2000 by the American Society for Testing and Materials

REFERENCE: Sridharan, A. and Prakash, K., Shrinkage Limitof Soil Mixtures, Geotechnical Testing Journal, GTJODJ, Vol.23, No. 1, March 2000, pp. 38.

ABSTRACT: Shrinkage limit, one of the Atterberg limits, iswidely linked with many plasticity-based soil behaviors. However,in a great majority of these cases, such correlations have been foundto exhibit poor performance. Recently, it has been brought out thatthe shrinkage limit of a natural soil does not depend upon plasticitycharacteristics, and it is primarily governed by the relative grain sizedistribution of the soil. The present study confirms this mechanismwith the results obtained using clay-clay, clay-non-cohesive soil,and non-cohesive soil mix systems. The present study gains impor-tance from the point of view of criteria with respect to the design ofback fill materials to be used in various applications, such as nuclearwaste disposal projects.

KEYWORDS: shrinkage limit, soil mixtures

When a soil-water system traverses from liquid to solid state,three characteristics limiting water contents with well-defined andunique mechanisms controlling them can be identified. The lowestlimiting water content is the shrinkage limit: the first two being thefree-swell limit and the settling limit (Sridharan and Prakash1998a). Sridharan and Prakash (1998b) have conducted a detailedstudy on the factors and mechanisms controlling the shrinkagelimit of soils and have proposed the following hypothesis to ex-plain the mechanism governing the shrinkage limit of soils.

Shrinkage is a process of volume reduction that takes place dueto capillary pressures induced by the evaporation of water from thesoil. As the evaporation continues, the radius of the meniscus de-veloped in water in every pore where there is air-water interfacecontinues to decrease, and the menisci will retreat into the soil massuntil the shear stresses induced by the capillary pressures are equal-ized by the shear strength at the particle level. The natural fine-grained soils have sand, silt, and clay-size fractions in some pro-portions. During the shrinkage process, larger void spaces betweensand particles are filled with finer sand and silt particles, andsmaller void spaces between silt particles are filled by finer clayparticles. Hence, relative grain size distribution plays a dominantrole.

Sridharan and Prakash (1998b) have shown that the shinkageprocess is a packing phenomenon and that the shrinkage limit of anatural soil is primarily a function of the relative grain size distri-bution of the soil, irrespective of the principal clay mineral of thesoil and that the shrinkage limit does not depend on plasticity char-acteristics of the soil.

Of late, the shrinkage properties are assuming greater impor-tance as the soil is being used as backfill material in many in-stances, e.g. the nuclear fuel waste disposal systems. The backfillmaterial is often designed as soil mixtures primarily requiring lowshrinkage property along with other stringent requirements (Yonget al. 1986). Thus, further understanding of the mechanism con-trolling the shrinkage of soil mixtures leads to increasing the con-fidence level before adopting the mechanism in the field. In thiscontext, this article gives an account of the experimental investiga-tion of the shrinkage property of soil mixtures, including non-co-hesive soils. The outcome of this study will give insight into the de-sign of soil mixtures used as backfill materials in various wastedisposal projects in general and nuclear fuel waste disposalschemes in particular.

Experimental Program

The soils used in the present study can be grouped in to three se-ries:

Series 1: clay-clay mixturesSeries 2: sand-clay mixturesSeries 3: non-cohesive soil mixtures

Even though the shrinkage limit determination is done on minus425 mm soil fractions, for conducting some of the confirmatorytests, sand fractions of maximum size 2 mm were also used. Theshrinkage limits of soils were determined by working the soils atabout their liquid-limit water contents into shrinkage dishes(ASTM designation D427-83 1989). In those cases where the liq-uid limit values were not available (i.e., non-cohesive soil mix-tures), the amount of water added was such that no segregation andliquefaction occurred during the sample preparation. The wet soilpats were allowed to air dry and were then dried at a temperature of40C for 24 h and again at 110C for 24 h.

Results and Discussions

In the first series, the liquid limit, which is considered as one ofthe plasticity characteristics of fine grained soils, is compared withthe corresponding value of the shrinkage limit of clay-clay mix-tures.

Clay-Clay Mixtures

Table 1 gives the details of the fine-grained, clay soils used in thepreparation of clay-clay mixtures and sand-clay mixtures. Figure 1shows the grain size distribution curves for the same soils. Figure2 presents the variation of liquid and shrinkage limits for differentproportions of two constituent soils forming the mix. If the shrink-age limit is a plasticity characteristic of a soil, then the shrinkagelimit is expected to decrease with the increase in the liquid limit ofthe mixture. However, it can be noted from Fig. 2 that even though

3

A. Sridharan1 and K. Prakash2

Shrinkage Limit of Soil Mixtures

1 Honorary professor, Department of Civil Engineering, Indian Institute ofScience, Bangalore, 560 012, India.

2 Former research scholar, Department of Civil Engineering, Indian Instituteof Science, Bangalore, 560 012, India.

the liquid limit increases from a minimum value to a maximumvalue, the shrinkage limit first decreases and then starts increasing.This indicates that the shrinkage limit is not a plasticity character-istic.

In the second series of the investigation, the results obtainedfrom the tests on sand-clay mixtures are analyzed. The non-cohe-sive soils used in the second and final stages of tests includedwashed and graded river sands, sand flour of predominantly siltsize (i.e., clay size fractions 5 2%), and the rock flour (granite) ofsilt size (Table 2). The grain size distributions of these non-cohe-sive soils are indicated in Figs. 3a and b.

Sand-Clay Mixtures

Two sand-clay mixtures were prepared and examined: (1) Theminus 75-mm fractions of the black cotton soil (Soil No. 2) weremixed with different proportions of fine sand fractions (Table 3).By conducting various trials, the percentage of the fine sand frac-tion to be added with the black cotton soil to achieve minimumshrinkage limit was found to be 12.4% (the proportions of differentsized sand particles composing the 12.4% fine sand were alsoworked out likewiseTable 3). Keeping this ratio of the percent-age of the different-sized sand particles to the percentage of total

fine sand fraction the same, different sand-clay mixtures were pre-pared and their shrinkage limits were determined. For the sake ofpresentation, a term mix ratio-1 (i.e., MR1) is defined herein asthe ratio of fine sand content to the silt 1 clay (black cotton soil)content.

MR1 5 (1)Figure 4a shows the variation of the shrinkage limit with MR1.There is a decrease in the shrinkage limit with a decrease in theblack cotton soil content up to a certain value. Below a certain lim-ited black cotton soil content, the shrinkage limit shows an in-creasing trend. It is important to observe that changing the internaldistribution of different-sized particles keeping the total fine sandcontent the same as that resulted in minimum shrinkage limit, hasresulted in a considerable increase in the shrinkage limit (i.e.,Points A and B in Fig. 4a). This highlights the importance of therelative grain size distribution in controlling the shrinkage limit ofsoils.

The bentonite clay was mixed with fine sand fraction (150 mm# D # 212 mm) in different proportions. The shrinkage limits ofthese mixtures were determined (Table 4). Figure 4b shows thevariation of the shrinkage limit of bentonite-sand mixture

Percentage fine sand content}}}}Percentage (silt 1 clay) content

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TABLE 1Details of the clayey soils used in the present study.Grain Size Distribution, %

Liquid Plastic ShrinkageSoil No. Soil Limit, % Limit, % Limit, % Clay Size Silt Size Sand Size Principal Clay Mineral(s)

01 Bentonite 393.4 50.1 13.7 65.5 34.5 zero Montmorillonite02 Black cotton soil 90.8 44.0 09.4 62.5 37.5 zero Montmorillonite03 Brown soil-1 64.6 26.6 14.5 40.0 41.6 18.4 Montmorillonite, Kaolinite04 Red earth-1 38.6 18.0 14.7 40.5 23.9 35.6 Kaolinite

FIG. 1Grain size distribution of cohesive soils.

Non-Cohesive Soil Mixtures

The third series of confirmatory testing involves non-cohesivesoil mixtures. Even though the conventional shrinkage limit test isdone on soil fractions having minus 425 mm size, to verify the hy-pothesis proposed to explain the mechanism governing the shrink-age limit, medium sand (Soil Nos. 49 and 50) were also used. In or-der to overcome practical difficulties in carrying out the shrinkagelimit test on only fine and medium sands, sand flour of predomi-nantly silt size was also used in preparing the sand mixtures. Ut-most care was exercised in conducting the tests so as to avoid pos-sible segregation and liquefaction during testing. Differentnon-cohesive soil mixtures prepared and studied are indicated inTable 5. For the sake of convenience, a term mix ratio-2 (i.e.,MR2) is defined as

MR2 5

(2)

Shrinkage limits of mixtures for different values of MR2 (0 # MR2# 1) were obtained and plotted as shown in Fig. 5. The observa-tions made from the study of Fig. 5 and Table 5 are indicated be-low.

1. When the soil is essentially silt sized with no sand sized par-ticles, maximum shrinkage limit was obtained.

2. With the inclusion of medium and fine sand fractions, the rel-ative grain size distribution gets improved, resulting in de-creased shrinkage limit.

3. With proper proportioning of the non-cohesive soil fractionsin the mix, a lower shrinkage limit can be obtained which canbe even less than those obtained for cohesive soils (the mini-mum value of 12.6% of the shrinkage limit so obtained is lessthan that for highly plastic bentonite clay).

4. Any further increase in the proportion of the coarser fractionresults in an increase in the shrinkage limit.

Different combinations of non-cohesive soil fractions can be hadwith the same value of mix ratio-2, resulting in different shrinkagelimits. Hence, the results listed in Table 5 are purely qualitative.These results clearly rule out the possibility of considering theshrinkage limit as one of the plasticity characteristics of a soil. In-stead, they highlight the validity of the hypothesis that explains theshrinkage limit based on the relative grain size distribution of thesoil.

Percentage of non-cohesive soil (0.425 mm , D ,2 mm)}}}}}}

Percentage of non-cohesive soil (D , 0.425 mm)

SRIDHARAN AND PRAKASH ON SOIL MIXTURES 5

FIG. 2Variation of the liquid and shrinkage limits with the percentageof soil in the clay-clay mix: (a) bentonite and brown soil-1 mix; (b) brownsoil-1 and red earth-1 mix.

TABLE 2Properties of the non-cohesive soils used.Liquid Shrinkage

Soil No. Soil Size Limit, % Limit, % D10, mm D30, mm D60, mm Cu Cc

49 Medium sand-1 1.180 mm , D ,2.000 mm 1.24 1.380 1.600 1.290 0.96050 Medium sand-2 0.425 mm , D ,1.180 mm 0.480 0.600 0.760 1.583 0.98751 Fine sand-1 0.075 mm , D ,0.425 mm 0.205 0.245 0.310 1.512 0.94552 Fine sand-2 0.212 mm , D ,0.425 mm 30.5 0.212 0.222 0.270 1.274 0.86153 Fine sand-3 0.150 mm , D ,0.212 mm 33.2 0.154 0.162 0.177 0.149 0.96354 Fine sand-4 0.075 mm , D ,0.150 mm 35.9 0.076 0.080 0.098 1.289 0.85955 Sand flour D , 0.075 mm 31.4 26.6 0.0086 0.024 0.047 5.465 1.42556 Rock flour D , 0.075 mm 39.4 32.6 0.0205 0.0348 0.052 2.537 1.136

* obtained by core penetration method.Cu 5 coefficient of uniformity.Cc 5 coefficient of curvature.

with MR1, the trend of which is very similar to that indicated inFig. 4a.

These illustrations add to the argument in favor of a packing phe-nomenon controlling the shrinkage limit rather than the plasticitycontrolling it.

AB

TABLE 3Details of tests conducted on black cotton soilsand mixtures.Proportion of Black

Cotton Soil (Combining Silt andClay Size Fraction

Only) and Sand Size Particles in the Mix, % Split up proportion in c, %

Soil No. c* d** (0.425 mm0.212 mm) (0.212 mm0.150 mm) (0.150 mm0.075 mm) MR1 5 c/d Ws, %

02 00 100 00 09.457 12.4 87.6 05.25 2.25 04.9 0.142 08.758 12.4 87.6 08.00 3.00 01.4 0.142 11.659 25.0 75.0 10.585 4.536 09.879 0.333 10.860 50.0 50.0 21.169 9.073 19.758 1.000 15.3

* c 5 Fine sand (combination of soils 52, 53, and 54 of Table 2).** d 5 Black cotton soil (Soil No. 2 of Table 1).NOTE: The ratio of percentage of the soils 52, 53, 54 constituting c for soils 57, 59, and 60 to the percentage of c is the same.

FIG. 3bGrain-size distribution of non-cohesive soils.

FIG. 3aGrain-size distribution of non-cohesive soils.

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SRIDHARAN AND PRAKASH ON SOIL MIXTURES 7

FIG. 4Variation of shrinkage limit of clay-sand mixture with the mixratio-1: (a) Black cotton soil and sand mixtures; (b) Bentonite and sandmixtures.

TABLE 4Details of the tests conducted on bentonite-sand mixtures.Proportion of (Clay1Silt)

Size and Sand SizeParticles in the Mix* (%)

Soil No. c d MR1 5 c/d ws (%)

01 00 100 00 13.761 25 75 0.333 11.862 50 50 1.000 25.263 75 25 3.000 32.064 85 15 5.667 35.2

* c : Fine sand (Soil No. 53 of Table 2).d : Bentonite (Soil No. 1 of Table 1).

Effect of Angularity of Soil GrainsThe most common shape of clay size particles is platy and most

of the particles in the range of silt size and coarser are approxi-mately equi-dimensional. The study of the effect of the shape ofclay size particles on the shrinkage limit is very complex. However,the effect of shape of particles in the range of silt size and coarseron the shrinkage limit can be studied. The lesser the angularity, thedenser will be the packing of the particles and lower will be theshrinkage limit expected.

Two soils of silt-size particles, equi-dimensional in shape, wereused in the present work. One is crushed river sand (i.e., sandflourSoil No. 55) and the other is the crushed granite (i.e., rockflourSoil No. 56). The particles of the sand flour are relativelymore rounded than those of rock flour. Hence the shrinkage limit ofsand flour is expected to be less than that of rock flour. The exper-imental results indicate that the shrinkage limit of the sand flour is26.6% while that of rock flour is 32.6%. This trend is as expectedsince rock flour has higher frictional properties at the particle leveland, hence, lesser shrinkage. So, if two natural soils have identicalgrain size distribution, the one that has higher shearing resistanceat the particle level will have higher shrinkage limit than that of theother whose shear resistance at the particle level is lesser. In other-words, the shearing resistance at the particle level also governs theshrinkage limit (Sridharan and Venkatappa Rao 1971).

TABLE 5Details of the non-cohesive soil mixtures studied.

SoilProportion of sands in the mix (%)

Number a* b c$ d# f 5 (a 1 b) (%) g 5 (c 1 d) (%) MR2 5 f/g w%

55 0 0 0 100 0 100 0 26.665 9 11 23 57 20 80 0.250 15.866 11 13 26 50 24 76 0.316 16.567 13 15 26 46 28 72 0.389 16.068 15 17 26 42 32 68 0.471 14.269 16 18 25 41 34 66 0.515 14.670 17 19 24 40 36 64 0.563 13.571 17 19 26 38 36 64 0.563 13.372 18 20 26 36 38 62 0.613 12.973 19 21 25 35 40 60 0.666 12.674 19 21 26 34 40 60 0.666 12.675 20 22 24 34 42 58 0.724 12.776 21 23 23 33 44 56 0.786 12.877 24 26 18 32 50 50 1.000 13.0

* a 5 size range: 1.180 mm ,D ,2 mm (Soil No. 49) $ c 5 size range: 0.075 mm ,D ,0.425 mm (Soil No. 51) b 5 size range: 0.425 mm ,D ,1.18 mm (Soil No. 50) # d 5 size range: D ,0.075 (Soil No. 55)

Conclusions

The results obtained from extensive testing program conductedon cohesive soil mixtures, cohesive-non-cohesive soil mixturesand non-cohesive soil mixtures prepared in the laboratory, high-light the following facts.

1. The shrinkage limit of a soil is not a plasticity characteristicof the soil.

2. The shrinkage limit of a soil is the result of packing phe-nomenon and is primarily controlled by the relative grain sizedistribution of the soil.

3. For the systems having the same grain size distribution, theone which has higher shearing resistance at the particle levelwill shrink less.

These observations enchance the ability to design most effec-tively and efficiently the soil mixtures as the back fill materials tomeet various functional requirements.

References

ASTM designation: D427-83 (1989), Standard Method for Shrink-age Factors of Soils, Annual Book of ASTM Standards, Vol.4.08, ASTM, West Conshohocken, PA.

Sridharan, A. and Prakash, K., 1998a, Characteristic Water Con-tents of Fine Grained Soil-Water System, Geotechnique, Vol.48, No. 3, pp. 337346.

Sridharan, A. and Prakash, K. (1998b), Mechanism Controllingthe Shrinkage Limit of Soils, Geotechnical Testing Journal,GTJO DJ, Vol. 21, No. 3, pp. 240250.

Sridharan, A. and Vekatappa Rao, G, 1971, Effective Stress The-ory of Shrinkage Phenomena, Canadian Geotechnical Journal,Vol. 8, No. 4, pp. 503513.

Yong, R. N., Boonsinsuk, P., and Wong, G., (1986), Formulationof Back Fill Material for a Nuclear Fuel Waste Disposal Vault,Canadian Geotechnical Journal, Vol. 23, pp. 216228.

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FIG. 5Variation of shrinkage limit of non-cohesive soil mixtures with mix ratio-2.