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L thuyt n hi do l tng Morh - Coulomb
1
GII THIU CHUNG
I. Tng Quan Vn Rt nhiu vn cng trnh t i hi s hiu bit trng thi ng sut bin
dng ca t. Vi mc ch ny, nhng miu t v nhng m hnh ton hc c
pht trin t cc l thuyt n hi v l thuyt do c in. Tuy nhin, t khc mt
cch r rt so vi nhng vt liu xy dng khc (nh thp hoc b tng) do tnh phn
tn v tnh rng vn c ca chng. Do s thay i ti trng bn ngoi v s thot nc
khi t s c s thay i ng k c v th tch v m. cht, cng v cc
c trng bin dng tt c u b thay i khng phc hi nn nhng thay i gia ti
tip theo thc ra tc ng ln mt loi t khc.
L thuyt Mohr-Coulomb l mt m hnh ton hc (xem xt b mt do) m t
ng x ca vt liu gin nh b tng, hoc ng gch vn, ng sut ct cng nh ng
sut php tuyn. Ni chung l thuyt p dng i vi cc vt liu cng chu nn
vt xa mc bn ko. Trong a k thut, n c s dng xc nh sc chng
ct ca t v ti nhng im c ng sut c hiu khc nhau. N c th biu din
c mt vt liu b ph hoi theo gi thuyt ma st ca Coulomb.
Ngy nay phng php phn t hu hn c bit n nh l mt phng php
s c s dng d bo n nh v bin dng ca t nn. u im ca phng
php ny l ng x ca t c th m phng tng i chnh xc v hp l trong qu
trnh thi cng. Tuy nhin, bn cnh mt s u im vn cn mt s kh khn nht nh
trong cch tip cn do mc phc tp ca n.
Do , m hnh n hi - do l tng Morh-Coulomb thng c s dng v
tnh n gin ca n v cc thng s t c th d ng thu c t phng th nghim.
Tuy nhin, vn c mt s hn ch trong m hnh Morh-Coulomb cn c khc phc,
v lm sao khi a cc thng s vo m hnh ta kim sot c mc chnh xc ca
n.
II. MC CH NGHIN CU
Vic tnh ton cng trnh ngm hin nay, a phn da trn m phng PTHH
c kt qu kh chnh xc, nhng phi chu nh hng nhiu n cc thng s u vo
khi a vo m hnh PTHH. V s liu cng tr nn phc tp hn khi iu kin th
L thuyt n hi do l tng Morh - Coulomb
2
nghim Vit Nam cha p ng c nh nc ngoi. Do , nhm tc gi nghin
cu theo hng phn tch cc thng s u vo cho m hnh t Morh-Coulomb, lp
ra cng kho st cho n v kho st a cht nhm c c s liu cn tnh ton v
tit kim kinh t
Xc nh cc mt hn ch ca m hnh Morh-Coulomb. Nghin cu bn cht
tnh ton ca phn mm Plaxis.
III. NGHA V GI TR THC TIN CA TI Cc thng s u vo n gin, la chn giai on phn tch ngn hn hay lu
di cho tng loi bi ton thit k.
H thng tng hp cc kin thc c bn lin quan v cc m hnh t.
IV. PHNG PHP NGHIN CU
thc hin cc mc tiu nghin cu trn y, nhm tc gi la chn phng
php nghin cu nh sau:
1. Tnh ton l thuyt: S dng cc l thuyt tnh ton sau y:
- L thuyt kim tra n nh, cng ca t nn v h o su.
- L thuyt kim tra n nh thnh h o.
- L thuyt c hc t ti hn
- L thuyt do
2. M phng: s dng phn mm Plaxis phn tch n nh v bin dng ca h
o trong qu trnh thi cng.
V. NI DUNG NGHIN CU - Nghin cu l thuyt n hi do l tng
- Nghin cu m hnh Morh-coulomb trong phn mm Plaxis
L thuyt n hi do l tng Morh - Coulomb
3
MC LC
Chng I: C s l thuyt tnh ton ......................................................................... 4 I.1 Vng trn morh nh gi ng sut ti mt im ............................................. 4 I.2 Vng trn Morh bin dng ............................................................................. 7 I.3 Cc gi thuyt chnh ...................................................................................... 9 I.4 Tiu chun do Morh-Coulomb ....................................................................10 I.5 Phng trnh sc chng ct ...........................................................................11
Chng II: M hnh Morh-Coulomb ......................................................................14 II.1 Mt do .......................................................................................................14 II.2 Th nng do ca t ...................................................................................16 II.3 Cc thng s c bn ca m hnh M-C ........................................................18
II.3.1 Modul n hi (E) ...............................................................................18 II.3.2 H s poison () ..................................................................................20 II.3.3 Lc dnh, gc ma st trong (c, ) .........................................................21 II.3.5 Gc gin n () ..................................................................................24
II.4 Cc thng s nng cao ca m hnh M-C .....................................................24 II.4.1 Increase of stiffness (Eincrement) .............................................................24 II.4.2 Increase of cohesion (Cincrement) ............................................................24 II.4.3 Tension cut off .................................................................................25
Chng III: Cc phng php A, B, C trong m hnh Morh-Coulomb................25 III.1 ng x thot nc .....................................................................................25 III.2 ng x khng thot nc .......................................................................... 25 III.3 ng x non porous .....................................................................................28 III.4 Phng php A, B, C trong m hnh Morh-coulomb ..................................28
III.4.1 nh ngha cc phng php A, B, C .................................................28 III.4.1.1 Phng php A ................................................................................28 III.4.1.2 Phng php B ................................................................................29 III.4.1.3 Phng php C ................................................................................31 III.4.2 Tiu chun do TRESCA ...................................................................32 III.4.3 Tiu chun do VON MISES .............................................................33
III.5 Phn tch l trnh ng sut ca t la chn giai on thit k ...............33 III.5.1 Phn tch tc thi v lu di ...............................................................33 III.5.2 L trnh ng sut ca h o ..............................................................36
Chng IV. Kt lun v kin ngh ..........................................................................37 IV.1 Kt lun .....................................................................................................37 IV.2 Hn ch ca ti ......................................................................................37 IV.3 Kin ngh ...................................................................................................37
L thuyt n hi do l tng Morh - Coulomb
4
I. C s l thuyt tnh ton I.1 Vng trn morh nh gi ng sut ti mt im
Xt 1 im M c ng sut php xx , yy v ng sut tip xy . Quay mt phng cha im ang xt 1 gc sao cho ng sut tip xy = 0. Lc ny, cc ng sut php s c gi l ng sut chnh 1 , 3 . ng sut ln nht c tn l ng sut chnh i k hiu l 1 . ng sut b nht c tn l ng sut chnh tiu k hiu l 3 . Vng trn morh ng sut l tp hp cc im , trn tt c cc mt i qua im tc ng ca ng st P v thng gc vi mt mt ta trc.
Hnh 1: Quan h gia cc ng sut Hnh 2: Vng Morh ng sut trn cc V ng sut chnh mt song song vi trc z
Cc ca vng trn Morh ng sut l im P nm trn vng Morh t v ng song
song vi mt mt ( ) trong phn t s ct vng morh ti mt im c ta , l
cp ng sut tc ng ln mt ( ) nh hnh sau:
L thuyt n hi do l tng Morh - Coulomb
5
ng sut tc ng trn mt ( ) c th vit li nh sau:
cos 2 sin2 2
x y xym R R R
s in2 cos 22 2
x y xyRR R
Thay gc vo v sp xp li, ta c ng sut trn mt ( ):
cos cos 2 sin sin 2 cos 2m R R (1)
cos cos 2 sin sin 2 sin 2R R (2)
Nhng trng hp khc nhau ca ng cong ng sut gii hn
Tr s ca ng sut ct khng th ln hn gi tr gii hn, ng vi khi xut hin
s trt lin tc ngha l: tangh c . Gi tr ng sut nm trn ng thng gii
hn ng vi im thc nghim M no , ng thi n cng nm trn vng Morh ng
sut gii hn. iu ny ch c th xy ra trong trng hp ng thng OM hoc OM
tip xc vi vng trn Morh ng sut.
ng bao ng sut gii hn, t ri (a), t dnh (b)
iu kin nu c th vit di dng gii tch, khi bit nhng gi tr ng sut chnh
ln nht 1 v nh nht 3 v bit rng trn tam gic OMC hoc OMC l tam gic
vung, theo hnh ta c:
t ri: sin CMOC
(3)
Vi 1 3 1 3 1 33;2 2 2CM OC
L thuyt n hi do l tng Morh - Coulomb
6
Nn: 1 31 3
sin
t dnh: 1 31 3
sin' 2 . t
CMO C c co g
(4)
C hai phng trnh (3), (4) ny l s din t ton hc ca iu kin cn bng
gii hn (iu kin bn ca Morh), ca t ri v t dnh tng ng. iu kin ny c
tnh thc tin rt ln v c dng xc nh ti trng gii hn trn t, khi tnh n
nh ca khi t v p lc t ln tng chn.
Cng cn ch rng nhng ch tiu sc chng trt ca t l c v tan ch l
nhng thng s ton hc thuc ng thng bao vng trn morh ng sut gii hn, tuy
nhin nhng nghin cu chi tit ch r, nu xt sc chng trt gii hn ( ph hoi
ca t ) trong phm vi bin thin ln ca ng sut nn v cc trng thi ng sut khc
nhau ( n gin v phc tp ) ng bao ca vng trn morh ng sut gii hn trong
trng hp tng qut s l ng cong. Cn khi bin thin p sut khng ln lm
0.5 0.7Mpa th ng bao ng sut gii hn ( on ab trn hnh) c y
c s xem l ng thng, c ngha l i vi nhng ng sut nh hn nh lut
Coulomb v nhng iu kin v trng thi ng sut gii hn sau ny ca t suy ra t
nh lut s hon ton ng.
Trng hp tng qut ca ng bao ng sut gii hn
L thuyt n hi do l tng Morh - Coulomb
7
I.2 Vng trn Morh bin dng
Cc bin dng thng gp
Hnh 3: Bin dng trt v th quan h gia bin dng v ng sut trt
Hnh 4: Vi phn chuyn v
L thuyt n hi do l tng Morh - Coulomb
8
T hnh hc gii tch v cc khi nim c bn v c hc t v chuyn v, ta c mi
quan h vi phn gia cc bin dng v chuyn v ca phn t c miu t nh sau:
w ; ;
; ;
x y z
xy yz zx
u vx y zu v v w w uy x z y x z
(0.1)
Cc ng sut c bn tc dng trn phn t v cc bin dng trt thun ty c miu
t bng vng trn Mohr xc nh cc ng sut chnh, bin dng chnh v gc ph
hoi tng ng.
Hnh 5 (a) cho thy trng thi bin dng nh trong phn t mt phng OABC. Nu bin
dng , ,x z xz c bit, chng ta c th tnh ton cc bin dng trong phn t OEFG
trong hnh. 5 (b) quay mt gc quanh O.
Hnh 5: biu quan h cc bin dng
Hnh trng thi bin dng ca hai phn t ph hp vi vng trn bin dng Morh
L thuyt n hi do l tng Morh - Coulomb
9
Chng ta c th s dng vng trn Mohr ca bin dng mt cch chnh xc tng t
nh i vi ng sut.
Vng trn Morh ca bin dng trong hnh 5(c) tng ng vi trng thi bin dng c
th hin trong hnh. 5 (a). Vng trn ca bin dng c v trn s vi trc 12 (=
bin dng ct thun ty) v (= bin dng) v c v thng qua thng qua cc im
1 1; ; ;2 2x xz z zx
R Q
i din cho cc bin dng c bit n. v vng trn
Mohr ca bin dng, v vi mc ch ny, chng ta chp nhn cc quy c, tng thch
vi iu c thng qua i vi cc vng trn Mohr ng sut, rng bin dng ct
ngc chiu kim ng h c a ra l dng. Do bin dng ct ngc chiu kim
ng h 12 zx "trong hnh. 5(a) l dng v trong hnh. 5 (c) bin dng ct theo chiu
kim ng h 12 xz l m.
Trong cch xc nh tng t nh i vi cc vng trn Mohr ng sut, chng ta xc
nh v tr cc P bng cch v RP hoc QP song song vi cc mt phng OA hoc OC
trong hnh. 5(a). Sau , chng ta c th rt ra PN theo gc so vi PQ v bin dng
1;2
N
l cc gi tr ca cc thnh phn bin dng tng ng trong OEFG phn t
trong hnh 5(b).
I.3 Cc gi thuyt chnh
Gi thuyt ny ch yu phc v m t s ph hoi do trt ca t v cc vt liu
dng ht, chng hn nh , ct, hoc t. Nhng vt liu ny ch c th thc hin
tng i nh, trong gii hn, khng c lc ko.
nh lut Coulomb, p dng cho nhng ng sut, nguyn l trt khi t ti mt gi
tr ti hn t l vi p sut : tan . y l gc ma st trong ca t.
Khi 0 dn ti 0 , ng sut ko l khng th c trong trng hp ny.
Tuy nhin trong nhiu trng hp, ngay c i vi = 0, khi bt u trt ng sut ct
khc khng. Ngoi ra, vt liu thng xuyn c th c ng sut ko n mt mc
no. V vy l hp l sa i iu kin trt nh sau:
tan c
L thuyt n hi do l tng Morh - Coulomb
10
Mi quan h ny c gi l gi thuyt Coulomb - Mohr (CA Coulomb (1736 - 1806);
O. Mohr (1835-1918)). Cc tham s c gi l lc dnh.
Trong s - , phng trnh trn c biu din bng hai ng thng to thnh
ng bao ca vng trn Mohr . Trt xy ra i vi nhng ng sut m ln nht ca
cc vng trn Mohr ng bao. Dn ti iu kin sau:
1 3 1 3 sin2 tan 2
c
Nu chng ta a vo trong phng trnh ny chng hn 1 = t v 3 = 0, chng ta c
c bn ko mt trc 2 cos / 1 sint c . Tng t, vi 1 = 0 v 3 = -p
cng chu nn sau 2 cos / ( 1 sinp c .
I.4 Tiu chun do Morh-Coulomb
Tiu chun im nhng cng l tiu chun bn ca Morh-coulomb c s dng rng
ri trong c hc t, n ph hp vi trng thi lm vic thot nc ca t.
' ' 'tan c
Dng suy ra t ng bao cc vng trn Morh ng sut chnh:
' '' 1 3
' ' ' '1 3
' ' ' ' ' ' '1 3 1 3
sin2 cot
sin 2 cos 0
c g
f c
Vi 1 2 3 : nu din t theo cc bt bin tenseur ng sut v gc Lode th tiu
chun Coulomb c th vit li:
' '' '
2 1
, sin, cos 0
3f J m I m
' 2'3, ; 2
3 cos sin sinm HM J
Suy ra:
' '' ' '
2 1
, sin, cos 0
3m
J I m c
Trong trng hp: ' 0 ' ' '330 , 0 , 1
3 cos sin sinc m
L thuyt n hi do l tng Morh - Coulomb
11
1
2
1
H
s3
s2
= 0O
s3
s1
s2
H
= 30O
= -30O
s1
O 3
I.5 Phng trnh sc chng ct
Hnh 6: th ng sut ct v bin dng ct
N c hin th trn m trn bt k im no trong t, khi ng sut ct
t n sc chng ct nh ca t. Coulomb, trong nm 1773, ngh mt mi quan
h n gin ca sc chng ct ca t l mt hm tuyn tnh ca ng sut nh sau:
tanf nc (5.1)
Trong : f l sc chng ct ca t, c lc dnh ca t, n ng sut hot ng trn
mt ca ph hoi, v gc ma st trong.
Cng thc trn c tnh ton trong iu kin ng sut tng, sau khi Terzaghi a ra
ng sut c hiu th cng thc c iu chnh li:
' '' tanf nc (5.2)
Trong ' ',c thng s sc chng ct trong iu kin ng sut c hiu, v 'n n wu
l ng sut c hiu. trong thng s sc chng ct ' ',c khng phi l hng s. Nhng
L thuyt n hi do l tng Morh - Coulomb
12
ph thuc vo nhiu yu t nh: h s rng, kt cu ban u, p lc nc l rng. Cc
thng s ny thu c t nhiu kiu th nghim:
Hnh 7: ng bao gi hn Morh-Coulomb
Trng thi ng sut trong mt khi t ti thi im ph hoi c th c miu
t trong iu kin ng sut c hiu chnh ln v nh. Hnh 7 miu t cho ba vng trn
Mohr cho ba b ng sut ti thi im ca s ph hoi trong mt khi t. Mt tip
tuyn v ra t nhng vng trn ny c gi l ng bao ca vng trn Mohr, v iu
ny tha mn phng trnh 5.1. Bt k s kt hp ca p lc nm trong ng bao ny
miu t cho mt trng thi n nh. Trng thi ng sut nm trn ng bao ph hoi
khng th tn ti. Nh vy, mt cch khc nu r iu kin ph hoi ca Coulomb
rng nu vng trn Mohr trng thi ng sut ti mt im l tip tuyn mt ph hoi
Coulomb, sau thi im c cho l trong mt trng thi ca s ph hoi. iu
ny thng c bit n nh l tiu ch ph hoi Mohr-Coulomb.
Tiu chun ph hoi Mohr-Coulomb c s dng rng ri. Trong thc t,
ng bao ph hoi khng c th l mt ng thng, nhng phm vi ca nhng ng
sut lin quan n t, xp x ng thng l hp l, v cc thng s sc chng ct
c xc nh cho giai on .
Kin thc v ng sut ct v sau khi b ph hoi v hnh dng ca cc ng
cong ng sut bin dng ht sc quan trng trong cc nghin cu v vn n nh, v
c bit hn, trong cc ti liu kinh nghim s ph hoi (Hvorslev, 1960).
Hnh 8 m t cho cc ng cong ng sut bin dng in hnh cho t st c
kt thng (NC) v qu c kt (OC) th nghim rt chm. Ti im ng sut c hiu
vung gc vi mt phng ct, sc chng ct nh trong c hai trng hp tng ng vi
ng sut ct ti a t st c th c. Tip tc bin dng sau khi vt qu bin dng nh
L thuyt n hi do l tng Morh - Coulomb
13
s lm gim sc khng, v trong tng lai bin dng s ln, Do , cc thng s cng
cn li c th c th hin nh sau:
Hnh 8. Sc khng ct nh ca t st
' ' '
' ' '
tan
tanf n
r r n r
c
c
Trong : c: Lc dnh tng ng vi sc chng ct nh,
'rc : Lc dnh tng ng vi sc chng ct cn li
' : Gc ma st trong tng ng vi sc khng ct nh
'r : Gc ma st trong tng ng vi sc khng ct cn li
Mt s c im chnh lin quan n hnh hnh.93 (Skempton, 1964) nh sau:
S suy gim cng sc chng ct sau khi vt qua nh trong t st qu c
kt l r rt hn ( V d St cng ) so vi t st c kt thng (v d st mm). Vi
hm lng st cao th vic suy gim sc chng ct trong hai trng hp l rt ng k.
iu kin cn li, ng sut c hiu c lp ca lch s ng sut trong qu
kh.
ng bao ph hoi morh-coulomb thng nm v tr thp hn mt cht so
vi cng nh ca t st c kt thng nhng cc k thp hn so vi t st qu
c kt.
Gi tr lc dnh 'rc l tng i thp v ni chung l thp v c th l bng 0.
L thuyt n hi do l tng Morh - Coulomb
14
Ni chung gi tr 'r gim vi s gia tng hm lng st. Hnh dng ng
cong hon chnh biu din quan h ng sut chuyn v trong iu kin cn li r rng
c miu t mc gin ca t st. Hnh 9.4 i din cho ba ng cong in hnh
quan h ng sut v bin dng. Bishop (1967) gii thiu mt h s gi l ch s gin
c lin quan n sc khng ct nh v sc khng ct cn li:
f rBf
I
Hnh 9: ng cong ng sut ct v chuyn v ng vi gin khc nhau
Trong hnh 9, ng cong b i din cho t st c tnh gin cao, Trong hnh. 9,
ng cong i din cho t st do khng gin, trong khi cc ng cong b i din
cho mt t st gin cao. Skempton v Hutchinson (1969) cho thy hnh dng ca
ng cong ng sut - chuyn v cng l quan trng t hai ng cong ng sut
chuyn v khc nhau nhng li c cc ch s gin tng t (v d: ng cong b v
c). S bt thng ny c th c a vo tnh ton bng cch xem xt cc thng s
nng lng c gii thiu bi Bishop (1967).
II. M hnh Morh-Coulomb
II.1 Mt do
- Do l gii hn trng thi n hi ca vt liu v nu sau vt liu chuyn sang
ng x do, do trong tl do cc ht t b gy, b vn ng thi ti cu trc
ht cng xy ra.
- Mt do ca t l mt lm vic ca t trng thi ti hn hay trng thi bin
dng do. c m t bng nhng ng bao sc chng ct.
L thuyt n hi do l tng Morh - Coulomb
15
- Cc thng s sc chng ct thng c xc nh t th nghim ct trong phng
(casagrande, nn ba trc, nn n v ct n) hay th nghim hin trng (SPT,
CPT, ct cnh)
- Cc thng s chng ct ( ', ')c ph thuc vo trng thi ng sut ban u, m
ca t, iu kin thot nc, iu kin th nghim, v sc chng ct ph thuc
vo ng sut php hu hiu ca t. theo cng thc sau:
' ' 's tg c Mt do trong m hnh Morh-Coulomb:
Phng trnh mt ngng Morh-coulomb:
- Xc nh t ng bao cc vng trn Morh ng sut chnh:
' ' ' ' ' ' '1 3 1 3 sin 2 cos 0f c
Vi 1 2 3 Phng trnh mt do tng qut c dng:
L thuyt n hi do l tng Morh - Coulomb
16
- Mt gii hn ng sut Morh-Coulomb : mt ngng ca Morh Coulomb trong
khng gian ng sut c dng thp trc i xng. Mi nh ca lc gic c trng
thi ng sut c th khc nhau.
- Khng gian ng sut: (m t ng bao mt ng sut chnh)
- C th m t nh mt ng bao trong mt phng ng sut chnh
Vi f > 0: khng th chp nhn
f = 0: n do
f < 0: n hi
II.2 Th nng do ca t
- Vn ct li ca l thuyt do l lm sao tnh ton c bin dng do khi m
trng thi ng sut t n ngng do f(ij)? Hu ht cc l thuyt do ang c s
dng rng ri hin nay da trn gia s bin dng do (von Mises, 1928; Melan, 1938;
Hill, 1950):
'p
ijij
g
Trong : l m s v hng dng
L thuyt n hi do l tng Morh - Coulomb
17
g = g(ij) = g(I1, I2, I3) l hm th nng do, n c th trng hoc khng
trng vi hm ngng do f(ij).
- Cng thc trn c xem nh quy lut chy do l c s tnh gia s bin dng
do. Quy lut chy do ny c dng ln theo quan st bin dng do si kim lai
ca Saint-Venant (1870), trong trc chnh bin dng do trng kht vi trc chnh
ng sut, nguyn l ng trc ny thng c s dng trong hu ht m hnh chy
do ca cc vt liu. Nhng cc kt qu thc nghim gn y trn t cho thy rng
gi thuyt ng trc khng ng vi ng x ca t.
- Nu hm th nng do trng vi hm ngng do th quy lut chy do c gi
l quy lut chy do trc giao hay kt hp (associated flow rule) v vt liu gi l
chun, nu khng th l quy lut khng kt hp (non-associated flow rule) v vt liu
khng chun.
Phng trnh hm th nng do:
L thuyt n hi do l tng Morh - Coulomb
18
Phng trnh tng qut:
II.3 Cc thng s c bn ca m hnh M-C
M hnh Morh-Coulomb l m hnh ni ting thng dng tnh ton gn
ng cc ng x giai on u ca t.
Cc thng s u vo ca m hnh Morh-Coulomb nh sau:
- E: Modun n hi ca vt liu (KN/m2)
- : H s poisson
- : Gc ma st trong ()
- c : Cng khng ct ca vt liu (lc dnh) (KN/m2)
- : Gc gin n ca vt liu ()
II.3.1 Modul n hi (E: KN/m2)
- M un n hi ca mt vt liu c xc nh bng dc ca ng cong
ng sut-bin dng trong vng bin dng n hi
stressEstrain
- E l m un n hi
- ng sut l lc gy ra bin dng c chia cho din tch m lc tc ng vo
- Bin dng l t s s thay i c gy ra bi ng sut cho trng thi ban u
ca i tng.
- Xc nh E t kt qu th nghim nn c kt. t th nghim nn c kt ta c c
chuyn v ca mu t ng vi tng cp ti ( h v )
L thuyt n hi do l tng Morh - Coulomb
19
Ta c: (1 )(1 ) (1 )oi i o i o
h e h ee e hh h e h e
T kt qu bin dng v ng sut v biu quan h ng sut v bin
dng xc nh E:
- Xc nh Eo v E50 qua th nghim nn ba trc thot nc:
Ta c modul tng bin dng:
1
1
(1 )1 2 (1 )eod
d EEd
L thuyt n hi do l tng Morh - Coulomb
20
Modul ct: ef 2(1 )xy
rxy
d EGd
- Cng thc xc nh E t kt qu th nghim SPT v CPT cho mt s loi t:
Phn loi t Th nghim SPT Th nghim CPT
Ct c kt thng
NENE
NE
NE
s
s
s
s
ln)220001500(6000
)(7000
)15(500
22
(2 4)8000
1.2(3 2)
(1 )
s u
s c
s r c
s r c
E qE qE D qE D q
Ct bo ha 250( 15)sE N 1.0, 3.50.6, 7.0
s cE Fqe Fe F
Ct qu c kt ( ) ,s OCR sE E nc OCR
(6 30)s cE q
St pha ct 320( 15)sE N (3 6)s cE q
Bn, ct bn, bn st 300( 6)sE N (1 2)s cE q
St yu hay bn st 300( 6)sE N (3 8)s cE q
II.3.2 H s poisson ()
H s poisson l thng s nh hng n bin dng ca t nn, xc nh t t
s gi bin dng theo phng ngang v bin dng theo phng ng c xc nh t
th nghim nn mu vt liu
L thuyt n hi do l tng Morh - Coulomb
21
Bng h s poisson mt s loi t
Loi t H s poisson
Ct ri
Ct cht trung bnh
Ct cht
Ct pha st
St mm
St c cng trung bnh
0.2-0.4
0.25-0.4
0.3-0.45
0.2-0.4
0.15-0.25
0.2-0.5
Gi tr h s poisson ca stqu c kt nh: 0.25 0.00225( )PI
Gi tr h s poisson thot nc theo Trautmann and Kulhawy 1987
250.1 0.345 25
oto o
II.3.3 Lc dnh, gc ma st trong ,c
- Lc dnh c l lc ct khi chu p lc bng 0, v l giao im ca ng bao
Morh-Coulomb v trc tung.
- Gc ma st trong th hin dc ca ng bao vng Morh-Coulomb
Lc dnh c v gc ma st trong c xc nh t nhng th nghim sau:
- Nn n (Unconfined compression test): p dng cho t dnh, n gin, cho kt
qu trc tip, mt ph hoi s l mt yu nht.
- Ct trc tip (Direct shear test): p dng cho c t dnh v t ri, cho kt qu
trc tip, mt ph hoi l mt nm ngang gia 2 tht ca hp ct c n nh trc.
L thuyt n hi do l tng Morh - Coulomb
22
- Nn 3 trc (Triaxial compression test): p dng cho c cc loi t, c 3 pp TN;
Undrained Unconsolidated (UU), Undrained Consolidated (CU), Drained
Consolidated (CD).
Xc nh ,c :
T th nghim ct trc tip
- Xc nh gi tr c v bng phng php hnh hc t g c
s
t
0
c
- Xc nh gi tr c v theo cng thc bnh phng cc tiu
1 1 1
22
1 1
n n n
i i i ii i i
n n
i ii i
ntg
n
21 1 1 1
22
1 1
n n n n
i i i i ii i i i
n n
i ii i
cn
T th nghim ba trc:
- Xc nh gi tr c v bng phng php hnh hc:
t g c
L thuyt n hi do l tng Morh - Coulomb
23
- T th nghim ba trc UU
cu
ccu
1 3 O O
T
n
- Kt qu t th nghim ba trc CD
Cng thc xc nh gi tr c v : c xc nh t phng trnh trng thi cn
bng:
L thuyt n hi do l tng Morh - Coulomb
24
1 3
1 3
sin2 .cotc g
Hay c th xc nh theo cng thc quan h gia 1 v 3 :
21 3 45 2 . 452 2
o otg c tg
III.3.4 Gc gin n ()
Gc gin n tnh bng , t st xem nh khng co gc gin n (=0), gc
n hng ca ct ph thuc vo t trng v gc ma st trong.
Trong hu ht cc trng hp th gc gin n bng 0 cho gc < 30o.
V 30o vi trng hp 30o II.4 Cc thng s nng cao ca m hnh M-C
II.4.1 Increase of stiffness (Eincrement)
- Thc t cng ca t gia tng theo chiu su v cng ph thuc vo ng
sut.
- S gia modul n hi theo chiu su ca lp vt liu, c xc nh t th nghim
ct trc tip hay th nghim ba trc.
- T th nghim theo tng cp ti trong khc nhau tng dn th ta s c nhng gi tr
modul n hi tng ng cho mi cp ti v chnh lch gia cc gi tr modul
n hi theo mi cp ti chnh l s gia modul n hi.
- Ta c modul n hi tht ca lp t
)()( refincrementrefrefactual yyEyyEE Trong : actualE : Modul n hi tht ca vt liu
refE : Modul n hi ca vt liu su bt u xut hin lp vt liu
refy : su bt u xut hin lp vt liu
incrementE : S gia modul n hi
II.4.2 Increase of cohesion (Cincrement)
- S gia cng khng ct ca vt liu theo chiu su, c xc nh t th
nghim ct trc tip hay th nghim ba trc.
L thuyt n hi do l tng Morh - Coulomb
25
- T th nghim theo tng cp ti trong khc nhau tng dn th ta s c nhng gi
tr cng khng ct ( c ) cho mi cp ti v chnh lch gia cc gi tr (c)
theo mi cp ti chnh l s gia cng khng ct.
- Ta c cng khng ct tht ca lp t
)()( refincrementrefrefactual yycyycc Trong : actualc : Cng khng ct tht ca vt liu
refc : Cng khng ct ca vt liu su bt u xut hin lp vt liu
refy : su bt u xut hin lp vt liu
incrementc : S gia cng khng ct
II.4.3 Tension cut off
- ng sut ko t thng xut hin nhng khu vc c ng sut ko pht trin.
Theo ng bao morh-coulomb th hin th iu ny cho php khi ng sut ct
(bn knh ca vng trn Morh) nh. Tuy nhin b mt t gn nhng di t
st xut hin nhng vt nt ko.
- iu ny cho thy rng t cng b ph hoi khi ko thay cho ng sut ct. quan
h ny vng trn Morh vi ng sut m khng cho php. Thng trong m hnh
Morh-Coulomb mc nh gi tr cng ko bng khng.
III. ng x ca t III.1 ng x thot nc - Xy ra khi khng c s thay i p lc nc l rng do ti bn ngoi.
- Trong iu kin thot nc, nc l rng c th thot ra ngoi mt cch d dng
gy bin dng th tch trong t.
III.2 ng x khng thot nc - Xy ra khi nc l rng khng thot ra khi t
- Trong iu kin khng thot nc, t l bc hi nhanh hn rt nhiu so vi t l
m ti cc nc l rng c th thot ra khi t
- Hu ht cc ti bn ngoi c thc hin bi nc l rng, dn n s gia tng
p lc nc l rng
- Cc xu hng ca t b chn thay i th tch trong thi gian ti khng thot
nc.
L thuyt n hi do l tng Morh - Coulomb
26
- t thot nc hoc khng thot nc th ph thuc vo nhng iu kin sau:
- Cc loi t (v d nh ht mn hoc ht th)
- a cht (cc vt nt, cc lp ct trong t st, vv)
- T l ti
- Nu t l ti nhanh (v d nh trong mt trn ng t), thm ch t ht th
c th l khng thot nc, kt qu thng thng dn n ha lng.
- Cc h s p lc nc l rng
- Cc h s p lc nc l rng ng vai tr quan trng trong vic xc nh sc
chng ct ca t. S thay i p lc nc l rng do s thay i trng thi ng
sut tc dng c trng bi cc h s khng th nguyn c gi l h s p lc l
rng A v B. Cc h s ny c ngh bi GS. A.W. Skempton (1954).
- Trong th nghim nn ba trc khng thot nc, p lc nc l rng tng giai
on u khi gia tng p lc bung v tip tc bin i khi gia tng ng sut lch.
- T s gia p lc nc l rng gia tng v gia tng p lc bung c gi l
h s B:
3
uB
- H s p lc nc l rng B c th thay i theo trng thi ng sut v ph
thuc ng k vo cng ca mu t cng nh bo ha. Trong trng hp B
= 1, mu t c xem bo ha nc hon ton.
- p lc nc l rng s thay i khi chu tc dng ca ng sut lch trc trong
qu trnh nn ba trc. H s p lc nc l rng A c xc nh theo biu thc:
31
duA
- Vi du : s thay i p lc nc l rng trong qu trnh nn lch trc.
- Biu thc tng th v p lc nc l rng khi chu tc dng ca s thay i cc
thnh phn ng sut chnh:
)( 313 ABu
L thuyt n hi do l tng Morh - Coulomb
27
- t c xu hng nn trong thi gian gia ti c thot nc biu hin tng l p
lc nc l rng trong cc giai on gia ti khng thot nc, dn n gim
ng sut c hiu.
- c trng khi d ti l t s c xu hng n ra (expansion), hin tng ny
cng mnh i vi t qu c kt nng, dn n xut hin p lc nc l rng
m (suction), do trng thi undrained li khng phi l trng thi nguy him
nht trong trng hp ny. Sau giai on khng thot nc c p lc nc l
rng thng d m l giai on c kt, tc nc s cn bng li (do chnh lch
p sut thng d), a phn t t v trng thi ~0
L thuyt n hi do l tng Morh - Coulomb
28
III.3 ng x non porous Vi loi hnh vt liu non-porous th c xem nh ko thm v ko xt n p lc
nc l rng. Ni m nc khng th chy qua). Theo mc nh vt liu th c gii quyt trong gii hn ca ng sut tng.
III.4 Phng php A, B, C trong m hnh Morh-coulomb III.4.1. nh ngha cc phng php A, B, C
III.4.1.1 Phng php A
- L phn tch khng thot nc dng b thng s hu hiu.
- Cho t rt yu, trng hp ny l Marine Clay, th phng php A s c bit
khng ng. Cn t tt phng php A c khuyn ngh.
iu ny gii thch da vo ng ng sut trong h ta (p,q). Theo nh th
nghim c kt ba trc khng thot nc CU ca t st yu c kt thng (normally
consolidated clay), th ng ng sut hu hiu ESP s nh tay li theo 1 ng cong
n ng ph hoi Kf.
i vi t Morh Coulomb (c, ), ng ng sut hu hiu ESP s i theo 1
ng thng n ng ph hoi Kf.
Nh vy, c th rt ra:
+ Lc dnh khng thot nc Cu trong trng hp Morh-Coulomb vt qu c
lng
L thuyt n hi do l tng Morh - Coulomb
29
+ p lc nc l rng trong m hnh Morh-Coulomb a ra thp hn thc t.
Do vy s rt nguy him nu p dng method A (Morh Coulomb c, ) vo t yu.
III.4.1.2 Phng php B
- Ta c th m hnh lm vic theo gi tr Cu thc t ca t
L thuyt n hi do l tng Morh - Coulomb
30
L thuyt n hi do l tng Morh - Coulomb
31
- Tnh Cu t c,
III.4.1.3 Phng php C
Nu dng cu v u=0 tc phi dng la chn drained ( m phng gi lp
ci undrained m dng thng s undrained) v ng x ca p lc nc l rng khng
c tnh ton m ch yu lin quan n sc chu ti v bin dng. Vic dng cu v
u=0 v phi c u=0.495, Eu tng ng vi p sut tng (total stress) cn c xc
nh l thng s u vo.
Vi cu v u=0 th bn thn b thng s ny tng ng vi p sut tng ri nn
chng c ng x ca p lc nc l rng trong ci vic dng b thng s ny (ph hp
cho Tresca v Von Mises v cu khng ph thuc gi tr 3 - total stress).
L thuyt n hi do l tng Morh - Coulomb
32
Tresca cng c tiu chun ph hoi khng ph thuc vo p sut thy tnh (p') v
trong khng gian ng sut chnh mt ph hoi song song vi ng thy tnh. V vi
kt qu th nghim UU th cng cho ci ng bao ph hoi cng gn nh song song
vi ng thy tnh (vic khng song song do nh hng ca bo ha....). V th nn
vn c th dng Tresca cho t c.
III.4.2 Tiu chun do ca TRESCA Tiu chun im nhng u tin cho ng x ca kim loi do Tresca xut
nm 1864, theo tiu chun ny ng phi n hi ch xy ra sau khi ng sut tip cc i
t gi tr ti hn, m ng sut tip cc i bng na hiu s ng sut chnh i v ng
sut chnh tiu (ng knh vng trn Mohr) v c th vit di dng:
1 3max 2 2
uu
qs c
ng dng m hnh Tresca c dng: 1 - 3 = 2su f = 1 - 3 -2su = 0 thay cc gi tr ng sut theo cc bt bin hm f tr thnh
2 cos 0uf J s
L thuyt n hi do l tng Morh - Coulomb
33
III.4.3 Tiu chun do VON MISES
M hnh Tresca thuc loi m hnh ng ni ti v kh c th vi phn dc
cc ng sinh c 1 = 3; 2 = 3; 3 = 1, thun tin tnh ton Von Mises
ngh im nhng ch c th xy ra khi bt bin th 2 ca tenseur ng sut lch t gi
tr ti hn tiu chun ngng ca von Mises nh sau:
2 0f J k Trong c hc t k l sc chng ct khng thot nc.
Chn 2
cos 3u
usk s
c vng trn qua nh ca Tresca
Chn cos
uu
sk s
c vng trn ni tip lc gic u Tresca
III.5 Phn tch l trnh ng sut ca t la chn giai on thit k III.5.1 Phn tch tc thi v lu di
Trong tnh ton kt cu , TCVN ta v cc nc u quy nh r tnh ton theo
trng thi gii hn, 2 trng thi gii hn chnh l TTGH1 v TTGH2 . Nhng trong tnh
ton nn mng /a k thut cc tiu chun nc ngoi h quy nh vic tnh ton theo
L thuyt n hi do l tng Morh - Coulomb
34
cc giai on rt r rng (Eurocode...). C th tnh ton theo 2 giai on l tc thi
v lu di.
Nu khng am hiu th c th tnh ton c 2 giai on : tc thi v lu di , xong
ly min tnh ton . C trng hp tnh ton vi giai on tc thi l bt li , trng
hp khc th vi giai on lu di s bt li hn.
i vi t c kt trc nng th giai on lu di l nguy him, cn li t c
kt thng v c kt trc nh th tc thi nguy him.
Cch gii thch theo ci l trnh ng sut. C th nh sau:
i vi t NC:
th nghim (NC) khng thot nc
Nhn hnh ta thy khi p ng sut lch i vi t NC th nghim khng thot
nc th l trnh ng sut khi chm ng CSL ngn hn ci l trnh ng sut khi chm
ng CSL ca th nghim thot nc. Nh vy thy rng t NC th phn tch tc thi
nguy him hn phn tch lu di.
Tng t cho t OC nh
Th nghim (OC) nh khng thot nc
L thuyt n hi do l tng Morh - Coulomb
35
Th nghim (OC) nh thot nc
t OC nng
i vi t OC nng th l trnh ng sut s i qua ng CSL, khi tip tc tng
ti th l trnh ng sut s i ngc li n khi chm ng CSL th t s b trt trong
th nghim thot nc (chiu vo trc p'-q). Tng t cho th nghim khng thot nc.
Tuy nhin nhn hnh th s chnh lch v l trnh gia hai th nghim khng qu sai
lch nh t NC, nn cn cn thn. Nhng nhn vo l trnh th thy th nghim khng
thot nc c l trnh di hn 1 cht so vi th nghim thot nc.
L thuyt n hi do l tng Morh - Coulomb
36
Th nghim (OC) nng thot nc
Th nghim (OC) nng khng thot nc
III.5.2 L trnh ng sut ca h o L trnh ng sut ca h o, s thy rng khi d ti (unloading) th sc chng
ct khng thot nc giai on undrained (im U) ln hn sc chng ct giai on
drained (im T). Do trng thi nguy him h o l trng thi drained. N ngc
vi trng hp gia ti (loading).
L thuyt n hi do l tng Morh - Coulomb
37
i vi m hnh Morh-coulomb th khi d ti (unloading) th ci sc chng ct
ca TSP n nh hn ci sc chng ct ca ESP, ngc vi trng hp gia ti (loading).
l l do ti sao trng hp drained mi l trng thi nguy him cho ci h o.
IV. Kt lun v kin lun IV.1 Kt lun
- Vng trn Morh c th c s dng phn tch trng thi ng sut v bin
dng, mt phng php phn tch n gin s dng im c xy dng.
- Vng trn Mohr ng sut tng v hu hiu c cng ng knh v c phn chia
bi mt khong cch bng ln ca p lc nc l rng.
- Bin dng ct thun ty nh xz phi c phn bit vi bin dng ct 2xz xz
ng sut ct l bng khng trn mt phng chnh ca ng sut, bin dng ct l
bng khng trn mt phng chnh ca bin dng.
L thuyt n hi do l tng Morh - Coulomb
38
- Vic hiu loi t, trng thi t ca cng trnh trc khi m hnh l rt quan
trng.
- Cn ch thm n qu trnh tng hay l gim ti.
- Khuyn ngh s dng phng php A cho t tt vi b thng s ng sut c hiu,
c, ', trng hp t st yu th phng php A s c bit khng ng.
- Phng php B s dng cho t st yu c kt thng vi b thng s ng sut c
hiu, cu, u=0.
- Phng php B c thng s n gin v d th nghim.
IV.2 Hn ch ca ti - Ch tp trung nghin cu m hnh morh-coulomb.
- Cha xt n cc nh hng ca p lc nc ngm.
- Cha nghin cu s thay i cc ch tiu c hc ca t theo su .
- Cha so snh vi cc m hnh t khc.
IV.3 Kin ngh - Cn lp cng kho st a cht c th khi thit k cng trnh ngm.
- Cn so snh n nh v bin dng gia cc m hnh t vi s liu quan trc thc
t la chn m hnh ph hp v kinh t.
L thuyt n hi do l tng Morh - Coulomb
39
Ti liu tham kho [1] n, Chu Ngc. C hc t. s.l.: Nxb i hc Quc gia TP.HCM, 2004.
[2] Chu Ngc n. L thuyt chy do
[3] Nguyn Minh Tm. ng x thot nc v khng tho nc ca t
[4] Nguyn Minh Tm. Cc m hnh
[5] Wong Kai Sin. Understand the Mohr-Coulomb Soil Model
[6] Material Models Manual V8
[7] Braja M, Das. Principles of Advance Soil Machenic. s.l.: PWS Engineering,
1984.
[8] Chapter 5. Cause of the collapse & findings
[9] C Hc t. N.A.X T Vich
[10] Soil Mechanics & Foundation Engineering By Purushothama Raj [11] Atkinson The mechanics of soil