Liquid limit of soils from equilibrium water content in one-dimensional normal compression

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1 & Liquid limit of soils from equilibrium water content in one-dimensional normal compression A. Sridharan, PhD, DSc, H. B. Nagaraj, MTech and P. S. Prasad, ME Consistency limits are extensively used in geotechnical engineering practice. Conventional test procedures which have been developed to determine the liquid limit are based on the strength, with the liquid limit corresponding to a shearing resistance of 1 7±2 0 kpa. However, the mechanisms controlling the test procedures do not simulate the mechanisms controlling the water-holding capacity of soils which the liquid limit is supposed to represent. Further, the test procedures have their limitation in that they are relatively arbitrary. In this paper an attempt has been made to devise a test procedure which will give the water-holding capacity equivalent to the liquid limit as the equilibrium water content under a speci ed e ective vertical stress of 0 9 kpa in normal compression. It has been found that the proposed test procedure is simple, accurate, relatively experimental and personal error-free, and could also be carried out easily for soils of low plasticity. Keywords: foundations; geotechnical engineering; roads & highways Notation G s speci c gravity of soil I P plasticity index I illite K kaolinite k 0 coe cient of earth pressure at rest M montmorillonite Q quartz w e equilibrium water content in percent w i initial water content in percent w L liquid limit w s shrinkage limit w Lk0 liquid limit, k 0 stress method w Lc liquid limit by cone method w 0 9 kpa equilibrium water content by 0 9 kpa (k 0 stress) method Introduction The consistency limits initially proposed by Atterberg in 1911 for agricultural purposes were later adopted by Terzaghi for classi cation of ne-grained soils for engineering purposes. The consistency limits are the liquid limit (w L ), plastic limit (w P ) and shrinkage limit (w S ). These limits are determined using relatively simple tests, known as index tests. These tests have provided a basis for the preliminary assessment of the engineering properties of ne-grained soils, on the basis of correlations with the consistency limits. The reliability of such correlations depends on the consistency limits being determined reasonably accurately through standardized procedures having universal acceptance. The liquid limit in particular is used in many correlations with engineering properties. In this paper, an attempt has been made to evolve a simple, yet reliable method of determining the liquid limit of soils. Liquid limit 2. The liquid limit of a soil is de ned as the water content above which the soil behaves as a viscous liquid (i.e. a soil±water mixture with little measurable shear strength). Casagrande 1,2 deduced that the liquid limit corresponds approximately to a water content at which the soil has a shear strength of about 2 5 kpa. Subsequent studies have indicated that the liquid limit corresponds to a shearing resistance of about 1 7±2 0 kpa. 3,4 On the basis of the strength criterion, many methods of nding the liquid limit have been developed. Currently, two methods are popular in practice for the determination of the liquid limit of a ne-grained soil. They are (a) the percussion cup method 5 (b) the fall cone method Both of these methods have limitations and practical di culties. This paper describes an attempt to determine the liquid limit by a simple procedure, which can be standardized for universal acceptance after thorough examination. Basic concepts of the method 4. It is widely accepted that the liquid limit test is essentially a measure of the shear strength of a soil that is so soft it approaches the liquid stage. 7 In the percussion cup method the impact of the soil- lled cup on the base induces a dynamic stress in the soil which results in shear, and the soil ows in the sloping walls of the groove. Thus, the force resisting the deformation of the sides of the groove is the shearing resistance of the soil and hence the Proc. Instn Civ. Engrs Geotech. Engng, 2000, 143, July, 165±169 Paper Written discussion closes 1 November 2000 Manuscript received 21 April 1999; revised manuscript accepted 13 March 2000 A. Sridharan, Professor, Department of Civil Engineering, Indian Institute of Science, H. B. Nagaraj, Lecturer, BMS College of Engineering, P. S. Prasad, Project Assistant, Department of Civil Engineering, Indian Institute of Science, 165

2 SRIDHARAN ET AL. 166 number of blows required to close the groove of soil represents an indirect measure of dynamic shearing resistance of the soil at that moisture content. In a cone penetrometer test the resistance o ered to a static load gives the shearing resistance of the soil to plastic ow at that moisture content. Thus, the strength measured represents an indirect static shear strength. 5. Scherrer 8 used a device consisting of a 908 cone, which is gradually loaded from 0 to 1 kg in 1 min. The nal load remains constant at this value. Unlike other types of penetration test, it does not measure the resistance to plastic ow of the soil, but measures the equilibrium pressure proportional to the shear strength of the material. As the shear strength of a saturated clay depends directly on the water content, so does the equilibrium pressure. For the soil tested, Scherrer found that there was a linear relationship between moisture content and equilibrium pressure when plotted on a semi-logarithmic plot. He further concluded that the moisture content corresponding to a de nite equilibrium pressure may be regarded as the liquid limit. He found the equilibrium pressure corresponding to the conventional liquid limit moisture content to vary from 0 2 to 1 kg/cm 2. Thus, this method could not arrive at a unique equilibrium pressure at the liquid limit which could enable a standard test procedure. In addition to this, the cone apparatus, as concluded by Scherrer himself, required a more complicated installation. 6. It is well-known that in a conventional oedometer test, a saturated soil mass reaches an equilibrium water content upon any increment in pressure. The equilibrium water content depends upon the level of the pressure and the initial water content. Thus it may be stated that if the equilibrium water content happens to be the liquid limit water content, then the corresponding pressure and initial water content required to reach this equilibrium condition can be determined and compared for di erent soils. Based on this surmise, experiments were conducted using oedometer rings to obtain the pressure required for a saturated slurry sample to reach the equilibrium water content equal to that of the liquid limit water content. 7. Since it is well-accepted that all soils at the liquid limit possess very small but measurable shear strength, the same can be analogous to some unique consolidation stresses at which a saturated sample has a water content equivalent to the liquid limit water content. But it has been well-recognized that the void ratio±logarithm of pressure will be a family of curves depending upon the initial water content at which the consolidation test is started. 9 Similarly, depending on the initial water content, the equilibrium water content reached under any stress will be di erent. Sridharan and Prakash 10 observed a similar behaviour in sedimentation tests. The straight line extension of these equilibrium points obtained by plotting initial water content (w i ) against equilibrium water content (w e ) will meet the w i ±w e line (458 line) to get a unique minimum equilibrium water content which will be taken as the liquid limit of the soil. In other words, at the liquid limit water content, a saturated soil sample has a unique external e ective vertical stress under k 0 conditions. This concept is used to develop a procedure to determine the liquid limit as explained later. Materials and methods 8. A number of natural soils, along with commercially available kaolinite, covering a wide range of liquid limit (31 5%<w L <128 5%) were selected, tested for their physical properties, and are reported in Table The speci c gravity was determined using a pycnometer (stoppered bottle having a capacity of 50 ml) as speci ed by British Standards. 6 The speci c gravity values are an average of three individual test determinations di ering from the mean by less than The liquid limit of the soils was determined by the cone penetrometer method as speci ed by British Standards. 6 The liquid limits were determined to obtain a minimum of ve points for plotting the ow curve. The consistency of the soil specimens was adjusted such that the cone penetration ranged between 15 and 25 mm. The plastic limit of clay specimens was determined by the rolling thread method as per British Standards. 6 The shrinkage limit of soil specimens was also determined as per British Standards. 6 The shrinkage limits reported are the average of three determinations with a di erence of less than 0 5%. 10. The mineralogical analysis of the soil was performed using an X-ray di ractometer. The principal clay minerals present in the soils are given in Table 1. Test procedure of the new k 0 stress method 11. Figure 1 shows the diagrammatic representation of the apparatus used for determining the liquid limit. Saturated samples with varying initial water contents and greater than their respective liquid limits were remoulded in rings, 60 mm in diameter and 20 mm high, which were similar to that used in the standard one-dimensional consolidation test. These were placed on a saturated porous stone of 76 mm diameter with a lter paper placed in between. On top was placed a lter paper, over which was placed a loading cap with saturated porous stone of 58 mm diameter. The entire assembly was kept in a steel container, and su cient water was poured to maintain the saturation of the sample through the bottom porous stone. On the top of the sample a loading cap was

3 METHOD TO DETERMINE THE LIQUID LIMIT OF SOILS Table 1. Physical properties of soils used Sample No. Soil description G s w L :% w 0 9kPa :% I P :% w S : % Casagrande classi cation Mineralogy 1 Red earth, CL K, Q 2 Red earth, CL K, Q 3 Silty soil, Ð CL I, Q 4 Silty soil, ML I, Q 5 Silty soil, ML I, Q 6 Silty clay CL M, Q 7 BC soil, Ð CL K, Q 8 Kaolinite, ML K, Q 9 Red earth, CL K, Q 10 Brown soil, ML M, K, Q 11 Kaolinite, MH K, Q 12 Brown soil, MH M, K, Q 13 Kaolinite, MH K, Q 14 Illitic soil MH I, K, Q 15 BC soil, MH M, Q 16 BC soil, MH M, Q 17 Illite MH I, Q Notes to Table 1 G s speci c gravity w L liquid limit w 0 9 kpa equilibrium water content by 0 9 kpa (k 0 stress) method BC black cotton I P plasticity index w S shrinkage limit I illite K kaolinite M montmorillonite Q quartz placed such that the weight of the saturated porous stone and the loading cap induced a certain uniform vertical consolidation pressure. Based on the preliminary experiments, it was found that the equilibrium water content, which is very near to the liquid limit water content of the soil, could be reached under a small consolidation pressure of 0 9 kpa. Hence 0 9 kpa was selected as the e ective vertical pressure for the k 0 condition. 12. The initial water content (w i )ofthe sample was determined accurately by the oven drying method. The load or pressure of 0 9 kpa was kept constant for 24 h to reach equilibrium. After 24 h the water content of the equilibrated sample was accurately determined. The equilibrium water content (w e ) obtained for samples started with varying initial water contents just above the liquid limit is plotted in Figs 2±4. The points are joined by a straight line and extended backward to intersect the w i ±w e line (458 line) to give the water content which is the liquid limit of the soil. The test results for all the soils are tabulated in Table 1. If the initial water content is very close to the conventional liquid limit, then the equilibrium water content reached under the pressure of 0 9 kpa is almost equal to the liquid limit water content. As shown in Figs 2±4, the straight line extension of the points gives an equilibrium water content which is equal to the initial water content. This water content is found to be very close to the liquid limit obtained by the 308/80 g cone penetrometer method. The equilibrium water content of 17 soils obtained as described earlier is tabulated in Table 1. Fig. 5 plots the results of the equilibrium water content of 17 soils as obtained by the 0 9 kpa method (k 0 stress condition) against the liquid limit by the cone penetrometer method. There appears to be very good correlation between the liquid limit obtained by the cone penetration Fig. 1. Diagrammatic representation of the apparatus used to determine liquid limit by the 0 9 kpa k 0 stress method Loading cap fixed with porous stone (5 8 cm dia., 0 9 kpa) Ring (6 cm inside dia.) Results and discussion 13. As already discussed, the equilibrium water content reached by a saturated sample in a consolidation ring under a particular e ective vertical pressure depends on the initial water content of the saturated soil sample (Figs 2±4). Saturated soil sample Steel container Filter papers Bottom porous stone 167

4 SRIDHARAN ET AL Red earth (soil sample No. 2; w L = 37 0% by cone method) Fig. 2. Relationship between initial water content and equilibrium water content under a consolidation pressure of 0 9 kpa for a red earth BC soil (soil sample No. 15; w L = 73 5% by cone method) Fig. 4. Relationship between initial water content and equilibrium water content under a consolidation pressure of 0 9 kpa for a black cotton soil Brown soil (soil sample No. 12; w L = 53 0% by cone method) Fig. 5. Relationship between liquid limit by theconepenetration method and equilibrium moisture contentbythek 0 stress method Fig. 3. Relationship between initial water content and equilibrium water content under a consolidation pressure of 0 9 kpa for a brown soil method and the equilibrium water content as obtained by an e ective vertical stress of 0 9 kpa under k 0 conditions. 14. Thus, it can be concluded that the equilibrium water content attained by a saturated ne-grained soil sample with an initial water content very near to its liquid limit, placed in a ring of 60 mm diameter and 20 mm height with a pressure of 0 9 kpa for 24 h, can be taken as the liquid limit of the soil. Since it is di cult to start with an initial water content very near to its liquid limit without knowing the liquid limit itself, it is convenient to do the test with varying initial water contents (three or four) just above the liquid limit of the soil and then arrive at an equilibrium water content which is equal to the initial water content under 0 9 kpa, as explained earlier (Figs 2±4). The water content thus obtained can be taken as the liquid limit of the soil. 15. This recommended test procedure to determine the liquid limit is almost free from personal errors, and also very easy to perform with a simple apparatus and good reproducibility. Three to four trials will be enough to determine the liquid limit of the soil. The proposed procedure has a limitation in the sense that chemically contaminated and thixotropic soils may be prone to variations; this is due to the fact that the procedure takes 24 h to reach equilibrium. Conclusions 16. A simple test procedure has been developed to determine the liquid limit of a soil usingtheconceptthatasaturatedsoilslurry reaches an equilibrium water content under a known e ective vertical stress in the k 0 condi-

5 METHOD TO DETERMINE THE LIQUID LIMIT OF SOILS tion. The e ective vertical stress under the k 0 condition is found to be 0 9 kpa, at which the equilibrium water content happens to be the liquid limit water content. Results obtained by the proposed method compare very well with those obtained by the conventional 308/80 g cone method of liquid limit determination. The proposed procedure is not subject to the limitations of the existing method for determining the liquid limit, is simple and relatively error-free, and could also be carried out easily for soils of low plasticity. References 1. CASAGRANDE A. Research on the Atterberg limits of soils. Public Roads, 1932, 13, No. 3, 121±130 and CASAGRANDE A. Notes on the design of the liquid limit device. GeÂotechnique, 1958, 8, No. 2, 84± WROTH C. P. and WOOD D. M. The correlation of index properties with some basic engineering properties of soils. Canadian Geotechnical Journal, 1978, 15, No. 2, 137± WHYTE I. L. Soil plasticity and strengthða new approach using extrusion. Ground Engineering, 1982, 15, No. 1, 16± ASTM Test Method for Liquid Limit, Plastic Limit and Plasticity Index of Soils, Designation: D Annual Book of ASTM Standards, American Society for Testing of Materials, Philadelphia, 1995, vol , 554± BRITISH STANDARDS INSTITUTION. British Standard Methods of Test for Engineering Purposes. BSI, London, 1990, BS 1377: Part SOWERS G. F., VESIC A. and GRANDOLFI M. Penetration tests for liquid limit. Proceedings of a Symposium on Atterberg Limits, 1959, ASTM No. STP 254, pp. 216± SCHERRER H. V. Determination of liquid limit by the static cone penetration test. Proceedings of the 5th International Conference on Soil Mechanics and Foundation Engineering, Paris, 1961, 1, 319± LEONARDS G. A. and RAMIAH B. K. Time e ects in the consolidation of clays. Symposium on Time Rates of Loading in Soil Testing, 1959, ASTM No. STP 254, pp. 116± SRIDHARAN A. and PRAKASH K. Characteristic water contents of a ne-grained soil±water system. GeÂotechnique, 1997, 48, No. 3, 1±10. Please , fax or post your discussion contributions to the secretary: wilson_l@ice.org.uk; fax: +44 (0) ; or post to Lesley Wilson, Journals Department, Institution of Civil Engineers, 1±7 Great George Street, London SW1P 3AA. 169

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