ATTERBERG LIMITS IN RELATION TO OTHER PROPERTIES OF FINE-GRAINED SOILS

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1 ATTERBERG LIMITS IN RELATION TO OTHER PROPERTIES OF FINE-GRAINED SOILS BOJANA DOLINAR and STANISLAV SKRABL about th authors corrsponding author Bojana Dolinar Univrsity of Maribor, Faculty of Civil Enginring Smtanova ul. 17, 2000 Maribor, Slovnia Stanislav Škrabl Univrsity of Maribor, Faculty of Civil Enginring Smtanova ul. 17, 2000 Maribor, Slovnia Abstract In soil mchanics th Attrbrg limits ar th most distinctiv and th asist proprty of fin-graind soils to masur. As thy dpnd on th sam physical factors as th othr mchanical proprtis of soils, th valus of th liquid and plastic limits would b a vry convnint basis for thir prdiction. Thr ar many studis concrning th us of th Attrbrg limits in soil mchanics; howvr, thir rsults vary considrably and ar not gnrally applicabl. This papr xplains th main rasons for th diffrnt conclusions in ths studis, which do not tak into account th following: a) th watr in fin-graind soils appars as intrparticl and intraggrgat por watr as wll as adsorbd watr onto th surfacs of clay minrals; b) th physical proprtis of fin-graind soils dpnd on th quantity of por watr only, bcaus th adsorbd watr is tightly tid on th clay s xtrnal and intrnal surfacs and thus cannot influnc to thm; c) th quantity of adsorbd watr on th xtrnal surfacs of th clay minrals in soils dpnds mostly on th siz and th quantity of th clay minrals, whil th intrlayr watr quantity dpnds mostly on th quantity and th typ of th swlling clay minrals in th soil composition and thir xchangabl cations. From this it follows that for swlling and non-swlling soils, th uniform rlationships btwn th Attrbrg limits (which rprsnt th total quantity of por watr and th adsorbd watr onto th xtrnal and intrnal surfacs of clay minrals) and othr physical proprtis dos not xist. This papr prsnts som possibilitis for th us of th Attrbrg limits in prdicting th soil s othr proprtis for non-swlling and limitd-swlling soils. Kywords Attrbrg limits; spcific surfac ara; undraind shar strngth; comprssibility; hydraulic conductivity 1 INTRODUCTION Th Attrbrg limits rprsnt th watr contnt whr th consistnc of a fin-graind soil is transformd from a plastic stat (plastic limit PL) to a liquid stat (liquid limit LL) and from a smi-solid stat (shrinkag limit SL) to a plastic stat, as wll as th watr contnt at which diffrnt fin-graind soils hav an approximatly qual undraind shar strngth, which is kpa at th LL (dpnding on th mthod of masurmnt) and about 100 tims gratr at th PL. Th quantity of watr at th Attrbrg limits and for th othr physical proprtis dpnds on th sam, mostly compositional factors, such as th typ of minrals, th amount of ach minral, th shaps and siz distribution of th particls and th por-watr composition [1], which lads to th conclusion that th xactly dfind rlationships btwn th valus of th Attrbrg limits and th soil s othr proprtis must xist. Svral rsarchrs hav trid to find th gnrally valid rlationships btwn th quantity of watr at th LL, th PL or at th plasticity indx (PI=LL PL) and various physical proprtis. Th rsults of ths studis, howvr, varid considrably and wr valid in most cass for th invstigatd soils only. Th main rasons for th diffrnt conclusions in ths studis ar xplaind in Sction 2. Th nxt sction shows th mpirically obtaind rlationships btwn th Attrbrg limits and som othr proprtis of th soil with an xplanation about th limitations of thir us. Th comparison btwn th masurd and th calculatd valus from th proposd corrlations for diffrnt proprtis of th soils ar shown in Sction 4. ACTA GEOTECHNICA SLOVENICA, 2013/2 5.

2 This papr brifly summarizs all our alrady-publishd and nw findings with th intntion to undrstand mor asily th impact of th minralogical composition on th physical proprtis of fin-graind soils, th basic mchanisms that dtrmin th physical proprtis, and thus th possibl corrlations btwn thm. As an xampl, th possibilitis of using th Attrbrg limits to prdict th soil s othr proprtis ar shown. 2 BASIC ASSUMPTIONS Fin-graind soils contain both clay minrals and associatd minrals, and th intractions btwn th clay minrals and watr affct th soil s watr-holding capacity. Watr is strongly adsorbd onto th xtrnal surfacs of hydrophilic non-swlling clay minrals, whras watr adsorbs onto both th xtrnal and intrnal surfacs of swlling clay minrals. Bsids th adsorbd watr soils also contain fr intrparticl and intraggrgat por watr [2]. It was found also that: 1. most of th watr in soils is associatd with clay minrals [3]; 2. th por sizs that ffctivly control fluid flow at th liquid limit ar th sam siz for all soils [1] and, hnc, th quantity of fr por watr at th liquid limit is a constant; 3. soils hav similar por watr suction at th liquid limit [4-6]. This mans that th ratio of adsorbd watr to clay surfac ara should b about th sam at th liquid limit; 4. at th liquid limit, diffrnt fin-graind soils hav approximatly qual undraind shar strngth [7-9]; 5. at th plastic limit th undraind shar strngth is about 100 tims th undraind shar strngth at th liquid limit [10 and numrous subsqunt authors]; 6. th quantity of intrlayr watr in swlling clays is mostly dpndnt on th typ of th clay minrals, th xchangabl cations and th chmical composition of th por watr [11, 12]. On th basis of th abov findings, Dolinar and Traunr [13, 14] assumd that th quantity of fr por watr and xtrnal surfac watr at th liquid limit w LL and th plastic limit w PL can b xprssd in trms of th xtrnal spcific surfac ara and th clay minrals contnt by Eqs. (1) and (2). w = p ( w + w ) = p ( w + t A )(1) LL fll all fll all w = p ( w + w ) = p ( w + t A )(2) PL fpl apl fpl apl SC SC whr w f LL and w f PL ar th quantitis of fr por watr. Ths quantitis ar constant at th liquid and plastic limits (according to itm 2, 4 and 5). w a LL and w a PL ar th quantitis of firmly adsorbd watr on th clay s xtrnal surfacs. Ths quantitis of watr dpnd on th siz of th xtrnal surfacs of th clay minral particls A SC bcaus th thicknsss t a LL, t a PL of th firmly adsorbd watr on th xtrnal surfacs ar, for most clay minrals, constant at th liquid and plastic limits (according to itm 3). Th watr contnt (por watr and xtrnal surfac watr) dpnds on th quantity of clay minrals in th soil, assuming that all th watr in th soil is associatd with th clay minrals (according to itm 1). Th xprimntal tsts on artificial mono-minral clay mixturs confirmd th abov assumptions (Fig.1). For non-swlling soils th liquid limit LL (%) and plastic limit PL (%) can thus b xprssd as: LL = p A (3) PL = p + A (4) whr A S = p A SC (m 2 /g) is th xtrnal spcific surfac ara of th soil and p is th contnt (%) of clay minrals in th soil dividd by 100 (0 < p 1). Not that LL = LL for non-swlling soils and LL = LL + w i for swlling soils (w i is th quantity of intrlayr watr). Th abov findings can b summarizd in th following conclusions: - for non-swlling soils th watr contnt at th LL and PL dpnds mostly on th spcific surfac ara A S and th contnt of clay minrals p in th soil composition; - for swlling soils th quantity of fr por watr and adsorbd watr on th clay s xtrnal surfacs dpnd on A S and p, whil th intrlayr watr contnt w i is mostly dpndnt on th quantity and typ of th swlling clay minrals, xchangabl cations and th chmical composition of th por watr. This xplains why a gnral critrion cannot b found rlating th watr contnt at th Attrbrg limits to th total spcific surfac ara A S = A S + A Si (A Si is intrnal spcific surfac ara) for soils with and without swlling clay minrals. It should b notd that using a standard mthod for masuring th watr contnt w, th total quantity of fr por watr w f and strongly adsorbd watr on th xtrnal w a and intrnal w i clay surfacs can always b dtrmind by drying at a tmpratur of ºC; - th physical proprtis of fin-graind soils dpnd only on th fr por watr bcaus th adsorbd watr is tightly tid on th clay s xtrnal and intrnal surfacs. S S 6. ACTA GEOTECHNICA SLOVENICA, 2013/2

3 Figur 1. Quantity of por watr plus th xtrnal surfac watr at th liquid limit w LL (%), plastic limit w PL (%) and plasticity indx w PI (%) as a function of th spcific surfac ara A S (m 2 /g) for clay minrals (p=1). Th abov findings allow us to bttr undrstand th rlationships btwn th quantity of watr at th liquid and plastic limits and othr proprtis of th soil and hnc thir propr us in prdicting othr physical proprtis of fin-graind soils. 3.2 DETERMINATION OF THE UNDRAINED SHEAR STRENGTH Koumoto and Houlsby [9] prsnt a rlationship btwn th watr contnt w and th undraind shar strngth s u using th following quation 3 CORRELATION OF THE ATTERBERG LIMITS WITH THE SOIL'S OTHER PROPERTIES 3.1 DETERMINATION OF THE EXTERNAL SPECIFIC SURFACE AREA paramtrs a and b can only b obtaind xprimntally, For non-swlling soils, which only contain por watr a) whil Traunr t al. [17] found that for non-swlling b) and adsorbd watr on th xtrnal surfacs of clay minrals, th spcific surfac ara A S (m 2 soils ths paramtrs (a, b ) dpnd mainly on th /g) can b xtrnal spcific surfac ara A S (m 2 /g) of soils and th xprssd with Eqs. (3) and (4), dpnding on th LL contnt of clay minrals p in th soil s composition and and PL. Th portion of clay minrals p could b qualld can b xprssd by Eqs. (7) and (8). A S in th quations can b dtrmind xprimntally or calculatd with th grain quantity < μ2m, dtrmind using a hydromtr mthod. using Eqs. (3), (4) or (5), whil p can b stimatd from a particl siz analysis. For soils that contain limitd-swlling clay minrals, th quantity of intrlayr watr (w i ) at th LL and PL is approximatly th sam (w i LL w i PL PI PI ), and th xtrnal spcific surfac ara A S (m 2 /g) can b xprssd with Eq. (5), dpnding on th plasticity indx PI (%). PI = LL -PL A = ( PI p) 0.54 (5) S For soils with othr swlling clay minrals a corrlation btwn th spcific surfac ara and th Attrbrg limits dos not xist [15, 16]. b w= a s - (6) u whr a and b ar soil-dpndnt paramtrs. a (%) is th watr contnt at th undraind shar strngth s u =1kPa, and b is th slop of th linar function that rprsnts th ratio btwn th watr contnt w(%) logarithm and th th undraind shar strngth s u (kpa) logarithm. According to Koumoto and Houlsby [9] th a = p A = 1.22 LL p (7) S LL p b = 0.05 ( AS p) = 0.05 ( ) 0.81 p For both th swlling and non-swlling fin-graind soils, th undraind shar strngth could b dtrmind using th Attrbrg limits and a modifid plasticity indx or modifid consistncy indx. Equations (10) (8) ACTA GEOTECHNICA SLOVENICA, 2013/2 7.

4 and (11), which show ths rlationships, ar drivd as follows: Th undraind shar strngth of th soils at th liquid limit s ull, dtrmind by th fall con tst, can b calculatd using Eq. (9) W su = K (9) h 2 whr K is a constant dpnding on th typ of con and W is th con mass. Th thortically dtrmind valu of th constant is K = 1.33 for th British con [9] and th mass of th con is W = 80 g. Th dpth of con pntration that corrsponds to th watr contnt at th LL is h = 20 mm. Th undraind shar strngth is s ull =2.66 kpa. Th data of Skmpton and Northy [10] and numrous subsqunt authors show that th undraind shar strngth at th PL is about 100 tims th undraind shar strngth at th LL (s upl =266 kpa). Considring th abov findings th watr contnt at th LL and PL can b xprssd as LL = a b (%) and PL = a 266 -b (%). Th form of ths xprssions suggsts that it would b convnint to dfin a modifid plasticity indx as PI M = log LL log LP, which maks it possibl to xprss th paramtrs a and b in trms of PI M as follows [9]: b=log LL log PL / log s ull log s upl =PI M /-2 and -b a = LL / s ull = LL / PIM/-2. At th slctd watr contnt w (%) th undraind shar strngth s uw (kpa) of th soils can thus b dtrmind in trms of th liquid limit LL (%) and th modifid plasticity indx PI M by Eq. (10). 2 PIM 2 PIM s = 2.66 LL w - (10) uw Th consistncy indx (CI) is dfind as th ratio of th diffrnc btwn th LL and th natural watr contnt (w) to th plasticity indx (PI) of a soil (CI=(LL w)/pi). Consistnt with th abov discussion of th variation of strngth with watr contnt, it would b appropriat to dfin a nw, modifid consistncy indx as CI M = (log LL log w) / PI M. By considring that log LL = log a b log s ull, log PL = log a b log s upl and log w = log a b log s uw, th modifid consistncy indx CI M can b writtn in th form CI M =(logs ull logs uw ) / (logs ull logs upl ) = log s uw which maks it possibl to xprss th undraind shar strngth at a particular watr contnt as: ( M )/0.5 s 10 CI + uw = (11) 3.3 DETERMINATION THE WATER CONTENT - EFFECTIVE STRESS RELATIONSHIP In a comprssibility tst of saturatd soils th quantity of fr por watr and adsorbd watr on xtrnal clay surfacs dpnds on th strss stat and th physicochmical proprtis of th clay minrals. It is known that th intrlayr watr cannot b draind from an xpanding minral undr usual strsss, which lads to th conclusion that in th cas of swlling soils a gnrally applicabl rlationship btwn th total watr contnt and th ffctiv strss dos not xist. On th basis of xprimntal tsts Dolinar [18] found that th rlationship btwn th fr por watr plus th adsorbd watr on th xtrnal clay surfacs w (%) and th ffctiv strss σ' (kpa) is compltly linar whn both variabls ar shown in a doubl logarithmic scal and can b xprssd as: logw = logi - j log s ' w = i ( s ') -j (12) whr i (th watr contnt in th soil at σ' = 1 kpa) and j (th slop of th linar function that rprsnts th ratio btwn th watr contnt w (%) logarithm and th ffctiv strss σ' (kpa) logarithm) ar soil-dpndnt paramtrs. It was also found that ths paramtrs dpnd mainly on th xtrnal surfac ara A S (m 2 /g) and th contnt of clay minrals p in th soil's composition and can b xprssd as: i = p A (13) S j = 0.05 ( A p) (14) S Th known rlationship btwn A S (m 2 /g) and th Attrbrg limits (Eqs. (3), (4) and (5)) maks it possibl to xprss both paramtrs using th LL (%), th PL (%) or th PI (%) in th cas of limitd-swlling soils. Th portion of clay minrals p in th soil composition can b stimatd from th particl siz analysis. i = 2.57 PI p (15) PI -8.7 p j = 0.05 ( ) 0.54 p (16) 3.4 PREDICTING THE NORMALIZED UNDRAINED SHEAR STRENGTH It is vidnt from Sction 2 that th normalizd undraind shar strngth can only b corrlatd with th PI in th cas of non-swlling soils. It mans that thr is no uniform critrion to dtrmin th normalizd undraind shar strngth from th plasticity indx for all fin-graind soils. Th dpndnc of th undraind shar strngth s u on th vrtical ffctiv strss σ v ' at which th soils wr prviously consolidatd can b xprssd by considring Eq. (6) and (12), [19]. Not that th paramtr j = b. 8. ACTA GEOTECHNICA SLOVENICA, 2013/2

5 s u a = b sv ' (17) i Equation (17) shows that th valu s u / σ v ' is constant and dtrmind for diffrnt soils with th matrial paramtrs a, b (j ) and i. Bcaus ths paramtrs dpnd on th xtrnal surfac of soils A S and th portion of clay minrals p in th soil composition, Eq. (17) can b writtn as: su a p A = b = b s ' i p A v S b = 0.05 ( A p) S Th known rlationships btwn A S (m 2 /g) and th valus of th Attrbrg limits mak it possibl to xprss th s u / σ v ' valu in trms of th LL (%), th PL (%) or th PI (%) in th cas of limitd-swlling soils (Eq. (19)). s p PI = ; s ' p PI u b v b = 0.05 (( PI-8.74 p) 0.54 p) 3.5 PREDICTING THE HYDRAULIC CONDUCTIVITY OF SATURATED CLAYS Th xprimntal data of Dolinar [20] and many othr rsarchrs [21-24] indicat that a powr quation of th form (20) can b mployd to dscrib th variation of th hydraulic conductivity k (m/s) with th void ratio of soils. In th quation α and β ar soil-dpndnt paramtrs. k= a b (20) Th paramtrs α and β, which rflct th tortuosity of th flow path and th cross-sctional charactristics of th flow conduit, dpnd on th shap and th siz of th particls. Dolinar [20] found that for plat-lik clay particls ths paramtrs can b xprssd with Eqs. (21) and (22), dpnding on th xtrnal spcific surfac ara A S (m 2 /g) a = AS (21) b = 2.30 AS (22) Taking into account Eqs. (20), (21) and (22), th hydraulic conductivity k (m/s) of th clays can b xprssd as follows: S ; (18) (19) A S S k= A (23) Combining Eq. (23) with Eq. (5) lads to Eq. (24), which allows us to prdict th hydraulic conductivity k (m/s) of non-swlling or limitd-swlling clays using th plasticity indx PI (%) k= (PI -8.74) ( PI-8.74) 4 PRACTICAL EXAMPLES (24) Th us of th proposd quations for prdicting diffrnt proprtis of soils from th valus of thir Attrbrg limits ar prsntd in data takn from th litratur. Th first fiv sampls in Tabl 1 blong to htrognous fin-graind soils from diffrnt locations in which th minralogical and chmical compositions and th siz of th grains wr invstigatd [15, 19]. Th bulk minral composition and th clay fraction of th sampls wr dtrmind using th X-ray diffraction tchniqu (Tabl 1 and 2). Th rsults of chmical analyss wr usd to chck th quantity of individual minrals in th soils. Th grain siz distribution was dtrmind using a hydromtr mthod (Tabl 3). Th xtrnal spcific surfac aras of th invstigatd soils wr masurd using a fiv-point BET mthod with N 2, (Tabl 3). Th liquid limits of th sampls wr dtrmind by th fall-con tst and th plastic limits by th rolling-thrad tst in accordanc with th standard BSI [28], (Tabl 4). A mor dtaild dscription of th usd mthods can b found in th citd litratur. Th data for th pur clay sampls of kaolinit (sampl 6) and illit (sampl 7) aris from th papr of Msri and Olson [25], and wr usd for th comparison btwn th masurd and calculatd valus of th hydraulic conductivity of clays (Tabl 9). Th minralogical analyss indicat that htrognous soils contain montmorillonit in I/M, K/M, and Ch/M mixd layrd minrals or as Ca-montmorillonit. This mans that th quantitis of watr at th liquid and plastic limits consist of por watr w f, adsorbd watr on xtrnal clay surfacs w a and intrlayr watr w i ; thrfor, ths limits cannot b usd dirctly for prdicting th mchanical proprtis of invstigatd soils. In this cas it was ncssary to dcras th total watr contnt w at th LL and PL for th intrlayr watr portion w i in th xpanding soils. Th intrlayr watr quantity w i was calculatd with Eq. (25), [26]. A Si (d2-d 1) wi = p m (%) (25) ACTA GEOTECHNICA SLOVENICA, 2013/2 9.

6 Th basal spacing (th distanc btwn layrs) in th c dirction in th crystal structur, which is d 1 = 0.96 nm for calcium montmorillonit (drid at 105 C), incrasd to d 2 ~ 1.54 nm at a rlativ humidity of 80% and to d 2 = 1.9 nm in watr [27]. In th cas of xchangabl calcium ions in montmorillonit, th adsorption of watr btwn th layrs was thn compltd and th basal spacing rmaind practically constant. Whn calculating th intrlayr watr quantity w i with Eq. (25), considration was givn to th intrnal spcific surfac ara A si = m 2 /g (th adoptd valu from th litratur [13]) and appropriat mass portions of montmorillonit p m in th individual soils (Tabl 4). Th assumd basal spacings (d 2 ) of th montmorillonit at th PL and LL wr, rspctivly, 1.54 and 1.90 nm. Tabl 1. Minralogical composition of th whol soil sampls. Minral. composition Sampl (% mass) 6 7 Muscovit /Illit Chlorit Kaolinit Ca-montmorillonit Quartz Plagioclas Microclin Calcit Tabl 2. Th minralogical composition of th clay fraction < 2 μm. Minral. composition Sampl (% mass) Illit (I) Chlorit (Ch) Kaolinit (K) Ca-montmorillonit Mixd layr Tabl 3. Particl siz distribution and xtrnal spcific surfac ara of th soil sampls. Sampl % Clay % Silt % Sand A S m 2 /g ± ± ± ± ± 0.2 Tabl 4. Soil clay fraction (p), % Ca-montmorillonit (p m ), intrlayr watr contnts at th liquid and plastic limits (w i LL, w i PL ), intrgrain watr contnts at th liquid and plastic limits and plasticity indx (LL, PL, PI ), th liquid limit (LL), th plastic limit (PL), and th plasticity indx (PI). Physical Sampl proprtis 6 7 p p m (%) w i LL (%) w i PL (%) LL (%) LL (%) PL (%) PL (%) PI (%) PI (%) EXPERIMENTALLY DETERMINED AND CALCULATED EXTERNAL SPECIFIC SURFACE AREA Du to th prsnc of Ca-montmorillonit in th invstigatd soils th xtrnal spcific surfac ara was calculatd with Eq. (5) using th data of th plasticity indx PI (%) and th portion p of clay minrals in th soil s composition (p is th contnt (%) of clay minrals in th soil dividd by 100 (0 < p 1). Th xprimntally dtrmind and calculatd valus ar shown in Tabl 5. Tabl 5. Masurd and calculatd valus of th xtrnal spcific surfac ara A s (Dolinar, 2012). Input data Sampl Contnt of clay minrals p PI (%) A s (m 2 /g) masurd by BET mthod A s (m 2 /g) calculatd by Eq. (5) EXPERIMENTALLY DETERMINED AND CALCULATED UNDRAINED SHEAR STRENGTH Th undraind shar strngth of slctd sampls was tstd with a laboratory van tst [28]. Th disturbd sampls with th watr contnt nar th liquid limit wr prviously consolidatd at σ v ' = 50 kpa. Th most appropriat way to calculat th undraind shar strngth is th us of quations (10) or (11) du to th prsnc of 10. ACTA GEOTECHNICA SLOVENICA, 2013/2

7 Tabl 6. Masurd and calculatd valus of th undraind shar strngth s u. Input data Sampl Contnt of clay minrals p LL (%) LL = LL w i LL (%) Paramtr a calculatd by Eq. (7) Paramtr b calculatd by Eq. (8) PI M = log LL log PL CI M = (log LL log w) / PI M w (%) w * i (%) w = w w * i (%) Masurd s uw (kpa) Calculatd s uw (kpa) by Eq. (6) Calculatd s uw (kpa) by Eq. (10) or (11) * w i - Th avrag quantity of intrlayr watr in th plasticity rang of th soils is considrd. Ca-montmorillonit in th soils. Whn using Eq. (6) it is ncssary to calculat both paramtrs a and b from th intrgrain watr contnt and to dcras th total watr quantity w of th soils for th intrlayr watr portion w i *. Th quantity of intrlayr watr can only b calculatd for limitd-swlling clay minrals (Tabl 6). This procdur is givn as an xampl only and it is not usful in practic bcaus it rquirs prcis knowldg of th qualitativ and quantitativ minral composition of th soils. 4.3 EXPERIMENTALLY DETERMINED AND CALCULATED WATER CONTENT EFFECTIVE STRESS RELATIONSHIP Th quantity of watr in th saturatd soils was masurd undr an ffctiv strss σ' = 50 kpa using an odomtr consolidation tst. Th initial moistur contnt in th sampls was nar th liquid limit. Th quantitis of fr por watr and xtrnal surfac watr at th slctd axial strss wr calculatd using Eq. (12). To calculat th paramtrs i and j th quations (15) and (16) wr chosn du to th prsnc of limitdswlling minral in th soils (Tabl 7). Not that PI PI for limitd-swlling soils. 4.4 EXPERIMENTALLY DETERMINED AND CALCULATED NORMALIZED UNDRAINED SHEAR STRENGTH Th undraind shar strngth of slctd sampls was tstd with a laboratory van tst [28]. Th saturatd disturbd sampls wr prviously consolidatd at Tabl 7. Masurd and calculatd watr contnt ffctiv strss rlationship. Input data Sampl Contnt of clay minrals p PI (%) w * i (%) Paramtr i calculatd by Eq. (15) Paramtr j calculatd by Eq. (16) Masurd w at σ v ' = 50 kpa Calculatd w at σ v ' = 50 kpa by Eq. (12) w = w + w * i (%) * w i - Th avrag quantity of intrlayr watr in th plasticity rang of th soils is considrd. ACTA GEOTECHNICA SLOVENICA, 2013/2 11.

8 Tabl 8. Masurd and calculatd normalizd undraind shar strngth s u / σ v '. Input data Sampl Contnt of clay minrals p PI (%) Masurd s u (kpa) at σ v ' = 50 kpa Masurd s u /σ v ' Calculatd s u /σ v ' by Eq. (19) σ v ' = 50 kpa. Masurd and calculatd valus of th normalizd undraind shar strngth ar shown in Tabl 8. Mor xampls with a prcis xplanation of th proposd procdur ar givn in th papr of Dolinar [19]. 4.5 EXPERIMENTALLY DETERMINED AND CALCULATED HYDRAULIC CONDUC- TIVITY OF SATURATED CLAYS A comparison btwn th masurd and calculatd valus of th hydraulic conductivity using Eq. (24) was mad using data from th litratur [25]. Th shown sampls blong to sodium kaolinit with th plasticity indx PI = 19 % and sodium illit with th PI = 72 %. 5 CONCLUSION Th first part of this papr discussd rcnt findings that show how th soil composition influncs th watr contnt at th liquid and plastic limits. It was found that th quantity of watr at th Attrbrg limits dpnds mostly on th siz and th portion of clay minrals in non-swlling soils, whil in swlling soils it also dpnds on th quantity of intrlayr watr, which is mostly dpndnt on th typ of clay minrals, xchangabl cations and th chmical composition of th por watr. This mans that thr is no uniform critrion for dtrmining th intrdpndnc of th liquid and plastic limit valus and th minralogical proprtis of diffrnt soils. Considring that th mchanical proprtis of fingraind soils dpnd on th fr por watr only bcaus th adsorbd watr is tightly tid on th clay xtrnal and intrnal surfacs, that th rlationship btwn th quantity of fr por watr and th adsorbd watr on th xtrnal clay surfacs is xactly dfind, whil it is not tru for th fr por watr intrlayr watr rlationship and that Attrbrg limits always show th total watr contnt, lads to th conclusion that for swlling and non-swlling fin-graind soils, a uniform rlationship btwn th Attrbrg limits and othr mchanical proprtis dos not xist. Th abov findings hav allowd us to driv gnrally valid rlationships btwn th watr contnt and th diffrnt physical proprtis and thus also btwn th quantity of watr at th Attrbrg limits and othr physical proprtis for non-swlling soils and in som cass for limitd-swlling soils. Th paramtrs in th quations wr dtrmind by tsting artificially prpard sampls of mono-minral clay mixturs and ar valid for soils without organic mattr. Tabl 9. Masurd and calculatd valus of hydraulic conductivity. Sampl Void ratio Kaolinit PI = 72 % Masurd k (m/s) Calculatd k (m/s) by Eq. (24) Illit PI = 72 % Masurd k (m/s) Calculatd k (m/s) by Eq. (24) ACTA GEOTECHNICA SLOVENICA, 2013/2

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