MODIFIED MESRI CREEP MODELLING OF SOFT CLAYS IN THE COASTAL AREA OF TIANJIN (CHINA)

Transcription

1 ISSN (Pin), ISSN (Online) hps://doi.og/ /tv MODIFIED MESRI CREEP MODELLING OF SOFT CLAYS IN THE COASTAL AREA OF TIANJIN (CHINA) Ying Zhai, Yuanzhan Wang, Yanhe Dong Oiginal scienific pape The nonlinea ceep chaaceisics of ypical clays in he coasal aea of Tianjin wee sudied by consolidaed-undained iaxial ceep ess. The ess wee pefomed via he sepwise loading mehod, and he ceep cuves of he sof clays unde diffeen sess saes wee obained fom he aw daa pocessed by Chen and Kang s mehod. The expeimens showed ha he long-em defomaion of sof clays can be divided ino wo sages, ha is, he defomaion poduced by inceasing sess and he defomaion poduced by a consan load. By analysing he es daa, a modified Mesi model was esablished based on he classical Mesi ceep model, which eaed he final sain of he fis-sage soil defomaion as he iniial sain and descibed he second-sage soil defomaion using a combinaion of a sess-sain hypebolic funcion and sain-ime hypebolic funcion. The modified model conains fou paamees; all of he paamees have clea physical significance and can be deemined by expeimen. Veificaion indicaed ha he calculaed esuls wee in good ageemen wih he expeimenal ones. Fo fuhe veificaion, he model was applied o he calculaion of he long-em selemen in he coasal aea of Tianjin. The esuls showed ha he modified model can pedic he long-em ceep defomaion of sof clays wih a saisfacoy accuacy. Keywods: coasal aea of Tianjin; modified Mesi model; sof clay; ceep; iaxial ceep es Izvoni znansveni članak Kaakeisike nelineanog puzanja ipičnih glina obalnog podučja Tianjina analiziane su konsolidianim-nedenianim oosnim povjeama puzanjem. Povjee su izvedene sepwise meodom opeećenja, a kivulje puzanja mekih glina pod azličiim sanjima napezanja dobivene su iz podaaka obađenih Chen i Kang meodom. Ekspeimeni su pokazali da se dugoajna defomacija mekih glina može podijelii na dvije faze, defomaciju dobivenu povećanjem napezanja i defomaciju dobivenu konsannim opeećenjem. Analizom podaaka povjee posavljen je modificiani Mesi model emeljen na klasičnom Mesi modelu puzanja koji je eiao finalno napezanje defomacije la pvog supnja kao počeno napezanje i opisao defomaciju la dugog supnja pimjenom kombinacije hipeboličke funkcije napezanje-izduženje i hipeboličke funkcije izduženje-vijeme. Modificiani model sadži čeii paamea; svi paamei imaju jasno fizikalno značenje i mogu se odedii ekspeimenom. Povjea je pokazala da se ezulai dobiveni poačunom dobo slažu s ekspeimenalnima. Zbog daljnje povjee model se pimijenio u poačunu dugoočnog naselja u obalnom podučju Tianjina. Rezulai su pokazali da se modificianim modelom može uz zadovoljavajuću očnos pedvidjei dugoajna defomacija mekih glina uslijed puzanja. Ključne iječi: meka glina; modificiani Mesi model; obalno podučje Tianjina; puzanje; oosna povjea puzanjem 1 Inoducion Wih he chaaceisics of low sengh, high compessibiliy, low pemeabiliy and high sensiiviy, he sof clay ofen exhibis ceep defomaion, i.e., defomaion behaviou unde consan effecive sess. The coninuous defomaion and failue ha occu afe he compleion of a consucion pojec may be caused by soil ceep [1 3]. In he ceep pocess, viscous defomaion and elasoplasic defomaion occu simulaneously, which makes he soil have visco-elasoplasic chaaceisics. I is pecisely his feaue ha esuls in he coninuous defomaion of soil. The ceep popey of soil has led o he lage displacemen of numeous pos and offshoe sucues buil off of sof-clay coass, posing an enomous hea o sucual sabiliy. Fo insance, due o soil ceep on he sof-clay bank slope, lage elaive displacemens beween pile caps and supesucues in ecen yeas have occued on some cones of piled whaf in Tianjin Po, which has esuled in an inadequae seaed lengh of beams, placing whaf sucues in dange [4]. Hence, in ode o avoid o conol he engineeing geological disase caused by sof-clay ceep, i is indispensable o cay ou he sudy on he ceep es of he sof clay and se up a suiable ceep model. Reseach on sof-clay ceep popeies has esuled in some advancemens in ecen yeas. Yin e al. [5] developed an anisoopic visco-elasoplasic sof-clay model based on Pezyna s Ovesessing Theoy and hen validaed he model using a ceep es wih consan sain ae. Leoni e al. [6, 7] poposed an anisoopic model fo ime-dependen behaviou of sof soils assuming oaed Modified Cam Clay ellipses as conous of volumeic ceep sain aes, and hen pefomed seveal validaion ess o assess he capabiliy of he model. Kelln e al. [8] evealed he ceep behaviou of sof clays using viscoelasic mechanics. Luo e al. [9] pefomed a seies of ess o invesigae he ceep chaaceisics of sof soil in ineacive maine and eesial deposis of he Peal Rive Dela, and hey demonsaed ha iaxial ceep feaues wee closely associaed wih he dainage condiions and consolidaion could weaken he effec of ceep. Scholas have dedicaed gea effos o sudying he sof-clay ceep poblem in he coasal aea of Tianjin. Wang e al. [10] sudied he ceep defomaion law of muddy sof clays in he coasal aea of Tianjin in ems of yield heoy and esablished a nonlinea heological consiuive model of he coasal sof clays. Tian e al. [11] descibed he ceep chaaceisics of ypical sof clays in Tianjin Po combining he iaxial ceep es and Singh-Michell s model. Yan e al. [12] pefomed an unconsolidaed-undained iaxial ceep es using undisubed samples wih lage diamees, and hen esablished a no-yield-suface model o simulae he ceep of foundaion soils in he coasal aea of Tianjin. Wang e al. [13] fied cuves based on he esuls of iaxial ceep ess using he Mechan ceep model and buil a ceep model fo he sof clay in he Tianjin lioal aea. Tehnički vjesnik 24, 4(2017),

2 Modified Mesi ceep modelling of sof clays in he coasal aea of Tianjin (China) The use of soil ceep models has led o many conibuions o soil science. Howeve, hese models ae no sufficien o fully explain he ceep popeies of sof clays in he coasal aea of Tianjin. The main eason of his eseach gap is ha ceep sain pesens diffeen non-linea chaaceisics fo diffeen ypes of sof clays, hee is a poblem associaed wih he adapabiliy of he ceep model iself. Fo example, when fiing he ceep cuves of ypical clay in Tianjin using Singh-Michell model, lage eos may occu a he lae sage, especially unde high pessue [11]. Lage eos may also occu when fiing ceep cuves wih he Mechan model unde high sess [13]. Ceep models wih nonlinea elemens can pinpoin ceep along ceain sess pahs. Howeve, his abiliy is no convenien o exend o engineeing because of he massive paamees and complex heoy involved in he models. This pape pesens a sudy on he ceep behaviou of sof clays in he coasal aea of Tianjin hough a seies of consolidaed-undained iaxial ess. Based on he classic Mesi empiical model poposed by Masi e al. [14], a modified Mesi model wih fou paamees was esablished, which was hen veified fo he effeciveness and applicabiliy by es daa. The poposed model can be applied o calculaing he long-em selemen of impoan sucues in he acual pojecs, meanwhile some mehods and ideas may be povided fo ohe sof clays in diffeen egions. 2 Tiaxial ceep es 2.1 Tes appaaus and samples The es equipmen is he SLB-1 iaxial shea and pemeabiliy appaaus wih sess-sain conol. The insumen is a ype of mulifuncion flexible iaxial es appaaus which can pefom unconsolidaed- undained es (UU), consolidaed-undained es (CU) and consolidaed-dained (CD) es as well as some ohe ess such as anisoopic consolidaion, isoopic consolidaion, backpessue sauaion, K 0 es and iaxial ceep es. Evey uni of he appaaus is conolled by micopocesso and i no only can be opeaed independenly, bu can conduc daa exchange wih Ying Zhai e al. compue and daa acquisiion pocessing as well. The axial load capaciy can each 20 kn, and he confining pessue anges fom 0 o 1,99 MPa. The measuemen accuacy is conolled o wihin 1 %. Wih a diamee of 39,1 mm and a heigh of 80 mm, es samples used in he sudy wee emoulded clay dilled fom he 5 10 m soil laye in he Tianjin Po aea. The physical popeies of he soil samples ae shown in Tab. 1. Table 1 Basic physical paamees of soil samples Densiy γ / Moisue Dy densiy Sauaion Void (kn/m 3 ) conen ω / % γ d / (kn/m 3 ) S / % aion e 18,201 45,62 12, , Tes mehod Two diffeen ypes of loading mehods can be employed in a ceep es, he sepaaely loading mehod and he sepwise loading mehod. Fo he sepaaely loading mehod, i is assumed ha some idenical specimens ae aken fom he same soil and he ess ae caied ou a he same ime unde condiions of idenical insumens and diffeen sess levels. This mehod can heoeically mee he needs of heological es unde he desied condiions and can even diecly obain he heological cuve of he es soil, howeve, due o he difficuly in ensuing he same condiion beween ess and in deploying a lage numbe of insumens o pefom ceep ess ove a long peiod, i is no easy o pefom sicly sepaae loading [15]. Fo he sepwise loading mehod, he sess a diffeen levels is applied o a sample sep by sep. This mehod equies fewe soil samples and fewe insumens, which is easy o pefom, and ovecomes he limis of he sepaaely loading mehod. Moeove, he mehod can educe he disceeness of he es esuls fo diffeen samples. Theefoe, he sepwise loading mehod was adoped in his sudy. Consideing he poo pemeabiliy of sof clay, he undained iaxial ceep es was adoped. Depending on he soil deph, he confining pessue was 50 kpa, 100 kpa o 150 kpa. Soil popey Muddy clay Table 2 Scheme of sep loading σ 3 / kpa (σ 1 σ 3 ) / kpa Level 1 Level 2 Level 3 Level 4 Level The es pocedue was as follows: (1) A consolidaed undained iaxial es was conduced on he soil samples unde confining pessues of 50 kpa, 100 kpa and 150 kpa. The expeimenal esuls showed ha he deviaoic sess a failue (σ 1 σ 3 ) f (when he axial sain eached 15 %) a he diffeen confining pessues was 70,2 kpa, 120,5 kpa and 178,8 kpa, especively. (2) The deviaoic sess level was deemined by (σ 1 σ 3 ) f. In his es, five loading levels wee adoped and he loading scheme is shown in Tab. 2. (3) The samples wee sauaed using vacuum sauaion mehod. The poe wae pessue coefficien B-value was measued o confim he sauaion unil i eaches 98 %. (4). The samples wee isoopically consolidaed fo 24 hous due o he poo pemeabiliy of clay. (5) Loading was pefomed on he sample sep by sep unde undained condiions. The loading ime fo each level was 48 hous. 2.3 Tes esuls The mehod of daa pocessing In his pape, Chen and Kang s mehod [16] was used o pocess he sepwise loading daa. Chen and Kang s mehod can be summaized as follows: 1114 Technical Gazee 24, 4(2017),

3 The sep load wih he incemen of Δσ i in each sep is applied on he soil sample shown in Fig. 1(a), and he sain-ime cuves ae obained in Fig. 1(b). Fom = 0 o = 1, he fis level load Δσ 1 is applied on he soil sample and he ceep eached a seady sae. If he nex level load Δσ 2 is no applied subsequenly, he defomaion will develop along he doed line due o he seady sae ceep. Theefoe, he effec of he second level load Δσ 2 is leading o addiional defomaion beween he doed line and he solid line. The addiional defomaion is added o he defomaion caused by he fis level load Δσ 1 fom = 0 o = 1, which is consideed as he defomaion caused by he load Δσ 1 +Δσ 2 fom = 0 o = 1. The same mehod is used unde ohe load, hen he sain-ime ceep cuves unde diffeen sess sages can be obained. ime and wen o zeo asympoically. Moeove, he sain ae inceased wih he deviaoic sess. Figue 2 ε- cuves of he ceep es Figue 3 Relaionship beween ln ε and ln Figue 1 Schemaic diagam of Chen and Kang s mehod: (a) sep load, (b) nonlinea supeposiion of he defomaion Discussion of he esuls (1) The axial sain-ime cuve is shown in Fig. 2. The defomaion pesened an aenuaion-seady sae pocess befoe he deviao sess eaches he deviaoic sess a failue. Wih he incease of deviao sess, he sain of he specimen inceased significanly. Unde low-sess levels, he sain clealy evealed a end of aenuaion ceep, and he ceep phenomenon was no disinc; while unde high-sess levels, he ceep cuve consised of obvious aenuaion and seady sae sages, and he slope of he cuve in he seady sae sage inceased wih he incease of deviao sess. No significan consan-ae ceep is obseved befoe he damage of he sample. (2) The logaihmic sain-logaihmic ime cuve is shown in Fig. 3. The double logaihm cuves pesened a linea elaionship and he cuves ae almos paallel wih each ohe a diffeen deviao sess levels. The linea elaionship of he double logaihm cuve was slighly wose when he deviao sess was close o he deviaoic sess a failue. (3) The sain ae-ime cuve is shown in Fig.4. Unde each sess level, he sain ae deceased ove Figue 4 Relaionship beween ln ε and ln Figue 5 σ-ε isochonal cuves (4) The sess-sain cuve is shown in Fig. 5. The elaionship beween sess and sain was linea a he iniial ime = 0 (when he load was applied gadually), Tehnički vjesnik 24, 4(2017),

4 Modified Mesi ceep modelling of sof clays in he coasal aea of Tianjin (China) while afe he load was seady, i pesened a disincly nonlinea behaviou and he sess-sain cuves wee simila a diffeen momens. Thus all of he cuves can be descibed by a unified funcion, excep fo ha epesening he iniial momen. 3 Empiical ceep model The ceep model of soil can be soed ino a componen model, endochonic model, yield suface model and empiical model [17]. Among hem, he elemen model is no applicable o descibe he nonlinea ceep popey of sof soil; he endochonic model and he yield suface model descibe he ceep popeies of sof soil based on he essence of sess. Howeve, boh models ae elaively complex and involve a lage numbe of paamees. The empiical model, alhough lacking igoous heoeical basis compaed wih he endochonic model and he yield suface model, could ofen obain a good fiing esul using a small numbe of paamees. Theefoe, i has been applied widely in many geoechnical engineeing. The empiical nonlinea ceep model of soil is based on flow heoy and aging heoy. Is sess-sain-ime elaionship can be obained compleely based on ceep es esuls. The ceep equaion feaues wo ems a defomaion funcion (sess-sain elaionship) and a ceep funcion (sain-ime elaionship). The sess-sain elaionship can be epesened by a powe funcion o hypebolic funcion, while he sain-ime elaionship can be epesened by a powe funcion, logaihmic funcion, exponenial funcion o hypebolic funcion [18]. 3.1 Defomaion funcion (sess-sain elaionship) The Singh-Michell equaion [19] and he Mesi equaion [14] ae wo famous ypes of empiical nonlinea ceep models. The sess-sain elaionships in hese models ae exponenial funcions and hypebolic funcions,especively. When he uni ime is aken, he sess-sain elaionship of he Singh-Michell equaion can be wien as e = B exp( ) 1 βd (1) Ying Zhai e al. The es daa unde a confining pessue of 150 kpa is aken as an example o illusae boh models. The uni ime is aken as 1d. I can be obseved fom he plo of lnε agains D shown in Fig. 6 ha he measued daa pesens a linea elaionship in he middle peiod of he deviaoic sess level. Howeve, he cuve appeas nonlinea when he deviaoic sess appoaches 1 o 0. An exponenial funcion can only descibe he sess-sain elaionship when he deviaoic sess level is in he middle peiod (anging fom %). In conas, a hypebolic funcion can accuaely descibe all sess levels. Theefoe, he hypebolic funcion is adoped o descibe he sess-sain elaionship in he poposed model. Figue 6 D -ln ε isochonal cuves 3.2 Ceep funcion (sain-ime elaionship) In he classic Mesi model, he sain-ime elaionship is descibed by a powe funcion, which can be expessed as λ 2 D u / u 1 f 1 ε = E S RD The model conains hee paamees: he efeence sain 2/(E u /S u ), he fiing aio R f and he ceep paamee λ whee 2/(E u /S u ) and R f can be deemined by he mehod descibed above, and λ is he slope of he ln.ε-ln. cuve shown in Fig. 3. Finally, he ceep cuve, which is fied by he classic Mesi model, is shown in Fig. 7. (3) whee D is he deviaoic sess level (σ 1 σ 3 )/(σ 1 σ 3 ) f, and (σ 1 σ 3 ) f is he deviaoic sess a failue, which can be obained by he undained iaxial compession es; B 1 and β ae he paamees and can be obained fom a plo of ln ε agains D. When he uni ime is aken, he sess-sain elaionship of he Mesi equaion can be wien as 2 D ε = E / S 1 RD u u f (2) whee E u is he angen modulus; S u =1/2(σ 1 σ 3 ) f ; 2/(E u /S u ) is he efeence sain, which can be defined as a paamee; R f is he fiing aio. 2/(E u /S u ) and R f can be obained fom a plo of ε/d agains ε. Figue 7 Compaison beween es daa and calculaed esuls using Mesi s model 1116 Technical Gazee 24, 4(2017),

5 The fiing esul clealy showed ha he sain inceases coninuously wih ime and a seady sae sage may no be obained when a powe funcion was chosen fo he sain-ime elaionship. Compaed wih he es cuve, he fiing cuve had a slowe ceep speed in he ealy sage and a fase ceep speed in he lae sage. Moeove, he fiing cuve deviaed significanly fom he es cuve in he lae sage of he ceep. Theefoe, he classic Mesi model should be modified o impove is accuacy in modelling he ceep of sof clays in he coasal aea of Tianjin. 3.3 Modified Mesi model I can be seen fom Fig. 5 ha he sess-sain isochonous cuves ae simila o each ohe excep a he iniial ime = 0. A simila condiion [14] fo sess-sain isochonous cuves is expessed as follows: ϕε ( ) = Dψ() (4) whee φ(ε) is a funcion elaed o he sain and sess a any ime, which can be expessed in he fom of Eq. (2); D is he deviaoic sess level; ψ() is a ime-dependen funcion and can be deemined by phenomenology: ψ ( ) = K() d (5) C. C. Bялов [20] pu fowad he following geneal ime funcion expession: K T = T + 2 () ( ) n 1 (6) By subsiuing Eqs. (9) and (10) ino Eq. (8), he following equaion can be obained: * * ε = ε0 + ( ε ε0 ) (11) * T + whee T * =1/δ(ε /ε * 0)T. Eq. (11) is a hypebolic funcion; hus, i can be used o descibe he aenuaion-seady sae ceep behaviou. The expeimenal esuls demonsaed ha he long-em defomaion of sof clay could be divided ino wo sages: he pimay sage, duing which sain was poduced by inceasing sess, and he ceep sage, duing which sain was poduced by a consan load. The sain-sess elaion had diffeen funcional foms in he wo sages. I can be seen fom he sess-sain isochonal cuve shown in Fig. 8 ha he sess-sain elaionship includes wo basic ypes of funcions. A he iniial ime, sess inceases almos linealy wih sain and he sess-sain cuve can be descibed by he linea funcion σ = φ 0 (ε), bu his sage is sho in duaion. Then he elaionship beween sess and sain exhibis disincly nonlinea chaaceisics and he sess-sain cuve can be descibed by he nonlinea funcion σ = φ 1 (ε). I can hus be infeed ha he fis funcional fom belongs o he pimay sage of sof-clay defomaion, and he second sicly belongs o he ceep sage ha is he second sep of sof-clay defomaion. The wo sages ae divided by he momen a which he sess-sain cuve becomes nonlinea. The sess-sain funcion in he ceep model is no applicable o he fis sage of sof-clay defomaion, so each sage should be analyzed sepaaely. Pevious empiical ceep models usually ake no accoun of he iniial sain and include all of he es daa in he fiing ange, which geneaes eos. whee T 1, T 2 and n ae undeemined paamees. Accoding o aenuaion-seady sae ceep chaaceisics of he es, n=2, T 1 =T, and T 2 =[T(δ 1)] 1/2 ae aken, whee T is an undeemined paamee and he ime funcion can be expessed as ψ( ) = 1 + ( δ 1) T + (7) whee δ is he ceep paamee. Fo A=2/(E u /S u ), wiing Eq. (2) in he fom D =φ(ε) and hen subsiuing i and Eq. (7) ino Eq. (4), he following equaion is obained: DA δ( T+ δ) ε = (1 DR ) δt+ (1 DRδδ ) f f A = 0, Eq. (8) is expessed as DA * ε 0 = (9) 1 DR f A =, Eq. (8) is expessed as (8) Figue 8 Analysis of he σ-ε isochonal cuves Based on he foegoing analysis, in conjuncion wih he es esuls obained, he ime equied o each a seady sae unde an applied load (2 min in his es) is egaded as he cuoff poin of he wo sages. The sain of he cu-off poin ε 0 is eaed as he iniial sain, and his momen is seleced as ime zeo in he ceep sage, ha is 2 D ε ε = 0 E / S 1 RD u u f (12) ε = DA δ 1 DRδ f (10) Thus, ε * 0 and in Eq. (11) ae edefined, yielding he following modified Mesi empiical ceep model: Tehnički vjesnik 24, 4(2017),

6 Modified Mesi ceep modelling of sof clays in he coasal aea of Tianjin (China) ε = ε + 2 D 0 * Eu / Su 1 RD f + T (13) The modified model conains fou paamees: ε 0, 2/(E u /S u ), R f and T * whee ε 0 is he iniial sain when he momen of he load is seady; 2/(E u /S u ) and R f ae paamees of he (ε -ε 0 ) D isochonal cuve when ime ends owad infiniy, which have he same physical meaning as he classical Mesi model; T * is a ceep paamee. The mehods o deemine he paamees in he modified model ae descibed as follows: (1) Deeminaion of paamee ε 0. Accoding o he expeimenal condiions and sess-sain isochonal cuve, i is se o 2 min fom he beginning o he seady sae of he load a each level. ε 0 unde diffeen deviaoic sess level is shown in Tab. 3. (2) Deeminaion of paamee T *. By subsiuing Eq. (12) ino Eq. (13), he following expession is obain ( ) ε ε = ε ε + T 0 0 * (14) Le ε * =ε ε 0, Y=/(ε-ε 0 ), a=1/ε *, and b=t * /ε *. By conveing Eq. (14) o he linea fom Y=ax+b, he /(ε-ε 0 ) elaion can be obained, as shown in Fig. 9. The values of T * unde five diffeen loads can be obained by linea fiing. Ying Zhai e al. inecep and slope of he fied line, he wo abovemenioned paamees can be deemined. The ceep-model paamees of sauaed emodelling sof clays in Tianjin Po unde diffeen confining pessues ae shown in Tab. 3. Table 3 Values of paamees fo he modified Mesi model σ 3 / kpa /(E u /S u ) / % 1,7711 1,6643 1,6701 R f 0,8544 0,8308 0,8158 T (Aveage) ,94 96,12 Level1-ε 0 / % 0,0845 0,0728 0,061 Level2-ε 0 / % 0,3835 0,2923 0,1890 Level3-ε 0 / % 0,6823 0,5485 0,4687 Level4-ε 0 / % 1,0360 0,7986 0,5762 Level5-ε 0 / % 1,6823 1,1610 0, Model veificaion In ode o assess he capabiliy of he modified Mesi model o pedic he eal behavio of sof clays in he coasal aea of Tianjin, es daa of boh emoulded and undisubed sof clays have been used as a benchmak. 4.1 Remoulded sof clays The compaisons beween he modified Mesi model and es daa fom chape 2 unde confining pessues of 50 kpa, 100 kpa and 150 kpa ae shown in Figs , especively. Good ageemens ae seen fo mos of he cases and he maximum eo is less han 5 %. The poposed model is appaenly moe pecise han he classical Mesi model, especially fo pedicing he ceep behaviou duing he lae sage. Figue 9 Convesion of he ceep cuves unde a confining pessue of 150 kpa Figue 11 Fiing he ceep cuves unde a confining pessue of 50 kpa Figue 10 ε * /D wih ε * unde confining pessue of 150 kpa (3) Deeminaion of paamees 2/(E u /S u ) and R f. ε * /D is ploed vesus ε * accoding o he esuls descibed above, as shown in Fig. 10. Based on he Figue 12 Fiing he ceep cuves unde a confining pessue of 100 kpa 1118 Technical Gazee 24, 4(2017),

7 consolidaed undained (CU) es was 134,4 kpa. Fo sily clay, he levels of he deviaoic sess wee 50 kpa, 100 kpa, 150 kpa and 200 kpa, and he deviaoic sess a failue was 244,9 kpa. Figue 13 Fiing he ceep cuves unde a confining pessue of 150 kpa 4.2 Undisubed sof clays Undisubed muddy clay and sily clay wee seleced fom ypical sof clays in he coasal aea of Tianjin. Expeimenal daa wee adoped fom Tian e al. [11]. The physical popeies of clays ae summaized in Tab. 4. Accoding o he soil deph, he ceep es daa fo muddy clay unde a confining pessue of 100 kpa and fo sily clay unde a confining pessue of 200 kpa wee seleced. Fou load levels wee used. Fo muddy clay, he levels of he deviaoic sess wee 25 kpa, 50 kpa, 75 kpa and 100 kpa, and he deviaoic sess a failue of he Table 4 Basic physical paamees of he soil samples Clay ype Muddy clay Sily clay Deph /m 0~13 13~17 Moisue conen / % 63,26 41,80 Densiy / g cm 3 1,70 1,84 Liquid limi w l / % 1,07 0,87 Plasic limi w p / % 21,39 18,26 Void aio e 1,237 0,965 Values of paamees fo he modified Mesi model ae shown in Tab. 5. The fiing cuves and he measuemen cuves ae compaed in Figs. 14 and 15. Fo muddy clay, he modified Mesi model showed high fiing pecision wih espec o he es daa; fo sily clay, he fiing cuves and he es daa ae lagely consisen, excep fo he eos in he fiing esuls obseved unde he highes sess sae. Addiionally, he eo ange of he low sess can be conolled o wihin 5 %, and he maximum eo unde he highes sess can also be conolled o wihin 10 %. Table 5 Values of paamees fo Modified Mesi model Clay ype σ 3 / kpa 2/(E u /S u ) / % R f T (Aveage) Deviaoic sess ε 0 / % Level 1 0,1065 Muddy clay 100 3,0599 0, Level 2 0,2440 Level 3 0,3556 Level 4 0,4735 Level 1 0,0863 Sily clay 200 2,1676 0, Level 2 0,1998 Level 3 0,3010 Level 4 0,3802 Figue 14 Fiing ceep cuves of he muddy clay unde a confining pessue of 100 kpa In conclusion, calculaed esuls agee well wih he es daa of boh emoulded and undisubed sof clays, which povides convincing evidences fo he aionaliy and applicabiliy of he poposed model. Figue 15 Fiing ceep cuves of he sil clay unde a confining pessue of 200 kpa 5 Applicaion of he modified Mesi model 5.1 The selemen model based on he modified Mesi ceep model In his pape, he foundaion selemen is calculaed by combining he modified Mesi model wih he laye-wise summaion mehod. The fomula can be expessed as follows: Tehnički vjesnik 24, 4(2017),

8 Modified Mesi ceep modelling of sof clays in he coasal aea of Tianjin (China) n n n i εihi = ε0hi + A Hi i= 1 i= 1 i= 1 1 BDi + T D (15) whee D i = (σ 1 σ 3 )/q f, and D i is he deviaoic sess. Paamees A, B and T ae deemined by he indoo ceep es. ε 0 is he insananeous sain of loading, which can be obained fom he measued value of he iniial sedimenaion (S 0 = ε 0 H); i can also be obained by an indoo ceep es. σ 1 is he sum of he gaviy sess and he addiional sess of he foundaion. σ 3 = σ 1 K 0, and K 0 can be obained by he indoo es o by esimaing Poisson s aio. q f is he value of he deviaoic sess a failue. The es esuls indicae ha hee is a linea incease in he deviaoic sess a failue wih confining pessue (Fig. 16), by which diffeen values of he deviaoic sess a failue of diffeen soil layes can be obained. Figue 16 Relaionships beween he failue deviao sess and he confining pessue Ying Zhai e al. 5.2 Long-em selemen in he coasal aea of Tianjin Eigheen yeas ago, he Tianjin Economic - Technological Developmen Aea (TEDA) was buil in Tianjin Binhai New Aea, which lies along he coas. Unde he effecs of suchages of lage aea backfill, whose hickness is 2 m, he selemen of his aea gew o be as lage as 505 mm wihin 18 yeas ( = 5, s). Howeve, in ecen yeas, he sedimenaion ae has aenuaed. The muddy clay laye in he coasal aea of Tianjin lies beween a hick sily clay laye and he laye of he backfill. Theefoe, i is consideed ha he muddy clay mainains undained condiion in he selemen pocess. Based on pevious eseach, he deph of he backfill is 2 m, he specific weigh is 17,8 kn/m 3, and he aveage deph of he muddy clay is consideed o be 8 m in he coasal aea of Tianjin. Combined wih he expeimenal daa [21] obained fo muddy sof clay in he coasal aea of Tianjin, he values of he paamees A, B and T can be deemined o be 3,05, 0,805 and 146, especively. The iniial sain can be obained based on a linea fiing using indoo ceep es esuls. Accoding o Eq. (15), fo = 5, s, he long-em selemen daa ae as shown in Tab. 6. The long-em selemen in he coasal aea of Tianjin is calculaed o be 548 mm. The sedimenaion ae wihou exenal disubance, such as consan consumpion of goundwae o subsanive consucion of undegound engineeing, ends owad zeo. The ceep cuve shows aenuaion-sabilisaion chaaceisics. The esuls of he calculaed daa agee well wih he acual obsevaion. Soil laye hickness /m σ 1 / kpa Table 6 Selemen calculaion combining he modified Mesi model wih he laye-wise summaion mehod σ 3 / kpa q / kpa q f / kpa D Iniial selemen / m Sain ε Ceep selemen/ m Sum of selemen / m 0,5 40,3 24,18 16,12 40,83 0,394 0,0153 0,0177 0,0088 0,5 49,3 29,58 19,72 46,69 0,422 0,0187 0,0195 0, ,8 37,68 25,12 55,49 0,452 0,0239 0,0217 0, ,8 48,48 32,32 67,22 0,480 0,0308 0,0239 0, ,8 59,28 39,52 78,95 0,500 0,0376 0,0256 0, ,8 70,08 46,72 90,68 0,515 0,0445 0,0269 0, ,8 80,88 53,92 102,4 0,526 0,0513 0,0279 0, ,8 91,68 61,12 114,1 0,535 0,0582 0,0287 0, ,8 102,48 68,32 125,9 0,543 0,065 0,0295 0,0295 0,548 6 Conclusion The ceep behaviou of ypical sof clays in he coasal aea of Tianjin was sudied based on consolidaed-undained iaxial ess. Subsequenly, a modified Mesi model wih fou paamees was esablished o pedic he undained ceep behaviou. Each paamee has a definie physical meaning and can be obained using he ceep es. Finally, he modified model was veified by he es daa and applied o calculaion of he long-em selemen in he coasal aea of Tianjin, he following conclusions may be dawn: (1) The sof clays in he coasal aea of Tianjin pesen disinc aenuaion-seady sae ceep chaaceisics. Wih he incease of deviaoic sess, he ceep effec becomes moe obvious. The ceep sain ae is no high in he seady sae, and no significan consan-ae ceep is obseved. (2) Soil defomaion should be divided ino wo sages, one in which sain is caused by an incease in sess and one in which sain is caused by ceep defomaion. A modified Mesi model is esablished, which eas he final sain of he fis-sage soil defomaion as he iniial sain and descibes he second-sage soil defomaion using a combinaion of a sess-sain hypebolic funcion and sain-ime hypebolic funcion. (3) The poposed ceep model was compaed wih some es daa and bee pedicion was achieved fo modelling he ceep sain of sof clays in he coasal aea of Tianjin. The long-em selemen in he coasal aea of Tianjin is calculaed o be 548 mm, which agees well 1120 Technical Gazee 24, 4(2017),

9 wih he acual obsevaion. The modified Mesi model can be well used o pedic he ceep behavious of he ypical sof clays in he coasal aea of Tianjin. Acknowledgemen This wok was suppoed by he Naional Naual Science Foundaion of China (ID ). 7 Refeences [1] Kim, Y. T.; Leoueil, S. Modeling he viscoplasic behaviou of clays duing consolidaion: applicaion o Behieville clay in boh laboaoy and field condiions. // Canadian Geoechnical Jounal. 38, 3(2001), pp hps://doi.og/ / [2] Leoueil, S. The isoache appoach. Whee ae we 50 yeas afe is developmen by Pofesso Šuklje? // Poceedings of he 13h Danube-Euopean Confeence on Geoechnical Engineeing / Ljubljana, 2006, pp [3] Kim, D. K. A consiuive model wih damage fo cohesive soils. // KSCE Jounal of Civil Engineeing. 8, 5(2004), pp hps://doi.og/ /bf [4] Li, Y. S.; Zhao, C. J.; Zhao, L. P. Influence of bank soil ceep defomaion on high-piled whaf in Tianjin po. // China Habou Engineeing. 4(2009), pp [5] Yin, Z. Y.; Chang, C. S.; Kasunen, M.; Hiche, P. Y. An anisoopic elasic-viscoplasic model fo sof clays. // Inenaional Jounal of Solids and Sucues. 47, 5(2010), pp hps://doi.og/ /j.ijsols [6] Leoni, M.; Kasunen, M.; Vemee, P. A. Anisoopic ceep model fo sof soils. // Géoechnique. 58, 3(2008), pp hps://doi.og/ /geo [7] Leoni, M.; Vemee, P.; Kasunen, M. Validaion of anisoopic ceep model fo sof soils. // Gound Impovemen, 2nd Inenaional Wokshop on Geoechnics of Sof Soils / Glasgow, 2009, pp [8] Kelln, C.; Shama, J.; Hughes, D.; Gaham, J. An impoved elasic-viscoplasic soil model. // Canadian Geoechnical Jounal. 45, 10(2008), pp hps://doi.og/ /t [9] Luo, Q. Z.; Chen, X. P. Expeimenal eseach on ceep chaaceisics of Nansha sof soil. // The Scienific Wold Jounal. 2014, (2014). hps://doi.og/ /2014/ [10] Wang, Y. Z.; Wang, T. T.; Wang, J. A nonlinea heological model of sof clay and is applicaion o Tianjin lioal aea. // Rock and Soil Mechanics. 30, 9(2009), pp [11] Tian, S. Z.; Li, Y. S.; Ji, C. N. Ceep es of sof clay fo Tianjin Po. // Jounal of Waeway and Habo. 30, 6(2009), pp [12] Yan, S. W.; Liu, K. J.; Li, W.; Hou, Y. M. Sudy of ceep popeies of sof clay in Tianjin Binhai New Aea and no-yield-suface consiuive model. // Rock and Soil Mechanics, 31, 5(2010), pp [13] Wang, Y. Z.; Huang, D. X.; Xiao, Z. Expeimenal eseach on ceep popeies of wo ypical sof clays in coasal egion of Tianjin. // Jounal of Geoechnical Engineeing. 34, 2(2012), pp [14] Mesi, G.; Rebes-Codeo, E.; Shields, D. R.; Caso, A. Shea sess-sain-ime behaviou of clays. // Geoechnique, 31, 4(1981), pp hps://doi.og/ /geo [15] Sun, J. Ceep of geomeical and is applicaion. Chinese Consucion Pess, Beijing, [16] Tan, T. K.; Kang, W. F. On he locked in sess, ceep and dilaaion of ocks, and he consiuive equaions. // Chinese Jounal of Rock Mechanics and Engineeing. 10, 4(1991), pp [17] Yuan, J.; Gong, X. N.; Yi, D. Q. Compaison sudy on heological consiuive models. // Chinese Jounal of Rock Mechanics and Engineeing. 20, 6(2001), pp [18] Liu, Y. K.; Deng, Z. B.; Cao, P.; Huang, Y. H.; Lin, H. Tiaxial ceep es and modified Singh-Michell ceep model of sof clay. // Jounal of Cenal Souh Univesiy (Science and Technology). 43, 4(2012), pp [19] Singh, A.; Michell, J. K. Geneal sess-sain-ime funcion fo soils. // Jounal of he Soil Mechanics and Foundaions Division. 94, 1(1968), pp [20] Bялов, C. C. Rheologic heoy of soil mechanics. Science Pess, Beijing, [21] Wang, T. T. Sudy on he heological model of lioal sof clay and is applicaions in he sabiliy analysis of coasal sucues (Ph.D. Thesis), Tianjin Univesiy, China, Auhos addesses Ying Zhai, D. Tianjin Key Laboaoy of Po and Ocean Engineeing, Tianjin Univesiy No. 92 Weijin Road, Nankai Disic, Tianjin , China iffany_zy@ju.edu.cn Yuanzhan Wang, Pof. Tianjin Key Laboaoy of Po and Ocean Engineeing, Tianjin Univesiy No. 92 Weijin Road, Nankai Disic, Tianjin , China yzwang@ju.edu.cn Yanhe Dong Tianjin Key Laboaoy of Po and Ocean Engineeing, Tianjin Univesiy No. 92 Weijin Road, Nankai Disic, Tianjin , China @qq.com Tehnički vjesnik 24, 4(2017),