Áp lực đất và tường chắn đất

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 qu

LOI NOI DAU

Tinh to d n dp luc dd't vd tuang chan dd't Id m ot trong nhung van de ldn cua dia

2 Ung dung li thuyet phdn m dnh (thoi) vd van dung ph ep phdn tich he thd'ng d $ giam bdc sieu tinh cua bai todn dang ndng cao hieu qua p h ep tinh tren m dy tinh dien tii.

3 H oan chinh li thuye't dp luc dd't Coulom b 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 d t 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 Coulom b m dc du khdi diem xud't la xa xua n h d t (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 n a y gidi thieu loi gidi chinh xdc theo li thuyi't Coulom b ve ap luc dd't chu ddng vdi ca c s a dd tudng chdn dd't, m dt dd't ddp vd cac dang tdi trgng, thudng gdp trong thuc te xd y dung ddn d u n g , giao thdng vd thuy Igi, Ldi gidi nay ddp ung td't hai yeu cdu cdn thie't: m dt Id x et dugc dp luc nude Id rdng dm trong khd'i dd't ddp khdng bao hoa nude; x et dugc tdc dung cua cd't dd't trong khd'i d d t ddp H ai la ldp trinh tinh todn d i ddng vi vdi m dt thudt todn duy n hdt 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

p hd p 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 u dng ch£n Sa cong trinh g ia cho m ai dat ds'p hoftc m ai hd' dko khoi bi sat truat

T udng ch k n dat d u ac 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 cu a k i t cku cdng trinh khdng phai lk tu d n g chan dkt nhung cd tac dung tu an g 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 d u ac m d rQng ra cho tk't ca nhtfng bd phan cu a cdng trinh cd tac dung tu an g hd g iaa 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 ia a nhOng bQ phan a'y vdi da't

T u d n g ch an dat trong cac cdng trinh thuy cdng lam viec trong nhOng d ilu ki£n r i t khac so v d i d ilu kien lam viec cua tudng chkn dk't trong giao thdng vk xay dung do dkc d ilm c u 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

cu a 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 h an so vdi trudng h g p ddng d i t lo^ii ckt dkp sau tudng chan

I PH An l o a i t uOn g CHAN DAT

T u d n g chkn dk't thudng d u g c phan loai theo bd'n ckch sau day nhkm muc dich khac nhau:

1 P h a n lo a i th e o d d c u n g

B iln d an g cua bkn than tu d n g chkn dk't (dd ud'n) 1km thay ddi

d ilu kien tie'p xuc g iaa lung tudng chkn vdi khdi dk't dkp sau

tu d n g , do do lam thay ddi tri sd' ap luc dk't tac dung len lung

tu d n g va c a n g 1km thay doi dang b ilu d6 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 i ln dang do chju ap luc dkt thi b ilu dd phan bd' ap luc

dk't cd d an g d udng cong (hinh I -1), n lu phan g iaa thkn tudng bj

bie'n dang n h ilu thi bieu do phan bd' ap luc dk't ckng cong va

c u 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 c u an g d6 ap lire ban dau, con c u a n g dQ ap luc d

phan dudi tu an g thi lai giam (d u an g 3)

Theo cach phan loai nay, tu an g du ac phan lam hai loai: tu an g cu n g va tuang m£m

T u an g co bidn dang udn khi chiu ap luc da't nhu neu tren day goi la tudng mem hoac tudng m dng T u an g m dm thudng la nhung ta'm g6, thep, be tOng cd t thep ghep lai

T u an g c u cung xep vao loai tu an g 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 tu an g cung xoay quanh mep dudi, nghla la dinh tu d n g co xu nudng tach rdi khdi khd'i dat dap va chuydn vi vd phia trudc thi nhidu thi n g h iem da chung td

la bidu d6 phan bd ap luc cu a 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 cu a B.L T araxdp 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 tr6n, 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 d6 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 c u a tudng va & vho

khoang phan giua lung tudng (hinh I-2c)

T udng cung thudng la nhdrng khd'i be tdng,

be tdng da hQc, gach da xay nen con goi

la tudng khdi T u dng chan bang be tdng

cd't thep co dang ta'm hoac ban nhung tao

vdi cac bd phan khac cu a cdng trinh thanh

nhttng khung hoac hdp cung cung duac

xe'p vao loai tudng cung

N h u trSn da phan tich, cdch ti'nh toan tri

sd' ap luc dat len tudng cung va tudng mdm

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 c h u n g cua tudng T heo 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 C ac loai tudng cung deu thuQc loai tudng trong luc

Tu&ng nua trong luc (hinh I-3b): dd dn djnh dugc d im b ao 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 L oai tu d n g nay thudng lam be tdng cd't thep nhung chidu day cu a tu d n g tving kha ldn (do dd loai tudng nay cdn cd ten goi l i tudng day).

Tuong bdn g o c (hinh l-3c): d0 6’n dinh dirge dam bao chu ye'u do trong lugng khdi dat d ip de len ban m ong T u ong va m ong la nhtfng ban, tam be tdng cd't thep m ong nen trong lugng cu a ban than tuong va m ong khong ldn T udng ban goc cd dang chtf

L nfin cd khi cdn g o i la tudng ch u L

Tucrng m ong (h in h I-3d): sir dn dinh cua loai tudng nay dugc dam bao bang cach

chdn chan tudng v ao 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 cu a tudng ngudi

ta thudng dung day neo

Hinh 1-3

3 P h a n lo ai th e o c h ie u cao

Chidu cao cu a tu d n g thay doi trong m dt pham vi kha ldn tuy theo yeu cdu thie't ke

H ien nay, chidu cao tudng chdn da dat de'n 40m (tudng chdn d nha m ay T huy dien

L6nin tren sdng V onga) Trj sd' dp lyc da't tac dung len lung tudng chdn ti le bac hai vdi chidu cao cu a 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 tu d n g cndn co chidu cao vao khoang trung gian cua hai loai trdn (tuc cao ti* 10 de'n 2 0m) dugc xe'p vao loai tuang trung binh.

T heo quy p h am tam thdi thie't ke' tudng chdn da't Q P-23-65 cu?\ ta thi la'y gidi han

phan ch ia ba loai tu d n g tha'p, cao, trung binh la 5 va 10m: tudng chdn tha'p cd chidu cao nhd hon 5m , tu d n g 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

T heo 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 tu an g doc nghich (hinh I-4b)

T rong tru d n g h g p cu a tu d n g dd'c khdi d at tru g t cd m dt m at gidi han trung vdi lung tudng

Ne'u gdc n g h ien g a cu a lung tudng ldn qua m dt m uc do nao dd thi khd'i ddt trugt sau lung tirdng k hdng lan de'n lung tu d n g (hinh I-4c); tudng loai nay dugc goi la

tudng thodi.

1

Nguyfin t i c 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 i t chu dQng len tudng th o ii dugc trinh bdy trong m yc 2 ch u an g VIII

Hinh 1-4

5 P h i n lo ai th e o k e t c a u

V6 m at ke't c iu , tu d n g c h in dugc chia thdnh tudng lien khQi v i tu d n g l ip ghep

Tudng liin khdi lim bang be tdng, be t&ng d i hQc, gach xay, d i xdy hay bang be

t6ng cd't thep T u dng lidn khdi dugc xay (gach d i ) hoac dd (be tOng, be tOng d i hQc,

be tOng cdt th6p) true tie'p trong h d m ong H d mQng p h ii rQng h an m dng tu d n g c h in

mQt k h o in g d£ ti^n thi c&ng vd dat v in khuOn MQng cu a tudng be tfing v i be tdng cdt

thep liSn khdi vdi b in than tudng, cQn mQng cua tu d n g c h in b&ng g ach d i xay thi cd th£ l i nhtfng ke't c iu d&c lap b d n g d a xay hay be t&ng M $t c i t ngang cu a tu d n g lidn khdi l i t k h ie nhau MQt s&' dang tu d n g loai n iy dugc trinh b iy tren hin h 1-5 vdi nh&ng ten goi n h u sau: a) H inh ch& nhat, b) Hinh thang c6 nguc tu d n g n g h ien g , c) H inh thang

cd lung tudng nghieng, d) H inh thang cQ nguc vd lung nghieng, e) H inh thang n g h ien g

v6 phia d it d ip , g) CQ m ong nhd ra p hia trudc, h) Cd lung gay khuc, i) C d lu n g bac

c ip , k) CQ be g iim t i i , 1) Co m ong nh& ra hai phia

T udng ban gQc (hay tudng cho- L) ki£u cOngxon (hinh I-6a) ho$c ki£u cQ bSn sudn (hinh I-6b) cQng th u d n g lim b in g be tdng cd't th6p dd liSn khdi

* &

V7m7ZZZZZ!

llin h 1-6

Tuang ldp ghep gdm cac ca'u kien bang be

tdng cot thep due sSn lap ghep lai v ai nhau theo

nhtfng sa do ke't ca'u dinh sSn Ca'u kien due sSn

th u an g la n h u n g thanh hoac nhung tam khong

la n (th u an g d u a i 3m) && tien van chuy^n.

Tuy theo s a d6 ke't ca'u ldp ghep, tu an g lap

ghep th u a n g co may kieu sau day: k ii’u chic L

gdm nhung khdi va tam be tong cdt thep lap rap

lai (hinh I-7a), k ii’u hdng rao gdm nhidu thanh

be tOng cd t th ep larn tru dung hay tru chdng va

cac ban ghep lai (hinh l-7b ), k ii’u hdp m6t tdng hay hai tang, trong h5p dd day cat soi

(hinh I-7c), k i i ’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 ch6 trong h d m ong H d m ong khdng c^n dao rong m a 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 cu a dat ndn va da't dap khdng xam nhap vao d a hdc trong ro, thuang d£ mOt ldp vai dia ki thuat ngan cach day tu an g va lung tu an g vdi da't n6n va da't ddp

Uu di^m ndi bat cu a tu an g ro la chju lun cua n6n ra't tdt va ki thuat lam tu an g d an giSn H ien nay cac nha khoa hoc dang nghien cuu bien phap cdng n h u vat lieu de tang tudi tho cu a rg

Tudng dd't cd cd't: la dang tudng hien dai cua cac bao tdi da't chat ddng thd s a cua

nhan dan (hinh I-7f) T u an g 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 m a sat gitfa da't va cdt neo m at bi lai T u dng 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 d at cdt, cach ti'nh toan dugc trinh bay trong cac sach chuyen d6 v6 da't

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 d at 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 th o at 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 k h u 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 m ua 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 a t nude N di chung, thie't bi thoat nude gdm bd'n bQ phan: bd phan th u nha't - th o at nude m at; b0

phan th u hai - gi&m nhd lugng nude ng£m vao khd'i d£t ddp; b0 phan th u b a - th o at nude trong khd'i d£t dap; bd phan th u tu - thoat nude ra ngoai p ham vi tu d n g chdn.TQy theo tinh cha't cu a da't dap rdi hay dinh va didu ki$n cu thd cu a tu d n g chdn, cd thd su dung cac loai thie't bi th o at nude trinh bay tren hinh 1 - 8 vdi cac d ac didm n h u sau: a) C hi cd 16 th o at nude, b) L6 th o at 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) T dng th o at nude nghieng (theo h u d n g

III Dl£U KI$N SU DUNG CAC LOAI TUOfNG CHAN

Hien nay tu d n g c h in co nhidu loai hinh khac nhau; m6i 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 kin h n g h iem da due ke't duac

So vdi cac loa> tu an g thi loai tu an g 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 c d ‘ thep nhieu h a n mdt khd'i lirang khdng dang k i Uu diem ndi bat cu a loai tudng

bang be tdng cdt thep la cd the’ su dung p h u an g phap thi cdng l ip ghep va yeu c iu v£

n6n khdng cao nen it khi phai xu li n£n

Ne'u k hdng cao qua 6m, loai tudng ban gdc (kieu cdngxon) bang be tdng cd't thep cd khdi lu an g it h an tu d n g cd ban sudn Ne'u cao tir 6 den 8m thi khd'i lu an g cu a hai loai tudng nay xa'p xi nhau Ne'u cao han 8m thi tudng cd ban sudn cd khd'i lu an g be tdng cd't thep nho h an tu d n g 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 u dng c h in da't bang be tdng chi nen dung khi cd't thep qua d i t hoac khan hie'm, bdi

vi be tdng cu a cac tu d n g c h in trong luc chi p h it huy m0t phan nhd kha nang chiu lyc

m a 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 ch d n g D u n g loai tudng co be giam tai dat d k h o in g 1/4 chiSu cao tudng, tudng cd lung nghieng v6 phia dat dap cQng tie't kiem d u ac be tdng

T udng c h in b an g da xay c in ft xi m ang h an tudng be tdng, cd th i h o in th in h trong thdi gian tu a n g dd'i n g in va td’ chuc thi cdng d an gian N ai s in da, dung tu d n g d i xSy thirdng co hi$i» q u a kinh IS' cao Ddi vdi tudng c h in cu a cQng trinh thuy cQng diing d i x&y cd sd' hieu tu 200 trd len, vtfa xi m ang p u d alan cd sd' hieu tir 50 trd len Lung tudng

d a xay th u d n g lam th in g dung hoac nhi6u bac c ip

T ru d n g h o p 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 u dng g^ich xay chCr n h at hoac lung bac cap thudng dugc dung cho nhung cdng trinh nhd dudi d it DQ'i vdi cac lo ai tu d n g c h in Id thien chju tac dung true lie'p cu a mua n in g v i cac tudng

c h in cua cac cdng trinh thuy cdng khdng nen dung gach xay G ach xay tirdng c h in cd sd' hieu k h dng nen nhd h an 200 va vtfa xay tir 25 trd len, khdng d u g c ddng lo a : gach silicat

T u d n g 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 Ap LUC DAT LfiN TUONG ChAn

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 d0 cung (bie'n dang) cua tirdng, cd thd phan cac thuye't hien nay thanh hai loai: loai khdng xet de'n d0 cung cu a tirdng v& lo ai co x6t de'n dd cung cua tudng

Loai khdng xet de'n dd cung (bie'n dang) cua tudng gia thie't tu d n g tu y et 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 c an b a n g g id i 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 tru g t sau tu d n g ch an , gidi han bdi

m at tru g t co hinh dang dinh trudc, n h u m dt khdi xin d trang thai c an bang gidi han

Tuy theo hinh dang m at trugt gia thie't, nhdm nay hien nay phat tridn th eo hai xu hudng:

Xu hudng gid thii't m d t truat p h d ng : dai dien cho xu hudng n ay cd thuye't C.A

C uldng (1773) va sau do dugc I.V P d n g x ale, K C unm an, G R ep h an , F E ngetxe, B.A

U retxki, G.A D ubrdva, I.P P rd k d fie p v.v phat tridn them

Xu huang gid thii't m d t 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 h6n hgp p h d n g va cong T heo

xu hudng nay cd W Feie.niut, L R andulic, J Ode, H Kray v.v

2 N h d m th e o th u y e t cSn b a n g g id i h a n p h a n td' (d iem )

N hdm nay chu tru an g tinh cac tri sd' ap luc da't (ap luc deft chu d d n g va ap luc ddt

bi ddng) vdi gi& thie't cdc didm cu a m di trudng da't d ip dat trang thdi c§n bang g id i han cung m dt luc, li thuye't nay da dugc G iao su ngudi A nh ten la W J.M R angkin dd ra nam 1857 va ve sau dugc goi la thuye't R angkin Thuye't R angkin d u g c J C d n g x id era,

J B utxinet, J R ezan, A C aco v.v phat tridn them De'n nay, li thuye't can b an g gidi han phan td dugc phat tridn m anh me theo hai xu hudng:

X u 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 V ien si Lien X d V.V X dkdldpxki Ldi g iai cua R angkin, de'n nay, chi dugc xem nhu m dt trudng hgp dac biet cu a ldi giai cu a X dkd ld p x k i H u d n g nghien cuu cua V.V X dkdldpxki dugc tie'p tuc nghien cuu d B a L an , Phap va n i0t sd' nude khac

X u huang dd gidi: khac vdi V.V X dkdldpxki giai he p huang trin h vi phan can b a n g

gidi han bang toan giai tich, G iao su Lien Xd X.X G olutkevit da th a n h cdng tro n g viec giai cac bai toan ve li thuydt can b in g gidi han theo p h u an g phap d6 giai b in g he v o n g trdn dac trung

Den nay, li thuye't tinh ap lire da't len tudng m6m 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 p h at tri£n theo hai hudng nhu sau:

Xu h udng 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 t i 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 p h u an g phap theo xu hudng nay Khdng nhung cho phep xac dinh ap luc da't len tu d n g m6m (tuc phan luc nen) m a cdn xac dinh dugc c l c h u y ln vi cua tudng m em

Ngoai ra cdn c l n phai neu them loai li thuye't tinh ap lire dat len tudng cung va cd xet de'n chuye’n vi cu a tudng cung T udng cung khdng bj bie'n dang khi chiu tac dung

cu a ap luc da't n h u n g tuy tru d n g hgp, tudng cd chuye’n vj tjnh tie'n hoac quay C h u y ln

vi cua tu d n g c u n g k hdng nhung lam thay d6i dang bie’u dd phan bd' ap luc da't len lung tirdng ma cdn l l m thay d6i trj sd' ap luc da't T heo quan di£m n ly I p luc dat dugc phan

ra loai ap luc da't u n g vdi trang thai can b ln g gidi han va ap luc da't ung vdi trang thai chua can b ln g g id i 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 u l6ng(*) 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 k h ac p h at triln them Thuye't CulOng d an 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 d6ng 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 cu a dat d i p lkm giam tri s0' ap lye da't chu dQng va lam tang tri sO' dp lyc

bi dQng cu a da't T ru d c day, anh hudng cu a luc dinh k h6ng dugc x e t de'n khi tinh toan

ap luc d at len tudng c h in do mQt sQ n g u ai cho r in g dQ'i vdi da't d i p loai da't cat thi luc dinh k h6ng dang k l so vdi lyc m a sat trong, cdn dd'i vdi d at d ip thuQc lo ai 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 cu a 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 n h a bac hoc tren the' gidi nghien cuu va d l ra cac p h u an g phap tinh toan ap lyc dat len tu d n g c h in , c d xet de'n luc dinh cCia d at d ip theo n h ilu each khac nhau

I CAC GIA THlfiT VA NHUNG LlfcN H $ CO BAN

1 C a c g ia th i£ t c a b a n va so* d o lire

Thuye't ap luc da't CulOng d u a tren m iy g i i thie't c a ban n h u sau:

1 T rang thai gidi han cua tudng c h in cung

va khQi da't d i p sau tu d n g dugc xac dinh b in g

su c h u y ln dich (tru g t hoac lat) cu a tudng du gay

cho mQt khQi da't sau lung tudng cQ xu the' tach

ra va tru g t theo mQt m d t trugt p h d n g nao do.

Mat lung tu d n g cQng la mQt mat tru g t (quy udc

gpi ia m at tru g t thu hai)

2 Khoi dat tru g t xem nhu mQt khd'i rdn tuyet

dd'i dugc gidi han bang hai m at trugt: m at trugt

phat sinh trong khQi d at d ip va m at lung tudng

(*) C.A Culdng la mdt si quan cdng binh nguai Phap.

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 b an g nhtfng hgp lire cua chung va ung dung true tie'p cac ke't qud cu a mdn c a hpc vSt r^n.

3 T ri sd' ap luc da't chu ddng len tu an g chdn dugc xac dinh tu an g ung v di 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 tru g t (tri sd' ap luc da't bj ddng dugc xac dinh tu an g ung vdi luc chdng c u a khd'i da't trugt "ran tuyet dd'i" len luang )

Gid thie't nay ch o phep ta Chira uhan:

a) C ac phan luc cu a tu d n g va cu a da't (phdn nguyen) len khd'i da't tru g t "tuyet dd'i

rdn" lech vdi p h u a n g phap tuye'n cu a 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 m a sat tiong (p (gitfa ddt nguyen vdi khd'i

da't trugt)

b) D a giac luc k h e p kin

N guyen trudc d ay , C uldng khdng xet de'n luc dinh cCa dat ddp va n h u vay trong s a

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 s u dung trong cac quy pham hien dting trong nude va ngoai nude

Do dd, dd m d rd n g p ham vi su dyng li thuye't C uldng cho ddt dinh, hi£n nay phdi

them gid t h i f t th u 4 v i luc dinh cu a ddt.

4 L uc dinh cua da't ddp dugc xem n h u tac dung theo p h uang cd a m at tru g t v k phan

bd' ddu tren m ^t tru g t

N h u vay, dnh h u d n g cu a tinh dinh cu a dat dugc xet de'n qua hai luc tac dung len hai

m at tru g t, tren m at tru g t th u nhdt, lire dinh dugc xac dinh theo cdng thuc (xet bdi toan phdng):

2 N g u y en h' ti'nh to a n

TCr so d6 lire I I - 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 tu an g vdi m at th&ng dung;

0O- 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 p huang trinh can bang:

XU = - G sin (0 o - q>) + E sin (y + 0 O - cp) = 0

TO1 do, co c6ng thuc tinh lire d iy cu a da't rai len tudng:

sin(ip + 0O - cp)

(Luc d^y cu a da't len lung tu an g dugc suy ra tir phan luc E trong so dd luc).

T u s a d6 luc II-2 (da't di'nh), cflng lam nhu tren ta co:

Z U = - G sin (0 o - cp) + E sin (y + 0 O - cp) + T osin (0 o - 9 - a ) + Tcoscp = 0

T u do, co c6ng thuc ti'nh lire d^y cu a da't di'nh len tudng:

^ G sin(0o - cp) - Tcoscp - T osin(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 sin y + T cos(0o + y ) - T0sin (y + a ) tt i ^

K = - 11-1 - j

sin(y + 0O - cp)Khi cho c = c0 = 0 thi c6ng thuc I I - 1 -2b tra lai c&ng thuc I I - 1 -2a D o do, tu day vd sau dung bidu thuc II-l-2 b dd xet cho dugc tdng quat

T rong p h u an g trinh I I - 1 -2b cac iln s6 la E va gdc 0 O C ac dai lu g n g G , T dugc bidu

thi qua goc 0 O> tri sd T0 xem nhu mOt dai lugng d a bie't N h u vay ta m di co mQt p h uang trinh ch u a hai ^n sd E va 0 o

Do do, dd co thd giai dugc bai toan ap luc da't, CulOng da dung n guyen U cu c tri dd

dua them vao mQt p h u an g trinh ntfa N guyen li cuc tri m a C ulong dd nghi cd thd hidu theo djnh li cu a A A G avSzdep n h u sau: "D ang pha hoai thuc cu a he th d n g tu d n g - d£t dap ung vdi trj sd nhd nha't cu a tai trong phu pha hoai" Tren c a sd do can chon goc nghieng cu a m at tru g t n h u the' nao cho luc day cu a da't dap len tirdng (ti'nh ap luc da't chu dong) la ldn nha't hoac luc chong cu a da't dap len lung tu d n g la nhd nha't (tinh ap luc dat bj dQng) N h u vay chi c&n phu them mQt luc kha nho la tu d n g dat tran g thai gidi han vd 6n dinh (tru g t hoac lat) L u c tidy ldn n h d t cua d d t ddp l in tu a n g d u a c quy udc g oi la dp luc d d t chu ddng ciia d d t (E cd) L u c chd'ng nho n h d t ciia d d t d d p lin tudng aucrc q u y udc goi Id dp luc dd't bi ddng cua d d t (E bd).

P huong trinh th d hai cu a bai toan do C uldng d l ra 14:

dE

d0

T ir h$ p h u a n g trinh c a ban cu a li th u y lt CulOng:

Gsin(90 - cp) - Tcoscp - T0sin(90 - cp - a )

B l g i£ i he p h u a n g tr in h I I -i-5, h i |n nay cd ba p h u an g phap d u g c s u d u n g tOy theo

d ilu k iS n 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

n goai tac d u n g len khd'i d£t t r u g t v.v )

P h u rn g p h d p g id n ti&p: dung cach thay ddi bie'n sd' (khdng diing tryc t il p bie'n sd

90 d l gidi) m a d u n g m dt d^i lu g n g dac trung khac, tu dd xac dinh d^ng gi&i tich tinh trj sd' Ecd

Phuomg phap nay chi gi&i d u g c ch o m dt vai trudng hgp d a n gi&n: lire dinh b&ng

k h d n g , lung tu d n g ph&ng, m at da't ph&ng

P huong p h d p tru e tiip : giai true tie'p tu he phuang trinh I I - 1-5 b an g cach liy dao

ham true tie'p dd'i vdi b ilu thuc tinh E, tir dd xac djnh dugc tri sd' 0 O th d a m an p huang trin h thu hai (p h u an g trinh I I - 1-4) Bie't tri s d 90 thay vao p h u an g trinh th u nh£t (phuang trinh II-1-2) thi xac dinh dugc tri sd' Ecd = E max P h u an g phdp n&y cd t h i gi&i dugc

n h ilu bai toan p h u c tap

P huong p h d p d d gidi: p h u an g ph4p n4y mS't n h ilu thdi gian nhung lai cd t h i gi£i

d u g c rhtfng bai to an phuc tap m a p h u an g phap giai tich (hai p h u an g phap neu tren)

k h d n g th i giai d u g c V a do cflng la uu d ilm duy nha't cu a p h u an g phap d6 giai

4 G ia th i£ t v£ s u p h S n bd' d p lure da't c h u d o n g len lu n g tu d n g

Dd'i v di bai toan ap luc d at, xac dinh dugc tri sd', p h u an g c h iiu cu a ap luc da't la

ch u a 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 v d i cac p h u an g phap v u a neu d tren, ta chi m di xac dinh d u g c tri sd' cu a

ap lyc d at chu d d n g theo p h u an g xac dinh n h d gdc m a sat ngoai cp0 cu a d£t d£p

Cdr chu y r&ng, ngoai p h u an g 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 = Ecdr0 - R r + G x0 f-G

DAI HOC QUOC GIA HA NOI_

TRUNG ’ AM THONG HN THLf VIEN

I H O i O , 0 0 0 3 3 5

I I - 1-6

17

T rong do:

X M b - tdng m dm en cu a cac luc la'y dd'i v ai didm B;

r0, r, x0- cac canh tay don lay dd'i vdi didm B cu a cac luc tu a n g ung E cd, R, G

CAc luc dinh T, T0 khdng gSy m dm en dd'i vdi didm B T rong p h u an g trinh I I - 1-6,

cac tri sd' E cd, R, G xem n h u da giai dugc, trj s6 x0 cOng dugc xac din h theo dang hinh hoc cua khd'i da't trugt N h u vay cdn lai hai an sd' r va r0 dd xac d in h diem dat cua Ecd

va R m a khdng thd xac dinh theo mM p h u cn g trinh raom en dugc (p h u an g trinh I I - 1-6)

T u nhung didm n6u tren, tha'y rang p h u an g trinh m dm en I I - 1-6 chi cho ta lien he gitfa cac canh tay don r0 va r c h u khdng cho phep ta xac djnh d u g c chung, tuc cdng khdng xac dinh d u a c didm dat cu a E cd va R

Vi vay dd xac dinh vi tri diem dat cu a E cd 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 p h d n tr in trong p h a m vi z,-

khdng p h u thudc vao s u x i dich cua h

p h d n du&i.

T rong trudng hgp td n g quat, m d t

d d t khdng p h d n g thi du&ng p h d n bo'

dp luc dd't cd dang p h i tuyi'n (hinh

II-3b) va xac dinh dugc g&n dung

theo tri sd' ap luc trung b inh tung doan nhd Ar (hinh II-3a)

V di E cd(j+1)- tri sd' dp luc da't chu ddng xac dinh

vdi tudng co chidu cao la z i+]\ E cd(i)- tri so ap luc

da't chu ddng cu a tu d n g cao la z-v

T rudng hgp m a t d d t phdng, du&ng phdn bo' dp

luc dd't cd d a n g tuyi'n tinh, cd tri so' lan nhd't &

chdn tu&ng.

Vi du bidu dd phan bd' ap luc chu ddng cu a da't

rdi dugc xac dinh tu cdng thuc (hinh II-4):

I I -1-7

Hinh II-4

p cd = y.z.K a (K a = const) tai z = 0 Pcd = 0

tai z = H pcd = yH K a

Truang h a p m d t dd't g a y (phdng cd b a t mai, cd c a bieu dd p h d n bd' dp luc

d d t co dang gay v a co th£ xac dinh theo m dt trong ba phuong phap sau day cho trudng

hop dat rdi:

Pz Pi

H inh 11-5

Theo p h u a n g p h a p nay, trj so Ecd thuc te' t&c dung 16n tirdng dugc x&c dinh theo difin tich b ilu dd phd'i h g p , tuc cd:

Trong hinh II-5 b , tri sd' p3 xac dinh theo Ecd3 tinh vdi tudng cao H va m at da't ngang:

2E

P3 = ct!3

HTri sd p2 xac d in h theo Ecd2 tinh vdi tudng cao H ’ va mat da't nghieng gdc (J:

2Ecd2

P2

H ’Tri sd p! xdc d in h th eo E cd| tinh vdi tu d n g cao H + a va m at da't ngang:

Pi =

2Ecdi

H + a

19

T ri sd' Ecd trong trudng hgp nay bang:

P huong p h d p th u hai (hinh II-6)

T rong hinh II-6, tri sd' p! xac djnh theo E c<1| ung vdi tudng cao lk H + a v& m$t

p h u an g phap gi&i true tie'p (xac dinh dugc goc

tru g t 9) P h u an g phdp th u hai nay dugc su dung

trong quy ph^m tam th d i thie't ke' tu d n g ch£n da't

cu a ta (Q P-23-65) N h u g c d ilm chung cu a hai

p h u an g phap neu tren la dien tich b ilu dd phd'i

h g p (b ilu d6 O A B C trong hinh II-5 va II-6)

khdng dung bang tri s d ap luc da't chu ddng xac

dinh tu an g ung vdi m at da't dap thuc te' (cd gay

khuc) m a hien nay d a cd p h u an g 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

p h u an g phap th u ba neu sau day:

P huong p h d p thu ba: ndi dung cu a p h u ang phap nay khac vdi hai p h u a n g phdp trudc

d chd xac dinh vi tri d ilm gay C, tuc xac dinh trj sd' pg trong hinh II-5 v a II-6 B ilu

dd phan bd' ap luc da't d u g c hoan toan xac djnh khi bie't trj sd' p] va p g T rj sd' pi xacdinh theo E cd) ung vdi tu d n g cao H + a va m at da't n&m ngang:

Tri so z g dirge xac dinh nhir sau:

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 o c lech c u a a p lire d a t th e o 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 E cd bang gdc ma sat ngoai (p0 (hinh

II-7a) va goc lech cua p cd 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 tru d n g hgp nay iung tudng chiu tac dung cua E cd

va luc dinh T 0 T d n g ap luc da't Q (hgp luc cua E C(] va

T 0) nghieng mOt gdc 5 xac dinh theo cCng thuc:

T„

IgS = E^ sin<p° + I g = tg<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:

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 E cd va T0 (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 t r 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 b iet khi nghien cuu ap luc chu dong cua da't dinh theo thuye't Culdng

21

D di vdfi daf ddp sau tu an g chan, thudc loai ddt rai (c0 = c = 0) thi tri s6 giai han

cua P 1 d goc m a sat trong <p; ta co:

Khi P > cp thi bai toan khdng gidi dugc va bdi toan khdng co y nghia thuc te' nfta

D ieu ddc b iet chu y la khi p = p gh = cp bai toan ap luc dat ra i van co lcri giai va cdng thuc tinh ap luc dd't chu ddng tu an g ung n h u sau [3]:

E cd = l/2 y H2.K cd vdfi Ked = — ^os (9 n 2 -2

cos a cos (cp0 + a )Tily theo tri sd' a , he sd' ap luc chu ddng cua dat ra i tinh theo cdng th u c II-2-2 cd th£ lcyn han 1 rat nhi£u

D di vdi d d t dinh ddp sau tu d n g chdn thi trudng hgp goc P > cp la rdt th u d n g gdp m a

den nay van d6 nay vdn chua dugc nghien cuu day du T heo quy ph am tam thdi thie't

ke tudng chdn dd't cu a ta (Q P-23-65) va theo quy pham L ien Xd (cO) vd tu d n g chdn dat (C H n n -1 0 -6 5 ) cung n h u tieu chuan thiet ke' tudng chdn cu a cac cdng trin h thuy cdng

cu a ta (TC X D 57-73) khi gdp trudng hgp P > cp phai giai gan dung bdng c ac h thay phan

m ai 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 s trtd n tai cu a goc nghieng gidfi han p gh

cu a khd'i dd't di'nh ddp sau tudng [1 2]

Khi gdc p tdng len, gdc tru g t 9 cung tdng len vd do dd trj sd' E cd cung tdng len N h u 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 di6u kien khac n h u nhau) khi p = p gh

= cp Tri sd ldn nhd't d'y dugc xac dinh theo cdng thuc 11-2-2 ta cd:

vdi A Id trj sd gidi ndi

D i6u nay d u g c m inh hoa d bdng sau:

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 D di 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 cu a no bang bao nhieu?

2 Trj sd' E C(J bang bao nhieu khi gdc P ldn bang trj sd Pgh

D e lam sang rS nhirng d ilu neu tren, ta xet ke't qua tinh loan cho m dt 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:

T heo tinh than cac quy pham hien dung, trudc he't

gi& thie't p = 0 (m at da't dap sau tudng nam ngang) va

tinh d u g c goc tru g t 0 tu an g ung bang 35° Trong

lugng khd'i da't AD C nam phia tren m at Ax dugc xem

nhu phan b d deu theo dang bac cap tren m at ngang

Ax rdi tu dd xac dinh dugc tri sd' ap luc da't chu ddng

E cd = 4 6T /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 rc tg l,8 7 = 6 1 ° 5 0 \ T ich sd'tgp.tgB =

0,53.1,87 « 1, nghia la m d t tru g t B C song song voi

m dt dd't d d p A D , khdi da't tru g t ldn vd cung D ieu dd

chung td r&ng trong trudng hgp nay trj so P = arctg(5,3) = 29° la trj sd' g id i han cua gdc nghieng cu a m at da't dap sau tu d n g chan (quy udc goi la gdc nghieng g id i 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 h an cp kha n h ilu

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

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

vk tri s6 G la n vd cung Didu nay 1km cho p huang phdp dd gi&i tin h ap luc da't chu

ddng [6] ma't hieu luc T rong tru an g h a p nay ((3 = Pgh) trj s6 G ldn vd cOng nhung tri sd' &p luc da't l6n lung tu an g E v ln c6 tri sd g iai ndi T ri sd' nay d u g c xac dinh bang

p h u an g phap giai tich [1 2]

2 X ac d jn h t r i so goc m a i g id i h a n Pgh c u a k h o i d&'t d in h d S p s a u tuw ng chdn

t hu an g phap giai tich chinh xac de xac dinh iri sd' pgj, da dugc tac gia dd ra [1 2] vagidi thi$u can ke trong ch u an g 4 cud'n sach nay G day neu phuong p h d p gdn dung dan

gidn dd ti6n dung Ndi dung p h u an g phap

nay n h u sau: gia du c6 m dt tu an g chdn dat

co chieu cao H va goc m ai P cu a khd'i da't

dap sau tu an g bang tri sd p gh (hinh II-9)

N hu tren da n6u, khi tri sd P dat de'n tri sd

pgh thi m at trugt thoai dan va tidn den song

song vdi mat da’t dap L uc nay khd'i da't

tru g t bao g6m m dt la p da't keo dai vd han

va cd chidu day khdng ddi bdng chidu cao

H c u a tudng T rong lugng cu a la p dat

trugt nay tac dung nhu t&i trong thdng

dung phan bd' deu tr6n m at tru g t BC va co

cudng dd q tinh theo cdng thuc:

q = yH cospghPhan q ra hai thanh phan: phap tuydn a va tie'p tuydn t tren m at tru g t BC

T hay cac bidu thuc cua a va t tu cac cdng thuc II-2-7, II-2-8 v ao ddng th u c II-2 -9

ta se cd p h u an g trinh tinh trj sd tg p gh nhu sau:

Vj d u I I - 1: T in h tri sd Pgh ung vdi cac tirdng chan d£t cd chidu cao l in lugt la 6, 8,

!0m lu n g tucrng th an g dung) Da't dap sau tudng la loai dat di'nh cd cac chi tieu nhusau: 7 = 2 T /'n r\ cp = 20°, c = 2T /m 2

G iii: Vi du ti'nh gdc Pgh ung v ai tudng cao H = 8m:

Tu b&ng tr6n n h an tha'y rang, v a i cac di£u kien

k hac i h u n h au , tri sd' Pgh tang len khi H giam

Tricrng h g p a * 0 ta cd quan he gitta ch i6u day ldp

da't trrg t z v a i H n h u sau (hinh 11-10):

z = H + a

Thay I I -2-12 v ao II-2-6 rdi thuc hi$n cac phep tinh

nhu te n se d u g c p h u a n g trinh ti'nh tri sd' tg p gh ung

vdi g jc a c u a lung tucrng:

) - o

25

, yH

1 - — tg a c

1 t h

l + 7 t8<l> _ PH +tgp

1 I H • D r i - t g a c

Chmmg III

LI THUYET VE KE NUT TRONG KHOI DAT DINH DAP

SAU TUONG CHAN VA ANH HUONG CUA KE NUT

Khi tinh toan ap lyc dat din h len tu d n g chdn, viec nghien cuu ke nut phat trie'n trong khdi d at ddp va &nh h u a n g cu a kg nut de'n tri sd ap luc da't co y nghla kinh te' va ki thuat ra't ldn

I CHlfeu SAU K£ NUT PHAT TRlfiN TRONG KH6 l DAT DINH DAP SAU TUONG CHAN

T ru d n g hop da't ddp sau tu d n g chdn thudc loai da't cat (cd c = 0), m at da't ddp thudng ndm ngang hoac nghieng m0t gdc khdng ldn h an gdc ma sat trong cu a da't ddp Khd'i da't dap ludn ludn d trang th ai ung sua't nen Khi dung da't dinh d l dap sau tudng thi

m at d at dap cd t h i cd dd dd'c tuy y, tri sd gdc (3 cd t h i ldn h an gdc m a sat trong (p

X et tru d n g h g p tirdng chdn da't xay cao de'n cao trinh m at da't ddp va m at ddt ddp nam ngang

T huc te' quan sa t can g n h u li thuye't chung m inh Id sdm hay m udn, phia tr6n khd'i da't dinh ddp sau tu d n g cd cac ke nut tu an g dd'i thdng dung xua't hien (hinh III-l)

O day ch u n g tdi phan b ie t ke h& tii'p gidp gitta tudng vdi da't ddp va k i n u t trong khoi dd't d d p (goi tat la ke nut)

1 K e n u t tr o n g k h o i d a t d d p

De d& xet, khd'i da't ddp sau tu d n g dugc xem nhu d trang thai can bang chu dQng

R angkin (tran g th ai can bdng gidi han cu a m dt nua khdng gian day da't dinh d trang thai keo dan) M dt phan td' da't la'y d dd sau z trong khd'i da't ddp cliiu tdc dung cua cdc thanh phan ung sua't nhu d hinh III-2 (khd'i phan td lay d vi tri du xa tu d n g d l su tdn tai cu a m at tu d n g dugc coi n h u khdng dnh hudng de'n trang thai ung sudt cCa phdn td' dy)

Trong do:

ctx = a , = y.z (ung su£t chinh Ion nh^i)

crx = 0 3 (ung sua't chinh nho nha't), co trj s6 phu ihudc vko trang thai ung su£t cua

khd'i da't dap

Khi khQi phan td' d£t a trang thai can bang gidi han chu ddng tb; tri s6 a? duoc x ic

djnh tu d iiu kien can bang gidi han M o R angkin

sd' CT3 cd th£ am (keo) hay d u an g (nen)

DO sau zn, tai do cr3 = 0, gidi han vDng ung su£t k6o va vung ung sua’t n6n trong khd'i d£t T rj sd' zn xac djnh tir diSu kien:

D£t trong vung c6 z > zn chiu ung su£t nen (ct3 > 0), da't trong vung cd 0 < z < zn chiu ung sua't keo (ct3 < 0), do do, sdm hay muQn ke ndt th&ng dung se x u at h ie n trong lap d£t chju k6o Vi vay, dd sau ke nut thdng dung h n theo W C H u n g tin to n va nhi£u tac gia khac dugc xac djnh theo cdng thuc:

2 K e h d tie p g ia p giira d a t d 5 p vdi lu n g tu a n g

De’ xac djnh chidu sau cu a ke h a tie'p giap gitfa dat dap (dat

dinh) vdi lung tu an g , xet m0t phan t6' da't tie'p giap vai lung tu an g

nhu da neu tren hinh III-3 Cac thanh phan ung sua't tac dung len

khdi da't phan td nay (khac vdi khdi phan td da't l£y cach du xa

iirng tu a n g ), phu thuQc vao su co m at cua lung tu an g qua cac

ye'u to v6 dO nham , dd nghieng v.v cua lung tuang D£ dan

gian, xet tru a n g h a p lung tu an g thang dung, m at da't dap nam

ngang (p = 0 ) Do co m a sat giUa lung tucrng vdi da't dap nen

thanh phdn ung sua't tiep t zx khac khOng, cac thanh phan ung sua't

phap ctx, a z khOng phai la nhung ung sua't chinh Trong tru an g

h a p li tudng: lung tu an g tran nh5n (cp0 = 0) thi t zx = 0, a z = c?|

va a x = ct3 T heo RSngkin, co the tinh dugc trj so c u an g dd ap

luc da't chu dong tac dung tai diem M d dd sau z nhu sau:

2

2cY

tgf45° + 5B— 1 - -III-1-8

v 2 ' 1 + tg a tgcp

D ac b ie t khi a = P = cp0 = c0 = 0, tCr cdng thuc I II- 1-8, ta lai cd:

29

TCr bieu thuc tinh tri sd z0 (cdng thuc III-1-8) ta tha'y km g tu a n g co dnh hudng d£n

d6 sau, tai do p cd = 0

T rong pham vi tu do sau z0 trd len, lung tu an g chiu ap su£t am (keo tu a n g v6 phia

da't d^p), dudi dd sau z0 (z > z0) lung tudng chju ap sudt du an g ( d iy tudng)

Do lien ke't dinh gitfa dat vdi lung tudng sdm mudn se mdt di va ap sua't am tac dung

I6n lung tudng chan kh6ng phat huy tac dung dugc ntfa va ke h d ti£p g iap giiJa lung

tudng vdi khdi dat ddp xudt hien D o sdu k i h& tii'p g id p du a c Idy bdng d d sdu z0 tai

dd p cj ~ 0 T a cd:

nh£t vd cua m at tru g t th u hai (lung tudng) bj gidm nh6

Chidu cao lung tudng chju tac dung cua ap sua't chii dQng (pc<1 > 0) d u g c kl h ie u Id

H a va tinh dugc tu cOng thuc sau:

trang thai can bang gidi han , cQng khQng gay nen ap luc da't chu d0ng len tu d n g chdn

II CHlfeu CAO KHONG CAN TUONG CHAN CUA KH6 l DAT DINH

N ghien cuu va'n d6 nay cd y nghla k l thuat va kinh te' ldn ddi vdi xay du n g n h u n g d£n nay cdn cd m dt sd qu an n iem ra't khac nhau

Chidu cao k h6ng cdn tu d n g la chidu cao cu a m0t khdi da't dinh cd th an h d u n g , du d

(ne'u c6 tirdng ch5n khdi da't) N h u vay didu kien d l xac dinh chidu cao khGng c&n tudng

C&ch tinh H0 cu a T eczaghi kh&ng dugc hg p li do khi ti'nh E cd b&ng phep tinh phan

d ien ti'ch b ilu d6 phan b d ap luc da't chu dQng trong pham vi 0 de'n z = H 0, hay ndi

c ac h k h a c 1& tich phan tir 0 de'n zn va tir z n de'n H0 rQi cQng

lai n e n da khOng x et de'n y nghia vat li cua p h in b ilu dQ

(0 < z < z n) cd pC(i < 0 T huc ra vdi chidu cao H0 tinh theo

III-2 -2 , tu d n g vSn chiu mQt trj sQ £p luc da't b&ng:

.H„

'Cd- f pc d dz > 0

D l x&c d in h chidu cao kh d n g can tudng, tQt nha't la dim g

c&ng th u c tin h ke nut ke't h g p vdi s a dQ tinh toan n h u d

h in h III-4 T ro n g tru d n g h g p nay goc tru g t b&ng:

Vay c h ii it cao khdng cdn tuang p h u thudc vao chiSu sdu n u t ne cua khd'i ddt ddp.

Ne'u ke nut khdng xua't hien, tuc h n = 0 thi ta lai co tri sd' H0 cua T eczaghi trong cOng thuc III-2-2

T rong thuc te' tinh todn, dd'i v a i da't di'nh lay:

2 )

nen c6:

h = 7 ' < 45° + ? ) - 7 ‘< 45° + ? )

2c / -o , £hay

VSy chidu cao khdng c in tu d n g bang chidu sau ke nut.

X dt tru d n g hgp phuc tap han: a * 0, p + <p0 = 0 (tuc <p0 = p = 0 va -P = <pQ)

Ne'u khdng x e t dS'n k i n u t (hinh III-5a) T heo [1] trj sd' ap luc da't chu d0ng c6 dang:

Hinh II1-S

III-2 -8 a

v a i

2c costp c o saYao= y - — - * -

T ir d d , c6 tri s6 chidu cao khdng c£n tudng H0:

^ _ 2c cos<p c o s a _

° " Y cos2 ( 4 5 ° + ^ )

H - — tg f 45° + < *L l9 : ) - - - III-2 -10

TCr cOng thuc III-2 -1 0 ta c<5:

- K hi a = 0 (khd'i d£t dinh c6 thanh thdng dung)

Ke't qud neu tren gidi thich hien tugng dd s£it cua khd'i ddi: ddo hdm e'ch

Ne'u x e t d i n ke n u t xud't hi$n thi s a d6 tinh todn n h u d hinh III-5b T ren d&y ta da xac d jn h d u g c trj sd' h n (cdng thuc I I I - 1-3, I I I - 1-4) X em Idp da't n d t nd trong ph?m vi

h n n h u tdi tro n g p han bd' ddu co cu d n g dQ Id p = yhn (didu n iy chm h xdc vdi trudng

h g p a = 0 , nd'u a * 0 thi gdn du n g do c6 khd'i ddt nh6 A A ’A ” ) ta cd b ilu thuc tinh E cd

n h u sau:

E r f ( h „ * 0 ) = ± y ( H - h n) 2 Kc4 + p ( H - h O K c a - c ( H - h , , )

-T u didu kien:

E c<t(h n * 0) = 0,xac d in h dirge chidu cao khdng cdn tu d n g c6 xet de'n ke nut xu&'t hien:

H0 (h n * 0) = — tg f 45° + ^ ) - - hn H I-2 -11

y \ 2 / 1 + tgcp tg a

K hi a = 0 , ta i^ii cd cdng thuc III-2-6

Cdn chu y r&ng cac trj sd' dd cao khdng cdn tudng, theo cach tinh da neu d tren, Id ung vdi he sd' an to a n bdng 1 (tuc d trang thdi can bdng g id i h?n) D o dd trong thuc t£

u n g d u n g ph&i x e t de'n m uc d § an to&n b&ng c&ch g ia m b d t chidu cao khOng cdn tudng mQt d ai lu g n g n ao d o (v l du la'y b a n g 2 /3 H0 xac d jn h th eo cOng th u c da neu) hoac dting cdc ch i tieu ti'nh to an c u a da't (x et de'n didu k ien d6ng c h a t, he sO' didu kiQn l&m vi$c).

V i d u I I I - l : X ac d in h c h ie u cao k h d n g cdn tu a n g c u a loai da't di'nh c6 goc m a sat tro n g cp = 2 4 °, lu c d in h d a n vi tieu ch u ^n c = 0 ,4 k G /c m 2, ybh = 2 T /m3 v a i a = 0°, a

III B lfiu b 6 PHAN B6 AP LUC DAT CHU D 0 N G CUA DAT DINH KHI XfeT d £ n K £ NUT XU AT HI$N

T rong m uc 4 c h u a n g II da nfiu n g u y e n ti c ve b i lu d6 p h an b d a p lire da't chu dQng chira xet den kg nut (kg h d tie'p g iap ) xua't h ien tro n g khd'i da't d ap D l x6t de'n su xua't hign ke n u t khi vg b ilu dd ph an bd' ap lu c da't chu dQng, d day n£u len hai p h u a n g phdp: phirang p h ap th eo li th u y e t can b a n g g id i han d iem va ph iran g p h a p th e o li thuye't canbang gidi han khdi

Phucmg p h d p th u nhd't (th eo li thuyg't can b a n g g id i h a n d ilm )

Do li thuye't nay x e t su can b a n g g id i h an c u a tu n g d ilm m dt nen ld i gi&i cud'i c u n g

cu a bai toan cho cac tri sd' ap sua't chu d d n g p cd tai cac d d sau k h ac n h au Vf d u , th eo cdng thuc III-1 -4 ta cd:

Pcd = Y z t g2 ( 4 5 ° - | ) - 2 c tg ( 4 5 0 - - ^ )

hay p cd = y z m - 2c V m , v d i m = tg2^ 45° - ^ ) I I I - 3 - 1Tir dd, ve d u g c n g ay b i lu d d p h an bd' ap lu c da't chu d § n g (h in h III-6)

D o cd ke nut xua't hign n£n tro n g p h a m vi lu n g tu d n g p h ia tren c d c h il u c ao b a n g

h0 = z0 kh d n g chiu t i c d u n g c u a p cd A p luc da't chu d0ng ch i tac d u n g len tu d n g d p h ia dudi sau h a n h 0 Do d d , b i lu d d p h an bd' a p luc da't ch u d d n g cd d a n g tam g ia c (h in h III-6), cd d in h tai z = h0 va c d d ay b&ng:

TO dd, ti'nh d u g c ap luc da't c h u d d n g E cd

Ecd = dign tic h ( A ’B C ) = ^ (yH m - 2cV m ) (H - h0) III-3 -3

T a cQng cd t h i cd d u g c ke't q u a a'y th eo c a c h sau day:

D o ldp da't m at, tro n g p h a m vi h n, bi c ac k e n u t th d n g d u n g p h a n d t ra n6n c d t h i xem trong lu g n g ld p da't n ay n h u t£i tro n g p h an bd' d l u q (h in h III-7 ) v a tu d n g cao

H ’ = H - h n

N h u vSy trj sd' pcd c6 x6t de'n q c6 dang.

- T ?i chan tu d n g tinh todn (tu d n g cao la H - h 0) tuc tai z = H - h0 cd:

Pcd = [Y(H - h0) + q]m - 2c Vin vdi q = 2c tg f 45°+

P huang p h d p th u hai (theo li thuye't can b&ng g idi hzm khdi rdn - li thuye't C uldng)

T l o H thuye't C uldng, cac p h u a n g phap tinh toan cho tri sd ap luc chu ddng E cd (m a khdng ch c trj sd' dp sulft chu dOng pcd(z)) Do dd mud'n ve ducrc bi£u a o phan bo' ap lyc dSit chu dQng lai p h ii van dung giS thie't 5 da neu trong m uc IV c h u an g II

D o cO 1 e thd'ng ke n u t thdng dung xudt hien nen cac chidu dai tinh todn L, L0 (h in hII-2a) bj g iim di do dd cac luc T0 = c0L 0, T = cL cflng gi&m nho va anh h u d n g de'n trj sd' Ecd N o i m dt cdch kh ac, trj sd' E cd tinh toan dugc theo hinh II-2 la da cd xet de'n ke

q = yhn = r y t g ( 4 5 0 + | ) = 2 c tg (4 5 ° + ® ) HI-3-4

nut xudt hi$n v& nd xem nhu phan bd' theo m0t quy lu$t nko ddy ts> chan ke hd tidp gidp (didm A ’ trong hinh II-2) xud'ng chan tudng Ta c 6 ddng thuc:

T^i z = h0, trj sd' pCd(z) bang khdng C6 hai trudng hop c6 thd xdy ra khi ve bidu d6

ap luc ddt chu ddng theo li th u y et Culdng

a) Bi&u dd ph d n b d hinh thang: mQt sd' tdc gid cho rang trudng hqrp ndy ddng khi

chidu sau ke nut trong khd'i d at ddp h n ldn h an ch i6u sau ke h a tie'p gidp h0 vd khi tinh

to an phdi gid thidt phdn ddt trong ph^m vi h n tdc dung n h u tdi tr<?ng phan bd' ddu

T heo T eczaghi, K lein vd mQt sd' tdc gid khdc dd nghj ldy:

* V - „ = f < 4 5 ° + § )

h- ^ = 2 f ‘< 4 5 V f )

Dd d an gian, cdc tac gid ndy dd nghi khi ti'nh loan ldy:

h0 = h„ = 2 , 6 7 5 ^ 4 5 ° + * )

N h u vay, trj sd' E cd tinh todn dugrc xem n h u phan bd' trong pham vi chidu cao tudng

tu z = h n ddn z = H va bidu dd phan bd' pcd c6 dang hinh thang (hinh III-8)

Dd lam sang td vdn dd ndy ta xdt vi du sau day [3]

V i du 111-2: X ac dinh dp luc ddt d sdt tren lung tudng co a = 0, H = 10m vdi

- Trong lugng khtfi dd't trugt A BCC’

G == y [ hnH - h n (H - hn) 2 n _ y(H2 - h2 n) _ 2(102 - 3 , 8 2 2) _ 85,4

tg e 0 2tge 0

Ung dung c6ng thuc I I - 1 -2b

G sin(90 - cp) - T coscp - T osin(0o - cp - a )

16,1015,60

(khfing phu thu0c 0 O)

18,2

(Nftu vi du ndy d l ldm sang t6 cach xdc djnh b ilu d6 phan b6' ap luc da't chu dQng

c h u k h6ng cd y dinh neu len cach gidi n h u the' ndy H i0n nay da c6 p h u a n g phdp tinh chinh xdc vd d a n gian hem)

\ hn‘ho a

i |§ k

i —iy b