Effect of Specimens’ Height to Diameter Ratio on Unconfined Compressive Strength of Cohesive Soil

Gebresamuel, Haile Tsegay; Tsige Melese, Damtew; Boru, Yada Tesfaye; Legese, Alemu Mosisa

doi:10.2478/sgem-2023-0001

Figures & Tables

Graph of standard Proctor compaction curves.

Peak value of unconfined compressive strength for specimens with diameter of 38, 50, and 100 mm with their respective H/D ratio.

Percentage of UCS difference from the mean value for 38, 50, and 100 mm specimen diameters.

Stress–strain curves for 38 mm, 50 mm, and 100 mm specimen diameters of Ajip test pit from top to bottom.

Stress–strain curves for 38 mm, 50 mm, and 100 mm specimen diameters of Aweytu test pit from top to bottom.

Stress–strain curves for 38 mm, 50 mm, and 100 mm specimen diameters of JIT campus test pit from top to bottom.

Stress–strain curves for 38 mm, 50 mm, and 100 mm specimen diameters of Mariam Church test pit from top to bottom.

Stress–strain curves for 38 mm, 50 mm, and 100 mm specimen diameters of Saris Sefer test pit from top to bottom.

Failure pattern of 38 mm specimen diameter: (a) Ajip, (b) Aweytu, (c) JIT campus, (d) Saris Sefer, and (e) Mariam Church.

Failure pattern of 50 mm specimen diameter: (a) Ajip, (b) Aweytu, (c) JIT campus, (d) Saris Sefer, and (e) Mariam Church.

Failure pattern of 100 mm specimen diameter: (a) Saris Sefer and (b) Mariam Church.

Failure pattern of 100 mm specimen diameter: (a) Ajip, (b) Aweytu, (c) JIT campus.

The scatter plot of UCS versus H/D ratio for 38, 50, and 100 mm specimen diameter from left to right.

Plot of UCS/UCS2.00 versus height to diameter ratio for a specimen diameter of 38 mm.

The plot of UCS/UCS2.00 versus height to diameter ratio of 50 mm specimen diameter.

The plot of UCS/UCS2.00 versus height to diameter ratio of 100 mm specimen diameter.

Model summary of UCS/(UCS at 2 H/D ratios)-50 mm diameter and H/D ratio_

Model summary^b

Model	R	R²	Adjusted R²	Std error of the estimate
2	0.969^a	0.938	0.937	0.0540444

Descriptive statistics of the peak UCS value for specimens of diameter 50 mm_

	Number of observations	Minimum (kPa)	Maximum (kPa)	Mean (kPa)	Std deviation	Skewness	Skewness std error	Kurtosis	Kurtosis std error
Mariam Church	9	196.73	321.97	254.91	41.74	0.132	0.717	−0.909	1.400
Ajip	9	245.42	503.90	358.01	79.63	0.529	0.717	0.005	1.400
Aweytu	9	203.80	396.40	285.28	62.33	0.627	0.717	−0.180	1.400
Saris Sefer	9	174.75	391.34	272.07	71.92	0.313	0.717	−0.757	1.400
JIT campus	9	292.35	546.82	401.37	85.46	0.525	0.717	−0.755	1.400

Descriptive statistics of the peak UCS value for specimens of diameter 38 mm_

	Number of observations	Minimum (kPa)	Maximum (kPa)	Mean (kPa)	Std deviation	Skewness	Skewness std error	Kurtosis	Kurtosis std error
Mariam Church	9	200.54	348.63	271.96	42.55	0.177	0.717	0.649	1.400
Ajip	9	299.33	525.21	395.97	71.13	0.527	0.717	−0.046	1.400
Aweytu	9	238.07	474.49	332.04	75.12	0.776	0.717	0.114	1.400
Saris Sefer	9	206.53	428.74	307.54	68.45	0.308	0.717	−0.111	1.400
JIT campus	9	397.37	728.32	528.64	108.76	0.682	0.717	−0.293	1.400

Shapiro–Wilk normality test_

	38 mm specimen diameter			50 mm specimen diameter			100 mm specimen diameter

	Statistic	Degrees of freedom	Sig.	Statistic	Degrees of freedom	Sig.	Statistic	Degrees of freedom	Sig.
Mariam Church	0.989	9	0.995	0.974	9	0.926	0.968	9	0.879
Ajip	0.974	9	0.925	0.977	9	0.946	0.936	9	0.538
Aweytu	0.952	9	0.709	0.956	9	0.759	0.959	9	0.784
Saris Sefer	0.988	9	0.994	0.974	9	0.925	0.935	9	0.532
JIT campus	0.953	9	0.725	0.958	9	0.776	0.981	9	0.969

Significance level (Sig_) and Pearson correlation coefficient (R) of UCS value for 100 mm specimen diameter_

		Height to diameter ratio	UCS of Mariam Church test pit	UCS of Ajip test pit	UCS of Aweytu test pit	UCS of Saris Sefer	UCS of JIT campus test pit
Height to diameter ratio (H/D)	R	1	−0.979	−0.988	−0.992	−0.987	−0.990
	Sig.		0.000	0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Mariam Church test pit	R	−0.979	1	0.965	0.965	0.958	0.979
	Sig.	0.000		0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Ajip test pit	R	−0.988	0.965	1	0.989	0.960	0.983
	Sig.	0.000	0.000		0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Aweytu test pit	R	−0.992	0.965	0.989	1	0.972	0.993
	Sig.	0.000	0.000	0.000		0.000	0.000
	n	9	9	9	9	9	9
UCS of Saris Sefer test pit	R	−0.987	0.958	0.960	0.972	1	0.974
	Sig.	0.000	0.000	0.000	0.000		0.000
	n	9	9	9	9	9	9
UCS of JIT campus test pit	R	−0.990	0.979	0.983	0.993	0.974	1
	Sig.	0.000	0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9

Regression equations of UCS(measured)/UCS2_00 ratio for different specimen diameters versus H/D ratio_

Specimens’ diameter	Regression equations	R²	Correlation state	Equation number
38 mm	UCS_2.00=(UCS(measured))/(1.596-0.288(H/D))	0.928	Strong	3
50 mm	UCS_2.00=(UCS(measured))/(1.658-0.318(H/D))	0.938	Strong	4
100 mm	UCS_2.00=(UCS(measured))/(1.671-0.328(H/D))	0.941	Strong	5

Descriptive statistics of the peak UCS value for specimens of diameter 100 mm_

	Number of observations	Minimum (kPa)	Maximum (kPa)	Mean (kPa)	Std deviation	Skewness	Skewness std error	Kurtosis	Kurtosis std error
Mariam Church	9	155.66	313.46	222.71	50.06	0.434	0.717	−0.176	1.400
Ajip	9	209.21	372.44	281.48	58.61	0.338	0.717	−1.415	1.400
Aweytu	9	181.44	321.42	251.30	48.41	0.130	0.717	−1.134	1.400
Saris Sefer	9	126.06	281.43	210.98	56.46	−0.386	0.717	−1.181	1.400
JIT campus	9	225.62	465.21	340.70	77.48	0.142	0.717	−0.629	1.400

Regression model accuracy for the developed equations_

Specimens’ diameter of regression equations	MAE	MSE	RMSE	MAPE
38 mm	13.44	289.05	16.70	3.84%
50 mm	12.53	215.77	14.64	4.15%
100 mm	11.21	232.69	14.86	4.42%

Model summary of UCS/(UCS at 2 H/D ratios)-100 mm diameter and H/D ratio_

Model summary^b

Model	R	R²	Adjusted R²	Std error of the estimate
3	0.970^a	0.941	0.940	0.0540500

Specimens’ height for each diameter, with respect of their H/D ratio at stain rate of 1%/min_

H/D ratio	Specimen's diameter

	38 mm		50 mm		100 mm

	Height (mm)	Strain mm/min	Height (mm)	Strain mm/min	Height (mm)	Strain, mm/min
3.0	114	1.14	150	1.50	300	3
2.75	104.5	1.05	137.5	1.38	2750	2.75
2.5	95.0	0.95	125	1.25	250	2.50
2.25	85.5	0.86	112.5	1.13	225	2.25
2.0	76.0	0.76	100	1.00	200	2.00
1.75	66.5	0.67	87.5	0.88	175	1.75
1.5	57.0	0.57	75.0	0.75	150	1.50
1.25	47.5	0.48	62.5	0.63	125	1.25
1.00	38.0	0.38	50.0	0.50	100	1.00

Model summary of UCS/(UCS at 2 H/D ratio)-38 mm diameter and H/D ratio_

Model summary^b

Model	R	R²	Adjusted R²	Std error of the estimate
1	0.963^a	0.928	0.926	0.053191

Summary of index properties, classifications, and compaction parameters of the soils tested_

Parameters	Pit sites

	Ajib	Aweytu	Saris Sefer	JIT campus	Mariam Church
Liquid limit, %	79	49	72	86	75
Plastic limit, %	32	22	36	28	49
Plastic index, %	47	27	36	58	26
Percentage of course soil, %	0.0	10.7	0.0	0.0	0.2
Percentage of sandy soil, %	16.7	33.6	1.6	2.7	1.6
Percentage of fine soil, %	83.3	55.7	98.4	97.3	98.1
Soil classification
USCS	CH	CL	MH	CH	MH
Group name	High-plasticity clay soil	Low-plasticity clay soil	High-plasticity silty soil	High-plasticity clay soil	High High-Plasticity plasticity silty
AASHTO	A-7-5	A-7-6	A-7-5	A-7-6	A-7-5
Group name	Clayey soil	Clayey soil	Clayey soil	Clayey soil	Clayey soil
Standard Proctor compaction test
Optimum moisture content, %	34	23	26.5	39	37.5
Maximum dry density, g/cm³	1.27	1.51	1.38	1.3	1.31

Coefficients of UCS/(UCS at 2 H/D ratios)-38 mm diameter and H/D ratio_

Coefficients^a

Model		Unstandardized coefficients		Standardized coefficients	t	Sig.

		B	Std. Error	beta
1	(Constant)	1.596	0.026		61.838	0.000
1	H/D ratio	−0.288	0.012	−0.963	−23.469	0.000

Significance level (Sig_) and Pearson correlation coefficient (R) of UCS value for 38 mm specimen diameter_

		Height to diameter ratio	UCS of Mariam Church test pit	UCS of Ajip test pit	UCS of Aweytu test pit	UCS of Saris Sefer	UCS of JIT campus test pit
Height to diameter ratio (H/D)	R	1	−0.968^**	−0.979^**	−0.970^**	−0.984^**	−0.979^**
	Sig.		0.000	0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Mariam Church test pit	R	−0.968^**	1	0.984^**	0.977^**	0.993^**	0.971^**
	Sig.	0.000		0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Ajip test pit	R	−0.979^**	0.984^**	1	0.991^**	0.996^**	0.992^**
	Sig.	0.000	0.000		0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Aweytu test pit	R	−0.970^**	0.977^**	0.991^**	1	0.988^**	0.995^**
	Sig.	0.000	0.000	0.000		0.000	0.000
	n	9	9	9	9	9	9
UCS of Saris Sefer test pit	R	−0.984^**	0.993^**	0.996^**	0.988^**	1	0.986^**
	Sig.	0.000	0.000	0.000	0.000		0.000
	n	9	9	9	9	9	9
UCS of JIT campus test pit	R	−0.979^**	0.971^**	0.992^**	0.995^**	0.986^**	1
	Sig.	0.000	0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9

Significance level (Sig_) and Pearson correlation coefficient (R) of UCS value for 50 mm specimen diameter_

		Height to diameter ratio	UCS of Mariam Church test pit	UCS of Ajip test pit	UCS of Aweytu test pit	UCS of Saris Sefer	UCS of JIT campus test pit
Height to diameter ratio (H/D)	R	1	−0.994	−0.978	−0.973	−0.993	−0.986
	Sig.		0.000	0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Mariam Church test pit	R	−0.994	1	0.983	0.981	0.997	0.987
	Sig.	0.000		0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Ajip test pit	R	−0.978	0.983	1	0.989	0.988	0.991
	Sig.	0.000	0.000		0.000	0.000	0.000
	n	9	9	9	9	9	9
UCS of Aweytu test pit	R	−0.973	0.981	0.989	1	0.992	0.992
	Sig.	0.000	0.000	0.000		0.000	0.000
	n	9	9	9	9	9	9
UCS of Saris Sefer test pit	R	−0.993	0.997	0.988	0.992	1	0.995
	Sig.	0.000	0.000	0.000	0.000		0.000
	n	9	9	9	9	9	9
UCS of JIT campus test pit	R	−0.986	0.987	0.991	0.992	0.995	1
	Sig.	0.000	0.000	0.000	0.000	0.000
	n	9	9	9	9	9	9

Coefficients of UCS/(UCS at 2 H/D ratios)-50 mm diameter and H/D ratios_

Coefficients^a

Model		Unstandardized coefficients		Standardized coefficients	t	Sig.

		B	Std error	beta
2	(Constant)	1.658	0.026		63.201	0.000
2	H/D ratio	−0.318	0.012	−0.969	−25.509	0.000

Coefficients of UCS/(UCS at 2 H/D ratios)-100 mm diameter and H/D ratios_

Coefficients^a

Model		Unstandardized coefficients		Standardized coefficients	t	Sig.

		B	Std error	beta
3	(Constant)	1.671	0.026		63.699	0.000
3	H/D ratio	−0.328	0.012	−0.970	−26.238	0.000

Effect of Specimens’ Height to Diameter Ratio on Unconfined Compressive Strength of Cohesive Soil

Figures & Tables

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Figure 13

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Figure 15

Figure 16

Model summary of UCS/(UCS at 2 H/D ratios)-50 mm diameter and H/D ratio_

Descriptive statistics of the peak UCS value for specimens of diameter 50 mm_

Descriptive statistics of the peak UCS value for specimens of diameter 38 mm_

Shapiro–Wilk normality test_

Significance level (Sig_) and Pearson correlation coefficient (R) of UCS value for 100 mm specimen diameter_

Regression equations of UCS(measured)/UCS2_00 ratio for different specimen diameters versus H/D ratio_

Descriptive statistics of the peak UCS value for specimens of diameter 100 mm_

Regression model accuracy for the developed equations_

Model summary of UCS/(UCS at 2 H/D ratios)-100 mm diameter and H/D ratio_

Specimens’ height for each diameter, with respect of their H/D ratio at stain rate of 1%/min_

Model summary of UCS/(UCS at 2 H/D ratio)-38 mm diameter and H/D ratio_

Summary of index properties, classifications, and compaction parameters of the soils tested_

Coefficients of UCS/(UCS at 2 H/D ratios)-38 mm diameter and H/D ratio_

Significance level (Sig_) and Pearson correlation coefficient (R) of UCS value for 38 mm specimen diameter_

Significance level (Sig_) and Pearson correlation coefficient (R) of UCS value for 50 mm specimen diameter_

Coefficients of UCS/(UCS at 2 H/D ratios)-50 mm diameter and H/D ratios_

Coefficients of UCS/(UCS at 2 H/D ratios)-100 mm diameter and H/D ratios_

Paradigm

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