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Estimation of Liquid, Plastic and Shrinkage Limits Using One Simple Tool

Kamil Kayabali Geological Engineering Department, Ankara University, Ankara 06100, Turkey

e-mail: kayabalik@gmail.com

ABSTRACT

There have been a number of attempts to develop alternatives to the conventional tests available to more accurately predict the liquid limit (LL) and plastic limits (PL). One of two major setbacks with conventional methods is the uncertainties inherent to the operator and the apparatus utilized. The second is the fact that critical water contents are strength states, in essence, and these two methods do not measure strength. The reverse extrusion test eliminates both setbacks by yielding undrained shear strengths free of operator effects. Ten experiments were performed on each of 100 soil samples for conventional LL, PL, and shrinkage limits (SL) and reverse extrusion test (RXT), totaling more than 4000 tests in all. The experimental data were utilized in multiple regression analyses to predict consistency limits through empirical relationships. The results indicate that about 90 percent of LL and PL can be predicted with an accuracy of plus/minus 10 percent using the recently introduced soil mechanics testing tool of RXT. Regarding SL, about 90 percent is predicted with a degree of plus/minus 20 percent accuracy. In conclusion, the reverse extrusion method accurately predicts LL and PL; its porential to estimate SL is also promising. KEYWORDS: Liquid limit, plastic limit, shrinkage limit, reverse extrusion

INTRODUCTION

The engineering behavior of fine-grained soils depends strictly on their moisture content. The liquid limit (LL) and plastic limit (PL) are peculiar water contents as well as undrained strength states constituting two important legs of plasticity index (PI), which is, in conjunction with LL, the main index parameter for the classification of fine grained soils. PI has also been used in correlation with many other engineering parameters such as internal friction angle, overconsolidation ratio, coefficient of lateral earth pressure, undrained shear strength, etc. Therefore, the determination of Atterberg limits on a reliable basis is considered crucially important. The shrinkage limit (SL), although less critical than the previous two consistency limits, is also a threshold water content related to soil behavior. It also draws attention in certain ground engineering applications.

While those three consistency limits refer to critical levels of moisture content corresponding to certain levels of undrained shear strength in a fine grained soil, they are all performed by totally different testing techniques. This important problem has drawn the attention of many scientists; a number of attempts have been made to combine at least two of the tests, LL and PL, to be determined with the same testing equipment. The fall cone method is most frequently used for this purpose (e.g., Feng, 2004; Lee and Freeman, 2007). The second major problem with the

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available testing techniques to determine consistency limits are the uncertainties inherent to LL, PL, and SL methods (see, for example, Wroth and Wood, 1978; Holtz and Kovacs, 1981; Whyte, 1982; Cerato and Lutenegger, 2006; Kayabali and Tufenkci, 2007; Kayabali and Tufenkci, 2010a). The total number of uncertainties involved in the three most commonly employed consistency tests indicated by those researchers is approximately 15.

There are different opinions as to whether or not the conventional methods to determine LL (i.e., the Casagrande percussion cup method) and PL (i.e., the bead rolling method) represent the plasticity characteristics of soils. For instance, Prakash (2005) argued that because the undrained shear strength at liquid limit water content varies from 0.5-5.6 kPa and the liquid limit cannot be correlated with shear strength, the plasticity index determined based on strength tests cannot be regarded as the plasticity characteristic of the soil. For plastic limit, Whyte (1982) proclaimed that the strength at the PL is not established reliably by the Atterberg-type rolling bead test and therefore bead rolling is not a suitable method. Prakash and Sridharan (2006) stated conclusively that LL and PL of soils measured using the percussion and 3 mm thread rolling methods are contributed by soil cohesion and therefore represent the plasticity characteristics. The authors opinion is that, because the consistency limits are threshold water contents, they should also be the threshold shear strengths since there is a log-linear relationship between water content and the undrained shear strength of soils (e.g., Kayabali and Tufenkci, 2010b). In this regard, the conventional methods of percussion cup and bead rolling cannot be considered thoroughly reliable tests for soil plasticity.

The extrusion method appears to have the premise to represent the shear strength of soils. The use of the extrusion method in soil mechanics was first introduced by Timar (1978), who employed direct extrusion to determine both plastic and liquid limits. Whyte (1982) used the reverse extrusion test to establish a relationship between soil strength and water content and concluded that extrusion of soils is a reliable method for determining soil plasticity. The first attempt to determine both the plastic and liquid limits using the reverse extrusion method was carried out by Kayabali and Tufenkci (2007). They followed the principles outlined by Whyte (1982) to determine LL and PL using the reverse extrusion test on twenty soil samples. For the areal ratio of 40 - the cross sectional area of the container divided by the cross sectional area of the orifice of die on the rammer - they tentatively determined liquid limit and plastic limit as the extrusion pressures corresponding to 2250 kPa and 30 kPa, respectively, when a 38 mm diameter container and a rammer with a die orifice of 6 mm diameter were used. Kayabali and Tufenkci (2010a) further refined the reverse extrusion test for use in determining consistency limits. They provided a detailed description for conducting the test and investigated its repeatability or operator dependency. Kayabali and Tufenkci (2010a), by conducting Casagrande cup, thread rolling, and reverse extrusion tests on thirty soil samples, concluded that the extrusion pressures corresponding to the plastic and liquid limits are 3000 kPa and 35 kPa, respectively. They showed that the reverse extrusion test is operator independent and stated that it also has the potential to determine the shrinkage limit.

One point to be addressed on the investigations by Kayabali and Tufenkci (2007) and Kayabali and Tufenkci (2010a) is the degree of scatter of extrusion pressures around the mean value. The authors of both investigations employed, particularly for LL and PL tests using the conventional methods, different operators in the same and/or different laboratories to conduct consistency tests to demonstrate the operator effects of LL and PL through conventional methods. It is very likely that a set of LL or PL data constructed by a single operator would yield a better correlation for the respective threshold water contents with much lower scatters.

This investigation aims to reassess the reverse extrusion test in order to finalize the determination of liquid limit and plastic limit based on the reverse extrusion pressures. Reverse extrusion is also extended to cover the shrinkage limit. This research differs from previous similar investigations because each of the consistency tests was performed by the same operator by significantly increasing the number of soil samples, as well as the number of tests performed on each sample.

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MATERIALS The soil samples used in this investigation came from a lacustrine clay formation. Soil

samples were collected in large bags from different locations. They were oven-dried and then pulverized for sieving. One hundred soil samples of different liquid limits were reserved for the investigation. In order for the results of present investigation to be as universal as possible the range of liquid limit was kept as wide as possible. LL of soil samples ranges from 38 to 100.

METHODS Liquid limit and plastic limit tests were conducted in accordance with the ASTM D4318

standard (American Society for Testing Materials, 2000a). The details of the percussion cup method using the Casagrande bowl is not given here due to space considerations. To minimize the uncertainties involved in this test, all tests were performed by the same operator using the same apparatus. Extreme care was taken regarding the speed of turning the crank and the calibration of drop height. Furthermore, the bench of the testing tool was kept at the same level throughout. Regarding the bead rolling for the plastic limit test, the rolling device shown in Figure 1 was employed. A second operator conducted the plastic limit tests. Care was taken to keep a clearance of 3.2 mm between the lower and upper plates of the rolling device throughout the tests. Also, sliding the upper plate back and forth was applied at nearly the same speed. The shrinkage limit tests involved the mercury method, whose guidelines are given in ASTM D427-98 standard (American Society for Testing Materials, 1998). A third operator performed the shrinkage limit tests on all soil samples. The guidelines of the reverse extrusion tests were well defined by Kayabali and Tufenkci (2010a) and will not be repeated here. A fourth operator conducted all reverse extrusion tests using a container of 38 mm inner diameter, along with a rammer of 6 mm die orifice as was done by Whyte (1982), Kayabali and Tufenkci (2007) and Kayabali and Tufenkci (2010a).

Figure 1: The rolling device utilized in running the plastic limit tests.

EXPERIMENTS, RESULTS AND DISCUSSION Ten liquid limit tests were run on 100 samples. A sample plot is given in Figure 2. The water

contents corresponding to 25 drops using a Casagrande cup for each soil sample are presented under the second column of Table 1. Also, the 100 soil samples were subjected to ten repetitions of the bead rolling test. The mean value of plastic limit per soil sample is given in the fifth column of Table 1. The numbers in the eighth column represent the average of ten shrinkage limit tests per soil sample. The classes of soils are presented as supplementary information in column 11. Concerning the reverse extrusion tests, the results of experiments conducted at ten different water contents were first plotted in the semi-log diagram shown in Figure 3. Then, the y-intercept

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and the slope of the best fit curve were determined. The resulting coefficients are listed under columns 12 and 13 in Table 1 (here, instead of dealing with so many decimals, the inverse slope was preferred for convenience).

Figure 2: Sample plot for the liquid limit test using the Casagrande cup for

soil sample 67.

Figure 3: Sample plot for the reverse extrusion test for soil sample 67.

The y-intercept and slope of each fit was utilized to compute the extrusion pressures corresponding to the conventionally determined LL, PL, and SL values. For instance, the y-intercept and the slope of the linear fit for soil number 67 is 5.87 and 0.08 (i.e., 1/12.5), respectively. The respective extrusion pressures computed for LL=53.0, PL=32.7, and SL=21.8 are PE(LL)=43 kPa, PE(PL)=1803 kPa, and PE(SL)=13366 kPa. This computation was repeated for 100 samples. The yielding PE(LL), PE(PL), and PE(SL) values are presented in Table 1 (columns 14-16).

Table 1 gives a summary of the experimental data and the results of analytical and statistical evaluations.

Column 2: Liquid limit (LL) from Casagrande method;

Column 3: LL corresponding to the extrusion pressure of 20 kPa;

Column 4: LL from statistical evaluations;

Column 5: Plastic limit (PL) from the bead rolling method;

Column 6: PL corresponding to the extrusion pressure of 2000 kPa;

Column 7: PL from statistical evaluations;

Column 8: Shrinkage limit (SL): from mercury method;

Column 9: SL corresponding to the extrusion pressure of 12000 kPa;

Column 10: SL from statistical evaluations;

Column 11: USCS symbol of soils - CH: high plasticity clay; MH: high plasticity silt; CL: low plasticity clay; ML: low plasticity silt - (USCS: Unified Soil Classification System; American Society for Testing Materials, 2000b);

Columns 12 and 13: y intercept and the inverse slope of extrusion pressure versus water content curve from reverse extrusion tests;

Columns 14-16: Extrusion pressures (kPa) corresponding to LL, PL, and SL, respectively.

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Table 1: Laboratory test results No. LL PL SL USCS a 1/b PE(LL) PE(PL) PE(SL) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

1 57.1 59.8 60.7 24.4 27.4 27.7 11.6 14.8 16.0 CH 4.99 16.2 29 3074 187912 54.5 57.9 57.5 25.6 28.5 28.4 14.9 17.1 17.3 CH 5.24 14.7 34 3187 168423 57.8 60.4 59.9 29.6 30.2 30.5 14.0 18.4 17.9 CH 5.30 15.1 30 2210 235974 49.3 50.0 47.3 29.8 28.4 28.2 22.6 20.0 21.4 ML 5.93 10.8 23 1468 6877 5 69.2 63.9 67.3 26.6 26.3 28.3 18.8 11.7 15.3 CH 4.70 18.8 11 1937 5012 6 57.0 61.0 62.4 29.9 27.4 28.0 15.2 14.3 15.7 CH 4.93 16.8 34 1409 105987 53.7 56.0 53.1 33.4 33.2 34.7 24.0 24.3 26.3 MH 6.21 11.4 32 1909 127278 52.6 55.0 52.8 30.5 30.4 30.8 22.7 20.8 21.3 MH 5.77 12.3 31 1962 8404 9 53.1 56.5 57.4 25.0 25.3 25.1 14.9 13.1 16.5 CH 4.92 15.6 33 2092 9223

10 50.3 51.3 49.7 24.8 26.5 25.2 20.1 16.9 18.6 CH 5.44 12.4 24 2777 6592 11 61.0 63.0 63.5 29.9 30.2 30.7 16.4 17.4 16.7 CH 5.14 16.4 26 2075 1380412 56.3 58.0 57.7 28.8 28.4 28.3 16.6 16.9 17.2 CH 5.22 14.8 45 2468 1254213 65.2 61.0 61.2 27.2 29.4 29.7 16.3 17.1 16.8 CH 5.16 15.8 11 2774 1343914 48.5 50.1 47.3 28.6 28.7 28.6 25.0 20.3 21.8 ML 5.98 10.7 28 2034 4401 15 57.4 58.4 58.3 25.3 28.2 28.2 18.2 16.5 16.9 CH 5.17 15.1 23 3138 9219 16 65.2 64.8 64.3 33.8 33.2 34.1 19.0 20.9 19.7 MH 5.40 15.8 19 1818 1575717 54.6 54.8 52.4 30.9 30.8 31.5 26.1 21.5 22.2 MH 5.87 12.0 21 1957 4955 18 58.5 56.0 56.5 24.2 25.8 25.3 17.2 14.1 16.6 CH 5.01 15.1 14 2574 7429 19 69.0 61.4 61.6 29.2 29.6 29.9 15.5 17.2 16.8 CH 5.16 15.9 7 2123 1531620 57.4 62.0 63.4 29.2 28.1 28.8 15.3 14.9 15.6 CH 4.96 17.0 38 1745 1141221 62.7 59.2 59.4 24.0 28.2 28.3 16.5 16.1 16.6 CH 5.12 15.5 12 3751 1136322 47.7 48.7 46.3 25.0 26.7 25.5 23.8 18.2 20.1 CL 5.73 11.0 25 2848 3684 23 57.9 61.9 60.3 37.0 33.5 34.7 23.9 22.4 22.3 MH 5.66 14.2 38 1139 9482 24 55.3 53.7 53.4 25.0 25.7 24.6 18.5 14.9 17.2 CH 5.14 14.0 16 2276 6585 25 54.0 53.7 52.9 29.8 26.5 25.5 18.9 15.9 17.5 MH 5.25 13.6 19 1145 7249 26 59.5 57.7 55.9 30.3 31.1 31.7 18.5 20.8 20.8 CH 5.64 13.3 15 2296 1774327 55.9 54.7 54.3 24.2 26.5 25.6 13.8 15.5 17.2 CH 5.18 14.1 17 2938 1589628 75.5 79.2 83.2 35.6 35.2 34.7 12.6 18.1 15.2 MH 4.90 22.0 30 1934 2124629 66.7 68.5 71.3 31.6 30.1 31.3 12.4 15.2 14.8 CH 4.87 19.2 25 1675 1675630 63.7 63.9 65.1 31.5 29.7 30.4 14.5 16.4 16.0 CH 5.04 17.1 20 1559 1556131 78.1 80.5 84.6 38.6 35.9 35.0 12.0 18.5 15.4 MH 4.91 22.3 26 1511 2354432 71.1 71.8 74.7 35.7 32.0 32.8 14.0 16.5 15.1 MH 4.91 19.9 22 1320 1608733 77.6 71.0 72.5 35.3 33.8 34.5 14.6 19.4 17.2 CH 5.12 18.6 9 1661 2163034 83.9 82.9 88.1 35.0 35.9 34.3 15.7 17.6 14.6 CH 4.83 23.5 18 2190 1451835 59.4 58.0 55.9 39.0 32.2 33.2 21.2 22.2 22.7 MH 5.80 12.9 16 596 1434136 81.0 61.5 64.4 26.5 25.5 27.2 14.0 11.5 15.7 CH 4.72 18.0 2 1778 8754 37 65.0 64.2 65.9 35.0 29.0 29.9 31.6 15.3 15.4 MH 4.95 17.6 18 912 1427 38 55.1 54.7 51.7 36.3 35.1 37.1 30.5 27.4 31.8 MH 6.88 9.8 18 1491 5858 39 58.9 61.3 60.7 30.8 31.1 31.6 18.2 19.3 18.6 MH 5.36 15.1 29 2111 1427940 64.3 62.8 65.5 27.3 26.6 28.1 14.6 12.5 15.3 CH 4.77 18.1 16 1818 9191 41 61.5 60.8 60.4 30.1 30.4 30.8 18.1 18.6 17.9 CH 5.30 15.2 18 2101 1285942 64.9 63.0 63.6 30.2 30.0 30.6 11.9 17.2 16.5 CH 5.12 16.5 15 1954 2504943 71.4 69.9 72.1 31.2 31.9 32.7 14.9 17.1 15.6 CH 4.98 19.0 17 2198 1569644 55.6 58.5 56.2 33.7 33.1 34.4 24.7 23.3 24.2 MH 5.91 12.7 34 1819 9228 45 67.8 67.0 70.3 27.6 28.4 29.9 16.9 13.3 14.7 CH 4.77 19.3 18 2198 7841 46 75.9 69.7 73.9 32.0 28.9 30.7 16.1 13.1 14.3 CH 4.72 20.4 10 1403 8527 47 65.0 65.1 66.7 30.5 29.7 30.6 14.5 15.9 15.6 CH 4.98 17.7 20 1796 1448148 61.5 65.2 64.0 34.0 34.8 36.1 22.8 23.0 22.5 MH 5.59 15.2 35 2232 1230349 71.8 70.1 72.2 30.2 32.1 32.9 14.0 17.3 15.7 CH 4.99 19.0 16 2502 1791350 51.9 56.0 57.8 25.2 23.8 24.2 12.5 11.3 17.1 CH 4.78 16.1 36 1650 1008351 62.2 67.0 70.3 27.8 28.4 29.9 14.6 13.3 14.7 CH 4.77 19.3 35 2120 1031652 46.4 51.1 48.5 28.1 29.1 29.2 20.1 20.6 21.8 ML 5.95 11.0 54 2512 1326653 78.4 70.7 75.5 29.1 28.5 30.5 14.8 12.0 14.2 CH 4.65 21.1 9 1883 8883

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54 61.4 62.8 61.4 35.9 33.6 34.7 23.9 22.2 21.8 MH 5.60 14.6 25 1393 9184 55 62.8 66.6 69.0 29.9 29.4 30.5 16.0 14.9 15.0 CH 4.88 18.6 32 1880 1046656 54.4 57.2 55.4 31.3 31.0 31.6 22.6 20.8 21.0 MH 5.67 13.1 33 1916 8807 57 68.0 64.6 66.6 30.8 28.8 29.8 13.7 14.9 15.2 CH 4.91 17.9 13 1549 1395258 64.1 68.5 67.8 36.6 36.1 37.4 24.8 23.5 22.6 MH 5.53 16.2 38 1869 9980 59 61.9 64.2 67.0 32.0 27.4 28.8 16.2 13.1 15.1 MH 4.79 18.4 27 1133 8120 60 65.1 62.2 61.7 30.7 31.4 32.0 30.3 19.4 18.5 CH 5.34 15.4 13 2209 2358 61 52.6 57.7 56.3 32.3 30.3 30.5 22.3 19.6 19.5 MH 5.51 13.7 47 1423 7625 62 60.7 59.5 59.1 30.5 29.5 29.7 15.2 17.9 17.6 CH 5.27 15.0 17 1711 1805863 60.2 62.5 61.2 33.2 33.3 34.3 21.3 21.9 21.4 MH 5.58 14.6 28 2002 1321664 62.2 67.6 67.2 35.3 35.0 36.1 22.6 22.3 21.1 MH 5.45 16.3 43 1942 1157465 61.7 61.4 62.1 30.3 28.8 29.2 16.9 16.2 16.2 CH 5.07 16.3 19 1617 1079466 52.6 57.8 55.5 33.9 32.6 33.8 22.7 22.8 23.6 MH 5.89 12.6 52 1579 1225867 53.0 57.1 54.8 32.7 32.1 33.1 21.8 22.4 23.1 MH 5.87 12.5 43 1803 1336668 56.7 58.6 57.3 32.5 30.8 31.3 17.6 20.0 19.8 MH 5.52 13.9 27 1513 1794069 58.0 59.6 61.1 25.6 26.4 26.9 15.3 13.5 15.8 CH 4.89 16.6 25 2236 9296 70 54.7 57.1 55.7 30.4 29.9 30.0 16.0 19.3 19.3 MH 5.50 13.6 30 1840 2106371 55.2 57.5 56.0 31.2 30.3 30.6 18.1 19.7 19.6 MH 5.53 13.6 30 1719 1581772 57.0 59.5 59.1 29.9 29.5 29.7 16.1 17.9 17.6 CH 5.27 15.0 29 1876 1572873 53.0 54.2 52.8 30.0 28.0 27.4 17.8 17.8 18.5 MH 5.44 13.1 25 1421 1205774 56.3 57.0 55.6 31.0 29.8 29.9 16.8 19.2 19.2 MH 5.49 13.6 22 1607 1797775 55.4 59.3 58.8 30.8 29.5 29.6 16.5 17.9 17.6 MH 5.28 14.9 36 1615 1488076 59.5 64.6 63.5 36.3 34.4 35.6 23.5 22.7 22.1 MH 5.58 15.1 44 1509 1056177 65.1 61.8 61.6 30.8 30.6 31.0 18.2 18.4 17.7 CH 5.26 15.6 12 1914 1239778 67.6 62.5 62.5 30.2 30.7 31.2 17.9 18.3 17.4 CH 5.23 15.9 10 2154 1271279 63.8 62.2 62.4 31.8 30.2 30.7 16.2 17.8 17.1 CH 5.19 16.0 16 1585 1504980 61.6 64.5 64.2 32.6 32.5 33.3 20.3 20.0 18.8 MH 5.33 16.0 30 1967 1151581 67.7 69.7 74.7 31.4 27.7 30.1 15.7 11.4 14.5 CH 4.62 21.0 25 1330 7454 82 60.5 61.0 61.3 30.4 29.2 29.6 17.8 16.9 16.6 CH 5.14 15.9 22 1684 1048383 64.6 64.3 64.3 32.9 31.9 32.6 19.0 19.3 18.1 MH 5.27 16.2 19 1741 1250784 63.4 63.8 64.6 30.7 30.2 30.9 16.1 17.1 16.4 CH 5.10 16.8 21 1878 1385785 78.0 71.5 74.1 33.5 32.3 33.1 14.2 17.1 15.4 CH 4.95 19.6 9 1737 1680886 100.2 83.0 88.4 34.4 35.8 34.2 13.7 17.5 14.5 CH 4.82 23.6 4 2314 1735887 97.9 79.6 83.2 34.9 36.2 35.6 14.8 19.3 16.1 CH 4.97 21.7 3 2312 1940888 96.6 85.9 92.8 31.4 35.5 32.7 12.5 15.9 13.5 CH 4.71 25.2 7 2886 1636789 96.0 82.4 90.8 31.3 31.2 30.7 14.4 11.3 13.1 CH 4.52 25.6 6 1999 9068 90 95.7 88.2 97.0 32.6 34.4 30.6 12.5 13.5 12.8 CH 4.58 26.9 10 2314 1304191 94.0 80.2 85.7 33.2 33.8 33.2 16.7 15.8 13.9 CH 4.76 23.2 5 2147 1096992 94.4 80.2 85.7 34.2 33.8 33.2 13.3 15.8 13.9 CH 4.76 23.2 5 1944 1537293 93.9 81.2 86.1 33.2 35.2 34.1 13.7 17.3 14.5 CH 4.83 23.0 6 2413 1715394 95.0 85.6 92.4 31.3 35.4 32.7 16.2 15.8 13.5 CH 4.71 25.1 8 2898 1160395 89.3 97.7 105.8 31.4 41.7 32.1 15.5 19.9 14.8 CH 4.79 28.0 3 2541 1723696 83.2 82.1 86.8 32.7 36.1 34.7 13.7 18.2 15.0 CH 4.87 23.0 18 2804 1880897 43.8 47.1 43.8 29.5 29.7 30.7 25.5 22.9 25.3 ML 6.71 8.7 48 2098 6011 98 41.0 42.9 40.1 31.3 28.9 29.6 26.0 23.5 26.8 ML 7.43 7.0 37 906 5197 99 45.1 49.0 46.0 27.9 29.0 29.3 21.7 21.2 23.0 ML 6.20 10.0 49 2570 10715

100 38.2 41.1 37.8 22.6 24.9 23.8 24.5 18.6 23.8 CL 6.37 8.1 45 3804 2215

The next step after determining the extrusion pressures corresponding to consistency limits involves setting up the specific extrusion values corresponding to LL, PL, and SL. Histogram of extrusion pressures corresponding to liquid limits determined using the Casagrande method (Figure 4) reveals that the majority of extrusion pressures matching liquid limits falls in a range from 10-30 kPa. The arithmetical average of extrusion pressure in this interval is exactly 20 kPa. Histogram of extrusion pressures corresponding to plastic limits (Figure 5) determined using the rolling device shows that most of the extrusion pressures in this category fall in range from 1500-2500 kPa. The average for this interval is computed as 1931 kPa and, because the ordinate of the

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extrusion pressure versus water content diagram is logarithmic, it is rounded to 2000 for practical purposes. Concerning the histogram of extrusion pressures corresponding to shrinkage limits (Figure 6) that were determined using the mercury method, the results fall in a wider range, from 5000-20000 kPa. The average for this interval is computed as 12293 kPa and is rounded to 12000 kPa. Following those observations, the representative extrusion pressures for LL, PL, and SL are fixed as 20, 2000, and 12000 kPa, respectively.

Figure 4: Histogram of extrusion

pressures corresponding to liquid limit.

Figure 5: Histogram of extrusion pressures

corresponding to plastic limit.

Figure 6: Histogram of extrusion pressures corresponding to shrinkage limit.

To back calculate the consistency limits from the representative extrusion pressures, the following procedure is employed. The y-intercept, the slope, and the extrusion pressure of 20 kPa for each soil sample are used to determine the liquid limit, and the computed liquid limits are obtained for 100 soil samples. The results are tabulated under column 3 in Table 1. Likewise, the computed plastic limits using the linear equation coefficients of each soil sample, along with the extrusion pressure of 2000 kPa, are obtained and presented in column 6. Finally, the extrusion pressure of 12000 kPa, along with the coefficients of a and b, are included in computations and the resulting predicted shrinkage limits are listed in column 9 of Table 1. Amounts of error involved in back calculation of liquid limit, plastic limit, and shrinkage limit using the respective extrusion pressures of 20kPa, 2000 kPa, and 12000 kPa in the form of certain ranges are presented in Table 2, which helps us make the following comments: 58 percent of the liquid limits are predicted with 5 percent error. Ninety percent of all computed liquid limits remain within 10 percent error. The degree of deviations of the computed plastic limits using the extrusion pressure of 2000 kPa along with the coefficients of a and b from those obtained through

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the bead rolling method is rather significant. Only 38 percent of plastic limits were estimated with 10 percent error. The deviations of computed shrinkage limits from those observed experimentally is also significantly high. This observation puts forward that while liquid limits were predicted in a good success using the constant extrusion pressure of 20 kPa along with the reverse extrusion test coefficients, the same success can not be accomplished for PL and SL using the constant extrusion pressures of 2000 kPa and 12000 kPa, respectively.

Table 2: Distribution of errors for LL, PL and SL from the use of the constant extrusion

pressures determined through the reverse extrusion method.

Liquid Limit Plastic Limit Shrinkage Limit Range % Range % Range %

0-5 58 0-10 38 0-15 30 5-10 32 10-20 42 15-30 31 10-15 7 20-30 15 30-45 21 15-20 2 30-40 4 45-60 12 20-25 1 >40 1 >60 4

Another attempt was made to predict the three consistency limits statistically. This time, the

y-intercept (the a coefficient) and the inverse slope (1/b) of extrusion pressure versus water content per soil sample, along with liquid limit data from the Casagrande method, were subjected to multiple regression analyses and the following empirical form with the regression coefficient (R2) of 0.89 was drawn:

LL = 1.051 (1.227a) b1.09 (1)

Inclusion of the coefficients of a and 1/b, along with the plastic limit data from the rolling bead method, yield the following relationship (R2=0.76):

PL = 185.5 + 3957/a 26891/a2 + 53143/a3 + 6.7b 0.1367b2 (2)

Concerning the determination of shrinkage limit statistically, collective use of the reverse extrusion constants and shrinkage limit data from the mercury method in a multiple regression analysis produced the following form (R2=0.62):

SL = 982 7882/a 5725/b + 15946/a2 + 8764/b2 + 23714/(ab) (3)

The results obtained from back calculations to predict the liquid limit, plastic limit, and shrinkage limits using the empirical relationships given in Eqn.s (1), (2), and (3) are presented in columns 4, 7, and 10, respectively, in Table 1. The computed LL, PL, and SL values versus the experimentally determined LL, PL, and SL values were plotted in Figures 7, 8, and 9, respectively. Table 3 includes percent deviations of the predicted values from the experimentally determined values for LL, PL, and SL, which reveals that the statistical assessment of consistency limit data, along with the reverse extrusion constants, resulted in much better predictions. For instance, 64 percent of liquid limits were predicted with 95 percent accuracy and 90 percent of liquid limits were done so with 90 percent accuracy. This is a remarkably good success. Seventy two percent of plastic limits, which may yield highly variable results even if a single operator performs repetitive tests on the same soil sample, can be predicted with a 95 percent degree of accuracy. Even better than the case for LL, 93 percent of predicted plastic limits were within 90 percent accuracy. Surprisingly, the level of improvement is also higher for the predicted shrinkage limits using the statistical method. Sixty nine percent of shrinkage limits were predicted with a 90 percent degree of accuracy. The fact that 90 percent of shrinkage limits can be predicted

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with a 80 percent degree of accuracy using the statistical method is highly encouraging for the reverse extrusion method to be used in predicting shrinkage limit.

Figure 7: Comparison between the liquid

limits determined using the empirical relationship and the liquid limits from

Casagrande method.

Figure 8: Comparison between the plastic

limits determined using the empirical relationship and the plastic limits from rolling

device method.

Figure 9: Comparison between the shrinkage limits determined using the empirical relationship and the shrinkage limits from mercury method.

Table 3: Distribution of errors for LL, PL and SL from the use of empirical relationships.

Liquid Limit Plastic Limit Shrinkage Limit Range % Range % Range %

0-5 64 0-5 72 0-10 69 5-10 26 5-10 21 10-20 21 10-15 7 10-15 6 20-30 5 15-20 2 15-20 1 30-40 4 20-25 1 >40 1

Note that some degree of inconsistency exists between the representative extrusion pressures for liquid limit and plastic limit cited by previous studies [e.g., 30 kPa and 2250 kPa in Kayabali and Tufenkci (2007) and 35 kPa and 3000 kPa in Kayabali and Tufenkci (2010a)] and this investigation. One further step was taken to examine the likely reason behind this inconsistency. The extrusion pressures corresponding to each LL, PL, and SL show a normal distribution around a mean value. Emphasis should be placed on the fact that if the extrusion pressure (say 20 kPa for LL) is unique for a consistency limit, there should not be any scatter around that specific value.

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To examine this further, a plot of the extrusion pressure versus liquid limit was constructed, as shown in Figure 10. Interestingly, the extrusion pressures corresponding to liquid limit increases as the liquid limit decreases. This can be attributed to the increasing internal frictional forces due to the increasing granular component as the plasticity decreases. Figure 11 has a similar pattern to Figure 10. That is, the extrusion pressures corresponding to plastic limit somewhat increases as plastic limit decreases. Figure 12 displays a similar comparison for shrinkage limits. This fact compels that some degree of corrections should be carried out to take into consideration the variability of extrusion pressure for LL, PL and SL. This point deserves further investigation and will not be addressed here. It is very likely that such a correction procedure will highly improve the quality of predictions of consistency limits using the reverse extrusion method.

Figure 10: Relationship between extrusion pressures corresponding to liquid limits and liquid limits as determined from Casagrande

method.

Figure 11: Relationship between extrusion

pressures corresponding to plastic limits and plastic limits as determined from rolling

device method.

Figure 12: Relationship between extrusion pressures corresponding to shrinkage limits and shrinkage limits as determined from mercury method.

CONCLUSIONS Based on more than 4000 tests of consistency limits and reverse extrusion, the present

analysis allows drawing of the following conclusions:

Liquid limit and plastic limit are both critical water contents corresponding to undrained shear strengths and are determined using techniques which do not measure it. In addition, a number of uncertainties are involved in conventional tests to determine those Atterberg limits. Presumably, reverse extrusion test measures the undrained shear strength and provides operator-

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free results. A large body of data was constituted for LL, PL, SL, and RXT using 100 soil samples. Each kind of test was carried by single person to avoid possible effects introduced by an operator.

The first stage of evaluations included determination of specific values of extrusion pressures corresponding to LL, PL, and SL, which were found to be 20 kPa, 2000 kPa, and 12000 kPa, respectively. Back calculations of LL, PL, and SL using the respective extrusion pressures of 20, 2000, and 12000 kPa along with the reverse extrusion coefficients of each soil sample provided a significant agreement with LLs determined using the Casagrande cup method. Nevertheless, the same success can not be achieved for PL. It was not as good for SL either. It is concluded that extrusion pressures corresponding to Atterberg limits are not unique and the use of fixed values of extrusion pressures to determine LL and PL as were done by Kayabali and Tufenkci (2007) and Kayabali and Tufenkci (2010a) may lead to inaccurate results.

The second stage of evaluations involved running a multi-regression analysis to establish empirical relationships between the reverse extrusion coefficients and Atterberg limits. Evaluation of those empirical relationships revealed that liquid limit and plastic limit of about 90 percent of 100 soil samples can be predicted within 10 percent error using the reverse extrusion test. Considering the variations inherent with each of the two Atterberg limit test methods, the results of reverse extrusion tests appear to be highly reliable. The shrinkage limit of approximately 90 percent of 100 soil samples was predicted within 20 percent error, which deserves attention regarding the use of reverse extrusion tests to predict the shrinkage limit as well. It turned out that empirical relationships predicted consistency limits much better than did the representative extrusion pressures corresponding to LL, PL, and SL.

It appears that the extrusion pressures corresponding to LL, PL, and SL are all affected by soil plasticity. A further investigation considering the variation of extrusion pressure with respect to plasticity is suggested; such a procedure may significantly improve the quality of prediction of consistency limits by introducing a correction procedure for the reverse extrusion method.

ACKNOWLEDGMENTS This research was funded by Grant No. 09B4343015 from Ankara University.

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3. American Society for Testing Materials, 2000b. Standard practice for classification of soils for engineering purposes (Unified Soil Classification System): ASTM D2487-00, West Conshohocken, PA.

4. Cerato, A. B. and Lutenegger, A. J., 2006, Shrinkage of clays: Proceedings of the 4th International Conference on Unsaturated Soils, Phoenix, AZ, April 2-6. GSP No. 147. 1: 1097-1108.

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7. Kayabali, K. and Tufenkci, O. O., 2007, A different perspectve for the determination of soil consistence limits: International Symposium on Geotechnical Engineering, Ground Improvement and Geosynthetics for Human Security and Environmental Preservation, Bangkok, Thailand, 423-432.

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