656 Xay dung mo hinh s6 va mo phong nut ne trong da XAY DU>sG M O H I N H SO VA M O P H O N G N f T NE T R O N G DA Yoshinori Sanada, Naotoshi Yasui Toshifiimi Matsuoka, Yuzuru Ashida Kvoto Universit][.]
656 Xay dung mo hinh s6 va mo phong nut ne da XAY DU>sG M O H I N H SO VA M O P H O N G N f T N E T R O N G DA Yoshinori Sanada, Naotoshi Yasui Toshifiimi Matsuoka, Yuzuru Ashida Kvoto Universit]- TOM TAT Trong bdo cdo ndy, sir truyin sdng ddn hdi qua cdc nirt ne se dugc dnh todn Ly thuvd r&i rgc bien vi (Displacement Discontinuity Theoiy - DDT) cho rdng nirt ne ciing dugc coi Id mdi tru&ng cirng ddc bid vd phirong phdp phdn tir r&i rgc (Discrete Element Method - DEM) tinh todn sir tuong tdc giira cdc hgt v&i tru&ng ddn hdi bdt biin Tu quan diim ndy, DEM la mdt nhimg phirang phdp phu hgp nhdt ddi v&i ly thuyet DDT Cdc sdng phdn xg vd sdng lan truyin qua da nirt ne se dugc tinh todn Cdc he sd truyin vd hi sd phdn xg dugc so sdnh v&i DDT Kit qua thu dugc tien hdnh v&i cdc vgt thi cimg ddc bid khdc vd tdn sd khdc diing phuong phdp DEM phii hgp ly thuyit DDT MO DAU Nirt ne da eo vai tro quan doi vai co hoc da e6ng nghe tang chiia, tham nuac, v.v Trong tham dia chan song phan xa va song tru\'en dem lai nhung th6ng tin ve dae tnmg ciia nirt ne Phuong phap phan tir rai rac (DEM) da duge Cundall giai thieu (1979) nhu la mot tiep can hoan toan mai Cundall quan niem rang cac hien tugng \\ m6 la t6ng hgp ciia cac tuong tac rat nho giira mot s6 \6n cac hat Phuong phap eo im diem hon so vai phuang phap truyen th6ng, vi du nhu phuong phap vi phan hiru han, phuang phap phan tir htru han de m6 ph6ng cac chuyen dong kh6ng lien tuc hoae nhting truong hgp no Nhung img dung viec m6 ph6ng eae song dia chan nhu la cac song P va S co sir dung DEM da dugc Tommy va Bean ap dung nam 2000 va Matsuoka ap dung nam 2003 Ke tir ehua dua dugc dieu kien bien hap thu rieng ITnh \'irc m6 hinh mot each thoa dang, nhtrng song truyen nhanh (fast waves) bi phan xa tir cac giai han phan each ciing nhu cac song phan xa phii len cae song cham (low wa\es) la song chimg ta can nghien cim De ngan chan hien tugng chong phii ehiing ta can mot kh6ng gian tinh toan Ion dieu eo nghia la bo nha may tinh Icm va thai gian tinh toan Icm D6i \ai phuang phap \i phan hiiu han nang lirgng phan xa giam tai khu \ire bao quanh viing m6 hinh tai eae ham s6 lam tron va ham tre se dugc ap dung (Cerjen 1985) Theo each tuong tu ehiing toi de xuat nai eo nhcrt sut giam duge coi nhu dieu kien bien hap thu de ap dung DEM Mot nhtrng uu diem cua mo hinh song vai DEM la eo the xir ly dugc cae cau true khong lien tuc nhir nirt ne mot cac de dang Trong bao eao chimg toi giai thich DEM va DDT De loai bo nhiing phan xa khong cin thilt tir ranh giai ngoai, chung toi dua dieu kien bien hap thu Sau cac 657 Tuygn tap bao cao Hdi nghj KHCN "30 nam Phu Viet Nam: Co hdi mdi, thach thuc mdi' song phan xa va song truyin se duge tinh toan eho cae m6i truong cimg dac biet va tin sl khae nhau, va so sanh vai DDT M O PHONG SONG DAN HOI B A N G P H U O N G PHAP PHAN TU ROI RAC Trong m6 phong DEM, m6i truang bao g6m mot s6 eae hat ao tiep xue vai bai cae 16 xo day chimg t6i chi xem xet m6 hinh hai chieu, cae hat dugc m6 ta eo dang hinh dTa D I m6 phong m6 hinh vT m6, mot s6 lugng lc5n cac hat duge djnh hinh mot tap hgp hinh lue giac (Hinh 1) Cac hat tiep giap tuong tae vai bai cac 16 xo Cac tham s6 vi m6 (cac phan tir) va cac tham s6 vT m6 (vat chat dan h6i) gan lien vai sir bao toan nang lugng dan h6i va nang lugng co gian Cac tham s6 vi m6 va vT m6 dugc hien thi a Bang Bang 1: Cac tham s6 m6 hinh cua hat va m6i truong dan h6i Ccic tham sd vi md Cdc tham sd vi md Hang so Lame A,, |i Khoang each hat: ro Van tic P: Vp Trong khoi hat: m(kg) Van tic S: V,s Khoang each 16 xo: K(kg/s") Mat do: p(g/cm-^) Cac phuong trinh tuang tac lan sir dung cac tham s6 vi m6 va vT m6 duge dua nhu sau: A= P Ll= (1) A _2M_ (2) Sdi Do vay, van toe song dan hoi P va S, goi la Vp va Vs se dugc xac dinh bang phuang trinh (3) va (4) (Hoover, 1974): K \X + 2p \9K 8w P V = ^= - (3) (4) Hinh 1: DEM gia thuyet m6i truoTig gom mot so cac phan tir Hinh la anh chup nhanh tai mot thai dilm qua trinh truyin song dan hii 658 Xay dung mo hinh sd va mo phong nu1 ne t r o n g ^ b) a) 400 particles " " '" Hinh 2: Sir truyen song dan h6i theo phuong phap DEM (a) Md hinh ddng nhdt (phdn tu mdu den dao ddng v&i sdng t&i) (h) Anh chup nhanh thdnh phdn theo true X cua xung luc truyen sdng Vdng ngoiii Id sdng P vd vdng Id sdng S D I tinh toan qua trinh truyin song, nhtrng phan xa kh6ng can thiet tir cac bien ngoai phai dugc loai b6 Chiing t6i dl xuat nen sir dung m6 hinh diem t6i (dashpot) ciing vai nhcDt dilu kien bien hap thu ciia phuang phap phan tir rai rac Trong m6i truong dan h6i, moi mot phuang trinh chuyen dong gitia cac phan tir dugc xac dinh bang phuang trinh (5): d'x (5) m dt'- - -kx Mat khae nhtrng viing tr6ng, s6 hang nhot dugc them vao ve ben phai eiia phuong trinh (5): d'x dx m —r- = -kx n dt' dt (6) MO HINH SONG DAN HOI QUA NUT NE Khi mot song dan h6i truyen qua mot nirt ne, img suat tren cac be mat ciia nirt ne van lien tuc nhung bi dieh chuyen va van t6c dieh chuyen eiing kh6ng lien tuc Shoenberg (1980) da dua thuyet bien vi rai rac (DDT); img suat ty le thuan vai dich chuyen Thuyet DDT gia djnh phan lire dan h6i co phuong phap tuyen va tiep tuyen tren be mat ciia nirt ne (Hinh 3) Luc dan h6i the hien cimg dae biet cua niit ne Hieu s6 dich chuyen tren ca hai be mat ciia nirt ne va cac img suat dugc the hien bang phuang trinh sau: K, „ Kz 5a bD(-, Jiciient ! -oDoocoe -OiXWOLX- TETismil -OflOOOOS -OffX-jUt Hinh 5: Duong hinh sin duoc ghi lai (a) Cdc sdng t&i vd sdng phdn xg 50 (b) Cdc sdng t&i vd sdng khiic xg 100 150 200 250 300 a) K[ , = K\ , = 10% ' \ bond \ bond b) Kl.d = Ki,d = 20% A- -"t.- ^ R p i c c t t e d fiom DDT E 05 A R m ea;raiEd nim e a r a J V ii ^^^ mooEl T pi>jcU:3;ci — c ' T m easured r 50 100 15C 20C fccifent P wd^^ i i s q a s r i c y c) Jr'' = AT' 250 300 iiz = 50% Hinh 6: He s6 phan xa va he s6 khuc xa ciia song toi P doi vol mit ne tinh theo phuong phap DEM Tuyin tap b^o cao Hdi nghj KHCN "30 nSm D2u Viet Nam: Co hdi mdi, thach thuc mdi' 66] KET LUAN Trong bao cao thi sir truyin s6ng dan hii qua nirt ne da duge tinh toan Phuong phap DEM thich hgp dii vai ly thuyit DDT Cac song phan xa va song khiic xa dugc quan sat He sl phan xa va he sl khiic xa duge so sanh vai DDT Ket qua thu nhan dugc tiln hanh theo phuang phap DEM dii vai m6i truang cirng dac biet khae va tan s6 khae rit triing hgp vai ly thuyit DDT Muc tieu tiep theo ciia chiing t6i la he th6ng da niit ne va chirng thuc bang thuc nghiem TAI LIEU THAM KHAO Cerjen C , Kosloff R., Restog, M., 1985 A non-reflecting boundary condition for discrete acoustic and elastic wave equations Geophysics, 50, p 705 - 708 Cundall P.A., Strack O.D.L, 1979 A discrete numerical model for granular assemblies Geotechnique, 29(1), p - Hoover W.G., Ashurst W.T., Olness R.J., 1974 Two-dimensional computer studies of crystal stability and fluid viscosity The Joumal of Chemical Physics, Vol 60, p 4043 - 4047 Matsuoka T., Kusumi H., Wakatsuki Z., Ashida Y., 2003 A study of elastic waves and Hopkinson bar effect using granular model Zairyo, Vol 52, No 5, p 472 - 477 (in Japanese) Raul del Valle-Garcia, Francjsco J Sanchez-Sesma, 2003 Rayleigh waves modeling using an elastic lattce model Geophysical Reserch Letters, Vol 30, No 16, 1866, doi: 10.1029/2003, GL017600 Schoenberg M., 1980 Elastic wave behavior aeeross linear slip interfaces J Acoust Soc Am., 68, 1980, p 1516-1521 Toomey A., Bean C.J., 2000 Numerical simulation of seismic waves using a discrete particle scheme Geophys J Int., Vol 141, p 595 - 604 ... la phuang phap vi phan htru han Trong phuong phap DEM, nhtrng tuang tac giiia cac hat ao dugc xac dinh bcri dinh luat Hcx)k: r (,.j) JNii.n^Y''dj) (8) TQI(IJ)'' Trong K la hang s6 lire dan hoi,... h6i Ccic tham sd vi md Cdc tham sd vi md Hang so Lame A,, |i Khoang each hat: ro Van tic P: Vp Trong khoi hat: m(kg) Van tic S: V,s Khoang each 16 xo: K(kg/s") Mat do: p(g/cm-^) Cac phuong trinh... hinh diem t6i (dashpot) ciing vai nhcDt dilu kien bien hap thu ciia phuang phap phan tir rai rac Trong m6i truong dan h6i, moi mot phuang trinh chuyen dong gitia cac phan tir dugc xac dinh bang