Determination of the Atterberg Limits of Eemian Gyttja on Samples with Different Composition

Equations (no.)	Range of liquid limit	Cone type	Soil type	References
Linear relationships
(1) $W_{L 60} = 0.95 W_{LC} + 9.4$	85%–200%	60°–60 g	Danish Eocene clays	Grønbech et al. 2011 [16]
(2) $\begin{matrix} W_{L 60} & = 0.86 W_{LC} + 3.75 \\ R^{2} & = 0.99, n = 63 \end{matrix}$	13%–117%	60°–60 g	Fine-grained soils	Matusiewicz et al. 2016 [28]
(3) $\begin{matrix} W_{L 60} & = 0.772 W_{LC} + 10.71 \\ r & = 0.993, n = 33 \end{matrix}$	30%–390%	60°–60 g	Fine-grained soils, kaolin–bentonite mixtures	Mendoza and Orozco 2001 [29]
(4) $\begin{matrix} W_{L 30} & = 0.832 W_{LC} + 13.28 \\ r & = 0.989, n = 9 \end{matrix}$	30%–350%	30°–80 g
(5) $W_{L (FC)} = 0.95 W_{LC} - 0.85$	<150%	30°–80 g/100 g60°–60 g	Fine-grained soils	Shimobe 2010 [36]
(6) $W_{L 30} = 1.0056 W_{LC} + 4.92$	27%–110%	30°–80 g	Turkish natural soils	Wasti 1987 [42]
(7) $W_{L 30} = 0.841 W_{LC} + 11.686$	80%–150%	30°–80 g	Soil–bentonite mixtures	Mishra et al. 2012 [30]
(8) $\begin{matrix} W_{L 30} & = 0.91 W_{LC} + 3.20 \\ R^{2} & = 0.99, n = 63 \end{matrix}$	13%–117%	30°–80 g	Fine-grained soils	Matusiewicz et al. 2016 [28]
Power relationships
(9) $W_{L 30} = 2.56 W_{LC}^{0.78}$	>100%	30°–80 g	Natural clays	Schmitz et al. 2004 [34]
(10) $\begin{matrix} W_{L 30} & = 1.86 {(W_{LC, BS cup})}^{0.84} \\ R^{2} & = 0.98, n = 216 \end{matrix}$	Up to approx. 600%	30°–80 g	Fine-grained soils	O’Kelly et al. 2018 [27]
(11) $\begin{matrix} W_{L 30} & = 1.62 {(W_{LC, BS cup})}^{0.88} \\ R^{2} & = 0.96, n = 199 \end{matrix}$	<120%
(12) $\begin{matrix} W_{L 30} & = 1.90 {(W_{LC, ASTM cup})}^{0.85} \\ R^{2} & = 0.97, n = 199 \end{matrix}$	Up to approx. 600%
(13) $\begin{matrix} W_{L 30} & = 1.45 {(W_{LC, ASTM cup})}^{0.92} \\ R^{2} & = 0.97, n = 188 \end{matrix}$	<120%

[i] Note: w_L(FC), fall cone liquid limit; w_L30, liquid limit using 30°–80 g fall cone; w_L60, liquid limit using 60°–60 g fall cone; w_LC, Casagrande liquid limit; w_{L, BS cup}, BS Casagrande cup liquid limit; w_{L, ASTM cup}, ASTM Casagrande cup liquid limit; R², determination coefficient; r, correlation coefficient; n, number of data points.

Table 2

Relationships between the Atterberg limits and the clay and organic matter contents in the literature.

Equations (no.)	Soil type	References
(14) $\begin{matrix} LL = 13.75 + 0.637 \cdot clay + 2.937 \cdot organic C \\ R^{2} = 0.86, n = 276 \end{matrix}$	Fine-grained soils with organic content below 6%	De Jong et al. 1990 [5]
(15) $\begin{matrix} PL = 10.95 + 0.239 \cdot clay + 1.156 \cdot organic C \\ R^{2} = 0.35, n = 256 \end{matrix}$
(16) $\begin{matrix} PI = 3.11 + 0.394 \cdot clay + 1.726 \cdot organic C \\ R^{2} = 0.55, n = 259 \end{matrix}$
(17) $\begin{matrix} W_{p} & = 3.45 + 13.05 I_{om}^{0.69} \\ r & = 0.98, n = 43 \end{matrix}$	Holocene gyttja I_om = 0.6%–73.1% CaCO₃ = 2.0%–88.4%	Długaszek 1991 [8]
(18) $\begin{matrix} W_{LC} & = 5.96 + 4.08 I_{om}^{1.325} \\ r & = 0.96, n = 43 \end{matrix}$

[i] Note: LL or w_LC, Casagrande liquid limit in %; PL or w_P, plastic limit in %; PI, plasticity index in %; clay, clay content in %; organic C or I_om, organic matter content in %; R², determination coefficient; r, correlation coefficient; n, number of data points.

Tested samples of Eemian gyttja according to the classification of Długaszek [7]: I_om = 0%–2% mineral soils.
Note: 1, low organic lacustrine marl; 2, high calcareous mineral gyttja; 3, low calcareous mineral gyttja; 4, high organic lacustrine marl; 5, high calcareous mineral-organic gyttja; 6, low calcareous mineral-organic gyttja; 7, high calcareous organic gyttja; 8, low calcareous organic gyttja; 1–16, test number

Table 3

Laboratory test results of the index properties of Eemian gyttja.

Test no.	Soil type	Water content w_n (%)	Plastic Limit w_p (%)	Liquid limit w_L(%)			Calcium carbonate content CaCO₃ (%)	Organic matter content I_om (%)

				Casagrande w_LC	Cone 60° w_L60	Cone 30° w_L30
1	Gyttja (3)	62.3	50.9	81.0	76.7	81.5	29.6	7.44
2		67.8	62.4	88.0	86.4	87.2	31.7	9.41
3		61.3	60.7	80.9	75.1	78.1	34.9	7.69
4		58.5	56.6	82.3	81.5	85.5	37.9	7.92
5	Gyttja (6)	74.4	68.0	104.5	101.5	105.5	31.1	12.0
6	Gyttja (5)	102.1	119.2	150.4	148.5	163.6	54.7	17.8
7		98.7	122.2	136.1	135.5	137.5	60.9	18.6
8		98.9	100.8	140.0	137.1	143.6	63.8	18.1
9		110.1	116.8	156.2	156.8	159.0	66.7	18.4
10		115.6	130.7	152.5	154.8	160.1	70.4	23.3
11		87.1	130.9	159.2	166.1	171.0	77.7	20.6
12		100.3	125.9	155.2	159.5	162.0	74.0	20.2
13		97.7	97.7	121.3	125.4	130.6	65.4	20.7
14		118.5	110.5	164.5	171.6	173.8	73.6	23.8
15	Marl (4)	90.6	114.3	139.1	131.6	140.1	81.0	18.1
16		79.9	110.1	131.0	130.8	133.4	82.1	16.2

Note:

3 low calcareous mineral gyttja;

4 high organic lacustrine marl;

5 high calcareous mineral-organic gyttja;

6 low calcareous mineral-organic gyttja.

Tested samples shown on Casagrande’s plasticity chart.
Note: 1–16, test number.

Average values of the liquid limit *w_L* depending on the test method.

Table 4

Linear and power regression models of relationships between the liquid limit w_L determined by Casagrande method and fall cone methods for Eemian gyttja.

Equations (no.)	R² (−)	n (−)	SEE	Max. RE (%)
(25) $W_{L 60} = - 10.39 + 1.08 W_{LC}$	0.989	16	3.62	±5
(25a) $or W_{L 60} = 3.07 W_{LC}^{1.08}$
(26) $W_{L 30} = - 8.93 + 1.10 W_{LC}$	0.990	16	3.58	±7
(26a) $or W_{L 30} = 1.32 W_{LC}^{1.10}$
(27) $W_{L_{60}} = 1.07 + 0.97 W_{L 30}$	0.990	16	3.41	±5

[i] Note: RE, relative error; SEE, standard error of estimation.

Regression models of relationships between the liquid limits: a) *w_L*₆₀ = f(*w_LC*), b) *w_L*₃₀ = f(*w_LC*).
Note: RE, relative error.

Comparison of relationships obtained by the authors for Eemian gyttja with relationships for cohesive soils taken from the literature: a) *w_L*₆₀ = f(*w_LC*), b) *w_L*₃₀ = f(*w_LC*).

Table 5

Single- and two-factor linear regression models of the plastic limit (w_P) and liquid limit (w_L_C) relationship versus the organic matter content (I_om) and/or calcium carbonate content (CaCO₃) relationship for Eemian gyttja.

Equations (no.)	R² (−)	SEE	Max. RE (%)
(28) $W_{P} = 22.12 + 4.70 I_{om}$	0.833	12.15	±17
(29) $W_{P} = 20.75 + 1.33 {CacO}_{3}$	0.786	13.75	±20
(30) $W_{P} = 15.79 + 2.96 I_{om} + 0.59 {CaCO}_{3}$	0.874	10.93	±16
(31) $W_{LC} = 44.25 + 5.12 I_{om}$	0.876	11.13	±20
(32) $W_{LC} = 47.80 + 1.37 {CaCO}_{3}$	0.731	16.39	±20
(33) $W_{LC} = 40.81 + 4.18 I_{om} + 0.32 {CaCO}_{3}$	0.887	11.04	±15

[i] Note: RE, relative error; SEE, standard error of estimation.

Comparison between the measured and calculated values: a) *w_P* and *w_P* from Equation (30) in Table 5, b) *w_LC* and *w_LC* from Equation (33) in Table 5 of Eemian gyttja, with zones of maximum RE for regression models.
Note: RE, relative error.

References

Authors

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Articles in this issue

DOI: https://doi.org/10.2478/sgem-2019-0041 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 168 - 178

Submitted on: Jul 10, 2019

Accepted on: Feb 3, 2020

Published on: Jun 30, 2020

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2020 Katarzyna Goławska, Zbigniew Lechowicz, Władysław Matusiewicz, Maria Jolanta Sulewska, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 42 (2020): Issue 2 (June 2020)

Determination of the Atterberg Limits of Eemian Gyttja on Samples with Different Composition

Figures & Tables

Table 1

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

Table 2

(14)

(15)

(16)

(17)

(18)

Figure 1

Table 3

Figure 2

Figure 3

Table 4

(25)

(25a)

(26)

(26a)

(27)

Figure 4

Figure 5

Table 5

(28)

(29)

(30)

(31)

(32)

(33)

Figure 6

Figure 7