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

Katarzyna Goławska; Zbigniew Lechowicz; Władysław Matusiewicz; Maria Jolanta Sulewska

Open Access

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

Katarzyna Goławska

Zbigniew Lechowicz

Władysław Matusiewicz

and

Maria Jolanta Sulewska

| Jun 30, 2020

Studia Geotechnica et Mechanica

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

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Cite

Published Online: Jun 30, 2020

Page range: 168 - 178

Received: Jul 10, 2019

Accepted: Feb 03, 2020

DOI: https://doi.org/10.2478/sgem-2019-0041

Keywords
plastic limit, liquid limit, Eemian gyttja, Casagrande cup, cone penetrometer, statistical analysis

© 2020 Katarzyna Goławska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Tested samples of Eemian gyttja according to the classification of Długaszek [7]: Iom = 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

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

Average values of the liquid limit wL depending on the test method.

Regression models of relationships between the liquid limits: a) wL60 = f(wLC), b) wL30 = f(wLC).Note: RE, relative error.

Comparison of relationships obtained by the authors for Eemian gyttja with relationships for cohesive soils taken from the literature: a) wL60 = f(wLC), b) wL30 = f(wLC).

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

Comparison of relationships obtained by the authors for Eemian gyttja with the relationships for Holocene gyttja obtained by Długaszek: a) wP = f(Iom), b) wLC = f(Iom).

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

Equations (no.)	Soil type	References
(14) $\begin{matrix} LL = 13.75 + 0.637 \cdot clay + 2.937 \cdot organic C \\ R^{2} = 0.86, n = 276 \end{matrix}$ \matrix{ {LL = 13.75 + 0.637 \cdot {\rm{clay }} + {\rm{ }}2.937 \cdot {\rm{organic\, C}}} \hfill \cr {R^2 = 0.86,\,{\rm{n}} = 276} \hfill \cr }	Fine-grained soils with organic content below 6%	De Jong et al. 1990 [5]
(15) $\begin{matrix} PL = 10.95 + 0.239 \cdot clay + 1.156 \cdot organic C \\ R^{2} = 0.35, n = 256 \end{matrix}$ \matrix{ {PL = 10.95 + 0.239 \cdot {\rm{clay}} + 1.156 \cdot {\rm{organic\, C}}} \hfill \cr {R^2 = 0.35,\,{\rm{n}} = 256} \hfill \cr }
(16) $\begin{matrix} PI = 3.11 + 0.394 \cdot clay + 1.726 \cdot organic C \\ R^{2} = 0.55, n = 259 \end{matrix}$ \matrix{ {PI = 3.11 + 0.394 \cdot {\rm{clay + 1}}{\rm{.726}} \cdot {\rm{organic\, C}}} \hfill \cr {R^2 = 0.55,\,{\rm{n}} = 259} \hfill \cr }
(17) $\begin{matrix} W_{p} & = 3.45 + 13.05 I_{om}^{0.69} \\ r & = 0.98, n = 43 \end{matrix}$ \matrix{ {W_p } \hfill & { = 3.45 + 13.05\,I_{{\rm{om}}}^{0.69} } \hfill \cr \,\,\,\,\, r \hfill & { = 0.98,{\rm{n}} = 43} \hfill \cr }	Holocene gyttja I_om = 0.6%–73.1% CaCO₃ = 2.0%–88.4%	Długaszek 1991 [8]
(18) $\begin{matrix} W_{LC} & = 5.96 + 4.08 I_{om}^{1.325} \\ r & = 0.96, n = 43 \end{matrix}$ \matrix{ {W_{LC} } \hfill & { = 5.96 + 4.08\,I_{{\rm{om}}}^{1.325} } \hfill \cr \,\,\,\,\,\,\,\, r \hfill & { = 0.96,\,{\rm{n}} = 43} \hfill \cr }

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

Equations (no.)	R² (−)	SEE	Max. RE (%)
(28) $W_{P} = 22.12 + 4.70 I_{om}$ W_P = 22.12 + 4.70\,I_{{\rm{om}}}	0.833	12.15	±17
(29) $W_{P} = 20.75 + 1.33 {CacO}_{3}$ W_P = 20.75 + 1.33\,{\rm{CacO}}_3	0.786	13.75	±20
(30) $W_{P} = 15.79 + 2.96 I_{om} + 0.59 {CaCO}_{3}$ {\bf{W}}_{\rm{P}} {\bf{ = 15}}{\bf{.79 + 2}}{\bf{.96 \, I}}_{{\rm{om}}} {\bf{ + 0}}{\bf{.59}}\,{\bf{CaCO}}_3	0.874	10.93	±16
(31) $W_{LC} = 44.25 + 5.12 I_{om}$ W_{LC} = 44.25 + 5.12\,I_{om}	0.876	11.13	±20
(32) $W_{LC} = 47.80 + 1.37 {CaCO}_{3}$ W_{LC} = 47.80 + 1.37\,{\rm{CaCO}}_{\rm{3}}	0.731	16.39	±20
(33) $W_{LC} = 40.81 + 4.18 I_{om} + 0.32 {CaCO}_{3}$ {\bf{W}}_{{\rm{LC}}} {\bf{ = 40}}{\bf{.81 + 4}}{\bf{.18 \, I}}_{{\rm{om}}} {\bf{ + 0}}{\bf{.32}}\,\,{\bf{CaCO}}_3	0.887	11.04	±15

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

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

Equations (no.)	R² (−)	n (−)	SEE	Max. RE (%)
(25) $W_{L 60} = - 10.39 + 1.08 W_{LC}$ W_{L60} = - 10.39 + 1.08\,W_{LC}	0.989	16	3.62	±5
(25a) $or W_{L 60} = 3.07 W_{LC}^{1.08}$ {\rm{or}}\,W_{L60} = 3.07\,W_{LC}^{1.08}
(26) $W_{L 30} = - 8.93 + 1.10 W_{LC}$ W_{L30} = - 8.93 + 1.10\,W_{LC}	0.990	16	3.58	±7
(26a) $or W_{L 30} = 1.32 W_{LC}^{1.10}$ {\rm{or}}\,W_{L30} = 1.32\,W_{LC}^{1.10}
(27) $W_{L_{60}} = 1.07 + 0.97 W_{L 30}$ W_{L_{60} } = 1.07 + 0.97\,W_{L30}	0.990	16	3.41	±5

Relationships between the fall cone liquid limit and the Casagrande liquid limit for cohesive soils in the literature.

Equations (no.)	Range of liquid limit	Cone type	Soil type	References
Linear relationships
(1) $W_{L 60} = 0.95 W_{LC} + 9.4$ W_{L60} = 0.95\,\,W_{LC} + 9.4	85%–200%	60°–60 g	Danish Eocene clays	Grønbech et al. 2011 [16]
(2) $\begin{matrix} W_{L 60} & = 0.86 W_{LC} + 3.75 \\ R^{2} & = 0.99, n = 63 \end{matrix}$ \matrix{ {W_{L60} } \hfill & { = 0.86\,\,W_{LC} + 3.75} \hfill \cr \,\,\,\,\, \,{R^2 } \hfill & { = 0.99,\,{\rm{n}} = 63} \hfill \cr }	13%–117%	60°–60 g	Fine-grained soils	Matusiewicz et al. 2016 [28]
(3) $\begin{matrix} W_{L 60} & = 0.772 W_{LC} + 10.71 \\ r & = 0.993, n = 33 \end{matrix}$ \matrix{ {W_{L60} } \hfill & { = 0.772\,\,W_{LC} + 10.71} \hfill \cr \,\, \,\,\,\,\,\, \,r \hfill & { = 0.993,\,{\rm{n}} = 33} \hfill \cr }	30%–390%	60°–60 g	Fine-grained soils, kaolin–bentonite mixtures	Mendoza and Orozco 2001 [29]
(4) $\begin{matrix} W_{L 30} & = 0.832 W_{LC} + 13.28 \\ r & = 0.989, n = 9 \end{matrix}$ \matrix{ {W_{L30} } \hfill & { = 0.832\,\,W_{LC} + 13.28} \hfill \cr \,\,\,\,\,\,\,\, \, r \hfill & { = 0.989,\,{\rm{n}} = 9} \hfill \cr }	30%–350%	30°–80 g
(5) $W_{L (FC)} = 0.95 W_{LC} - 0.85$ W_{L(FC)} = 0.95\,\,W_{LC} - 0.85	<150%	30°–80 g/100 g60°–60 g	Fine-grained soils	Shimobe 2010 [36]
(6) $W_{L 30} = 1.0056 W_{LC} + 4.92$ W_{L30} = 1.0056\,\,W_{LC} + 4.92	27%–110%	30°–80 g	Turkish natural soils	Wasti 1987 [42]
(7) $W_{L 30} = 0.841 W_{LC} + 11.686$ W_{L30} = 0.841\,\,W_{LC} + 11.686	80%–150%	30°–80 g	Soil–bentonite mixtures	Mishra et al. 2012 [30]
(8) $\begin{matrix} W_{L 30} & = 0.91 W_{LC} + 3.20 \\ R^{2} & = 0.99, n = 63 \end{matrix}$ \matrix{ {W_{L30} } \hfill & { = 0.91\,\,W_{LC} + 3.20} \hfill \cr \,\,\,\,\, {R^2 } \hfill & { = 0.99,\,{\rm{n}} = 63} \hfill \cr }	13%–117%	30°–80 g	Fine-grained soils	Matusiewicz et al. 2016 [28]
Power relationships
(9) $W_{L 30} = 2.56 W_{LC}^{0.78}$ W_{L30} = 2.56\,\,W_{LC}^{0.78}	>100%	30°–80 g	Natural clays	Schmitz et al. 2004 [34]
(10) $\begin{matrix} W_{L 30} & = 1.86 {(W_{LC, BS cup})}^{0.84} \\ R^{2} & = 0.98, n = 216 \end{matrix}$ \matrix{ {W_{L30} } \hfill & { = 1.86\,\left( {W_{LC,BS\,{\rm{cup}}} } \right)^{0.84} } \hfill \cr \,\,\,\,\,\, {R^2 } \hfill & { = 0.98,\,\,{\rm {n}} = 216} \hfill \cr }	Up to approx. 600%	30°–80 g	Fine-grained soils	O’Kelly et al. 2018 [27]
(11) $\begin{matrix} W_{L 30} & = 1.62 {(W_{LC, BS cup})}^{0.88} \\ R^{2} & = 0.96, n = 199 \end{matrix}$ \matrix{ {W_{L30} } \hfill & { = 1.62\left( {W_{LC,BS\,{\rm{cup}}} } \right)^{0.88} } \hfill \cr \,\,\,\,\, {R^2 } \hfill & { = 0.96,\,{\rm{n}} = 199} \hfill \cr }	<120%
(12) $\begin{matrix} W_{L 30} & = 1.90 {(W_{LC, ASTM cup})}^{0.85} \\ R^{2} & = 0.97, n = 199 \end{matrix}$ \matrix{ {W_{L30} } \hfill & { = 1.90\left( {W_{LC,ASTM\,{\rm{cup}}} } \right)^{0.85} } \hfill \cr \,\,\,\,\, {R^2 } \hfill & { = 0.97,\,{\rm{n}} = 199} \hfill \cr }	Up to approx. 600%
(13) $\begin{matrix} W_{L 30} & = 1.45 {(W_{LC, ASTM cup})}^{0.92} \\ R^{2} & = 0.97, n = 188 \end{matrix}$ \matrix{ {W_{L30} } \hfill & { = 1.45\,\,\left ( {W_{LC,ASTM\,{\rm{cup}}} } \right)^{0.92} } \hfill \cr \,\,\,\,\, {R^2 } \hfill & { = 0.97,\,{\rm{n}} = 188} \hfill \cr }	<120%

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

Article Category: Original Study

Published Online: Jun 30, 2020

Page range: 168 - 178

Received: Jul 10, 2019

Accepted: Feb 03, 2020

DOI: https://doi.org/10.2478/sgem-2019-0041

Keywords
plastic limit, liquid limit, Eemian gyttja, Casagrande cup, cone penetrometer, statistical analysis

© 2020 Katarzyna Goławska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

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

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

Laboratory test results of the index properties of Eemian gyttja.

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

Relationships between the fall cone liquid limit and the Casagrande liquid limit for cohesive soils in the literature.

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

Article Category: Original Study

Published Online: Jun 30, 2020

Page range: 168 - 178

Received: Jul 10, 2019

Accepted: Feb 03, 2020

DOI: https://doi.org/10.2478/sgem-2019-0041

Keywordsplastic limit, liquid limit, Eemian gyttja, Casagrande cup, cone penetrometer, statistical analysis

© 2020 Katarzyna Goławska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

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

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

Laboratory test results of the index properties of Eemian gyttja.

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

Relationships between the fall cone liquid limit and the Casagrande liquid limit for cohesive soils in the literature.

Keywords
plastic limit, liquid limit, Eemian gyttja, Casagrande cup, cone penetrometer, statistical analysis