ATTERBERG LIMITS IN RELATION TO OTHER PROPERTIES OF FINE-GRAINED SOILS
BOJANA DOLINAR and STANISLAV ŠKRABL
about the authors
corresponding author
Bojana Dolinar University of Maribor, Faculty of Civil Engineering Smetanova ul. 17, 2000 Maribor, Slovenia E-mail: bojana.dolinar@um.si
Stanislav Škrabl University of Maribor, Faculty of Civil Engineering Smetanova ul. 17, 2000 Maribor, Slovenia E-mail: stanislav.skrabl@um.si
Abstract
In soil mechanics the Atterberg limits are the most distinctive and the easiest property of fine-grained soils to measure. As they depend on the same physical factors as the other mechanical properties of soils, the values of the liquid and plastic limits would be a very convenient basis for their prediction. There are many studies concerning the use of the Atterberg limits in soil mechanics; however, their results vary considerably and are not generally applicable. This paper explains the main reasons for the different conclusions in these studies, which do not take into account the following: a) the water in fine-grained soils appears as interparticle and interaggregate pore water as well as adsorbed water onto the surfaces of clay minerals; b) the physical properties of fine-grained soils depend on the quantity of pore water only, because the adsorbed water is tightly tied on the clay's external and internal surfaces and thus cannot influence to them; c) the quantity of adsorbed water on the external surfaces of the clay minerals in soils depends mostly on the size and the quantity of the clay minerals, while the interlayer water quantity depends mostly on the quantity and the type of the swelling clay minerals in the soil composition and their exchangeable cations. From this it follows that for swelling and non-swelling soils, the uniform relationships between the Atterberg limits (which represent the total quantity of pore water and the adsorbed water onto the external and internal surfaces of clay minerals) and other physical prop-
erties does not exist. This paper presents some possibilities for the use of the Atterberg limits in predicting the soil's other properties for non-swelling and limited-swelling soils.
Keywords
Atterberg limits; specific surface area; undrained shear strength; compressibility; hydraulic conductivity
1 INTRODUCTION
The Atterberg limits represent the water content where the consistence of a fine-grained soil is transformed from a plastic state (plastic limit PL) to a liquid state (liquid limit LL) and from a semi-solid state (shrinkage limit SL) to a plastic state, as well as the water content at which different fine-grained soils have an approximately equal undrained shear strength, which is 1.7-2.7 kPa at the LL (depending on the method of measurement) and about 100 times greater at the PL. The quantity of water at the Atterberg limits and for the other physical properties depends on the same, mostly compositional factors, such as the type of minerals, the amount of each mineral, the shapes and size distribution of the particles and the pore-water composition [1], which leads to the conclusion that the exactly defined relationships between the values of the Atterberg limits and the soil's other properties must exist. Several researchers have tried to find the generally valid relationships between the quantity of water at the LL, the PL or at the plasticity index (PI=LL-PL) and various physical properties. The results of these studies, however, varied considerably and were valid in most cases for the investigated soils only. The main reasons for the different conclusions in these studies are explained in Section 2. The next section shows the empirically obtained relationships between the Atterberg limits and some other properties of the soil with an explanation about the limitations of their use. The comparison between the measured and the calculated values from the proposed correlations for different properties of the soils are shown in Section 4.
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This paper briefly summarizes all our already-published and new findings with the intention to understand more easily the impact of the mineralogical composition on the physical properties of fine-grained soils, the basic mechanisms that determine the physical properties, and thus the possible correlations between them. As an example, the possibilities of using the Atterberg limits to predict the soil's other properties are shown.
2 BASIC ASSUMPTIONS
Fine-grained soils contain both clay minerals and associated minerals, and the interactions between the clay minerals and water affect the soil's water-holding capacity. Water is strongly adsorbed onto the external surfaces of hydrophilic non-swelling clay minerals, whereas water adsorbs onto both the external and internal surfaces of swelling clay minerals. Besides the adsorbed water soils also contain free interparticle and interaggregate pore water [2]. It was found also that:
1.	most of the water in soils is associated with clay minerals [3];
2.	the pore sizes that effectively control fluid flow at the liquid limit are the same size for all soils [1] and, hence, the quantity of free pore water at the liquid limit is a constant;
3.	soils have similar pore water suction at the liquid limit [4-6]. This means that the ratio of adsorbed water to clay surface area should be about the same at the liquid limit;
4.	at the liquid limit, different fine-grained soils have approximately equal undrained shear strength [7-9];
5.	at the plastic limit the undrained shear strength is about 100 times the undrained shear strength at the liquid limit [10 and numerous subsequent authors];
6.	the quantity of interlayer water in swelling clays is mostly dependent on the type of the clay minerals, the exchangeable cations and the chemical composition of the pore water [11, 12].
On the basis of the above findings, Dolinar and Trauner [13, 14] assumed that the quantity of free pore water and external surface water at the liquid limit we\LL and the plastic limit we\pL can be expressed in terms of the external specific surface area and the clay minerals content by Eqs. (1) and (2).
We\LL = P-(wef\LL + Wea\LL ) = P - (wef\lL + ta\LL ' ASCe ) (1)
We\PL = P ■(wef\PL + Wea\PL ) = P - (wef\PL + ta\PL ' ASCe ) (2)
where w^ll and w^pl are the quantities of free pore water. These quantities are constant at the liquid and
plastic limits (according to item 2, 4 and 5). wea\LL and wea\PL are the quantities of firmly adsorbed water on the clay's external surfaces. These quantities of water depend on the size of the external surfaces of the clay mineral particles Agce because the thicknesses ta\LL, ta\PL of the firmly adsorbed water on the external surfaces are, for most clay minerals, constant at the liquid and plastic limits (according to item 3). The water content (pore water and external surface water) depends on the quantity of clay minerals in the soil, assuming that all the water in the soil is associated with the clay minerals (according to item 1).
The experimental tests on artificial mono-mineral clay mixtures confirmed the above assumptions (Fig.1). For non-swelling soils the liquid limit LLe (%) and plastic limit PLe (%) can thus be expressed as:
LLe = 31.90 ■ p + 0.81- ASe (3)
PLe = 23.16- p + 0.27 ■ ASe (4)
where Ase = p • Asce (m2/g) is the external specific surface area of the soil and P is the content (%) of clay minerals in the soil divided by 100 (0 < p < 1). Note that LL = LLe for non-swelling soils and LL = LLe + wt for swelling soils (w, is the quantity of interlayer water).
The above findings can be summarized in the following conclusions:
-	for non-swelling soils the water content at the LL and PL depends mostly on the specific surface area Ase and the content of clay minerals p in the soil composition;
-	for swelling soils the quantity of free pore water and adsorbed water on the clay's external surfaces depend on Ase and p, while the interlayer water content wt
is mostly dependent on the quantity and type of the swelling clay minerals, exchangeable cations and the chemical composition of the pore water. This explains why a general criterion cannot be found relating the water content at the Atterberg limits to the total specific surface area AS = ASe + ASi (ASi is internal specific surface area) for soils with and without swelling clay minerals. It should be noted that using a standard method for measuring the water content w, the total quantity of free pore water wef and strongly adsorbed water on the external wea and internal wt clay surfaces can always be determined by drying at a temperature of 100-110°C;
-	the physical properties of fine-grained soils depend only on the free pore water because the adsorbed water is tightly tied on the clay's external and internal surfaces.
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3-Ca-montmorillonite 7-43,5%(1)+56,5(3) 6-51,9%(1)+48,1(3) |
5-62,3%(1)+37,7%(3) i 2-kaolinile 4-kaoliniteJ 1-kaolinite^j
Ase (m=/g)
Figure 1. Quantity of pore water plus the external surface water at the liquid limit wejn (%), plastic limit we\pi (%) and plasticity index we\Pl (%) as a function of the specific surface area ASe (m2/g) for clay minerals (/>=1).
The above findings allow us to better understand the relationships between the quantity of water at the liquid and plastic limits and other properties of the soil and hence their proper use in predicting other physical properties of fine-grained soils.
3 CORRELATION OF THE
ATTERBERG LIMITS WITH THE SOIL'S OTHER PROPERTIES
3.1 DETERMINATION OF THE EXTERNAL SPECIFIC SURFACE AREA
For non-swelling soils, which only contain pore water and adsorbed water on the external surfaces of clay minerals, the specific surface area ASe (m2/g) can be expressed with Eqs. (3) and (4), depending on the LL and PL. The portion of clay minerals p could be equalled with the grain quantity < ^2m, determined using a hydrometer method.
For soils that contain limited-swelling clay minerals, the quantity of interlayer water (wt) at the LL and PL is approximately the same (w^ll ~ wp ^ PI ~ PIe), and the external specific surface area ASe (m2/g) can be expressed with Eq. (5), depending on the plasticity index PI (%).
PI = LL - PL ^ ASe = (PI - 8.74p)/0.54 (5)
For soils with other swelling clay minerals a correlation between the specific surface area and the Atterberg limits does not exist [15, 16].
3.2 DETERMINATION OF THE UNDRAINED SHEAR STRENGTH
Koumoto and Houlsby [9] present a relationship between the water content w and the undrained shear strength su using the following equation
W = asu-b (6)
where a and b are soil-dependent parameters. a (%) is the water content at the undrained shear strength su=1kPa, and b is the slope of the linear function that represents the ratio between the water content w(%) logarithm and the the undrained shear strength su(kPa) logarithm. According to Koumoto and Houlsby [9] the parameters a and b can only be obtained experimentally, while Trauner et al. [17] found that for non-swelling soils these parameters (ae , be) depend mainly on the external specific surface area Age (m2/g) of soils and the content of clay minerals p in the soil's composition and can be expressed by Eqs. (7) and (8). Age in the equations can be determined experimentally or calculated using Eqs. (3), (4) or (5), whilep can be estimated from a particle size analysis.
ae = 33.70-p + 0.99-ASe = 1.22 ■ LLe - 5.29-p (7)
be = 0.05■ (ASe/pf27 = 0.05-(LLe "811.90•p)°-27 (8)
0.81 ■ p
For both the swelling and non-swelling fine-grained soils, the undrained shear strength could be determined using the Atterberg limits and a modified plasticity index or modified consistency index. Equations (10)
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and (11), which show these relationships, are derived as follows:
The undrained shear strength of the soils at the liquid limit sun , determined by the fall cone test, can be calculated using Eq. (9)
W
su = K ■W (9)
h
where K is a constant depending on the type of cone and W is the cone mass. The theoretically determined value of the constant is K = 1.33 for the British cone [9] and the mass of the cone is W = 80 g. The depth of cone penetration that corresponds to the water content at the LL is h = 20 mm. The undrained shear strength is sull=2.66 kPa. The data of Skempton and Northey [10] and numerous subsequent authors show that the undrained shear strength at the PL is about 100 times the undrained shear strength at the LL (supl =266 kPa). Considering the above findings the water content at the LL and PL can be expressed as LL = a • 2.66-b (%) and PL = a •266-b (%). The form of these expressions suggests that it would be convenient to define a modified plasticity index as PIm = log LL - log LP, which makes it possible to express the parameters a and b in terms of PIm as follows [9]: b=log LL - log PL / log Sull - log Supl =PIm/-2 and a = LL / suLL-b = LL / 2.66"PIM/"2. At the selected water content w (%) the undrained shear strength suw (kPa) of the soils can thus be determined in terms of the liquid limit LL (%) and the modified plasticity index PIm by Eq. (10).
Suw = 2.66 ■ LL
2pIm ■ w-2PIM
(10)
The consistency index (CI) is defined as the ratio of the difference between the LL and the natural water content (w) to the plasticity index (PI) of a soil (CI=(LL - w)/PI). Consistent with the above discussion of the variation of strength with water content, it would be appropriate to define a new, modified consistency index as CIm = (log LL - log w) / PIm. By considering that log LL = log a - b • log Sull , log PL = log a - b • log Supl and log w = log a - b • log suw , the modified consistency index CIm can be written in the form ClM=(logsuLL-logSuw) / (logSuLL - logSuPL) = -0.212 + 0.5log Suw which makes it possible to express the undrained shear strength at a particular water content as:
S = 10 (CIM +°-212)/°-5	(11)
3.3 DETERMINATION THE WATER CONTENT - EFFECTIVE STRESS RELATIONSHIP
In a compressibility test of saturated soils the quantity of free pore water and adsorbed water on external clay
surfaces depends on the stress state and the physico-chemical properties of the clay minerals. It is known that the interlayer water cannot be drained from an expanding mineral under usual stresses, which leads to the conclusion that in the case of swelling soils a generally applicable relationship between the total water content and the effective stress does not exist.
On the basis of experimental tests Dolinar [18] found that the relationship between the free pore water plus the adsorbed water on the external clay surfaces we (%) and the effective stress d (kPa) is completely linear when both variables are shown in a double logarithmic scale and can be expressed as:
log we = log ie - je log s' ^ we = ie ■ (s')-je (12)
where ie (the water content in the soil at d = 1 kPa) and je (the slope of the linear function that represents the ratio between the water content w (%) logarithm and the effective stress d (kPa) logarithm) are soil-dependent parameters. It was also found that these parameters depend mainly on the external surface area Age (m2/g) and the content of clay minerals p in the soil's composition and can be expressed as:
ie = 33.46 ■ p + 1.39-ASe (13) je = 0.05 ■ (Ase/p)0'27 (14)
The known relationship between ASe (m2/g) and the Atterberg limits (Eqs. (3), (4) and (5)) makes it possible to express both parameters using the LLe (%), the PLe (%) or the PI (%) in the case of limited-swelling soils. The portion of clay minerals p in the soil composition can be estimated from the particle size analysis.
ie = 2.57 ■ PI +10.96 ■ p (15)
e = 0.05 P-^)»." (16) 0.54 ■ p
3.4 PREDICTING THE NORMALIZED UNDRAINED SHEAR STRENGTH
It is evident from Section 2 that the normalized undrained shear strength can only be correlated with the PI in the case of non-swelling soils. It means that there is no uniform criterion to determine the normalized undrained shear strength from the plasticity index for all fine-grained soils.
The dependence of the undrained shear strength su on the vertical effective stress dV at which the soils were previously consolidated can be expressed by considering Eq. (6) and (12), [19]. Note that the parameter je = be .
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Su = ~ ■ sv ' (17)
V ie
Equation (17) shows that the value su / aV is constant and determined for different soils with the material parameters ae , be (je) and ie . Because these parameters depend on the external surface of soils ASe and the portion of clay minerals p in the soil composition, Eq. (17) can be written as:
s„
- b
33.70-p + 0.99 ■ A
Se
' 33.46-p +1.39 ■ A
Se
(18)
be = 0.05 ■ (Ase/p)
0.27
The known relationships between Ase (m2/g) and the values of the Atterberg limits make it possible to express the su / aV value in terms of the LLe (%), the PLe (%) or the PI (%) in the case of limited-swelling soils (Eq. (19)).
=	be
17.68-p +1.83-PI
35
sv'	y 10.96-p + 2.57-PI
be = 0.05 - ((PI - 8.74p)/0.54p)°'27
PREDICTING THE HYDRAULIC CONDUCTIVITY OF SATURATED CLAYS
(19)
The experimental data of Dolinar [20] and many other researchers [21-24] indicate that a power equation of the form (20) can be employed to describe the variation of the hydraulic conductivity k (m/s) with the void ratio e of soils. In the equation a and ft are soil-dependent parameters.
k =
(20)
The parameters a and ft, which reflect the tortuosity of the flow path and the cross-sectional characteristics of the flow conduit, depend on the shape and the size of the particles. Dolinar [20] found that for plate-like clay particles these parameters can be expressed with Eqs. (21) and (22), depending on the external specific surface area A& (m2/g).
a = 4.08 -10-6 A-3'03 (21)
ß = 2.30 A0e234
(22)
Taking into account Eqs. (20), (21) and (22), the hydraulic conductivity k (m/s) of the clays can be expressed as follows:
k = 4.08 -10-6 A-3'03 e2'30 Ase
(23)
Combining Eq. (23) with Eq. (5) leads to Eq. (24), which allows us to predict the hydraulic conductivity k (m/s) of non-swelling or limited-swelling clays using the plasticity index PI (%).
k = -
6.3110-
2.66 (PI-8.74)0'
(PI - 8.74)
3.03
(24)
4 PRACTICAL EXAMPLES
The use of the proposed equations for predicting different properties of soils from the values of their Atterberg limits are presented in data taken from the literature. The first five samples in Table 1 belong to heterogeneous fine-grained soils from different locations in which the mineralogical and chemical compositions and the size of the grains were investigated [15, 19]. The bulk mineral composition and the clay fraction of the samples were determined using the X-ray diffraction technique (Table 1 and 2). The results of chemical analyses were used to check the quantity of individual minerals in the soils. The grain size distribution was determined using a hydrometer method (Table 3). The external specific surface areas of the investigated soils were measured using a five-point BET method with N2, (Table 3). The liquid limits of the samples were determined by the fall-cone test and the plastic limits by the rolling-thread test in accordance with the standard BSI [28], (Table 4). A more detailed description of the used methods can be found in the cited literature. The data for the pure clay samples of kaolinite (sample 6) and illite (sample 7) arise from the paper of Mesri and Olson [25], and were used for the comparison between the measured and calculated values of the hydraulic conductivity of clays (Table 9).
The mineralogical analyses indicate that heterogeneous soils contain montmorillonite in I/M, K/M, and Ch/M mixed layered minerals or as Ca-montmorillonite. This means that the quantities of water at the liquid and plastic limits consist of pore water wef, adsorbed water on external clay surfaces wea and interlayer water wi ; therefore, these limits cannot be used directly for predicting the mechanical properties of investigated soils. In this case it was necessary to decrease the total water content w at the LL and PL for the interlayer water portion wi in the expanding soils. The interlayer water quantity wi was calculated with Eq. (25), [26].
ASi(d2 - d1) „
= 2-103 - p«
(%) (25)
s
u
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The basal spacing (the distance between layers) in the c direction in the crystal structure, which is = 0.96 nm for calcium montmorillonite (dried at 105°C), increased to d2 ~ 1.54 nm at a relative humidity of 80% and to d2 = 1.9 nm in water [27]. In the case of exchangeable calcium ions in montmorillonite, the adsorption of water between the layers was then completed and the basal spacing remained practically constant. When calculating the interlayer water quantity wj with Eq. (25), consideration was given to the internal specific surface area Asj = 626.80 m2/g (the adopted value from the literature [13]) and appropriate mass portions of montmorillonite pm in the individual soils (Table 4). The assumed basal spacings (d2) of the montmorillonite at the PL and LL were, respectively, 1.54 and 1.90 nm.
Table 1. Mineralogical composition of the whole soil samples.
Mineral. compo-				Sample		
sition (% mass)	1	2	3	4	5	6 7
Muscovite /Illite	25	35	28	35	34	100
Chlorite	8	14	16	0	18	
Kaolinite	5	0	0	12	0	100
Ca-montmoril-lonite	14	0	0	34	0	
Quartz	34	25	42	19	43	
Plagioclase	9	3	9	0	3	
Microcline	5	0	4	0	3	
Calcite	0	23	0	0	0	
Table 2. The mineralogical composition of the clay fraction < 2 |im.						
Mineral. composition				Sampl		e
(% mass)			1	2	3	4 5
Illite (I)			11	12	6	13 12
Chlorite (Ch)			0	3	7	00
Kaolinite (K)			4	3	0	57
Ca-montmorillonite			14	4	2	34 0
Mixed layer			10	19	14	19 25
Table 3. Particle size distribution and external specific surface area of the soil samples.						
Sample % Clay		% Silt		% Sand		m2/g
1 39.1		58.1		2.8		30.1 ± 0.4
2 40.7		56.9		2.4		28.5 ± 0.4
3 29.2		60.6		10.2		16.7 ± 0.1
4 70.7		27.2		2.1		54.1 ± 0.3
5 44.2		53.9		1.9		32.6 ± 0.2
Table 4. Soil clay fraction (p), % Ca-montmorillonite (pm), interlayer water contents at the liquid and plastic limits (w^n , Wjpi), intergrain water contents at the liquid and plastic limits and plasticity index (LLe , PLe , PIe), the liquid limit (LL), the plastic limit (PL), and the plasticity index (PI).
Physical				Sample			
properties	1	2	3	4	5	6	7
P	0.39	0.41	0.29	0.71	0.44	1.00	1.00
Pm (%)	14	4	2	34	0	0	0
Wi|LL (%)	4.12	1.18	0.59	10.02	0	0	0
Wi\PL (%)	2.54	0.72	0.36	6.18	0	0	0
LL (%)	47.2	44.0	31.2	82.1	43.1	50	104
LLe (%)	43.1	42.9	30.6	72.7	43.1	50	104
PL (%)	24.3	22.7	18.7	44.9	22.0	31	32
PLe (%)	21.7	22.0	18.3	39.1	22.0	31	32
PI (%)	22.9	21.3	12.5	37.2	21.1	19	72
PIe (%)	21.4	20.9	12.3	33.6	21.1	19	72
4.1 EXPERIMENTALLY DETERMINED AND CALCULATED EXTERNAL SPECIFIC SURFACE AREA
Due to the presence of Ca-montmorillonite in the investigated soils the external specific surface area was calculated with Eq. (5) using the data of the plasticity index PI (%) and the portion p of clay minerals in the soil's composition (p is the content (%) of clay minerals in the soil divided by 100 (0 < p < 1). The experimentally determined and calculated values are shown in Table 5.
Table 5. Measured and calculated values of the external specific surface area Ase (Dolinar, 2012).
Input data			Sample		
	1	2	3	4	5
Content of clay minerals p	0.39	0.41	0.29	0.71	0.44
PI (%)	22.9	21.3	12.5	37.2	21.1
Ase (m2/g) measured by BET method	30.1	28.5	16.7	54.1	32.6
Ase (m2/g) calculated by Eq. (5)	36.1	32.8	18.4	57.4	32.0
4.2 EXPERIMENTALLY DETERMINED AND CALCULATED UNDRAINED SHEAR STRENGTH
The undrained shear strength of selected samples was tested with a laboratory vane test [28]. The disturbed samples with the water content near the liquid limit were previously consolidated at aV = 50 kPa. The most appropriate way to calculate the undrained shear strength is the use of equations (10) or (11) due to the presence of
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Table 6. Measured and calculated values of the undrained shear strength su
Input data			Sample		
	1	2	3	4	5
Content of clay minerals p	0.39	0.41	0.29	0.71	0.44
LL (%)	47.2	44.0	31.2	82.1	43.1
LLe = LL - Wj|LL (%)	43.1	42.9	30.6	72.7	43.1
Parameter a calculated by Eq. (7)	50.49	50.07	35.81	84.18	50.25
Parameter b calculated by Eq. (8)	0.1719	0.1683	0.1689	0.1664	0.1641
PIm = log LL - log PL	0.2883	0.2874	0.2223	0.2621	0.2921
CIm = (log LL - log w) / PIm	0.3477	0.2311	0.2697	0.3606	0.3214
W (%)	37.47	37.76	25.82	66.04	34.72
wj*(%)	3.33	0.95	0.47	8.10	0
We = W - Wj*(%)	34.14	36.81	25.35	57.94	34.72
Measured suw (kPa)	11.3	10.8	9.4	10.9	10.1
Calculated suw (kPa) by Eq. (6)	9.7	6.2	7.7	9.4	9.5
Calculated suw (kPa) by Eq. (10) or (11)	13.2	7.7	14.6	14.0	11.7
Wj - The average quantity of interlayer water in the plasticity range of the soils is considered.
Ca-montmorillonite in the soils. When using Eq. (6) it is necessary to calculate both parameters ae and be from the intergrain water content and to decrease the total water quantity w of the soils for the interlayer water portion wj. The quantity of interlayer water can only be calculated for limited-swelling clay minerals (Table 6). This procedure is given as an example only and it is not useful in practice because it requires precise knowledge of the qualitative and quantitative mineral composition of the soils.
4.3 EXPERIMENTALLY DETERMINED AND CALCULATED WATER CONTENT-EFFECTIVE STRESS RELATIONSHIP
The quantity of water in the saturated soils was measured under an effective stress a' = 50 kPa using
an oedometer consolidation test. The initial moisture content in the samples was near the liquid limit. The quantities of free pore water and external surface water at the selected axial stress were calculated using Eq. (12). To calculate the parameters je and je the equations (15) and (16) were chosen due to the presence of limited-swelling mineral in the soils (Table 7). Note that PI ~ PIe for limited-swelling soils.
4.4 EXPERIMENTALLY DETERMINED AND CALCULATED NORMALIZED UNDRAINED SHEAR STRENGTH
The undrained shear strength of selected samples was tested with a laboratory vane test [28]. The saturated disturbed samples were previously consolidated at
Table 7. Measured and calculated water content-effective stress relationship.
Input data			Sample		
	1	2	3	4	5
Content of clay minerals p	0.39	0.41	0.29	0.71	0.44
PI (%)	22.9	21.3	12.5	37.2	21.1
w-(%)	3.33	0.95	0.47	8.10	0
Parameter i calculated by Eq. (15)	63.17	59.28	35.33	103.46	59.09
Parameter j calculated by Eq. (16)	0.1698	0.1633	0.1535	0.1637	0.1591
Measured w at aj = 50 kPa	37.5	37.7	25.8	66.0	34.7
Calculated we at aj = 50 kPa by Eq. (12)	32.5	31.3	19.4	54.5	31.7
We = W + Wj*(%)	35.8	32.2	19.9	62.6	31.7
Wj - The average quantity of interlayer water in the plasticity range of the soils is considered.
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Table 8. Measured and calculated normalized undrained shear strength su / av'.
Input data			Sample		
	1	2	3	4	5
Content of clay minerals p	0.39	0.41	0.29	0.71	0.44
PI (%)	22.9	21.3	12.5	37.2	21.1
Measured su (kPa) at aj = 50 kPa	11.3	10.8	9.4	10.9	10.1
Measured su /aj	0.23	0.22	0.19	0.22	0.20
Calculated su /aj by Eq. (19)	0.24	0.24	0.24	0.24	0.24
aj = 50 kPa. Measured and calculated values of the normalized undrained shear strength are shown in Table 8. More examples with a precise explanation of the proposed procedure are given in the paper of Dolinar [19].
4.5 EXPERIMENTALLY DETERMINED AND CALCULATED HYDRAULIC CONDUCTIVITY OF SATURATED CLAYS
A comparison between the measured and calculated values of the hydraulic conductivity using Eq. (24) was made using data from the literature [25]. The shown samples belong to sodium kaolinite with the plasticity index PI = 19 % and sodium illite with the PI = 72 %.
5 CONCLUSION
The first part of this paper discussed recent findings that show how the soil composition influences the water content at the liquid and plastic limits. It was found that the quantity of water at the Atterberg limits depends mostly on the size and the portion of clay minerals in non-swelling soils, while in swelling soils it also depends on the quantity of interlayer water, which is mostly
dependent on the type of clay minerals, exchangeable cations and the chemical composition of the pore water. This means that there is no uniform criterion for determining the interdependence of the liquid and plastic limit values and the mineralogical properties of different soils. Considering that the mechanical properties of finegrained soils depend on the free pore water only because the adsorbed water is tightly tied on the clay external and internal surfaces, that the relationship between the quantity of free pore water and the adsorbed water on the external clay surfaces is exactly defined, while it is not true for the free pore water-interlayer water relationship and that Atterberg limits always show the total water content, leads to the conclusion that for swelling and non-swelling fine-grained soils, a uniform relationship between the Atterberg limits and other mechanical properties does not exist.
The above findings have allowed us to derive generally valid relationships between the water content and the different physical properties and thus also between the quantity of water at the Atterberg limits and other physical properties for non-swelling soils and in some cases for limited-swelling soils. The parameters in the equations were determined by testing artificially prepared samples of mono-mineral clay mixtures and are valid for soils without organic matter.
Table 9. Measured and calculated values of hydraulic conductivity.
Sample			Void ratio e		
	1.90	1.80	1.70	1.50	1.30
Kaolinite PI = 72 %					
Measured k (m/s)	1.1310-8	8.0940-9	5.7840-9	2.9540-9	1.5110-9
Calculated k (m/s) by Eq. (24)	1.0340-8	9.0740-9	6.2M0-9	3.4940-9	1.8110-9
Illite PI = 72 %					
Measured k (m/s)	2.68-10-10	1.93-10-10	1.39-10-10	7.19-10-11	3.73-10-11
Calculated k (m/s) by Eq. (24)	1.9940-10	1.3640-10	9.1240-11	3.7940-11	1.3940-11
12. ACTA GeOïeCHNICA SLOVENICA, 2013/2
B. DOLINAR & S. SKRABL: ATTERBERG LIMITS IN RELATION TO OTHER PROPERTIES OF FINE-GRAINED SOILS
references
[1]	Mitchell, J. K. (1993). Fundamentals of Soil Behaviour. John Wiley&Sons, Inc., New York.
[2]	Fripiat, J.J., Letellier, M., Levitz,P. (1984). Interaction of water with clay surface. Philosophical Transactions of the Royal Society of London, A311, 287-299.
[3]	Seed, H.B., Woodward, R.J., Lundgren, R. (1964). Clay mineralogical aspects of Atterberg limits. Journal of Soil Mechanics and Foundations Division 90, 4, 107-131.
[4]	Russell, E.R., Mickle, J.L. (1970). Liquid limit values of soil moisture tension. Journal of soil mechanics and Foundations Division 96, 967-987.
[5]	Tuller, M., Or, D. (2005). Water films and scaling of soil characteristic curves at low water contents. Water Resources Research 41:W09403.
[6]	Dolinar, B., Skrabl, S. (2012). The matrix potential of fine-grained soils at the liquid limit. Eng. geol. 135-136, 48-51, doi: 10.1016/j.enggeo.2012.03.003.
[7]	Casagrande, A. (1932). Research on the Atterberg limits of soils. Public Roads, 13, 121-136.
[8]	Wroth, C.P., Wood, D.W. (1978). The correlation of index properties with some basic engineering properties of soils. Canadian Geotechnical Journal 15, 2, 137-145.
[9]	Koumoto, T., and Houlsby, G.T. (2001). Theory and practice of the fall cone test. Geotechnique LI, 8, 701-712.
[10]	Skempton, A., Northey R.D. (1953). The sensitivity of clays. Geotechnique 3, 1, 30-53.
[11]	Grim, R.E. (1962). Applied Clay Mineralogy. McGraw-Hill Company, USA.
[12]	Bergaya, F., Theng, B.K.G., Lagaly, G. (2006). Handbook of clay science, first ed. Elsevier Science, Netherlands.
[13]	Dolinar, B., and Trauner, L. (2004). Liquid limit and specific surface of clay particles. Geotechnical Testing Journal 27, 580-584.
[14]	Dolinar, B., and Trauner, L. (2005). Impact of Soil Composition on fall Cone test Results. Journal of Geotechnical and Geoenvironmental Engineering 131, 1, 126-130.
[15]	Dolinar, B., Misic, M., Trauner, L. (2007). Correlation between surface area and Atterberg Limits of fine-grained soils. Clays and clay miner., 55, 5, 519-523.
[16]	Dolinar,B. (2012). A simplified method for determining the external specific surface area of non-swelling fine-grained soils. Applied clay science, 64, 34-37, doi: 10.1016/j.clay.2009.12.013.
[17]	Trauner, L., Dolinar, B., Misic, M. (2005). Relationship between the undrained shear strength,
water content, and mineralogical properties of fine-grained soils. International journal of geome-chanics 5, 4, 350-355. http://dx.doi.org/10.1061/ (ASCE)1532-3641(2005)5:4(350).
[18]	Dolinar, B. (2006). The impact of mineral composition on compressibility of saturated soils. Mechanics of materials 38, 7, 599-607. http://dx.doi. org/10.1016/j.mechmat.2005.11.003.
[19]	Dolinar, B. (2010). Predicting the normalized, undrained shear strength of saturated fine-grained soils using plasticity-value correlations. Applied clay science 47, 3/4, 428-432, doi: 10.1016/j. clay.2009.12.013.
[20]	Dolinar, B. (2009). Predicting the hydraulic conductivity of saturated clays using plasticity-value correlations. Applied. clay science 45, 1/2, 90-94. doi: 10.1016/j.clay.2009.04.001.
[21]	Carrier, W.D., Beckman, J.F. (1984). Some recent observations on the fundamental properties of remoulded clays. Geotechnique 34, 2, 211-228.
[22]	Krizek, R.J., Somogyi, F. (1984). Perspectives on modelling consolidation of dredged materials. Proc. ASCE Symp. On Sedimentation Consolidation Models, San Feancisco.
[23]	Al-Tabba, A., Wood, D.M. (1987). Some measurements of the permeability of kaolin. Geotechnique 37, 4, 499-503.
[24]	Pane, V., Schiffman, R.L. (1997). The permeability of clay suspensions. Geotechnique 47, 2, 273-288.
[25]	Mesri, G., Olson, R.E. (1971). Mechanisms controlling the permeability of clays. Clays and Clay minerals, 19, 151-158.
[26]	Fink, D.H., Nakayama, F.S. (1972). Equation for describing the free swelling of montmorillonite in water. Soil Science 114 (5), 355-358.
[27]	Brindley GW, Brown G. (1980). Crystal structures of clay minerals and their X-ray identification. Mineralogical Society, London, pp. 495.
[28]	British Standards Institution, 1990. Methods of test for soils for civil engineering purposes, BS 1377.
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