NGANG CUA DAT Tl/dNG CHAN CO XET HINH DANG KHONG Ll/C DAT Bl DONG LEN CAC CONG THUfC GIAI TICH DE TINH AP

i ^ l W B i e i t b d OlfcN B A N KHOA H Q C • CbNOJIGHg

^

CAC CONG THUfC GIAI TICH

DE TINH AP Ll/C DAT Bl DONG LEN Tl/dNG CHAN CO XET HINH DANG KHONG N A M NGANG CUA M A T DAT

+ TS. PHAN D O N G

L Gidi thiOu chung: dtfdc xem xdt vd ddnh gid ttfdng minh.

1.1 Khi thiet ke ttfdng ctf, cpc chiu Itfc De khac phuc hien trang neu tren, nh^m ngang hoac cdc kdt ca'u cdng trinh khdc cd ddp tfng nhu clu thtfc td thidt kd, muc tieu dieu ki|n lam viec ttfdng ttf thtfdng khdng cda nghien ctfu ndy la xay dtfng cdng thtfc tranh khdi phdi tinh todn dp Itfc da't chd gidi tich chung cho dp Itfc da't chd ddng dOng va bi dOng cda da't dip hode da't nIn. cdng nhtf bj dOng cd xdt cau hinh phtfc tap c l n chd y r^ng dp Itfc da't chd dOng Id mOt cua dtfdng mdt da't.

ngoai Itfc quan trpng tde dung tren phtfdng IL Phtfcfng phdp ludn:

ngang cdn dp Itfc da't bj dOng lai la mOt Itfc, 2.1 Pham vi nghien ciiu bdi todn dp lUc mOt nhan td thien vl cd ldi cho stf lam viec ddt nhu sau :

cda cdng trinh. Vi vay viec xdc djnh dung 1. Ttfdng chin tuyet ddi ctfng va liftig dan va chinh xac chung se gdp phln ndng ttfdng thing dtfng, bo qua gdc ma sat ngoai cao dO tin cay vl chat Itfdng dd an thie't kd. gitfa Itfng ttfdng vdi khdi dat tnfdt.

1.2 Trong nhilu do dn thie't ke', khdng it 2. Da't sau ttfdng chin dtfdc phdn thanh trtfdng hdp ta cln phai bidt gia trj dp Itfc da't hai loai rieng biet :

chd va bj dOng khi mat da't nghieng mdt gdc - Da't rdi : gdc ma sat trong tp , Itfc dinh

±P so vdi dtfdng nam ngang hay tdng qudt dpn vi c = 0.

hdn, khi mat da't cd hinh dang khdng nim - Da't dinh: gdc ma sdt trong (p va life ngang trong pham vi Idng the trtfdt. dinh ddn vj c.

1.3 Cac tdi Ueu chuyen khao vl dp Itfc 3. Ca'u hinh dtfdng m | t da't ke ttf dinh da't hien nay khd nhilu [3],[4] v.v... nhtfng ttfdng trong pham vi Idng the trtfdt dtfdc khi van dung vao mOt sd' bdi todn cdng trinh chia thdnh 4 loai khdc nhau:

cu the nhilu khi van cdn gdp khd khdn, ddc - Mdt dd't nlim ngang : dtfdng mat dat biet nhtf: nim hodn toan nim ngang.

1-Ap Itfc diftbjdOng trong nhilu tdi liOu - Mdt da't nghieng: dtfdng mat dat chuyen khdo thtfdng dtfdc gidi thieu nhtf Id nghidng so vdi dtfdng nim ngang mOt gdc kdt qud dtfdc suy ra ttf cdch gidi bai todn dp p, dtfdc phdn bift thdnh :

Itfc d^t chd dOng nen thidu cdn ke. MOt sd ^ Nghidng trdn, +^

rat It tai lieu trinh bdy chi tiet ve loai dp Itfc

nay thi lai qua phtfc tap [2]. + Nghidng dtfdi, /5

2- Hinh dang mat da't trong pham vi Idng " Mat da't ntfa nghidng: difdng mat da't the trtfdt, mOt yeu td dnh htfdng nhilu ddn nam nghieng mOt doan rdi chuydn htfdng kich thtfdc va do do, the tich cd the trtfdt. It nam ngang cung dtfdc phan bidt thanh:

22 Sd3+4. Nim2012 i

i

Bi^uabd

Dli:N D A N KHOA HQC C 6 N G N G H | :

+ Ntfa nghidng tren,-I-/?

+ Ntfa nghieng dtfdi,-/?.

Mat dd't ntfa ngang: dtfdng mdt dd't nim ngang mOt doan rdi chuyin htfdng nim nghieng cung dtfdc phdn biet thdnh:

+ Ntfa ngang trdn, + /?

+ Ntfa ngang dtfdi, p

2.2 L:^ thuydt dp Itfc da't dtfdc chpn ddng la cda Coulomb cdn dtfdc gpi Id 1;^ thuydt mat trtfdt phlng hay 1;^ thuydt can blng gidi han cda cd the trtfdt.

L;^ thuydt dp Itfc da't Coulomb ra ddi da ma'y trdm ndm, mdc dd Id ldi gidi gin ddng nhifng ddn gian ndn nay vln cdn dtfdc stf dung rOng rdi trong thtfc td thid't kd cdng trinh.

2.3 Cdch x&y dung cong thiic gidi tich:

Ddi vdi ly thuydt dp Itfc da't Coulomb, theo [3], cd hai cdch tie'p can de xay dtfng cdng thtfc giai tich.

- Phtfdng phdp gidn tie'p.

- Phtfdng phdp trtfc tie'p.

Bai vidt nay chpn ddng phtfdng phap thtf hai vdi nOi dung cd the dien dat tdm tat nhtf sau:

Ndu gpi 9 la gdc pha hoai cda mat trtfdt, tao bdi Itfhg ttfdng va mat trtfdt thi dp Itfc da't khdng phdn biet chd hay bi dOng cd thi bieu dien bdi:

E = E(0) = Kxf(0) (1) Ap dung nguyen I^ ctfc tri vdo (1) ta lap

dtfdc phtfdng trinh quan trpng sau:

dE ^dE(e)_^jf{ei_^

d9 dG de Ndu ddt nghidm mdi:

Z = t g ^ .

thi (2) trd thanh phtfdng trinh dang chung Id mOt phtfdng trinh bdc hai hoac bdc bdn dly dd:

N,Z'+N^Z^ + N^Z^+N,Z + N,=0 (4b) NghiOm cda (4) trong trtfdng hdp cd the trtfdt nim trong trang thdi can blng gidi han chd dOng se cho ta gdc phd hoai cda mat trtfdt chd dOng:

0 = ^„ax = Oc (5)

Thd (5) vdo (1) se nhdn dtfdc dp Itfc dd't chd dOng:

^r=^n,ax=£(^r) (6)

Ttfdng ttf nhtf vdy, ndu cd the trtfdt dat trang thdi cdn blng gidi han bj dOng thi ttf (4) ta cd gdc phd hoai cda mat trtfdt bj dOng:

e =

e^,^

=

9, (6)

Lai thd (6) vdo (1) d l thu dtfdc dp Itfc da't bj dOng:

E„=E^-E(e,) (7) Va'n dl md'u chdt d day la xac dinh gia trj

cua cdc he sd ^1,2,3.4,5 trong cac phtfdng trinh (4) cho ttfng loai dp Itfc da't chu dOng cdng nhtf bi dOng tfng vdi ca'u hinh khdc nhau cda dtfdng mat da't.

Do khudn khd cda bdi bao nen chi tap trung gidi thieu ve dp Itfc da't bi dOng.

m . Thidt i$p cdng thtfc giai tich vdi dp Itfc ddft bi dOng M^t ddft nkm ngang.

3.1. Ddt rdi:

Sd dd tinh toan nhtf tren hinh 1 va la trtfdng hdp ddn gidn nhd't.

(2) (3)

N,Z^+N,Z + N,=0 Hoac:

(4a)

w

9 0 - ( 5 - ^ )

Hinh 1: Mat da't nim ngang - da't rdi a. Cd thi trtfdt bi dOng.

b. Tam giac Itfc.

Sd 3+4 - Nim 2012

23

I Bieu^bd

Goc mat triTdt bi dong:

Ap life dat bi dong:

3.2. Ddt dinh:

Sd do tinh toan nhu* tren hinh 2.

(8)

(9)

>90-(6-<p>

Hinh 2: Mat dat nam ngang daft dinh a.Co' the trifdt bi dong.

b. Da giac \\ic.

Tu" dieu kien:

2 ^ = 0

Ta rut ra:

E,o-W + T- cos<p tan{d-<p) sin(<9-^) Vdi

1 . 2 .

W =-yh'tge

(10)

(11)

(12)

DifiN

DAN KHOA HQC

-

C 6 N G NGH|:

BC = h^\+tg'0 (13)

T = ch,]\+(g'0 (14) The (12), (14) v^o (11) ta nhan diTcJc

phiTdng trtnh dang (1)

cos ^yj\+tg^0

K, = ^

_lg{0-(p) ^{IgO + T-}

Trong do:

s i n ( ^ - ^ ) (15)

A ^•yh'

(16) 2'

T = ch

Vdi c 1^ life dinh ddn vi cua dat.

Sau nhieu phep bien ddi lifdng giac, phiTdng trlnh (15) neu chu y den (3) duTdc chuyen ve dang cuo'i cung:

E,„ = A{Z + tg(pZ^) + B{\ + Z^)

(17) Z-tg(p

Goc ph^ hoai cua mat tru'dt bi dong, ^, tim dtfdc nhd phifcJng trinh (4a) vdi cac he

bo

so:

-la

N,=\ (18)

Trong do:

a = tg(p (19) 3.3. Vi du kiem tra 1.

Giai phiTdng trinh (4a) vdi cdc da't dinh CO goc ma s^t trong kh^c nhau ta thu dtfdc

^i„ nhirdBang 1:

Bang 1: Gia tri goc phd hoai cua mat triTdt bi dong dat dinh - mat da't nam ngang.

Goc ma sat trong: <p (do) 7

14 20

Z = tg(p

1.13031 1.27991 1.42819

^..(46) 48*^30'

520 55^

24

So 3+4 • Nam 2012

iBieu^d

^{Dif:N D A N KHOA HQC} C 6 N G N G H | :

Gia tri 6'^„ trong bang nay triing vdi ket qua tinh theo (8).

He (18) cung nhu" so lieu Bang 1 hoan toan phii hdp vdi ket luan trong [3] rang goc pha hoai mat tru'dt bi dong cua dat dinh theo ly thuyet Coulomb chi phu thuoc vao goc ma sat trong ma hoan toan khong bi anh hu'dng cua life dinh ddn vj.

IV- Thie't lap cong thi?c giai tich \6i ap li/c da't bi dOng - M a t dS't nghi^ng (Trdn/

burdri).

4.1.Ddtrdi:

Xet mat daft nghieng du'di du'dc bieu dien tren hinh 3.

H i n h 3: M a t da't n g h i e n | difdi - da't rdi a. Co the triTdt bi dong

b. Da giac liic

Chieu dai canh BD:

C0Sy9 BD = h

cosi0-/3) ⁽²⁰⁾

Trong lu-dng co the triTdt:

„, 1 , cos/?sin^

W = —yh

2 cos{e-l3) Phu-dng trinh (1) c6 dang:

1 ,. cosBsmOcotgiO-cp) E — — yh —^ •

*/»" 2 c o s ( ^ - ^ ) Neu chu y den (3) thi viet lai (22) thanh:

Z^AZ"-

(21)

(22)

bp r Zi\-ab) + bZ' a ⁽²³⁾

-tim du'dc nhd phu'dng trinh (4a) vdi cac he so: A '

N,=a-a^b-h N^ = -la

(24)

(25) yv, = -a

Vdi:

b-'tgp-

4.2. Bat dinh:

Xet mat daft nghieng du'di du'dc bieu dien tren hinh 4.

a) A c

b) Efcs

w,-Y~}9Q-(d-q>)

ffinh 4: Mat da't nghidng dufdi - daft dinh.

a. Co the tru'dt bi dong;

b. Da giac life.

Tif dieu kien (10) ta rut ra du'dc:

1 _ COS(Z»

r -w . + 7 1-—

*^' ^"tan(6'-^) I"'sm{e-(p) (26) Vdi:

BD = h- cos/?

cosi0-/3)

1 , 2 C O s y 9 s i n ^

W„. =—yh

P 2 cos{e-f3)

(27)

(28) (29)

^" cos{e-p)

The (28) va (29) vao trong (26) ta nhan du'dc phifdng trinh dang (1):

, cos/? sin ^ 1

r =A + Goc pha hoai cua mat tnfdt bi dong, 0,^ "i^' cos(^ - P) tg{e -cp)

S6 3+4-Nam 2012

25

ien^bd

DiiiN B A N KHOA H Q C . C 6 N G N G H | !

+ 5- cos/? cos^

cos(^-/?)sin(^-<?>) ^^^^

Sau nhieu phdp bidn ddi Itfdng gide, phtfdng trtnh (30) dtfdc chuyin vl dang cudi cud'i cdng:

E A{tg0 + tg(ptg'e) + B(\+lg'9)

"^ ~ tgj3tg'0 + (\-lg<ptg/3)tg0-tg<p ^^'^

Ndu chd S den (3) thi (31) dtf^c vidt lai thanh:

{aA + B)Z^+AZ + B

(33)

'" bZ^+{l-ab)Z-a ⁽³²⁾ Gdc phd hoai cda mdt trtfdt bj dOng, ^hfi- tim dtfdc nhd phtfdng trinh (4a) vdi cdc hO so:

'N^=(\-ab)(aA + B)-bA

• N^=-2a(aA + B)-2bB Nj=Biab-\)-aA

Ghi chd: trong trtfdng hdp mdt dl^t nim nghidng trdn, /3* vln stf dung cdc cdng thtfc (23) vd (21) ddi vdi dSft rdi, (32) vd (33) ddi vdi d^t dinh nhtfhg ddi dl'u ngtfdc lai d cdc sd hang cd chtfa b.

4.3. V( du kiim tra 2:

Cho mOt ttfdng chin h=2,8m, dii sau ttfdng cd cdc tham sd sau: 7^ = 1,87/m',

(p = U° vd c = 4,17'/w' Hay tim E^ vd E,p vdi (3 =0,5 vd 100 (Ntfa nghidng dtfdi)

Kdt qud tinh todn ghi d Bdng 2.

Bdng 2: Ldi giai cda vi dyi kilm tra 2.

Gid trj cac dai lugmg

ill

LA (T/m) 2.B (T/ra) 3.N,(T/m) 4.N2(T/m) 5. N3 (T/m) 6.Z

8.£,^.(T/m)

Gdc nghieng cda mdt dat, p (dO)

m.

0^

7,0560 11,4800 1,0000 -0,4986 -1,0000 1,27991 52°

40,9455

131 7,0560

11,4800 12,3329 -8,6100 -12,9886

1,43305 55^5' 36,6165

10' 141 7,0560

11,4800 11,4132 -10,6488 -12,7345 1,62124 58°20'

32,7183 Vdi cdch ldm nhtf thd ta gidi cdc bdi todn

cdn lai vd trinh bdy ngln gpn tidp sau.

V. Thidt lap cdng thtfc giai tich vdi dp Itfc ddft b | dOng - M$t dd't nila nghidng (Trdn/Dtfdi).

5.7. Mdt ddt nUa nghiing dudi:

1. Da't rdi:

Sd dd tinh todn dtfdc bilu dien trdn hinh 5.

.* • •

R.-

26

Hinh 5: Mat d^t ntfa nghieng dtfdi - dd't rdi.

Sd 3+4 ' Nim 2012

ienabd

DI£N DAN KHOA HQC - C6NG NGH|:

Mat da't ADC nam dtfdi dtfdng nim ngang AF- ntfa nghidng dtfdi:

KS hidu:

W^. = Trpng Itfdng phln ADE.

W = Trpng Itfdng phln EBC.

W^.=W, + W (34) Mdt sd cdng thtfc dan xua't de xdy dtfng

phtfdng trinh dang (1):

Chilu dai canh AD:

tim dtfdc nhd phtfdng trinh (4a) vdi cdc he so:

(44)

AD = hi cot gp

Trpng Itfdng phln ADE:

w,=^rh\cotgp

Chilu dai canh EC:

EC = h^tg0

Trpng Itfdng phln EBC:

w =^rfhtg0

(35) (36) (37) (38) Trpng Itfdng Idng the trtfdt bi dOng thtfc:

W^. = A^cotgp + A^tge (39) Vdi:

A=\yh\

Ap Itfc hi dOng cda dat rdi E^p - dtfdc Idp dtfa trdn cdng thtfc (1):

^ _D,tg'0 + D,tg0 + D,

*''' tg0-tg(p Yidt lai (41) ndu chd S ddn (3):

A^'+A^ + A

'P' Z-a Trong dd:

D2=A,tg<p : Di=A2 + Afot Do = A,cotgP

(41)

(42)

(43) 0,

N,=D,

N^=-2tg<pD^

N,=-{D,+tg(pD,)

Nghidm z Id mOt sd dtfdng nhd nhl^t vd thda man bd't ding thtfc sau:

z = tg0>Zg^=-^cotgP (45) h,

2. Ddt dinh.

Sd dd tinh todn bieu diln tren hinh 6.

(40) Hinh 6: Mat dlt ntfa nghieng dtfdi- da't dinh.

Ngoai cdc Itfc tde dung Idn cd thi trtfdt bj dOng cd mdt dl^t ntfa nghieng dtfdi nhtf trtfdng hdp dl't rdi, d day cdn them Itfc dinh

T„. xud't hidn trdn b l mdt trtfdt BG.

p • • •

Ttf nhdn xdt tren, dp Itfc bi dOng cda da't dinh E* . bao gdm 2 thdnh phln:

F* = F + E

bB- bWp- bTp- (46)

Gdc pha hoai mat trtfdt bi dOng%- se

Trong dd:

Ebwp- = Ap Itfc bj dOng thanh phln do trpng Itfdng Idng the trtfdt bj dOng ^p gdy ra, cd thi ddng cdng thtfc (8).

EbTp- - Ap Itfc hi dOng thdnh phln do Itfc

sd 3+4 - Nim 2012

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D I £ N D A N KHOA H Q C - C 6 N G N G H ( :

dinh Tp. gay ra, se dtfdc khdo sdt ridng d l thiet lap phtfdng trinh (1) cda bdi todn.

Sau dd phdi hdp kdt qud lai ta se nhdn dtfdc gid trj dp Itfc bj dOng theo phtfdng U-inh (46).

Chieu dai mdt trtfdt bj dOng BC:

BC =

cos^

Ltfc dinh T,

a

^ cos^

(47)

(48) (49)

tg0-tg, (^«>

Phdi hdp phtfdng trinh (41) vdi (50) theo (46) ta cd:

Vdi B, =ch2

Ap ltfc bj dOng thdnh phln £„.^.

\-^ig'9 E =B,

hrp - 2

^. D^tg'0 + D,tg0 + D,

*''" tg0-tg(p Ndu chu S tdi (3) vidt lai (51):

. _D\Z'+D\Z + D\

"P' Z-a Trong dd:

D\=D^ + B^

D\ = D, D\=D, + B,

(51)

(52)

(53)

Gdc phd hoai cda mdt trtfdt bj dOng 0,,^.

tim dtfdc ttf phtfdng trinh (4a) vdi cdc he sd:

iN^=D, + \

N,=-2N,tg(p (54) N3 = -(D, + D,tg(p + \)

NghiOm Z dtfdc chpn Id nghiem dtfdng nhd nhd't vd phdi thda mdn dilu kien (45).

3. Vi du kilm tra 3.

Hay tinh dp ltfc bj dOng cda ddft rdi, mdt dd't ntfa nghidng dtfdi vdi cdc tham sd sau:

vd

(p= 26°

P= 10°

r= l,8T/m' h= 2,8 m

hl= 0,5 m h2= 2,3 m Gidi

Tinh cdc dai Itfdng: Ai= 0,225 T/m, A2 = 4,761 T/m

Tinh cdc he sd theo (43): D2 = 2,32194 , Di = 5,38432, Do =1,27623

Tinh cdc he sd theo (44): Ni = 2,32194 , N2 = -2.26482 , N3 = -3,9027

Giai phtfdng tf-inh (4a): z = 1,87277 Kiem tra dilu kidn (45): zgh = 1,23306 <

z = 1,87277 Dilu kien (45) thoa man Tinh dp Itfc hi dOng theo (42): E^ _hp-

=14,0813 T/m

Cdng vdi sd liOu ndy, tinh dp Itfc bi dOng cda dd't rdi ed cdc tham sd mdt da't ntfa nghidng dtfdi khdc nhau (Bdng 3).

Bang 3: Ap lyre bj dOng cda dlt rdri m$t ddt ntfa nghieng dudi Ket qua

tinh toan Z = tg0

^p-^TIm)

p= 5"

0 1,92252

15,681

hi(m) 0,3 1,77438 15,8118

0,5 Khdng thda diduki^n(45)

P= 10°

0 2,49171

13,5028

h2(m) 0,3 1,68985 15,1206

0,5 1,87277 14,0813

Sd lieu trong bang ndy cho tha'y cdc cdng ^ = i,87'/m\ ^ = 14°, c = 4,17'/m^ p = 5'^

thtfc da thidt lap Id ddng din. . „ , . , , r^ f\i -r^<

XT'A 1 T- iTx i ^ u - . * - ' A-'.A'x, vd /3 = 10°, hl=0; 0,3 va 0,5m.

Vl du 2: Tinh dp Itfc bi dong cua dat dinh <- »

cd mat dd't ntfa nghiengdtfdi vdi cdc tham ^^^ ^"^ tinh todn ghi d bang 4.

sd cda ttfdng va dd't nhtf sau: h= 2,8 m.

28

Sd 3+4 - Nim 2012

Bieit3bd

DI£:N DAN KHOA HQC - C6NG NGH|:

Bang 4: Ap lyre bi dpng cda dlt dinh - mdt ddt ntfa nghidng dudi.

Kit qua tinh toan

Z = tge E^piT/m)

P= 5"

hi(m) 0

1,43305 36,6165

0,3 1,46233 36,8137

0,5 Khdng thda dieu kifn (45)

P= 10°

h2 (m)

0 1,62124 32,7183

0,3 1,37415 36,0931

0,5 1,54622 33,8822 Sd heu trong bang ndy cho tha'y cdc cdng

thtfc da thidt lap la ddng din.

5.2. Mat da't ntfa nghieng trdn:

1. Da't rdi:

Sd dd tinh todn bieu diln nhtf trdn hinh 7.

W=^rih + h,ytg0 Chilu ddi canh EF:

EF = h^cotgp

Trpng Itfdng phln AEF:

W^=-yh\cotgp

(57)

(58)

(59) Trpng Itfdng Idng thi trtfdt bj ddng thtfc ABCE:

W^^ = (^ + 4o + A)tg0 - AfotgP (60) Vdi:

Hinh 7: Mat da't ntfa nghieng trdn- dd't rdi.

Mat da't AEG nim tren dtfdng AD- ntfa nghieng tren:

Ky hieu:

W^, = Trpng Itfdng Idng the trtfdt bj dOng tiitfc ABCE.

W = Trpng Itfdng phln ao AEF.

}y = Trpng Itfdng phln FBC.

A = -rh^

2 Ao=rhh,

(61)

Theo dd, ta thidt Idp dtfdc phtfdng trinh dang (1) d l tinh dp Itfc hi dOng cua da't rdi - mat da't nghidng tren:

^ D^tg^0 + D,tg0 + D, 'P' tg0-tg<p Yidt lai (62) dang:

(62)

_, D^Z'+DiZ-i-D,

(63)

w^,=w-w^

⁽⁵⁵⁾

MOt sd cdng thtfc dan xuat de xay dtfng phtfdng trinh dang (1):

Chieu dai canh FC:

FC = (h + h,)tg0 (56) Trpng Itfdng phln FBC:

Trong dd:

D^=(A + Aio+A)tgq}

D,=A + A,o + A,- A,cotgPtg(p (64) p,=-A,cotgP

Gdc phd hoai mat trtfdt bj dOng ^^^* tim dtfdc nhd phtfdng trinh (4a) vdi cac he sd:

Sd 3+4 - Nim 2012

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DI£N DAN KHOA HQC - C6NG NGH$

A^.=A

(65) N^=-2tg(pD,

[N,=-(D,^tg(pD,)

Nghifm z Id mOt sd dtfdng nhd nhd't vd thda man bd't ding thtfc sau:

(46) ta cd:

^ . _D\tg^0 + D\tg0 + D' 'P' tg0-tg(p Ndu chd ^ tdi (3) vidt lai (51):

Z)*,Z' + D*.Z + D*„

z = ig0>r^=^ cotgP (66)

E' =-=-^

Trong dd:

Z-a

(72)

(73)

2. Dd't dinh:

Sd dd tinh todn bilu diln trdn hinh 8.

f £ C

D\=D^ + B + B^

D\ = Z), (74)

D\ = B + B,-D,

Hinh 8: Mat dat ntfa nghieng tren- ddt dinh.

'V'xl-'?

Ngodi cdc ltfc tde dung Ien co the trtfdt bj dOng cd mdt da't ntfa nghieng dtfdi nhtf trtfdng hdp da't rdi, d day cdn thdm Itfc dinh

r.. xua't hien tren b l mdt trtfdt BC.

p • • •

MOt sd cdng thtfc dan xua't d l Idp phtfdng trinh (1) nhtf sau:

Chilu dai canh FC:

FC = (h + h,)tg0 (67) Chilu ddi mdt trtfdt bi dOng FC:

BC = (h-hi)y]\ + tg'0 Ltfc dinh T^,:

T^.={B-B,)4\^-tg'0

\B = ch

(68)

(69) (70) Ap Itfc bi dOng thdnh phln E

bTp

^^rp^=^^-^Wi^Z^

⁽⁷¹⁾

Phdi hdp phtfdng trinh (71) vdi (62) theo

Cdc kS hilu D2, Di vd Do dtfdc tinh theo cdng thtfc (64)

Gdc phd hoai cua mdt trtfdt bj dOng 0^^, tim dtfdc ttf phtfdng trtnh (4a) vdi cdc hO sd:

N, = D\

N, = -2N,tg<p (75) N3 = -(D\+D\tg<p)

3. Vi du kiem tra 4:

VI du 1:

Stf dung sd lifu trong vi du 1 - vi du kiem tra 3 nhtfhg mdt dCt ntfa nghieng tr6n - dd't rdi de tinh dp ltfc bi dOng cda dl^t rdi len ttfdng chin da cho.

Tinh cdc dai Itfdng tiieo (61): A=7,056 T/m, Aio = 2,52 T/m, Aio = 0,225 T/m

Tinh cdc h i sd theo (64): D2 = 4,77995, Di = 9,17858, Do = -1,27623

Tinh cdc hO sd theo (65): Ni = 4,77995, N2 = -4,66236 , N3 = -3,20998.

Gidi phtfdng trinh (4a): z = 1,44135.

Kilm tra dilu ki|n (66): z = 1,44135 >

Z*^ = 1,01288 Dilu kidn (66) tiioa man Ap Itfc hi dOng cda dd't rdi - mat dd't ntfa nghidng trdn dtfdc tinh theo phtfdng trinh (63): i:,^. =22,9472 T/m.

Cung vdi sd lieu ndy, tinh dp ltfc bi dOng cda dd't rdi cd cdc tham sd mdt da't khac nhau (Bdng 5).

30

Si 3+4 - NSm 2012

Bilit3i>d

DI£N DAN KHOA HQC

- CdNG NGHf:

Bang 5: Ap lyc bj dOng cda ddt rdi mdt dat ntfa nghieng trdn Ket qua tinh

toan Z^tgG E\pAT/m)

/?= 5°

hi (m) 0

1,38777 20,7639

0,3 1,49213

20,794

0,5

Khdng thda dilu ki^n (45)

.

P= 10°

h2(m) 0

1,23381 23,8847

0,3 1,53672 20,9843

0,5 1,44135 22,9472 Sd lidu trong bang nay cho thd'y cdc cdng D*i = 9,48283 , D*o =12,2538

thtfc da thidt lap la dung din.

Vl du 2:

Stf dung cdc sd lidu trong vl du 2- vi du

Tinh cdc he sd theo (75): Ni = 15,9734 , N2 =-7.96433, N3 =-14,6179

Giai phtfdng trinh (4a), thu dtfdc: z = kiem tra 3 nhtfng mat dat ntfa nghieng tren 1,23788

de tinh dp ltfc bj dOng cua da't dinh len ttfdng chin da cho.

Ap ltfc bj dOng da't dinh E^^, dtfdc tiiidt lap dtfa tren cdng thtfc (46):

Kiem tra dilu kien (66): Zgh = 1,23788 >

Z\^ = 1,01288 Dilu kien (66) thoa man.

Ap ltfc bj dOng cua da't dinh- mat da't ntfa nghieng tirdn dtfdc tinh theo phtfdng trinh Tmh cdc dai Itfdng: A= 7,056 T/m, B= (73) vdi cdc he sd tinh theo (74): E\^.

11,48 T/m, Aio= 2,52 T/m, Bi= 2,05 T/m ^ 9 0 2 9 1 T/m.

^ ^ ^ ?'^^,^ T("^.' u .^.^ T^ o AArtnc^ Cung vdi sd lieu nay, tinh dp ltfc bj dOng Tinh cac he sd theo (64): D2 = 2,44339 , , ^.' ,. , ^ ^ 1 -' -* ^-'. v

!. /o«oo' ^ , ^-;^oo cda dat dinh cd cac tham so mat dat ntfa Dl =9,48283 , D o = 1,27623 ^.^ ..^ n . - u ^-D- AN

L . V . ,.- y^ ,nA^ T^* icm-j/i nghidng tren khac nhau (Bang 6).

Tinh cac he sd theo (74): D*2 = 15,9734, & &

Bang 6: Ap luc bi dOng cua ddt dinh- m^t dlt ntfa nghidng tren.

Ket qua tinh toan

tgS E\pXTIm)

P= 5°

0 1,15226 45,8026

hi(m

I

0,3 1,24145 44,6345

0,5 Khdng thda dilu kien (66)

P= 10°

0 1,04363 51,3183

h2(m) 0,3 1,26386

46,112

0,5 1,23788 49,0291 Sd Ueu trong bang ndy cho thd'y cdc cdng

thtfc da dtfdc thidt Idp Id ddng din.

VL Thidt lap cdng thtfc giai tich vdi dp ltfc da't bj dOng-Mdt da't ntfa ngang (Tren/Dtfdi)

6.1. Mat da't ntfa ngang dtfdi:

1. Dd't rdi:

Sd dd tinh toan bieu dien nhtf ti-dn hinh 9.

Hinh 9: Mat da't ntfa nghidng dtfdi- da't rdi.

Sd 3+4 - Nim 2012

31

Bien^bd

DifsN D A N KHOA H Q C - C 6 N G NGH<;

Mdt da't: AEG. Doan nghidng EC nim dtfdi AD.

Ttf sd dd ndy cd till vidt dtfdc:

W^.=W-W, (76) Trong dd:

fV^. = Trpng Itfdng Idng thi tf-tfdt bj dOng thtfc ABCE.

W = Trpng Itfdng phln do ECD.

W = Trpng Itfdng phln ABD.

MOt sd cdng thtfc din xua't d l xdy dtfng phtfdng trinh dang (1):

Chilu ddi canh AD:

AD = htg0 (77) Trpng Itfdng phln ABD:

W^'^rhUg0

Chilu ddi canh ED:

ED = hcotg0-s Chilu ddi canh CD:

CD = {hcotg0-s) s'lnP cos{0-p) Trpng Itfdng phln do ECD:

W^=- Yihcotge - sf ]•

^ 2 cotgP+tg0 (78)

(79)

(80)

(81) Trpng Itfdng Idng till tiifdt bi dOng tiitfc ABCE tiieo (76):

^ 1 ih'cotgP+2hs)tg0-s' P' 2 cotgp+tg0

Ap Itfc bi dOng cda dift rdi:

D,tg'0 + D,tg0 + D,

v=^

E,tg'0 + Eitg0 + E,

(82)

(83) Ndu chd S ddn (3) Yie't lai (83) dang:

D,Z' + AZ + D„

E^bp- =^P r>^2

E^Z^-^E^Z + E^

Trong dd:

Ap=0,SY

Dj = (h^cotgP + 2hs)tg(p Di=h^ + Iks - s^tgcp

(84)

(85) D, = -s'

E,=\

E,=cotgP-tg<p

[Eo=-tg<pcotgP ^ ^ Gdc phd hoai mdt trtfdt bj dOng 0^^ tim dtfdc nhd phtfdng trinh (4a) vdi cdc hd sd:

> , =D2E,-DjEj

N,=2iD,E,-D,E,) (37) A^3 = D,Eo-DoE,

NghiOm z Id mOt sd dtfdng nhd nhl^t vd thda man bd't ding thtfc sau:

Z = tg0>Z^,=-

(88) 2. DSft dinh:

Sd dd tinh todn bidu diln trdn hinh 10.

90-{d-fi'

Hinh 10: M$t dit ntfa nghiang dudi- dlt dinh.

Ngodi cdc ltfc tde dung ldn cd' thi trtfdt bi dOng cd m$t dd't ntfa nghidng dtfdi nhtf trtfdng hdp dd't rdi, d ddy cdn thdm ltfc dinh

Tp xud't hiln trdn b l mdt trtfdt BC.

Ttf nhdn xdt trdn, dp ltfc bi dOng cua dlt dinh E\p bao gdm 2 thdnh phln gidng nhtf (46).

MOt sd cdng thtfc din xudft di Idp phtfdng trinh (1) nhtf sau:

Chilu ddi mdt trtfdt BC:

BC = {h + stgP)

Ltfc dinh T„

l+tg0tg^ (89)

32

sd 3+4 - Nim 2012

DI£:N DAN KHOA HQC - C6NG NGH|:

T = B ^ ^ ^

P' '\ + tg0tgP (90) Ap ltfc bj dOng cda dd't dinh Vdi B^=c(h + stgp) (91)

Ap ltfc bj dOng thdnh phln £^^^ do ltfc dinh Tp gdy ra :

E =B ^-^^^ (92)

"^P- '(\+tgPtg0)(tg0-tgP)

^. ^D,tg'0 + D,tg'0 + D^tg0 + D,

"P- E,tg'0 + E,tg'0 + E,tg0 + E, Ndu chd S t<5i (3) vidt lai (93):

. D^Z^+D.Z^+D.Z + D^

— —21

*^" E^Z'^+E^Z''+E,Z + Eo

(93)

(94)

Trong dd:

D3 = AptgtptgPih^cotgP + 2hs) + B^

D^ = Aptg(p{h^cotgP + 2hs) + AptgPQt^cotgP + 2hs- shgq)) + B^cotgp D, = AptgPih'cotgP •\-2hs- s^tgtp - s'tgP) + 5,

p, = B^cotgP-Aps'

(95)

E,=tgP

E^=2-tg(ptgP

E,=cotgP-2tg<p (96) .^0 = -tg<pcotgp

Gdc pha hoai mdt tiifdt bj dOng 0^^- tim dtfdc nhd phtfdng tiinh (4b) vdi cdc he sd:

N,=D^E.^-D.,E^

N,=2(D,E,-D,E,)

. A^3 = 3(D3Eo - D0E3) + AE, - AE^

N,=2(^D,E,-D,E,) (97) N,=D,E,-D,E,

Nghiem z Id mOt sd dtfdng nhd nh^t vd dtfdi:s=l,0 m, y5 = 10°

tiioa man bd't dang tiitfc (88) Qi^i

rmh cdc he sd tiieo (86): E2 = 1, Ei = 5,18445, Eo =-2,76631.

rinh cdc he sd tiieo (87): Ni = 77,0171, N2 =-113,10i,N3 =-131,975.

Giai phtfdng trinh (4a): z = 2,43262 Kiem tra dilu kien (88): z = 2,43262 >

Z ^ = - ^ =0,357143

** 2,8

Vdy dilu kidn (88) tiioa man vi du 2:

Hay tinh dp ltfc bj dOng ldn ttfdng chin cao h=2,8m cua da't rdi vdi 9) = 14°,

c = 4,lT/m\ mdt dd't ntfa ngang

Tinh cdc dai Itfdng:^ =0,9 r / m 3. Vi du kilm tra 5:

VI du 1:

Hay tinh dp Itfc bi dOng Idn ttfdng chin 5, = 12,2028 TI m

cao h=2,8m cua dd't rdi vdi y = \,%Tlm\ Tinh cdc he sd theo (95):D3 = 14,1834, - ^x-, V „ ^,y/»i.c-.i n D2= 88,3552, Di = 56,8824, Do = 68,3162 ffl = 26°, mat ddt ntfa ngang dtfdi:s=l,0 ^ z ° » '^ \^ • " n n ^ a

^ ' • Tinh cdc he so theo (96): E3 = 0,1763, m, y0 = lO° E2 = l,95605,Ei = 5,173555,Eo=-1,41407

Gidi Tinh cdc hd sd theo (97): Ni = 12,1664 , Tinh cdc he sdtheo (85): D2 = 24,419, Di N2 = 126,7 , N3 = 249,554 , N4 = 517,14

= 49,582, Do = -1

Sd 3+4 - Nim 2012

33

Bi^it3bd

D I £ N D A N KHOA HQC C 6 N G N G H | :

N5 = -433,872.

Giai phtfdng trinh (4b): z = 1,61616 Kiem tra dilu kiOn (88): z = 1,61616 >

^ « / . = ^ =0,357143

Vay dilu kifn (88) thda man.

Tinh dp ltfc bj dOng theo (93):

E\„. =35,2251 Tim

hp

6.2. Mat da't ntfa ngang tren:

1. Dat rdi:

Sd dd tinh todn bilu dien nhtf tren hinh 11.

90'-(e-p)

Hinh 11: Mat dat ntfa ngang tren- dat rdi.

Mat da't: AEG. Doan nghieng EC nim dtfdi AD.

Ttf sd dd ndy cd the viet dtfdc:

W^,=W+W^ (98) Trong dd:

W^^ = Trpng Itfdng Idng till tiifdt bi dOng thtfc ABCE.

W^ = Trpng Itfdng phln do CDE.

W = Trpng Itfdng phln ABD.

MOt sd cdng thtfc din xu^t dd xdy dtfng phtfdng trinh dang (1):

Chilu dai canh CD:

sin/?

CD = {htg0-sy

cos(0 + P) Trpng Itfdng phln CDE:

(99)

W,=A, (htg0-sy

(100) cotgp-tg0

Trpng Itfdng Idng thd trtfdt bj dOng thtfc cda dl't rdi:

(^h^cotgp-2s)tg0 + s^

^ p ^ = ^ (101) cotgP-tg0

Ap ltfc bj dOng cua ddt rdi cd thd tinh theo (83) hode (84) vdi:

1

1

A = (h^cotgP - 2hs)tg(p

D, = h^cotgp -2hs + s^tg<p (102)

Do =5^

[ £ , = - 1

E^^cotgP^-tgcp

E,=-tg(pcotgp ^^^^^

Gdc phd hoai mdt trtfdt bj dOng 0^^ tim dtfdc nhd phtfdng trtnh (4a) vdi cdc hd sd:

>

A^, = D 2 E , - D . E j

N,=2{D^E,-D,E^)

k=AEo-^oE,

(104)

2. Dd't dinh:

Sd dd tinh todn bidu diln trdn hinh 12.

9 < ^ P )

Hinh 12:

Mdt dat ntfa ngang tren- da't dinh.

34

Sd 3+4 - Nim 2012

Bi^i^d

^Dii:N D A N KHOA H Q C - C 6 N G N G H | :

Cong thtfc (46) van dung cho trtfdng hdp ndy:

MOt sd cdng tiitfc dan xud't dd lap phtfdng trinh (1) nhtf sau:

Chilu dai mdt trtfdt BC:

BC^ih-stgP) Ltfc dinh T^,:

^\ + tg'0

\+tg0tg<j> (105)

T„. = B,

a* c

yl\+tg'0

hip •

\-tg0tgP

Ap ltfc bj dOng thdnh phln E^

dinh Tp. gay ra :

E = 5 ^ _ l ± i £ ! ^ _

"•'P' '(\-tgPtg0){tg0-tgP) Ap ltfc hi dOng cda da't dinh cd the tinh tiieo (94):

D\Z^ + D\Z^ + D\Z + D\

(106) do ltfc

(107)

^"P* E\Z'+E\Z'+E\Z + E\ ⁽¹⁰⁸⁾

(109) Vdi:

D\=-(^ApD,tgP+B,)

D\ = ApD, - ApD,tgP + B, cot gP D\=ApD,-ApD,tgP-B,

p \ = ApD, + B^cotgP Vdi:

1^

2'

Bc = c(,h-stgP)

Trong (108): tinh theo cdng thtfc (102);

^p=-::r (102)

con:

(110) 'E\=tgP

E\=-{2+tg(ptgP) E\=cotgP + 2tg^

E\=-tg(pcotgP

Gdc phd hoai mat trtfdt bi dOng 0,p. tim dtfdc nhd phtfdng trinh (4b) vdi cac hd sd:

A^',=D*3E\-D\E'3 Ar,=2(D-3E*,-D',E-3)

^ 3 = 3 ( D ' 3 E ; - D * O E - 3 ) + D \ E ' , -D\E\

N*,=2(D\E\-D\E\) (111) N',=D\E\-D\E\

3. VI du kiem tra 6:

VI du 1:

Tinh dp ltfc bj dOng cda da't rdi, mdt daft ngang trdn khi ddng sd Hdu vi du 1- Yi du kilm tra 5.

Gidi

Tinh cdc he sdtheo (102): D2 = 18,9567, Di = 33,3574, Do =1,0

Tinh cdc he sd theo (103): E2 = -1 , El = 6,15985, Eo =-2,76631.

Tinh cdc hd sd tiieo (104): Ni = 156,128, N2 =-102,88 ,N3 =-115,035.

Giai phtfdng tirinh (4a): z = 1,2489 Kilm tra dilu kien (88) thoa man.

Tinh dp ltfc bj dOng theo (84):

£,,, =21,3096 r//M

hp

YI du 2:

Tinh dp ltfc bi dOng cda da't dinh, mat da't ngang tirdn khi ddng sd lieu vi du 2- VI du kiem tra 5.

Giai

Tinh cdc dai Itfdng phu: Ap = 0,9 T/m^-, 5, =10,7572 r / w

Tinh cdc hd sd theo (102): D2 =9,6902;

Dl = 39,199; Do = 1

Tinh cdc hdsd tiieo (108):

D*3 = -12,2947; D*2 = 63,5306 ; D*i =24,2912

D*o = 61,9164

Tinh cdc hd sdtheo (110): E*3 = 0,1763;

E*2 =-2,04395 ;E*i =6,17075 E*o =-1,41407

Tinh cdc he sd tiieo (111): N*i = 13,9293;

N*2 =-160,3; N*3 =461,091 N*4 = -73,4346; N*5 = -416,42

Sd 3+4-Nim 2012

35

iin^ihd

D I £ N D A N KHOA HQC - C 6 N G N G H | :

Giai phu'dng trinh bac bon (4b) va chon nghiem difdng nho nhaft: z = 1,4043

Kiem tra dieu kien (88) thoa man.

Tinh ap life bi dong cua da't dinh:^',^. =50,49017/m

VII. Kd't luSn:

7.1 DiTa tren ly thuyet ap life dat Coulomb, tie'p can theo phu'dng phdp trufc tiep da difa den cac cong thiJc giai tich de tinh ap life bi dong cua daft rdi cung nhif da't dinh len tifdng chan tuyet doi ciJug th^ng diJng vdi cafu hinh phiJc tap cua du'dng mat dat.

Cac cong thiJc kien nghi da du'dc kiem tra chat che ve mat vat ly va toan hoc suot trong cac qua trinh xay difng. Do tin cay va tinh hdp ly cua chiing bifdc dau du'dc chitng to qua ket qua cac vi du kiem tra.

7.2 Vdi each lam hoan toan gio'ng nhif ap life da't bi dong, ap liJfc da't chu dong cung se thu du'dc nhd c^c cong thiJc giai tich tifdng tif da difdc trinh bay trong [9].

He thong cac cong thiJc giai tich de tinh ap life da't doi hoi ty my can than khi thie't lap nhifng rat ddn gian nhanh chong khi suf dung.

7.3 Vdi mot so lifdng hiJu han cac cong thiJc giai tich tong quat nhifng c6 the cho ta bie't thong tin quan trong ve goc phd hoai cua mat tru'dt va ap life dat tifdng iJng vdi cac tham so daft khac nhau, dac biet la vdi cac du'dng mat dat cd hinh dang phiJc tap khac nhau, dap iJng du'dc yeu cau cua thi/c tien san xua't. Cung xin lufU y rang lufc dinh anh hifdng nhieu den dp life daft tinh du'dc nen phai than trong khi chon gia tri tinh.

He thong cac cong thifc giai tich di xac dinh ap lu^c da't nay se du'dc vtng dung vao viec tinh coc chiu life ngang khi mat dat khong nam ngang da difdc trinh bay d [10]

va se difdc gidi thieu chi tiet hdn d bai viet tie'p sau.

TAI L I $ U THAM K H A O

[1]- PD.31.31-27-81: "Hifdng dan thie't kecong trinh ben cang bien", Moskva,1984 (Tieng Nga).

[2]- Bowles J.E: Foundation Analysis and Design, Fifth Edition, McGraw- Hill, 1997

[3]- Dinh Xuan Bang, Nguyen Tien Cifdng, Phan Tifdng Phiet: Tinh todn ap life daft 6i len cong trinh. Nh^ xua't ban Khoa hoc va Ky thuat, H^ Noi, 1973.

[4]- Phan Trifdng Phiet: Ap life da't da va ttfdng ch^n daft. Nha xua't ban Xay difng. Ha Noi, 2001.

[5]- Bronstein, Xemediaep: So tay toan hoc gi^nh cho ky sif va hoc vien cdc tnfdng cao dang ky thuat. Nh^ xua't ban Tien bo, Matxcdva. (Tran Hilng Thao dich).

[6]- Phan Dung: "Mot cich ddn gian de danh gia miJc dp giam ap life bi dong do mat daft nghieng" Noi san Khoa hoc va Giao due, No.3-2003, Trifdng Dai hoc Dan lap ky thuat Cong nghe Tp.HCM, tr.41-45.

[7]- Phan Dung: "Ap life da't bi dong khi mat dat nijfa nghieng" Tap chi thong tin khoa hoc ky thuat, No.8-2003, Tnfdng Dai hoc giao thong van tai Tp.HCM, tr.28-37.

[8]- Phan Dung: "Ap Itfc daft bi dong cua da't khi mat dat nufa ngang" Noi san Khoa hoc va Gido due, No.4-2003, Tnfdng Dai hoc Dan lap ky thuat Cong nghe Tp.HCM, tr.32-37.

[9]- Phan Dung: "Mot cdch tinh Ap Wc da't chu dong cua daft" Tap chi thong tin khoa hoc ky thuat, No.2-2003, Tnfdng Dai hoc giao thong van tai Tp.HCM, tr.15-21.

[10]- Phan Dung: "Cach xet mat dat khong nkm ngang khi tinh coc chiu life ngang" Ky yeu cua Hoi nghi Khoa hoc va Cong nghe Ian thtf 10, Tnfdng Dai hoc Bach khoa Tp.HCM, tr. 330-337.

36

S6 3+4 - Nam 2012