Correlation between estimated clay contents and hydrometer ...

1

Correlation between estimated clay contents and hydrometer

measurements: statistical variability

F. Thaimo* and S.O. Ekolu

Department of Civil Engineering Technology, University of Johannesburg, South Africa

*Corresponding author: [email protected]

ABSTRACT

Estimated soil clay content (P0.002) obtained from consistency limits (Savage, 2007) was

evaluated by comparing its results with those of the conventional hydrometer test (P0.002h).

Altogether, 180 soil samples were tested for Atterberg limits, linear shrinkage and clay content,

to generate the data used for statistical evaluation. It is shown that a strong correlation with

realistic and valid statistical equality, exists between P0.002 and P0.002h. However, variability of

P0.002 estimations, which is up to 50%, is quite high for practical purposes. Counter findings of

the study confirm the credibility of the hydrometer method.

Keywords: Hydrometer; Clay content; Atterberg; Consistency limits; Soil classification;

Statistical analysis.

1. Introduction

Drawing from Skempton’s (1953) work on Clay Activity, Savage (2007) proposed an

equation for estimating clay content using basic data from routine Atterberg limit tests and

from Clay Activity. The work also expressed doubts on accuracy of the hydrometer test, but

provided no validation of the equation to support its veracity and/or to discount accuracy of the

hydrometer test method. Also, the authors are not aware of comprehensive researches

subsequently done to further examine or resolve these issues.

1.1 Clay content estimation from Atterberg limits

Savage (2007) analysed the results of Atterberg limits for different clays, using the data

published by Cornell University in 1951. The data included the Atterberg limits of different

clay minerals comprising Montmorillonite, Illite and Kaolinite. Savage’s (2007) findings

showed that the plasticity ratio, R = liquid limit (LL)/plastic limit (PL) varied with the type of

clay mineral. The average values of R for the various clay minerals were:- 6.0 for

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Montmorillonite, 2.25 for Illite and 1.50 for Kaolinite. Using these results and Skempton’s

(1953) “Clay Activity” data of PI/P0.002h values for the common groups of clay minerals i.e.

0.38 for Kaolinite, 0.9 for Illite and 7.2 for Montmorillonite; Savage (2007) then proposed that

the P0.002h of a given soil can be estimated using Equation (1).

P0.002 = 6.25(PI x P0.425)R-2.13 (1)

where P0.002h is the measured clay content determined using the hydrometer test, P

0.002 is the estimated percentage of clay fraction i.e. clay content, PI is plasticity

index, P0.425 is the percentage of soil material passing the 0.425 mm sieve, and R is

the plasticity ratio (LL/PL).

1.2 Study objectives

The objectives of the present paper were to evaluate the accuracy of P0.002 obtained using

Savage’s (2007) equation while simultaneously counter - evaluating the veracity of the

hydrometer test method, to allay or confirm criticisms found in some literatures. Accordingly,

the estimated P0.002 values were compared with the actual measured results of P0.002h obtained

from the hydrometer test. Statistical error analysis was conducted to evaluate correlation.

2. Experimental study

The experiment was conducted using 180 samples of natural soils collected from different

regions of Gauteng province in South Africa. The soil samples were of residual and transported

formations and were extracted from different depths, extending from surface level to about two

(2) metres below the surface. For convenience, the samples have been randomly grouped into

four (4) sets of 45 No., as given in Tables 1A to 1D.

The LL tests were done according to the Casagrande cup method given in ASTM D4318

(2017), while the PL tests were carried out as per the manual thread - rolling procedure of

ASTM D4318 (2017). The linear shrinkage (LS) test was conducted as specified in ASTM

D4318 (2017).

The hydrometer test was conducted with 50 g of soil specimen < 0.425 mm particles, using

125 mls of the dispersant comprising a mixture of sodium carbonate and sodium

hexametaphosphate, as specified in ASTM D7928 (2017).

3. Results and discussions

Tables 1A to 1D give results of the:- (i) percentage of particles < 4.75 mm, which is the

boundary between gravel and sand as per the Unified Soil Classification System, USCS

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(ASTM D2487, 2011); (ii) percentage of particles < 0.075 mm, being the boundary between

coarse grained and fine grained soils (ASTM D2487, 2011); and (iii) Atterberg limits LL, PL,

PI, and the LS. Also included in Tables 1A to 1D are the P0.002h and P0.002 values, giving the

hydrometer - measured clay contents and the corresponding estimates obtained using Savage’s

Equation (1). Plots of P0.002h versus P0.002 are given in Figure 1a-d for each of the four (4) group

sets of samples. A close agreement between the two sets of results is evident for each group of

samples, with results falling along the line of equality (also Figure 2).

3.1 Statistical analysis

Statistical error analysis was conducted employing five (5) parameters comprising the:-

global mean and global standard deviation values of P0.002h and P0.002 for all 180 soil samples,

ratio P0.002h /P0.002, root mean square of errors (RMS) and coefficient of variation errors (CV).

RMS quantifies the difference in results of any two methods that should ideally give the same

value. For a given sample, the difference between corresponding results obtained using the two

methods, is the residual. RMS is given by Equation (2) while CV is the ratio of RMS to the

mean of measured results, expressed as a percentage (Chai and Draxler, 2014; Solomon and

Ekolu, 2020).

N

N

1

2(Residual)

RMS

(2)

where, N is the total number of samples.

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Table 1A. Samples 1 to 45 – percentages of particles < 4.75, 0.425 and 0.075 mm, plasticity index (PI) and ratio (R),

hydrometer clay content (P0.002h), Savage’s estimated clay content (P0.002), linear shrinkage (LS), and Unified Soil

Classification System (USCS).

Sample

No

<4.750

mm

(%)

<0.425

mm

(%)

<0.075

mm

(%)

LL

(%)

PL

(%)

PI

(%)

LS

(%)

R P0.002h

(%)

P0.002

(%)

P0.002h/

P0.002

USCS

1 98 81 74 44 27 17 9 1.630 31 30 1.017 ML or OL

2 97 72 63 41 24 17 9 1.708 20 24 0.817 CL or OL

3 99 86 81 54 26 28 13 2.077 53 32 1.669 CH or OH

4 100 90 85 58 30 28 14 1.933 50 39 1.291 CH or OH

5 100 95 82 55 32 23 11 1.719 34 43 0.788 MH or OH

6 96 78 70 50 29 21 10 1.724 29 32 0.902 MH or OH

7 77 47 40 49 29 20 10 1.690 15 19 0.775 SC

8 83 30 22 34 18 16 7 1.889 12 8 1.550 SC

9 82 42 29 29 17 12 3 1.706 10 10 0.988 SC

10 90 26 16 21 12 9 4 1.750 9 4 2.027 SC

11 84 69 61 41 27 14 6 1.519 16 25 0.642 ML or OL

12 68 28 17 23 16 7 3 1.438 5 6 0.884 SC or SM

13 98 78 44 20 13 7 3 1.538 18 14 1.320 SC or SM

14 88 63 50 33 24 9 5 1.375 12 18 0.673 ML or OL

15 99 85 74 35 24 11 6 1.458 21 26 0.799 CL or OL

16 99 80 70 42 31 11 5 1.355 20 29 0.698 ML or OL

17 96 72 29 17 12 5 2 1.417 14 11 1.303 SC or SM

18 62 32 18 21 15 6 3 1.400 7 6 1.183 SC or SM

19 98 71 38 18 14 4 2 1.286 13 10 1.254 SC or SM

20 98 81 68 38 25 13 7 1.520 27 27 1.007 ML or OL

21 74 33 23 27 17 10 5 1.588 7 8 0.918 SC

22 59 47 39 33 24 9 4 1.375 9 13 0.669 GC

23 100 81 45 19 15 4 2 1.267 18 12 1.469 SC or SM

24 94 84 70 44 28 16 8 1.571 19 32 0.593 ML or OL

25 64 27 18 22 16 6 2 1.375 6 5 1.168 SC or SM

26 85 40 28 29 17 12 6 1.706 12 10 1.245 SC

27 83 35 24 28 19 9 4 1.474 8 9 0.936 SC

28 78 32 21 30 17 13 6 1.765 9 8 1.150 SC

29 69 56 46 28 20 8 4 1.400 13 14 0.946 GC

30 69 56 45 32 24 8 4 1.333 13 15 0.861 GC

31 96 72 53 36 29 7 4 1.241 20 20 1.012 ML or OL

32 59 26 16 27 19 8 3 1.421 7 6 1.143 SC

33 98 78 54 40 29 11 5 1.379 20 27 0.741 ML or OL

34 100 94 69 40 27 13 7 1.481 27 33 0.815 ML or OL

35 98 82 78 49 25 24 12 1.960 50 29 1.696 CL or OL

36 85 71 64 42 26 16 8 1.615 19 26 0.741 ML or OL

37 97 80 73 47 26 21 11 1.808 42 30 1.412 CL or OL

38 99 75 69 51 28 23 11 1.821 33 30 1.104 CH or OH

39 79 57 51 56 27 29 11 2.074 26 22 1.197 CH or OL

40 100 73 42 27 18 9 5 1.500 20 17 1.150 SC

41 98 63 39 27 17 10 5 1.588 14 15 0.960 SC

42 98 64 34 22 15 7 3 1.467 10 12 0.809 SC or SM

43 93 76 43 17 13 4 3 1.308 12 11 1.114 SC or SM

44 58 33 23 25 14 11 5 1.786 7 7 1.048 GC

45 100 87 44 20 12 8 3 1.667 15 15 1.019 SC

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Table 1B. Samples 46 to 90 – percentages of particles < 4.75, 0.425 and 0.075 mm, plasticity index (PI) and ratio (R),

hydrometer clay content (P0.002h), Savage’s estimated clay content (P0.002), linear shrinkage (LS), and Unified Soil

Classification System (USCS).

Sample

No

<4.750

mm

(%)

<0.425

mm

(%)

<0.075

mm

(%)

LL

(%)

PL

(%)

PI

(%)

LS

(%)

R P0.002h

(%)

P0.002

(%)

P0.002h/

P0.002

USCS

46 100 89.7 47.3 22 15 7 3.3 1.467 17 17 0.979 SC or SM

47 100 91.8 54.2 23 14 9 5.3 1.643 22 18 1.227 CL or OL

48 91 82.7 73 42 31 11 4 1.355 20 30 0.672 ML or OL

49 31 18.5 10 18 13 5 3.3 1.385 3 3 1.038 GC or GM

50 97 54.5 29.2 20 13 7 3.5 1.538 13 10 1.365 SC or SM

51 47 25.3 19 34 21 13 6.7 1.619 10 7 1.358 GC

52 100 89 74.5 37 19 18 8 1.947 35 24 1.446 CL or OL

53 100 90.1 74 43 19 24 10.7 2.263 40 24 1.686 CL or OL

54 77 53 34.9 25 17 8 4 1.471 14 12 1.201 SC

55 100 87.3 44.1 21 15 6 3.3 1.400 27 16 1.689 SC or SM

56 78 30.3 20.7 18 11 7 3.3 1.636 8 5 1.723 SC or SM

57 96 39.7 21.5 14 11 3 1.7 1.273 8 4 1.796 SM

58 94 50.9 32.8 12 9 3 1.3 1.333 13 5 2.514 SM

59 99 81.7 44.8 17 13 4 2.7 1.308 19 12 1.647 SC or SM

60 91 64.6 40.2 20 16 4 1.3 1.250 13 10 1.295 SC or SM

61 96 70.7 30 24 12 12 6.7 2.000 9 12 0.743 SC

62 74 42.3 28 27 21 6 4.3 1.286 8 9 0.861 SC or SM

63 65 31.9 20.1 28 21 7 4.3 1.333 5 8 0.661 SC or SM

64 99 95.9 93.1 38 28 10 5.3 1.357 28 31 0.895 ML or OL

65 94 83.8 68 23 20 3 2 1.150 19 12 1.629 ML or OL

66 93 80.8 69.2 34 25 9 4 1.360 16 24 0.678 ML or OL

67 100 97.4 60 21 14 7 4.7 1.500 15 18 0.835 CL or ML

68 92 58.8 49.7 34 29 5 2 1.172 9 13 0.687 SC or SM

69 76 37.6 26.7 33 25 8 4.3 1.320 7 10 0.673 SC

70 100 97.6 62.2 25 18 7 4 1.389 21 21 0.990 CL or ML

71 97 65.5 53.6 33 27 6 4.3 1.222 11 16 0.687 ML or OL

72 98 84.2 55 28 16 12 5.3 1.750 22 19 1.147 CL or OL

73 92 66.9 42.1 30 19 10 5.3 1.579 12 16 0.759 SC

74 77 44 24 23 15 8 4 1.533 10 9 1.130 SC

75 99 82 53 31 21 10 5.3 1.476 15 22 0.671 CL or OL

76 97 86.7 72.1 43 28 15 8.7 1.536 34 33 1.043 ML or OL

77 99 87.1 64.3 37 23 14 8.3 1.609 31 28 1.120 CL or OL

78 79 35.8 19.6 22 14 8 3.3 1.571 5 7 0.732 SC

79 65 37.2 25.3 37 27 10 5.5 1.370 8 12 0.673 ML or OL

80 78 33.3 20 24 15 9 4.7 1.600 5 7 0.726 SC

81 65 35.1 21.8 25 15 10 5 1.667 8 7 1.083 SC

82 83 55.7 43.8 35 26 9 4.7 1.346 13 17 0.782 SC

83 76 58.6 48.3 37 26 11 6.7 1.423 19 19 1.000 SC

84 35 21.9 14.8 31 21 10 6.7 1.476 6 6 1.005 GC

85 99 82.9 38.1 22 15 7 2.7 1.467 16 16 0.997 SC or SM

86 75 50.7 33.9 39 28 11 6.7 1.393 17 17 0.988 SC

87 100 78.2 47.7 21 15 7 4 1.400 14 17 0.838 SC or SM

88 100 99.6 98.4 43 27 16 5 1.593 38 37 1.028 ML or OL

89 100 98.3 90.4 60 27 33 11.3 2.222 39 37 1.054 CH or OH

90 94 75.4 68.1 41 27 14 6.7 1.519 24 27 0.886 ML or OL

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Table 1C. Samples 91 to 135 - percentages of particles < 4.75, 0.425 and 0.075 mm, plasticity index (PI) and ratio (R),

hydrometer clay content (P0.002h), Savage’s estimated clay content (P0.002), linear shrinkage (LS), and Unified Soil

Classification System (USCS).

Sample

No

<4.750

mm

(%)

<0.425

mm

(%)

<0.075

mm

(%)

LL

(%)

PL

(%)

PI

(%)

LS

(%)

R P0.002h

(%)

P0.002

(%)

P0.002h/

P0.002

USCS

91 67 49.7 40.5 32 24 8 3.7 1.333 10 13 0.743 GC

92 99 93.4 86.1 36 27 9 4.7 1.333 25 28 0.878 ML or OL

93 98 91.9 86 34 24 10 5.3 1.417 25 27 0.914 ML or OL

94 69 34.4 24.4 28 17 11 6 1.647 9 8 1.102 SC

95 100 96.8 77.4 35 18 17 7.3 1.944 33 25 1.323 CL or OL

96 99 93.1 68.9 27 15 12 6.7 1.800 30 20 1.503 CL or OL

97 100 96.9 69.8 29 17 12 6.7 1.706 34 23 1.459 CL or OL

98 100 99.8 73.9 36 18 18 8.7 2.000 38 26 1.481 CL or OL

99 98 77.1 57.1 42 15 27 9.7 2.800 37 15 2.549 CL or OL

100 100 98.1 88.3 53 29 24 9.3 1.828 27 41 0.663 MH or OH

101 96 87.7 74 39 24 15 6 1.625 32 29 1.095 CL or OL

102 100 77.4 38.6 21 14 7 3.3 1.500 14 14 0.981 SC or SM

103 100 74.7 35 18 14 4 1.7 1.286 14 11 1.280 SC or SM

104 99 91.1 80 41 25 16 7.3 1.640 33 32 1.039 CL or OL

105 97 78 65.5 38 24 14 7.3 1.583 25 26 0.975 CL or OL

106 32 19 13.7 30 20 10 4.7 1.500 4 5 0.799 GC

107 100 94.8 87.2 70 22 48 15.3 3.182 54 24 2.234 CH or OH

108 93 79.9 67.1 52 24 28 8 2.167 49 27 1.819 CH or OH

109 57 23.7 16.6 31 19 12 4.7 1.632 4 6 0.638 GC

110 88 47.8 33 24 17 7 4.7 1.412 11 10 1.096 SC or SM

111 89 70.4 46.5 22 17 5 2.3 1.294 14 13 1.102 SC or SM

112 98 62.2 51.6 52 27 31 9 1.926 26 30 0.871 CH or OH

113 90 70.1 54.2 41 20 21 8.3 2.050 19 20 0.953 CL or OL

114 100 99 41.8 25 15 10 4.6 1.667 24 21 1.151 SC

115 95 70.5 47.2 26 14 12 4 1.857 17 14 1.202 SC

116 51 32.1 23.8 27 16 11 6.8 1.688 9 7 1.243 GC

117 97 76.1 67.2 43 30 13 4.3 1.433 19 29 0.662 ML or OL

118 93 90.1 84.1 42 27 15 7.3 1.556 25 33 0.759 ML or OL

119 98 80.4 47.4 24 15 9 3.3 1.600 14 17 0.842 SC

120 69 52.1 40.1 27 18 9 3.7 1.500 11 12 0.890 GC

121 100 85.6 36.4 18 12 6 3.3 1.500 17 14 1.256 SC or SM

122 100 95 82.2 35 23 12 6.7 1.522 26 29 0.892 CL or OL

123 88 72 55.8 47 20 27 8.7 2.350 43 20 2.184 CL or OL

124 100 81.2 40.1 20 14 6 3 1.429 16 14 1.123 SC or SM

125 99 94.4 89.9 48 29 19 8 1.655 26 38 0.678 ML or OL

126 87 72.8 31.3 15 12 3 1 1.250 15 8 1.768 SM

127 100 78.4 33.2 16 12 4 2 1.333 16 11 1.507 SC or SM

128 98 76.5 48.3 33 25 8 4 1.320 15 21 0.708 SC

129 82 52.8 33.5 21 15 6 2.3 1.400 9 10 0.931 SC or SM

130 94 69.2 47.6 20 14 6 4 1.429 14 12 1.153 SC or SM

131 97 72.5 45.4 26 20 6 3 1.300 15 16 0.965 SC or SM

132 96 83.5 75.6 43 25 18 9.3 1.720 26 30 0.879 CL or OL

133 99 93.4 60.1 21 15 6 2.7 1.400 22 17 1.286 CL or ML

134 100 94.3 67.1 24 17 7 2.3 1.412 20 20 1.010 CL or ML

135 100 98.4 43.3 17 15 2 1 1.133 15 9 1.592 SM

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Table 1D. Samples 136 to 180 – percentages of particles < 4.75, 0.425 and 0.075 mm, plasticity index (PI) and ratio (R),

hydrometer clay content (P0.002h), Savage’s estimated clay content (P0.002), linear shrinkage (LS), and Unified Soil

Classification System (USCS).

Sample

No

<4.750

mm

(%)

<0.425

mm

(%)

<0.075

mm

(%)

LL

(%)

PL

(%)

PI

(%)

LS

(%)

R P0.002h

(%)

P0.002

(%)

P0.002h/

P0.002

USCS

136 100 98.9 73.2 28 16 12 5.7 1.750 31 23 1.376 CL or OL

137 99 76.2 48 19 17 2 0.7 1.118 13 8 1.730 SM

138 68 57.1 42.3 30 20 10 4 1.500 13 15 0.864 GC

139 97 89.1 74.8 31 17 14 7.7 1.824 34 22 1.568 CL or OL

140 100 96.3 69.3 24 15 9 4 1.600 26 20 1.306 CL or OL

141 100 98.8 69 22 17 5 1.3 1.294 21 18 1.178 CL or ML

142 100 98.8 61 20 17 3 1.3 1.176 15 13 1.145 ML or OL

143 22 15.9 10 22 15 7 2.7 1.467 3 3 0.975 GC or GM

144 98 89.1 54 21 16 5 1.3 1.313 19 16 1.218 CL or ML

145 80 71.3 55.6 26 20 6 1.3 1.300 15 15 0.981 CL or ML

146 73 62.8 49 32 23 9 3.3 1.391 17 17 0.972 GC

147 46 31.9 21.8 26 18 8 4 1.444 10 7 1.372 GC

148 74 51.1 24.5 18 15 3 1.2 1.200 10 6 1.539 SM

149 100 79.7 41.4 15 12 3 1.3 1.250 18 9 1.937 SM

150 68 36.6 29.3 46 28 18 6.3 1.643 11 14 0.769 SC

151 99 84.3 72.6 43 24 19 9.3 1.792 23 29 0.796 CL or OL

152 97 85.6 72.1 39 17 22 8.7 2.294 35 20 1.743 CL or OL

153 79 51.9 43.6 40 22 18 8.7 1.818 21 16 1.285 SC

154 99 85.3 75.8 46 23 23 10 2.000 28 28 1.000 CL or OL

155 100 96 90.2 49 25 24 12 1.960 34 34 0.990 CL or OL

156 56 27.9 23.7 38 23 15 6.7 1.652 6 9 0.668 GC

157 93 73.5 65.2 51 23 28 10.7 2.217 28 24 1.187 CH or OH

158 99 77.9 70.4 61 27 34 12 2.259 37 29 1.268 CH or OH

159 96 81.2 47.2 21 13 8 4 1.615 12 15 0.821 SC

160 75 47.1 30.5 18 10 8 4 1.800 9 7 1.337 SC

161 99 84.1 54 23 13 10 5.3 1.769 14 16 0.898 CL or OL

162 93 73.1 46.7 24 14 10 5.3 1.714 10 14 0.690 SC

163 71 32.5 25.6 31 19 12 6.7 1.632 6 9 0.698 SC

164 100 91.2 40.8 19 12 7 2.7 1.583 26 15 1.734 SC or SM

165 35 19.3 12 22 14 8 4.7 1.571 2 4 0.543 GC

166 99 82.9 63.2 27 17 10 5.3 1.588 19 19 0.982 CL or OL

167 100 88.4 58.9 26 16 10 5.3 1.625 24 20 1.222 CL or OL

168 30 24.8 19 28 17 11 5.3 1.647 5 6 0.849 GC

169 52 38.4 26.7 26 15 11 5.3 1.733 9 8 1.100 GC

170 100 89.3 60.5 27 16 11 5.3 1.688 26 20 1.291 CL or OL

171 93 51.5 35 27 11 16 6 2.455 17 8 2.235 SC

172 98 49.1 32.4 20 13 7 3.3 1.538 12 9 1.398 SC or SM

173 93 57.6 38 38 29 9 5.7 1.310 14 18 0.768 SC

174 40 24.2 14 22 16 6 3 1.375 4 5 0.869 GC or GM

175 100 78 35 18 14 4 2 1.286 11 11 0.963 SC or SM

176 100 74.7 35.1 21 15 6 3.3 1.400 12 14 0.877 SC or SM

177 94 75.2 45.1 36 27 9 5.3 1.333 15 23 0.654 SC

178 76 60.7 40 35 29 6 3.3 1.207 12 15 0.787 SC or SM

179 71 40.4 30.3 36 26 10 6 1.385 14 13 1.109 SC

180 79 60.9 43.5 23 17 6 2.7 1.353 12 12 1.000 SC or SM

8

Figure 1. Hydrometer - measured clay content (P0.002h) versus estimated clay content (P0.002) for the

various group sets of samples.

Figure 2 compares the values of P0.002h and P0.002 for all the 180 soil samples. It can be seen

that data points lie along the line of equality, which indicates statistical equality between the

two sets of results. However, the equality appears to be limited to clay contents of 40%, as

indicated with the dotted line shown in Figure 2a. Also, variations between P0.002h and P0.002

are shown in Figure 2a, using the plotted upper and lower envelopes. Clearly for any given clay

content, the estimated P0.002 values vary from as low as 0.4 times to as high as 1.6 times the

hydrometer P0.002h value, i.e. variability of 50%.

Both of the foregoing limitations, seem to improve by considering the log - log model as

seen in Figure 2b plot of log P0.002h versus log P0.002, giving a consistent correlation for all clay

contents including those above 40%. Also, the variability has improved.

Table 2 gives the associated statistical indicators. Clearly, the values of global mean

/standard deviation for the two sets of results are similar, giving 18.5 /10.7 for P0.002h and 17.3

/10.0 for P0.002, respectively. The mean value obtained for P0.002h /P0.002 is 1.11 (Table 2, Figure

3), which is very close to 1.0, thereby depicting near equality between the two sets of results.

9

The values of P0.002h /P0.002 for the individual soil samples, generally fall between 0.70 and 1.30

with a standard deviation of 0.377 (Tables 1A to 1D, Figure 3).

The close agreement between the two sets of results, is also indicated by the RMS and CV

values, which were found to be 6.67 and 36.0% respectively (Table 2). The CV value of 36%

falls within the accepted range of 20 to 50% for internationally recognised standard code – type

models (Bazant and Baweja, 1995; Lifecon, 2003; Bazant and Panula, 1978; Ekolu, 2018).

Accordingly, the accuracy of Savage’s equation may be considered comparable to those of

established standard models.

Differences between P0.002h and P0.002 are expressed in the residuals plot, also giving normal

distribution, as seen in Figure 4a,b. The plotted chart in Figure 4a shows fanning - out

heteroscedasticity with increase in clay content. This natural tendency is also commonly

observed among properties of other materials such as concrete etc. (Bazant and Panula, 1978;

Ekolu, 2018; Naghizadeh and Ekolu, 2019).

The foregone statistical analysis was also employed to cross – check concerns or criticisms

on the hydrometer test as found in some literatures (Jacobsz and Day, 2008; Stott and Theron,

2016). As mentioned earlier, Savage (2007) doubted the hydrometer method, highlighting its

several underlying assumptions to be potential sources of errors.

On the contrary, however, findings of the present study appear to dispel doubts on the

hydrometer method. If for arguments sake, the test method is erroneous, then correlation

between P0.002h and P0.002 cannot depict statistical equality. As discussed in the foregone

statistical analysis, the results of P0.002h and P0.002 are similar, which simultaneously affirms

veracity of the hydrometer test method. The only other possibility that both sets of results may

be wrong yet in close agreement, is remote and unlikely to be true.

10

Table 2. Statistical indicators comparing the clay content estimates from Savage’s equation with the

hydrometer test results.

Parameter Hydrometer method:

clay content, P0.002h (%)

Savage’s equation: clay

content, P0.002 (%)

Global mean for all 180 samples (%) 18.5 17.3

Global standard deviation for all 180

samples 10.7 10.0

P0.002h /P0.002 1.11

RMS 6.67

CV (%) 36.0

Figure 2. Hydrometer - measured clay content (P0.002h) versus estimated clay content (P0.002), for all 180

soil samples, showing plots done at (a) normal scale, (b) log-log scale.

11

Figure 3. Histogram of P0.002h /P0.002 showing normal distribution.

Figure 4. Residuals between estimated clay content (P0.002), and hydrometer test results (P0.002h) (a) error

values, (b) distribution.

12

3.2 Limitations and practical implications

Savage’s Equation (1) is based on the three main clay minerals comprising Montmorillonite,

Illite, and Kaolinite. Its applicability for use with other clay or mineral types such as the

Chlorite group etc., is unkown. For example, Atterberg limits are reportedly not appropriate

for peat soils, which would disqualify use of this equation (O’Kelly, 2015).

Statistical equality of the estimated P0.002 seems to be limited to clay contents not exceeding

40%. Also, the estimated P0.002 may vary widely from 0.4 to 1.6 times the true value, a

variability of up to 50% which is typically quite high for practical engineering purposes.

4. Conclusions

In the foregone study, estimated clay content values P0.002 obtained using Savage’s (2007)

equation, were compared against the hydrometer test results P0.002h of 180 different soil

samples. It was found that the results of P0.002h and P0.002 were strongly correlated. However,

the variability of up to 50% for P0.002 is quite high for practical purposes as it gives estimates

that may vary widely by 0.4 to 1.6 times the true value. Nonetheless, findings of the present

study affirm the veracity of the hydrometer test method, contrary to criticisms in some

literatures.

References

ASTM D4318 (2017), Standard test methods for Liquid Limit, Plastic Limit, and Plasticity

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