Introduction The British Standard (BS 1377:1990) recommends the fall cone method as the preferred technique for determining the liquid limit of soils. The BS fall cone test uses a cup to hold the soil specimen. A major concern in preparation is trapping air in the specimen during filling.
In view of this concern, Feng (2000) recommended replacing the cup with a ring of the same dimensions to facilitate specimen preparation and to improve specimen quality. As the difficulty in specimen preparation is increased with decreasing water content, a conventional consolidation ring, 19mm high and 63.5mm in diameter, was used to prepare specimens for fall cone penetrations less than 10mm. A smaller specimen ring has recently been made so that the volume of soil specimen is greatly reduced.
Therefore two specimen rings are now available for the BS fall cone test. One has the same dimensions as the specimen cup and the other is 20mm high and 20mm in diameter.With these two specimen rings, it is proposed that the BS fall cone apparatus be used to determine both the liquid limit and the plastic limit. In addition, this paper describes the results of applying the proposed fall cone method on four high plasticity clay samples having fall cone liquid limits ranging from 70% to 316%.
Defining the fall cone plasticity index The fall cone apparatus has been commonly used to determine the undrained shear strength with the following equation by Hansbo (1957):
cu= k W (1) 2Where c uis undrained shear strength, k is a cone constant, W is the weight of cone, and d is penetration depth.Based on a large amount of experimental data (eg Skempton and Northey, 1953; Wood and Wroth, 1978), the undrained shear strength at the plastic limit may be approximated as 100 times the undrained shear strength at the liquid limit.The liquid limit is the water content at the BS fall cone penetration depth of 20mm (BS 1377:1990).
Therefore, according to Equation 1, the penetration depth at the plastic limit is 2mm.Figure 1 shows a model of linear log d versus log w flow curve developed from an assumption that the relationship between the logarithm of undrained shear strength and the logarithm of water content is linear (Feng, 2000; 2001). The slope of the flow curve, denoted as m , is then defined by Equation 2:
m= Dlogw/Dlogd (2) As the penetration depth at the liquid limit, w Lc , is 20mm and the penetration depth at the plastic limit, w Pc , is 2mm, Equation 3 can be derived from Equation 2 for computing the value of m :
m = log (w Lc / w Pc )(3) Therefore, the plasticity index, I Pc , may be computed by using Equation 4:
IPc = w Lc (1 - 10 -m )(4) Equation 4 shows that the plasticity index is a function of both the liquid limit and the slope of the flow curve. For any pair of soils having the same slope on the flow curve but different liquid limits, Equation 4 implies that the plasticity index would be different.
On the other hand, for any pair of soils having the same liquid limit but different slopes on the flow curve, Equation 4 implies that the plasticity index would also be different. It may be noted that the plasticity index and the liquid limit are commonly used in soil classification and empirical correlations with engineering properties.
Test programme The fall cone method was used to determine the liquid limit and the plastic limit of four highly plastic clay samples. These samples were kaolin; a mixture of 90% kaolin and 10% bentonite; a mixture of 80% kaolin and 20% bentonite; and bentonite. The samples were originally powders and were thoroughly mixed with distilled water to give water contents near their liquid limits and then stored overnight before testing.
The liquid limit and plastic limit of the samples were also determined by using the percussion method and the thread rolling method respectively.
When using the two specimen rings in the fall cone test, the larger specimen ring was used for penetration depths between 25mm and 10mm and the smaller one for penetration depths between 8mm and 3mm.
It is not practical to prepare soil specimens with water contents lower than the plastic limit, ie penetration depths smaller than 2mm, since the soil becomes stiff and brittle at such low water contents. At least two data points should be obtained from each of the two specimen rings for defining the flow curve.These data points should be as evenly distributed as possible with penetration depths between 3mm and 25mm.The plastic limit is determined by extrapolating the flow curve to the penetration depth of 2mm.
Test results and discussions The results of the fall cone tests are shown in Figure 2. It can be seen that a linear log d versus log w flow curve is obtained for each of the clay sample tested.The liquid limit, the plastic limit, and the m value of each clay sample are directly determined from its flow curve and are shown in Table 1. This shows that the fall cone plastic limits of the clay samples vary only slightly; however, the fall cone liquid limits and the m values vary significantly.
Table 1 also shows that the m value for the pure kaolin sample is 0.381 and for the pure bentonite sample is 0.959.By assuming a freedom of interaction between kaolin and bentonite in a sample, the liquid limit and the plastic limit of the mixture of 90% kaolin and 10% bentonite are proportionally estimated to be 95% and 30% respectively, and an m value of 0.501 is obtained.
Furthermore, the liquid limit and the plastic limit of the mixture of 80% kaolin and 20% bentonite are estimated to be 119% and 30% respectively, and an m value of 0.598 is obtained. These estimated values are considered to be in good agreement with the measured values in Table 1.
The plasticity index may also be computed by using Equation 4 with known values of w Lc and m from the flow curve. Furthermore, for the clay samples tested, the plasticity index is equal to their activity since the clay fractions of these samples are all equal to 100%. It can be shown from Table 1 that the activity of the clay samples tested ranges from 0.41 to 2.81. On the other hand, activity is determined by both the plasticity index and the clay fraction for soils with clay fractions less than 100%. In this case, a hydrometer test is also required for determining the activity of the soil sample.
Table 1 also shows that the percussion liquid limits are higher than the fall cone liquid limits.This is consistent with the data of Leroueil and Le Bihan (1996), Farrell et al (1997), and Feng (2001) that the percussion liquid limit is greater than the fall cone liquid limit for liquid limits greater than 50%, but the difference is rather limited for liquid limits lower than 120%.
Figure 3 shows that the data of percussion liquid limit versus fall cone liquid limit from this study agree well with the data from previous investigations. It is of practical interest to convert the fall cone liquid limit into the percussion liquid limit. The correlation equation in Feng (2001) can be used for this purpose and is rewritten as:
wL= 1.06 (w Lc - 2.6) (5) It should be noted that Equation 5 is now derived for the fall cone liquid limits lower than 130%.The liquid limits of the bentonite samples are higher than 300% so that Equation 5 is not applicable. As both the percussion test and the fall cone test are actually strength tests, the excessive discrepancy between w Lc and w Lfor bentonite implies that the measured strengths are significantly different. It is probably due to both the nature of bentonite at its liquid limit and the difference in the mode of failure. On the other hand, it can be seen from Table 1 that the fall cone plastic limits are in good agreement with the thread-rolling plastic limits for all the clay samples tested.
Conclusions 1The BS fall cone apparatus with the specimen rings presents a scientific and economic way of determining the consistency limits of high plasticity clays.
2The larger ring is used to prepare specimen for fall cone penetrations between 25mm and 10mm, whereas the smaller ring is for fall cone penetrations between 8mm and 3mm. For each sample, at least two data points should be obtained from each of the two specimen rings, with penetrations distributed as even as possible between 25mm and 3mm.
3For each sample tested, a linear log d versus log w flow curve is found from the data points. The liquid limit, the plastic limit, and the plasticity index are then determined from the flow curve. It is found that the fall cone liquid limits of the samples tested, except for the bentonite, are slightly greater than their percussion liquid limits.The fall cone plastic limits are in good agreement with the thread-rolling plastic limits.
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