GEOTEXTILE AND GEOMEMBRANE USAGE IN AN IRAQI SANDY GEOENVIRONMENT

Transcription

1 umbr 3 Volum 14 Spmbr 008 Journal of Enginring GEOTEXTIE AD GEOMEMBRAE USAGE I A IRAQI SADY GEOEVIROMET Dr. Omar al-farouk S. al-damluji Dparmn of ivil Enginring Univrsiy of Baghdad Musafa Malik Jasim Formrly Posgradua Sudn Dparmn of ivil Enginring Univrsiy of Baghdad ABSTRAT Th work in his rsarch prsns an xprimnal and a horical sudy o obain h ffc of using a low prmabiliy gosynhic marial on h longiudinal and laral cofficins of disprsion. This would hav is ffc on h conaminans migraion hrough an isoropic, homognous and saurad soil. Th firs sag of his rsarch involvs h sudy of h gosynhic marial and in calculaing h longiudinal and laral cofficins of disprsion for an Iraqi sandy soil by using an xprimnal s-up o simula h procsss. To invsiga h ffc of using a gosynhic marial on h disprsion cofficins, h s was conducd for ach vlociy ha was usd in h xprimnal work and as follows: wihou using h gosynhic marial firs, and by using h gosynhic marial as a bas and a covr for h soil sampl. Th scond sag of his rsarch is inrsd in dvloping a numrical modl abl o simula h conaminans disprsion phnomnon. To solv h wo-dimnsional advciondisprsion quaion, a numrical modl was drivd using h fini lmn mhod. This numrical modl was vrifid by comparing i wih h analyical soluion of on-dimnsional disprsion. To sudy h ffc of using a gosynhic marial on h conaminans disprsion hrough soil, a proposd fild problm is sd. الخالصة يتضمم هذامملبذب درممةذع بميمموذظ ييمموذثيرميمموذ تمموايمذبيممت عبتذ ممثبعذومميةظيوذلبعذيلةليمموذثباالمموذظيمم ذ ة مم ذب ت ممتعذدة ت ممة ذ ب اممث وذثب مضمموذثدة تممة وذتوايماممةذظيمم ذلمترممة ذب يثاممةعذ ممو ذتمممجذ ثرممعشذب ممثب ذ ت ةييمموذث ممد و ذتهممتتذب مريمموذ ب ث ذ هذب درةذدع بميوذب ثبعذب وميةظيوذث ريمةجذ ة م ذب ت متعذب امث وذذث ة م ذب ت متعذب مضموذ تمدموذم ييموذظ بم يموذ ظهذاميقذليت عبتذ هةنذ ت اي ذب ت تعذب اث وذثب مضوذدوت ة ذثبرعذث مفوذ مع ذتموايمذليمت عبتذب مثبعذب وميةظيوذظيم ذ ة ذب يت ةمذفقعذتتذل بمءذب ت ةمجذدوثمشذ كممشذ ك ذيمظوذ هذب يمعذب يت ع وذفوذب لر ذب يوذثكة تو:ذ- ذ دعثهذلي عبتذب ةعشذب ويةظيو ثدةيت عبتذب ةعشذب ويةظيوذكقةظعشذثغاةءذ ي ثلجذب تمدوذ ذ 77

2 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn ذثتهممتتذب مريمموذب اةييمموذ ممهذب درممةذدتامثيمذي مثلجذظممعع ذ ممةعمذظيمم ذرمم ذرممةامشذب ت ممتعذ ي يثاممةع ذث ممعذتممتذليممت عبتذي ممثلجذ ظعع ذ ر ذ ةع وذب ت تعذب ر يوذب ايةاليوذب د هذ و ذل بمءذ قةميموذ ماذب رم ذب يرمم ذب تريييموذب رمةع ذب ت متع ذاملب ثتمتذذفرم ع بميوذتوايمذث ثعذب ةعشذب ويةظيوذظي ذبيت ةمذب يثاةعذعب ذب تمدو ذ ةعذدويت عبتذاميقموذب يةوممذب رمععشذث معذ مم ذب ترقمقذ مهذومروذب ي مثلجذ ذ يمو وذرقييموذ لتمضموذثل م ذ مم ذ ITRODUTIO Gochnical nginring is by now bcoms mor involvd wih problms of polluan migraion hrough soil. This involvmn ariss from h concrn rgarding h conaminaion of soil and h groundwar sysm which rsric or prvn hm from us in h various applicaions whr hy normally play a par in (16). Th lacha from landfills or indusrial was disposal rprsns h main problm of soil and groundwar sysm conaminaion. Many rgulaory auhoriis now rquir h us of linrs o conrol polluans migraion and his ofn involvs sparaing h landfill from h narby ara by using a low prmabiliy marial such as a compacd clay linr () or a gosynhic marial (GS) (17). Gosynhic Marial In gnral, gosynhics ar fabric lik marials mad from polymrs. Goxils and gommbrans ar wo yps of hs marials which includ also ohr yps. Each yp of gosynhics prforms on or mor of h following four major funcions (7) (6) (13) : * Sparaion:- as a sparaion layr. Gosynhics ar usd o prvn adjacn soil layrs or fill marials from inrmixing. Th main us of his funcion is for road and railway consrucions, and hydraulic and landfill nginring, Fig. 1 (7) (14). * Filraion:- as a filr. Whn placd in conac wih soil, hy allow war o pass hrough whil prvn h passag of fin soil paricls. Thir main uss ar as hydraulic nginring marials and drainag sysms, Fig. (7). * Drainag:- as drainag marials whr hy collc liquids or gass and convy hm owards a collcion poin or an oul poin, Fig. 3 (7). 4- Rinforcmn:- Gosynhics ar insalld bnah or bwn soil layrs o improv is mchanical propris, by incrasing h baring capaciy of h soil and minimizing h dformaion, Fig. 4 (7) (14). 77

3 umbr 3 Volum 14 Spmbr 008 Journal of Enginring ذ (1) () (3) (4) Figs. (1,, 3 and 4) Gosynhic marial applicaions (7) (14). Typs of Gosynhic Marials A- Goxil: - Dfind as prmabl fabrics, which ac composily wih soils and rocks. Thy ar producs of xil indusris. Thr ar wo main yps of goxils which ar mad mainly from four yps of synhic polymrs (polyamid, polysr, polyhyln and polypropyln), wovn and non- wovn goxils (7) (6). B- Gommbrans: - Dfind as imprmabl liquid barrirs mad primarily from coninuous polymric shs ha ar flxibl. Gommbran yps may b classifid, according o h yp of polymric marial mad from, as hrmoplasic and hrmos (6). Gosynhics in andfill Enginring In landfill nginring, gosynhic marials ar usd in: - 1- basal linings, and - caps or covrs (14). Basal inings:- Th main objciv of a bas lining is o prvn h scap of conaminans from landfill was ino undrlying soils. Proprly consrucd linr sysms should also allow for h conrolld collcion and rmoval of landfill lacha for subsqun ramns, Fig. 5 (14). Typs of Gosynhic Marials Usd in andfill Bas ining:- 1- Bnofix: - is a ndl- punchd rinforcd gosynhic clay linr (G) ha uss wo goxil layrs o ncapsula a layr of naural sodium bnoni. Th ndl- punchd fibrs ransmi shar forcs hrough h bnoni cor. I is usd as a saling barrir agains liquid and gass in various civil and nvironmnal applicaions (1). 777

4 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn - arbofol: - is a gommbran mad from high dnsiy polyhyln usd o proc and sal h subsoil from h rlas of ponial conaminans (13). 3- Scux: - is a ndl-punchd sapl fibr nonwovn goxil usd for sparaion, filraion, procion and drainag. I is usd in many civil nginring applicaions such as hydraulic nginring, landfill nginring and road consrucion (14). Fig. (5) Basal linings ( 14). andfill apping (ovring) Th main objciv of a cap or covr in landfill nginring is o prvn h inrusion of prcipiaion ino h was and his will rduc and ulimaly sop lacha gnraion, Fig. 6 (6). Typs of Gosynhic Marials Usd in andfill apping:- In addiion o Bnofix and arbofol which ar usd in landfill basal lining, landfill capping includs also: Scudran: - is a hr- dimnsional drainag sysm dsignd o discharg liquids and gass. Th scudran gosynhic drainag sysm consiss of hr individual layrs mad up of h following componns (14) :- 1- a filr which procs h drainag layr from clogging, - a drainag layr which ransmis h war in h filr lvl, and 3- a filr/procion which srvs as a filr or a sparaion layr o h minral componn or h procion layr for h gommbran (HDPE). 77

5 umbr 3 Volum 14 Spmbr 008 Journal of Enginring Fig. (6) andfill capping (14). *TRASPORT THROUGH POROUS MEDIA On of h arlis obsrvaions of h phnomna of ranspor and disprsion in porous mdia is rpord by Slichr in 1905 (3) (4). Th ranspor of conaminans or polluans hrough porous mdia is mainly aribud o h advcion-disprsion procss (4) (9) (0). Advcion Procss:- Th ranspor a h sam vlociy as groundwar of dissolvd solids is calld advciv ranspor (0). Disprsion Procss:- Disprsion rfrs o mixing and sprading causd in par by molcular diffusion and in par by variaions in vlociy (mchanical disprsion) wihin h porous mdia (0). Molcular Diffusion:- is a physical procss which dpnds upon h kinic propris of h fluid molculs and causs mixing a a conac fron bwn wo fluids (5). Mchanical Disprsion:- is causd by h diffrnc in vlociy of flow insid h porous mdia (10). Th amoun of mchanical disprsion occurring in porous mdia dpnds on h physical propris of h soil (siz and shap of h pors) and h absolu magniud of h avrag linar vlociy in porous mdia (5). 77

6 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn * MATHEMATIA MODE Th advcion-disprsion quaion for on dimnsional flow, on dimnsional disprsion hrough homognous, isoropic porous mdia and sady flow is (5) (18) (11) :- D u (1) x x whr:- = concnraion of conaminan a any im () a any disanc (x), D = longiudinal cofficin of disprsion (/T), and u = por or avrag linr vlociy (/T). Th analyical soluion of h govrning diffrnial quaion undr condiions:- (x, 0) =0 (0, ) =o (, ) =0 is givn by (0) (10) : - x u. ux x u. () rfc( ) xp( ) rfc( ) 1 1 O ( D ) ( D ) Th scond rm is vry small compard o h firs on and may b nglcd; hus: x (( ) 1) (3) rfc u 1 O ( D u ) whr:- O : iniial conaminan concnraion (mg/l), x: disanc ravld by h conaminan in h dircion of flow (), : im. By using h invrfc, q. (3) can b convrd ino () :- D x M (( ) 1) (4) u u whr:- M 0.5invrfc( ) (5) O A similar procdur is applid o h sady sa ransvrs disprsion quaion (10) :- u = D (6) x T y An analyical soluion of h govrning diffrnial quaion undr condiions:- c 0 for y= y (y, 0) =o for 0<y<+ (y, 0) =0 for - <y<0 is obaind (10) :- 77

7 umbr 3 Volum 14 Spmbr 008 Journal of Enginring y 1 rf ( ) 1 O D T x ( ) u whr:- y: disanc ravld by h conaminan in h prpndicular dircion of flow (), and D T : ransvrs cofficin of disprsion ( /T). By using h invrfc, q. (7) can b convrd ino () :- y D T M ( ) (8) x ( ) u * EXPERIMETA SIMUATIO SET-UP Th schmaic diagram dpicd in Fig. 7 shows h xprimnal apparaus consrucd by h auhors which was usd in h masurmn of h disribuion of a dilu, sal war racr. To dscrib h sing quipmn usd in h xprimnal work, h following poins ar s:- 1. Th porous mdium box has our dimnsions of ( ) cm. I is consrucd ou of glass shs of 6 mm hick whr h rmovabl uppr covr was consrucd of Prspx glass of 4 mm hick in ordr o giv flxibiliy which is rquird for h i closr o prvn any lakag. Ths shs ar suppord by a sl fram.. Two- galvanizd sl anks of ( ) m, on as a sorag ank and h ohr as a supply consan had ank. Th wo anks ar conncd oghr by a flxibl plasic ub. Th amoun of sal-war racr (soluion) discharg from h firs ank o h scond ank is conrolld by a ap. 3. Floaing quipmn ar usd in ordr o conrol h had of h soluion in h supply consan had ank. 4. Th supply consan had ank provids h porous mdium (soil sampl) wih salwar racr (soluion) by a flxibl plasic ub. A valv is insalld a h inl lin o aid in conrolling flow ino h box. 5. Th oul ub. Sal-War Tracr A soluion of ap war and sodium chlorid wih an iniial concnraion of 1000 mg/l is usd in ordr o drmin h disprsion characrisics of h porous mdium. This racr has bn widly usd by many invsigaors (5) (8) (1) du o:- safy, chapnss and availabiliy, and for no bing affcd by h liquid's dnsiy and viscosiy. oncnraion masurmn is don by using a Toal Dissolvd Solids (TDS) mr, which is a digial dvic ha masurs h concnraion variaions as (mg/). (7) 77

8 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn Fig. (7) Schmaic diagram of h apparaus for h drminaion of h longiudinal and laral disprsion cofficins Soil Sampl and Goxil Marial Soil Sampl An Iraqi sandy soil is usd in h xprimnal work in ordr o invsiga is disprsion characrisics. Th paricl siz disribuion was drmind by mchanical siv analysis. Th uniformiy cofficin for h sd soil is qual o.69. Th discharg vlociy may b drmind by masuring h cofficin of prmabiliy of h soil. A consan had s is usd o drmin h cofficin of prmabiliy, bcaus consan hads ar mor suiabl for 77

9 umbr 3 Volum 14 Spmbr 008 Journal of Enginring coars-graind soils ha hav high cofficins of prmabiliy (14). Th discharg vlociy can b calculad as (9) : - v k i (9) whr:- v : discharg vlociy, k: cofficin of prmabiliy, and i: hydraulic gradin. Goxil Marial Th yp of goxil marial usd in his xprimnal work is Bnofix (GS). Fig. (8) shows phoos of h Bnofix marial. Fig. (8) Phoos of h Bnofix marial Exprimnal Work Procdurs This scion prsns h procdur usd in ordr o obain h daa ncssary for h valuaion of h longiudinal and laral disprsion cofficins for various discharg vlociis. This procdur includs:- 1. Prparing an amoun of h soluion which is usd in h xprimnal work as cid in scion (4-1).. A firs, h soil sampl in h s scion is saurad wih ap war. 3. Th valv conrolling h flow ino h box is opnd a a im qual o zro. A sharp inrfac is crad bwn h sal-war racr and h ap war. Thn, his inrfac will advc and disprs hrough h soil sampl. 4. Th soluion from h oul ub is collcd wih consan im sps in ordr o masur h concnraion. 5. Th sam procdurs ar adopd wic:- Firs wihou using h goxil marial (W.O.M), and Scondly wih h us of h goxil marial (W.M) which lays as a bas and covr marial for h soil sampl insid h porous mdium box. 77

10 /O /O /O /O O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn 6. Th s finishs whn h concnraion rachs h maximum valu ( O ). Th Drminaion of h Disprsion officins Basak and Mury () usd a vry simpl and dirc mhod for drmining (D ) and (D T ), rquiring only on xprimnal poin a any arly im. ongiudinal disprsion cofficins ar drmind from h mporal disribuions of h racr brakhrough curvs and according o Equaion (4). Figs. (9a), (9b) and (9c) rprsn h s rsuls wihou using h goxil marial (w.o.m) whil Figs. (10a), (10b) and (10c) show h s rsuls by using h goxil marial (w.m). According o Basak and Mury () h laral disprsion cofficins can b calculad by using Equaion (8). Tabl (1) summarizs h disprsion xprimnal s rsuls Ts (1-1) W.O.M 0.60 Ts (1-) W.M Tim (min) Tim (min) 1.00 Fig. (9a) longiudinal brakhrough curv for v= cm/min Fig. (10a) longiudinal brakhrough curv for v=0.584 cm/min Ts (-) W.M 0.40 Ts (-1) W.O.M Tim (min) Fig. (9b) longiudinal brakhrough curv for v= 0.70 cm/min Tim (min) Fig. (10b) longiudinal brakhrough curv for v= 0.70 cm/min. 77

11 /O /O umbr 3 Volum 14 Spmbr 008 Journal of Enginring Ts (3-) W.M 0.40 Ts (3-1) W.O.M Tim (min) Fig. (9c) longiudinal brakhrough curv for v= 0.85 cm/min Tim (min) Fig. (10c) longiudinal brakhrough curv for v= 0.85 cm/min. Ts o. 1 3 Tabl (1) Disprsion xprimnal s rsuls Typ of Discharg Tim Ts vlociy whn m /min m / min (cm/ min) /O =0.1 (min) W.O.M W.M W.O.M W.M W.O.M W.M D D T * FIITE EEMET SOUTIO OF THE ADVETIO-DISPERSIO EQUATIO Th following fini lmn discrizaion of h diffrnial quaion dpnds on h prvious work of Wang and Andrson (0). Th advcion-disprsion quaion for on dimnsional flow and wo dimnsional disprsion is wrin as: D DT vx (10) x y x Assuming a rial funcion of h form which shows ha h rial soluion (funcion) wihin an lmn is an inrpolaion of h nodal valus (0) () : ODE ( ) ( x, y) (11) 1 whr: - = indicas summaion, = lmn, 7

12 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn 7 = nodal basis (shap) funcions, and = 1,, ODE, whr h lar is h oal numbr of nods pr lmn. Applying h wighd rsidual mhod wih Galrkin's mhod o quaion (10) yilds ino h following funcional (0) : - 0 ), ( ) ( y x x T D d d y x X v Y D X D (1) Th scond spaial drivaiv rms ar ingrad by pars and h ingraion ovr h problm domain is don lmn by lmn (0) : - d n Y D n X D dxdy X Y Y D X X D y T x x T ) ( ) ( _ (13) whr: - = h boundary of h problm domain, x n y n, = h componns of a uni vcor normal o h boundary, and = h ingraion variabl rprsning disanc along h boundary in counrclockwis sns. Th sysm of quaions rprsnd by q. (13) can b wrin in marix noaion in h form: f P U G (14) = h column marix of nodal concnraion, = h column marix of h im drivaiv of nodal concnraion, G, U, P = squar cofficin marics corrsponding o individual rms in h ingral on h lf hand sid of q. (13), and f = column marix corrsponding o h boundary ingral on h righ hand sid of Equaion (5-5). Whr: - dxdy Y Y D X X D G T a a b b ) ( 1 1,1 (15) dxdy P a a b b 1,1 (16) dxdy X U a a b b x 1 _ 1, (17)

13 umbr 3 Volum 14 Spmbr 008 Journal of Enginring Soluion of h Marix Diffrnial Equaion Eq.(14) is a firs-ordr marix diffrnial quaion. To solv i, a fini diffrnc approximaion is mad for h im drivaiv in marix noaion (0) : - 1 whr: - : ngh of im sp, : oncnraion valu a h nw im, and : oncnraion valu a h old im. ow, i has o b kp in mind ha: (18) which is h valu of h concnraion a nod () a im (). Thus, h im drivaiv approximaion a a paricular nod is: whr: : chang in nodal concnraion wih rspc o im. If {} is approximad a h nw im (+ ), hn h soluion of Equaion (14) is said o b fully implici and is givn by: - f G U P 1 Eq. (0) can b rarrangd o hav all h concnraions a h old im o b on h righhand sid and all h nw im o b on h lf-hand sid:- G U P P f (0) 1 1 (1) (19) Th Quadrilaral Elmn I is a wo-dimnsional lmn known as h muliplx lmn. Th quadrilaral lmns wih igh-nods ar rfrrd o as h quadraic lmns bcaus h inrpolaion (shap) funcions ar quadraic along lins of consan ζ or consan η as dpicd in Fig.11 (19) 77

14 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn (a) Fig. (11) (a) Quadraic lmn (b) ocal coordina sysm (15) (b) * OMPUTER PROGRAM A compur program prsnd by Wang and Andrson (0) which solvs h advciondisprsion quaion by using on-dimnsional fini lmns is xndd hrin as o includ wo dimnsional muliplx ons. All ncssary marix changs hav bn don in h program according o Eqs. (19-1). Th program has bn wrin in FORTRA 77 languag, and h compilr usd is FORTRA Powr Saion 04- Microsof Dvlopr Sudio. Th program has bn modifid by h auhors in ordr o carry ou h rquird compuaions. Vrificaion Exampl Th numrical modl has bn sd o drmin is validiy. Th vrificaion was don by comparing h fini lmn rsuls wih a on-dimnsional analyical soluion for Eq. 1. Th analyical soluion for Eq. 1 is prsnd in Eq. 3. For h vrificaion of h program, inpu paramrs ar chosn from h rfrnc of Wang and Andrson (0). A uniform squar lmn of siz of (5 5) m is usd o discriz h rgion. To idnify h cas solvd, h msh Pcl numbr is dfind as (1) :- P v whr:- x x () D v x : discharg vlociy, and x : ravld disanc. Th ouran numbr, r, which is rsponsibl for h im sp valuaion is known as (1) : vx r (3) x whr:- : ravld im. 7

15 /o umbr 3 Volum 14 Spmbr 008 Journal of Enginring Inpu daa for Eqs. () and (3) ar (0) :- v x = 0.1 m/day, x = 5 m, D = 1.0 m /day, and = 10.0 days. Th soluion rsuls in:- P 0.5, and r 0. Wang and Andrson (0) found ha h fini lmn soluion prdics h solu fron ravl somwha fasr han h analyical soluion dos. umrical rsuls ar obaind from h dvlopd program and compard wih h analyical soluion program. Fig. (1) shows his comparison and i can b sn ha h dvlopd fini lmn program rsuls ar in agrmn wih h rsuls obaind by Wang and Andrson (0) Fini Elmn 0.80 Analyical Soluion Disanc (m) Fig. (1) omparison curvs of h concnraion profil a =400 days, for P=0.5 * FIED PROBEM A proposd fild problm is chosn for h illusraion of h ffc of using a gosynhic marial on h procss of conaminans migraion hrough porous mdia. Fig. (13) shows h fini lmn msh and dimnsions of h slcd problm. Two yps of ffcs can b 7

16 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn obaind whn using gosynhic marials on h procss of conaminan's migraion. Ths ffcs ar: - Th dcras of h longiudinal cofficin of disprsion, and Th dcras in h volum of soluion lacha from h sourc of polluion according o h low prmabiliy of h gosynhic marial. According o h ffcs dscribd abov, wo fild cass ar adopd: - 1. wihou using h gosynhic marial (Fig. 14) : - vlociy= v =.5 m/hr., D = 10.0 m /hr D T = 0. m /hr, im = 10.0 hr im inrval = Δ = 0.5 hr, iniial concnraion= O = 0000 mg/l. wih h us of h gosynhic marial (Fig. 15): - vlociy= v =.5 m/hr., D =.5 m /hr D T = 0. m /hr, im = 10.0 hr im inrval = Δ = 0.5 hr, iniial concnraion= O = 1000 mg/l. Using h abov daa, h rsuls of h fini lmn algorihm ar prsnd in: Figs. (14) and (15) which show h polluan concnraion as mporal quiconcnraion curvs. Fig. (13) Fini Elmn Msh of h Fild Problm 7

17 umbr 3 Volum 14 Spmbr 008 Journal of Enginring Fig. (14) Equi-concnraion curv Fig. (15) Equi-concnraion curv OUSIOS Th following, conclusions ar drawn from boh h xprimnal and numrical modls:- - In h vrificaion of h numrical modl, a good agrmn is obaind bwn h fini lmn algorihm dvlopd program and h program prsnd by Wang and Andrson (0). In 7

18 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn boh analyss, i was found ha h solu in fini lmn soluions ravld fasr han whn using h analyical ons. - Incrasing h valu of discharg vlociy during h xprimnal run incrass h valu of longiudinal and laral cofficins of disprsion. - Incrasing h valu of discharg vlociy during h xprimnal run dcrass h im rquird o rach h 10% of h oal concnraion. - A significan ffc is obaind by h us of h gosynhic marial rprsnd by h dcras in h longiudinal cofficin of disprsion many ims and a rducion in h amoun of volum of lacha from h sourc of polluion. Ths ffcs rsul in dcrasing h conaminans migraion hrough h porous mdia and rducing h disancs ravld by hm. - According o h hory adopd o calcula h laral cofficin of disprsion, hr is no ffc obaind from h us of a gosynhic marial on h valu of h laral cofficin of disprsion. AKOWEDGMETS Th auhors wish o hank h xpor assisan of au Fasrchnic Gmbh & o. Ms Kirsn Hohmir for hr hlp in providing h rlvan informaion abou h gosynhic marials. Apprciaion is also xndd o Mr. Bassam al-aa for his hlp in providing h ncssary gosynhic marials for his rsarch work from Grmany. REFEREES * Al-Rawi, M.A., "Exprimnal and umrical Invsigaions of Disprsion and Transpor in an Iraqi Soil", M.Sc. Thsis, Dparmn of Environmnal Enginring, Univrsiy of Baghdad, 00. * Basak, P., and Mury, V., "Drminaion of Hydrodynamic Disprsion officins Using "invrfc"", Journal of Hydrology, Volum.41, pp (43-48), * Bar, J., "Som Exprimns in Disprsion", Journal of Gophysical Rsarch, Volum 66, o. 8, pp ( ), Augus * Bar, J. and Vrruij, A., "Modling Groundwar Flow and Polluion", D. Ridl Publishing ompany, * Bruch, J.., and Sr, R.., "Two-Dimnsional Disprsion", Journal of Saniary Enginring Division, ASE, Volum 93, o. SA6, pp (43-48), * Das, B.M., "Principls of Gochnical Enginring", Wadsworh Group, 00. * E-Shabrawi "Inroducory cours on goxils and rlad marials", Kuwai Univrsiy, March * Faah, Q.., "Invsigaion and Vrificaion of Modl for h Disprsion officin Tnsor in Flow hrough Anisoropic Porous Mdia wih Applicaion o Flow From Rcharg Wll Through a onfind Aquifr", Ph.D. Thsis, Dparmn of ivil and Environmnal Enginring, Univrsiy of Wisconsin, Madison, Wisconsin, * Frz, R.A., and hrry, J.A., Groundwar, Prnic-Hall, Inc., Englwood liffs,.j., * Frid, Jan, J., "Groundwar Polluion", Elsvir Scinific Publishing ompany, * Hoops, J.A., and Harlman, D.R.F., "Was War Rcharg and Disprsion in Porous Mdia", Journal of Hydraulic Division, ASE, Volum 93, o. HY5, pp (51-71), * AUE Fasrchnic Gmbh & o., "Slop dsign wih Bnofix (GS)", o.7, saus 04/003. * AUE Fasrchnic Gmbh & o., "Hydraulic Enginring", saus 06/003. * AUE Fasrchnic Gmbh & o., "andfill Enginring", saus 05/004. 7

19 umbr 3 Volum 14 Spmbr 008 Journal of Enginring * ikishkov, G.P., Inroducion o h Fini Elmn Mhod, cur os. Univrsiy of Aizu, Japan, 004. * Row and Bookr, "Two-Dimnsional Polluan Migraion in Soils of Fini Dph", anadian Gochnical Journal, Volum, o.4, * Row and Bookr, "1-D Polluion Migraion in Soils in Fini Dph", Journal of Gochnical Enginring, Volum 111, o.4, April, * Schidggr, A.E., "Gnral Thory of Disprsion in Porous Mdia", Journal of Gophysical Rsarch, Volum 66, o.10, pp ( ), * Sgrlind,.J., "Applid Fini Elmn Analysis", John Wily and Sons, w York, * Wang, H.F., and Andrson, M.P., Inroducion o Groundwar Modling, Fini Diffrnc and Fini Elmn Mhods, W.H. Frman and ompany, w York, 198. * Yh, G.T., "An Orhogonal-Upsram Fini Elmn Approach o Modling Aquifr onaminan Transpor", War Rsourc Rsarch, Volum, o.6, pp. (95-964), * Zinkiwicz, O.., and Morgan, K., " Fini Elmns and Approximaions", John Wily and Sons, w York, 198. IST OF SYMBOS O r D DT GS HDPE i k u W.M W.O.M x y h mass concnraion wih rspc o h fluid. compacd clay linr. iniial conaminan concnraion. ouran numbr. longiudinal cofficin of disprsion. ransvrs or laral cofficin of disprsion. lmn. gosynhic marial. high dnsiy polyhyln. hydraulic gradin. cofficin of prmabiliy. numbr of nod. im. por or avrag linr vlociy. wih h us of gosynhic marial. wihou using h gosynhic marial. disanc ravld by h conaminan in h dircion of flow. disanc ravld by h conaminan in h prpndicular dircion of flow. indicas summaion. 7

20 O. al-farouk Goxil and Gommbran Usag M. M. Jasim in an Iraqi Sandy Gonvironmn n x, n y nodal basis (shap) funcions. h boundary of h problm domain. h componns of a uni vcor normal o h boundary. h ingraion variabl rprsning disanc along h boundary in G U P f x P, ounrclockwis sns. h column marix of nodal concnraion. h column marix of h im drivaiv of nodal concnraion. squar cofficin marix. squar cofficin marix. squar cofficin marix. column marix corrsponding o h boundary ingral on h righ hand sid of Equaion (5-5). lngh of im. concnraion valu a h nw im. concnraion valu a h old im. chang in nodal concnraion wih rspc o im. ravld disanc. Pcl numbr. h local coordinas. 7