. Do dd, b i l n dang t h i tich m l u 11 mdt qua trinh phu thudc vao qua trinh t h i m .

Mau khdng bao hda, dUdi t i e dung cOa Ong suat l i c h b i l n dang doc x i y ra ciing vdi b i l n dang ngang va b i l n dang t h i tich Trong dd, nudc d Id h6ng cd t h i t h i m ra n g o l i hodc phan bd lai tren toan t h e tfch m l u , t i t c l d i u I n h hudng den bien dang t h i tich ciia mSu.

TU nguyfen iy khdng doi ed t h i x i y dUng b i l u thOc bleu dien mdi quan he eua ba thSnh p h l n bien dang nhusau:

Neu goi the tieh ban dau eiia mau hlnh tru la V=7tH.R^. Tai m d t thdi d i l m trong q u i trinh b i l n dang, mau cd e h i l u cao giam A^^ v l chieu rdng tang la A„ khi dd t h i tich mau se I I (H-AH)7t(R + AR)^

Trong mdt dieu k i l n trang thai ilng suat nhat dinh, dudi t i e d u n g doc true, b i l n ddi t h i tfch cila mau dUoc b l o t o i n theo nguyen 1^ khdng ddl vdi sU rang budc bdi b i l u thOc sau:

H-AH

:TtHR2=n I W d R + VtD (6)

"const = 1=0 i,AR,

Dat AR = X — ' ^^'' f(R)^dR = R + A R I I b i n 1=0 "

kinh trung binh quy ddi va (6) dUOc viet dUdi dang:

TtRil^ - (H - A H )n(R + AR )2 + Vtp = 0 Trong dd, V- t h i tich mau flit H- Chieu cao mau d i t R- b i n kinh m i t e l t ngang mau d i t A^- b i l n dang doe mau d i t V - b i l n dang t h i tich toan phan.

n- so mat c i t ngang cdt m l u H-A^

A„- bien ddi dUdng kinh m i t ngang trung binh cua mau d i t

- Trong trUdng hap mau bao hoa nudc, khi nen khdng thodt nudc cd V = 0 , bleu thdc (4) sfe CO phuong trinh qua cac b i l n ddi sau.

irH.R^-(H-AH)Jt(R + A R ) ^ = 0

- 2 H A R J 1 - H A R ^ + A H J 1 ^ + 2 A H . R . A R + A H A R ^ = C

( H - A H J A R ^ + 2 ( H - A H ) R . A R - A H . R ^ - 0

^h^^n

A R ^ + 2 R . A R - ( H - A H )

131

(3)

H

AH 1

R

H R 2 -

( H - A H )

Chia c l tis v l m l u cua (9) eho HR', v l theo o.ssa 0345

£.515

A^.O\A j _ 4

Hmh 3 bi^u dfl bieu dien quan he V viJI e.

Gill phuong trinh b l c 2 vdi A^ theo R, H v l A^

nghidm cua phuong trinh I I

V H - A H Chia t o va mau eho H sfe ed AR =

v l chia 2 ve cOa cho R vdi ^2 = " ^

TU bleu thOc(7) bleu dien quan he glOa b i l n dang doc vdi ngang, ed t h i lap thanh b i l u d d (hinh 3 . ) T 0 b l l u d d eho t h i y , vdi g i l trj b i l n dang doe rat nhde,<0.014. t h i hfesd b i l n dang ngang v n h i n g i l t n tUv=0.5 d i n v=0.505. trong khi theo b i l u thOc Kerisel v l Quatre's v=OJ vd^ moi gia

V trj e , . D i l u do chOng t d b i l u thOc — = 2e2 + ei

AV chi c h i p nhan vdi v i t r i n ilng xd bien dang nhd

- Trong trUdng hop tdng quat, bao g d m c l d i t b l o hoa cd t h o i t nudc v l d i t khdng bao hoa, khi dd mdi quan he giijfa b i l n dang dpc va ngang duoc b i l u dien

V + 7iHJl^-(H-AH)ii(R + Af,)2 = 0 7i(H-AH)AR^+27t(H-AH)RAR-nAHR^+V = 0

' i R = - R ± „ 1 A H - H

Til bleu thdc (8) chi 2 v l eho R va bien dang AR ngang e^ duoc dinh nghia ^2 = " ^ se cd b i l u thile (9) ^

"

\ \

A -l 2 1 0

/ '

2 Q

b i ^ u d i S n nhif sau.

6 2 - (10)

„ H R 2

v l ^ - " T T . khi d d mdl quan hfe glCta ba t h i n h p h l n bien dang se dupc

B i l u thOc (10) la sU m d t l tdng q u i t gida e i c t h i n h phan b i l n dang cho moi t r u d n g hop, khdng phu thudc vao kich thudc cOa m3u„ Trong dd, b i l n dang t h i tfch e^= 0 chi la mdt trUdng hop d i e bifet

Tir b i l u thOc (10) thay e,= 2e^ t h i se cd:

( 2 + e ] ) 2 ( l - e i ) = 4 ( 1 - e v )

, 0 1 ) e f ( e i + 3 ) = 4 e v

Bilu thOc {11) I I phuong trinh b l c 3 se t o n tai nghifem khi e^>0, vdi -0.2 <e,<0.2 e l cd 2 gia tri ngupc dau nhau Ong vdi mdt g i l tri e^ khi e^=0 cdc cap g i l tri e,=0 ed t h i t h i y trfen hinh (4).

Nhuvay, trong q u i trinh b i l n dang dpc true, t h i n h phan b i l n dang ngang dat d i n g i l tri e,=

2ej p h u thudc vao g i l trj e^.Trong khi t r u d n g hop ev=0 la trudng hpp d i e bifet vi e,=0 si khdng cd y nghTa thUcte.

Nhan xet tren, cho p h i p k h i n g d]nh; e,= 26^

hay he sd v ^ . 5 la g i n dOng khi v l ch! khi b i l n dang I l m mau cd t h i tich t i n g Ifen e^>0, trong d d cd sd k h i c nhau giOa b i l n dang k l o e,<0 v(A b i l n d^ng n i n e,>0

Tdm lai, d l x i c dinh chfnh x i c g i l t n b i l n dang ngang v l xem x l t d l y d i i c i c trudng h p p nfen v l n d t h l t f c h m l u khi b i l n dang dpe d i l n ra vdl gid trj Idn, t h i n i n sOdung b i l u thdc (10) cho mdi quan he giOa ba t h i n h p h l n .

3. X i c ffinh t h i t f c h b i £ n d a n g cOa m a u

Hinh 5. Thi nghiem ba true Controls

Gia sO vdt ran hinh dang b i t ky cd t h e tich V v l khdng t h a m nudc. Khi t h i v i t vdo trang binh hinh t r u t r d n , difen tieh mat c i t ngang F dang chila nddc vdi e h i l u cao cdt nUdc h, khi d d mUc nude tnang binh se ddng cao hOn mUe nudc ban dau AH. The tich vat r i n vdl c h i l u cao edt c h i t Idng tang t h e m trong binh se I I :

AH=V/F

N l u binh hd, I p s u i t mat nUdc la I p suat khi quyen va ludn khdng ddi sfe cd quan he AH=V/F, Neu binh kin, trudc khi t h i cd I p s u i t p^ mUc nude H, sau khi t h i , binh se c6 I p s u i t P^ v l mUc nude H^. GiCia ehilng c6 mdl quan he

P-Ps

Trong dd, K I I hfe sd se nhan g i l tri khdng ddi, n l u binh kfn khdng chOa khi, khi do K la hfe sd nfen t h i tfeh, Ngupc lai khi binh ed khi, K b i l n ddl p h u thude v i o nhieu y l u t d .

N h u vay, m d t vdt trong binh kfn hay h d khi thay ddl t h e tich d i u I l m cho mue nifdc cua binh thay d d i . ThUe t e nhOng t h i l t bj thf n g h i i m ba t m c frudc a i y da dp d u n g nguyfen t i c binh hd v& cdt thuy n g i n d l d o v l t a o I p s u i t trong b u f i n g n h u n g rat phOc tap khi thuc hifen d dp s u i t cao va khdng chfnh x l e . Ddi vdi binh kfn. do dp s u i t binh cd n h i l u g i l i phap lua chon d l ed d ^ chmh x i c eao v l d o l i l n tuc. Vcii v i l c tao cho binh khdng cd khi, thi b i l n ddi t h i tich eda m l u d i t trong binh ed t h i x i c dinh theo b i l n d6i I p suat d o duoc qua bieu thdc

(Hs-H)F = K(P-P5)

Trong dd, {H^-H)F==AV Id b i l n ddl t h i tich v i t r i n .

Theo b i l u t h & g i i tri M tich x i c ftnh bSng W n a & ap s u i t =4 i<h6ng p h u thudc v i o hanh dang cua binh.

Do d6, vdi t h i a b|ba true cua- i , n „ B a , h n r KiSn t n i c H i N6i ( h l n h S , Contra, „ " , , ^ s i n x u i t Y t a l i a c O a a u a o i p s u . „ i j u a dSu d o c h u y i n vi doc true v a u i , J t r i « ^ . " ^ I S c a c t h H t b i d o d i S n d a d i / o c t K , , , ^ " ; ^

132|B

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bi v l k i t ndi may tfnh. Bi xic dinh he sd b i l n dang ngang ehi c i n chuyen c h i dd do dp suat nudc Id hdng sang do dp suat budng va thay dot quy trinh nghidm sfe xac djnh dupc cac d i e trUng b i l n dang ciia mau d a t Quy trinh thi nghifem nhu sau:

Ngoai viec chuan bl gia cdng l i p dat mau v l gia t i l thUc hien nhU c i c thf nghifem ba true binh thudng, Nhung cd nhUng k h i e biet c i n chO y Id - Ddng cOng mau trUdc v l sau khi bpe m i n g cao su cho mau,

- Hieu chinh h i sd dp Iyc c h i t Idng trong binh thudng xuyfen

- Sau khi da dua nudc v i o binh den trang thai I p s u i t d l / k i l n se dUa budng v l trang thdi hodn t o i n ddc l i p , ddc biet vcfi van dieu dp. TCf cac k i t q u i do I p s u i t P^ va bien dang doc true e sfe xae djnh he sd b i l n dang ngang cOa mau theo cdng thOc

_ e 2 ^ _ H _ l ( H - A p | l R ^ - 5 r ^

^ " e i RS^ H - S , Ap dyng n g u y i n li^ can b i n g dp s u i t , b i l u thOe x l e * n h h i sd b i l n dang ngang dupc xdy dung nhu sau:

A\^=K(APo-Ap,)-S,7ir2 AV AV Vdl e v = - r r = — 5 - v a e i =

_ K ( A P o - A p | ) Sjr^

itR^H HR^

= secd

V ( H - S )

H I sd bien dang ngang s l tfnh theo b i l u thilc

v = ^ = — t " - f t P i ) ' ^ ^ - S f ^ (12) e i R S \ H - S j

Trong c i c b i l u thdc trfen H- c h i l u cao mau H= 76mm R - b d n k i n h m l u R=19mm S| - bien dang t h i n g d i l n g eda mSu r- b i n kfnh true gia t i l ciia budng ba true la hing 56

A P „ - l p s u i t ban d i u

AP, - I p s u i t d c l p thO I tuong i l n g d p lOn S, Trong b i l u thOc S,vl P, la c i c g i l trj b i l n ddi trong q u i trinh thi n g h i i m tUdng dng vdi Ong suStlfechAo,

Nhuvay, t o khi b i t d i u b i l n dang cho d i n khi n ^ u p h i huy c l e sd lifeu t h i n g h i i m cho p h i p xic dinh duoc c l e thdng sd sau:

- Cle t h i n h p h l n b i l n dang dpc ngang vd t h i tfeh

- Hfe sd b i l n dang ngang - Modul b i l n dang doc E = A o / e , - Modul b i l n dang thfe tfch K =

3(1-2v) - Hfe sd dp luc ngang X - -

(l + v)(1-2v) "

tribi> ,. ldi theo sU b i l n diSi cda hfe sd b i l n dang

ngang _ - Modul t r U 0 t G = u = ,

2(1+v) Ap dung nhiing k i t qua nghifen cOu nay cho eae Ioal d i t k h i e nhau, so bd nhan thay

- H I sd bien dang ngang cua c i c Ioal dat k h i c nhau ed quy l u l t bifen ddi khdc nhau theo Ong s u i t lech, ddng thdi cd sU k h i c bifet vdi cde gid trj 0,5 vd dao ddng Idn hon nhung gia trj tra bang. N l u s d d u n g b i l u thOc (3) ciia Frohlich tfnh dng suat tai m d t d i l m d u * t l i tap trung thi Ong s u i t theo phuang ddng se ldn hon va dng s u i t ngang se nhd hon khi he sd v= 0,5. d i l u dd cho t h i y n l u cd b i l u thde t i n h Ong s u i t dUdi mdt difen chiu tai theo k i t q u i l l y tfch p h l n bieu thde (3) eiia Frohlich thi cac tinh t o i n Ong s u i t b i l n dang dudi nen cdng trinh se chinh xdc phii hpp vdl b i n chat Ong x d cua d i t n i n

- Bien dang trUcJt dtiang thdi can bang gidi han Td b i l u thOc dinh nghta modul b i l n dang t m o t G = -

^ (13) Trong d d y bifen dp b i l n dang trUpt

T inig s u i t cdt d trang thai cUc han T = otgqt-tC Cd t h i thay, mdi lo^i d i t ed edc ddc trUng khang e l t xae djnh, khi d trang thdi cUc han cd mdt mdl quan he xdc dinh gida b i l n dang trUpt vdl vdi c l e dae trUng b i l n dang

crtgi|i+C_ E

y 2(1+v) (14)

thay c l e T, G , v l cle bien d?ing ty ddl doc e, va ngang e^ vao bieu thde quan hfe E vdi G se dUdc:

Aotgcp+C _ Efr] (14)

_ Aotgtp+C Ee,

2 ( 6 2 + e i ) 2(62 + ei) = 2(62 + e i )(tgqn B i l u thde (14) cho b i l t dUdi mpt dng s u i t Ifech Idn nhat de nau d trang thai cUc han thi b i l n dang trUot cua mdt loai dat cd cac d i e trung khang c i t <p va C x l e dinh, cdn phu thudc vdo mdi quan h f giCra e i c thanh p h l n b i l n dang trong d d e, b i l n ddi theo Ao.Tir nhdn xet nay cho p h i p dat v l n d l

Aang(p+C-2Ei'Act

^ ~ 2E(Acrtg(p+C)

GlOa e, vdi A o la quan he phi t u y i n vdi e-Y2E

tg(p

^ j j _ _ i _ _ J § . . Nhuvay:

2tg<ti tg<ti

Khi l ^ o n g cd bien dang ngang e, s 0 v l n cd the x i y ra trang tfili trang t h l i gici han, khi dd

t g * tg$

Khi A o = — ed b i l n dang n i n ngang 2 t g ^ tg4i

tdn n h i t ed t h i x i y ra eho cho m d t loai 6it cd e, q),V, E xde djnh, d u cd t i n g hay g i l m Ao. Tdm 1^1, qua mpt sd trinh b i y so luoc viee sO dung c i c

k i t thf nghifem danh g f l sd phan bd dng s u i t v l sU hinh thanh trang t h l i cdn b i n g gidi han trong qua trinh b i l n cJang d l eho t h i y , n l u cd dUoc cac thdng tin ve b i l n dang ngang cOa dat nen thi n h i l u van d l v l dng x d eua d i t n i n se dUoc s i n g t d

K i t luan:

T h i l t bj t h i n g h i i m ba truc cua TrUdng Oai Hpc k i l n trOc H I ndi la thf n g h i i m cua Hang Controls s i n xuat tai Ytalia ndm 2000 vdi dau do dp s u i t , b i l n dang va Ide la c l e linh kifen di^n tO ed ket ndi may tinh, nfen khdng can thay ddi cau tao cOa thiet bj van h o i n todn phO hpp vdi vifec t h i nghiem xac dinh cle d i e trdng b i l n dang cda dSt theo mpt quy trinh mdi.

Ket q u i t h i nghiem xac d m h b i l n dang theo nguyen ly do bu the tfch c6 t h i t i l n h l n h ddng thdi vdl x l e dinh eie d i e trung d d b i n theo quy trinh gia t l i thdng thddng vdl tdc do b i l n d^ng khflng ddi Vdi v i l c t i l n h l n h dong t h d i trfen mdt mau d i t , nhdng sd lieu t h u dUcK t d k i t q u i cho p h i p sang t d r i t nhieu van d l , trong d d cd mdl lifen he giCia qua trinh b i l n dang vdi q u i trinh hinh thanh trang thai gidl han.

Ket qud e i c d i e trung b i l n dang phu hop vcfi danh g i l i j ^ g xCr d i t n i n khi chju t i e dung cda t i l trong edng trinh.TrUdng hc»p d i n h gid Ong x d dat n i n vdl x u l t hifen cua hd d i o thi cdc thdng sd dat nen p h l i dupe xdc dinh b i n g bi thi nghifem b a t r u c d d t l l ngang.

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12 N AXutovidi.(19S3),'Cohoc dSt',ban dich t i f n g Nga N h i xuat b i n Ndng nghiep

13 P.PunjshothamaRa|(199S),"6eotedinical.Englneerlng", NewYork.

14. R. Whitlow (1997),'CiJhocdar,NXB Giio d u t 15. Arnold Verrujit (2005),'Soil Dynanm", Deift University of Technology.