One Dimensional Non-linear Consolidation of Unsaturated Fine Grained Soils

Transcription

1 World Appled Senes Journal 6 (10): , 009 ISSN IDOSI Publaons, 009 One Dmensonal Non-lnear Consoldaon of Unsauraed Fne Graned Sols M. A. Teknsoy, T. Taskran and C. Kayadelen Deparmen of Cv. Engneerng, Çukurova Unversy, 01330, Adana, Turkey Absra: In he onen of hs sudy, non-lnear onsoldaon behavor of unsauraed sols as nvesgaed. In hs respe a non lnear dfferenal equaon for onsoldaon has been proposed. Ths proposed dfferenal equaon and s soluons enlghen boh he dffusve haraerss and he me rae of selemen of sols. Besdes, hs sudy also enables o perform he mar suon alulaon hh s he one of he mos mporan parameer of unsauraed sols. To ypes of unsauraed onsoldaon es, onsan aer onen es and onrolled mar suon es ere arred ou, respevely. Theoreal and expermenal resuls ere ompared and as found ha hey are n lose agreemen h eah oher. I as also observed ha he proposed mehod an be appled o he sauraed sols. Key ords: Non-lnear onsoldaon unsauraed onsoldaon mar suon INTRODUCTION When a onsoldaon es s arred ou n an approxmaely onsan emperaure ondons n a laboraory, an be assumed ha an sohermal ondon s vald for hs es and for aer flo n a sol sample [1]. Addonally, f he sauraon degree of a sol sample dereases o 95%, ar phase n he sample gans onnuy [, 3]. Hoever, every sol has a ral aer onen hh remans onsan beause of unhanged egh of aer. If a ohesve and granular sol have sauraon degrees of 85% and 0%, respevely, beomes que dfful o ge ou any aer from he sol sample n a normal ondon [5]. Bu n hs ase, hle he volume hange omes no ve for a loadng sep, he gravaonal aer onen remans onsan. In oher ords, he gravaonal aer onen has a eran value n all pressure seps n an oedomeer es. Ths peulary an be seen n he follong defnon. W = (1) W d n hh, s he gravaonal aer onen of a sol sample, W s he egh of aer and W d s he egh of sol grans, In a onsoldaon es, he man problem s o fnd he hange n volume of a sol spemen n an oedomeer for a loadng sep. Therefore, he volumer aer onen beomes mporan for an unsauraed sol spemen. Is defnon has been gven n he follong equaly [1, ]. V θ= () V here, V s he onsan value of aer volume and V s he varable volume of a sol spemen. In addon, f he value of oeffen of volume hange m v s aeped as a onsan for a loadng sep, he onsoldaon dfferenal equaon an be gven as [5]; u 1 K u u σ + = v m γ v here, v s he oeffen of onsoldaon hh has been defned as v = K/(m v γ ); m v s he oeffen of volume hange, u s he pore pressure and σ s he oal pressure hh has been loaded on he sol spemen n an oedomeer. Applaon of load ono a sol spemen resuls selemen. Ths auses o hange he vod sruure and apllary fores a on he sol aer and a he same me, hanges he aer and ar flo n a sample. If he sauraon degree of a sol sample s belo 95%, an generally be assumed ha he sem-sauraed ondon s vald. As a resul, he aer flo n an unsauraed sol s an sohermal, apllary, barorop and non-lnear flo [6]. Teragh (1943) has solved he onsoldaon problem assumng ouer effe σ, hydraul onduvy and he oeffen of volume hange are onsan for a loadng sep. We use hs soluon n our onsoldaon ess [5]. Correspondng Auhor: Dr. C. Kayadelen, Deparmen of Cv. Engneerng, KSU, 01330, Kahramanmaras, Turkey 1 (3)

2 World Appl. S. J., 6 (10): , 009 Under he aforemenoned reales, Fredlund and Hassan (1979) gave he follong non-lnear dfferenal equaon of onsoldaon for unsauraed sols [3]. u u K u m = a ( m m 1k ) + γ 1 K u K + + γ n hh, m 1k s he oeffen of aer volume hange h respe o a hange n he ne normal sress; m s he oeffen of aer volume hange h respe o a hange n mar suon; K s he hydraul onduvy, u s pore aer-pressure and u a s pore ar pressure. Alhough he gven equaly s a non-lnear equaon, he oeffens of volume hange have been assumed as onsan parameers. Bu he expermenal resuls sho ha hey have varably h respe o volumer aer onen and hey are funons of sauraon degree. For hs reason, he menoned parameers should be aken n queson and hey should also be gven under dervaves. So onsoldaon dfferenal equaon an be gven as shon belo [10]. u u = v K = v m v γ (4) (5a) (5b) here, u s he oal pore pressure, v s he oeffen of onsoldaon as n he lassal heory, m v s he oeffen of volume hange, K s he hydraul onduvy and γ s he un egh of aer. In addon, he lassal soluon o he onsoldaon dfferenal equaon does no gve any nformaon abou he me rae of selemen. Therefore, ll be very useful o ake he phenomenon no onsderaon by hs pon of ve. The man purpose of hs nvesgaon s o gve possble soluons o Eq. 5a for an unsauraed sol. Seondly, s o sho he valdy of he proposed approxmaons by ay of expermenal proedures. EXPERIMENTAL STUDIES Sol properes: One ype of sol has been used n hs sudy. Index properes of he sol are presened n Table 1: Index properes of he resdual sol Lqud Lm (%) 77 Plas Lm (%) 3 Plasy Index 46 Passng from 00No (%) 95 <0.00 mm. (%) 58 Collod onan <0.001 mm (%) 55 Avy 0.79 Volumer Shrnkage (%) 9,50 Gran Densy,50 Group Symbol CH Table 1. Ths sol has lay parles of 65% and sly par of %30. For he frs group of expermens, reonsued sol samples are prepared. For hs purpose, he sol sample has been dred and seved by he seve of No 40. The passng sol parles have been eed by some amoun of pure aer. Weng proedure gves a aer onen hh s 1.5 mes larger han lqud lm. Ths proess gves a pase. Ths pase has been remoulded under a pressure of 00 kpa. A he end of s selemen, es spemens for onsoldaon are prepared. Axs ranslaon ehnque, hh s relaed o he unsauraed ondons, has been appled o he prepared spemens [3] The seond group of es s also performed on he same ype of sol. Good qualy of undsurbed sol samples ere olleed from he se. Ths resdual layey sol from a layer hh has a hkness of 1-9 m on a basal rok bed. X-ray dffraon analyses gave he follong peulares: ) Domnan sruure of he sol s a mxure of symee and hlorde mnerals. ) Seondary mnerals suh as Quar, Cale and Pheldspa ake plae. Ths ype of layey sol has a sell poenal beause of he mneral ngredens. Consan volume sell es resuls gave a sell pressure of Kgf/m and s free sell perenage s %. TESTING PROGRAM Consoldaon es h onrolled mar suon: Unsauraed sol ess are generally performed under onrollng mar suon [8, 3, 4]. In order o onrol he mar suon n sol spemens, some spef ehnques lke osmo, relave humdy and axs ranslaon ehnque are used for unsauraed sol ess. The axs ranslaon ehnque s mosly preferred due o beng easer and applable. In hs ehnque, he

3 World Appl. S. J., 6 (10): , Fg. 1: Modfed onsoldaon es apparaus for esng unsauraed sols. 1-Volume hange ransduer; -Consan pressure deve ; 3-Ar pressure regulaor; 4-Ar ompressor; 5-Dffused ar volume ndaor (DAVI); 6- Veral dsplaemen ransduer; 7-Pore-aer pressure ransduer; 8-Hgh ar enry eram ds (1500 kpa); 9-Sol; 10-Load ell; 11-Daa logger pore-ar pressure s arfally rased above amospher pressure o nrease he pore aer pressure by he same amoun o posve values so ha he avaons rsk of aer n he measurng sysem s prevened [4]. For hs sudy, a speal desgned oedomeer ell as bul o perform he unsauraed onsoldaon ess and o measure he laeral sress. The oedomeer ell s apable of onrollng as ell as measurng pore ar and pore aer pressure n he sol spemen ndependenly by usng axs ranslaon ehnque. Pore-aer pressure as measured and onrolled hrough a sauraed eram dsk havng 1500 kpa of ar enry value negraed a he base of he spemen. The spral grooved aer omparmen as esablshed n he pedesal. The spral grooves n he aer omparmen ork as aer hannels for flushng ar bubbles ha may have aumulaed as resuls of dffuson. The eram ds as ghly sealed no he pedesal by usng epoxy resn along s perphery. In hs ay he leakage of he ar appled no he sol spemens as prevened. The aer onen varaon as measured by means of volume hange ransduer onneed o aer omparmen belo he hgh ar enry eram ds. The 3 volume hange ransduer allos onnuous eleral monorng of volume hange of pore aer hange h 0.01 m 3 sensvy. Dffused ar volume hanges ere measured va Dffused Ar Volume Indaor (DAVI) suggesed by Fredlund and Rahardjo (1993). The sysem arrangemen and speal desgned onsoldaon ell for hs researh s shon n Fg. 1. The sysem nludes a speal desgned onsoldaon ell, a pressure-volume onroller, plumpng arrangemens, DAVI and daa aquson sysem. The sysem enables ompuer-onrolled sress an gve real-me graphal oupus. The base plae of onsoldaon ell has o dranage valves. One of he valves onneed o volume hange ransduer served o measure and onrol he pore aer pressure and aer onen hange durng he ess. Anoher valve as used as flushng sysem onneng dffused ar volume ndaor. In he expermens, he ar bubbles aumulaed n he aer omparmen due o dffuson as perodally removed by flushng and he measuremens of pore volume hange ere orreed. Consan aer onen onsoldaon ess: A ha par of expermenal sudy, onsan aer onen

4 World Appl. S. J., 6 (10): , 009 n an unsauraed sol hh s he sum of mar poenal, φ m, pneuma poenal, φ p and he poenal of soluon, φ sol s value hanges h he onenraon of hemals n a sol sample. U =φ m +φ p +φ sol (6) Ths oal poenal an be gven as he sum of pore pressure poenal, ψ sp and gravaonal poenal, ψ g, as n U =ψ +ψ (7) sp g Fg. : Consoldaon ell and meall porous sone onsoldaon ess ere arred ou. Sne, he mar suon of sol s no onrolled durng he loadng seps; hs ype of onsoldaon es s more represenave for he real n-su ompressons. In order o perform he es, a onsoldaon ell hh an gve opporuny o see he aer ha omes ou of spemen, as desgned. For hs purpose, a aer omparmen o olle and a dranage hannel o onvey aer s onsued belo he boom porous sone. On he oher hand, s knon ha he onvenonal ype of porous sone an absorb an amoun of aer from he sol spemen. Sne, durng he onsan aer onen onsoldaon ess, aer onen of sol should be kep onsan, herefore hs suaon should be prevened. For hs am, a meall dsk havng 1mm dameer and 16 number/m of holes o perms passage of aer s manufaured. Sne he holes are opened only a boom porous sone, one-ay dranage ondon s vald. Meall porous sone and onsoldaon ell s seen a Fg.. In order o preserve humdy of sol spemen durng he es, onsoldaon ell as overed h a e loh holly and heked h some nervals. Appled loadng seps ere kpa In hs sudy kpa of loadng seps as evaluaed. Measuremens a he begnnng and end of he es ere shoed ha here s no sgnfan hange n he aer onen of spemen. No ex of aer s observed durng he es. Theoreal prelmnares: If e noe he expressons gven n Eq. 5a and 5b, v and u are under dervave and hey have varably. Sne v has a varaon, K and m v are also a funon of and. Hoever, he researhes shoed ha K and m v are funons of pore aer pressure beause of aer haraers urve hh hanges h respe o aer onen [1]. Toal poenal auses apllary flo 4 If hese values are dvded by he un egh of aer, oal head s obaned as shon belo. u= h+ (8) here h s he pressure head and represens he gravaonal head hh s alled as geomer head. The subsuon of u no Eq. 5a gves he follong non-lnear dfferenal equaon of onsoldaon [10]. h h = v v v = = (9a) (9b) n hh v s he me rae of selemen. Ths gven expresson s a non-lnear paral dfferenal equaon of dffuson ype. The boundary ondons of he problem are as n he follongs [5, 9]. p h=, = h,0 = (10a) γ ( ) ( ) = ( ) = ( ) = (10b) h, h, 0 f here and f are nal and fnal heghs of a sol sample, respevely. The problem should be onsdered n an unseady sae ondon. Therefore, n order o solve he equaon he follong ransforms an be performed [6, 10, 11] h h = f ( λ) and φ( λ ) = dh and λ= (11) 1 v h Aordng o hs ransform, he gven dfferenal equaon s onvered no he lnear form.

5 World Appl. S. J., 6 (10): , 009 φ = φ v d (1) In hs ase, dervave of φ h respe o λ s obaned as: d d dh = = (17) h h The frs negral gves u = /and he resul of 1 he seond negral s u =(h-h ) The exa soluon s φ = λ Ae λ 4 v (13) ( ) h h C C = 1 + (18a) here A s an negraon onsan. Consderng Eq. 11 and subsung Eq. 13 no Eq. 9a and akng no aoun he boundary ondons gven n Eq. 10a and Eq. 10b, he follong soluon has been obaned for Eq. 9a C h h = C + (18b) 1 In hs ase he boundary ondons of he problem an be onvered no he follong form. x= v h x = 1 e dx H (14) π 0 h(,) = h(,0) = h (,) = h( f, ) = 0 (19a) (19b) Where H= P/γ and P s a pressure dfferene for a loadng sep. The found expresson s n negral form hh s alled omplemenary error funon. In order o elmnae he negral form and o gve a more approprae soluon, he ransform h=f(γ) and γ= / an be used agan. In hs ase, he follong equaly an be ren (1, 10). v h h 1 = dh (15a) The subsuon hs resul no Eq. 9a gves h h dh 1 = dh d h (15b) Applaon of Lebn s rule for he rgh sde of hs equaly yelds o [1] n hh and f sho nal and fnal heghs of a sample, respevely and s he me of onsoldaon. The soluon of he problem s h= h 1 f (0) If e go bak o Eq. 15a, he value of v an be gven as n: 1 v = dh + C h (1) n hh C s negraon onsan. Neessary dervaves are aken and onsderng he veloy of pore aer s v = v / hh s equal o ero a he end of selemen. (v ( f, ) = 0), he negraon onsan C s obaned as C = -4h f /3. Consequenly, he expressons for pore aer veloy and for he oeffen of onsoldaon are obaned. h 1 h h h = dh + h vv= f 1 f (a) h h h h = v1 = f (b) h h + = h h ( ) Auxlary sysem of hs paral df eq. s (16) 5 Dranage pah has an mporan role on v and v In he presen soluon here exss o ays dranage. Therefore, H d =/ should be subsued no expressons.

6 World Appl. S. J., 6 (10): , 009 H = f d v f 1 (3a) H d v = 1 3 (6a) H d v1 = 1 3 f (3b) H = d v 1 (6b) here H d shos he lengh of dranage pah hh hanges h he hegh of a sol sample. In addon, v s no relaed h he selemen bu expresses he dffusve propery of pore aer and depends upon he pore geomery. The neessary dervaves of Eq. 0 and Eq. b sasfy he gven nonlnear dfferenal equaon n Eq. 9a. As a resul, hey are soluons o he dfferenal equaon and hey are also funons of and. On he oher hand, effeve sresses have mporan role on he selemens [10]. These sresses are drely relaed o he nal hegh of a sample. Effeve sress hanges are equal o he pore aer pressure hanges, as ell. The hange n he effeve sresses affes me rae of selemen, v, of an unsauraed sol sample n an oedomeer. Therefore, he follong equales sasfy he non-lnear onsoldaon df. Eq. h= h 1 v = v = 1 (4a) (4b) (4) I s possble o ge some nformaon abou he me rae of selemen v of a sol by usng Eq. 4. In addon he oeffen of volume hange, m v s also relaed o he effeve sress hanges (7) and an be gven by a funon of. In hs ase, hydraul onduvy an be expressed by ay of v and m v γ H d K= m v vγ = 1 1 q 3 (7) Where γ s he un egh of aer (F/L 3 ) and q s he pressure dfferene n a loadng sep (F/L ). Agan, f e examne Eq. 0, he pore pressure goes o ero hen a sample has a hegh of f and =. For he same me, pore pressure gven n Eq. 4a does no yeld o ero beause of he exess pressure There exs unbalaned posve pressures hh ause o he seondary onsoldaon. In order o fnd he end of he prmary onsoldaon, Eq. 4a should be equaed no ero. Thus, he me of prmary onsoldaon s obaned. 4 f = (8) Ths found me an be aeped as he me of prmary onsoldaon and s value s used n he ompuaons. Afer hs pon, posve pressures ause some resdual small selemens of a sol sample. As menoned prevously, selemens depend upon also he hange n mar suon. Sne he oeffen of volume hange has been defned n erms of selemen and pressure, s value s also relaed o he mar suon hanges n a loadng sep. Therefore, no f e onsder he defnon of he oeffen of volume hange, an be equaed o Eq. 5b. for he hange of mar suon. Consequenly, he follongs an be ren m = = (5a) v q q d 1 mv = = 1 dq q (9a) 1 mv = 1 q (5b) dq d = q ( ) (9b) n hh q s he onsan pressure dfferene for a loadng sep. No f e reonsder he problem n he sense of dranage pah, he gven above equales an be ren as n he follongs 6 In addon, hen = f, mar suon dsspaes and akes a value of q= p a he end of a loadng sep. In hs ase, he negraon of Eq. 9b gves an expresson of q hh saes suon pressure.

7 World Appl. S. J., 6 (10): , f q = p f 1 (30) 0,005 0,004 0,003 y = -0,0701x + 1,333 R = 1 Ths quany refles behavor of hange n pore aer. Whle he gravaonal aer onen remans onsan, he value of volumer aer onen nreases beause of volume reduon. Degree of sauraon approahes o one a he end of a pressure sep. As a resul, mar suon depends upon volumer aer onen and apllary flo n a sample. RESULTS AND DISCUSSIONS Axs-Translaon Tehnque has been appled o he sol (prepared as reonsued) n frs group of expermen. In hs ehnque, mar suon remans onsan for all pressure seps. The onsoldaon es resuls for mar suon of 00 kpa have been gven n Table. Ne normal pressure and mar suon ause o he selemen of a sample and hey also ause o hange n aer onen of a sol spemen. In addon, he oeffen of a hydraul onduvy an vary sgnfanly h respe o mar suon, hh n urn an vary n he -dreon [3]. The values of selemen and her orrespondng mes have been summared n Table 3. Sne he applaon of mar suon (u a -u ) auses o hange n aer onen, hydraul onduvy and he volumer ompressbly hange n magnude. Consequenly, he applaon of he axs ranslaon ehnque does no refle he real suaon of onsoldaon ondons of an unsauraed sol. The mehod supples a aer haraers urve. Therefore, he seond ype of onsoldaon es (onsan aer onen) as arred ou. In hs proedure, he preservaon of evaporaon of sol aer s an mporan faor for a onsoldaon es. In order o preven he evaporaon, oedomeer ell should be overed by a pee of eed lohe. As anoher resul, he fnal selemen of an unsauraed sol s smaller han ha of a sauraed sample. In addon, he onsoldaon me for 100% of selemen s larger, as ell. The onsoldaon es resuls for he onsan aer onen onsoldaon es s gven n Table 4. In hs proess, he resuls for loadng sep beeen 175 kpa and 50 kpa have been abulaed n Table 5. In all oedomeer ess, an approprae duraon for a loadng sep has been deded as 4 hours. Ths fnal me of 0,00 0,001 0,000 0,006 0,004 0,00 0,000 18,94 18,95 18,95 18,96 18,96 18,97 18,97 18,98 18,98 (mm) (a) y = 0,0003Ln(x) + 0,001 R = 0, (mn) (b) Fg. 3: Change of he oeffen of volume hange ,5 4 3,5 3,5 Expermenal Compued 18,94 18,95 18,96 18,97 18,98 Hegh of sample, (), mm Fg. 4: Comparson of ompued values of m v h expermenal ounerpars onsoldaon may represen he fnal selemen of a sample for a pressure nremen. Usng Eq. 3a, Eq. 5b and Eq. 6b, he ompuaonal values of pore aer veloy, he oeffen of volume harge and he me rae of selemen are ompared h he es resuls n Fg As an be seen he ompued heoreal values are very lose o he approxmae expermenal values. Ths lose agreemen shos he valdy of he soluon for he unsauraed onsoldaon. These ompuaons also 7

8 World Appl. S. J., 6 (10): , 009 Table : Resuls of he onsoldaon es for mar suon of 00 kpa Ne Normal Pressure Vod Rao Waer Conen Sauraon Degree Selemen σ (kpa) e = Vv/Vs (%) = W/Ws (%) Sr (%) (mm) Mar Suon: u a u = 00 kpa; Dameer of he Sample: D= 75 mm; Hegh of he Sample: H 0 = 48 mm; Gran Densy:γ s =.50 grf/m 3 ; Waer Conen of he Sample: W 0 = 5,9 % Table 3: Tes resuls of onrolled suon onsoldaon for he ne normal sress of 00 kpa Tme Selemen Hegh of he sample Tme Selemen Hegh of he sample (mn) (mm) (mm) (mn) (mm) (mm) Mar suon: u a u = 00 kpa, Hegh of he sample: H o = mm, Ne normal sress: σ - u a = 00 kpa Table 4: Consoldaon resuls for he onsan aer onen es Loadng Sep Selemen Hegh of he sample (kpa) H (mm) (mm) Hegh of he sample: 0 = 19.0 mm, Dameer of he sample: D= 50 mm, Gravaonal aer on. = 3.6%, Gravaonal aer on. f = 3.3% supply addonal nformaon suh as me rae of selemen, pore aer dffusvy and he pore pressure hanges. In hs respe, he values gven n Table 6 have been ompued. If e examne he values n Table 6, here exs dfferen quanes for he oeffen of onsoldaon ,98 18,97 18,96 Expermenal Compued Hegh of sample, (), mm 18,95 18,94 Fg. 5: Comparson of ompued values of v 1 h expermenal ounerpars and he pressure hanges. In hs Table, he ompued values of v from Eq. 3b mean dffusve propery of pore aer and ar phase. Bu he values obaned from Eq. 6a sho he relaonshp beeen selemen and suon pressures. The same peulary an also be observed from he pressure hanges. The las olumn

9 World Appl. S. J., 6 (10): , 009 Table 5: Tes resul for loadng sep of kpa Tme Selemen Hegh of Sample Coeffen of Volume Change Approx. Pore Waer VeloyApprox. Tme Rae of Selemen T (mn) H (mm) (mm) m v = / q (m /kgf)(*10 3 ) v l = / (m/mn)(*10 3 ) v = / (m/mn)(*10 5 ) Table 6: Compuaonal resuls of he loadng sep Hegh of Sample v from Eq. 3b. v from Eq. 6a. Pressure Head from Eq.0 Pressure Head from Eq.4.a (mm) v1 (m /mn)(*10 3 ) v (m /mn)(*10 3 ) h 1 (m) h (m/se) f = m, = 1440 mn, 4 4 f = 1440 = = mn ,98 18,97 18,96 Hegh of sample, (), mm Expermenal Compued 18,95 Fg. 6: Comparson of ompued values of v h expermenal ounerpars 18,94 has a negave value a he las lne hh s ompressve pressure. Ths pressure auses o he seondary onsoldaon. As a resul, he menoned resdual pressure shorens he sol sample as f ere 9 reep. Sne he sol sample s n unsauraed ondon, posve pressures sho he suon peulary. Thus he negave pressure means he ell knon normal ompressve effes. If e observe v values n Table 6, alhough he dffusve and apllary haraer of sol aer s domnaed a he begnnng, hey los her peulary n queson a he end of loadng sep. Thus, he quanes found from Eq. 3b, s depend upon he geomery of pore sruure. For example he value found from Eq. 3b, hh shos dffuson haraerss of sol aer approahes he same value of v found from Eq. 6a. The value obaned from Eq. 6a s also relaed o he selemen and he effeve sress hanges. If he aer onen of a sol sample s nreased, he mar suon redues and onsoldaon me for a selemen of 100% redues, as ell. In hs ase, he magnudes of he me rae of selemen ake hgher values han n unsauraed ondons. Addonally, as seen n Fg. 3a and Fg. 3b, he oeffen of volume hange m v has a hgher

10 World Appl. S. J., 6 (10): , 009 Table 7: The Change of mar suon Tme Hegh of Sample Suon Pressure (mn) (mm) q (m) ,898 1,897 1,896 1,895 y = -0,004x + 0,0138x + 1,8865 R = 0,9994 1,894 0,6 0,8 1 1, 1,4 1, q/100- Pressure (a) y = 1495,7x -0,099 R = 0, Tme (b) Fg. 7: Change of mar suon n he pressure sep deposon n hegh, s hsory and mneral onen have domnan role on he suon and s srengh. As seen n Table 6 and n Table 7, hle he values of pore-pressures derease, mar suon dereases as ell. The reason for hs phenomenon s he nrease n degree of sauraon. CONCLUSIONS In hs nvesgaon, non-lnear dfferenal equaon of dffuson ype has been solved by a dfferen approxmaon. Ths soluon an also be used for a sauraed sol. I s possble o see he refleons of he effeve sress hanges, me rae of selemen and he mar suons no he onsoldaon phenomena n he proposed approxmaon. Mar suon has a onsderable mporane on he hange n effeve sresses. I depends upon he degree of sauraon of an unsauraed sol. Alhough he mar suon has hgher values a he begnnng; dereases oards o he end of a loadng sep beause of he nrease of volumer aer onen. In a pressure sep, gravaonal aer onen remans onsan. Bu he value of volumer aer onen nreases and has a domnan role on apllary flo. Addonally, he hange n mar suon sgnfanly affes o vary he magnude of he oeffen of onsoldaon and hydraul onduvy. A he begnnng of a pressure sep, here exss a very fas me rae of selemen hh s relaed o he pore-ar phase of flo ou. Hoever, fnal selemen of an unsauraed sample for a onsan pressure dfferene s smaller han ha of he same sauraed sample. On he oher hand, surfae dranage has an mporane for he unsauraed ondons. In hs sage, nadequae suaons may our n behalf of he nflraed aer. I may ause o sell or o quk selemen of a sol layer. Therefore, neessary prevens should be esablshed for suh a ondon. REFERENCES orrelaon h and. Bu he oher quanes suh as selemen, he oeffen of onsoldaon v and he me rae of selemen v are more orrelaed h he hange n me han n hange n. Therefore, he oeffen of volume hanges should be onsdered as a man parameer for an unsauraed onsoldaon. The values of mar suons have been gven n Table 7. The values of q ere ompued by Eq. 30. The obaned pressures ere ploed n Fg. 7. As seen n hs fgure and behalf of Eq. 30, he values of and f have an mporan role on mar suon. Consequenly, he srafaon haraerss of a sol and s Bau, V., A Generaled To-dmensonal Analyal Soluon for Hydroynam Dsperson n Bounded Meda h he Frs-ype Baundary Condon a he Soure. Waer Resoures Researh. Ameran Geophysal Unon, USA, 5 (6): Capper, P.L. and W.F. Casse, The Mehans of Engneerng Sols. E. and F, N. spon LTD, England. 3. Fredlund, D.G. and H. Rahardjo, Sol Mehans for Unsaured Sols. John-Wley and Sons INC, Neyork, USA.

11 World Appl. S. J., 6 (10): , Lanelloa, R., Geoehnal Engneerng. A.A. Balkema Publshers. Old Pos Road, Brookfeld, VTO5036, USA. 5. Nelsen, D.R., J.W. Cary and D.D. Evans, 197. Sol aer. Amer.so. of Argon and solse. Soeyof Amer., Wsonsn, US. 6. Önalp, A., Knoledge abou Geoehnque I-Sol Mehans. Sakarya Unversy Publaon, Publaon No: 7, Adapaar, Turkey. 7. Phlp, J.R. 1957b. The Theory of Inflraon:1. The Inflraon and s Soluon, Sol S., USA, 83: Smh, R., 198. Smlary Soluons of a Nonlnear Dffuson. Equaon. IMA. Jour of Appl. Mah., USA, 8: Teknsoy, M.A., 00. Index and Hydraul Properes of Unsauraed Sols. S.D.Ü. Publaon, No:, Ispara, Turkey. 10. Teknsoy, M.A. and T. Hakanar, One Dmensonal Consoldaon of Unsauraed fne Graned Sols. Journal of Geoehnque Eng. Dv. ASCE, USA, 116 (5): Teragh, K., Theoreal sol mehans. Wley, Neyork. 1. Tsyovh, N.A., Sol Mehans. Mr Publshers, Moso. 13. Wyle, C.R., Advaned Engneerng Mahemas MGra-H. Book Company, Ne York, USA. 11