9 Liquid and Plastic Limits Donald J. Campbell Scottish Agricultural College, Edinburgh, Scotland I. INTRODUCTION Plasticity is the property that allows a soil to be deformed without cracking in response to an applied stress. A soil may exhibit plasticity, and hence be remolded, over a range of water contents, first quantified by the Swedish scientist Atterberg (1911, 1912). Above this range, the soil behaves as a liquid, while below it, it behaves as a brittle solid and eventually fractures in response to increasing applied stress. The upper limit of plasticity, known as the liquid limit, is at the water con- tent at which a small slope, forming part of a groove in a sample of the soil, just collapses under the action of a standardized shock force. The corresponding lower limit, the ‘‘plastic limit,’’ is at the water content at which a sample of the soil, when rolled into a thread by the palm of the hand, splits and crumbles when the thread diameter reaches 3 mm. By convention, both water contents are expressed gravimetrically on a percentage basis. The numerical difference between the liq- uid and plastic limits is defined as the plasticity index. Remarkably, these simple empirical tests have been used, essentially unchanged, for nearly a century by soil engineers and soil scientists (BSI, 1990). Engineers found the limits, particularly the plastic limit, to be useful in the design and control testing of earthworks and soil classification (Dumbleton, 1968) as a result of the development by Casagrande of apparatus to measure the limits (Casagrande, 1932). Although his apparatus was based on that of Atterberg, Casa- grande appreciated the need, where empirical tests were concerned, to specify closely every detail of the test procedure so that both the repeatability of the test by one operator and the reproducibility between operators were optimized (Sher- wood, 1970). Consequently, the Casagrande tests became widely adopted as the Copyright © 2000 Marcel Dekker, Inc. official standard by engineers in the United Kingdom (BSI, 1990), the United States of America (Sowers et al., 1968), and elsewhere. Soil scientists have made less use of the Atterberg limits, which do not fea- ture in soil survey or land capability classification systems but have been used mainly as indicators of the likely mechanical behavior of soil (Baver et al., 1972; Archer, 1975; Campbell, 1976a). This has generally been done by establishing simple correlations between the plasticity limits or plasticity index and other prop- erties considered important in determining soil behavior. An example is shown in Table 1. It has been suggested, however, that liquid and plastic limit values would be a useful addition to soil particle size distributions in the classification of soils in the laboratory (Soane et al., 1972). This is particularly relevant as the Atterberg limits are related to the field texture, as determined in the hand, a method often preferred by soil scientists concerned with practical problems of soil workability in the field (MAFF, 1984). Two further index values can be derived from the Atterberg limits. The li- quidity index, LI, is related to the percentage gravimetric soil water content, w%, the plastic limit, PL, and the plasticity index, PI,by w% Ϫ PL LI ϭ (1) PI The activity, A, is the ratio of the plasticity index to the percentage by weight of soil particles smaller than 2 mm, C, thus 350 Campbell Table 1 Relation Between Potato Harvesting Difficulty, as Indicated by the Number and Strength of Clods in Potato Ridges, and Plasticity Index of Soil (A) Yield of 30 –75 mm diameter clods (t /ha) (B) Crushing resistance of 30 – 45 mm diameter clods (N) (A) ϫ (B) Plasticity index 76.2 73.7 5615 12.8 95.0 17.6 1672 11.2 19.0 65.9 1252 10.3 60.5 40.4 2444 8.8 48.0 38.5 1848 8.1 29.2 26.8 782 6.2 26.8 19.4 519 5.1 1.4 52.2 73 3.6 Copyright © 2000 Marcel Dekker, Inc. PI A ϭ (2) C The activity of a soil depends on the mineralogy of the clay fraction, the nature of the exchangeable cations, and the concentration of the soil solution. II. THEORIES OF PLASTICITY In attempting to explain the mechanism behind the existence of the liquid and plastic limits, two basic approaches have been adopted. Traditionally, soil behav- ior is considered in terms of the cohesive and adhesive forces developed as a result of the presence of water between the soil particles (Baver et al., 1972). The critical state theory of soil mechanics that is used in the second approach has been detailed by Schofield and Wroth (1968) and is mathematically complicated. However, the basic concepts and their importance have been discussed by Kurtay and Reece (1970). A. Water Film Theory Cohesion within a soil mass is due to a variety of interparticle forces (Baver et al., 1972). Bonding forces include Van der Waals forces; electrostatic forces between the negative charges on clay particle surfaces and the positive charges on the par- ticle edges; particle bonding by cationic bridges; cementation effects of sub- stances such as iron oxides, aluminum, and organic matter; and the forces associ- ated with the soil water. Taken together, these forces will determine whether a soil will, when stressed, undergo brittle failure, plastic flow, or viscous flow. At low water contents, most of the soil water forms annuli around the inter- particle contact (Haines, 1925; Norton, 1948; Schwartz, 1952; Kingery and Francl, 1954; Vomocil and Waldron, 1962). These annuli provide a tensile force that increases with decreasing particle size, through this relationship breaks down at higher water contents because the individual annuli of water start to coalesce (Haines, 1925). Just above the plastic limit, the soil becomes saturated, and, in a cohesive soil, the soil water tension and other bonding forces are in equilibrium with the repulsive forces due to the double layer swelling pressure. Nichols (1931) showed that, for laminar clay particles, the interparticle force F was related to the particle radius r, the surface tension of the pore water T, the angle of contact between the liquid and the particle a, and the distance between the particles d,by 4kprT cos a F ϭ (3) d Liquid and Plastic Limits 351 Copyright © 2000 Marcel Dekker, Inc. where k is a constant. He also showed that, for each of three soils, the product of the cohesive force and the water content was a constant at low water contents. At higher water contents, however, the cohesive force decreased rapidly with increas- ing water content. Although the existence of a relationship between water content and cohe- sion, which exhibits a maximum, has been demonstrated experimentally (Nichols, 1932; Campbell et al., 1980), the relation is valid only for dry soils that have been rewetted. When puddled soil is allowed to dry, cohesion increases with decreasing water content and reaches a maximum when the soil becomes dry. This effect probably arises because, in puddled soils, the number of interparticle contacts are maximized, and hence cohesive forces other than those due to soil water are large. Baver (1930) suggested that when a soil at the plastic limit is stressed, the laminar clay particles, which are each surrounded by a water film and which were previously randomly orientated in the friable state, are rearranged so that they slide over each other. Thus the cohesive forces associated with the tension effects in the water films are overcome, and the soil deforms. When the stress is removed, the particles remain in their new position under the action of the cohesive forces and there is no elastic recovery. The soil has undergone plastic deformation or flow. Before the soil reaches the liquid limit, the water films have completely coa- lesced, and the soil water tension has greatly decreased. Thus cohesion decreases and the soil is capable of viscous flow. As the water content and particle separation further increase, the liquid limit is reached, and the viscosity of the outermost layers of water is reduced to that of free water, allowing the soil to flow like a liquid (Grim, 1948; Sowers, 1965). The liquid limit is related to clay content and its surface area for most types of clay mineral. Montmorillonite is an exception in that the liquid limit is con- trolled essentially by the thickness of the diffuse double layer, thereby giving a linear relation between the liquid limit and the amount of exchangeable sodium ions present (Sridharan et al., 1986). Although the interparticle forces associated with soil water may not provide a comprehensive explanation of the mechanism of plasticity, it is clear the soil particle sizes, their specific surface, and the nature of the clay minerals are all important. This is consistent with the common experience that, generally, the liq- uid and plastic limits are both dependent on both the type and the amount of clay in a soil (DSIR, 1964). B. Critical State Theory If a relatively loose sample of soil is subjected to a progressively increasing uni- axial (deviatoric) stress while the confining stress (spherical pressure) is kept con- stant, then the soil volume will decrease. This will occur for both unsaturated soil 352 Campbell Copyright © 2000 Marcel Dekker, Inc. and soil that is saturated but allowed to drain as it is compressed. Eventually, a point will be reached where the soil can be compressed no further. However, if the deviatoric stress is maintained and the soil continues to distort without any change in volume, then the soil is said to be in the critical state. In terms of the three- dimensional relationship of spherical stress, deviatoric stress, and specific vol- ume, the point describing this critical state is one of the many possible critical state points that together form the critical state line. The critical state line is an extremely important concept in that it allows, within the confines of a single theory, the stress–strain behavior of a soil with any particle size distribution to be explained, be it wet or dry, dense or loose, confined or unconfined. As the line describes all conditions under which a soil will undergo continu- ous remolding without a change in volume, it follows that soil being prepared for either the liquid or the plastic limit test must be described by a point on this line. Thus the liquid and plastic limit tests can give more than simple qualitative infor- mation about soil behavior. During the liquid limit test, the soil water content, and hence the specific volume, is adjusted by adding water and remolding the soil until, in effect, the soil has a fixed undrained shear strength determined by the conditions of the test. Be- cause the soil is continuously remolded as water is added, it is in the critical state and under the action of a negative pore water pressure. When soil is prepared for the plastic limit test, it is continuously remolded and hence once again is in the critical state. However, since the soil is much drier than in the liquid limit test, the pore water pressure (matric potential) is even more negative. This negative pore water pressure acts in the same way as if the soil were subject to an additional externally applied stress and serves to increase the shear strength of the soil. It is reasonable to speculate that the plastic limit should, like the liquid limit, correspond to a state in which the soil has a fixed undrained shear strength. Atkinson and Bransby (1978) reported that the undrained shear strength data obtained for four clay soils by Skempton and Northey (1953) revealed that all four soils had very similar undrained shear strengths at the plastic limit. Per- haps more remarkably, the undrained shear strength of each soil at the plastic limit was almost exactly 100 times the undrained shear strength at the liquid limit. Knowing the ratio of the shear strengths at the liquid and plastic limits, it is possible to define the slope of the critical state line on a plot of the logarithm of the spherical pressure versus the specific volume in terms of the plasticity index (Schofield and Wroth, 1968; Atkinson and Bransby, 1978). Thus the plasticity index can be used as a direct indicator of soil compressibility. The description of soil behavior at the liquid and plastic limits offered by critical state theory is, at first sight, quite different from that given by the water film theory and may give the impression that soil water content is irrelevant. How- ever, the water content is important in critical state theory, but only insofar as it affects the pore water pressures. Liquid and Plastic Limits 353 Copyright © 2000 Marcel Dekker, Inc. III. DETERMINATION OF THE LIQUID AND PLASTIC LIMITS The methods initiated by Atterberg (1911, 1912) and subsequently developed by Casagrande (1932) were adopted by the British Standards Institution and the American Society for Testing and Materials as the standard tests in civil engineer- ing. However, in 1975, a new test for the liquid limit, based on a procedure in- volving a drop-cone penetrometer, was introduced and is included in the current British Standard (BSI, 1990). The Casagrande tests were retained, but the cone penetrometer method was described as the preferred method for the determination of the liquid limit. Although various other methods of determining the liquid and plastic limits have been suggested, usually, but not always, based on correlation of the limits with other soil rheological properties, by far the most widely used methods are the Casagrande and, to a lesser extent, drop-cone tests. A. Casagrande Tests In the Casagrande liquid limit apparatus (BSI, 1990) (Fig. 1), the sample is con- tained in a cup that is free to pivot about a horizontal hinge and which rests on a rubber base of specified hardness. A rotating cam alternately raises the cup 10 mm above the base and allows it to drop freely onto the base. The test soil is mixed with distilled water to form a homogeneous paste, allowed to stand in an air-tight container for 24 hours and remixed, and then a portion is placed in the cup. The sample is divided in two by drawing a standard grooving tool through the sample at right angles to the hinge. The crank is then turned at two revolutions per second until the two parts of the soil come into contact at the bottom of the groove over a length of 13 mm. The number of blows to the cup required to do this is recorded and the test repeated. If consistent results are obtained, a subsample of the soil is taken from the region of the closed groove for the measurement of water content. More distilled water is added to the test sample and the procedure repeated. This is done several times at different water contents to give a range of results lying between 50 and 10 blows. The linear relation between the water content and the log of the number of blows is plotted, and the percentage water content corre- sponding to 25 blows is recorded, to the nearest integer, as the liquid limit of the soil. A simplified test procedure for liquid limit determination using the Casa- grande apparatus is that known as the ‘‘one point method.’’ Essentially the method involves making up a soil paste such that the groove cut in the sample in the cup closes at a number of blows as close as possible to 25, and certainly between 15 and 35, blows. A correction factor, which varies with the actual number of blows, is applied to the water content of the soil to give the liquid limit (BSI, 1990). The method has the advantage of speed, but this is at the expense of reliability (Nagaraj and Jayadeva, 1981). 354 Campbell Copyright © 2000 Marcel Dekker, Inc. For the Casagrande plastic limit test (BSI, 1990), the sample is mixed with distilled water until it is sufficiently plastic to be molded into a ball. A subsample of approximately 10 g is formed into a thread of about 6 mm diameter, and the thread is then rolled between the tips of the fingers of one hand and a flat glass plate until it is 3 mm in diameter. The thread is then remolded in the hand to dry the sample and again rolled into a thread. The operation is repeated until the thread crumbles as it reaches a diameter of 3 mm. A second subsample is similarly tested, and the mean of the two water contents (expressed as percentages) at which the threads crumble on reaching a diameter of 3 mm is recorded, to the nearest integer, as the plastic limit of the soil. Where the plastic limit cannot be obtained or where it is equal to the liquid limit, the soil is described as nonplastic. Liquid and Plastic Limits 355 Fig. 1 The Casagrande grooving tool and liquid limit device, showing a soil sample divided by the tool prior to testing. Copyright © 2000 Marcel Dekker, Inc. Both these tests are undertaken on air-dried material passing a 425 mm sieve, although it has been susggested that, when the bulk of the soil material passes 425 mm, it may be more convenient to test the whole soil (BSI, 1990). However, it is generally agreed that the results for soils tested in the natural con- dition may be different from tests conducted on material that has previously been air-dried, and this is certainly the case when soils are at above-ambient tempera- tures (Basma et al., 1994). This is particularly true of organic soils. Where an appreciable proportion of the soil is retained on the 425 mm sieve, removal of such material can influence the plasticity characteristics of the soil (Dumbleton and West, 1966). Because of these various aspects of the test procedures and because the tests are conducted on remolded soil, the results should be interpreted with caution in relation to the likely behavior of soil in the field. B. Drop-Cone Tests Most of the shortcomings of the Casagrande liquid limit test are related to its subjectivity and to the tendency for some soils to slide in the cup or liquefy from shock, rather than flow plastically (Casagrande, 1958). After reviewing five alter- native cone penetrometer tests, Sherwood and Ryley (1968) concluded that a method developed by the Laboratoire Central des Ponts et Chausse´es, 58 Boule- vard Lefebre, F-75732 Paris Cedex 15, France (Anon., 1966) offered the possi- bility of a suitable method for liquid limit determination. The new method, which used apparatus already available in most materials testing laboratories, was shown to be easier to perform than the Casagrande method, to be less dependent on the design of the apparatus, to be applicable to a wider range of soils, and to be less susceptible to operator error. Largely as a result of the work of Sherwood and Ryley (1968), the drop-cone penetrometer test was adopted as the preferred method for liquid limit determination by the British Standards Institution (BSI, 1990) in the United Kingdom. The apparatus used in the drop-cone penetrometer test is shown in Fig. 2. The mass of the cone plus shaft is 80 g, and the cone angle is 30Њ. The test soil, which is prepared to give a selection of water contents in exactly the same way as in the Casagrande test, is contained in a 55 mm diameter, 50 mm deep cup. At each water content, the soil is pushed into the cup with a spatula, so that air is not trapped, and then levelled off flush with the top of the cup. The cone is lowered until it just touches the soil surface, and the cone shaft is allowed to fall freely for 5 s before the shaft is again clamped and the cone penetration noted from the dial gauge. Usually, the 5 s release is automatically controlled via an electromagnetic solenoid clamp as shown in Fig. 2. A duplicate measurement is made, and the procedure is then repeated for a range of water contents. The linear relation be- tween cone penetration and water content is plotted, and the percentage water content corresponding to a penetration of 20 mm is recorded, to the nearest inte- 356 Campbell Copyright © 2000 Marcel Dekker, Inc. ger, as the cone penetrometer liquid limit. Typical test results for four soils are shown in Fig. 3. Attempts have been made to develop a one-point cone penetrometer liquid limit test analogous to the one-point Casagrande test. As with the latter, the method is a compromise between speed and accuracy but has been shown to be a satisfactory alternative (Clayton and Jukes, 1978). The one-point cone pene- trometer test has been shown to be theoretically sound and not based simply on statistical correlations (Nagaraj and Jayadeva, 1981). Liquid and Plastic Limits 357 Fig. 2 The drop-cone penetrometer, showing the cone position at the start of a test. Copyright © 2000 Marcel Dekker, Inc. The drop-cone liquid limit method has been compared with the Casagrande method for a range of soils used in civil engineering (Stefanov, 1958; Karlsson, 1961; Scherrer, 1961; Sherwood and Ryley, 1968, 1970a, b) and agriculture (Towner, 1974; Campbell, 1975; Wires, 1984). Generally, the two tests give equivalent results (Littleton and Farmilo, 1977; Moon and White, 1985; Sivapul- laiah and Sridharan, 1985; Queiroz de Carvalho, 1986). A comparison of the two methods is shown in Fig. 4, which also shows the reproducibility of the drop-cone method. With the widespread adoption of the drop-cone method for measuring the liquid limit, there were obvious advantages in using the same apparatus to measure the plastic limit, if that were possible. Scherrer (1961) proposed a method of plas- tic limit determination that involved extrapolation of the linear relation between 358 Campbell Fig. 3 The results of cone penetrometer liquid limit tests on four arable topsoils of con- trasting texture. The horizontal broken line indicates the cone penetrometer liquid limit. (From Campbell, 1975.) Copyright © 2000 Marcel Dekker, Inc. [...]... 37 49 28 31 30 36 37 38 37 47 29 31 30 36 36 36 38 45 22 26 26 24 28 26 31 44 17 17 18 19 19 19 25 27 15 18 19 17 26 21 22 30 Source: Campbell, 197 6b, 197 5 Copyright © 2000 Marcel Dekker, Inc Liquid and Plastic Limits 363 Lack of reproducibility between operators carrying out liquid (Dumbleton and West, 196 6; Campbell, 197 5; Wires, 198 4) and plastic (Ballard and Weeks, 196 3; Gay and Kaiser, 197 3;... unchanged and so the plasticity index remains the same (Baver et al., 197 2) In general, organic matter influences the plasticity properties of a soil (Odell et al., 196 0; Hendershot and Carson, 197 8; Copyright © 2000 Marcel Dekker, Inc 366 Campbell de la Rosa, 197 9; McNabb, 197 9; Hulugalle and Cooper, 199 4; Emerson, 199 5; Mbagwu and Abeh, 199 8), but the role of organic matter in this context may vary with... Maidenhead, U.K.: McGraw-Hill Atterberg, A 191 1 Die Plastizitat der Tone Int Mitt Bodenk 1 : 1 0-4 3 ¨ Atterberg, A 191 2 Die Konsistenz und die Bindigkeit der Boden Int Mitt Bodenk 2 : ¨ 1 49 –1 89 Ballard, G E H., and W F Weeks 196 3 The human factor in determining the plastic limit of cohesive soils Mater Res Stand 3 : 726 –7 29 Basma, A A., A S Al-Homoud, and E Y Al-Tabari 199 4 Effects of methods of drying... Marcel Dekker, Inc Liquid and Plastic Limits 375 Soane, B D., D J Campbell, and S M Herkes 197 2 The characterization of some Scottish arable topsoils by agricultural and engineering methods J Soil Sci 23 : 93 –104 Sowers, G F 196 5 Consistency In: Methods of Soil Analysis, Part 1 (C A Black et al., eds.) Madison, WI: Am Soc Agron., pp 391 – 399 Sowers, G F., A Vesic, and M Grandolfi 196 8 Penetration tests... : 1 9 Campbell, D J 197 6b Plastic limit determination using a drop-cone penetrometer J Soil Sci 27 : 295 –300 Campbell, D J., and R Hunter 198 6 Drop-cone penetration in situ and on minimally disturbed soil cores J Soil Sci 37 : 153 –163 Campbell, D J., J V Stafford, and P S Blackwell 198 0 The plastic limit, as determined by the drop-cone test, in relation to the mechanical behaviour of soil J Soil. .. and Casagrande tests Ground Eng 10 : 39 – 40 Livneh, M., J Kinsky, and D Zaslavsky 197 0 Correlation of suction curves with the plasticity index of soils J Materials 5 : 2 09 –220 MAFF (Ministry of Agriculture, Fisheries and Food) 198 4 Soil textures Leaflet 895 London: MAFF Mbagwu, J S C., and O G Abeh 199 8 Prediction of engineering properties of tropical soils using intrinsic pedological parameters Soil. .. subsoil in a moist climate and some effects of traffic management Soil Use and Manage 8 : 60 – 67 O’Sullivan, M F., D J Campbell, and D R P Hettiaratchi 199 4 Critical state parameters derived from constant cell volume triaxial tests Eur J Soil Sci 45 : 2 49 –256 Pandian, N S., T S Nagaraj, and G L S Babu 199 3 Tropical clays, I Index properties and microstructural aspects J Geotech Eng 1 19 : 826 – 8 39. .. 197 1 Topsoil reaction to mechanical pressure Swed J Agric Res 1 : 1 79 –1 89 Blackmore, A V 197 6 Subplasticity in Australian soils, IV Plasticity and structure related to clay cementation Aust J Soil Res 14 : 261–272 Boekel, P 196 3 The effect of organic matter on the structure of clay soils Neth J Agric Sci 11 : 250 –263 BSI (British Standards Institution) 199 0 British Standard methods of test for soils... Dekker, Inc Liquid and Plastic Limits 361 characteristics There have been attempts to relate the liquid and plastic limits to specific viscosities (Yasutomi and Sudo, 196 7; Hajela and Bhatnagar, 197 2), to the residual water content of a soil paste subjected to a standard stress (Vasilev, 196 4; Skopek and Ter-Stephanian, 197 5), and to various mechanical properties (Sherwood and Ryley, 197 0a) However, none... 151–164 Baver, L D 192 8 The relation of exchangeable cations to the physical properties of soils J Am Soc Agron 20 : 92 1 94 1 Baver, L D 193 0 The Atterberg consistency constants: Factors affecting their values and a new concept of their significance J Am Soc Agron 22 : 93 5 94 8 Baver, L D., W H Gardner, and W R Gardner 197 2 Soil physics New York: John Wiley Benson, C H., H Zhai, and X Wang 199 4 Estimating . circumstances either air-drying (Allbrook, 198 0; Pandian et al., 199 3) or removal of any soil particle size fraction ( Dumble- ton and West, 196 6; Sivapullaiah and Sridharan, 198 5; BSI, 199 0) can markedly affect. Limits 365 Copyright © 2000 Marcel Dekker, Inc. de la Rosa, 197 9; McNabb, 197 9; Hulugalle and Cooper, 199 4; Emerson, 199 5; Mbagwu and Abeh, 199 8), but the role of organic matter in this context may. (Dumbleton and West, 196 6; Campbell, 197 5; Wires, 198 4) and plastic (Ballard and Weeks, 196 3; Gay and Kaiser, 197 3; Campbell, 197 6b) limit tests led to the development of the drop-cone test for