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PHAN T R U O N G PHIET
GlAO Sir TIEN ST DIA Ki THUAT

Ap luc dat
VA

tudng chan dat
(Tai ban)

NH A X U A T B A N X A Y Dl/NG

HA NOI - 2008



LOI NOI DAU
Tinh todn dp luc dd't vd tuang chan dd't Id m ot trong nhung van de ldn cua dia
ki thuat.
Trong n h u n g ndm gdn day, li thuye't ve dp luc ddt duoc ph a t tr ii’n vd hoan chinh
them theo ba hudng chinh:
1. H oan chinh cach gidi theo li thuyet cdn bdng gidi han cho nhung so dd tuong
chdn th u a n g gap trong thuc te nhdm ldp dugc he thd'ng bdng bieu tien dung hodc ldp
dugc chuong trinh tinh todn bdng m ay tinh dien tii:
2. Ung dung li thuyet phdn m dnh (thoi) vd van dung phep phdn tich he thd'ng d $
giam bdc sieu tinh cua bai todn dang ndng cao hieu qua phep tinh tren m dy tinh dien tii.
3. H oan chinh li thuye't dp luc dd't Coulomb cho dd't ddp thuoc loai da't dinh hodc
d d t cd cd't vd gidi chinh xdc cho cac trudng hop phiic tap ve lung tuong, m dt ddt ddp
vd tai trgng ngoai.
Ke't qua d a t dugc theo ba hudng n iu tren cdng khdng dinh tinh uu viet cua li thuyet

dp luc dd't ciia Coulomb m dc du khdi diem xud't la xa xua nhdt (1776). Sai sd' tinh todn
trong truong hop tinh dp luc dd't chu dong la khdng dang ke nhung trong truong hop
ap luc dd't bi ddng vdi tudng lung nhdm (cd q>0 > 0,3cp) thi sai so m dc p h a i la qua ldn.
Cud'n sach nay gidi thieu loi gidi chinh xdc theo li thuyi't Coulomb ve ap luc dd't chu
ddng vdi ca c sa dd tudng chdn dd't, m dt dd't ddp vd cac dang tdi trgng, thudng gdp
trong thuc te xd y dung ddn dung, giao thdng vd thuy Igi, Ldi gidi nay ddp ung td't hai
yeu cdu cdn thie't: m dt Id xet dugc dp luc nude Id rdng dm trong khd'i dd't ddp khdng
bao hoa nude; xet dugc tdc dung cua cd't dd't trong khd'i ddt ddp. H ai la ldp trinh tinh
todn d i ddng vi vdi m dt thudt todn duy nhdt md cd the tinh todn cho td't cd cac trudng
hop v i tudng chdn, m at dd't ddp, cdc loai tdi trong thudng gap theo nguyen li cdng
tdc dung.
V i dp luc dd't tinh vd dp luc dd't bi dong, cud'n sach nay trinh bay nhung phuong
phdp tie'll bo hien nay duoc gidi thieu n h iiu d nude ngoai.
Chung tdi hi vong cud'n sach ddp ung dugc yeu cdu thiet ke, hge tdp va. nghien ciiu
hien nay.
P h a n T r iw n g P h ie t

3



Chtromg I
NHUNG KHAI NlfiM MQ DAU

T udng ch£n Sa cong trinh g ia cho m ai dat ds'p hoftc m ai hd' dko khoi bi sat truat.
T udng chkn dat duac su dung rdng rai trong cac ngknh xay dung, thuy lai, giao thdng.
Khi 1km vide, iung tudng chan tie'p xuc vdi khd'i d it sau tudng va chiu tac dung cua dp
luc da't.
T rong cac cdng trinh thuy cdng, cd m dt sd' bd phan cua k i t cku cdng trinh khdng
phai lk tu d n g chan dkt nhung cd tac dung tuang hd vdi da't va cQng chiu kp luc cua da't

gid'ng n h u tu d n g c h in da't. Do do, khai niem v l tudng chan da't duac m d rQng ra cho
tk't ca nhtfng bd phan cua cdng trinh cd tac dung tuang hd giaa da't tilp xuc vdi chung
vk ap luc dk't len tudng chan cdng dugc h ilu nhu ap luc tie'p xuc g iaa nhOng bQ phan
a'y vdi da't.
T ud n g chan dat trong cac cdng trinh thuy cdng lam viec trong nhOng d ilu ki£n r i t
khac so v di d ilu kien lam viec cua tudng chkn dk't trong giao thdng vk xay dung do
dkc d ilm cu a cdng trinh thuy lai q u y lt djnh.
Dk't dkp sau tudng chan, do ydu cau chd'ng tham nude tu thugng luu xud'ng hfl luu
cua cdng trinh thuy cdng, thudng dOng dat lo^ii set cd tinh chd'ng thkm td't. D ilu nky
dkn d in vide tinh toan thie't k l tudng chkn phuc tap han so vdi trudng hgp ddng d it
lo^ii ckt dkp sau tudng chan.
I. PH A n

l o a i t u On g

CHAN DAT

T u d n g chkn dk't thudng dugc phan loai theo bd'n ckch sau day nhkm muc dich
khac nhau:
1. P h a n lo ai th eo dd c u n g
B iln dan g cua bkn than tudng chkn dk't (dd ud'n) 1km thay ddi
d ilu kien tie'p xuc giaa lung tudng chkn vdi khdi dk't dkp sau
tudng, do do lam thay ddi tri sd' ap luc dk't tac dung len lung
tu d n g va c an g 1km thay doi dang b ilu d 6 phan bd ap luc dkt theo
c h iiu cao tudng. Thi nghigm cua G,A. D ubrdva da chung td khi
tu d n g bj b iln dang do chju ap luc dkt thi b ilu dd phan bd' ap luc
dk't cd dang dudng cong (hinh I - 1 ), n lu phan giaa thkn tudng bj
bie'n dang n h ilu thi bieu do phan bd' ap luc dk't ckng cong va
cu d n g dd ap luc dat d phkn tren tkng len (dudng 2 ), n lu chkn
tu d n g cd c h u y ln vj ve phia trudc thi d phan tren tudng tkng len

Hinh /-/

5


ra't nhidu, co khi de'n

2 ,5

lan so voi cuang d 6 ap lire ban dau, con cu an g dQ ap luc d

phan dudi tuang thi lai giam (duang 3).
Theo cach phan loai nay, tuang duac phan lam hai loai: tuang cung va tuang m£m.
T uang co bidn dang udn khi chiu ap luc da't nhu neu tren day goi la tudng mem hoac
tudng m dng. T uang mdm thudng la nhung ta'm g 6 , thep, be tOng cdt thep ghep lai.
T u an g cu cung xep vao loai tuang mdm.
Tuang cieng khdng co bien dang udn khi chiu ap luc da't ma chi co chuyen vi tinh
tid'n va xoay. Ne'u tuang cung xoay quanh mep dudi, nghla la dinh tudng co xu nudng
tach rdi khdi khd'i dat dap va chuydn vi vd phia trudc thi nhidu thi nghiem da chung td
la bidu d 6 phan bd ap luc cua da't rdi co dang dudng thang va co tri sd cudng dQ ap
luc dat ldn r.hat a chan tudng (hinh I-2a). Ddi vdi da't dinh (da't d ip sau tudng), theo
ke't qua thi nghiem cua B.L. Taraxdp thi bidu do phan b d ap luc da't co dang hai cong
va cung co tri sd cudng dQ ap luc ldn nha't d chan tudng (hinh I-2b). Ne'u tudng cung
xoay quanh m ep tr 6 n, nghla la chan tudng rdi khdi khd'i da't dap va chuydn vi ve phia
trudc thi theo ke't qua thi nghiem cua nhidu tac gia (K. T erzaghi, G .A . D ubrdva, I.V.
Y ardpdnxki, I.P. Prdkdfiep v.v...) bidu d 6 phan b d ap luc da't (da't rdi cQng nhu d^t dinh)
co dang cong, tri sd ldn nhat phu thuQc vho muc dQ chuydn vi cu a tudng va & vho
khoang phan giua lung tudng (hinh I- 2 c).
T udng cung thudng la nhdrng khd'i be tdng,

be tdng da hQc, gach da xay nen con goi
la tudng khdi. T udng chan bang be tdng
cd't thep co dang ta'm hoac ban nhung tao
vdi cac bd phan khac cua cdng trinh thanh
nhttng khung hoac hdp cung cung duac
xe'p vao loai tudng cung.
N hu trSn da phan tich, cdch ti'nh toan tri
sd' ap luc dat len tudng cung va tudng mdm
khac nhau.

A
= \
~~~A
—
■
■■■ \
--\
\ = --- \
)

\
\ = = -\\
\ ----- \
\ —
' ------ -\
' ---- \
b)

/
/

/
1

/
I
I
/
/

c)

Hinh 1-2

2. P h a n loai th eo n g u y en ta c lam viec
T udng c h in da't la loai cdng trinh thudng xuyen chiu luc dSy ngang (ap luc da't), do
dd tinh dn dinh chdng trugt chie'm m ot vj tri quan trong dd'i vdi ti'nh dn dinh ndi ch u n g
cua tudng. Theo quan diem nay tudng chan dugc phan lam ma'y loai sau day:
Tu&ng trong luc (hinh I-3a): do dn dinh dugc dam bao chii yeu do trong lugn g ban
than tudng. Cac loai tudng cung deu thuQc loai tudng trong luc.
Tu&ng nua trong luc (hinh I-3b): dd dn djnh dugc d im bao khdng nhtfng chi do trong
lugng ban than tudng va ban m dng ma cdn do trong lugng cua khd'i da't dap n a m tren
b in m ong. Loai tudng nay thudng lam be tdng cd't thep nhung chidu day cua tudng
tving kha ldn (do dd loai tudng nay cdn cd ten goi l i tudng day).

6


Tuong bdn goc (hinh l-3c): d 0 6’n dinh dirge dam bao chu ye'u do trong lugng khdi
dat d ip de len ban m ong. T uong va m ong la nhtfng ban, tam be tdng cd't thep m ong
nen trong lugng cua ban than tuong va m ong khong ldn. T udng ban goc cd dang chtf

L nfin cd khi cdn goi la tudng chu L.
Tucrng m ong (hinh I-3d): sir dn dinh cua loai tudng nay dugc dam bao bang cach
chdn chan tudng vao trong ndn. Do dd loai tudng nay cdn goi la tudng coc va tudng
cu.
giam bdt dd sau chdn trong dat cua tudng va dd tang dd cung cua tudng ngudi
ta thudng dung day neo.

Hinh 1-3
3. P h a n lo ai th e o ch ieu cao
Chidu cao cua tudng thay doi trong m dt pham vi kha ldn tuy theo yeu cdu thie't ke.
Hien nay, chidu cao tudng chdn da dat de'n 40m (tudng chdn d nha m ay Thuy dien
L 6 nin tren sdng V onga). Trj sd' dp lyc da't tac dung len lung tudng chdn ti le bac hai
vdi chidu cao cua tudng. T heo chidu cao, tudng thudng dugc phan lam 3 loai:
Tuong thd'p: cd chidu cao nhd hon 10m.
Tudng cao: cd chidu cao ldn hon 20m.
Loai tudng cndn co chidu cao vao khoang trung gian cua hai loai trdn (tuc cao ti* 10
de'n 2 0 m) dugc xe'p vao loai tuang trung binh.
Theo quy pham tam thdi thie't ke' tudng chdn da't QP-23-65 cu?\ ta thi la'y gidi han
phan chia ba loai tudng tha'p, cao, trung binh la 5 va 10m: tudng chdn tha'p cd chidu
cao nhd hon 5m , tudng chdn cao cd chidu cao ldn hon 10m.
4. P h a n lo ai th e o goc n g h ien g c u a lu n g tu d n g
Theo cach phan loai nay, tudng dugc phan thanh tudng dd'c va tudng thodi.
Tuang doc iai phan ra tudng dd'c thuan (hinh I-4a) va tuang doc nghich (hinh I-4b).
T rong tru d n g h g p cua tudng dd'c khdi dat trugt cd m dt m at gidi han trung vdi
lung tudng.
Ne'u gdc nghieng a cua lung tudng ldn qua m dt muc do nao dd thi khd'i ddt trugt
sau lung tirdng khdng lan de'n lung tudng (hinh I-4c); tudng loai nay dugc goi la
tudng thodi.

1

Nguyfin tic tinh toan ap luc d i t tic dyng len lung tudng dd'c vd lung tudng th o ii
k h ic nhau. Phuang p h ip tinh toan i p luc d it chu dQng len tudng th o ii dugc trinh bdy
trong myc 2 chuang VIII.

Hinh 1-4
5. P h i n loai th eo k e t cau
V 6 m at ke't c iu , tudng c h in dugc chia thdnh tudng lien khQi v i tudng lip ghep.
Tudng liin khdi lim bang be tdng, be t&ng d i hQc, gach xay, d i xdy hay bang be
t 6 ng cd't thep. T udng lidn khdi dugc xay (gach d i) hoac dd (be tOng, be tOng d i hQc,
be tOng cdt th 6 p) true tie'p trong h d m ong. H d mQng p h ii rQng han m dng tud n g c h in
mQt k h o in g d£ ti^n thi c&ng vd dat v in khuOn. MQng cua tudng be tfing v i be tdng cdt
thep liSn khdi vdi b in than tudng, cQn mQng cua tudng c h in b&ng gach d i xay thi cd
th£ l i nhtfng ke't c iu d&c lap bdngda xay hay be t&ng. M$t c it ngang cua tud n g lidn
khdi l i t k h ie nhau. MQt s&' dang tudng loai n iy dugc trinh b iy tren hinh 1-5 vdi nh&ng
ten goi nhu sau: a) H inh ch& nhat, b) Hinh thang c 6 nguc tudng nghieng, c) H inh thang
cd lung tudng nghieng, d) H inh thang cQ nguc vd lung nghieng, e) H inh thang nghieng
v 6 phia d it d ip , g) CQ m ong nhd ra phia trudc, h) Cd lung gay khuc, i) Cd lung bac
c ip , k) CQ be g iim tii, 1) Co m ong nh& ra hai phia.
T udng ban gQc (hay tudng cho- L) ki£u cOngxon (hinh I- 6 a) ho$c ki£u cQ bSn sudn
(hinh I- 6 b) cQng thudng lim b in g be tdng cd't th 6 p dd liSn khdi.


Tuang ldp ghep gdm cac ca'u kien bang be
tdng cot thep due sSn lap ghep lai vai nhau theo
nhtfng sa do ke't ca'u dinh sSn. Ca'u kien due sSn
thuang la nhung thanh hoac nhung tam khong
lan (thuang d u a i 3m) && tien van chuy^n.
Tuy theo sa d 6 ke't ca'u ldp ghep, tuang lap

*&
ghep th u an g co may kieu sau day: k ii’u chic L
V7m7ZZZZZ!
gdm nhung khdi va tam be tong cdt thep lap rap
lai (hinh I-7a), k ii’u hdng rao gdm nhidu thanh
llin h 1-6
be tOng cdt thep larn tru dung hay tru chdng va
cac ban ghep lai (hinh l-7b), k ii’u hdp m 6 t tdng hay hai tang, trong h5p dd day cat soi
(hinh I-7c), k ii’u chuong gdm nhidu thanh dat doc ngang xen ke nhau, trong chudng dd
cat soi (hinh I-7d).
Cac loai tu an g lap ghep deu dugc lap rap tai ch 6 trong h d m ong. H d m ong khdng
c^n dao rong ma chi can dam bao vua bang binh dd cua ke't ca'u lap ghep.
Tuang ro dd: gdm cac ro da ndi ghep lai vai nhau (hinh I-7e). Nhtfng ro da bang
ludi sat hoac ludi p&lime dugc xe'p tung lap, ke't ndi vori nhau rdi xe'p da hoc vao tuang
ro. De’ da't hat m in cua dat ndn va da't dap khdng xam nhap vao da hdc trong ro, thuang
d£ mOt ldp vai dia ki thuat ngan cach day tuang va lung tuang vdi da't n 6 n va da't ddp.
Uu di^m ndi bat cua tuang ro la chju lun cua n 6 n ra't tdt va ki thuat lam tuang dan
giSn. Hien nay cac nha khoa hoc dang nghien cuu bien phap cdng nhu vat lieu de tang
tudi tho cua rg.
Tudng dd't cd cd't: la dang tudng hien dai cua cac bao tdi da't chat ddng thd sa cua
nhan dan (hinh I-7f). T uang chinh la m at b l (da) lam bang cac ta'm kim loai hoac be
tdng cdt thep. M at bi dugc ndi vdi cac dai kim loai hoac pdlim e chdn ttfng ldp trong
da't ddp sau tudng. Da't dap cd tac dung day m at bi ra khdi da't nhung trong lugng cua
da't ddp co tac dung tao nen luc ma sat gitfa da't va cdt neo mat bi lai. T udng da't co cdt
co nhidu uu didm: nhe, chiu lun ra't tdt nen cd thd thich ung vdi cac loai ddt nen khdng
tdt. K i th u at dat cdt, cach ti'nh toan dugc trinh bay trong cac sach chuyen d 6 v6 da't
cd cd't.

m

n

I-I

a)

El
EE

EE

221

JZ L

e)

d)
Hinh 1-7

9


II. THOAT NUOC CHO KHdl DAT DAP SAU TUftNG CHAN
Du dat dap sau tu an g chan la loai dat rdi ho3c dat dinh, nude trong khdi dSft dap lam
thay ddi tinh chat vat li, c a hoc cua da't va cd thd lam cho tudng chan da't dat trang thai
nguy hidm do ap luc dat tang len va cd ap luc thuy tinh phu them.
Viec thoat nude cho khdi da't dap sau tudng chan thudng nham hai m uc dich chu ydu
nhu sau: a) T ao di£u kien cho nude tich chua trong 16 rdng cua da't thoat ra nha^h chdng
hoac ngSn ngua nude than: vao khd'i dat dap, b) Ngan ngua nude iie'p xiic vdi lung

tudng de tru khu ap luc nude tac dung len lung tudng.
N ude th^m vao khd'i daft dap sau tudng cd thd cd ma'y ngudn sau day:
1. N ude mua rai ngdm xud'ng;
2. N ude m at d cac vung lan can ngam vao;
3. N ude ng£m d cac vung khac tdi.
Dd thoat nude cho khd'i dzft dap sau tudng thudng p h ii dung thie't bj th o at nude. N di
chung, thie't bi thoat nude gdm bd'n bQ phan: bd phan th u nha't - thoat nude m at; b 0
phan thu hai - gi&m nhd lugng nude ng£m vao khd'i d£t ddp; b 0 phan th u ba - thoat
nude trong khd'i d£t dap; bd phan thu tu - thoat nude ra ngoai pham vi tudng chdn.
TQy theo tinh cha't cua da't dap rdi hay dinh va didu ki$n cu thd cua tudng chdn, cd
thd su dung cac loai thie't bi thoat nude trinh bay tren hinh 1 - 8 vdi cac dac didm nhu
sau: a) Chi cd 16 thoat nude, b) L 6 thoat nude cd bd' tri I q c , c ) R anh th o at nude thdng
dung, d) T in g thoat nude ap sat lung tudng, e) Tdng thoat nude nghieng (theo h u dng
m at trugt).

*

d)
Hinh 1-8
Tac dung ctia thie't bi thoat nude dd'i vdi dat dinh dap sau tudng dugc trin h b ay tro n g
m uc 3 chuang 9.

10


III. Dl£U KI$N SU DUNG CAC LOAI TUOfNG CHAN
Hien nay tudng c h in co nhidu loai hinh khac nhau; m 6 i mdt loai chi nfin su dung
trong m dt sd' didu kien cu the’ mdi dem lai hieu qua kinh te cao. Sau day nfiu so iugc
mdt sd kinh n ghiem da due ke't duac.
So vdi cac loa> tuang thi loai tuang m ong bang be tdng cd't thep thudng cho hi£u

qua kinh te' cao so vdi loai tirdng trong lire; xi mang diing cho tirdng mdng it ban

2

lin

va cd ‘ thep nhieu h a n mdt khd'i lirang khdng dang k i. Uu diem ndi bat cua loai tudng
bang be tdng cdt thep la cd the’ su dung phuang phap thi cdng lip ghep va yeu c iu v£
n 6 n khdng cao nen it khi phai xu li n£n.
Ne'u khdng cao qua

6 m,

loai tudng ban gdc (kieu cdngxon) bang be tdng cd't thep cd

khdi lu an g it han tudng cd ban sudn. Ne'u cao tir
tudng nay xa'p xi nhau. Ne'u cao han

8m

6

den

8m

thi khd'i luang cua hai loai

thi tudng cd ban sudn cd khd'i lu an g be tdng

cd't thep nho h an tudng kieu cdngxon. Do dd loai tudng m dng be tdng cd't thep cd b in
sudn dung thi'ch h a p nha't khi cd chieu cao tir trung binh trd len.
T udng c h in da't bang be tdng chi nen dung khi cd't thep qua d it hoac khan hie'm, bdi
vi be tdng cu a cac tudng c h in trong luc chi p h it huy m 0 t phan nhd kha nang chiu lyc
ma thdi. COng do nguyen nhan nav, khdng nen dung loai be tdng cudng dQ cao d l lim
tudng c h in d i t be tdng. D l giam bdt khd'i lirang tudng c h in bang be tdng cd th i lim
them tru chdng. D ung loai tudng co be giam tai dat d k h o in g 1/4 chiSu cao tudng,
tudng cd lung nghieng v 6 phia dat dap cQng tie't kiem duac be tdng.
T udng c h in bang da xay c in ft xi mang han tudng be tdng, cd th i h o in th in h trong
thdi gian tu an g dd'i n g in va td’ chuc thi cdng dan gian. N ai s in da, dung tudng d i xSy
thirdng co hi$i» qua kinh IS' cao. Ddi vdi tudng c h in cua cQng trinh thuy cQng diing d i
x&y cd sd' hieu tu 200 trd len, vtfa xi m ang pudalan cd sd' hieu tir 50 trd len. Lung tudng
da xay th u d n g lam th in g dung hoac nhi 6 u bac c ip .
T rudng hop s in da vun hoac da nhd thi nen thay tudng da xay b in g t;idng be tdng
da hdc.
Tucrng gach xay khdng cao qua 3-4m thi nen dung loai cd tru chd'ng. T udng g^ich
xay chCr nhat hoac lung bac cap thudng dugc dung cho nhung cdng trinh nhd dudi d it.
DQ'i vdi cac loai tudng c h in Id thien chju tac dung true lie'p cua mua n in g v i cac tudng
c h in cua cac cdng trinh thuy cdng khdng nen dung gach xay. Gach xay tirdng c h in cd
sd' hieu khdng nen nhd han 200 va vtfa xay tir 25 trd len, khdng dugc ddng lo a:
gach silicat.
T udng c h in d i t loai cao va trung binh xay d vung ddng d it nen bang be tdng
cd't thep.

11


IV. SO LUOC vfc LI THUYfiT TINH TOAN A p LUC DAT LfiN TUONG C h An
De'n nay co kha nhieu thuye't vd ap luc dat theo nhtfng quan didm kh£c nhau.
Tuy theo li thuye't co xet de'n d 0 cung (bie'n dang) cua tirdng, cd thd phan cac thuye't

hien nay thanh hai loai: loai khdng xet de'n d 0 cung cua tirdng v& loai co x6 t de'n dd
cung cua tudng.
Loai khdng xet de'n dd cung (bie'n dang) cua tudng gia thie't tudng tuyet ddi cung va
chi xet de'n cac tri sd ap luc dat d trang thai gidi han: ap lire dat chu ddng va ap lgrc
dat bi ddng (co ep trdi).
Thudc loai nay cd thd kd ba nhdm chinh nhu sau:
1. N h d m th e o U th u y e t can b a n g g idi h a n c u a k h o i r2 n
Cac thuye't theo nhdm nay ddu gi& thie't khd'i da't trugt sau tudng chan, gidi han bdi
m at trugt co hinh dang dinh trudc, nhu m dt khdi xin d trang thai can bang gidi han.
Tuy theo hinh dang m at trugt gia thie't, nhdm nay hien nay phat tridn theo hai xu hudng:
Xu hudng gid thii't m dt truat phdng: dai dien cho xu hudng nay cd thuye't C.A.
C uldng (1773) va sau do dugc I.V. P dngxale, K. Cunm an, G. R ephan, F. Engetxe, B.A.
U retxki, G.A. D ubrdva, I.P. P rd k d fiep v.v... phat tridn them.
Xu huang gid thii't m dt truat cong: theo xu hudng nay, m at tru g t cong dugc thay
b in g m at tru tron hay m at x o ln d'c Idgarit hoac m dt m at h 6 n hgp phdng va cong. Theo
xu hudng nay cd W. Feie.niut, L. R andulic, J. Ode, H. Kray v.v...
2. N hdm th e o th u y e t cSn b a n g g idi h a n p h a n td' (diem )
N hdm nay chu truang tinh cac tri sd' ap luc da't (ap luc deft chu ddng va ap luc ddt
bi ddng) vdi gi& thie't cdc didm cua m di trudng da't d ip dat trang thdi c§n bang gidi han

cung m dt luc, li thuye't nay da dugc G iao su ngudi Anh ten la W .J.M . R angkin dd ra
nam 1857 va ve sau dugc goi la thuye't Rangkin. Thuye't R angkin d u g c J. C dngxidera,
J. B utxinet, J. Rezan, A. Caco v.v... phat tridn them . De'n nay, li thuye't can bang gidi
han phan td dugc phat tridn manh me theo hai xu hudng:
Xu huang gidi tich: dai dien cho xu hudng ndy, trudc he't phai kd de'n cac cdng trin h
nghien cuu If thuye't cua Vien si Lien Xd V.V. X dkdldpxki. Ldi g iai cua R angkin, de'n
nay, chi dugc xem nhu m dt trudng hgp dac biet cua ldi giai cua X dkdldpxki. H u d n g
nghien cuu cua V.V. X dkdldpxki dugc tie'p tuc nghien cuu d Ba L an, Phap va n i 0 t sd'
nude khac.
Xu huang dd gidi: khac vdi V.V. X dkdldpxki giai he phuang trinh vi phan can b a n g

gidi han bang toan giai tich, G iao su Lien Xd X.X. G olutkevit da th an h cdng tro n g viec
giai cac bai toan ve li thuydt can b in g gidi han theo phuang phap d 6 giai b in g he v o n g
trdn dac trung.

12


Den nay, li thuye't tinh ap lire da't len tudng m 6 m chua dirge nghien ciru day du bang
li thuye't ti'nh ap lire da't len tucrng cung. Loai li thuye't ap lire dat co xet de'n bie'n dang
cua tudng dugc phat tri£n theo hai hudng nhu sau:
Xu hudng ti'nh gan dung cac bi£u thuc tinh ap luc da't chu ddng va bi dOng do'i vdi
tudng cung.
Xu hudng ti n h t u d n g m em nhu dam tira len nen dan hdi va dung cac ioai md hinh
ccv hoc ve nen (m d hinh V inkle, md hinh nen ban khdng gian vd han bien dang tdng
the...) de giai. C ac phuang phap theo xu hudng nay Khdng nhung cho phep xac dinh ap

luc da't len tudng m 6 m (tuc phan luc nen) ma cdn xac dinh dugc c l c h u y ln vi cua
tudng mem .
Ngoai ra cdn c ln phai neu them loai li thuye't tinh ap lire dat len tudng cung va cd
xet de'n chuye’n vi cua tudng cung. T udng cung khdng bj bie'n dang khi chiu tac dung
cua ap luc da't nhung tuy trudng hgp, tudng cd chuye’n vj tjnh tie'n hoac quay. C h u y ln
vi cua tudng cung khdng nhung lam thay d 6 i dang bie’u dd phan bd' ap luc da't len lung
tirdng ma cdn l lm thay d 6 i trj sd' ap luc da't. Theo quan di£m n ly Ip luc dat dugc phan
ra loai ap luc da't ung vdi trang thai can b ln g gidi han va ap luc da't ung vdi trang thai
chua can b ln g g idi han.

13


Chmmg II

THUYliT AP LUC DAT CULONG
MO RONG CHO DAT DINH

T h u y lt ap li/c da't C ul 6 ng(*) dugc xay dung tCr nSm 1773. Sau do thuye't nay dugc
POngxale (1840), C unm an (1866), R ephan (1871) va n h ilu ngudi khac phat triln them .
Thuye't CulOng dan gi&n, co kha nSng giai dugc n h ilu bai toan thuc te' phuc tap va
cho ke't q u i du chinh xac trong tru an g hgp tinh ap luc da't chu d 6 ng. Do do, d£n nay
thuye't CulOng van dugc dung phd bie'n d l tinh ap luc d£t chu dOng len tudng c h in .
Luc dinh cua dat d ip lkm giam tri s0' ap lye da't chu dQng va lam tang tri sO' dp lyc
bi dQng cua da't. T rudc day, anh hudng cua luc dinh kh 6 ng dugc x et de'n khi tinh toan
ap luc dat len tudng c h in do mQt sQ nguai cho rin g dQ'i vdi da't d i p loai da't cat thi luc
dinh kh 6 ng dang k l so vdi lyc ma sat trong, cdn dd'i vdi dat d ip thuQc loai da't set thi
luc dinh bi g iim di n h ilu khi bi am udt va khi nhiet dQ thay ddi.
Hi£n nay, lyc dinh cua cac loai da't da dugc tieu c h u in hoa va da dugc xet de'n khi
tinh toan ap luc dat chu dQng (Q P-23-65.T C X D 57-73 v.v...).
M d rQng thuye't ap luc da't CulOng cho d£t dinh da dugc n h ilu nha bac hoc tren the'
gidi nghien cuu va d l ra cac phuang phap tinh toan ap lyc dat len tudng c h in , c d xet
de'n luc dinh cCia dat d ip theo n h ilu each khac nhau.
I. CAC GIA THlfiT VA NHUNG LlfcN H$ CO BAN

1. C ac gia th i£ t c a b a n va so* do lire
Thuye't ap luc da't CulOng dua tren m iy g i i thie't c a ban nhu sau:
1. T rang thai gidi han cua tudng c h in cung
va khQi da't d ip sau tudng dugc xac dinh b in g
su c h u y ln dich (trugt hoac lat) cua tudng du gay
cho mQt khQi da't sau lung tudng cQ xu the' tach
ra va trugt theo mQt m d t trugt phdng nao do.
Mat lung tudng cQng la mQt mat tru g t (quy udc
gpi ia m at tru g t thu hai).
2. Khoi dat trugt xem nhu mQt khd'i rdn tuyet

dd'i dugc gidi han bang hai m at trugt: m at trugt
phat sinh trong khQi dat d ip va m at lung tudng
(hinh I I - 1).
(*) C.A. Culdng la mdt si quan cdng binh nguai Phap.

14

Hinh II-l


Gid thie't nay cho phep ta thay the' cac luc thd tich va lire bd m at tac dung len khdi
ddt tru g t bang nhtfng hgp lire cua chung va ung dung true tie'p cac ke't qud cua mdn c a
hpc vSt r^n.
3. T ri sd' ap luc da't chu ddng len tuang chdn dugc xac dinh tuang ung vdi luc ddy
cua khd'i da't trugt "ran tuyet dd'i” len tudng chdn ung vdi trang thai cdn bdng gi&i han
cua nd tren hai m at trugt (tri sd' ap luc da't bj ddng dugc xac dinh tuang ung vdi luc
chdng cu a khd'i da't trugt "ran tuyet dd'i" len luang...).
Gid thie't nay cho phep ta Chira uhan:
a) Cac phan luc cua tudng va cua da't (phdn nguyen) len khd'i da't trugt "tuyet dd'i
rdn" lech vdi p h u an g phap tuye'n cua m at trugt m dt goc bdng gdc m a sat ngodi (p0 (gitta
lung tu d n g vdi khd'i ddt trugt) hoac bdng gdc ma sat tiong (p (gitfa ddt nguyen vdi khd'i
da't trugt).
b) Da giac luc k h ep kin
N guyen trudc day, Culdng khdng xet de'n luc dinh cCa dat ddp va nhu vay trong sa
dd luc (hinh I I - 1) cd ba luc: G, E, R. Vd sau, luc dinh cua ddt ddp da dugc x£t de'n va
da dugc quy djnh su dung trong cac quy pham hien dting trong nude va ngoai nude.
Do dd, dd m d rdng pham vi su dyng li thuye't Culdng cho ddt dinh, hi£n nay phdi
them gid th ift thu 4 v i luc dinh cua ddt.
4. L uc dinh cua da't ddp dugc xem n hu tac dung theo phuang cda m at trugt vk phan
bd' ddu tren m ^t trugt.

N h u vay, dnh hudng cua tinh dinh cua dat dugc xet de'n qua hai luc tac dung len hai
mat trugt, tren m at trugt th u nhdt, lire dinh dugc xac dinh theo cdng thuc (xet bdi
toan phdng):
T = c.L

13-1 -1 a

L uc dinh tac dung len m at trugt thu hai (lung tudng) bdng:
T 0 = c 0 .L 0

II- 1 - lb

T rong dd:
c- luc d inh d an vi cua dat ddp;
c0- luc dinh d an vi cua ddt
ddp v di lung tudng;
L- chidu dai m at trugt
thu nhdt;
L0- chidu dai m at trugt
thu hai.
T rong trudng h gp dat ddp la
lo?i ddt dinh, s a dd luc n h u d
hinh II-2 va gdm 5 luc G, R, T,
T E
°’ C '

a)
Hinh 11-2

15

2. N guyen h' ti'nh to a n
TCr so d 6 lire II -1 (ling vai da't rdi). chie'u ta't ca cac luc tac dung v&o khdi da't trugt
len true U vu5ng goc vai R va chu y de'n cac goc gitfa cac luc va cac ki hieu:
a - goc giffa lung tuang vdi m at th&ng dung;
0 O-

goc gitfa m at nam ngang vai m at trugt giS dinh;

ij/ = 90° - a

cp0

G- trong lugng khdi da't trugt.
T a sg co phuang trinh can bang:
XU = - G sin(0o - q>) + E sin (y + 0 O - cp) = 0
TO1 do, co c 6 ng thuc tinh lire d iy cua da't rai len tudng:
e

=

n i 2 a

g

sin(ip + 0O- cp)
(Luc d^y cua da't len lung tu an g dugc suy ra tir phan luc E trong so dd luc).
T u s a d 6 luc II-2 (da't di'nh), cflng lam nhu tren ta co:
Z U = - G sin(0o - cp) + E sin (y + 0 O - cp) + T osin(0o -

9

- a ) + Tcoscp = 0

T u do, co c 6 ng thuc ti'nh lire d^y cua da't di'nh len tudng:
^

G sin(0o - cp) - Tcoscp - Tosin(0o - cp - a )

L = ------------------------------------------------------------------------ 1 1 - I - z b

sin(y + 0O- cp)

Chie'u da giac luc len true vudng goc vdi E s6 x&c dinh dugc bidu thuc tinh R:
„

G siny + Tcos(0o + y ) - T 0sin(y
K = --------------------------------------------------

+ a)

sin(y + 0O- cp)

tt i ^
11-1 -

j

Khi cho c = c 0 = 0 thi c 6 ng thuc I I - 1-2b tra lai c&ng thuc I I - 1-2a. Do do, tu day vd

sau dung bidu thuc II-l-2 b dd xet cho dugc tdng quat.
Trong phuang trinh I I - 1-2b cac iln s6 la E va gdc 0 O. Cac dai lugng G , T dugc bidu
thi qua goc 0 O> tri sd T 0 xem nhu mOt dai lugng da bie't. N hu vay ta m di co mQt phuang
trinh chua hai ^n sd E va 0 o.
Do do, dd co thd giai dugc bai toan ap luc da't, CulOng da dung nguyen U cuc tri dd
dua them vao mQt p huang trinh ntfa. N guyen li cuc tri ma C ulong dd nghi cd thd hidu
theo djnh li cua A. A. G avSzdep nhu sau: "Dang pha hoai thuc cua he thdng tudng - d£t
dap ung vdi trj sd nhd nha't cua tai trong phu pha hoai". Tren c a sd do. can chon goc
nghieng cua m at trugt nhu the' nao cho luc day cua da't dap len tirdng (ti'nh ap luc da't
chu dong) la ldn nha't hoac luc chong cua da't dap len lung tudng la nhd nha't (tinh ap
luc dat bj dQng). N hu vay chi c&n phu them mQt luc kha nho la tudng dat tran g thai
gidi han vd 6 n dinh (trugt hoac lat). L uc tidy ldn nh d t cua ddt ddp lin tuang d u a c quy
udc goi la dp luc d d t chu ddng ciia ddt (Ecd). L uc chd'ng nho n hdt ciia d d t d d p lin
tudng aucrc quy udc goi Id dp luc dd't bi ddng cua ddt (E bd).

16


Phuong trinh th d hai cua bai toan do Culdng d l ra 14:
dE

=

II - 1-4

0

d0 .
T ir h$ p h u an g trinh c a ban cua li th u y lt CulOng:
E =

Gsin(9 0 - cp) - Tcoscp - T 0sin(9 0 - cp - a )
sin(M/ + 9 0 - cp)

dE

=

II- 1-5

0

d0 „
V I nguyen tac, xac dinh dirge trj sd' Ecd va goc trugt 0 O tuang ung. T uy nhifin khdng
phai trudng hgp n£o cflng tim dugc nghiem dudi dang gi£i tich dan giSn.
3. C ac p h u rn ig p h a p tin h to a n £ p lire d a t ch u d d n g th e o h' th u y e t C u ld n g
B l g i£ i he p h u a n g trin h I I - i -5, h i|n nay cd ba phuang phap dugc su d u n g tOy theo
d ilu kiSn c u a bai to a n dat ra ( h in h dang lu n g t u d n g , hinh dang m at da't dStp v& tSi trQ ng
ngoai tac d u n g len khd'i d£t tr u g t v.v...).
P h u rn g p h d p gidn ti&p: dung cach thay ddi bie'n sd' (khdng diing tryc tilp bie'n sd
9 0 d l gidi) m a dung m dt d^i lugng dac trung khac, tu dd xac dinh d^ng gi&i tich tinh
trj sd' Ecd.
Phuomg phap nay chi gi&i dugc cho m dt vai trudng hgp d an gi&n: lire dinh b&ng
khdng, lung tu d n g ph&ng, m at da't ph&ng.
Phuong p h d p true tiip : giai true tie'p tu he phuang trinh I I - 1-5 bang cach liy dao
ham true tie'p dd'i vdi b ilu thuc tinh E, tir dd xac djnh dugc tri sd' 0 O thda m an phuang
trin h thu hai (p h u an g trinh I I - 1-4). Bie't tri sd 9 0 thay vao phuang trinh th u nh£t (phuang
trinh II-1-2) thi xac dinh dugc tri sd' Ecd = E max. P huang phdp n&y cd th i gi&i dugc
n h ilu bai toan phuc tap.
Phuong p h d p dd gidi: p huang ph4p n4y mS't n h ilu thdi gian nhung lai cd th i gi£i

d ugc rhtfng bai toan phuc tap ma p huang phap giai tich (hai phuang phap neu tren)
khdng th i giai dugc. V a do cflng la uu d ilm duy nha't cua phuang phap d 6 giai.
4 . Gia th i£ t v£ s u p h S n bd' d p lure da't ch u d o n g len lu n g tu d n g
Dd'i vdi bai toan ap luc dat, xac dinh dugc tri sd', phuang c h iiu cua ap luc da't la
chua du rna con can phai bie't quy luat phan bd' cua ap luc da't len lung tudng. T heo
thuye't C uldng vdi cac phuang phap vua neu d tren, ta chi m di xac dinh dugc tri sd' cua
ap lyc dat chu ddng theo p huang xac dinh nhd gdc ma sat ngoai cp0 cua d£t d£p.
Cdr. chu y r&ng, ngoai p huang trinh can b&ng £ U = 0, d ilu kien can bang cua khd'i
d at trugt r in tu y et ddi cdn phai la:
Z M b = Ecdr 0 - Rr + G x 0 f-G

DAI HOC QUOC GIA HA NOI_
TRUNG ’ AM THONG HN THLf VIEN

IH O iO , 0 0 0 3 3 5

II - 1-6

17


Trong do:
X M b- tdng m dm en cua cac luc la'y dd'i vai didm B;
r0, r, x0- cac canh tay don lay dd'i vdi didm B cua cac luc tu an g ung Ecd, R, G.
CAc luc dinh T, T 0 khdng gSy m dm en dd'i vdi didm B. T rong p huang trinh I I - 1-6,
cac tri sd' Ecd, R, G xem nhu da giai dugc, trj s6 x 0 cOng dugc xac dinh theo dang hinh
hoc cua khd'i da't trugt. N hu vay cdn lai hai an sd' r va r0 dd xac d in h diem dat cua Ecd
va R ma khdng thd xac dinh theo mM phucng trinh raom en dugc (p h u an g trinh I I - 1-6).
T u nhung didm n 6 u tren, tha'y rang phuang trinh m dm en I I - 1-6 chi cho ta lien he
gitfa cac canh tay don r 0 va r ch u khdng cho phep ta xac djnh d u g c chung, tuc cdng

khdng xac dinh du ac didm dat cua E cd va R.
Vi vay dd xac dinh vi tri diem dat cua Ecd cdn ph£i them gi£ thie't thu 5 nhu sau:
Khi tu&ng chdn cd c h iiu cao H bi
x i dich (hinh I I - 3) thi dp luc dd't tdc
dung lin ph dn trin trong p ham vi z,khdng p h u thudc vao su x i dich cua h
p h d n du&i.
T rong trudng hgp tdng quat, m dt
d d t khdng ph d n g thi du&ng p h d n bo'
dp luc dd't cd dang p h i tuyi'n (hinh

Hinh 11-3

II-3b) va xac dinh dugc g&n dung
theo tri sd' ap luc trung binh tung doan nhd Ar (hinh II-3a).
AEcd
Pcd —

I I -1-7

Ar

Trong do:
Ar =

Az
c o sa

(Az = z i+1 - Zj)

AEcd —Ecd(i+|) - Ecd(j)

Vdi Ecd(j+1)- tri sd' dp luc da't chu ddng xac dinh
vdi tudng co chidu cao la z i+]\ Ecd(i)- tri so ap luc
da't chu ddng cua tudng cao la z-v
T rudng hgp m at d d t phdng, du&ng phdn bo' dp
luc dd't cd dang tuyi'n tinh, cd tri so' lan nhd't &
chdn tu&ng.
Vi du bidu dd phan bd' ap luc chu ddng cua da't
rdi dugc xac dinh tu cdng thuc (hinh II-4):

18

Hinh II-4


pcd = y.z.K a (K a = const)
tai z =

0

tai z = H

Pcd =

0

pcd = yH K a

Truang h a p m d t dd't gay (phdng cd bat mai, cd c a
bieu dd p h d n bd' dp luc
d dt co dang gay v a co th£ xac dinh theo m dt trong ba phuong phap sau day cho trudng

hop dat. rdi:
Phuang p h d p th u n h d t (h)nh 11-5)
Trong hinh II-5a, tri sd p 2 xac dinh theo tri sd ap lyc dat chu ddng E cd2 vdi tudng
cao la H va m at dat nghieng gdc [3:
2 E cd2

P2 =

II - 1 -9a

H

Tri sd p, xac dinh theo tri sd Ecdi vdi tudng cao la H + a va m at da't ngang:
2 Ecdi

Pi =

I I - 1-9b

H+a
O'.
M wW
APo
o

y

Pcd
\

:
===^ \ C
__Pa_ IB
Pz

b)

Pi

H inh 11-5
Theo p h u an g ph ap nay, trj so Ecd thuc te' t&c dung 16n tirdng dugc x&c dinh theo difin
tich b ilu dd phd'i hgp, tuc cd:
Ecd = dien tich (OABC)

II-l-1 0 a

Trong hinh II-5b, tri sd' p 3 xac dinh theo E cd3 tinh vdi tudng cao H va m at da't ngang:
2 E ct!3

P3 =

H

Tri sd p 2 xac din h theo E cd2 tinh vdi tudng cao H ’ va mat da't nghieng gdc (J:
2E cd2
P2

H’

Tri sd p! xdc din h theo Ecd| tinh vdi tudng cao H + a va m at da't ngang:

2 Ecdi

Pi =

H+a

19


Tri sd' Ecd trong trudng hgp nay bang:
Ecd = dien tich (OA BCD)

IM -lO b

Phuong p h d p thu hai (hinh II- 6 )
T rong hinh II- 6 , tri sd' p! xac djnh theo Ec<1| ung vdi tudng cao lk H + a v& m$t
da't ngang:
2 Ecd,

Pi =

H+a

D ilm C cua b ilu d 6 phd'i hgp O A BC dugc xac dinh bang tri sd' zg ung vdi chan
dudng song song vdi m at trugt ve tu d ilm gay cua m at d£t.
Trj sd zg (tuc vj tri d ilm C) xac dinh theo hai phuang phap neu tren khac nhau do
cach xac dinh khac nhau. P huang phap thu nha't thudng dung cho c£c p h u an g phap gi&i
gian tie'p (khdng xac dinh dugc gdc trugt 9). P huang phap thu hai th u d n g dung cho
p huang phap gi&i true tie'p (xac dinh dugc goc
trugt 9). P huang phdp thu hai nay dugc su dung

trong quy ph^m tam thdi thie't ke' tudng ch£n da't
cua ta (Q P-23-65). N hugc d ilm chung cua hai
phuang phap neu tren la dien tich b ilu dd phd'i
hgp (b ilu d 6 OA BC trong hinh II-5 va II- 6 )
khdng dung bang tri sd ap luc da't chu ddng xac
dinh tuang ung vdi m at da't dap thuc te' (cd gay
khuc) m a hien nay da cd p huang phap tinh chinh
x£c. D l kh£c phuc nhugc d ilm vua neu i y ma
khdng cd gi p h iln phuc them , cd t h i ung dung
Hinh 11-6
phuang phap thu ba neu sau day:
Phuong p h d p thu ba: ndi dung cua phuang phap nay khac vdi hai p h u an g phdp trudc
d chd xac dinh vi tri d ilm gay C, tuc xac dinh trj sd' pg trong hinh II-5 va II- 6 .B ilu
dd phan bd' ap luc da't dugc hoan toan xac djnh khi bie't trj sd' p] va pg. Trj sd' pi xac
dinh theo Ecd) ung vdi tudng cao H + a va m at da't n&m ngang:
2 E cdl

Pi

I I - 1 - 1 la

H+a

Trj sd' p g dugc xac djnh sao cho dien tich b ilu dd phoi hgp O A BC bang trj sd' E cd
ti'nh theo chi£u cao tudng thuc te' va vdi m at cat gay thuc te'. T a phai cd dang thuc:
dien tich (O A BCD ) = Ecd
hay

T u dd cd:

20

1

Pg =

Pg = E cdl

'Cd

I I -1 -llb


Tri so z g dirge xac dinh nhir sau:

a + Zg

pg

a -f H

^(Ecdi

Ecd)

2E.cdl

a+H ■p,
Ecd i

a + z.

hay

a+H

a

E cd

Ecdj

Cdn chu y rang ba phuang phap ve bieu d6 phan b d ap lire dat vua n6u tren day chi
dung dirge cho truang hap dat rai (c = 0). Ddi vdi truang hgp dat di'nh, khi co he thong
ke nut thang dung xua't hien trong khdi da't dap thi ca ba
phuang phap neu tr6n deu k h 6ng thich dung.
5. G oc lech c u a a p lire d a t th eo If thuye't
a p lu c d a t C u lo n g
Khi da't dap la loai da't rai (c = 0) thi gdc iech cua ap
luc d*t chu d&ng Ecd bang gdc ma sat ngoai (p0 (hinh
II-7a) va goc lech cua pcd cQng bang cp0.
Khi da't dap la loai dat dinh thi luc di'nh anh hudng
tdi gdc I6ch 5 cua ap luc da't toan phan Q (hinh II-7b).
Trong trudng hgp nay iung tudng chiu tac dung cua E cd
va luc dinh T 0. T dng ap luc da't Q (hgp luc cua EC(] va
T 0) nghieng mOt gdc 5 xac dinh theo cCng thuc:
T„
IgS = E^ sinEcd cos(p0
EC(J cos(p0

Do gia thie't lire dinh phan b d deu tren mat trugt (lung tudng) nen gdc l$ch 8 cOng
thay ddi theo chieu cao:
_
pcd sin(p0 + c0
tgS (z) = — ry— £ = tg(Po +
Pcd COS(Po

c„

I I- 1- 12b

Pcd COS(Po

Theo I I - 1-12b thay ro rang khi z thay ddi, tri sd pC(j(z) thay ddi nen 6 (z) cQng thay
ddi tu tri sd ldn nha't xap xi 90° (d didm cd tri sd z ra't nhd) de'n tri sd nhd nhat being
(p0 (d diem sau vo han).
De tranh moi didu phidn phuc khi tinh toan, trong thuc te, ddi vdi dat dinh, nen ve
rieng hai bieu dd phan b d cua Ecd va T 0 (phan b d c hu nhat, theo gia thie't) hoac chi xet
de'n goc lech cua tdng ap luc da't Q (c6ng thuc I I - 1-12a) khi can thie't ma th6i.
II. ANH HUONG GOC NGHIENG j3 CUA MAT DAT DAP DOI VOI AP LUC CHU D 0 N G
VA GOC NGHIENG GIOI HAN pgh CUA KHOI DAT DINH DAP SAU TUONG CHAN
THEO THUYET CULONG
o

1. A n h h iro n g c u a gdc p dd'i v d i tr i sd' a p lu c da't chii d o n g
Ap luc chu dOng cua da't phu thuOc nhieu ye'u td, trong dd gdc nghieng p cd mot y
nghia dSc biet khi nghien cuu ap luc chu dong cua da't dinh theo thuye't Culdng.

21

Ddi vdfi daf ddp sau tuang chan, thudc loai ddt rai (c 0 = c = 0) thi tri s6 giai han
cua P 1 d goc ma sat trong Pgh = 9

n -2 - 1

Khi P > cp thi bai toan khdng gidi dugc va bdi toan khdng co y nghia thuc te' nfta.
Dieu ddc biet chu y la khi p = pgh = cp bai toan ap luc dat rai van co lcri giai va cdng
thuc tinh ap luc dd't chu ddng tuang ung nhu sau [3]:
Ecd = l/2.y.H 2 .Kcd vdfi Ked = — ^os .(9
cos a cos (cp0 + a )

n . 2-2

Tily theo tri sd' a , he sd' ap luc chu ddng cua dat ra i tinh theo cdng thuc II-2-2 cd
th£ lcyn han 1 rat nhi£u.
Ddi vdi d dt dinh ddp sau tudng chdn thi trudng hgp goc P > cp la rdt thudng gdp ma
den nay van d 6 nay vdn chua dugc nghien cuu day du. T heo quy pham tam thdi thie't
ke tudng chdn dd't cua ta (Q P-23-65) va theo quy pham Lien Xd (cO) vd tudng chdn dat
(C H n n -1 0 -6 5 ) cung nhu tieu chuan thiet ke' tudng chdn cua cac cdng trinh thuy cdng
cua ta (TCXD 57-73) khi gdp trudng hgp P > cp phai giai gan dung bdng cach thay phan
mai dd'c cua dat ddp bdng tai trong phan b d deu. Cdch giai gdn dung ndy cGng cdn phidi
bdn them vi nd ddn tdi ke't qua khdng hgp H do strtd n tai cua goc nghieng gidfi han pgh
cua khd'i dd't di'nh ddp sau tudng [ 1 2 ].
Khi gdc p tdng len, gdc trugt 9 cung tdng len vd do dd trj sd' E cd cung tdng len. N hu
tren dd neu, dd'i vdi dd't rdi khi p tdng len vd cd gidi han tren la gdc m ai tu nhien (bdng
gdc cp) thi Ecd tdng len va cd tri sd ldn nhdt (cac di 6 u kien khac nhu nhau) khi p = p gh
= cp. Tri sd ldn nhd't d'y dugc xac dinh theo cdng thuc 11-2-2 ta cd:

Ecd(P = Pgh) = A (c 0 = c = 0 )

H-2-3

vdi A Id trj sd gidi ndi.
D i 6 u nay du gc m inh hoa d bdng sau:
(dO)
•P

(dO)
a
(dO)

i
20

25

30

35

40

20

25

30

35

40

25

CPo

2/3.cp

(dO)
Kcd
( P * 0)

Kcd
P= o

22

1,55

1,65

1,72

1,80

1,85

0,67

0,60

0,55

0,52

0,45


D oi vdi dat dinh, cac quy luat n£u tren van dung nhimg do gdc P cua khdi dat dinh
cd the" ldn hem gdc ma sat trong cp cua dat dinh rat n h ilu lan nen khi m d rdng li thuye't
C uldng cho dat dinh can thie't lam sang to may van de cd lien quan den gdc p nhu sau:
1. Ddi vdi khd'i da't dinh dap sau tudng chan co ton tai m dt gdc Pgh khdng va ne'u
cd thi tri sd cua no bang bao nhieu?
2. Trj sd' EC(J bang bao nhieu khi gdc P ldn bang trj sd Pgh.
De lam sang rS nhirng d ilu neu tren, ta xet ke't qua tinh loan cho mdt trudng hop
khdng cd gi dac biet sau day:
K ich thirdc tudng cho tren hinh II - 8 va cac sd lieu khac cho nhu sau:
cp = 20°, cp0 = 2/3cp = 15°
c = 2T /m 2, c 0 = l/2 c = IT /m 2, y = 2T/m 3
D /l
T heo tinh than cac quy pham hien dung, trudc he't
2,85 m
gi& thie't p = 0 (m at da't dap sau tudng nam ngang) va
tinh dugc goc trugt 0 tuang ung bang 35°. Trong
lugng khd'i da't ADC nam phia tren m at Ax dugc xem
nhu phan b d deu theo dang bac cap tren m at ngang
tgcp= 0,364

Ax rdi tu dd xac dinh dugc tri sd' ap luc da't chu ddng
tgp = 0,550
Ecd = 46T /m . T heo cach giai dung (cd th i dung
phuong phap giai tich) trong trudng hop nay ta cd
tgG = 1,87, G = a rctg l,8 7 = 6 1 ° 5 0 \ Tich sd'tgp.tgB =
Hinh II-8
0,53.1,87 « 1, nghia la m dt trugt B C song song voi
m dt dd't ddp A D , khdi da't trugt ldn vd cung. Dieu dd
chung td r&ng trong trudng hgp nay trj so P = arctg(5,3) = 29° la trj sd' gidi han cua
gdc nghieng cua m at da't dap sau tudng chan (quy udc goi la gdc nghieng gidi han Pgh).
Bai toan ap luc dat chi co ldi giai khi P < Pgh. DO'i vdi da't rdi, nhu trfin da n£u, Pgh = cp;
ddi vdi da't di'nh Pgh cd th i ldn han cp kha n h ilu .

T u vi du tren va tCr nhtfng cdng thuc tinh G va E [13]
G =

AptgG + B 0
1 - tgp tgG

E =

II-2-3

•y

K 0 + KjtgG + k2tg G
(1 - tgP tgG)(A tgG + B)

II-2-4

Y

cdng tha'y rang khi gdc p cd tri so gidi han P,,h thi cd dang thuc:
1

- tgPghtgG = 0

hay

tg p gh = 1/tgG = tgG0, (tuc p gh =

hay

Pgh = 90° -

0,

II-2-5a

6 ^0 /

II-2-5b

23