Relationship Between the Atterberg Limits and Clay Content

SOILS AND FOUNDATIONS Vol. 47, No. 5, 887–896, Oct. 2007 Japanese Geotechnical Society

RELATIONSHIP BETWEEN THE ATTERBERG LIMITS AND CLAY CONTENT

ENNIO POLIDORIi)

ABSTRACT This study investigates the liquid limit (Casagrande's method) and plastic limit (rolling and thread method) of six inorganic soils and their respective mixtures with ˆne silica sand. It was observed that the liquid limit and plastic limit values of the mixtures tested, except those with a low clay percentage, are linked to the respective clay size contents by a linear relationship. The Atterberg limits were subsequently recalculated using the equations of the regression lines of the mixtures governed by linear law with the clay percentages. The plotting of the plastic limit as a function of the liquid limit of these data made it possible to determine the relationship among the liquid limit, the plastic limit and clay fraction valid for inorganic soils that contain platey clay minerals and for clay size contents that are not too low.

Hence, on the basis of the interdependence among the parameters considered (WL, Wp, Ip, CF, A), for a given inorganic soil, knowing only two of three parameters (WL, Wp, CF ) that are measurable using standard tests, the values of other three parameters can be obtained.

Key words: Atterberg limits, clay, laboratory tests, plasticity, soil classiˆcation (IGC:D1/D3)

kedly, while the liquid limit of the clay mineral kaolinite INTRODUCTION is not in‰uenced (Di Maio and Fenelli, 1994). Hence, for If a clayey soil is mixed with ever increasing amounts of a given soil, the values of the Atterberg limits, which are water it becomes softer and softer and a point will be the result of the combination of all the factors, provide reached at which the soil ceases to behave as a plastic insight into that soil's plasticity characteristics for every material and becomes essentially a viscous ‰uid. Atter- possible combination of the factors that in‰uence the berg (1911) suggested a method for deˆning this change, plasticity of a soil. and the water content of the soil at this point is its liquid There are few studies in literature on the Atterberg limit, WL. Likewise, Atterberg deˆned the change from a limits of soils as a function of their clay size contents and plastic to a semi-solid state, and the water content of the the results of these studies are not always in agreement. soil at this point is its plastic limit, Wp. The methods to These studies have focused primarily on the liquid limit determine the liquid and plastic limits, later developed by of clay minerals mixed with silica sand (Seed et al., 1964a, Casagrande (1932, 1958), are considered standard inter- 1964b; Sivapullaiah and Sridharan, 1985; Tan et al., national tests. These limits and the numerical diŠerence 1994; Nagaraj et al., 1995; Kumar and Muir Wood, between them, the plasticity index, Ip, are very useful to 1999). Seed et al. (1964b) in a study on the Atterberg characterize, classify and predict ˆne soils engineering be- limits of the clay minerals kaolinite, illite and montmoril- haviour. lonite and their respective mixtures with sand, concluded The Atterberg limits of a soil depend on its composi- that, for clay percentages which are not too low, the liq- tion (quantity and type of clay minerals) and so-called dy- uid and plastic limits are both linked by a linear relation- namic factors (Veniale, 1983) such as, pH, temperature, ship to their clay size contents. The respective regression cation exchange capacity, type and quantity of cations in lines pass through the origin of the axes. Nevertheless, the the solution, etc., which vary in space and time for natur- plastic limit values reported by Seed et al. (1964b) of the al soils. An example of dynamic variables can be found in montmorillonite-sand mixtures are less than those of the continuous alteration of the environment by human kaolinite-sand mixtures with the same clay percentages. activities, such as the impact of acid rain and chemical Conversely, White (1949) in his study of the Atterberg products used in agriculture. Dynamic factors can have a limits of the most common clay minerals concluded that strong eŠect on the liquid limit value, though such eŠects the plastic limit of montmorilloniteÀ(illite)Àkaolinite. may vary according to the type of clay minerals. For ex- The same conclusion was traced later by Mitchell (1993). ample, as the concentration of salts increases, the liquid Several attempts to link plasticity index with liquid limit of the clay mineral montmorillonite decreases mar- limit, mostly through the empirical correlations, ignoring

i) Institute of Applied Geology, University of Urbino `Carlo Bo' `Sogesta' Scientiˆc Campus, Italy (ennio.polidori＠uniurb.it). The manuscript for this paper was received for review on December 11, 2006; approved on May 29, 2007. Written discussions on this paper should be submitted before May 1, 2008 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

887 888 POLIDORI the content of non-clay particles (À2 mm) are reported in fraction, CF (º2 mm) in each soil was lowered in succes- literature (Casagrande, 1948; Seed et al., 1964b; Nagaraj sive steps by adding sand to obtain changes of 10z and Jayadeva, 1983; Sivapullaiah and Sridharan, 1985; weigth of CF up to a minimum of 10z (for bentonite Panadian and Nagaraj, 1990). ``c''). The silica sample used in the mixtures is composed This study, based on compositional factors (amount of 85z ˆne sand. and type of clay minerals), investigates how the liquid The geotechnical characterization was performed ac- limit and the plastic limit vary as a function of clay size cording to international ASTM standards (D 422 and D contents in inorganic soils with platey clay minerals. On 4318). First the grain size distribution was determined the basis of the average values (using equations of the and then the liquid limit (Casagrande's method) and the regression lines) of the experimental data collected a plastic limit (rolling thread method) of the soils and mix- relationship between the Atterberg limits and the clay fractions is then investigated. Since the non-platey clay minerals such as halloysite, allophane, attapulgite have characteristics very diŠerent from that of platey clay minerals (e.g., high plastic limit, low index plasticity) (Mitchell, 1993), they are excluded from the present research as organic soils are.

GEOTECHNICAL AND MINERALOGICAL CHARACTERIZATION Experiments were carried out on six inorganic soils and on their respective mixtures with ˆne silica sand. Three of the soils were composed of bentonite, one was composed of kaolinite (commercially available), another was composed of 1:1 mixture of kaolinite- bentonite whereas the Fig. 1. Liquid limit, WL and plastic limit, Wp as function of clay frac- last soil was a natural soil belonging to the Formation of tion CF (º2 mm) of soils and their respective mixtures with ˆne sili- Varicoloured Clays (upper Cretaceous-lower Eocene) ca sand. 1＝kaolinite-sand mixtures; 2, 5 and 6＝bentonite ``a'', Central Italy. Their characteristics are summarized in ``b'' and ``c''-sand mixtures, respectively; 3＝(1:1) kaolinite-bentonite ``c''-sand mixtures; 4＝varicoloured clays-sand mixtures Tables 1 and 2. In the soil-sand mixtures (Fig. 1) the clay

Table 1. Index properties of inorganic soils used in present study

Soil Soil type Sand Silt Clay WL Wp Ip A r 1 kaolinite — 8 92 62 36 26 0.28 2.64 2 bentonite ``a'' 5 20 75 153 36 117 1.55 2.76 3 (1:1) soils 1–6 mixture — 19 81 170 38 132 1.63 2.69 4 varicoloured clays — 14 86 193 41 152 1.77 2.79 5 bentonite ``b'' 3 27 70 260 39 221 3.16 2.75 6 bentonite ``c'' — 30 70 343 42 301 4.30 2.75

3 Sand, silt, clay, WL, Wp and Ip are in z. r (density) is in gWcm . A＝activity.

Table 2. Mineralogical composition of inorganic soils used in present study

Soil Soil type Fraction size C D Mineralogy

1kaolinite zº2 mm — — Kaolinite (97z) with a good degree of crystallinity and illite (3z) zÀ2 mm — — Aggregations of kaolinite crystals. 2 bentonite ``a'' zº2 mm — — Montmorillonite (100z)withgooddegreeofcrystallinity. zÀ2 mm 3 — Quartz and calcium carbonate. 4 varicoloured clays zº2 mm — — In order of respective quantities: vermiculite with low degree of crystallinity, interbedded illite-vermiculite, kaolinite and traces of illite. Presence of quartz. zÀ2 mm 3 — Quartz and calcium carbonate. 5 bentonite ``b'' zº2 mm — 4 Montmorillonite (96z) with good degree of crystallinity and dolomite. zÀ2 mm 2 — Quartz and calcium carbonate. 6 bentonite ``c'' zº2 mm — 8 Montmorillonite with low degree of crystallinity, interbedded illite- montmorillonite. Presence of dolomite and amorphous ferrous hydroxides. zÀ2 mm 2 14 Dolomite, quartz and calcium carbonate. C (calcium carbonate) and D (dolomite) are in z ATTERBERG LIMITS AND CLAY CONTENT 889 tures with sands. Some standards, in addition to etc.). The combination of these factors provides a very Casagrande's method, have included the fall-cone wide range of slope values (from 0.67 to 4.86 in Fig. 1), method. Both methods have advantages and disavan- where the minimum and maximum values belong to tages. For example, (with reference to this study) the cone kaolinite and montmorillonite in monovalent ionic form, penetration method is not suitable for very expansive respectively. WL and CF are deˆned in percentages. soils (Wasti and Bezirci, 1986). In a saturated soil also composed of non-clay particles, Grain size distribution of the silica sample and the soils assuming that all of the water is associated with the clay was obtained using the sieve and hydrometer methods, phase (Seed et al., 1964b; Mitchell, 1993), the constant respectively. The percentage of clay in the mixture was volume of the non-clay fraction and the volume of the determined as the percentage by weight of particles ˆner clay-water system, which varies as a function of water than 2 mm in the commercial clay and the natural soil contents, can be distinguished. From experimental data added to the ˆne silica sand. collected, in agreement with Seed et al. (1964b), the linear

The liquid limit of the samples was determined to es- relation (WL, CF ) is respected until the volume of the tablish a minimum of four points in order to plot the ‰ow clay-water system is greater than the volume of the void line. The plastic limit was determined by the average of of the non-clay fraction in the mixtures, or in other four or more water contents. This procedure was applied words, until the non-clay particles are still not in contact to each soil and later to the mixtures with silica sand. with one another. Since the thread-rolling method is considered operator- The volume of voids in the non-clay fraction is: dependent (see below), the plastic limit tests were repeat- (xWrs)es (2) ed, and the average of the values was considered in order to improve the alignment of the points of the mixtures in which x is the mass of the non-clay fraction; rs＝den- plotted on the graph. sity of the soil particles in the non-clay fraction; es＝void The mixtures were prepared by mixing the above-men- ratio in the non-clay fraction. tioned dry components followed by, adding deionized The volume of clay-water mixture at its WL,is: water. Since the mixtures are composed of percentages in (yWrc)＋[(WLc yW100)Wrw](3) weight of the respective components, the samples were placed in an oven at 609C to eliminate humidity absorbed in which y is the dry-mass of the clay particles required from the atmosphere before being mixed. The silica silt (when mixed with the water) just to ˆll the voids in the

(87z silt and 13zº2 mm) used in some mixtures (with non-clay fraction; rc is the density of the solid particles in soils no. 1, 3 and 6) did not yield diŠerent values of the the clay fraction; rw is the density of the water (＝1); WLc Atterberg limits than those obtained by adding ˆne silica is the liquid limit of the clay particles y (CF＝100z). sand. This will just ˆll the voids in the non-clay fraction The qualitative and semiquantitative mineralogical when: analyses (Table 2) were performed using the XRD analy- (yWrc)＋[(WLc yW100)Wrw]＝(xWrs)es (4) sis with a Philips PW 2273W20 diŠractometer, CuKa radi- ation, Ni ˆlter with a scanning velocity of 0.0392uWs. The Solving Eq. (4) for y (and neglecting rw), will be: clay fraction (º2 mm) was analyzed on samples that were y＝(xes)W[rs(1Wrc＋WLc W100] (5) air dried and treated with glycol-ethylene.

the percentage of dry clay (Cm) which, when mixed with

the water at its WL, will ˆll the voids in the granular EXPERIMENTAL DATA AND DISCUSSION phase, is: Liquid Limit Cm＝[ yW(x＋y)]100 (6) Figure 1 shows the liquid limit and the plastic limit as a function of the clay size contents of the soils and the mix- Since the values of rs and rc generally diŠer slightly, the tures tested. The values of the liquid limit of the mixtures value of Cm mainly depends on the void ratio (es)ofthe of each soil with sand, except those with a low clay frac- non-clay fraction and the liquid limit slope (k1)ofthe tion, lie more or less linearly with the clay percentage. soil. The best average linear relationship was found to pass An inorganic soil with a water content equal to its liq- through the origin, in agreement with Seed et al. (1964b), uid limit, (mainly as a function of its CF and es) could be Nagaraj et al. (1995) and Kumar and Muir Wood (1999). found in one of the following two physical states: The respective equations are shown in Fig. 1. (a) soils in which all the round particles are scattered

Hence, the liquid limit equation valid for inorganic in the clay-water system (CFÀCm); soils containing platey clay minerals (with CFÀCm,de- (b) soils in which all or a part of the round particles ˆned below) is: are in contact with one another (CFº or slightly ÀC ). W ＝k CF (1) m L 1 The soils found in condition (a) should have a liquid where the WL-slope k1 depends on the factors that in- limit directly proportional to their clay fractions, as ‰uence the plasticity of a soil (such as type of clay miner- shown in Eq. (1). In condition (b), the greater resistance al, type of adsorbed cation, pH, degree of crystallinity, of the soil (placed in the cup apparatus) to deformation, 890 POLIDORI

produced by contact of the non-clay particles, allows this into the equation (CFWrc)＋(WWrw)＝[(100－CF )Wrs] es soil to retain a larger amount of water and as a conse- (that is equivalent to Eq. (4), setting W＝WLc yW100). The quence the values of the liquid limit will be greater than determination of es of the fraction À2 mm of a soil is the values predicted by Eq. (1). In fact, the slurrie soils cumbersome and time consuming. Nevertheless, on the with low clay size content tend to slide rather than ‰ow as basis of the data collected in this study and insights into plastic material when placed in the cup. On the basis of clayey soils reported in Mitchell (1993), the liquid limit the data of the tested mixtures, it was observed that the should be determined in the soil fraction with a clay frac- relative increase of the liquid limit values passing from tion greater than 20–25z so that the relationship WL-CF physical state (a) to physical state (b) occurs gradually, is governed by a linear law also for soils that contain less with initial values of CFÀCm (probably for the geometri- expansive clay minerals (kaolinite) and with high values cal proximity of the round particles andWor the contact of of es. some particles). For the sake of clarity, these values (not proportional with CF) are here deˆned as `ànomalous'' Plastic Limit (Fig. 1) and they are not included in the elaboration of the The data of the plastic limit (Figs. 1 and 3) show less data. The present study is based (on physical state (a)) on linearity and relatively little variation (especially accord- thevaluesoftheAtterberglimitsgovernedbylinearlaw ing to the type of clay minerals) in comparison with the with clay size contents. This condition is also important data of the liquid limit. Note how small the range of the in order to look for relationships between the Atterberg plastic limit values is compared with that of the liquid limits and the intrinsic geotechnical properties of the limit values. Except for the mixtures with low clay frac- soils. Casagrande (1932) reported that the physical sig- tion (see `ànomalous'' values Fig. 3), the best link be- niˆcance of the liquid limit of a non-plastic soil is fun- tween the plastic limit and the clay percentages is a linear damentally diŠerent from that of a plastic soil. The relationship. The regression lines of the plotted mixtures author believes that Casagrande's consideration for non- intersect the Wp axis randomly between 8.4z and 11.9z. plastic soils can also be extended to `ànomalous'' values The equations shown in Fig. 3 refer to the average value of the Atterberg limits. In fact, as these values increase of the intercept, Wp＝10z. Hence, the general equation (in a relative sense), so do the values of the residual fric- is: tion angle because both mainly depend on the character- W ＝(k CF )＋10 (7) istics of the granular phase. p 2

The values of Cm for the soils plotted in Fig. 2 are where the Wp-slope k2 depends on the type of clay miner- overestimated because the calculation of es was only als (chemical state enclosed) contained into the soil (as oc- based on the added sand (the components À2 mm found cur, in a very ampliˆed way, for k1 to WL). in the soils were not taken into consideration). The equa- To understand the reasons for the non-zero intercept tion in Fig. 2 (for the average values of assumed es, rs and value in Eq. (7) further investigations are necessary. rc), permits to obtain the Cm value as a function of the Atterberg limits (for the mixtures with CF ranging 10 water content (or vice versa) to have the same volume that z) were subsequently recalculated using the equations is when the clay water system will ˆll the voids in the (from Figs. 1 and 3) of the regression lines of the mixtures granular phase and the round particles will be in contact governed by linear law with the clay size contents in order with one another. It is graphically shown by the marked to obtain a better correlation. These data, Wp against WL line and it was obtained by inserting the selected values are plotted in Fig. 4. The dashed lines of regression deˆne the variation of the plastic limit as a function of the liquid limit in mixtures with the same percentage of clay. These lines are parallel (slope＝0.04) and if they are extended,

Fig. 2. Relationship between water content, W and amount of clay,

Cm needed to ˆll the voids in a granular soil. es＝void ratio of the

granular phase. rs, rc＝density of round particles and clay size par-

ticles, respectively. 1, 4 and 6＝liquid limit regression lines of soil- Fig. 3. Plastic limit, Wp as function of clay fraction CF (º2 mm), sand mixtures, see Fig. 1 taken from Fig. 1. 1–6＝soil types, see Fig. 1 ATTERBERG LIMITS AND CLAY CONTENT 891

Fig. 4. Relationship among plastic limit, Wp, liquid limit, WL and clay fraction, CF based on recalculated data. The regression lines deˆne Fig. 6. Activity against clay fraction, CF (º2 mm) of soils and mix- variation of W as function of W in mixtures with same clay frac- p L tures tested. 1–6＝soil types, see Fig. 1 tion. 1–6＝soil types, see Fig. 1

Fig. 5. Measured plasticity index, Ip (``anomalous'' values excluded) as function of clay fraction CF (º2 mm). 1–6＝soil types, see Fig. 1 Fig. 7. Activity calculated with Eq. (11) as function of clay fraction, CF (º2 mm). 1–6＝soil types, see Fig. 1 they pass through the axis of the ordinate at the value (q＝0.26CF＋10), which is a function of the clay percentage. The relationship among W , W and CF obtained L p I ＝0.96 W －(0.26 CF＋10) (9) allows the calculation of the plastic limit of an inorganic p L soil with platey clay minerals when the liquid limit value Hence, for a given inorganic soil (with platey clay miner- and the percentage of clay of the tested sample (linearly als) known WL and CF values, the WL and Ip values for proportional to one another) are known, precisely: any other CF can be estimated using Eqs. (1) and (9), respectively. On the other hand, if the values of the Atter- W ＝0.04 W ＋(0.26 CF＋10) (8) p L berg limits are known, it is possible to calculate the clay It can be concluded that the plastic limit has little in- fraction: ‰uence on the plasticity of soils with high contents of very expansive clay minerals, whereas it is important in soils CF＝[(0.96 WL－Ip)－10]W0.26 or with clay minerals that are not very expansive and its im- CF＝[(Wp－0.04 WL)－10]W0.26 (10) portance increases as the clay size contents in the soils decreases. This CF value should be (about) equal to the clay percentage of grain size distribution of the soil (or soil fraction) Plasticity Index used to the Atterberg limits test. For common inorganic soils the plasticity index, de-

ˆned by the numerical diŠerence between WL and Wp Activity values (Fig. 5), can be obtained directly (without per- Of particular interest in any evaluation of Atterberg forming the test for Wp) if the values of the liquid limit limits is the relationship between plasticity index and clay and the clay fraction are known and are linearly propor- fraction because this has been used as the basis (Skem- tional to one another, precisely: pton, 1953) for deˆning the activity, A of clayey soils, 892 POLIDORI represented by a straight line passing through the origin

(A＝Ip WCF ). The regression lines that represent the activity of soils tested (Fig. 5) have non-zero intercept values

(Ip＝－10, intercept average value). Hence, the activity of a clayey soil can be redeˆned as follows:

A＝[0.96 WL－(0.26 CF＋10)]WCF (11) Figures 6 and 7 show how the activity (measured and calculated) varies as a function of the clay fraction for the investigated soils. It can be observed that for a given soil, the activity against CF is not constant as suggested by the relationshipproposedbySkempton(1953)(andinFig.6, the activity values should not decrease with an increase of clay size content in the mixtures). The activity (Fig. 7) should reach its maximum value when CF＝100z;it Fig. 8. Liquid limit, WL and plastic limit, Wp against clay fraction CF drops slightly and almost linearly with high clay contents, (º2 mm) of bentonite-sand mixtures. Data from Lupini et al. whereas there is a marked decrease in activity in the mix- (1981). Wp calculated with Eq. (8) also shown tures with low clay percentages. In this case, the dashed lines are theoretical, because the Atterberg limits (for CFÃ20z and 30z for kaolinite) are not linearly proportional to their respective clay size contents. In routine assessments of soil properties, it is usually assumed that the fraction º2 mm (equivalent diameter) termed clay fraction, is composed entirely of clay minerals. In practice, a part of the fraction º2 mmcanbecom- posed of round particles (with diŠerent behaviour from clay minerals). Because the eŠect of the round particles

º2 mm is incorporated in the WL value, any possible diŠerence between the real and conventional contents of the clay minerals would produce an error for the calculated values (Wp, Ip and A). On the other hand, this also occurs when the activity is calculated with Skempton's relationship.

Fig. 9. Liquid limit, WL and plastic limit, Wp against clay fraction CF (º2 mm) of illite, bentonite and their mixtures. Data from Seed et COMPARISON BETWEEN DATA MEASURED AND al. (1964a). Wp calculated with Eq. (8) also shown DATA CALCULATED WITH THE PROPOSED INTERRELATIONSHIP In Fig. 8 the plotted data of the bentonite-sand mix- its percentage. The pointed out interaction is attributable tures (from Table 5) conˆrm the linear variation of WL to the salt contained into the illite that, when mixed with with CF and the non-zero intercept value for Wp regres- the bentonite, prevented full expansion of the bentonite sion line (excluding the mixture with the lowest bentonite in the presence of water. content). On the contrary, a mixture of two or more soils In conclusion, the eŠect of the physical-chemical inter- with water (even if it is deionized) constitutes a system, action is contained in the Atterberg limits values of the the properties of which depend on the composite eŠects mixtures. The relative parameters (WL, Wp, Ip, A and of their physical-chemical interaction. A mixture of two CF ) are linked in accordance to the proposed quantita- or more soils may therefore yield a soil with plasticity tive relationship. In addition, diluting each mixture with characteristics that are not linearly proportional to the non-clay particles (2–425 mm) shows the linear relation- clay contents of the soils that make it up. For example, ship between Atterberg limits and its clay fraction.

Fig. 9 shows the data (WL, Wp against CF )oftheclay When a soil's clay content is very low, such as the case minerals illite (with CF＝35z), bentonite (with CF＝95 of the inorganic soils (Lupini et al., 1981; Sridharan and z) and their mixtures (Seed et al., 1964a). Here it can be Nagaraj, 2000) shown in Table 3, the Atterberg limits are observed (from the degree of curvature of the lines on not linearly proportional to the respective clay fractions which the data lie) that there is a high level of physical- (the behaviour of these soils will not be dominated by the chemical interaction among the minerals for the liquid clay phase) and clearly the proposed equations cannot be limit and almost negligible interaction for the plastic applied. limit, considering its link with the liquid limit (0.04 WL). In a previous paper the writer proposed a new plasticity The straight dashed line shows the expected liquid limit chart (Polidori, 2003) to classify the soils (or their frac- values if each clay mineral contributed in proportion to tion) º425 mm using the well note Atterberg limits. On ATTERBERG LIMITS AND CLAY CONTENT 893

Table 3. Index properties from literature

CF WL Wp A 13 38 21 1.31 B 9.54835.61.30K 11.5 58.7 45.2 1.17 K 53929.51.901 17.5 56.4 38.1 1.04 1

B＝bentonite; K＝kaolinite; I＝illite; CF, WL and Wp are in z

Fig. 10. Plasticity chart (after Polidori, 2003). C-line and 0.5C-line correspond to 100% CF and 50% CF (º2 mm), respectively. CL, CH＝clay zone (CFÆ50%)withlowandhighplasticityrespec- Fig. 11. Location on plasticity chart (see Fig. 10) of 125 soil samples tively. ML, MH＝silt zone (2–425 mmÀ50%)withlowandhigh from literature (Seed et al., 1964a; Lupini et al., 1981; Skempton, plasticity respectively. OL, OH＝organic soils with low and high 1985; Wasti and Bezirci, 1986; Burland, 1990; Di Maio and Fenelli,

plasticity respectively. Low plasticity (L) and high plasticity (H) 1994): a) Ip measured against WL. Casagrande's A-line also shown

based on ASTM standard (D 2487). NPC＝soils with non-platey and b) Ip calculated with Eq. (9) against WL clay minerals

the chart shown in Fig. 10, all the Ip-WL values of the in- relationship between the Atterberg limits and clay frac- organic soils containing platey clay minerals and tion is in agreement with the Polidori's plasticity chart CFº100z should lie above the C-line and the distance of and has lead to little improvements in that chart (Fig 10). the points from the C-line should be inversely propor- The main are: a) the (absolute) intercept value of the C- tional to clay percentage of the respective soils. The 0.5C- line equation decreases by one unit and b) the 0.5C-line line allows us to distinguish the points that fall below the andtheC-lineareextendedtotheWL axis, to fully deline- line, clays (C), from the points lying above the line in the ate the clay zone where the inorganic soils with platey clay silt zone (M). In turn, the silt and clay zones can be sub- minerals should lie. divided in groups with low (L) or high (H) plasticity, ac- The plotting of the following data on the plasticity cording to the ASTM standard (D 2487) when the liquid chart (without distinction between low and high plastici- limit value is less than or greater than 50z, respectively. ty) is a simple and better method for data comparison. In the original paper it has been demonstrated that the silt Figure 11(a-b) shows the data of the plasticity index zone is found above the clay zone. (measured and calculated) as a function of the liquid limit The residual inorganic soils (NPC) composed of non- of 125 natural and artiˆcial soils taken from literature platey clay minerals (allophane, halloysite, attapulgite) (except the soils with CFº25z and the residual soils). In should lie below the C-line because their characteristics Fig. 11(a) the A-line (Casagrande, 1948) has also been in- (high plastic limit, low plasticity index) are very diŠerent cluded in order to show where the same soils would lie on from those of platey clay minerals for which the plasticity Casagrande's plasticity chart, since the respective posi- chart was developed. The soils (NPC) that contain both tions of the silt and clay zones are reversed on the two platey and non-platey clay minerals as well as the organic charts. All plotted soils (except 3 soils) lie above the soils (O) can lie above or below the C-line according to A-line in the clay zone (according to Casagrande) regard- characteristics of the soil constituents. Clearly, for these less of their clay size contents. In Fig. 11(a), all plotted soils the proposed quantitative relationship is not valid. points should lie above the C-line and the distance of the The original plasticity chart was calibrated using also points from the C-line (that correspond to CF＝100z) some of the experimental data shown in this paper and should be inversely proportional to clay fractions of the available in Polidori (2003). Hence, the proposed inter- respective soils (º425 mm), such as shown in Fig. 11(b) 894 POLIDORI

(obviously if the organic substance and non-platey clay –For60z of the soils (75 of the 125 soils plotted) the minerals are absent in the soils). average value of the diŠerence between both the Ip In Fig. 12, the measured and calculated values of the values (measured and calculated) is 1.3 units (ranging plasticity index for the soils plotted on Fig. 11 are com- ±3 units). pared and the following considerations can be made. –For90z of the soils (112 of the 125 plotted) the – In agreement with this study, from Figs. 12 and 13 it average value of this diŠerence is 2.5 units (ranging±6

can be inferred that the measured Ip (and Wp)against units). CF have non-zero intercept values. The plotted data – In the remaining 13 samples this discrepancy is often (Fig. 13) do not lie according to the hypothetical U-line very marked (for 5 soils ranging from ±10 to ±17 and the hypothetical 0.5C-line shown. In addition, the units). 0.5C-line is the line that best separates the soils with The above mentioned diŠerences (expressed in units)

CFº50z from soils with CFÀ50z. between the measured and calculated values of Ip (or Wp),

Fig. 13. Particular from Fig. 11(a). Dashed lines 1 (Ip＝0.96 WL)and2

(Ip＝0.96 WL–18) show expected hypothetical U-line and 0.5C-line

Fig. 12. Comparison between measured and calculated plasticity in- respectively, if Ip (and Wp) against CF was found (equally linearly dex of samples plotted in Fig. 11 proportional) to pass through the origin

Table 4. Index properties of inorganic soils from literature. (c)＝calculated values (of Wp, Ip and A with Eqs. (8), (9) and (11) respectively)

Wp-Wp(c) Soil CF WL Wp Wp(c) Ip Ip(c) AA(c) or Ip(c)-Ip 1 100 348 43.9 49.9 － 6 304.1 298.1 3.04 2.98 B 2* 100 330.6 55.2 49.2 6 275.4 281.4 2.75 2.81 B 3* 88 526 38 53.9 －15.9 488 472.1 5.54 5.36 B 4* 88 184 48 40.2 7.8 136 143.8 1.54 1.63 B 5* 56 234.4 18.5 33.9 －15.4 215.9 200.5 3.75 3.58 B 6 51.5 73.5 35.6 26.3 9.3 37.9 47.2 0.74 0.92 B 7507542.5 26 16.5 32.5 49 0.65 0.98 B 8 39 124.2 23.2 25.1 － 1.9 101 99.1 2.59 2.54 B 9378442 23 19 42 61 1.13 1.65 B 10 37 84 49 23 26 35 61 0.95 1.65 B 11* 100 57.5 37.8 38.3 － 0.5 19.7 19.2 0.20 0.19 K 12 100 45 29 37.8 － 8.8 16 7.2 0.16 0.07 K 13* 48 45 34.8 24.3 10.5 10.2 20.7 0.21 0.43 K 14 36 46.8 29.4 21.2 8.2 17.4 25.6 0.48 0.71 K 15 35 48 21.3 21 0.3 26.7 27 0.76 0.77 K 16 100 80 30 39.2 － 9.2 50 40.8 0.50 0.41 I 17 88 73 44 35.8 8.2 29 37.2 0.33 0.42 I 18 88 288 44 44.4 － 0.4 244 243.6 2.77 2.77 19* 86 350 35 46.4 －11.4 315 303.6 3.66 3.53 20* 84 362 29 46.3 －17.3 333 315.7 3.96 3.76 21 84 184 55 39.2 15.8 129 144.8 1.54 1.72 22 43 128 27 26.3 0.7 101 101.7 2.35 2.36 23 42 214.5 20.9 29.5 － 8.6 193.6 185 4.61 4.40 24* 41 80 32 23.9 8.1 48 56.1 1.17 1.37 25 40 198 25.4 28.3 － 2.9 172.6 169.7 4.31 4.24 26* 37 88 38 23.1 14.9 50 64.9 1.35 1.75

*Data from Fig. 11(a). B＝bentonite; K＝kaolinite; I＝illite; CF, WL and Wp are in z ATTERBERG LIMITS AND CLAY CONTENT 895

Table 5. Index properties from Lupini et al. (1981). (c)＝calculated values (of Wp, Ip and A with Eqs. (8), (9) and (11) respectively)

Bentonite Sand CF WL Wp Wp(c) Ip Ip(c) A A(c) 15 85 13 38 21 — 17 — 1.31 — 30 70 26 56 20 19 36 37 1.38 1.42 45 55 40 80 23 23 57 57 1.42 1.42 60 40 53 114 28 28 86 86 1.62 1.62 75 25 66 140 36 33 104 107 1.58 1.62 100 — 88 184 48 40 136 144 1.54 1.63

CF＝zº2 mm. Bentonite, sand, WL, Wp and Ip are in z

even if they are marked, have little in‰uence on the plas- was useful to repeat the plastic limit tests (and the average ticity value of the expansive soils with high clay fraction. of the values was considered in order to improve the However, they can be important for classifying the soils alignment of the points plotted on the graph) and it was because they can lie in a zone that does not correspond to essential that the average values of Wp and WL against CF their clay content or out of the zone (above the U-line or were used. below the C-line, see Fig. 11(a)). It should be noted that the linear variation of the Atter- In order to understand the causes of the above-men- berg limits as a function of CF is already routinely ap- tioned discrepancy, the values of the index properties plied for determining activity of a soil (Skempton, 1953).

(Table 4) of inorganic soils with CFÀ34z (Seed et al., In fact, the activity is based on the linear variation of Ip 1964a; Sides and Barden, 1971; Lupini et al., 1981; (and thus of WL and Wp) as a function of CF. Hence, the Sivapullaiah and Sridharan, 1985; Mesri and Cepeda measured activity values of the bentonite-sand mixtures Diaz, 1986; Wasti and Bezirci, 1986; Rao et al., 1989; Di reported in Table 5 should not decresase with an increase Maio and Fenelli, 1994; Sridharan et al., 1986; Sridharan of bentonite content in the mixtures. For example, for the and Prakash, 1998; Sridharan and Nagaraj, 2000) were mixture with CF＝88z,theWp value is high compared expressly chosen so that they can be compared with each with the other mixtures (see Fig. 8) and the other soils other. The samples are ordered according to the clay (soil no. 4 in Table 4) and consequently the Ip value is low mineral that they contain (when speciˆed) and their CF and lies below the C-line (see Fig. 11(a)). (from highest to lowest). The measured plastic limit values of these soils, in relation to the values of WL and CF, are di‹cult to understand (or better yet, incompre- CONCLUSIONS hensible) because they do not follow the same rule. This is This study permits to advance the following conclu- also shown by a comparison with the respective values of sions which should be valid for all inorganic soils with the plastic limit calculated on the basis of the proposed platey clay minerals and for clay percentages that are not interrelationship. too low, that is when the volume of the water-clay system If both the clay contents are equal (of the entire soil becomes greater than the voids of the non-clay fraction in and the soil used for the Atterberg limits test) and organic the soils. substances and non-platey clay minerals are absent, any – The liquid limit, plastic limit, plasticity index, activity possible diŠerence among the values (Wp, Ip and A)ob- and clay fraction of the soil (º425 mm) used to assess tained from the tests and the calculated values may be the Atterberg limits are interdependent parameters. mainly attributable to the poor precision of the standard – The Atterberg limits (WL, Wp and Ip) are linearly method for determining the plastic limit. The thread-roll- proportional to CF and only WL-CF regression line ing method is simple, but it has long been criticised since have zero intercept value. it is considered highly operator-dependent. For example, – The values of two of the three parameters (WL, Wp, Whyte (1982) reported that the plastic limit of a soil de- CF) that are measurable using standard tests, su‹ces termined in diŠerent laboratories ranged from 19z to 39 to obtain the values of other three parameters of the z with an average plastic limit of 23z. Another example tested soil (º425 mm). At this purpose two ways can be concerns the results of a reproducibility test (Focardi, followed: 1999) on a sample of Pliocenic Clays (Central Italy) tested a) knowing the Atterberg limits values of a soil, the in 35 geotechnical laboratories. It is composed of clay CF and A values of the tested soil can be calculated minerals, in order of decreasing quantities: illite, chlorite (or graphically estimated plotting Atterberg limits and kaolinite and non-clay minerals: quartz, calcite and values on the plasticity chart) or, plagioclase. This soil is characterized by the following b) knowing only WL and CF (linearly proportional) average values: CF＝48.2z and WL＝50z. The plastic of the soil tested, the Wp, Ip and A values (and for limit values ranged from 20z to 31z (average value Wp any other CF) can be calculated. ＝24.7z, calculated value with Eq. (8) Wp＝24.5z). Fi- The latter method seems to be more appropriate. Sec- nally, in order to obtain the interrelationship among the ondly, it is useful to know the grain-size distribution and parameters proposed in this paper, (as reported above) it the possible percentage of soil retained by the No. 40 (425 896 POLIDORI

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