Numerical simulation of a trial wall on expansive soil in Sudan

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Estella Ward
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Con seq u en tly, stru ctu ral d am ag es cou ld h appen if n o special m easu res wou ld h av e been taken d u rin g th e d esig n process.

1 Ayman Abed, Stuttgart University Introduction Th e expan siv e soil sh ows obv iou s v olu m etric ch an g es u n d er ch an g in g m oistu re con d ition s. Th ese v olu m etric d eform ation s u su ally resu lt in d ifferen tial m ov em en ts of sh allow fou n d ation s restin g on it. Con seq u en tly, stru ctu ral d am ag es cou ld h appen if n o special m easu res wou ld h av e been taken d u rin g th e d esig n process. Th is article illu strates th e possibility to pred ict su ch m ov em en ts u sin g PLAXIS prov id ed th at a su itable con stitu tiv e m od el for u n satu rated soil beh av iou r is u sed. T rial W all on E xpansive Soil Nin e trial walls were bu ilt on swellin g soil in Barakat site in Su d an. Th e area is kn own for its h ig h ly expan siv e soil. Th e test were carried ou t in ord er to in v estig ate th e effect of soil replacem en t on th e walls v ertical m ov em en t [SAEED ]. Th e walls are m ad e of brick (1 1/2 brick) with a len g th of 1.2 m an d a h eig h t of 1.9 m abov e th e g rou n d lev el. Th e fou n d ation d epth is 0.6 m. A sch em atic represen tation of th e walls with th eir d im en sion s is g iv en in Fig u re 1. Th e expan siv e soil u n d ern eath th e walls was replaced with d ifferen t m aterials n am ely A1, A2, A3, B1, B2, B3, C1, C2 an d C3 wh ere: A1: plain con crete, A2: Rein forced con crete with 20 % v oid s, A3: Big ston es, B1: 25 cm of Coh esiv e Non expan siv e Soil (CNS), B2: 5 0 cm of CNS, B3: 7 5 cm of CNS, C1: Natu ral soil, C2: Natu ral soil with 6 % lim e, C3: San d. Th e soil was th en exposed to two su ccessiv e wettin g -d ryin g cycles for a period of abou t 18 m on th s. Detailed d ata abou t th e v ertical d isplacem en ts of th e trial walls is reported by [SAEED ], Fig u re 2 presen ts on ly th e d isplacem en ts of th e wall C1 with n o replacem en t as th e pu rpose of th is stu d y is to sim u late th e beh av iou r of th e expan siv e soil itself. On in v estig atin g th e m easu rem en ts on e fi n d s th at th e test h as fou r stag es. Th e fi rst on e is a wettin g ph ase of abou t 27 0 d ays resu ltin g in a total h eav e of abou t 6.0 cm. Th e wettin g ph ase was followed by a d ryin g ph ase of 9 0 d ays resu ltin g in 2.5 cm of sh rin kag e. Th e secon d wettin g stag e lasted 127 d ays an d resu lted in 2.5 cm of h eav e, wh ich in d icates an elastic beh av iou r by recov erin g th e settlem en t in th e prev iou s d ryin g ph ase in alm ost sim ilar tim e. Th e fi n al ph ase was relativ ely sh ort of abou t 5 0 d ays an d resu lted in 0.5 cm of sh rin kag e. Fig u re 1. Geom etrical d etails of th e walls 14

2 wh ere : soil friction an g le c : effectiv e coh esion k sat : satu rated perm eability b : h u m id u n it weig h t p : precon solid ation pressu re Fig u re 2. Measu red d isplacem en ts of th e wall C1 as prov id ed by [SAEED ] Soil P roperties Th e soil is classifi ed as a clayey silt with a liq u id lim it LL = 6 8 % an d a plastic in d ex PI = 36 %. Th e 1-D com pression resu lts in Fig u re 3 sh ows th at th e soil is ov ercon solid ated an d it h as a m od ifi ed com pression in d ex * = C c / 2.3 = an d a m od ifi ed swellin g in d ex * C s / 2.3 = Th e h ig h K v alu e is typical for an expan siv e soil. Oth er av ailable soil properties are listed in Table 1. M aterial M odel for Soil Barcelon a Basic Mod el [ALONSO & GENS ] is u sed as a con stitu tiv e m od el in th is work. Th e m od el ad opts th e id ea of two in d epen d en t stress m easu res n am ely, th e n et stress * an d th e su ction s. th e n et stress is d efi n ed as th e d ifferen ce between th e total stress an d th e pore air pressu re u a wh ereas su ction is th e d ifferen ce between pore air pressu re u a an d pore water pressu re u w. In wh at follows th e air pressu re is assu m ed to be atm osph eric ev erywh ere in th e soil wh ich m ean s th at th e n et stress in th is special case is sim ply th e total stress an d th e su ction is eq u al to -u w. Th e m od el is an exten sion of th e Mod ifi ed Cam Clay Mod el by ad d in g th e effect of su ction on soil stren g th an d stiffn ess. At fu ll satu ration, wh en su ction = 0, th e m od el coin cid es with th e Mod ifi ed Cam Clay Mod el. On d ryin g th e soil (in creasin g th e su ction ), a capillary coh esion d ev elops an d con seq u en tly th e yield ellipse g rows in to th e ten sion reg ion with a rate eq u al to th e m od el param eter a as it sh own in Fig u re 4.a. Th e soil precon solid ation pressu re p p in creases as well. It can be related to th e precon solid ation pressu re at fu ll satu ration p po th rou g h th e followin g form u la p o - po p p = p c. p c - (1) wh ere pc is a referen ce pressu re an d e s (2) Fig u re 3. On e d im en sion al com pression resu lts Table 1. Oth er soil properties (a) (b) c p k sat b 30 o kpa m /d ay 17.6 kn/m 3 Fig u re 4. Th e yield su rface of Barcelon a Basic Mod el 15

3 Plaxis Practice C o ntinuatio n L is th e su ction d epen d en t com pression in d ex. Hen ce, for fu ll satu ration we h av e relation sh ips. Th e fi rst on e is kn own as th e Soil W ater Ch aracteristic Cu rv e wh ile th e s = 0, L = Lo an d pp = ppo. Th e larg er th e su ction, th e sm aller th e com pression in d ex L. In th e lim it for s = d th e abov e ex pression y ield s L Ld. Th e con stan t b con trols th e rate secon d is th e relativ e perm eability fu n ction. Th e term relativ e perm eability stan d s for th e ratio between soil perm eability k at a certain su ction lev el an d ksat. Both cu rv es are of d ecrease of th e com pression in d ex with su ction. sh own in Fig u re 6. W h en th e d ev iatoric stress q = 0, th e y ield su rface of Barcelon a Basic Mod el d eg en erates to th e so- called Load in g - Collapse cu rv e as it clear in Fig u re 4.a wh ere p* an d q are th e stress in v arian ts bein g d efi n ed as p* = 1 (S*1 3 q = 1 2 (S*1 S*2 S*3 - u a ; S*2 2 + (S*2 S*3 2 + (S*3 S*1 2 (3) For th e elastic beh av iou r, th e m od el assu m es th at th e soil h as d ifferen t stiffn ess param eters for ch an g es of n et stress an d ch an g es of su ction. For ex am ple startin g from stress state A in Fig u re 4.b th e soil sh ows d ifferen t stiffn ess d epen d in g on wh eth er it is ex posed to n et stress ch an g e or su ction ch an g e. In th e latter case th e soil swellin g in d ex with respect to su ction Ks con trols th e soil respon se wh ile th e n orm al swellin g in d ex K d om in ates th e oth er case. Th is m od el h as been im plem en ted in to PLAXIS fi n ite elem en t cod e as a u ser d efi n ed m od el by [ABED & VERMEER ] wh ere th e fu ll m ath em atical d escription of th e m od el is also presen ted. Th e swellin g in d ex with respect to su ction Ks is th e m ost im portan t param eter in th e trial wall case as su ction is th e on ly v ariable d u rin g th e test. It is assu m ed th at th e read er is aware of th e fact th at th e ch an g e of m oistu re con ten t an d th e ch an g e of su ction are sy n on y m. (a) F inite E lement C alculations Th e calcu lation s in v olv e tran sien t u n satu rated fl ow as well as d eform ation an aly ses. As th e calcu lation s are d on e in an u n cou pled way, th e u n satu rated g rou n d water fl ow an aly ses are d on e fi rst an d th e resu lted su ction fi eld s are u sed for later d eform ation calcu lation s. Th e PLAXFLOW fi n ite elem en t cod e [BRINKGREVE et al ] is u sed to sim u late th e u n satu rated g rou n d water fl ow an d to d eterm in e th e su ction v ariation with tim e. Th e d eform ation an aly ses are d on e u sin g th e Barcelon a Basic Mod el as im plem en ted in th e PLAXIS fi n ite elem en t cod e. G eometry, B oundary and Initial C onditions Fig u re 5.a sh ows th e bou n d ary con d ition s, th e in itial con d ition s an d th e fi n ite elem en t (b) m esh bein g u sed. Th e g rou n d water calcu lation is fou n d to be d ecisiv e for ch oosin g th e d epth of th e m esh. No local d eform ation s are ex pected to take place arou n d th e wall footin g, for th at reason n o fu rth er m esh refi n em en t is n eed ed in th at reg ion. Th e g rou n d water table lies at a d epth of 30 m below th e g rou n d lev el. Th e in itial pore water pressu re is assu m ed to be h y d rostatic, with ten sion abov e th e ph reatic lin e. Accord in g to [SAEED ], th e soil was alway s soaked with water d u rin g wettin g ph ase, wh ich su g g ests an in fi ltration rate eq u al to th e satu rated soil perm eability ksat. A h ig h ev aporation rate of 10 m m /d ay is applied d u rin g th e d ry in g ph ase to accou n t for th e observ ed sev ere sh rin kag e. Th e applied su rface d isch arg e with tim e is illu strated in Fig u re 5.b. PLAXFLOW req u ires in form ation abou t th e su ction - d eg ree of satu ration an d th e su ction - relativ e perm eability 16 Fig u re 5. Geom etry, bou n d ary an d in itial con d ition s

4 Fig u re 6. Soil W ater Ch aracteristic Cu rv e an d relativ e perm eability fu n ction P L A X F L O W output Fig u re 7 illu strates th e v ariation of su ction an d d eg ree of satu ration with tim e u n d ern eath th e wall as calcu lated by PLAXFLOW. Th e su ction d rops from 30 0 kpa to abou t 30 kpa at th e en d of th e fi rst wettin g ph ase. Th en it in creases ag ain to 240 kpa at th e en d of th e fi rst d ryin g ph ase. Th en beh av iou r is repeated in th e n ext wettin g -d ryin g cycle. It is also in terestin g to see h ow th e d eg ree of satu ration is in creasin g with th e d ecrease of su ction an d v ice v ersa. Fig u re 8 presen ts th e calcu lated su ction profi les at th e en d of th e fi rst wettin g ph ase as well as at th e en d of th e fi rst d ryin g ph ase. Th ey resem bles typical su ction d istribu tion s u n d er in fi ltration an d ev aporation bou n d ary con d ition s Suction [kpa] considered point Time [days] Fig u re 7. Su ction an d d eg ree of satu ration u n d ern eath th e wall degree of saturation suction D egree of saturation S r % Fig u re 8. Su ction profi le at d ifferen t tim e steps D eformation analy ses Su ction v alu es resu lted from g rou n d water fl ow calcu lation s are tran sferred to PLAXIS for d eform ation calcu lation s. Th e m aterial properties in Table 2 are u sed for th e Barcelon a Basic Mod el. No in form ation is prov id ed abou t th e soil swellin g in d ex with respect to su ction s, for th at reason it is th e calibration param eter in th ese calcu lation s. Its v alu e is v aried between to wh ich cov ers th e m ost com m on v alu es for th is in d ex as m en tion ed in literatu re [FREDLUND & RAHARDJO ]. A v alu e of s = is fou n d to g iv e th e best fi t to th e fi eld m easu rem en ts. In d eed th is v alu e is satisfactory in th e sen se th at it also refl ects th e expan siv e n atu re of th e soil bein g stu d ied. On u sin g th e m aterial properties as listed in Table 2 th e calcu lated d eform ation s are in g ood ag reem en t with m easu red d ata as sh own in Fig u re 9. Th e d ev iation at th e en d of th e fi rst d ryin g ph ase su g g ests th at on e sh ou ld u se a h ig h er swellin g in d ex d u rin g sh rin kag e. As th e m od el u ses th e sam e in d ex for both swellin g an d sh rin kin g it wou ld be better for fu rth er im prov em en t to u se th e id ea of yield in g on th e sh rin kag e path as it proposed also by th e Barcelon a Basic Mod el [ALONSO & GENS ] wh ere after a certain su ction lev el th e soil ten d s to yield with lower stiffn ess an d g iv in g m ore sh rin kag e. Table 2. Barcelon a Basic Mod el param eters Strength p arameters Stiffness p arameters Stiffness p arameters w ith resp ec t to suc tio n 30 o o s c a kpa -1 p co 9 7 kpa p c 5 0 kpa wh ere : soil Poisson s ratio for u n load in g -reload in g 17

5 C o ntinuatio n R eferences [ABED & VERMEER ] A. A. ABED, P. A. VERMEER: Fou n d ation an alyses with u n satu rated soil m od el for d ifferen t su ction profi les: In proc. Sixth Eu ropean Con feren ce on Nu m erical Meth od s in Geotech n ical En g in eerin g, Graz, Au stria. [ALONSO & GENS ] E. E. ALONSO, A. GENS, an d A. JOSA: A con stitu tiv e m od el for partially satu rated soils: Gé otech n iq u e (40 ), [BRINKGREVE et al ] PLAXFLOW User Man u al: Balkem a, Rotterd am, [FREDLUND & RAHARDJO ] Soil Mech an ics for Un satu rated Soils: Joh n W iley & Son s, Fig u re 9. Calcu lated v ersu s m easu red d ata C onclusions Th e PLAXFLOW -PLAXIS in teraction offers a n ice tool to sim u late th e m ech an ical beh av iou r of u n satu rated soil. In th is stu d y PLAXFLOW is u sed to solv e su ction v ariation in tim e wh ereas th e Barcelon a Basic Mod el as im plem en ted in PLAXIS is u sed to calcu late th e d eform ation s. It sh ows clearly h ow m u ch th is proced u re is effi cien t. Howev er, on e sh ou ld always em ph asize on th e com preh en siv e u n d erstan d in g of th e con stitu tiv e m od el bein g u sed an d its lim itation s. Th e u se of su ction in d eform ation or stability calcu lation is always critical an d n eed special m od el to h an d le it. Usin g it with th e wron g m od el or with ou t fu ll awaren ess lead s in m ost cases to a n on -con serv ativ e estim ation. [SAEED ] I. M. A. SAEED: Ev alu ation of im prov em en t tech n iq u es for strip fou n d ation on expan siv e clay soils in Gezira: Master Th esis: Un iv ersity of Kh artou m : Su d an, [VERMEER & BRINKGREVE ] PLAXIS Fin ite elem en t cod e for soil an d rock an alysis: Balkem a, Rotterd am, Fig u re 10. Deform ed m esh at th e en d of calcu lation s 18

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