KHOA HOC VA CONG N G H C MO
X/NGHIEN CUU sir PHAT TRIEN CUA VI KHE Nurr TRONG VRT ufu Dfl, BC TONG DE DU BAO THdl GIAN PHA HUY
V
gt lieu da vd bd tdng Id nhung logi vgt lieu d eau trtjc phirc tap vd ludn ludn tdn tgi cdc vi khe nirt. lo rong trong nd hay d n gpi la d c k h u y i t tat trong d u tnJC- Do ludn cd s y ton tai cita cdc k h u y i t tgt nay trong vdt lieu dd, be tdng ndn chiing d u g c xem la mpt trong nhii'ng y i u td chinh dnh hudng d i n do b i n vd t u i i thg cua vat lieu. Khi vdt lidu chju tdc ddng cua tai trpng, cac vi khe nirt cd t h i phat trien va lien k i t vdi nhau tao thdnh cac v i t nut ldn d i n den gay phd hiJy vdt ligu. Khi v i t nut hlnh thanh vd phdt t r i i n trong vat ligu d i n mdt thdi d i i m ndo do se ldm m i t kha nang lam vide an todn ciia edng trinh hogc gay pha htjy cdng trinh.Thdi diem vet nCet phat trien v u g t qud gidi han cho phep ddn tdi nguy co m i t an toan ciia edng trinh la rat quan trgng trong vige dua ra eae giai phap xiy ly thich hgp, d l dam bao cho cdng trinh lam vigc trong gldi hgn an todn.
D i n nay trdn the gidi da cd r i t n h i i u md hinh duge de x u i t vd dp dung de d y bao, phan tieh s y phdt t r i i n ciia v i t nut trong vat lieu da vd bd tdng [IJ, [2]. 0 n u d c ta. vide sir dung cae md hinh d i phan tich, ddnh gid s u pha hogi eae bd phan k i t eau cdng trinh da va dang d u g c dp dyng trong tinh todn thiet k i n h i m ndng cao dd chfnh xdc, dp tin cdy khi tinh todn t u i i thp cOa cdng trinh. Ly thuyit Cff hpc pha hiiy bd tdng da d u g c dp dyng d n u d c ta d i phdn tfch s y pha hoai ciJa d c bd phdn k i t cau n i i u d i m , vd ham hay t u d n g chan bd tdng do s y x u i t hidn vd lan t m y i n eae khe nirt [4], [5]. Tuy nhien, khi dp dung phijgng phap ndy de danh gia s y lam vide ciia k i t d u be tdng ddi hdi phdi ttln hanh r i t nhieu thf nghiem 6e xdc (Tmh d c dge trung eo hge eua vdt ligu. dac bigt la eae dac t m n g ni>t CO ban ciia vat ligu bg tdng, de lam eo s d cho vi^c tfnh todn t h i i t k i va d y dodn s y pha hogi. Cdc dgc t m n g nirt eiia mgt s i loai bd tdng thudng diing trong xay d y n g d Viet Nam dd d u g c xdc djnh thdng qua thi nghidm [6]. Ddy id cdc thdng sd r i t
TS. NGUYEN V A N M A N H ^ I Trwimg Dai hgc M6-Dia chat
h u u fch trong viec tfnh toan d y bdo s y phat trien eua cac khe nirt trong k i t c l u cdng trinh bdng be tdng va bd tdng d t thep.
Nhin chung cdc md hinh ly t h u y i t d u g c de xuat de nghien cuu s y phdt t r i i n eua vet nirt trong vdt lieu da va bd tdng d i u d y a trdn c o s o la cdc khe nirt ban d i u d dgng m d vd d o n le, t u dd phat triln cac phuang phdp tfnh toan s y phdt trien nirt ti> vet nirt m d ban ddu. Trong t h y c te. ngodi cdc khe nirt m d ban d i u edn d cdc vi khe n&t kin phdn bo trong vdt lieu. Do dd, vige nghien eiru md phdng sy lam vide eua cde vi khe nirt kin trong vat ligu dd vd bg tdng se giiip hieu rd h o n ban chat ciia s y phd huy cung nhu de d y bdo thdi glan pha hiiy,
1. Mo hinh n u ^ v a he s i tdp t r u n g ii>ng suat K C o e h i nirt va lan t r u y i n cae vet nirt trong cac vdt lieu d u d i tde ddng cua tai tn?ng ed the chia thdnh 3 dang chinh ggi la Mode I, Mode II vd Mode III vd dang hon hgp giua chiing [7]. Cac kieu nirt nay d u g c t h i hidn n h u trdn hinh H . l .
Trong thyc t i , cdc Mode hdn hgp la Mode k i t hgp hai hogc ba Mode c a ban ndi trdn la thudng gap hgn ea. V i du, trong e g che nijt do irng s u i t keo chfnh trong cac d i m chiu uon la Mode I va Mode II gay ra Be xdc dinh trgng thai ung s u i t trong nhung t m d n g hgp phirc tgp, t m d c het d n phai tfnh todn cho tirng dang c a ban rieng bigt.
He sd tap tmng irng s u i t (K) la mdt khai nidni d u g c Irwin [4] de d p l l n dau ttgn vao nam 1957.
Inwin chirng minh r i n g t i t ca cac trudng &ng s u i t dan hdi xung quanh v i t nu't d i u phdn b i giong nhau va tt Id vdi a V n a . De phdn bidt cdc dgng phat t r i i n cua v i t nut, n g u d i ta ddnh chi s i I, II va III eho ba Mode c o ban ndi trgn vd tinh todn hg s i tap ti-ung irng s u i t n h u sau [4]:
K , = a V 2 ^ (1) m GONB NGHlfP MO, S 0 1 - 2 0 1 6
KHOA HOC VA CfiNG NGHE MO
_ ^ ^
Trong d d : a - NCra chieu dai vet nut; o, T va T' - Lan l y g t la cdc thanh phan irng s u i t phdp, ii-ng suat cat ' ^ / trong mgt phang va ngoai mat phang.
1
ti. 1. Cac Mode nui cua v$t lieu [7]: Mode I Id d^ng ma rdng cdc vet ntW do hl$u ijng phdp tuyin gay ra;
Mode 11 la dfng cit phing do cac hieu Ong cit gay ra; Mode III Id dang cit ngoai m$t phdng do cdc hieu Cmg xoin gay ra
Trong t h y c td cac v i t nirt khdng chl phat trien theo mpt trong 3 dgng c o ban d trgn md la s y to hgp eua hai hay ba dang khdc nhau. Mgt khae, cae gid trj K|, Kn va Km d n phu thudc vdo vi tri v i t n i i i trgn vdt t h i , tt Id kich t h u d c cua vet nirt so vdi vgt t h i . Chinh vi vgy, vide xdc djnh cdc gia tri ndy se phirc tap hon rat nhieu doi vdi cac trudng hgp cd s y t i n g h g p ciia cdc Mode phd hogi.
Khi he so tgp trung irng s u i t K dgt den gia trj gidi han Kc thi vet ntjt se phdt t r i i n vd lan t m y i n ngoai ra thi v i t nirt van duy tri on djnh, Gia tn hg so tap trung irng s u i t gidi han Kc phu thudc vdo loai vgt ligu va d u g c xac djnh thdng qua thi nghidm.
2. Tinh toan t o e do phat trien nui Charies (1958) da dd xuat bieu thirc tfnh todn toe dp phdt t r i i n v i t nirt nhu sau [5]:
v = v„K''e'-"'"^»"'* (4) Trong dd: Vo - Hang s i vdt lidu; n - Chi s i suy giam
irng s u i t ; K - Hg so tgp trung u'ng s u i t ; u - Ndng l u g n g hogt ddng; T - Nhidt dp tuygt ddi; Kb - H l n g sd Boltzman.
Tren hinh H.2 t h i hign m i i quan he gl&a t i e dp lan t m y i n nirt (v) va he so tap tmng irng s u i t (K).
Vdi gia thiet nhidt dd (T) Id h l n g so, phugng trinh (4) cd t h i v i i t Igi d u d i dang don gian n h u sau [5]:
V = CK" (5) Trong dd: C - Hang so vgt lieu d u g c xac djnh t u thf
nghigm.
Ngodi s y phat t r i i n nirt do keo, ehOng ta eung d n chii y den phdt t r i i n nirt do e a t Gidi t h i i t toe do phdt t r i i n nirt Id s y k i t hgp ciia ea nirt do kdo va n&t do d t , khi dd t i c dd phat trien n&t ciia md hinh k i t hgp se Id;
V = V { K , ) + V ( K , | ) (6) V d i d c hd so tdp trung ung s u i t K| va Kn d u g c
tinh todn theo d n g th&c (1) va (2).
H.2. Quan he giu^ tdc do phdt tridn nui _____ vd hd sd tdp trung mg suat TCr (6) cd the nhdn thay rang t i c do phat t r i i n nirt phu thugc rat ldn vao c h i i u ddi v i t nut vd dd Idn ciia t m d n g irng s u i t tdc dyng. S y phat t r i i n ndt didn ra cho den khi he s i tdp trung irng s u i t dat d i n gia tri gidi han K c va Knc - Cac hang so.
3. Xay dung mo hinh dir bao thoi gian pha huy Tuoi thg ctia vdt lieu ran d u d i tdc dijng ciia tdi trgng kdo da d u g c nhieu tdc gid nghien c u u [3], [8].
Tuy nhidn, cdc nghidn c&u ndy chi phit hgp eho vdt lieu r i n va dge hodn todn. De h i i u sdu hon ve tuoi thg cita vat ligu r i n d n chu y den cae k h u y i t tdt (lo rdng, vi khe nirt,,.) trong vdt lidu. Qud trinh pha huy vdt ligu la mdt qud trinh pha huy d u d i tac dung ciia tdi trpng vd d u g c ggi la s y phdt trien tdi hgn cua vet nirt.
Ndi dung cua md hinh d i md phdng s y phat trien cua vi khe nut de d y bao t u i i thp cua vgt ligu chju tac dyng ciia tai trgng d y a trdn viec s& dyng ngon n g u FISH cita chuong trinh FLAC 2 D . Gia s u rang mdi p h i n t& cua md hinh cd chira mgt vi khe nut d c h i i u ddi cho trudc. S y phan bo trang thai ung s u i t d u g c tinh toan theo tidu chuan b i n Mohr-
CONG NGHIEP MO. so 1-2016
^ ^ _
KHOA HOC U CfiNG NGH| MO Coulomb. Hg so tdp tmng irng suat ctia m i l phant u d u g c tinh toan cho d c vi khe ni>t t u o n g ung theo d n g thirc (1) va (2). N i u hd s6 t#p tmng ung s u i t dgt d i n gid trj tdi han Kc liodc c h i i u dai v i t nirt dat den gia tii kich t h u d c cua phan t& thi phan t u se bj coi Id pha hiiy vd d u g c gan sang trgng thdi sau pha hiiy vdi tri so do b i n bang khdng. Qua trinh phat trien v i t nirt Id mdt qua trinh r i t phirc tap, bdi vi nd lien quan d i n s y phdn bo Igi trgng thai irng s u i t trong phdn t u va s y t u o n g tdc gi&a cac v i t nut. T u do, d the xdc djnh tuoi thg cua moi
phan t u bang each I l y tfch phan trdn todn bg chiiu ddi cua vet nt>t n h u sau [5]:
_ f dc
J V
m.
Trong do: Co - Chieu ddi ban dau cua vi khe nirt; Cc - Chieu ddi tdi hgn ciia vi khe n u t v - T i c dg phat t r i i n cda vl khe nut theo b i i u thirc Charies.
S u dung eac p h u o n g trinh (5) vd (6) thay vao p h u o n g trinh (7), chiing ta cd the viet lgi dugc n h u sau:
= l c K ^ 4 l k H
Trong dd: Co - C h i i u ddi tdi hgn ciia v i t ntit.
C h i i u ddi tdi hgn eua v i t nirt d u g c xdc dinh theo d i i u kien sau; la gia tri nhd nhat ciia 3 thdng s i : chieu ddi n&t tdl han tinh theo Kic, Knc vd kich thudc eua p h i n t& trong md hinh. ed nghTa Id [5]:
"cp
1 - n / 2 (8)^l(^J^f(^:
(9)Vdi dpt Id kich t h u d c tmng binh ciia phdn t t i trong md hinh va d u g c tinh theo dign tich p h i n t u nhu sau [5]:
Md hinh md phdng d u g c chia thanh n h i i u phan tir, moi phan tir tudn theo quy lugt Mohr-Coulomb, do do can cdc tham so vgt ligu sau: md dun ddn hdi (E), he s i Poat-xdng (v), lyc dfnh (c), gdc ma sdt trong (iji) vd do ben keo (at). Ngoai ra m i l phan t u cd chua mdt vi khe nirt. Cac vi khe n&t d u g c gid thiet la ed hudng n i m ngang. Do dd, ung s u i t e l t Idn n h l t trong m i l p h i n t& vd d c thdnh p h i n &ng suat chfnh d n d u g c tfnh todn than trgng trong qud trinh lan t r u y i n n i i i .
Thdi gian cua b u d c tfnh toan d u g c giu du nhd d i phu hgp vdi s y phan bd Igi trgng thdi ung s u i t khi lan t r u y i n v i t n&t. C h i i u dai v i t nirt hidn tgi anew d u g c ttnh todn theo thdi gian nhu sau [5]:
a.ew=ao,d + v.At (11) Trong do: aow - C h i i u ddi v i t nut cu; anew - C h i i u
ddi v i t nut mdi; v - T i c dp lan tmyen nirt; At - Khoang thoi gian lan tmydn ntjt.
Cac vi khe nirt phan bd trong cac p h i n t u theo phdn phdi c h u i n . Do dd. cac thanh phan ung suat trong p h i n t& d u g c s u dyng d i tinh toan s y phat t r i i n n & f t d i han.
4. Ket qua md phdng
S& dung ngdn ng& FISH d i xdy d y n g md hinh md phdng bai toan va tinh todn tuoi thg eiia vgt lidu.
VI du d u g c tfnh todn cho vdt lieu dd granit chju ndn vd chju keo vdi d c thdng sd eua vgt ll^u nhu trdn Bang 1.
Bang 1. Cac thdng s6 cua vat lieu [1]
ThSng so 1^5 dun dan h6i H f so Poat-xong Khoi lu-onq rignq G6c ma sat tronq LU'C dfnh l<lt B d ben Iteo H f so suy giam i>ng suSt
H f so t i p trung u-ng suat tCTi hgn Kic H f so t i p trung ung suat lo'i han Knc Hang s6 phat trien n u t C
B e n vj GPa T/m"
-
Ba
IWPa IVIPa
-
IvlPa.m'"
IWPa.m'"
(m/s)(Pa.m'°)-"
Gl'^'Mj 75 j 0,231
2 , ^ 3 0 ^ 4 5 ^ 1 ^ 32 4 2 ^
1,8 1,8
••,'»?4S
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Md hinh md phdng mau dd cd kieh thudc 2x2 (m) chju tai trpng keo (8 MPa) va nen (15 MPa). Mo hinh d u g c chia thdnh 50x50 phan t u , moi phan tu cd kieh t h u d c la 4x4 cm.
Hg t h i n g vi khe nirt ban dau phan bo trong v | t lidu ed c h i i u dai tmng binh la 1,0 cm vdi dd Idch c h u i n la 0,2 em va tao vdi phuang nam ngang mpt gdc 0° (hinh H.3). Tien hanh nghidn c&u s y phdt trien n&t do chiu tai trgng keo vd nen don tryc.
CfiNG NGHllP MO, S01 - 2016
II pham
KHOA HOC VA CtNG NGHl MO _ ^ ^
H.3. Phdn bd chudn cac vet nui ban dau trong phin tir md hinh (chiiu dai trung binh cua vit nui la 1,0 cm vai do lech chuin la 0,2 cm)
K i t qua trang thai phdt trien nut theo thoi gian trong d c md hinh chju keo vd nen don true n h u trdn hinh H.4 va H.5. T u ket qua nay cd t h i n h | n thay rang d u d i tac dung cua tai trgng keo chl cd mgt dai nirt phat t r i i n theo p h u o n g ngang (hinh H.4). Trong khi do d u d i tdc dung cua tai trpng nen, s y phat t r i i n nirt xay ra d n h i i u vj tri khdc nhau trong md hinh.
D i i u ndy cd nghTa la s y phat trien nirt t u cac vi khe nirt d i u ttdn xay ra d n h i i u vi tri khae nhau.
nhung sau 36 chiing hgp lai thanh mgt vai dai nut nghieng va tao thanh vet nii't Idn gay pha hiiy vat lieu ihinh H 5 ) .
I I
Ml
1 gid 28 phiit 30 giay (10 phan t& bi phd huy)
1 gid 34 phiit 27 gidy (50 p h i n t u bj phd hiiy) H.4 Si/phdt trien nui khi chiu tai trong keo 8 MPa
22 gio 35 phut (1 phan tip bj phd huy)
2 ngay 16 gio 55 phiit 8 ngay 0 gid 30 phiit 17 ngdy 8 gid 40 phut (10 p h i n t& bj pha hiiy) (50 phan t& bi phd hiiy) (319 p h i n t u bi phd huy) H.5. Sl/phat trien nui khi chju tdi trgng nen 15MPa
Md hinh bj coi la pha hiiy khi vet n&t phdt trien va d t ngang qua md hinh nhu trdn hinh H.4. K i t qua cho t h i y d u d i tae dyng cua tdi trpng keo khdng doi Id 8 MPa thi md hinh bj pha huy sau khoang thdi gian la 1 g i d 34 phut 27 gidy. Khi tai trpng keo tdc dijng Id 7 MPa thi md hinh bj pha huy sau khoang thdi gian Id 4 ngay 12 gid 56 phut 51 gidy. D i i u ndy cho t h i y s y t u o n g quan phi t u y i n giua tuoi thg eua vgt ligu vd d p dd tai tn?ng eung n h u kieu tdi trgng tdc dyng. So sanh k i t qua phdt t r i i n nirt eiia m l u chju tdi trpng keo vd nen cho t h i y t u i i thp ciia m l u khi chju nen 15 MPa Idn han r i t nhieu so vol t u i i thg cua mau khi chju keo 8
MPa. Dieu ndy Id hoan toan phit hgp vl vdi eae vdt lieu ddn nhu da va bd tdng thi dp ben keo nhd hon rdt n h i i u so vdi dp b i n nen eua vat lieu.
T u hinh H.4 va H.S d t h i nhgn thay khodng thdi gian x u i t hign phan t u bj phd huy dau ttgn cung n h u khoang thdi gian t& khi p h i n t& d i u tten bj pha huy ddn khi mau coi n h u pha hiiy cung khdc nhau khi chju tdi trpng keo vd ndn.
T r u d n g hgp chiu tai trgng keo thi khoang thdi glan t u khi p h i n t u d i u tidn bi pha hOy d i n khi m i u bj pha huy la 8 phut 27 giay, d n khi chju tai trgng nen thi khoang thdi gian nay id 16 ngdy 10 gid 05 phut.
CfiNG NGHllP MO, Sfi 1-2016
KHOA HOC VA CfiNG N6H| M O
5. Ket luan
Bai bdo da tiinh bdy thuat toan md phdng tfnh todn thdi gian phd huy vdt lieu da, be tong chju tai trpng keo va nen. C o s d d a phuang phap tfnh t d n la chieu dai nirt tdi hgn vd s y hgp nhat d a d c vi khe ntit thdnh v i t ntjt ldn d y a tren eg s d co hge phd huy dan hoi t u y i n tinh (LEFM - Linear Elastic Fracture Mechanics). C6 the de ddng nhdn t h i y s y khae bidt d a phd huy do keo vd do cat Dudi tdc dyng d a tai trgng nen, d c qua trinh phdt t i i n nut tiip dien d i n khi quan sdt dugc phd huy. Ngugc Igi, dudi tac dyng d a tai ttTpng keo, thi d i x u i t hidn d c v i t nirt don.
Khi so sdnh giira tai trgng nen va keo d o t h i y s y khac bigt ro rgt ve ttidi diem pha huy d a k i t d u vd mang v i t nut khi phd huy.G
T A I LIEU THAM KHAO
1. Atkinson BK (1987). Fracture mechanics of rock. Academic Press, London, p.534.
2. Griflith A.A. (1920). The phenomena of mpture and flow in solids. Philosophical Transactions of the Royal Society of India, series A221,pp.241-257.
3. Hilleriaorg A, Modeer M, Petersson P.E. (1976).
Analysis of crack formation and crack growrth in concrete by means of fracture mechanics and finite elements. Cement and ConCTete Res. 6: pp.773-782.
4. Ifwin G.R. (1957). Analysis of sfresses and stiains near ttie end of a crack traversing a plate. J. Applied Medanics, ASME, New York 24(3): pp.351-369
5. Konietzky H. Heftenberger A. and Feige M.
(2009). Life-time prediction for rocks under static compressive and tensile loads: a new simulation approach. Acta Geoteehniea, No. 4, pp.73-78.
6. Tran T h i T m y i n , N g u y i n Xuan Huy, (2011).
Pha hiiy, rgn nut be tdng: e g hgc vd &ng dyng, NXB Xdy d y n g . Ha Ngi, Vidt Nam. 200 trang, 2011.
7. Shailendra K. and Sudhirkumar V.B. (2011).
Concrete fracture models and applications.
Springer-Veriag Beriin Heidelberg, p.1-286.
8. Zhurkov SN (1965) Kinetic concept of the strengtti of solids. Int J Fract Mech 1 (4):311.
AfgifOT bien tap: Vo Trgng Hung
For many years, mines put forward an increase in the rock and concrete always contain the microstructural like micro-crack, voils etc. These parameters are effected to lifetime of materials. This article presents a computation algorithm to predict the lifetime of brittle materials like rock and concrete which depends on the distribution of micro- crack in the materials. T h e proposed model is based on subcritieal crack grc
the linear elastic fracture n __
approach. The algorithm considers both tensile and shear fracturing. The proposed model was applied to rock samples under uniaxial compressive and tensile loads for prediction of lifetime. T h e results showed that a significant difference of failure zones under uniaxial compressive and tensile
MOT SO VAN DE...
(T/dp theo trang 54) Ngwdfi bien tdp: Trin Van Trach
Mau Due-Ha Giang Antimony Mine is preparing deep exploitation. However, using current mining technology for deep-down period is inappropriate. In this paper, the authors assess the current state of the mine, which offer a number of issues to consider about mining technology in the next stage deep down in the mine.
1 . Chon con d u d n g doi lap v d i loi mdn vd bgn gan n h u se ludn Idm t i t . Jean Jacques j Rousseau.
2. Hanh phuc khdng phai la thir c 6 san. ' Hanh phiic d i n tip hanh dgng cita chfnh ta. \ DCFC Dat Lal Lat ma.
3. Ban than d i r n g qua lo l i n g hay nghiem 1 trong hda v a n d e , chang ai quan tam n h u J bgn lo s g d a u . Regina Brett.
4 . Kha nang thay b i i roi t r u d c s y v$t s y J viec la tien de cho mpi sdng tgo, dii Id ngh0 thuat hay khoa hgc. William Carlos Williams.
V VTHswutim^
CONG NGHIEP MO, S 0 1 - 2 0 1 6
