1. toanvanluanan.ncs ngoquotrinh

7/24/2019 1. Toanvanluanan.ncs NgoQuoTrinh

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LUN N TIN S K THUT


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62 58 02 08

LUN N TIN S K THUT

. .

. .


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Ti xin cam oan y l cng trnh nghin cu ca ring ti.

Cc s liu, v kt qu trong lun n l trung thc v cha tng

c ai cng b trong bt k cng trnh no khc.

Tc gi

Ng Quc Trinh


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LI CM N

Tc gi lun n xin by t lng bit n chn thnh i vi PGS.TS Vng

Vn Thnh v TS Trn Hu H tn tnh hng dn, cho nhiu ch dn khoa hc

c gi tr v thng xuyn ng vin, to iu kin thun li, gip tc gi trong

sut qu trnh hc tp, nghin cu hon thnh lun n v nng cao nng lc khoa

hc ca tc gi.

Tc gi xin chn thnh cm n cc Gio s, Ph gio s, Tin s, cc chuyn

gia, cc nh khoa hc trong v ngoi Trng i hc Kin trc H Ni, c bit

GS.TSKH H Huy Cng tn tnh gip , ch dn v ng gp kin lun

n c hon thin.

Tc gi xin trn trng cm n cc cn b, ging vin B mn Cng trnh

ngm a k thut, Khoa Xy dng, Khoa sau i hc Trng i hc Kin trc

H Ni; cc phng, ban, khoa, cc bn ng nghip v lnh o Trng i hc

Cng ngh GTVT to iu kin thun li, ng vin, gip v hp tc trong

qu trnh nghin cu v hon thnh lun n.

Cui cng tc gi by t lng bit n i vi ngi thn trong gia nh

ng vin khch l v chia s nhng kh khn vi tc gi trong sut thi gian thc

hin lun n.

Tc gi

Ng Quc Trinh


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MC LC

LI CAM OAN

LI CM N

MC LC

DANH MC CC K HIU C BN S DNG TRONG LUN N

DANH MC CC HNH, TH TRONG LUN N

DANH MC CC BNG BIU TRONG LUN N

M U

1 L do la chn ti ......................................................................... 1

2 Mc tiu nghin cu ..................................... ..................................... 33 i tng v phm vi nghin cu ...................................................... 4

4. Ni dung nghin cu .......................................................................... 4

5 Phng php nghin cu .................................... ................................ 4

6 B cc ca lun n ....................................... ...................................... 4

7 Nhng ng gp mi ca lun n ....................................................... 6

Chng 1: TNG QUAN CC PHNG PHP NGHIN CU TNG

TC GIA CC VI NN T CHU TI TRNG NGANG1.1 Tng quan v ng t................................................................................ 9

1.1.1 ng t ..................................................................................... 9

1.1.2 Ngun gc ng t ..................................................................... 10

1.1.3 Sng ng t ............................................................................. 13

1.1.4 Cc thang nh gi cng ng t ......................................... 15

1.1.5 Nhim v thit k khng chn cho cng trnh v cc thng s

chuyn ng nn t ............................................................................. 16

1.2 Tng quan cc phng php nghin cu tng tc gia cc vi nn t chu

ti trng ngang.................................................................................................. 18

1.2.1 Nhm cc phng php da trn m hnh nn Winkler ................ 18

1.2.2 Nhm cc phng php da trn m hnh n hi lin tc ........... 28


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1.3 Tm tt v nhn xt chng 1 .................................................................... 34

Chng 2: NGHIN CU TRNG THI NG SUT BIN DNG CA

NN T CHU TI TRNG TNH NM NGANG

2.1 Cc phng trnh c bn v phng trnh truyn sng ca mi trng

n hi ............................................................................................................. 36

2.1.1 Cc lin h c bn ca mi trng n hi .................................... 36

2.1.2 Xy dng cc phng trnh vi phn cn bng v phng trnh

truyn sng theo PPNLCT Gauss .......................................................... 38

2.1.2.1 Phng php Nguyn l cc tr Gauss ............................. 38

2.1.2.2 Xy dng phng trnh vi phn cn bng ........................ 41

2.1.2.3 Xy dng phng trnh truyn sng ................................ 44

2.2 Cc li gii i vi khng gian v hn n hi v na khng gian v hn

n hi ............................................................................................................. 47

2.2.1 Li gii khng gian v hn n hi .............................................. 48

2.2.2 Li gii na khng gian v hn n hi ....................................... 49

2.3 Xy dng bi ton tng tc gia khi t vi na khng gian v hn

n hi.............................................................................................................. 50

2.3.1 H so snh l na khng gian v hn n hi .............................. 512.3.2 H so snh l khng gian v hn n hi ..................................... 54

2.4 Gii bi ton bng phng php phn t hu hn ...................................... 57

2.5 Kim tra kt qu v cc nhn xt ............................................................... 61

2.5.1 Bi ton h so snh l na khng gian v hn n hi ................. . 61

2.5.2 Bi ton h so snh l khng gian v hn n hi ......................... 66

2.5.3 Bi ton tnh khi t c xt n trng lng bn thn ................. 68

2.6 Kt lun chng 2 ..................................................................................... 70Chng 3 NGHIN CU BI TON TNG TC GIA CC VI NN

T CHU TI TRNG TNH NM NGANG

3.1 L thuyt dm Timoshenko .................................... ................................... 71

3.2 Xy dng bi ton dm chu un c xt bin dng trt ngang theo


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Phng php nguyn l cc tr Gauss ............................................................... 73

3.2.1 Phng php th nht ...................................................................... 73

3.2.2 Phng php th hai ........................................................................ 75

3.3 Phng php phn t hu hn i vi dm c xt n bin dng

trt ngang.. .................................................................................................... 78

3.4 Xy dng bi ton tng tc gia cc n vi nn t

chu ti trng tnh nm ngang .................................................................. 82

3.4.1 Trng hp dng h so snh l na khng gian v hn n hi. ...... 82

3.4.2 Trng hp dng h so snh l khng gian v hn n hi ............. 85

3.5 Kho st mt s trng hp kim tra tin cy ca chng trnh tnh. ....... 88

3.5.1 So snh kt qu theo li gii ca chng trnh MstaticP1

khi cho m un n hi ca h so snh khc nhau .................................... 88

3.5.2 So snh kt qu ca hai li gii theo hai chng trnh tnh MstaticP1

v KstaticP1 khi lc ngang t ti chn cc .............................................. 89

3.5.3 Kho st bi ton so snh vi phng php ca Zavriev(1962)

da trn m hnh nn bin dng cc b. .................................................... 90

3.5.4 Kho st bi ton so snh vi phng php ca Poulos (1971)

da trn m hnh nn n hi lin tc ....................................................... 923.5.5 Kho st bi ton so snh vi kt qu nghin cu ca Kim,

ONeill, Matlock da trn phng php dng ng cong py ................. 93

3.6 Kho st cc thng s nh hng n s lm vic ca cc n

chu ti trng tnh nm ngang ........................................................................... 96

3.6.1 Kho st cc ngn v cc di trong nn n hi ng nht ............... 96

3.6.2 Kho st cc n ta trn lp cng ............................................. 98

3.6.3 Kho st nh hng ca cng t i vi s lm vic ca cc .... 1003.7 Kho st s nh hng ca cc ti chuyn v nn t ................................. 101

3.8 Kt lun chng 3 ...................................................................................... 102


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Chng 4: NGHIN CU BI TON TNG TC GIA CC VI NN

T CHU TI TRNG NG NM NGANG V TI TRNG NG T

4.1 Li gii xung n v ca khng gian v hn n hi ................................... 104

4.1.1 Li gii xung n v trong min thi gian ....................................... 105

4.1.2 Li gii theo bin i tch phn Laplace ......................................... 106

4.1.3 Li gii theo bin i tch phn Fourier ........................................... 106

4.2 H s gim chn vt liu ca t ................................................................ 107

4.3 Li gii s ca bi ton ng lc hc .......................................................... 109

4.3.1 S liu trn ng t El Centro, 1940 v bin i Fourier

ri rc DFT(Discrete Fourier Transform). ................................................ 109

4.3.2 Tch phn Duhamel trong min thi gian v min tn s.................. 111

4.4 Xy dng bi ton tng tc ng lc hc ca cc khi chu ti trng ng

nm ngang ........................................................................................................ 113

4.5 Kho st dao ng ca khi t v ca cc chu ti trng ng nm ngang . 115

4.5.1 Kho st dao ng khi t. ............................................................. 115

4.5.2 Kho st truyn sng ct (sng Love) trong nn t ....................... 119

4.5.3 Kho st dao ng ca cc n ........................................................ 123

4.6 Kho st dao ng ca cc chu ti trng ng t ..................................... 1254.7 Kt lun chng 4 ...................................................................................... 131

KT LUN KIN NGH ............................................................................. 132

DANH MC CC CNG TRNH CNG B CA TC GI ................ CT1

TI LIU THAM KHO ............................................................................... TK1

PH LC (Quyn 2)

Ph lc 1: Gi tr chuyn v ngang ca im nm gn tm khi t khi lc

nm ngang P tc dng b mt v ti chn khi t trongtrng hp m un n hi, h s Poisson ca h so snh bng

m un n hi, h s Poisson ca h cn tnh


nm ngang P tc dng b mt v ti chn khi t trong


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trng hp gi nguyn E1 nh trng hp 1, thay i E0 ca

h so snh


nm ngang P tc dng b mt v ti chn khi t trong

trng hp gi nguyn E0 ca h so snh nh trng hp 1,

tng E1 ca h cn tnh ln gp hai ln so vi trng hp 1


nm ngang P tc dng b mt, gia v ti chn khi t trong

trng hp tnh theo 2 chng trnh Mstatic1 v Kstatic1.

Ph lc 5: Gi tr chuyn v ngang, chuyn v ng ca im nm gn

tm khi t khi lc nm ngang P tc dng b mt khi xt v

khng xt trng lng bn thn

Ph lc 6: Chng trnh tnh khi t chu ti trng tnh nm ngang

Mstatic1

Ph lc 7: Chng trnh tnh khi t chu ti trng tnh nm ngang

Kstatic1

Ph lc 8: Chng trnh tnh cc chu ti trng tnh nm ngang MstaticP1

Ph lc 9: Chng trnh tnh cc chu ti trng tnh nm ngang KstaticP1Ph lc 10: Chng trnh tnh cc nm trong nn n hi nhiu lp chu ti

trng tnh nm ngang KstaticPLs

Ph lc 11: Chng trnh tnh khi t chu ti trng ng nm ngang

KdynaS

Ph lc 12: Chng trnh kho st truyn sng Love trong nn t KdynaL

Ph lc 13: Chng trnh tnh cc chu ti trng ng nm ngang KdynaP

Ph lc 14: Chng trnh tnh cc chu ti trng ng t KdynaPE.


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CC K HIU C BN S DNG TRONG LUN N

A Hng s ph thuc vo ti trng tnh hoc chu k chm

b Chiu rng tit din cc

c H s cn nht

C(f), C(f),C(f) Bin i Fourier ca hm y(t); x(t) v h(t)

DFT Bin i Fourier ri rc

E M un n hi ca t

E M un n hi ca cc

F Din tch tit din cc

FFT Bin i Fourier nhanh

f Tn s

f Tn s Nyquist

f(t) Lc cn nht

f(t) Lc qun tnh

f(t) Lc n hi

G M un trt ca t

G M un trt ca ccg Gia tc trng trng

h Chiu cao tit din cc

IFFT Bin i Fourier nhanh, ngc

J M men qun tnh ca cc

k cng l xo

k H s nn Winkler (m un phn lc nn theo phng ngang)

K, K cng phc i vi chuyn v ngangK , K cng phc i vi gc xoay

Khoc K cng phc hn hp chuyn v ngang gc xoay

l Chiu di cc

m Khi lng


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M M men un cc

NN, N, N, N,

NN

Cc hm ni suy

p Phn lc ca t trn mt n v di ca cc

p Sc khng ngang ti hn ca t

P Ti trng tc dng

PPNLCT Gauss Phng php nguyn l cc tr Gauss

p(t) Lc kch thch c hiu

q Lc phn b u

Q Lc ct cc

t Thi gian

T Chu k

u Chuyn v ngang nn t

u Chuyn v ngang cc theo chiu x

V Th tch khi t

V* Th tch khi t m rng xt iu kin bin

v Vn tc sng dc

v Vn tc sng cty Chuyn v ngang ca cc

z su dc theo cc

Z Phim hm lng cng bc

Z Thnh phn lng cng bc xt ti iu kin b mt AB ca

khi t na di

Z Thnh phn lng cng bc ca cc chu un

Z Thnh phn lng cng bc ca khi t Gc ni ma st

Trng lng th tch

Gc trt ngang do lc ct Q gy ra

Bin dng tng i


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Bin dng th tch

H s Poisson ca t

Thi im t xung

H s xt n s phn b khng u ca ng sut ct theo

chiu cao tit din cc

Tn s gc, tn s vng, tn s dao ng

Tn s dao ng ring khi khng xt nht

Tn s dao ng khi c gim chn

T s gim chn tng i

H s gim chn vt liu, , Cc ng sut php

, , , , ,

; , , ,,

,

sut, d h th

,

, ,

,

,

sut php, sut tp t h s sh

Du y ph(z) Th s Lre

, H s Le

G d v d e M y r

B d u

D th t AB

H det Dr

H s Kreer Kh v vt u


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DANH MC CC HNH, TH TRONG LUN N

Chng 1:

Hh 1.1 M ph t t h ( kinematic interaction)

Hh 1.2 M t t tr t

Hh 1.3 C t y v huy t t y

Hh 1.4 M ph thuyt t h t y y r t

Hh 1.5 Qu h r, v ht h v huy trt

t

Hh 1.6 B d t d s vt th y r

Hh 1.7 S t huy ht h truy s Reyeh

Hh 1.8 S t huy ht h truy s Lve

Hh 1.9 G t, v t v huy v the th t t the h

Ty t GryCr (1989) huy () v

t ()

Hh 1.10 S t u h t t d

Hh 1.11 Chu t h h h T

Hh 1.12 L t h ph tht h Newr v H (1982)Hh 1.13 Lp t tr th tr

Hh 1.14 Ph ph tru h (v 5% h ) h u

h hu

Hh 1.15 ACT3 h s d ph ph hu h tr tu

hu xy d

Hh 1.16 x hu t tr

Hh 1.17 M u ph t v p-y

Hh 1.18 M hh Wer ph - t

Hh 1.19 T t h t- - - trh: h y


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Hh 1.20 T t h t- - - trh: ph th

ph h

Hh 1.21

T t h t- - - trh: ph

th ph qu th

Hh 1.22 C ph t hh h v ph th h ph

tuy ph

Hh 1.23 S thy th s h s ht, ; S, Sv t

s h th uy v h s Pss t ( Nv v

s)

Hh 1.24 sut t d (), t ()

Hh 1.25

M hh hu t tr tr t h

Hh 1.26

M hh t 3 hu (Qus- 3D) ph - t.

Chng 2:

Hh 2.1 C sut t d ph t t

Hh 2.2 L v sut t d ph t t (), ph t h

t t d ()Hh 2.3 S t h hu t d v t t

tr t

Hh 2.4 M hh t th h t h tr h v

h h

Hh 2.5 H s sh h t tr h v h h

Hh 2.6 S th h t th d

Hh 2.7 M hh t th h t hu t d th hd h s sh h v h h

Hh 2.8 M hh t th h t hu t d h

d h s sh h v h h

Hh 2.9 Ch h t h th thh ph t h


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Hh 2.10 Ph t h h ht 20 t

Hh 2.11 S h trh th h t

Hh 2.12 M hh t th h t

Hh 2.13 Bu huy v h t h P t d t

t () v h () h t, tr hp E= E, =


t () v h () h t, tr hp = ;EE


t () v h () h t, tr hp = ;EE

Hh 2.16 T t h t v t

Hh 2.17 Bu huy v h t.

Hh 2.18 Bu huy v h t th the 2 h trh Mstt1

v Kstt1 h t tr P t d t v tr =0 (); =3

(); =5.4 ()

Hh 2.19 Bu huy v () v huy v (), t t t

th h t h xt v h xt tr th.

Chng 3:

Hh 3.1 C hu ph u q

Hh 3.2 Ph t d () v ph t d t d ()

Hh 3.3 Mh h v d h xt d trt

(), xt d trt ()

Hh 3.4 Ph t huy v d

Hh 3.5 Ph t t d

Hh 3.6 S t th tr h v h h:

()H th; () H s shHh 3.7 S h trh th

Hh 3.8 S th hu t d t tr th

Hh 3.9 Bu huy v (), e u () th the h

tr hp h s sh E= 10MP; E= 20MP


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Hh 3.10 Bu huy v (), e u () th the

h trh Mstt1 v Kstt1 h t t h .

Hh 3.11 Bu huy v (), e u () hu t tr

P=80N h th the PPNLCT Guss

Hh 3.12 Bu huy v hu P =89N h th the

PPNLCT Guss


h trh KsttPLs h hu t d t:

200N,400N,600N,800N.


K, ONe, Mt[51] h hu t d t:

200N,400N,600N,800N.

Hh 3.15 Bu huy v th the KsttPLs, K,

ONe, Mt h hu t d t: ()200N,

()400N, ()600N, (d)800N.

Hh 3.16 Bu e u th the KsttPLs, K, ONe,

Mt h hu t d t: ()200N, ()400N,

()600N, (d)800NHh 3.17 Bu huy v (), e u () d L = 4

Hh 3.18 Bu huy v (), e u () d L = 16

Hh 3.19 Bu huy v (), e u () tr

h ht v tr h, h

Hh 3.20 Bu huy v (); e u () tr tr

hp u h t thy h t t u .

Hh 3.21 Bu huy v t t v tr tr tr h vsu h .

Chng 4:

Hh 4.1 G t the h B- N tr t E Cetr 1940


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Hh 4.2 Bu ph th (); ph () t tr

t s the h B- N tr t E Cetr 1940

su h t th s

Hh 4.3 Bu t tr th the h

B- N tr t E Cetr 1940 su h t

t s s.

Hh 4.4 S tr t s

Hh 4.5 S tr t s the h t

Hh 4.6 M hh t t t h tr

h v h h

Hh 4.7 S th h t hu t d t tr

Hh 4.8 Bu huy v (), ph () p t, p y h

t h hu t tr d t t 0,5 30 Hz, t s

0,5 Hz



1,0 Hz

Hh 4.10 Bu huy v (), ph () p t, p y ht h hu t tr d t t 0,5 30 Hz, t s

0,5 Hz



1,0 Hz

Hh 4.12 S h h p t t h (G /< G/) tr

h h, u t t s LveHh 4.13 Bu huy v v the t s h h u h p

tr p d hu E= E= 10 MP

Hh 4.14 Bu huy v v the t s h u h p d

E= 20MP; u h p tr E= 4MP


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Hh 4.15 Bu huy v v p t the t s h u

h p d E= 20MP; u h p tr t E =

4MP ; 6MP ; 8MP

Hh 4.16 S th hu t d t tr

Hh 4.17 Bu huy v the t s t v tr u , v

h (). Bu huy v the hu d t t s

4,9 Hz ()

Hh 4.18 Bu huy v the t s t v tr u , v

h (). Bu huy v the hu d t t s

5,2 Hz ()

Hh 4.19 S th hu t d t tr t

Hh 4.20 Bu huy v the th t v tr u , h

(). Bu huy v (), t (), e (d) the

hu d t th 0,56s


(). Bu huy v (), t (), e (d) the

hu d t th 3,12s

Hh 4.22 Bu huy v the th t v tr u , h (). Bu huy v (), t (), e (d) the

hu d t th 8,24s


(). Bu huy v (), t (), e (d) the

hu d t th 18,48s.


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DANH MC CC BNG BIU TRONG LUN N

Chng 2:

B 2.1 B t t ph t h h ht 20 t.

B 2.2 G tr huy v h t

Chng 3:

B 3.1 G tr huy v h E= 10MP v E= 20MP

B 3.2 G tr e u h E= 10MP v E= 20MP

B 3.3 G tr huy v h th the MsttP1 v

KsttP1

B 3.4 G tr e u h th the MsttP1 v KsttP1

B 3.5 G tr huy v, e u ht the ph php

Zvrev v PPNLCT Guss

B 3.6 G tr huy v ht u the ph php Pus v

PPNLCT Guss

B 3.7 G tr huy v tr h ht v

tr h h t p .

B 3.8 G tr e u tr h ht v tr h h t p .

B 3.9 G tr huy v h u h t

E= 5 MP; 10 MP; 15 MP; 20 MP.

B 3.10 G tr e u h u h t

E= 5 MP; 10 MP; 15 MP; 20 MP.

B 3.11 G tr huy v t t v tr tr tr h v

su h .


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1

M U

1 L do la chn ti

t th t uy h th y r th h v

v ph hy h tr trh. Vt N tuy h tr

vh h hu v t tr th , h h tr

h h h tr t h, d tr h th Vt N t t

hu t y ht ph tp h t y L Chu - B, t y S

M, t y S L, t y S H, t y S C...C h u

h h h h, t u th 20 y hu v ph B t xy

r 2 tr t p 8-9 (th MSK-64), t 6,7-6,8 Rhter, h

h tr t p 7, t 5,1-5,5 Rhter v h tr tr

t yu h. hh tr t xy r t B 1935, v

6,7 Rhter, xy r tr t y S M; tr t t Tu G

1983, 6,8 Rhter, xy r tr t y S L, y st , t

t tr d r, st tr , y h h h tr ph v h

35 [14].

Vt N , v s t hh xy d hu trh xy d

h h y ht h; trh h; p thy , trhu, ; h t ph v s hp hp h, h h t

. S tr t h thh xy r t hu v thy S Trh

2- B Tr M, Qu N y t r h qu qu h

ph xy d t h ph trh v h hu qu t Vt

N tr yu u v tht h h h trh xy d ph

qu t t s t ht h trh v u s

d. Kh h ph xe xt t s v , t v tuhu tht h h, d u t; hh, ph php th t v..v.

H y, h tht trh xy d tr v t

th d tr ph php th t hh su: Ph php th

t ; ph php ph ph ; ph php th ph tr tp ph


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2

trh huy (ph php h). C ph php u u

h r v v tr tu hu tht h h

[19],[20],[21],[22],[37],[42],[44],[52],[59]... t, h tht h

h h trh xy d hu, trh th r th s

d t s tu hu hh dh t tu hu h Tu

hu 22TCN 272- 05[20]: Tu hu tht u dh the tu

hu AASHTO LRFD 1998 tr trh y h h t, ph

th t tr t, s h h h d th hh th; Tu hu

TCXDVN 375: 2006[22]: Tht trh hu t dh t

Tu hu Chu u: Erde 8, ph 1 v ph 5, h yu s d tr

tht trh h, , t h, h trh t

h h y ht h, trh h, p ph v

quy h tu hu y v h u yu u hu v ph th h

h h thu h h d h tt; Tu hu 22 TCN 221-

95[19]:C trh th tr v t tu hu s

r h trh th tr v t dh t tu

hu XNP II-7-81* N[59]. Tu hu TCXD 205-1998[21] h r t

s h d qu h hu t v t quth t d u tr h h h h d qu t t

h.

C h t th y r s ph h trh th qu

s ph h t d s hu t t , y d

v tr t s tr hp th d h t h t . D ,

v qu t th t tht v h trh h hu t tr

t t v rt qu tr. Tr trh, t php ph v hp v hu tr v h t, thut.

Nh h u thuyt v th h tr th t rt pht tr

v t hu thh tu qu tr, tuy h hu v ph tp t r

ph quyt. Kh h ht h tht hu t tr


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3

v t tr t th h x h tr th sut d

, uy h d s h h t t v . D

t t v qu ph tp th h hh.

Qu h u t u v t t v t, t thy r hu

ht ph php h y u tp tru h u the h h hh su:

- Nh ph php d tr hh Wer v x tuy

th v x ph tuy (Ch, 1937; Reese v Mt, 1956; Zvrev, 1962;

Tr Bh, 1968; ONe, 1984; Gzets 1992, Nr v Nv,1995; Thvrj

2001)[2],[4],[13],[15],[16],[17],[18],[31],[38],[41],[48],[51].

- Nh ph php d tr hh h t (Gv, 1967;

L Th, 1966; Pus, 1971,; Verrujt& Kj, 1989; L F,

2005...) [8],[17],[38],[50],[54].

xt t t v t, h ph php tr th

th t ph h x, hp ht v tr hh th t. Tuy h

v t h s x tuy th, x ph tuy ( p-y),

h s ht xt u x r v h x h v thu hh x,

t h t h v h yu d v th h xt v t

tr hp th. V t t v t h xe xt t hy , h xt h h t h xt h h

t. Mt h v xt u v h rt h h, t v

t truy s h xy r t....

T h ph th tr, thy r h u s v , tr

h u s t t v t h hu t tr v t

tr t v tht, h h h v th t, p ph xe

xt y h v ph php th t trh Vt N.2 Mc tiu nghin cu

Xy d ph php thuyt h u t t t -

t v ph th t x h tr th sut d hu t

tr v t tr t


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4

3. i tng v phm vi nghin cu

Lu h u th tr h v h

h hu t d t tr th , t tr v t

tr t.

Lu h th t tr hh t h ( d, ht),

h xt h t h tr t h xy r t; h xt h

h p r tr t h v h h u t

tr th h .

4. Ni dung nghin cu

Nh u tr th sut d h t hu t tr th

.

Nh u t t t th h v t h hu t

tr th .

Nh u t t t h v t h hu t

tr v hu t tr t tr t s v th

.

Xy d ph th t h tr hp h u tr.

5 Phng php nghin cu

Xy d t thuyt h s d ph php d h s

sh Ph php uy tr Guss (su y vt tt PPNLCT Guss)

h d th h v h h ( v t t t

th h) v h h v h h ( v t

t t h) h s sh. S d ph php ph t hu h

v d tr t qu s h t qu h h th

v t y thuyt th t.

6 B cc ca Lun n

Lu trh y ph u v 4 h, du th t

h h su:


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5

Chng 1:T qu ph php h u t t v

t h hu t tr . D tr t u thu thp , t

thu t h h qut v t v ph php h u t t

v t h hu t tr th h hu t tr

, tr s thu v h u u .

Chng 2:Nh u tr th sut, d t th qu

h u t t h t h v h v h h h

hu t tr th . Ch y trh y v PPNLCT Guss, h s

d PPNLCT Guss t ph trh tr h,

ph trh truy s; Kev v h v h h;

Md v h v h h; xy d t t t

h t h v h v h h h hu t tr

th the ph php d h s sh PPNLCT Guss; xy d

thut t v h trh th the ph php ph t hu h, tr th

t qu. Kt qu h u h s t h v h

u du tp the u .

Chng 3:Nh u t t t v t h hu t

tr th . Ch y trh y thuyt d Tshe; xy d t d hu u xt d trt the PPNLCT Guss; s d

ph php ph t hu h t d xt d trt ;

xy d t t t th h v t h hu t tr th

; d tr t qu s h st t s tr hp h u

hu t tr th .

Chng 4:Nh u t t t v t h hu t

tr v t tr t. N du h y trh y xu v h v h h; h s h vt u t;

s t h; xy d t t t h

- t h hu t tr ; xy d h trh th h


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6

st t s t d h t v hu t tr

t ; h st t d hu t tr t.

Phn kt lun, kin ngh:trh y h t qu u v h t s v h u tp the.

Phn ph lc:trh y du h trh hh p.

7 Nhng ng gp mi ca lun n

B h s d ph php d h s sh PPNLCT Guss tr v

h u t t t v t h hu t tr

h t tr t, t h t s t qu hh h su:

1. Th qu s ph php ph t hu h th Kev v Md, h h h v h

h t h v h h v t tr t t v tr t .

2. Xy d t t t th h, t t h

v t h hu t tr th, t tr t t v tr t . S

d ph php ph t hu h v t ph t h 3 hu 20 t; d

ph t 2 t v huy v, 3 t v t . Ph php y t

th u v , u tr h t h

h u tp x v t, t h t th t

ph h x, hp ht tr t tp x - t, tr h

t h . N r th h u th s h h s

v h: hu d , , t tr p v h

h s v t.

3. Tr th t h trh v th t t

xt h s ht trh. Tr u y, v t t h

d h s ht th th d h s h vt u (hysteret

dp) hy h s st h (dry rt). H s y h php xt h

t d d t h .

4. Xy d t truy s t (s Lve) t t truy

p t ph tr h xt th s t tr t ph


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7

v s t tr t ph th . D tr s ph php

ph t hu h h u h t huh d t the

ph th v ph truy s, ph hp v thuyt v truy s

Lve.

5. Xy d t t t h h hu t tr

t. S d th ph hp Duhe h tr t s,

su Furer hh, (IFFT) t qu tr th .

D t t tr t tht (E Cetr 1940) th s u v

h st, x h th s huy v, e, t t t

th .

6. D tr p trh Mt, xy d h trh ph

th t ph v tr hp h u, h st: Mstt1; Kstt1;

MsttP1; KsttP1; KsttPLs; KdyS; KdyL; KdyP; KdyPE.


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8

Chng 1

TNG QUAN CC PHNG PHP NGHIN CU TNG TC

GIA CC V NN T KHI CHU TI TRNG NGANG

Kh v t tr t d trh h t tr , t

tr xe hy tr u, t y r huy trh, h

h t ph h rt v trh. Tht vy the

Newr v Rseueth [35]: ng t lm bc l mt cch h thng cc sai st

trong thit k cng nh trong xy dng cng trnh, k c nhng sai st nh nht v

xt v phng din ny, ng t lm cho mn hc a chn cng trnh tr nn cp

thit v hp dn, c gi tr nghin cu, hc tp vt xa mc tiu trc tip ca n.Kh t th s huy t trh d t y r th

th th t tht trh the ph php h trh

h , ph php d u h. C t u v quy trh th t

t v Vt N r h d th t tht

trh hu t tr t ty the qu tr

[11],[14],[19],[20],[21],[22],[27],[37],[42],[44],[52],[59]...].

Tuy h, v h u t t trh v t huv v t r h hu t tr t t v ht

s ph tp v tr p tht h y hu h y ht h,

trh h, p thy ... h th rt xy

d tr th v Vt N. C th hu h t t

h hh du t thuy h v h tr tr s (hh 1.1) v t

thuy h h h vy h h th rt d s v hu d s

(hh 1.1)[43]. C thuy h t thy huy s,

thuy thy huy s. Nh vy t t hy h

ty thu v h th thuy s v hu d s. T thu t

h u th ph thh h t t: t t h (kinematic

interaction) h th t t xt h h h th v


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9

d h h trh huy tr v

t t qu th (inertial interaction)xt h h h trh

huy tr.

Hnh 1.1 M phng tng tc ng hc ( kinematic interaction)[43]

Tr v 30 tr y, h u t t v

t rt hu h h h qu t tr ph d thuyt ph

d th h. C th h th th h tr ru hy

th h tr y quy t. D tr t u thu thp , tr h

y t thu t h h qut t qu v t v

ph php h u t t v t h hu t tr ,tr s thu du h u u .

1.1 Tng quan v ng t

1.1.1 ng t

S dao ng ca b mt qu t do cc sng truyn n t mt ngun gy

ra trong lng qu t c gi l ng t[47], (hh 1.2).

Tru t huy h, pht r v t

thuyt, quy v t chn tiu. Hh hu h tu t qu t chn tm. Kh h t h t h tu

su chn tiu(H). Kh h t h t qu tr tm

ch khong cch chn tm(R). Kh h t h tu qu tr

tiu ch khong cch chn tiu(L).


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10

Hnh 1.2 M t mt trn ng t [36]

1.1.2 Ngun gc ca ng t

ng t c ngun gc t t gy kin to

T h u v ht, h ht h h r p

t qu t h v h ph h huy h th h. Lp

ph d hu p rt d p ph tr xu th h

d h s t tr th h st . Cu t

ht h r r rt hu ph hy xy r tr h h d vt

qu h . Kh h ph hy h vy, th h huy v trtt pht tr h t d t ph hy t r t y

t (hh 1.3). C t y th hu d t v t t hu et v

th h tr hh [35].

Hnh 1.3 Cc loi t gy v chuyn ng ti t gy [35,36]


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11

Kh ph h, tht r d ph d th

u v tr t y t. Mt ph d y r ph hu

tr xu quh h tu, t ph h truy tr

t qu t d d s huy v ( t).

t xy r h t thh t y t, t xy r d

ht t y y. G thh h y, h h h M H.F.Red

(1911) r thuyt t h (Est- Reud Thery) h qu st t t

y tr t t su tr t S Frs, Cr (1906),

[30],[35],[36],[46],[47]. Thuyt thh r d th y

tr t y, s ph h vt qu h h

vt u. N ph truy d d s truy the h

v d trh tr t t. L thuyt y thh h

t hu xy r tr t t y t; h t t h,

d h, t... C th hu thuyt y qu hh s h su : Hh

1.4 th h th th tr t h u. Hh 1.4 th h

qu trh th y d tr h t, th v t t. Hh 1.4

th h th t y su tr t v tr th tr t h

u (v th). V the thuyt y, vt u d th s th u , vt u th th th u h d

ph h.

) Th tr t h u

) Th tr d tr h t

)

Su h t

Hnh 1.4 M phng thuyt bt n hi ca t gy gy ra ng t [47]


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12

ng t c ngun gc t hot ng kin to mng

V u th 19, u th 20, hu h h h r thuyt

t (pte tets) hy thuyt tr (tet dr)

thh h u tr t tr th [35]( At Sder-

Peer, 1858; F.B Tyr, 1908; Ared Weeer, 1915).

Thuyt t h r p v qu t h t h

6 (Chu Ph, Chu M, Chu N , -, - u, Th Bh

D) v 14 h h. C t y thh . S

huy t xy r the th y d tr d

hp d the . S ph d y r t.

Nh vy v tr tr t h yu tp tru . C tr

h th h h u y.

N 1962, h ht h M H.H.Hess [35] Lh

s u v d h r h huy x hu

thh ph huy xu d. C h h yu y r s huy

t (hh 1.5): 1) D h thh ph d tr h

r y r x hu; 2) th t h, d

h th qu t uy h , v r t t s ph v thu hp t t s h th

qu huy tr trt t s v hu; 3) huy h

t p v v h t p v t p t y t y

huy t s v h the ph .

Kt hp h huy u tr v s hu t tr v

d u tr p v qu t, H.H.Hess thh y thuyt

tr. Chuy tr p th (tr p sthe) the huy v qu t. K t v thuyt tr thh tu h h t

h ht th 20.


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13

Hnh 1.5 Quan h gia g m rng, vng ht chm v chuyn ng trt ngangti cc b mng [36]

ng t pht sinh t cc ngun gc khc:d s d tr p v

qu t; d v ; d ht ; d sp t; d th

v h h [14].

1.1.3 Sng ng t

S pht r t t t the h v d h x t

t. S t s vt th v s t. S vt th

ph r h : s d P v s t S (hh 1.6). S d P y r d

tr, ht d the ph truy s v h truy qu

h rt ht h du h h . St S y r huy v h thy th th tr, ht d

tr t ph th v ph truy s. S t ph t

s t th SV v s t SH. S t h th truy

tr tr h h v tr y h h hu

sut t. M s v t tr r. V t s d h

v t s t. Chh h hu y v d tr d t t

tr h h hu th h v tr h t (us) v htu (epeter) tr t.

S h t t, d h h t v u t ph p

p v tr t s xut h s t s Ryeh (s d) v s

Lve (s t).


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14

Hnh 1.6 Bin dng nn t do sng vt th gy ra [36]

S Ryeh h ht huy the t qu hh

ep tr t ph th s s v h truy s (hh 1.7). S

Lve s t S h h thh ph th SV, h ht

huy tr t ph s s v t t, vu

v h truy s (hh 1.8).

B d s t tt hh the hu su. Nh vy d

t t ph thu rt hu v th ht tr s qu. C th

, p t h s d t s t s , t d t s h. Ch h th t trh

hu t d t ph xt u ht t h .

Hnh 1.7 S m t chuyn ng cht im khi truyn sng Reyleigh [30]


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15

Hnh 1.8 S m t chuyn ng cht im khi truyn sng Love [30]

1.1.4 Cc thang nh gi cng ng t.

H y h t tr t, th d v h

hu qu h y r tr t y [14],[35],[46].

Tr s su th t d M.S.Rss v F.A.Fre

r (1883) 10 p, 1902 h h h It G.Mer

r th t 12 p. 1931 Wd v New su hu qu tr h th 12 p y v t Th

Mer t (Mded Mer- MM). Th MM h h

t d h t v hu qu t d , vt v

trh xy d. p v yu u thut tr h v xy d, h xt

t trh xy d h hu v t ph tr trh h

h h h hu qu t, 1964 X.V Medvedev V.Spheuer

v Kr r Th t MSK-64. Th ht MSK-64 t h th th MM. Tr ht th MSK-64 ph t d

ph h t trh xy d (h h tt h h t

trh s v th MM), su t h qu h

huy d tu hu hu d r T= 0,25s.


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16

N 1935 Ch. Rhter (M) [14] r th t h

h ph h t.

The h h, M (Mtud) t tr t rt

thp ph A () h t t h h t 100

tr y h hu d r 0,8 s.

M = A (1.1)

Qu h E ph h tu v s

t M th the th

E = 11,8 + 1,5M (1.2)

T u th (1.2) h thy r h t Mt 1 th

E ph t 10h 32 ; h M t 2,

E ph t 1000 .

1.1.5 Nhim v thit k khng chn cho cng trnh v cc thng s chuyn

ng nn t

Kh tht trh hu t tr t t th s d h

tr t tht h su:

- Mt tr t v ph hp th xut h t tr tu th

trh s tht . C trh tht hu huy sh r tr t h y tht h qu

tr .

- Tr t h th xut h tr v xy d d

th t tr t h trh. V tr t y rt h h xy

r tr ph v tu th trh, t qu h t th h php

trh h h , tuy h s sp trh v t h t u

h php xy r.C th t h d h h yu h t

ph h hu t tr t v hh v h th the

t. N h th ph v tr tp h v th t h h trh.

th t trh, h t ph t d t h t.


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17

tr h, t t huy , v t

v huy v th th t t (hh 1.9). Qu t qu the th

t th h th s tht x h tr t .

Kh t xy r, s y r huy v v h trh.

Tuy h tr h h u, t th h qu t t huy

, d uy h h v trh. D tr trh

huy v the ph th t y uy h.

- C th s tr t tht hh th s huy

t v the yu u tht . C th s huy t t

th t (PHA: Pe Hrzt Aeert), v t

(PHV: Pe Hrzt Vety), huy v (PHD: Pe

Hrzt Dspeet) v trh y tr quy trh tht h h

.

a) b)Hnh 1.9Gia tc, vn tc v chuyn v theo thi gian tn ti theo hng ng Ty

ti GilroyCalifornia(1989) ca chuyn ng nn (a) v nn t (b)[46]


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18

Th t t huy h h h t tht h

d t. Mt v qu trh vt , h s suy v

h d t u v th u p r tr t h ht

h, thy s du t tr v sut h t. S

huy tr th h s sh t tr uy h tr t

u y u huy . Chuy v v ph,

h th d th sh r t tr du d t uy h .

Th huy h qu t th ph

th u hu d p t y. C h hu d h v h p

t y hu th th hu h. Kt qu th huy

u h h t h h. Kh th huy

ph thu v h h h h hu.

1.2. Tng quan cc phng php nghin cu tng tc gia cc v nn t

chu ti trng ngang

Ph th t t v t h hu t tr ,

t h hu t tr t t v rt ph tp tr tht

thut [51]. Ph th hh t t t- , t t -

, t t qu th v th ht ht ph tuy t. S t t y h h pht tr ph php u tr tht hu t tr

. Qu h u t u qu t t v

t, t h thy r hu ht ph php h y h ph th

th ph v 2 h hh: t d tr hh Wer v t d

tr hh h t.

1.2.1 Nhm cc phng php da trn m hnh nn Winkler

The ph php y, hu t xe h d hu u tr h. Ph php y th h r d tr Wer, t

h thy th t t x h p hu [50] (hh 1.10).


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19

Hnh 1.10 ng x ca cc chu ti trng ngang [50]

Ph trh v d vt h su:

EJdydz + p = 0 (1.3)

Tr : E- u h

J- e qu th tt d

p- ph t tr t v d

y- huy v Tr (1.3) h h y v p x h. Mu t h

ph th t ph trh . Chh h tht p th ph trh ph

y t h s h hu ph php.

Kh d hh Wer t : p = y (1.4)

y h s Wer hy u ph the

ph .

T qu ph php ph trh (1.3) v h s thy

the hu su trh y h y tr t u

[2],[9],[13],[15],[16],[17],[18],[50]...

Tr [38] thu ph php Ch (1937) h x s u th

h Fe. Ph php Ch s d h s h s the


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su th huy v, tr . u t r h

hu d t h v u h tr E t t

su . H s Wer x h v E /3. s d t qu

th h Fe v h th h t r hh th t

r th t qu th h. Ph php y v

quy trh Nht v ph v ht h.

Trh y tr h thy r v h h s v qu

tr h u h th t t v t h hu t tr . V x

h h s rt h v thu hh x, h yu d v th h v

t tr hp th. Mt h h s h h ph thu duy ht v

t ph thu v hu yu t h h hu d, ; thy

ph tuy the hu su v thy the t d t. The ph

php u tr h ph h t t y s v tr t

v ph php y h xt h h v h xt h s

h hu v t tr h.

* Phng php dng ng cong py

Kh r r h t, Mt, 1970; Resse, 1974;

Bhush, 1979 [38], [56] u d ph p h t h s huy v y v tht p ph trh ph th h p=(y) ph

trh (1.3). L y thy th x tuy th t h t

py ( x ph tuy) [38]. y h d

tr t qu th h h 0,6 hu t tr th v t

tr hu thp. y V du h M (API, 1993) p d

tr tht h trh h tr [31], [38], [51].

Ph trh hu p-y tr t t :

p=ApthHyAp

(1.5)

tr :

A- h s ph thu v t tr th h hu h


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21

p- s h t h t

- u ph the ph .

H- su

y- v

Hnh 1. 11M un phn lc ca nn t i vi ng cong py [38]

Tr hh 1.11, Reese (1974)[38] h tr v u t h

hu. y xe tr h ph d h. C tr h h Terzh (1955), tr y xe h

ph h v huy v u 2,5.

Mt (1970) [51] t hh th

h h tr, th h tr ph

h h tht v tr th th t t

h u. Tp tht p p-y v hu t tr

v t st t v ph trh h su:

p = 0,5p(

y

y)

(1.6)

tr : y huy v v t ph t h: y = 2,5B ;

B hu r ; d t v t s sut hh

ht.


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22

Murhs, ONe (1984) [38] h t y ph php

p-y d tr th h tr t h dh. H h u 4

p-y h hu tr h API. H h

thy r API d tt ht h r d xu

v s s . T t qu h u, Murhs v ONe (1984)[38] t u

r API h ph hp v v ph th th h t tr th v

t tr hu thp. H h r: Dng nh cc nhn t khc khng c a

vo trong cng thc py v mt thiu st c bn r rng l b st c ch truyn

lc ct gia cc l xo. Kh r h t t v qu h p-y tr

t dh h t u r: S tin cy trong vic d on vng v m men,

ng tic cn t hn!.

API (1993)[38] su h th h 54 th h h tr r

huy h tr tht s hn ch v kh nng d bo ng x tng tc cc

n t nn ph php.

Nh vy ph php d p-y th r r

h h t hy d; xt t h t v h s

. Tuy h v tht p h t h hu x h x h v

t d tr h u th h r ph trh p-yh hu th t. V y thy ph php h s trh y

tr.

* Phng php ca Thavaraj Chng trnh PILEPY (2001)[51]

M hh p-y v tr t v h trh ph

th h . V d h SPASM (Mt, 1978), NONSPS

(Kw v Krt, 1980) v PAR (PMB Eeer, 1988) [51]. Su y Thvrj

r ph PILE-PY (Thvrj, 2001) v hh th h r trhh 1.12.


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23

Hnh 1.12 M hnh Winkler ca phn ng cc t [38],[51]

Tr hh y, t t v t tr (near field)

hh h x ph tuy v hp ht. H - t v h

t u trh tr t (h thh)

huy t d v x Wer. Ph trh huy

r tr u th su :

EJv

z+A(

v

t+

v

t )+ (

v

t

-v

t

)+(v-v) = 0 (1.7)

tr EJ, A v t h u, d th v h

v ; u ph the ph , h s

h t ; v huy v t s v huy t

v; v huy v t t d s v huy t

v z hu su. v huy t tr

u y r huy , x h h th s s

t t t hu d ph s d ph t h ht xt h s hvt u (hysteretic damping) h s ht h ph thu t s (s trh

y tr h 4).


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24

H s h xt s x d t r tr

[46] ( th xe tr h h ( impedance) y the Gzets, s

trh y su).

M u ph the ph x h v v s d

p-y. Ch trh PILE-PY d Thvrj p ph trh (1.7)

v th s th t trh y tr.

The ph php y th xt h v xt th ht ph

tuy, t ph thu v th . Tuy h th t v s d

ph php h h hh h t t - t h x ph tuy

(s d p-y) v hp ht v xt t d ph.

* Phng php ca Gazetas, Fan v Kaynia (1993)[41].

S th trh y tr hh 1.13; 1.14; 1.15. C xe h d

tr Wer. u t y t r t ph php

hu ph th t t t- - - trh the trh t 3

h su:

+ B 1: Th huy v , xy h h xt h

trh tr ( t t t v t h

huy v t d d t y r) (hh 1.14).+ B 2 : X h tr h h (impedance) hy

ph : ph v huy v (K h K);

ph v xy (K h K) v ph h hp huy v

- xy (Kh K) (hh 1.15).

+ B 3 : Th trh tr x v ph x h

2 v hu huy v v xy x h 1 (hh

1.15).


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Hnh 1.13 Tng tc ng lc hc giat cc b mng cng trnh: h y.

Hnh 1.14 Tng tc ng lc hc gia tcc b cng trnh: phn tch phn ng nghc.

Hnh 1.15 Tng tc ng lc hc gia t cc b mng cng trnh: phn tchphn ng qun tnh [46]

B 1 h xt h trh, h th t t

h (kinematic interaction); 3 xt h trh tr

t t qu th (inertial interaction).

Nu h th t th t qu u .

Tr th t s d h s v h s ht d hh Gzets h h su:

1.2E (1.8)

2

+ vd (1.9)


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26

tr : E u h, h v, h s st

h, v v t s t t; d h ; t s v (rd/s);

t s h th uy = d/v.

T t, tr , th h t h h

d ph Nv [49] v t t t d tr tr t.

C t tr d ph php y t t t

tr h hu v t h hu t tr t t .

u ph php tr th trh h , v

th t t ph tp h.

X th, ph php d ph hu t

h u, t J.P.W [56] r hu ph h hu ph

v h v th t v su h hu t tr t.

* Phng php ca Naggar v Novak (1996)[48]

C xe th t t tt d tr h tr

p t ph tuy . t h thh hu p, h

thh v s v hu d t t h p t (hh 1.16). Ph

th trh y tr th d d hh h th ht ph tuy

v u h t t.

Hnh 1.16 Cc phn t ca m hnh ngh i vi phn tch ng lc hc phituyn ca cc n phn ng ngang [48]

Tr p, t h thh h ph: Ph th ht hh

, xt th ph tuy h h. Ph th h hh x,


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27

xt s truy s t r x. Tr hh y, ph t 2

hh h th r hu xt tr th sut v u

h t h h h t tr thy .

Phn t min gn. T t hh h

x ph tuy, th the u sut ph. M

tr ht, h v ht. C v tr. Kh s

th r t - t v huy v h.

K x h the Nv v Shet [55]:

K=8G(1-)(3-4)[(r/r)

+1](r/r)

+(3-4)[(r/r)+1](r/r)-1

(1.10)

tr :

r r h tr v tr, h s Pss t.

G u trt s ph hp v d, tht r h

s Pss h s, th:

G= G(1- ) (1.11)

G u trt ht u p t.

h s huy : =PP

(1.12)

P t x ; P t h x th t d the

tu hu API [31].

Phn t min xa.Nv t d . Tr

y, u d ph tht th t. Mt t h

h ph t v v hu d t hh tr

h tr ht tuy th tru h.

Ph t x hh h x v hp ht h s:

K= GS() (1.13)

C =Gr

vS(= 0.5, ) (1.14)

tr : S v S t s p v tr h h ty the

h s Pss t v t s h th uy h ph = r/v(hh 1.17).


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28

T s y p v v h s ht s d h ph th

tr th .

Hnh 1.17 S thay i cc thng s h s nht, cng ngang; S, Svitn s khng th nguyn av h s Poisson ca t ( Novak vcc cng s)[48]

1.2.2 Nhm cc phng php da trn m hnh nn n hi lin tc.

Tr ph php y v h d hu u, d t

h h h xy r t v tr t t tr xy r h h x

v tr t t tr.

* Phng php s dng li gii ca Mindlin

N 1968,L c Thng[17] t tr h u t s d

Md v t th t tr h v

h h th t . tht p ph trh ph th h h ph

trh (1.3) h h hp huy v t th the Md v huy

v .

- N 1971, Poulos[51] d v Md th huy v

t h t tp tru t tr h h,

huy v th the (1.3). C s thuyt ph php y h

su (hh 1.18):


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29

Hnh 1.18 ng sut tc dng ln cc (a), t (b) gn cc [51]

+ Tr hh 1.18, tht h hu r B, d L v

h u EJ h . C h thh (+1) ph t d h

hu, tr ph t u v hu d /2.

+ h th t h sut tp the ph

t v t v tr th t.

+ Th h t d tr ph t the ph ph

u v h the hu r

+ Th h t tr t: ht h vt u

h v h, u h E, h s Pss h h h s

t .

Tr php ph th y, Pus h huy v t v

t t ph t hu (hp huy v). Tuy h h ph t tr u

v u th h hp huy v ph th t. Ch x h huy

v h t t t ph t h h huy v t v

t h u hu d the hu v s d u

.Nh vy the ph php y h d t v xy d thuyt ph

tp h s v ph php h s Wer; h x h d ph

hp v t v u t t v ph hu th

h h tr tr v t th t [17]. M d xt


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30

t t - t h hp huy v h h y , h

xt h h t tr th sut h xt h

h tr th h t ( Pus th h t h h

h s t v h hp huy v ph t u v h

). Kh th h xt t t hu, t h xt sut php

h xt sut tp the ph t v t .

V y s t h u tr u , h php x h y s

h h t h t v th y

t 3 hu.

- N 2006, Trn Hu H [8] p d PPNLCT Guss tr xy d,

t t t v d t d t tr tr th

v. v t th t s d Md h s sh;

v t , d h h v h h h

s sh v h t qu hh x, t h t h t h

t.

Ph php y h php xt u hp th s v h

v t h ( t truy s); h php x h s

v tr h , h h s tr h t v xt h h t t truy s tr .

Tuy h t h d v h u h hu u v

h h u t t v h hu t tr h xt t

h, t t hu t tr t. V y s

t h u hu u xt d trt

v t t t v t h hu t tr t.

* Phng php tnh cc trong cc lp t n hi ca Verruijt &Kooijman [60].

D the hh h thu Verrujt & Kj

(1989)[54], t h thh p t h, hu su h h


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31

hh 1.19. C tr tr xe h d tr h hu t tr

th.

Hnh 1.19 M hnh cc chu ti trng nm ngang trong nn t n hi [54]

B t x h h s t t v t the ph

php p 4 su:

- B 1: H s x tt p t th t t t ph

th ph t hu h h p t v huy v v tr t p t,

huy v p t h h.

- B 2: C th the ph php s ph hu h h s d h

s x th 1 v qu h h p t h.- B 3: S d huy v t t tp x v t h u

, d t h ph php ph t hu h th tr huy v

p t.

- B 4: T t qu ph php ph t hu h t h

t xp x tt h h s t t t v . Qu trh ph th th

p hu v d h t hh x the yu u h su

t s p (v d 10 p).Nh vy the ph php y thy r v x h h s t t

t v th hu x h h ph php p. Mt h h s sh v

h hh h, hh y u th h h v r th tr


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32

d d v t t h v t. Tuy h t v thy t t

v t h r r v h xt tr t d ph.

*Phng php ca Finn (2005) (chng trnh PILE3D)[38]

Hnh 1.20 M hnh ta 3 chiu (Quasi 3D) ca phn ng cc t [38]

y ph php ph th h 3 hu v

tht h hh 1.20 tr.

D t d s t truy th tr, u tt d t tr t ph xy, tr , d

the hu h . B d sh r d t tr t ph yz.

Nh vy tht d tr ph th ph h h yu d

s t tr t ph xy, yz v s the hu d y. B d

the hu th v th v h h qu.

p d ph trh the hu y, ph trh h

yu h t d tr t t:

vt

= Gvx

+Gvy

+Gvz

(1.15)

Tr : G du trt ; v huy v the h h ,

h v t, h s qu h t s Pss t.


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33

C hh h h d tr h Euer th th.

C h u tr t ph yz. T t h t- - trh

duy tr huy v t thh v t.

Ph t 8 t s d th h t v ph t d 2 t s

d ph h hh 1.20. Ph trh hu vt

h h - t d d tr h:

[M]{

} + [C] {

}+[K] {}= -[M]{I}

(t) (1.16)

tr :

(t) t ; {I} vet t v; {

},{

},{ } t

t, v t, v huy v t t ; [M], [C] v [K] tr h

, ht, h - t h the ph . S tu h

hh h ht x s d ph php h

Gzets (1993) tr Ftr t v hu d t v v t t

h th ph t s d tr h trh PILE-3D

ph trh (1.16).

u : F r h h trh ph th h ph tuy

d tr hh 3 hu h PILE-

3D v PILE3D-E t ph th sut t v sut hu. Phphp y h thy d h h ph thu v v h

s ht ph thu v p r t. Ch trh PILE-

3D v PILE3D-E th th t s the th thh

ph v t h v t h tr u t. N r

F th h y t tr t t hu h h, s d

h trh PILE-3D ph th, h thy ph h t t rt

tt v s thy the th h d h thh t h trh PILE-3D. Ph php p-y s d hu h

ph th ph h s d d u t th h y t v

t qu t h trh PILE-3D. Tr h u y s d p-

y h API. Tuy h d p-y y rt h h ph th


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34

h h h xy r t h ph hp h ph th h

h, h, d s ph e tr h v th t rt tt.

C h u th h y t t t t hh Tr h

Cr tr t h h th h hh, s d h trh

PILE3D-E ph th tr h h t v s hh x,

y ph v h tht . Tr h h t, tp t xy d

d tr p r h hu h d t, hu qu

sut v t, th y r e u, t tr

h . sut hu trh y y th

ph h h h t y r p r v s h h

t ph qu tr tht h tr th t tht

.

Nh : h th t F tht t

t d h d sut t tr t ph xy, yz v sut the

hu huy y y r. Nh vy xt t d t hu t

h xt t d y 3 hu t . Mt h h thy r

s h h t t t v u x r v h

hu t tr t.1.3 Tm tt v nhn xt chng 1

T t qu h u trh y tr, t t s t tt v

h xt h su:

Tr s h u tr t h hu tr th , t

ph tr t the ph hy h ph the

Rhter d v ph h t. Nh h u v

t h t ph php hu h th s huy t v ph ph tht tht trh.

Kh t th s huy t t d trh th

th th t trh the ph php h h .


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35

Qu t qu thy ph php hh th t t t

v t h hu t d t tr v t tr t. C

ph php y h php xt th ph tuy t, s thy

t the hu su, the t d, xt h t h

h th ht t. V t t v t

hu t qu t h u v v s d h

ph...

S d hu ph php th h hu v ph php h yu

ph thu v h xt ph t th qu v x h

th s ph h h s xt ; h s ht xt u x

r v . u h thy rt h th x h th s t h

v hh x. V h vy th u v v

t th v t u h .

Mt h tr tt ph php u tr, h t t

th h thy h h t h thy h h

tr th sut t. The t d v h t hh thuyt

hu xt t t v t.

V vy, tr u h, t s d tr ph php d h ssh PPNLCT Guss xy d t t t v t h

hu t tr th , t tr v t tr t v

v xt y u v u x r v h

xt t t y v t. r ph y, tr du

h u tp the t s trh y:

+ Nh u tr th sut d t h hu t tr

th .+ Nh u t t t th h v t h hu t

tr th .

+ Nh u t t t h v t h hu

t tr v hu t tr t.


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36

Chng 2

NGHIN CU TRNG THI NG SUT BIN DNG CA NN T

CHU TI TRNG TNH NM NGANG

Tr h y t h u tr th sut d t

th qu h u t t t h t v h v h

h hu t tr th the ph php d h s sh PPNLCT

Guss [5],[6]. PPNLCT Guss t s t tr s d xy

d v t h hu t h h h trh

[1],[7],[8],[10],[23],[24],[25] tr t t t v

t [8],[24].

V t ph tp, h t t trh y v su: C

h tr h; s d PPNLCT Guss t ph

trh tr h, ph trh truy s; Kev

v h v h h; Md v h v h

h; xy d t t t h t h v h v

h h h hu t tr th the ph php d h s

sh PPNLCT Guss; xy d thut t v h trh th the phphp ph t hu h, tr th t qu. Kt qu h u

h s t h v h u du tp the u .

2.1 Cc phng trnh c bn v phng trnh truyn sng ca mi trng n

hi

2.1.1 Cc lin h c bn ca mi trng n hi

N t tr t, p u t h hu h

xe vt u h h th s u h E v h s Pss . Xtph t th r h tr h (hh 2.1). D tr t h

th xt u ph t [26],[46],[54],[57].

C sut t d t ph t :

-

C sut php: , ,


56/158

37

-

C sut tp: = = ; =

Hnh 2.1 Cc ng sut tc dng ln phn t t

G u, v, w huy v tr t ph t the hu x, y, z. Xe huy v h s v h th vt th th d ph t x

h the ph trh Cuhy h su:

=ux ; =

vy ; =

wz

=uy

+vx

; =uz

+wx

; =vz

+wy

(2.1)

L h tr th sut v tr th d h su:

= 2G+; = 2G+; = 2G+= G.; = G.; = G. (2.2)

Tr : G u trt: G =E

2(1+) ;

- B d th th: =

+

+

=++

=2G1-2

v t h, the uy DAeert, t

tr t ph xt qu th x h h su:

= ut ; =

vt ; =

wt (2.3)


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38

Tr (2.3), h v t, ; ; t qu

th the 3 ph h t vu (x,y,z).

2.1.2 Xy dng cc phng trnh vi phn cn bng v cc phng trnh

truyn sng theo PPNLCT Gauss

2.1.2.1 Phng php Nguyn l cc tr Gauss

Nuy tr Guss (NLCT Guss) t uy tr h

Guss K.F (1777 - 1855) pht u v 1829 v du h su

[5],[6]: Chuyn ng ca h cht im, c lin kt tu chu tc ng ca lc bt

k, trong mi thi im xy ra ph hp vi kh nng cao nht c th vi chuyn

ng m cc cht im c th thc hin c nu chng hon ton t do, c

ngha l n xy ra vi lng cng bc nh nht nu nh s o lng cng bc

trong thi on v cng b ly bng tng ca tch khi lng ca mi cht im vi

bnh phng lch v tr ca chng so vi v tr khi chng t do.

Bu th d hh h NLCT Guss vt h su:

! (2.4)

y

h h 2 B v C ht i h

. B v tr ht i h huy t d v C v tr h ht

huy t su th v dt.

Du du t y the s ht h. Nh vy t x h

huy h ht the NLCT Guss d t tr u th

d d hh h v u. D d , u th

NLCT Guss vt h su:

! (2.5)

Tr :

F t d ht i

t ht it u t d.


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39

NLCT Guss th suy r t uy v t Lre v

uy DAeert. Nh th NLCT Guss t qut h s v h

uy tr xt v t t v h r u u t

h.

V t h u ht , NLCT Guss d tr h

: L t, huy v h . Nu t t h p d uy

y h vt r d, th t h st tp hp t t v h

tr u h h su:

- L t th t h t tr:

+ L t t t h h xt v h h.

+ L t tr t t h t t.

Tr h vt r d, t tr th h qu

ph trh , ph trh t d, qu h

sut- d thuyt h.

- Chuy vt r d huy v t ph

vt th, t th hu u h d: Mt h, t

trt...

- Kh h thuyt ht v tr h ht . C tr h tr t h t t v

tr t .

Th d: Tr s vt u, t t hu d tr

EJ ; tr hp hu , t t thh EF ; tr hp

hu t, t t GF.

NLCT Guss p d v h ht . D tr s uy

y, 1979, GS.TSKH H Huy C xut s d Phng php NLCTGauss t v h vt r d. C u ph

php y th trh y h su:

- Kh h vt r d h t t ( t

t tt d tr s vt u hy t t ph t tr thuyt h).


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40

Mt t hu t ( h ) t h t d s

huy ( huy v, d ) v t v t d.

Nh vy tr t h h , th xe h t t t v

h ht tr h thuyt.

- C th r t t NLCT Guss s sh huy h

ht t tu v hh h h t t d the h

( r u ) t thu. Nu t t huy t tr h tr th

huy h th th t huy h tr th . Tuy h

PPNLCT Guss GS.TSKH H Huy C h t r th s sh huy

h t t tu v h t h t tu .

- huy h vt r d h s v h ht

h h y r huy the ph t y r

huy ( huy v, d ) tr t ph tr v qu h s

( Pss ) vt u. B d, huy v the ph t d

d, huy v v hh ph

PPNLCT Guss d GS.TSKH H Huy C r 1979.

T h h h tr, v h t u, PPNLCT Guss pht u h

su: Chuyn ng ca h kt cu c lin kt tu v chu tc ng bt k, trong

mi thi im xy ra lun c xu th gn nht c th vi chuyn ng ca h kt cu

khc khi cng chu tc ng . Ni cch khc, chuyn ng ca h kt cu s xy

ra vi lng cng bc nh nht.

Bu th r u h t u vt v t th

vt h su:

! (2.6)

y K t t th (t t tt d h t t ph t)

t v t t F ( h ). K hu v h s

0 hh t t h h t ( t d). Du t () tr u th


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41

y the tt t t h r r h tr h thy th ph h

xt tr t. v t h t xt th t th.

Nuy h h h v vy d y trh y h v d h h

th hu qu h p d PPNLCT Guss t h vt r

d.

2.1.2.2 Xy dng phng trnh vi phn cn bng

The h Hehtz [60], v tr t, x p huy

: huy th t; huy d v huy xy. T

th xt huy d ph t h h su (hh 2.2):

(a) (b)

Hnh 2.2 Lc v ng sut tc dng ln phn t c lin kt (a), phn t hon ton

t do (b).

Ph t th r t tr huy :B d the hu x, 2G

B d the hu y, 2G

B d the hu z, 2G

B d th th =

++ qu t h s Pss 0,

2G1-2

B d trt GB d trt G

B d trt G

Ph t hu t d h , , v qu th ,

, ( xe , hu v hu h) y r

= 0

0

= 0


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42

huy v u, v, w t (hh 2.2). huy th t y

h t.

Xt ph t h t t d (hh 2.2) hu t d ,

, v , , h ph t th r t tr. Ph t y h

t v ph t tr th d h. D

(-) t d, ph t huy wv w( h t).

x h t th t x h thy huy

ph t v 0:

=

-+

w (2.7)

T th t x h s the hu z v ph t th (ph t th r t tr).

V p u t t, t th t x , the hu x, y h

thy huy ph t v 0, 0.

=

-+

u; (2.8)

=

-+

v (2.9)

The NLCT Guss, (huy ) Z vt th h

th th V vt h su :

Z=

2G()dV +

2G()dV +

2G()dV +

2G1-2

()dV

+

G()dV +

G()dV +

G()dV +

(u-u)dV +

(v-v)dV

+

(w-w)dV (2.10)

T xt th ph h Z:

(u-u)dV =

-+ u

(u-u)dV =

(-+ )(u

u-2u+u)dV

(2.11)V th ph y tr t t min t :


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43

(u-u)dV =

2(- )udV (2.11)

T t t :

(v-v)dV =

-+ v(v-v)

dV =

2(- )vdV (2.11)

(w-w)dV =

-+ w

(w-w)dV =

2(- )wdV (2.11d)

L Z y vt h su :

Z=

2G(

ux )

dV +

2G(

vy )

dV +

2G(

wz )

dV

+

2G1-2 (

ux +

vy +

wz )dV +

G(

uy +

vx )dV +

G(

uz +

wx )dV

+

G(

vz +

wy )

dV +

2(- )udV +

2(- )vdV +

2(- )wdV

(2.12)

Ph h Z h h x h u, v, w. Th h php th

ph [34] ph h Z the h u t ph trh su (ph trh Euer

php th ph):

- 2Gux -

2G1-2

x (ux +

vy +

wz )-G

y (

uy +

vx )- G

z (

uz +

wx )

+ = 0 (2.13)

Rt u th tr t :

Gu +G

1-2 (

ux +

vxy +

wxz ) + =

ut (2.14)

Gv +G

1-2 (

uxy +

vy +

wyz ) + =

vt (2.15)

Gw +G

1-2 (

uxz +

vyz +

wz )+ =

wt (2.16)

Tr th tr: - t t Lpe:

=

x +

y +

z


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44

Nh vy, p d Ph php NLCT Guss v huy d

ph t h 3 hu, t h ph trh v ph h

h (ph trh Nver) h ph trh v ph

trh y tr hu t u vt v thuyt h [26],[46],[53],[60].

2.1.2.3 Xy dng phng trnh truyn sng

T th ph th huy ph t h thh huy v

d th th v huy xy h vt th ph t quh

tr x, y, z.

ph php th ht t xt r d , , 2G.

T d y t h d th th 2G. Nh vy ph

t h h d th th: d th th 2G v

d th th qu h s Pss 2G1-2

, t :

2G+2G1-2

=2G(1-)

1-2 (2.17)

Nh vy d th th 2G(1-)

1-2

Thy h t d ; ; y hh ph t h h

thy d th th, t th d xy h vt ph t

quh tr t x, y, z, t [60]:

=12(wy

-vz

); =12(uz

-wx

); =12(vx

-uy

) (2.18)

, , t xy quh tr x, y, z G t t

h d t.

Ph t h 4 huy : d th th ; xy , ,

p v hu v th hu d t qut. D t vt

qu th t :

=

t; =

t

; = t

; = t

(2.19)


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45

T xt d th th . Nu h ph t h t t d, h

t v ph t quh th:

x= 0;

y= 0;

z= 0 (2.20)

N h ph t tr tr h th:

x0;

y0;

z0 (2.21)

D t th vt huy h su:

Z =

2G(1-)1-2

(

x)dV +

2G(1-)1-2

(

y)dV +

2G(1-)1-2

(

z)dV

(2.22)Ph trh Euer ph h Z s :

- 2G1-

1-2 = 0 (2.23)

Tr hp t h th xt th qu th, t :

- 2G1-

1-2 +

t = 0 (2.24)

hy

t =

2G(1-)(1-2)

(2.25)

hyt = v

(2.26)

v v=

(2.27)

v th uy v t v v t s (s d) truy the

ph, qu huy ht the ph truy s. Ph trh

(2.25) ph trh truy s d (s ).Xt xy . Nu h ph t h t t d th:

x

= 0;y

= 0;z

= 0 (2.28)


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46

N tr tr h, d t v ph t xu

quh :x

0;y

0;z

0 (2.29)

D t vt huy xy quh tr x h su:

Z =

G2(

x

)dV +

G2(

y

)dV +

G2(

z

)dV (2.30)

Ph trh Euer ph h Z s :

- G= 0 (2.31)

Tr hp t h th xt th qu th, t :

- G+

t = 0 (2.32)

t =

G

(2.33)

hyt = v

(2.34)

v v=

(2.35)

v th uy v t v v t s t (s SV) truy the

tr x. Qu huy ht tr t ph yz. Ph

trh (2.32) ph trh truy s t.

T t t :

t =

G

(2.36)

y ph trh truy s the ph y, qu huy

ht tr t ph yz.

t = G (2.37)

y ph trh truy s the ph z, qu huy

ht tr t ph xy.


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Nh vy p d Ph php NLCT Guss v huy d

th th v huy xy h vt th ph t quh tr x, y, z,

t h 4 ph trh truy s (2.25), (2.33), (2.36), (2.37).

D th d ph trh Nver h ph trh truy

s h u huy tr h.

2.2 Cc li gii i vi khng gian v hn n hi v na khng gian v hn

n hi

Tr du tp the t s d th v h

h v h h v th h v h h tr

t t t, h y trh y .

C ph trh v u th tr h t vu x, y, z s

vt h tr h t 1, 2, 3 v v d u th tex su:

= +

+

= + + (2.38)

v hu Kreer

=

= (2.39)

Kh h ph trh Nver vt h su:

Gu + G1-2 u= 0 (2.40)

K hu u hu y h u the ph h ; u hu

y h uh the ph v ph j

The (2.38) t vt : u=ux +

uy +

uz (2.41)

s j = x th:

u=u

x

+v

yx

+w

zx

(2.42)

Tr tr hp v t t x = t d the ph j th

ph trh (2.40) d:


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48

+= 43116

1),(

Gu +G

1-2 u+ ( ,x)e= 0

(2.43)Tr (2.43) e v t h h; ( ,x) h det Dr (Dirac delta

function) h suy r hy h u t (Symbolic) v h h

su:

( ,x) = 0 h x

( ,x) = h x = (2.44)

-+ ( ,x)dx = 1

Nh vy h s d h det Dr d d u th

v ph trh (2.43). Nh ph trh (2.43) h s (fundamental solution).

2.2.1 Li gii khng gian v hn n hi

Hu t Kev (Ths W, 1824- 1907) [53],[60] r h

ph trh (2.43) v h v h h d d h su:

(2.45)

tr :U(,x)- Chuy v t x the ph j d tp tru v t t

, t d the hu y r.

,j = 1, 2, 3.

r = r(, x) h h t t v xt

tr h v h t x.

r, h h h r the h t i

r = (rr

)= (r

+ r

+ r

)

r= x(x) - x();

=

==

=

(2.46)

B d t t t x tr h h d

v t t t d the ph x h h su:


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49

(, x) =-1

16(1-)Gr[(1-2)(r, + r, r, )+ 3r,r,r,] (2.47)

T t sut t t tr h x h :

(, x) =-1

8(1-)r[(1-2)(r, + r, r, )+ 3r,r,r,] (2.48)

N v h v h Kev v t

ph v h [53],[60] h trh y y.

2.2.2 Li gii na khng gian v hn n hi

Nh ph trh (2.43) v h v h h d

Md R.D r (1936) [53],[60].

Theh Md v h v h t h Kev v h v h v h

ph:

Nghim ca li gii Mindlin = Nghim ca li gii Kelvin + Nghim ca li

gii ph.

Nh ph h h t th t

(hh 2.3) v t h trt tu sut tr t th h

v h.

( )

===

Hnh 2.3 S bi ton bn khng gian chu tc dng lc n v t ti im nm trong nn t [60]


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50

Nh Kev v h v h x h the (2.45),

(2.47), (2.48). C h ph trh y d y:

- L ph v huy v x h h su:

+

+

=

+

+

=

=

+

+

=

(2.49)

+

+

++

+=

+

=

=

=

+

+

++

+=

Tr : = 1, 2, 3; R = (RR); r= x(x) - x()

R= x(x) - x(); = x() 0 x = x(x) 0

K =1

16(1-)G

Tr [53],[60] trh y h ph v t ph v h, t

h thu y.2.3 Xy dng bi ton tng tc gia khi t n hi vi na khng gian v

hn n hi.

Tr y t h u t t h t h V v

h h h hu t tr th P


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, xt h t h ht V u h E, h s Pss .

N h h u h E, h s Pss . L P

t d tr h t h t d h t (hh 2.4).

T t tr th sut d h t V the ph php d

h s sh PPNLCT Guss.

PPNLCT Guss h php d tr th sut h s sh t

th h th h h h hu t d hu.

Hnh 2.4 M hnh bi ton tnh khi t n hi nm trong na khng gian v hnn hi

2.3.1 H so snh l na khng gian v hn n hi

Xt h s sh h v h h th s h E,

, hu P t d h h th (hh 2.5).

Hnh 2.5 H so snh l khi t nm trong na khng gian v hnn hi

D v Md trh y tr th huy v u, v, w;

d ,

,, ,

,

v sut

,

, , ,

h t h s sh.


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52

Ch r tr h t th sut t d (hh

2.4) v tr h t h s sh sut t d (hh 2.5).

S d tr th sut

h s sh t th tr th sut h th h vt ph h h su:

Z=

(-) dV

+

(-) dV

+

(-) dV

+(-

) dV +

(-) dV

+

(-) dV

(2.50)

Tr (2.50), V th th h t r xt u ; V th

th h t th (V> V); , ,, , , d h t;

,

,

,

,

,

tr th sut h s sh x h the Md (hh 2.5); sut , , , , , tr th sut

h t h th (hh 2.4).Thy d h (2.1), ph

h (2.50) vt h su:

Z=

(-

)ux dV

+

(-

)vy dV

+

(-

)wz dV

+

(-

) (uy

+vx

) dV +

(-

) (uz

+wx

) dV (2.51)

+

(-

) (vz

+wy

) dV

PPNLCT Guss xe huy v th u, v, w tr (2.51) huy v

, h xe d p v sut th u tr

(2.51) vt h su:

Z=

(-

) (ux)dV

+

(-

) (vy)dV

+

(-

) (wz)dV

+

(-

) (uy

+vx

) dV

+

(-

) (uz

+wx

) dV +

(-

) (vz

+wy

) dV = 0 (2.52)

tr du y ph.


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53

Ch y h t h h u, v, w, h t (2.52) t h

h 3 ph trh:

(-

)(ux)dV

+

(-

) (uy) dV

+

(-

) (uz)dV

= 0

(-

) (vy)dV

+

(-

) (vx

)dV +

(-

) (vz

)dV =0 (2.53)

(-

)(wz)dV

+

(-

) (wx

)dV +

(-

) (wy

)dV = 0

Th h php th ph [34] v (2.53) h ph trh su:

x +

y +

z =

x +

y +

zy +

x +

z =

y +

x +

z (2.54)

z +

z +

y =

z +

z +

y

V ph (2.54) th ph trh h P t

d tr h s sh y r (hh 2.4), h v tr (2.54)

ph trh h P t d tr h th (hh 2.3)

y r.

Nh vy h d h s sh, t h ph trh v

ph h th.

Phng php dng h so snh trnh by trn c cc u im ni bt sau:

+ Kh t r V h h t th V h t x h

tr th sut h h tr h t V tr . u y

h r u tr h t t th hh x.

+ D h t V tr h v h h u v t th .

thy r h h u u tr x trh y s th su (hh 2.6):


73/158

54

Hnh 2.6 S tnh khi t thng dng

D P t d tr h t, h h h t

h hh t t th x tr t

h t. H s y h x h (ging nh cc h s cng l xo ca

cc trnh by trong chng 1).

N trh xe tr h v h, d s th tr h xt t d sut tp tr t h t. Kh t

th r h tr, h u t t v tr.

D tr th sut th the s tr h u v

h v h.

v t h h t V, the PPNLCT Guss tr

ph h h xt th qu th h V v qu

th h s sh. u v tr tr hp y hh u x v th t h t (s c trnh by

chng 4)

2.3.2 H so snh l khng gian v hn n hi

H s sh d h v h h v Kev

trh y tr. Tr tr hp y th v u t d h

h th h , r d h h th h t h

ph u ( 2.4.1). Tr du h u u , trh y

t t t h v t, t s d ph h

( 2.4.2), v h th h v h v h,

h th h v h v h h

t t tr h .


74/158

55

Xt trng hp lc P tc dng thng ng ln khi t V nm trong na

khng gian v hn n hi (hnh 2.7a).

(a) (b) (c)

Hnh 2.7 M hnh bi ton tnh khi t chu tc dng lc thng ng khi dng hso snh l khng gian v hn n hi

Ch P t d h v h h, d Kev th

tr th sut tr . V h th tr h h

h th d tr th sut d h v h (hh 2.7)

h s sh. Tuy h tr th sut h h t

v P/2, v vy ph t 2 P th . Tr hp P t su s

v t th th t d h P t x qu t AB ( hh 2.7). Tr

hp t tr th tr t AB sut v

t d. L

Md v h h xut pht t Kev v s

th tr v t h trt tu sut v

tr t AB [68].

Xt trng hp lc P tc dng nm ngang trn khi t V (hnh 2.8a). Mt

AB l mt thong.

(a) (b) (c)

Hnh 2.8M hnh bi ton tnh khi t chu tc dng lc nm ngang khi dng hso snh l khng gian v hn n hi

K

K

,

,


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56

Ch P t d h h, d Kev th

tr th sut tr . V h th tr h

(hh 2.8) h h th d d h v h (hh 2.8).

Tr th sut h t v P/2 , h ph t 2 P

th sut the Kev. Tr hp P t su

s v t th th d h P t x qu t AB (hh 2.8). Kh

th s tr th tr t AB sut t d

L Md v h h h hu P

xut pht t Kev v s th h hh 2.8 v t h =

0 tr t AB. L h th.

T u s d s hh 2.8 th . D sut

t

d t AB d h xt t d y h

vt h su:

Z= [(-

)wd (2.55)

v d th t AB.

N r ph u = 0 tr t AB. T ,

t x h tr th sut h t h V h d Kev

vt h su:

Z = Z + Z (2.56)

V r u = 0 tr t AB.

Z=

(-) dV

+

(-) dV

+

(-) dV

+

(-) dV

+

(-) dV

+

(-) dV

(2.57)

Tr (2.57), V th th h t r xt u ; V th

th h t th (V


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57

Lre, t tr r u v t tr h r u h

su: F = Z+Z+ (2.58)

= (x,y) th s Lre h t.

u tr F s : F = Z + Z+ = 0 (2.59)

2.4 Gii bi ton bng phng php phn t hu hn

T s d ph php ph t hu h (PPPTHH) th h t

h ht th th V tr h v h h hu t d

P (hh 2.4). Xt h tr hp: H s sh h t tr

h v h h (hh 2.5) v h s sh h t tr h

v h h (hh 2.8). Tr h tr hp, h t th

h h t h s sh h thh ph t h h ht ( t 3

hu) h th ph t t . th xt u tr h

th, h s sh s ph t hu h s v h th 1 ph t the hu su

z v the hu x, hu y ( hh 2.9).

Hnh 2.9 Chia khi t h cn tnh thnh cc phn t khi


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58

* Phn t khi ch nht 20 nt

C th d ph t h h ht 8 t [38], h xp x tt

h, t s d ph t h h ht 20 t h hh 2.10 tr h t t

h v h th ph t x = y = z = 2 v d huy v . T

t h tr 2.1.

Hnh 2.10 Phn t khi ch nht 20 nt

Bng 2.1Bng ta nt phn t khi ch nht 20 nt.

1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

M t 3 th s () x h huy v u the hu x, v the

hu y, w the hu z. Nh vy tr ph t 3 x 20 = 60 th s huy v (

60 ) x h. Bt huy v t th huy v t t

tr ph t x h the h suy [39],[60]

C h suy:

- v t =18

N=(1+x.x)(1+y.y)(1+z.z)( x.x+ y.y+ z.z -2)

8

(2.60)

- v t =912

N=(1-x)(1+y.y)(1+z.z)

4 (2. 60)

- v t =1316


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N=(1-y)(1+x.x)(1+z.z)

4 (2. 60)

- v t =1720

N=(1-z)(1+x.x)(1+y.y)

4 (2. 60d)

G vet t h 60 ph t sp xp the t :

= [ u u... u v v... v w w2... w]

G vet d h 20 h suy x h huy v ut

tr ph t; vet d h 20 h suy x h huy v v;

vet d h 20 h suy x h huy v w.

= [ ... , (40 s 0)]= [ (20 s 0), ..., (20 s 0)] (2.61)

= [(40 s 0), ... ]

th huy v t tr ph t vt d d:

u= ; v= ; w

= (2.62)

Bt huy v x h d:

=x; =

y; =

z

=(y

+x

); = (z

+x

); = (z

+y

) (2.63)

Bt d, the h (2.1), s x h

tr th sut t tr ph t.

Ma trn cng phn t (dng tnh tch phn Z)

Xe ph t h trh, vt ph h tr

tr hp d h s sh h su:

Z=

[(-) + (-) + (-) + (-) + (-) + (-

) ]dxdydz (2.64)


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60

B v d h d t, t (2.64) h

t ph tr thh t t u th s t (60 ) s h Z

t tu. V vy u tr (2.64) vt d d su:

Z=

(-)

+ (-)

+ (-)

+ (-)

+ (-)

+ (-)

]dxdydz = 0 (2.65)

(=1,2,...,60)

Th h th ph tr v i, h t ph trh

, v tr d h 60 t v v ph t s. Ch i thy t 160 s

h ph trh tr su: = (2.66)tr : tr ph t h th (60x60)

v t t h th (60,1).

Tr th t th, tr ph t th h th

ph tr tp ph trh (2.65)

Kh t V hu ph t h hu. T d tr ph

t xy d tr t th h t V (th thh ph Z ) v h r

huy v t t ph t y th tr ph t .Tr tr hp d h s sh h v h h (

Kev) d sut t d t th AB h t V ph xt

th u th (2.55) v u = 0 tr t th AB.


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* Chng trnh tnh

Hnh 2.11 Chng trnh tnh khi t

2.5 Kim tra kt qu v cc nhn xt

Nh trh y tr, t huy v u, v, w t t

ph t. Bt huy v th th d v sut

t h t V. T t d v th Md hy

Kev th huy v u

, v

, w

t t v t th d v sut

t t h s sh.

2.5.1 Bi ton dng h so snh l na khng gian v hn n hi

Xt t t t h t V u h E v h s Pss

v h v h h u h E v h s Pss

N , : , , , ,

,, E1, E2, , P, ... C M

C 20 . X , , .

D M , , ,

.

X Z V.

K :AX=B.

V X : X=A\B( ).

I


81/158

62

(hh 2.12). D tr ph Mt, t xy d h trh th

Mstatic1h st t s tr hp su:

Hnh 2.12 M hnh bi ton tnh khi t

* Trng hp 1: Ch E= E, = (m un n hi, h s Poisson ca h

so snh bng m un n hi, h s Poisson ca h cn tnh)

Tr hh 2.13 trh y u huy v u(z) t

h t h P t d t (hh 2.13) v t h (hh

2.13) h t.

C t du t qu th huy v ( hu

U0_M1) the PPNLCT Guss. C t tr t qu th huy v

( hu U_M1) the th Md.Nh thy t qu th the PPNLCT Guss h t tr hp v t

qu th Md (xe Ph 1)

Kh thy th th h V, tr hp h V h 1 ph t, v

t qu hh x. Kt qu y th h h v xt tr

hp E= E, = h h t V v tr hp thh

h h y . u v h th . Nh vy

ph php d h s sh trh y tr t th u tr h t v u v .


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(a) (b)

Hnh 2.13 Biu chuyn v ngang khi t khi lc ngang P tc dng ti b mt(a) v chn (b) khi t, trng hp E= E, = .

* Trng hp 2: Ch = ;EE(gi nguyn E

nh trng hp 1, thayi Eca h so snh)

Tr hh 2.14 trh y huy v u(z) t h

t h P t d t t h t (hh 2.14) v t h h

t (hh 2.14).

Tr : U0_M1 hu huy v h t tr tr hp 1 the

PPNLCT Guss. U0_M2 hu huy v tr tr hp 2

the PPNLCT Guss. y thy s tr hp h t h t

qu th the PPNLCT Guss tr tr hp 1 v tr hp 2

(U0_M1 U0_M2). ( xe Ph 2)

(a) (b)

Hnh 2.14 Biu chuyn v ngang khi t khi lc ngang P tc dng ti b mt(a) v chn (b) khi t, trng hp = ; EE


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Kh th th V thy t v h t qu hh x h tr.

Nh vy, qu 2 tr hp h st tr thy r, d h s sh u

h h h u h h th th t qu huy v h

th h .

* Trng hp 3: Ch = ;EE (gi nguyn E ca h so snh nh

trng hp 1, tng Eca h cn tnh ln gp hai ln so vi trng hp 1)

Tr hh 2.15 trh y huy v u(z) t h

t h P t d t t h t (hh 2.15) v t h h

t (hh 2.15).

Tr : U0_M1 hu huy v th tr tr hp 1 the

PPNLCT Guss. U0_M3 hu huy v th tr tr hp

3 the PPNLCT Guss.

(a) (b)

Hnh 2.15 Biu chuyn v ngang khi t khi lc ngang P tc dng ti b mt(a) v chn (b) khi t, trng hp = ; EE

T thy t qu huy v h t th the PPNLCT Guss tr tr

hp 3 (U0_M3) h h h huy v h t th the PPNLCT Guss

tr tr hp 1 (U0_M1) ( xe Ph 3).

Kt qu h u tr tr hp 2 v 3 th xe h h

v the th Md tr th huy v (u, v, w) t hh v u

h E ( th (2.41), (2.45)); tr th sut h ph thu

v E, h ph thu v h s Pss ( th (2.44), (2.46)).


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65

T trh y tr thy r ph php d h s sh PPNLCT

Guss t d xy d t h php t th u

tr h V v u v .

* Trng hp 4: Ch EE, (h cn tnh v h so snh khc nhau

v m un n hi v h s Poisson)

tr hp tr, h s Pss h V v tr hu

(= )v h th th h V thy h u. By t xt tr hp

, th th h V h h thy th th V h r

(hh 2.16).

Hnh 2.16 Tng tc gia khi b tng v nn t

T vt h trh Mstatic2 tr tr Mt h tr

hp y. D y trh y t qu th h tr hp h V t E =

20.000 MP; = 0,15 tr t E= 10 MP ; = 0,3. Kh V d

th t 4x3 ph t; hu 2 ph t. Th th h r Vu

h th th h V t thu t ph t the hu x, y, z th xt

sut t d t h V. Kt qu t tr

huy v ( 2.2) v u huy v tr tr th qu

t h t V h hu P= 10N t d

t (hh 2.17). Tr : U0_M4 hu huy v th tr tr

hp 4 the PPNLCT Guss.

Bng 2.2Gi tr chuyn v ngang ca khi b tng

() 0 0.3 0.6 0.9 1.2U0_M4 () 0.162 0.061 0.037 0.026 0.019


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66

Hnh 2.17Biu chuyn v ngang khi b tng.

D h t h s Pss h v t h s Pss h

h th d Md s sh v t qu th h xt tr

tr hp tr.

By thy th th h r V h r s ph t the

hu su h the hu h h. Kt qu h hu h

t. u y h php t t u r s d ph php d h s

sh h t qu v h u tr t h

V h u v .

T v d tr h thy th d ph php h s sh h u t t t h trh v t.

2.5.2 Bi ton h so snh l khng gian v hn n hi

S d ph Mt, t xy d h trh Kstatic1 th

h t tr tr hp h s sh h v h h ( Kev).

Tr y t th h t E= E = 10MP, = =0,3 h h

P t t d t 3 v tr: = 0 (t th h t); = 3;

= 5,4 (y h t) h h trh th Mstatic1v Kstatic1.Tr hh 2.18 trh y u huy v u(z) t

h t h P t d t 3 v tr: = 0 (hh 2.18); = 3 (hh

2.18); = 5,4 (hh 2.18)


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67

(a)

(b)

(c)

Hnh 2.18 Biu chuyn v ngang khi t tnh theo 2 chng trnh Mstatic1 vKstatic1 khi ti trng ngang P tc dng ti v tr c=0 (a); c=3m (b);c=5.4m (c)


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68

T t qu tr h thy r, huy v h t h th the h

trh Kstatic1( hu U0_K), xp x t qu huy v h t h

th the h trh Mstatic1( hu U0_M) v s s ht h 6%

v t su s v t th th s s h t qu h v

h tr ht hu (xe Ph 4). S d s h h vy d h

h u t th. L t su d t th s h h

u t th . Nh vy th qu s ph php

ph t hu h, th h v h h ( Kev) v

h v h h ( Md).

2.5.3 Bi ton tnh khi t c xt n trng lng bn thn

L Md, Kev h Bussesq h xt tr th

h t, d v tr th sut t t h d tr

th y r h x h. Tuy h v t qu [10], tr th sut

t t h th x h . Tr tr hp t ph,

t th s ph sut tr t s :

(x,z) =

(x,z) = .z (2.63)

= 0

M r t 3 hu:

(x,y,z) =

(x,y,z) =

(x,y,z) = .z

= 0;

= 0;

= 0 (2.64)

Tr th sut tr th ph trh , u

tr t th v h thy the t ph , h thy

the hu su.

Bt tr th sut d tr th tr, d d xy d

t th h t h xt tr th the ph php d hs sh h t h u tr. T d h s sh h

v h h ( Md) v ph h t

vt h su:


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69

Z=

(--

) dV +

(--

) dV +

(--

) dV

+

(-) dV

+

(-) dV

+

(-) dV

(2.65)

hy:

Z=

(--.z) dV

+

(--.z) dV

+

(--.z) dV

+

(-) dV

+

(-) dV

+

(-) dV

(2.66)

S d ph Mt, t xy d h trh t Mstatic3

th h t tr tr hp xt tr th v h s sh

h v h h ( Md).

Tr y t th h t E= E= 10MP, = = 0.3, = 20

N/h h P t d t t th h t ( = 0).

Tr hh 2.19 trh y u huy v u(z) (hh 2.19) v huy

v w(z) (hh 2.19) t h t h P t

d t t th h t tr h tr hp xt tr th t (

hu U0G_M) v h xt tr th t ( hu U0_M).

(a) (b)

Hnh 2.19 Biu chuyn v ngang (a) v chuyn v ng (b), lc t ti mtthong khi t khi xt v khng xt trng lng bn thn.

D v u tr h thy t qu huy v h t h

, t qu huy v thy h xt h h xt tr th

( xe Ph 5). u y h t ph hp v quy ut v u hu

th t h t.


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2.6 Kt lun chng 2

- B ph php d h s sh PPNLCT Guss t xy d

ph trh v ph huy tr h

ph trh Nver v ph trh huy d d ph trh

truy s.

- B ph php d h s sh t xy d t x h

tr th sut d t h hu t tr th th qu

th t t t h t v h h .V ph

php y, u huy v v sut tr t h t

t th hh x, h ph th t ph (v d

t x) h ph php th d h y v u v

t th .

- T xy d h trh th ph php ph t hu

h tr tr Mt th h t. y d ph t h h ht 3

hu, 20 t. K tr s h thy s ph hp tt t qu th v

th.

- Th qu s ph php ph t hu h, t th

h v h h ( Kev) v h vh h ( Md), h h h v

h h t h v h h.

- Tr tr hp t ph, u t tr th sut

h t t tr h v h h d t d tr

th th ph php d h s sh, t xy d t

th h t hu t d v t d t tr th, ph

hp v u hu th t h t.- Kt qu h u t t h t v tr t

h v h u t t v t h hu t tr

tr du tp the u .


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71

Chng 3

NGHIN CU BI TON TNG TC GIA CC VI NN T KHI

CHU TI TRNG TNH NM NGANG

Tr

1. toanvanluanan.ncs ngoquotrinh

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