Professor V, Agricultural Machinery Division, Institute of Agricultural Engineering, College of Engineering and Agro-Industrial Technology, UPLB
Professor V, Agricultural Machinery Division, Institute of Agricultural Engineering, College of Engineering and Agro-Industrial Technology, UPLB
Professor V, Agricultural Machinery Division, Institute of Agricultural Engineering, College of Engineering and Agro-Industrial Technology, UPLB
Delfin C. Suministrado1
Introduction
Many theories in soil mechanics have been formulated and advanced to model
the interactions of soil with various tools, wheels and other soil-engaging instruments.
Generally, the purpose is to evaluate the strength behavior as affected by soil types
and moisture conditions. Along with these, soil classification systems have also been
devised to better understand soil characteristics with regards to their suitability as an
engineering material.
If a soil does not contain a substantial proportion of clay and its specific surface is
relatively small, the grading system involving particle size distribution and the
determination of specific volume may be enough for engineering purposes. However,
soils containing a considerable quantity of clay require additional tests. One set of these
tests which is used to classify soil for clay content and strength characteristics involves
the determination of soil consistency.
1
Professor V, Agricultural Machinery Division, Institute of Agricultural Engineering, College of
Engineering and Agro-industrial Technology, UPLB.
The Atterberg limits of soil
Current engineering practice mostly uses only two of these Atterberg limits,
the liquid and the plastic limits, while the shrinkage limit is referred to occasionally.
The liquid limit (LL or wL) is the water content of the soil at which the soil passes
from a plastic to a liquid state. The plastic limit (PL or wP) is the lowest moisture
content at which soil passes from the plastic state to the crumbly semi-solid condition.
The liquid and plastic limits define the range of water content over which the soil
exhibits plastic behavior. This range itself is referred to as the plasticity index (Ip).
The shrinkage limit is the moisture content that defines where the soil volume will not
decrease further if the moisture content is reduced.
The liquid limit, plastic limit and plasticity index of soils are used extensively,
either individually or together with other soil properties, to correlate with engineering
behavior such as compressibility, permeability, compactibility, shrink-swell
characteristics and shear strength. The plasticity chart of Casagrande which makes use
of these values is now an accepted handy tool for classifying soils (Holtz and Kovacs,
1981).
Sridharan and Nagaraj (2005) who worked with Indian soils, found that the
plastic limit bears a good correlation with the compaction characteristics, namely
optimum moisture content and maximum dry unit weight, much better than liquid
limit or plasticity index. Islam, et al. (2006) who used both the percussion method for
liquid limit determination and the thread rolling method for plastic limit determination,
reported about the physical properties and Atterberg limits of selected soils in
Mymensingh district in Bangladesh, and established relations between plastic limit
and soil gradations. Yukseleni and Kaya (2006) investigated the relationships between
cation exchange capacity (CEC) and various other soil engineering properties and
reported on a quick method of estimating CEC. Dolinar, et al. (2007) who used the
fall-cone method for liquid limit determination and the thread rolling test for plastic
limit determination, reported about the correlation between soil surface area and
Atterberg limits of five randomly selected soil samples. Using data from across the
2
US, Hawaii and Alaska, Seybold, et al. (2008) developed linear correlation models
between Atterberg limits and some basic soil properties such as clay content and CEC
in order to predict liquid limit and plasticity index.
For more than half a century since Casagrande proposed the plasticity chart, it
has not been given much scrutiny. Recently, a new plasticity chart, which also aims
to classify soils using the Atterberg limits, has been proposed by Polidory (2003). It
differs from Casagrande's plasticity chart, especially in terms of its silt and clay zones,
whose positions are reversed compared with Casagrande's chart. He explained that,
contrary to what is commonly believed, in inorganic soils—liquid limits being
equal—the plasticity index increases as the clay content decreases.
For the liquid limit, the percussion or Casagrande method has been the
standard in use in the United States and it must have been the de facto standard in the
country as Philippine engineers had borrowed many engineering traditional practices
from the Americans. This method was developed and standardized by Casagrande
(1932). To determine the liquid limit, the standard metal cup containing a pat of clay
is given repeated standard blows by being dropped through a height of 10 mm onto a
hard rubber or micarta base. When the soil is at its liquid limit, the groove made on
the soil with a standard grooving tool would close at its base over a distance of 13 mm
in exactly 25 blows. In real practice, liquid limit is obtained by interpolation from a
‘flow curve’ which relates water content and the number of blows that closes the
groove (Wood, 1990).
Many other countries have however already shifted to the drop-cone or fall-
cone penetrometer technique to determine liquid limit. To perform the test, a cone is
allowed to fall freely under its own weight from a position at rest with the point of the
cone just touching the surface of the soil sample. As the cone is released, it
accelerates initially and then decelerates to rest and penetrates a distance at which the
soil resistance is equal to the weight of the cone (Wood, 1990). The moisture content
of a soil at which a 60 gm cone of 60° tip angle would produce a penetration of 10
mm is designated as the liquid limit in Sweden and other Scandinavian countries.
Although Japan uses the same type of cone as that of Sweden, the adopted depth of
penetration is at 11.5 mm. A 30° cone of mass 80 gm at 20 mm penetration is the
standard in the UK. Table 1 below shows the variations of the cone standards adopted
by some countries to determine liquid limits of soils.
3
Table 1. Standards for the fall cone liquid limit test in different countries (Sampson and
Netterberg, 1984; Koumoto and Houlsby, 2001).
The preferred method by the ISO is the fall-cone while the Casagrande method
is considered as an alternate. The ISO recognizes that results using the percussion or
Casagrande method are subject to the performance and judgement of the operator.
The estimated soil strength at the liquid limit is 1.71 kPa according to the
Swedish definition and 1.67 kPa according to the British definition. Theoretical
values were reported by Koumoto and Houlsby (2001) to vary from 1.38 kPa to 4.52
kPa. Wroth and Wood (1978) suggested a strength of 1.7 kPa and indicated a possible
range of 0.7 -2.65 kPa. Liquid limit values obtained using the Casagrande apparatus is
assumed to correspond to a strength level of 2 kPa (Wood, 1990) which is within the
range suggested by Wroth and Wood above.
The current standard of most countries for plastic limit determination is the
thread-rolling method. The process involves rolling the clay with fingers until it
formed threads. The threads are put together and rolled again, and the process is
repeated until the clay could no longer be rolled but broke into pieces. Plastic limit is
defined as the moisture content at which the thread of soil crumbles at 3 mm diameter.
4
Kodikara, et al. 2006; Tanpo, et al., 2007). The fall-cone method of Feng (2004) is
already at a relatively high stage of development as a plastic limit measurement
method. Also, a patent for method and apparatus for determining plastic limit of soil
based on the drop-cone principle has been filed in Great Britain along with parallel
patent applications to many other countries around the world.
On the basis of the 100-fold variation of the shear strength of soil from liquid
limit to plastic limit, the undrained shear strength of soil at plastic limit is equivalent
to about 170 kPa. The model of Koumoto and Houlsby (2001) involving drop-cone
technique, however gave a value of only 138 kPa and an average of 108 kPa. Wood
(1990) proposed an average value of around 200 kPa.
There is a general trend to adopt the principle of the drop-cone method for
both the liquid limit and plastic limit determination for its reliability and consistency.
Although the technique has already been standardized in many countries for liquid
limit, it is only these later years that similar research and development investigations
are being conducted for its application to the plastic limit.
For plastic limit, the standard thread rolling technique has long been criticized
for its subjectivity, poor repeatability and unreliability. The simple but tedious
procedure appears as a primitive test in the age of electronics and computers. Current
proposals to adopt the drop-cone method for plastic limit determination is gaining
attention and favor. Although Koumoto and Houlsby (2001) had proposed that the
60°-60gm fall cone at 1 mm be used as standard for plastic limit, they realized the
practical problem of the 1 mm depth itself. Instead, Feng (2001, 2004) had developed
and proposed the use of the 30°-80gm cone at 2 mm depth.
Around the vicinity of the Philippines, Feng (2004) of Taiwan has been
working to refine the use of the small ring and fall-cone to determine the plastic limit
in continuation of his earlier work where he evaluated the relationship between the
fall-cone penetration and the water content of clays (Feng, 2000). Rashid (2005) in
Malaysia reported on the fabrication and testing of three cones with different sizes
and weight and compared their performance with the thread rolling method. He found
that the 20°-101.47gm, the 30°-240gm and the 30°-80gm cones could all feasibly
perform plastic limit test but concluded that the 20° cone gave the best correlations
with the standard thread rolling method. In Thailand, the group of Tanpo, et al. (2007)
is currently working to develop the use of the cone penetrometer to determine both the
5
liquid and plastic limits. In Australia, Weaver and Hulugalle (2001) found that
quicker and more consistent results were obtained by a less experienced operator with
the drop-cone penetrometer method than the thread rolling method.
Soil samples were obtained from different locations in the province of Laguna,
Philippines and used in the research work on the critical evaluation of the techniques
of Atterberg limits determination. The data of the soil textural analysis of eight soil
samples used by Polinga (2001), Suministrado (2001), Gareza (2005) and
Suministrado and Gareza (2007) are given in the Table 2 below.
Table2. Textural analysis of selected soil samples (Suministrado, 2001; Gareza, 2003).
Percentage
Source of soil sample sand silt clay Textural grade
CEAT, UPLB 11 42 47 Silty clay
Banago, Nagcarlan 25 56 19 Silt loam
San Roque, Luisiana 25 35 40 Clay
San Juan, San Pablo 47 35 19 Loam
Poblacion, Nagcarlan 21 34 45 Clay
Sabang, Nagcarlan 27 49 24 Loam
San Francisco, Victoria 18 44 38 Silty clay loam
Dita, Liliw 21 46 33 Clay loam
The soil samples were tested for liquid limits using the procedures for the
percussion and drop-cone methods explained above. However, instead of the standard
three-point or four-point method to establish ‘flow curves’, more data points were
obtained, and by statistical correlation analysis, the values of the liquid limits were
calculated.
6
For the Casagrande liquid limit, the linear log-normal relationship of the
number of blows at closure of the groove and the moisture content was used to
determine the liquid limit values.
Polinga (2001) and Suministrado (2001) had critically compared the use of the
two methods of liquid limit determination. They had reported data obtained by novice
operators on the measurement techniques using both the percussion (Casagrande) and
the drop-cone methods (See Table 3 below). The relative advantage of the drop-cone
method is clearly evident from the calculated correlation coefficients. Data set 1
involves 20 data points each for both the Casagrande method and the drop-cone
method while Data set 2 involves at least 5 data points for the Casagrande method and
6 data points for the drop-cone method.
Table 3. Liquid limit data reported by Polinga (2001) and Suministrado (2001) on three Laguna
soil samples.
Soil sample Data set 1 Data set 2
Casagrande Drop-cone Casagrande Drop-cone
CEAT, UPLB 56 (0.06)1 52 (0.18) 62 (-0.85) 62 (0.99)
Banago, Nagcarlan 46 (0.00) 54 (0.32) 50 (-0.21) 49 (0.98)
San Roque, Luisiana 83 (-0.42) 79 (0.61) 84 (-0.07) 81 (0.99)
1
The number in parentheses are correlation coefficients.
Gareza (2003) extended the above work by using five other soil samples.
Equipped with the basic theoretical knowledge and adequate practice in performing
the test procedure, the operator obtained the values with higher correlation
coefficients compared to the earlier data of Polinga (2001) and Suministrado (2001).
The test results are shown in Table 4 below. All liquid limit values were calculated by
statistical regression using 10 data points each.
7
Table 4. The liquid limits of the soil samples obtained by Casagrande and drop-cone methods
and the corresponding correlation coefficients (Gareza, 2003).
Method
Soil sample Casagrande Drop-cone
Liquid limit R Liquid limit R
San Juan, San Pablo 42 -0.81 46 0.98
Poblacion, Nagcarlan 58 -0.88 60 0.97
Sabang, Nagcarlan 55 -0.85 57 0.94
San Francisco, Victoria 47 -0.82 52 0.96
Dita, Liliw 59 -0.86 61 0.97
Overall, the experimental results of Gareza (2003) on liquid limit tests also
validated the relative advantage of the drop-cone method over the percussion
technique of Casagrande.
The analyses of data showed that the liquid limit values by the drop cone
penetrometer method were generally higher than those determined by the Casagrande
method at low plasticity (See Figure 1). The difference appeared higher by about 4
units at liquid limit values of 50 and below, but tapered to about 2 units as liquid limit
increased to 60. Although Sampson and Netterberg (1984) had found that the drop-
cone liquid limit values are at least higher by 4 units than the Casagrande liquid limits
for South African soils, other workers claimed that the difference in values is
negligible. In fact, Sridharan and Prakash (1998) wrote that the liquid limit obtained
by the percussion method can be as low as about 26% less and as high as 71% more
than the liquid limit obtained by the cone method.
8
90
85 Equality line
80
Drop-cone liquid limit
75 San Roque
Dita, Liliw
70
Pob lacion, Nag.
65
60 CEAT
55 San Francisco
Sab ang
50
Banago
45
San Juan
40
40 45 50 55 60 65 70 75 80 85 90
Casagrande liquid limit
Figure 1. Comparison of the Casagrande and drop-cone liquid limits of the eight soil samples
(Suministrado, 2001; Suministrado and Gareza, 2007).
Although Budhu (1985) has attributed this difference to the clay content of
soil, other researchers presented different observations. As cited by Sridharan and
Prakash (1998), the lateritic soils of Queiroz de Carvalho (1986) which contain
kaolinite as the only clay mineral gave higher values for the drop-cone method than
the percussion method. On the other hand, the montmorillonite-rich soils from
Turkey (Wasti and Bezirci, 1986) gave much higher liquid limit values for the
percussion method than the drop-cone method. Similarly, Sridharan and Prakash
(1998) had also observed that based on their own data, the kaolinitic clays had higher
liquid limit values obtained by drop-cone method than the percussion method, while
montmorillonitic soils had higher liquid limit values for the percussion than for the
drop-cone method.
9
Using the drop-cone raw data of Suministrado (2001), statistical correlation
analyses were performed and the regression lines were extrapolated to determine the
moisture content at 2 mm penetration. This procedure is proposed by Feng (2004) and
is based on the assumption that the undrained shear strength at the plastic limit is 100
times the undrained shear strength at the liquid limit (Feng, 2000). Table 5 also shows
the plastic limit values by this drop-cone method.
Table 5. Plastic limit data reported by Polinga (2001) and Suministrado (2001) on three Laguna
soil samples.
Soil sample Data set 1 Data set 2
Thread rolling Thread rolling Drop-cone1
CEAT, UPLB 35 38 38
Banago, Nagcarlan 34 39 29
San Roque, Luisiana 66 49 40
1
Obtained from the extrapolated liquid limit drop-cone data at 2 mm penetration (Feng, 2004).
Gareza (2003) determined plastic limits values by the thread rolling method
and by the drop-cone method suggested by Rio (1988) which the uses a 30°-240gm
cone. In the procedure explained by Rio (1988), the plasticity index, Ip, was first
calculated by the formula:
where Δ is the vertical difference of the best-fitted lines at 80gm cone and 240gm
cone at the 20 mm penetration. The plastic limit is obtained from the formula:
A third set of values of the plastic limit was also calculated from the liquid
limit drop-cone raw data reported by Gareza (2003) similar to the extrapolation
procedure of Feng (2004). Statistical correlation analyses were performed and the
regression line was extended to determine the plastic limit moisture content values at
the 2 mm penetration. The three sets of plastic limit values are given in Table 6
below.
Table 6. Plastic limits of three Laguna soil samples (Gareza, 2003; Suministrado and Gareza,
2007).
Soil sample Plastic limit
Thread rolling1 Drop-cone 12 Drop-cone 23
San Juan, San Pablo 35 (2.14) 24 27
Poblacion, Nagcarlan 38 (4.99) 24 35
Sabang, Nagcarlan 37 (0.65) 26 40
San Francisco, Victoria 34 (1.97) 27 35
Dita, Liliw 39 (1.94) 31 39
1
Average of at least six trials; Numbers in parentheses are the variances.
2
Obtained by the 30°-80gm and 30°-240gm drop-cone method of Rio (1988).
3
Obtained from the extrapolated liquid limit drop-cone data at 2 mm penetration (Feng, 2004).
10
The skill of the operator has been identified as a great factor that affects the
plastic limit values by the thread rolling method. The indicated variances given in
Table 6 offer some light on the degree of variation of the data obtained during the
laboratory tests. In Table 7 below, at least seven operators most of whom are
beginners performed the thread rolling method to determine the plastic limits of 12
soil samples. As beginners, the variances are relatively higher than those in Table 6.
Table 7. Plastic limit values by thread rolling method obtained by various operators (Gatchalian,
2007).
Source of soil sample Set 1 Set 2 Set 3 Set 4 Ave. Variance
Cabanbanan, Pagsanjan 34 34 38 42 37 3.72
Dayap, Calauan 41 42 46 41 42 2.46
Gatid, Sta. Cruz 30 33 43 27 33 6.98
Maahas, Los Banos 33 38 43 39 38 4.20
Malaking Ambling, Magdalena 33 39 45 36 38 5.01
Masapang, Victoria 36 38 43 40 39 2.95
Masiit, Calauan 50 47 51 52 50 2.16
Pagsawitan, Pagsanjan 33 36 40 31 35 3.91
Palayan, Nagcarlan 40 42 46 39 42 3.10
San Antonio, Pila 31 30 38 36 34 3.93
Sto. Domingo, Bay 41 52 49 47 47 4.62
Taytay, Nagcarlan 46 40 50 48 46 4.32
Rio (1988) outlined a procedure by which the plastic limit could be indirectly
determined from the 80 gm and the 240 gm cone penetration at 20 mm. He gave no
theoretical basis of the process although he must have drawn from the original idea of
Wroth and Wood (1978). A somewhat similar method was proposed by Kodikara et
al. (1986) who used 80gm and 230gm cone weights. As shown in Table 6 above, the
obtained plastic limit values by this method explained by Rio (1988) are much lower
than those of the standard thread rolling method and those of the drop-cone method
of Feng (2004). This procedure may not be an attractive alternate to the current
standard thread rolling method as this would require twice the amount of tests (Feng,
2006).
The comparison of the plastic limit data contained in Table 5 and Table 6 for
the thread rolling and the drop-cone methods involving eight soil samples is shown in
Figure 2. Some data points seem to lie along the equality line. But with many more
points lying towards inequality, there are two likely reasons. Either the plastic limit
values are not correct, or the theory itself that the plastic limit by the thread rolling
method and that of the drop-cone method are the same is not correct. However, with
all the previous claims and evidences in support of the equality of the two plastic limit
values at least for the 30°, 80 gm cone of the UK standard (Feng, 2004), the former
reason is the most likely problem that creates the discrepancy. The untrained
operators could have obtained wrong values of the plastic limits for the thread rolling
method, the drop-cone method or both. Also, the data used to extrapolate the plastic
limits may not be adequately representative of the appropriate data. It is to be
remembered that the raw data which were analyzed and extrapolated by statistical
11
method were not for plastic limit determination but were originally meant for liquid
limits such that the depths of penetration were not lower than 9 mm and were mostly
within the range of 10 mm and 35 mm.
60
Equality line
55
Drop-cone plastic limit
50
CEAT
45
40 Sabang
Dita, Liliw San Roque
35 San Francisco
Poblacion, Nag.
30
20
20 25 30 35 40 45 50 55 60
Thread rolling plastic limit
Figure 2. Comparison of the plastic limits values obtained (a) by the thread rolling method and (b)
by extrapolating the drop-cone data of Gareza (2003) and Suministrado and Gareza (2007) at
2 mm penetration.
In the overall, any test procedure which can satisfactorily provide the correct
values of the soil indices and which reduces if not totally eliminates subjectivity and
variation of the indices being measured must be considered.
The results of many research work on the Atterberg limits of soils conducted
worldwide provide the possibility of procedurally unifying the methods of
measurement of the two indices of soil plasticity. The use of the drop-cone method,
currently the standard for determining liquid limit in many countries, has been shown
capable of being extended to also measure plastic limit. With the established
advantages of drop-cone method over the percussion (Casagrande) method in
determining liquid limit, alongside the questionable values of plastic limits obtained
by the cumbersome thread rolling method, this unification can definitely provide for
the desired simplicity and time efficiency of soil plasticity tests.
12
percussion method for liquid limit and the thread rolling method for the plastic limit.
Therefore, if the country has to adopt a new standard, the 30°-80gm penetrometer of
UK is the most preferred. Although Koumoto and Houlsby (2001) had claimed that
the 60°-60gm has a relative advantage over the UK standard as it is less sensitive to
cone roughness, the prospect of performing another test involving another set of cone
and penetration standard is discouraging. The 30°-80gm cone which has been
thoroughly studied by Feng (2004) easily lends itself to the 20 mm penetration for
liquid limit and 2 mm penetration for plastic limit.
Research work along this line is definitely necessary if the standards on soil
plasticity index have to be redefined in the country. Currently, there is yet a dearth of
data on local soils regarding Atterberg limits. As we strive to accumulate similar basic
data on soil properties for purposes of application in agriculture and engineering, we
also have to continue the research and development work for proper measurement
methods and accurate and reliable instrumentation systems in order to obtain
meaningful results and data.
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13
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