Kamil Kayabali a, *, Ozgur Akturk b, Mustafa Fener a, Ali Ozkeser a, Ayla Bulut Ustun c,
Orhan Dikmen a, Furkan Harputlugil a, Ramin Asadi a
a Ankara University, Geological Engineering Department, 06100 Ankara, Turkey
b Akdeniz University, Geological Engineering Department, 07058 Ankara, Turkey
c Mineral Research and Exploration Institute, Ankara 06100, Turkey
a r t i c l e i n f o
Article history: Received 22 June 2015 Received in revised form 14 December 2015 Accepted 4 January 2016 Available online 5 January 2016
Keywords: Atterberg limits Remolded soils Mud press method Soil classification
a b s t r a c t
Consistency limits are one of the most prominent parameters to be determined in geotechnical in- vestigations. While these limits are akin to one another, different tools determine each one. Each method of determining consistency limits has its own uncertainties, the operator dependency being the top source of uncertainty. Liquid limit (LL) and plastic limit (PL) tests have a number of uncertainties affecting the test results. The very speculative nature of the bead-rolling method for the plastic limit has long been known. Besides this, its results can be barely accepted as quantitative. In the past, a number of attempts have been made to eliminate these setbacks for Atterberg limits. The scope of this investigation is to evaluate the potential of newly developed “mud press method (MPM)” to predict the two consistency limits. The material employed for this investigation covers 275 soils, whose liquid limits range from 28 to
166. The log(a) and 1/b parameters obtained from the MPM method were correlated to results of the conventional methods. The PL and LL for each soil were predicted using empirical forms and were compared with the laboratory values. Remarkably good matches were obtained between the conven- tionally determined test results and the predicted values for the liquid and plastic limits. The newly developed tool is superior in several aspects to the available conventional methods and tools. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction
The most easily noticeable property of fine-grained soils as the water content changes is probably their variation in consistency, which in turn directly affects their strength. A century has passed since Atterberg proposed the consistency limits in 1911 for agri- cultural purposes. Commonly known as Atterberg limits, they have become an inherent part of almost all geotechnical investigations on soils, ever since Casagrande standardized them (1932, 1958).
While a series of consistency limits was proposed initially, only the three of them are generally in use: the liquid limit (LL), the plastic limit (PL) and, to a lesser extent, the shrinkage limit (SL). The liquid limit is defined as the water content when a soil becomes sufficiently weak to flow like a fluid. The plastic limit is the water content when the soil is sufficiently stiff so that it becomes brittle and fractures.
There are two methods at present to determine liquid limit of soils. Casagrande’s falling cup method (or the percussion method) is included in ASTM standards (ASTM Designation D4318; American Society for Testing Materials, 2005) and still used in much of the world. While they have been pointed out in many investigations in the past, the limitations and/or uncertainties of the Casagrande method are given here for convenience. They include: i) the stiffness of the base rubber, ii) base dimensions, iii) insulation from the supporting table (or bench), iv) material, di- mensions and weight of the cup, v) drop height, vi) soil type, vii) frequency of drops, viii) wear of the grooving tool, ix) the tendency of the halves to slide together, x) the migration of water in dilatant soils, xi) operator judgment for closure length of the groove, and
xii) maintenance problems (Johnston and Strohm, 1968; Wroth and Wood, 1978; Whyte, 1982; Lee and Freeman, 2007; Kayabali and Tufenkci, 2010; Haigh, 2012).
Because of the limitations and/or uncertainties involved in the percussion method, an alternative method of the fall-cone test was developed to measure the liquid limit. The main advantages of the fall-cone method are simplicity, easy operation, and comparative reproducibility (Prakash and Sridharan, 2006). Some researchers such as Wasti and Bezirci (1986), Leroueil and Le Bihan (1996), and Sridharan and Prakash (2000) observed that the liquid limit values obtained from the Casagrande cup method and fall-cone methods are not the same. Prakash and Sridharan (2006) reported that the liquid limit determined from the cone penetration method could differ from that obtained by the percussion method by a margin of about þ10% to -200%. In contrary to those assertions, part of the data we used in the present study showed that the match between the liquid limits obtained by the fall-cone method and the liquid limits determined from the Casagrande cup method is perfect, with the exception that the liquid limit measured using the fall cone method slightly overestimates (less than 4% in error) the liquid limit by the percussion method (Fig. 1). Therefore, we opted to use the LL values from the fall-cone method.
We criticize that, while the number of drops is plotted against water content for a given soil in a numerical manner, the Casa- grande cup method fails to yield a thoroughly satisfactory rational basis for the liquid limit to rest on because of a number of the pa- rameters affecting the number of blows and thus the low repeat- ability. In this sense, the fall-cone method has relatively more reliable rational basis, or appears to be a better quantifiable means of achieving the liquid limit.
The present method for determining the plastic limit is the long established thread-rolling (or bead-rolling) test. This procedure subjects the soil to a very complex stress system in that it combines bar rolling distortion, cylinder compression, and lateral extrusion processes (Whyte, 1982; Medhat and Whyte, 1986). The un- certainties related to the factors affecting the test results can be listed as: i) applied pressure to the soil bead, ii) width of hand contact to bead diameter, iii) friction between soil, hand and base plate, iv) speed of rolling, v) personal judgment of the operator, and
vi) the risk of contaminating the sample (Whyte, 1982; Sivakumar et al., 2009; Nagaraj et al., 2012). Sherwood (1970) investigated the variations of standard test method results and concluded that clay with an average value of 23% for PL varied from as low as 19% to as high as 39% when tested in several different laboratories. Sivakumar et al. (2009) stated that this method is non-mechanical, and it brings with it some major drawbacks, most notably its sub- jective nature and the fact that considerable judgment is needed on the part of the operator. Numerous researchers (e.g. Belviso et al., 1985; Wood, 1990; O’Kelly, 2013) have highlighted the relatively
Fig. 1. Plot showing the perfect match between liquid limits obtained from Casagrande and fall-cone methods.
poor reproducibility of the Terzaghi’s bead-rolling method (Terzaghi, 1926). While the uncertainties involved in bead rolling by hand were somewhat reduced by the substitution of the rolling device (see ASTM D4318; American Society for Testing Materials, 2000), the subjective nature of the test still persists. Therefore, the plastic limit determined using the bead-rolling method is even less quantifiable than the liquid limit obtained from the fall-cone method, and thus weaker rational basis to determine test results on.
Concerning the non-mechanical or non-quantifiable nature of the thread-rolling test, many attempts have been made to deter- mine the plastic limit on a more rational basis. Most of such at- tempts have focused on utilizing the fall-cone device to determine the plastic limit as well. In this regard, Feng (2004) showed that the fall-cone method could also be used for determining the plastic limit. Prakash and Sridharan (2006) stated that even though a value of the plastic limit can be obtained using the cone penetration method (even for non-plastic soils), that value does not represent the true plastic limit because of the method used to measure the undrained cohesion, which contributes to soil plasticity. Sivakumar et al. (2009) employed some 24 different soils to test the ability of the standard fall-cone method to determine the plastic limit. They concluded that their new procedure could be used to evaluate PL with reasonable confidence. Timar (1974) introduced the concept of direct extrusion to determine both the LL and PL using the same apparatus. The extrusion method was further investigated by Whyte (1982) to determine the PL. Whyte (1982) showed that the reverse extrusion method is more reliable, which would later be confirmed by additional tests.
Attempts have been also made to determine both consistency limits, namely LL and PL, employing a single tool. In this regard Lee and Freeman (2007) provided an excellent summary of non-ASTM test methods to conduct the Atterberg limits tests. They compared eight non-ASTM test methods for LL and ten non-ASTM test methods for PL, of which seven methods combined LL and PL tests into a single procedure. Whyte (1982) stated that the extrusion method could be established as a method to predict PL, and could be extended to cover liquid limit as well. Kayabali and Tufenkci (2010) took the extrusion method one step forward and proposed that the reverse extrusion method be employed to determine both LL and PL. They redefined the LL and PL as water contents corre- sponding to specific extrusion pressures. Kayabali (2012) investi- gated the applicability of the reverse extrusion test for determining the most common Atterberg limits (namely LL and PL), as well as to include the shrinkage limit test. After conducting some 4000 tests, he concluded that about 90% of LL and PL could be predicted with an accuracy of plus/minus 10% error, using the recently introduced soil mechanics testing tool, the reverse extrusion test. He further showed that the shrinkage limits of about 90% of all soil samples tested were predicted within plus/minus 20% error.
In order to combine the LL and PL into a single device, the au- thors developed equipment called the “mud press machine (MPM).” This newly developed tool is essentially a miniature multi- hole direct extrusion machine. The scope of this investigation is to assess the mud press method as an alternative tool to determine the two consistency limits using only one piece of equipment. Conventional methods are employed to verify the findings from the MPM.
2. Materials
The nature of such an investigation requires the use of soil samples of a wide range of plasticity. A number of both natural soils and those prepared in laboratory were employed. The natural soil samples available in our soil mechanics laboratory had liquid limits ranging from 40 to 80. While this range appears to cover most soils found in nature, it was important to extend the range to ensure that the method proposed is applicable to all variety of soils and those artificial soils prepared in the laboratory were employed. To achieve this goal, bentonite and fine sand were used as additives. To obtain soils with higher plasticity, one of the most abundant soil samples in the laboratory was mixed with bentonite, with varying ratios of dry mass. In this way, soils with a liquid limit of up to 150 were obtained. Similarly, one of the soil samples was mixed with different amounts of fine sand to obtain soil samples with liquid limits below 30. At the end, 275 soil samples were prepared. All soil samples were sieved through #40 mesh prior to conducting the conventional and newly proposed methods of consistency limit tests.
The tool utilized for the liquid limit tests is the fall-cone device with a cone mass of 80 g and an apex angle of 300. The plastic limit test device comprises the components shown in Fig. 2. The newly devised mud press machine (MPM, Fig. 3) consists of a loadcell of 2 kN, a loading arm, a display screen, and a sufficient quantity of moulds, which are both 30 mm in height and diameter, consisting of 28 equally spaced extrusion channels at the bottom. The diam- eter of each extrusion channel is 2.5 mm. There is no specific reason for choosing the mould and extrusion channel dimensions. The selected mould dimension simply took into consideration the amount of test material commonly obtained as disturbed samples from the field tests such as the standard penetration test (SPT). The selected extrusion channel diameter was only for the convenience of manufacturing purposes. The spacing between the channels is same as the channel diameter.
3. Methods
The liquid limit tests were performed in accordance with the BS 1377 (British Standards Institution, 1990). At least five water con- tents were measured in order to catch the best match between data points and the curve fitted. The plastic limit tests were run, following the guidelines of ASTM D4318. Five to ten trials were employed per soil sample; afterwards, the mean value was taken by dropping the recorded highest and lowest plastic limit values.
As for the mud press method, approximately 150 g of minus #40 dry soil is taken. For the first stage of the test, about 100 g of dry soil is taken and a homogeneous, wet mixture is prepared, whose water content is slightly lower than liquid limit. This is adjusted by experience. Some 10e15 g of wet soil is reserved for the first water content determination. The test mould is filled with wet soil, just by finger pressure. The top of the mould is levelled and wiped by a cloth. The mould is then placed into the slot of the mud press machine. The operator applies a steady force onto the specimen using the lever arm. In the meantime, the device records the applied force for every second and displays it. As the applied force reaches to a certain level, the wet sample extrudes from the channels like spaghetti. At this time, the applied force remains nearly fixed and the display shifts to a flat curve, which gives the intensity of force at the time of extrusion, in other words, failure. The measured values are also recorded in the memory of the device for double-checking the intensity of force at failure. The next step involves the addition of a small amount of dry soil into the previ- ously prepared wet mixture. Again, it is mixed homogeneously to obtain a new specimen with somewhat lower water content than the previous mixture. Another 10e15 g of wet soil is reserved for the second water content determination. The mould is filled with the new wet mixture and a second value of force at the time of failure is obtained. Now, there are two pairs of water content and extrusion force at failure at hand. The procedure is repeated by adding more dry material, mixing homogeneously, and pressing to
Fig. 2. Roll device with the glazing paper for plastic limit tests.
form spaghetti several more times. The intensity of the force at the time of failure usually ranges from 10 to 100 kgf (i.e., 0.1e1.0 kN). Fig. 4 is a summary of six MPM tests conducted on one soil sample. Data pairs obtained at the end of each series of MPM tests are plotted per soil sample on a semi-logarithmic diagram (Fig. 5). To catch a good match for curve fitting, at least five or six water contents are required. The final stage of the MPM test involves the determination of the slope and y-intercept of the fitted curve. The total duration of time required to conduct an MPM at six different water contents is about 1 h. One point to be highlighted here is about the water content equalization of wet soil mixtures. Regarding this matter, the ASTM D4318 standard suggests that the wet soil mixture is allowed to be stored at least 16 h for the equalization of water content throughout the test sample before the test. However, this requirement appears to be impractical from the standpoint of test duration. In addition, a literature research reveals no investigation about whether or not the omittance of water equalization affects the test results. Therefore, it is not considered to be a significant issue for the tests conducted for the present investigation.
4. Results
To test the usability of the newly proposed technique to deter- mine the consistency limits, 275 soil samples were employed. The experimental results obtained from conventional methods of fall- cone and bead-rolling are presented in Table 1, which also in- cludes MPM data as log(a) and 1/b. The format of the latter was only chosen for practical purposes. A regression analysis was performed employing the log(a) and 1/b parameters as independent variables to obtain the dependent variables of LL. A number of equations relating the log(a) and 1/b parameters to LL were obtained, from the
Fig. 3. Mud press machine deviced for this investigation.
Fig. 4. An example plot for the test results of MPM.
Fig. 5. Semi-logarithmic diagram for the extrusion force at failure versus the water content for MPM test on soil sample 57.
most complex equation to the simplest forms. The most complex correlation equation yielded a regression coefficient (R2) of 0.96, which showed only a slight change on the third decimal from the following much simpler form:
LL ¼ 97:6 þ 378 logðaÞþ 3:291=b (1)
The predicted liquid limits using Equation (1) show remarkably good agreement with the experimentally determined liquid limits.
Equation (1) predicted 84% of all measured LLs within an error margin of 10%. The mean of the errors with the prediction of LLs is 5.6% with a standard deviation of 4.1%. The plot of the measured versus the predicted LLs is illustrated in Fig. 6.
Another multiple-regression analysis was carried out using the independent parameters of log(a) and 1/b to obtain the dependent parameter of PL. While the most meaningful relationship between log(a) and 1/b and PL yields a regression coefficient of 0.86, it is rather complex, including a number of constants, and is not pre- sented here for practical purposes. Instead, the following much simpler form is opted:
No.
LLm
PLm
log(a)
1/b
LLp
PLp
1
68.0
29.3
4.00
17.5
60.6
30.2
2
59.6
24.4
3.55
19.2
54.2
26.6
3
62.5
30.0
3.89
18.5
61.2
30.1
4
59.5
25.6
3.43
21.7
58.7
27.7
5
74.9
32.9
3.53
25.5
74.3
32.1
6
74.2
31.8
3.74
23.0
72.1
32.9
7
81.3
33.9
3.07
35.1
89.8
30.9
8
77.8
33.3
3.17
28.8
73.0
29.4
9
77.4
33.1
4.26
19.3
72.4
36.1
10
53.0
29.8
4.36
14.0
56.8
28.4
11
61.0
24.3
2.86
30.4
65.3
26.1
12
71.9
26.6
3.08
26.8
62.9
27.0
13
72.9
40.3
5.01
15.2
72.1
39.6
14
68.3
39.1
4.27
17.0
64.9
33.0
15
63.1
41.3
6.42
9.5
69.9
40.3
16
59.3
29.9
3.33
22.7
58.8
27.3
17
56.1
33.4
3.84
18.4
59.6
29.3
18
54.8
30.5
4.41
13.2
55.2
27.2
19
54.8
25.0
3.25
22.5
55.3
26.1
20
51.7
24.8
3.16
23.4
54.8
25.6
21
63.0
29.9
3.48
23.1
64.9
29.6
22
62.8
28.8
3.45
22.7
62.7
28.9
23
45.8
26.2
3.77
15.8
49.2
24.4
24
68.5
27.2
3.20
25.1
61.9
27.5
25
50.7
28.6
5.56
9.0
59.1
26.3
26
77.0
29.6
2.90
32.8
75.0
27.7
27
60.8
25.3
3.34
22.5
58.3
27.2
28
67.9
33.8
4.96
13.3
65.1
34.7
29
55.4
25.4
4.51
12.3
54.2
26.0
30
57.4
30.9
5.13
11.0
60.0
29.8
31
61.3
24.2
3.25
21.8
52.8
25.4
32
71.3
29.2
3.77
19.5
61.4
29.8
33
56.6
21.9
4.15
13.0
49.3
23.3
34
59.7
29.2
4.19
15.2
57.3
28.8
35
50.2
25.5
5.00
10.0
54.8
24.0
36
79.5
26.5
3.25
26.7
68.9
29.2
37
70.5
31.2
4.13
14.9
54.9
27.4
38
65.5
24.0
3.46
21.1
57.7
27.5
39
50.5
25.0
4.13
15.8
58.0
29.2
40
69.6
37.1
5.60
12.6
71.5
41.3
41
71.3
27.3
4.12
16.5
60.1
30.2
42
60.0
37.0
4.31
16.0
62.5
31.9
43
57.2
25.0
3.69
17.0
51.0
25.3
44
51.8
26.1
4.52
11.5
51.8
23.6
45
59.6
28.5
3.81
17.5
55.9
27.7
46
56.7
30.1
4.24
15.2
58.4
29.5
47
61.6
30.3
3.74
19.7
61.2
29.6
48
58.6
24.2
4.16
14.1
52.9
26.0
49
77.1
35.6
4.12
19.4
69.5
34.3
50
69.2
31.6
3.46
22.2
61.3
28.5
51
73.3
35.8
3.98
20.5
69.9
33.7
52
80.3
38.6
3.94
21.0
70.6
33.7
53
91.1
35.2
3.16
36.4
97.6
32.5
54
73.0
35.7
4.24
17.3
65.2
33.0
55
79.1
35.3
3.50
25.2
72.4
31.5
56
83.8
26.5
2.78
34.0
73.5
26.7
57
87.3
41.4
3.47
28.5
82.3
33.2
58
75.3
40.2
5.05
15.3
73.0
40.4
59
66.8
40.5
4.95
14.7
69.5
37.7
60
66.8
27.3
3.33
24.5
64.6
28.7
61
64.0
30.1
3.50
20.9
58.2
27.8
62
73.9
31.2
3.31
25.3
66.5
29.1
63
58.3
33.7
3.44
22.8
62.7
28.8
64
69.8
27.6
3.22
24.8
61.7
27.5
65
55.4
33.3
5.43
10.6
62.8
32.3
66
79.0
32.0
2.97
30.4
70.2
27.6
67
67.2
30.5
3.85
18.5
60.3
29.7
68
58.7
27.8
3.70
19.0
57.8
28.3
69
64.1
34.0
3.84
19.8
64.2
31.1
70
72.4
29.4
3.25
25.5
65.1
28.4
71
74.3
30.2
3.23
26.4
67.3
28.7
72
53.9
25.2
3.16
22.4
51.6
24.8
73
64.9
27.8
3.57
21.0
60.7
28.8
74
51.8
28.1
4.15
14.6
54.5
27.0
75
80.7
29.1
2.94
31.0
70.9
27.5
76
63.6
35.9
4.76
12.7
60.0
30.5
77
64.7
29.9
3.48
21.0
57.8
27.6
78
56.8
31.3
4.42
13.0
54.8
26.8
79
72.3
43.8
5.60
12.5
71.2
41.0
80
65.8
36.6
4.60
15.7
67.0
35.1
81
64.3
32.0
3.66
19.6
58.6
28.4
82
67.3
30.7
4.08
19.5
69.0
33.9
83
54.8
32.3
4.53
13.1
57.2
28.5
84
64.8
35.3
3.86
19.2
62.9
30.7
85
55.6
32.7
4.65
12.4
56.9
28.1
86
59.1
32.5
3.99
16.7
57.8
28.9
87
60.3
25.6
4.10
15.4
55.9
27.9
88
57.4
30.4
3.64
19.7
58.4
28.3
89
57.4
31.2
4.28
14.5
56.8
28.5
90
59.5
29.9
3.59
20.5
59.5
28.5
91
54.5
30.0
4.91
11.1
57.1
27.3
92
57.9
31.0
4.17
15.0
56.1
28.1
93
57.6
30.8
4.40
14.1
58.1
29.3
94
68.2
39.6
4.90
14.3
67.3
36.2
95
66.8
30.8
4.33
15.4
60.9
31.0
96
69.8
30.2
3.93
17.8
59.9
29.7
97
66.3
31.8
4.25
15.7
60.2
30.5
98
70.0
31.4
3.26
25.0
63.8
28.2
99
66.8
32.9
3.46
22.4
61.9
28.7
100
66.0
30.7
4.40
16.8
67.0
34.4
101
166
31.1
2.44
67.8
166
28.8
102
158
28.0
2.46
65.0
158
28.8
103
153
30.5
2.54
61.4
151
29.4
104
142
26.5
2.46
59.1
138
28.1
105
134
30.8
2.57
56.7
137
29.2
106
131
28.0
2.51
56.8
134
28.4
107
130
29.4
2.50
55.2
128
28.1
108
128
27.3
2.59
50.5
118
28.5
109
113
28.7
2.61
49.2
115
28.5
110
109
27.6
2.67
46.0
107
28.7
111
107
28.1
2.68
44.9
104
28.6
112
101
27.5
2.77
40.2
93.3
28.6
113
90.5
27.8
2.67
43.6
99.3
28.1
114
88.5
26.7
2.74
41.4
95.7
28.5
115
84.5
26.1
2.78
40.0
93.1
28.6
116
80.0
27.8
2.80
36.7
83.2
27.9
117
77.0
26.9
2.84
35.7
81.8
28.1
118
72.0
25.7
2.88
33.0
74.8
27.6
119
67.0
26.1
3.02
29.2
68.4
27.6
120
65.0
26.5
3.14
26.9
65.6
27.9
121
62.8
25.3
3.13
27.1
65.9
27.9
122
60.5
24.7
3.22
24.8
61.7
27.5
123
55.9
26.0
3.35
22.4
58.3
27.3
124
55.0
23.9
3.14
24.8
58.7
26.5
125
53.5
25.6
3.35
22.0
57.0
26.9
126
142
28.2
2.41
63.0
148
27.9
127
138
30.3
2.53
55.1
129
28.4
128
127
28.6
2.44
59.5
138
27.9
129
124
30.0
2.58
52.0
122
28.6
130
123
26.7
2.54
54.0
126
28.4
131
117
28.9
2.59
47.3
107
27.9
132
116
26.0
2.62
49.5
116
28.7
133
106
28.6
2.53
50.5
114
27.7
134
105
29.1
2.57
49.6
113
28.1
135
102
27.8
2.59
46.0
103
27.6
136
95.0
28.1
2.71
42.0
96.1
28.3
137
92.5
26.5
2.75
38.6
87.0
27.8
138
93.0
28.2
2.68
41.1
91.6
27.6
139
83.0
27.3
2.79
38.6
89.0
28.4
140
84.0
26.7
2.74
41.0
94.4
28.4
141
79.5
26.4
2.73
37.0
80.7
27.1
142
75.0
26.4
2.83
35.0
79.0
27.7
143
69.5
25.9
2.99
30.2
70.4
27.7
144
69.0
24.4
3.05
27.5
64.0
27.1
145
62.0
26.0
3.17
26.6
65.7
28.1
146
63.0
24.4
2.97
30.4
70.2
27.6
147
59.4
25.5
3.34
22.8
59.3
27.5
148
57.5
25.4
3.14
23.8
55.4
25.7
149
55.0
24.9
3.13
25.5
60.6
26.8
150
54.5
25.3
3.29
23.1
58.6
27.1
151
51.5
26.3
3.35
21.9
56.7
26.8
152
53.2
23.6
3.35
21.7
56.0
26.6
153
53.5
25.8
3.16
24.0
56.8
26.1
154
51.5
23.8
3.45
19.1
50.8
25.1
155
50.2
25.0
3.48
18.8
50.7
25.1
156
49.6
24.7
3.46
18.8
50.1
24.8
157
49.6
25.1
3.52
18.1
49.6
24.7
158
48.8
23.5
3.54
18.3
50.9
25.2
159
48.1
25.8
3.56
18.0
50.5
25.1
160
44.5
23.0
3.31
20.2
49.7
24.5
161
45.3
22.8
3.22
20.9
48.8
24.1
162
44.2
23.2
3.35
19.7
49.5
24.5
163
45.9
22.9
3.52
17.2
46.7
23.4
164
45.0
23.4
3.18
20.8
47.0
23.5
165
43.5
21.8
3.27
19.3
45.4
23.0
166
44.0
21.0
3.26
19.6
46.0
23.2
167
44.8
20.7
3.36
18.3
45.2
22.9
168
41.2
21.0
3.37
17.1
41.6
21.3
169
42.4
21.6
3.35
18.1
44.2
22.5
170
42.2
21.3
3.51
16.7
44.7
22.5
171
42.0
20.0
3.40
17.3
43.2
22.0
172
39.0
19.5
3.39
17.4
43.2
22.0
173
40.3
19.1
3.30
18.0
42.2
21.7
174
40.0
22.3
3.38
16.8
40.9
20.9
175
37.8
19.5
3.34
16.7
39.2
20.2
176
37.2
19.1
3.48
15.1
38.5
19.2
177
37.0
17.8
3.50
14.9
38.5
19.1
178
36.8
18.9
3.50
14.8
38.2
18.9
179
35.2
18.3
3.30
16.4
36.9
19.2
180
35.3
18.0
3.42
15.0
36.3
18.2
181
34.5
18.6
3.28
16.5
36.5
19.1
182
33.5
18.1
3.31
16.0
35.9
18.6
183
32.9
17.3
3.50
13.9
35.2
16.9
184
33.2
17.2
3.72
12.0
35.4
14.6
185
32.2
16.9
3.76
11.6
35.1
13.8
186
32.2
18.1
3.39
13.7
31.1
15.0
187
30.7
16.4
3.43
13.6
32.0
15.2
188
31.6
16.5
3.44
13.7
32.7
15.6
189
29.3
16.9
3.32
14.5
31.3
15.9
190
30.8
15.4
3.52
13.2
33.4
15.4
191
41.5
22.4
3.91
12.7
42.6
19.2
192
43.4
23.2
3.98
12.9
45.0
20.7
193
42.7
21.1
3.67
15
43.8
21.5
194
44.1
23.2
4.39
11.7
49.9
22.5
195
39.2
21.4
4.12
12.5
46.9
21.4
196
43.3
23.1
4.20
12.7
49.3
23.0
197
48.3
23.2
3.38
18.1
45.2
22.9
198
46.8
25.3
4.04
14
50.0
24.2
199
50.4
25.6
3.98
13.9
48.3
23.2
200
50.0
24.2
3.84
15.6
50.4
24.9
201
52.8
26.3
3.70
17.2
51.9
25.8
202
48.5
24.0
3.90
15.5
51.6
25.5
203
52.9
25.5
3.75
16.9
52.3
26.0
204
53.0
25.5
3.64
18.5
54.5
26.8
205
51.8
23.3
3.13
22.5
50.7
24.5
206
48.5
25.4
4.12
14.9
54.8
27.3
207
53.1
24.6
3.33
19.8
49.1
24.3
208
50.5
24.6
3.88
17
56.0
27.8
209
55.2
25.2
4.05
15.9
56.5
28.2
210
48.1
24.9
3.87
17.2
56.4
28.0
211
54.6
25.3
3.96
16.6
56.7
28.3
212
57.0
26.1
3.55
20.8
59.4
28.4
213
54.5
28.0
4.06
16.1
57.4
28.7
214
55.2
24.9
3.46
22.1
60.9
28.4
215
52.8
27.9
4.06
16.1
57.4
28.7
216
56.3
26.0
3.46
22.1
60.9
28.4
217
60.5
27.6
3.65
20
59.7
28.8
218
62.1
27.9
3.84
18.5
59.9
29.5
219
61.9
26.9
3.89
17.5
57.9
28.7
220
56.2
27.1
3.81
19.5
62.4
30.3
221
60.4
30.7
4.15
15.7
58.1
29.2
222
60.5
27.6
3.89
18
59.5
29.5
223
60.9
31.9
3.63
20.2
59.8
28.8
224
58.7
27.6
3.73
20.2
62.6
30.1
225
63.6
29.1
3.87
18.2
59.7
29.5
226
57.0
27.4
3.60
21
61.6
29.2
227
62.8
31.2
3.98
17.7
60.8
30.2
228
57.2
28.0
4.00
18
62.2
30.9
229
65.5
29.8
3.89
18.5
61.2
30.1
230
61.0
30.0
3.26
25.9
66.7
28.8
231
62.9
29.0
4.11
17
61.5
30.9
232
58.9
29.8
4.31
16.1
62.8
32.0
233
64.5
28.7
4.10
18.2
65.2
32.5
234
61.4
27.7
4.21
16.5
62.0
31.4
235
58.9
31.6
4.30
17.1
65.9
33.5
236
62.0
31.8
4.19
16.6
61.9
31.3
237
61.2
29.3
3.99
18.5
63.6
31.5
238
59.2
30.8
4.46
14.9
61.8
31.7
239
65.6
32.0
4.19
17.4
64.5
32.5
240
59.5
31.0
4.01
18.3
63.4
31.4
241
62.9
31.9
4.18
17.7
65.3
32.9
242
64.3
31.2
3.89
19
62.8
30.8
243
66.3
28.3
3.88
20.5
67.5
32.4
244
67.6
32.4
4.11
17.4
62.8
31.5
245
63.9
29.1
4.21
17.8
66.3
33.4
246
67.6
32.7
4.72
14.1
63.8
33.4
247
60.9
30.3
3.94
19.7
66.4
32.3
248
67.8
32.0
4.41
15.9
64.1
33.0
249
63.2
28.5
3.70
22
67.7
31.5
250
62.2
32.4
3.83
19.9
64.3
31.1
251
64.1
34.2
3.70
22
67.7
31.5
252
63.0
32.1
4.20
17.4
64.8
32.7
253
63.5
29.5
4.11
18.9
67.7
33.6
254
65.6
33.4
4.29
16.7
64.3
32.8
255
64.7
30.5
4.19
18.2
67.2
33.7
256
67.8
35.2
4.11
18.1
65.1
32.5
257
67.2
33.0
3.87
20.7
67.9
32.5
258
68.8
32.6
4.42
16.1
65.0
33.5
259
79.4
38.5
3.96
23.7
80.0
36.4
260
77.1
37.6
3.88
23.1
76.1
34.9
261
80.0
38.7
3.83
24.7
80.1
35.5
262
82.0
37.3
3.47
28.3
81.7
33.1
263
76.7
37.1
3.77
25.6
81.5
35.3
264
77.4
39.8
3.53
27.7
81.5
33.5
265
80.3
37.6
4.20
21.5
78.2
37.6
266
83.3
39.6
3.67
25.3
77.7
33.8
267
76.1
39.7
3.81
24.9
80.2
35.4
268
86.7
37.3
3.37
30
84.0
32.7
269
75.5
39.0
4.32
20.8
78.4
38.5
270
83.9
40.2
3.80
24.6
79.0
35.0
271
75.7
38.9
3.69
27.2
84.5
35.3
272
92.0
37.2
3.58
27.5
82.4
34.1
273
82.2
37.3
3.83
25.6
83.0
36.1
274
92.2
37.0
3.29
33
91.2
33.0
275
83.5
32.5
3.82
25.5
82.4
35.9
PL ¼ 3:27 þ 13:2a – 453b (2)
This equation has a regression coefficient of 0.80. It predicts 76% of all measured PLs within an error margin of 10%. When using the complex equation, the 10% error margin covers 84% of all measured PLs. When using Equation (2), the mean of absolute errors for predicting the PL becomes 6.4% with a standard deviation of 4.4 (they are 5.6% and 4.1%, respectively for the complex equation). The plot of the measured versus the predicted PLs is illustrated in Fig. 7.
5. Conclusions and discussion
The newly developed mud press machine is introduced as an alternative tool to determine the Atterberg limits on a more rational and quantifiable basis. The empirical equations based on the experimental data on some 275 soil samples help determine the liquid limit with a great degree of accuracy. The level of accu- racy to predict the plastic limit with the new approach is slightly lower than it is for the liquid limit. The authors attribute this to the very speculative nature of the bead-rolling test itself. Nevertheless, we emphasize that the degree of accuracy to predict PL using the new tool is still remarkably good. Therefore, the proposed device and the method are capable of predicting the two consistency limits employing the very same data, eliminating the second set of test devices and/or an operator.
The new approach is superior to the conventional methods in several aspects as follows:
It eliminates a number of uncertainties involved in the con- ventional tests of LL and PL.
Because it does not requires experience, the operator- dependency is no longer a matter of concern.
The most common two Atterberg limits can be determined us- ing only one tool.
The test duration is remarkably short. All the data needed to find these two Atterberg limits are obtained in about 1 h, which is also shorter than the duration for determining Atterberg limits using the reverse extrusion test as described by Kayabali and Tufenkci (2010) and Kayabali (2012).
The device is simple and lightweight. It can be used anywhere in a laboratory.
The cost of manufacture is low as well. The most prominent components of the new tool are a loadcell and the display unit.
We propose that the newly proposed method be denoted as “Kayabali method.”