Relationships between Shear Strength Parameters with Mineralogy and Index Properties of Compacted, Unsaturated Soils

Fondjo, Armand Augustin; Vanapalli, Sai K.; Ray, Richard P.; Theron, Elizabeth

Relationships between Shear Strength Parameters with Mineralogy and Index Properties of Compacted, Unsaturated Soils

Studia Geotechnica et Mechanica

Volume 47 (2025): Issue 1 (March 2025)

By:

Armand Augustin Fondjo, Sai K. Vanapalli, Richard P. Ray and Elizabeth Theron

Open Access

|Mar 2025

Figures & Tables

Sampling location map (https://www.exploresouthafrica.net/map/).

Whatman No. 42 filter paper calibration curve [4].

Typical specimen before and after failure.

3D relationship of (ϕ‘) dependence on W (%) and Gs.

3D relationship of (ϕ‘) dependence on liquid limit and plasticity index.

3D relationship of (ϕ‘) dependence on fine content (%) and clay content (%).

3D relationship of (ϕ‘) dependence on dry unit weight and void ratio.

3D relationship of (ϕ‘) dependence on FSR and FSI (%).

3D relationship of (ϕ‘) dependence on smectite (%) and plagioclase (%).

3D relationship of (ϕb) dependence on fine content (%) and clay content (%).

3D relationship of (ϕb) dependence on liquid limit (%) and plasticity index (%).

3D relationship of (ϕb) dependence on Gs and dry unit weight.

3D relationship of (ϕb) dependence on water content (%) and air entry value.

3D relationship of (ϕb) dependence on smectite (%) and FSI (%)

3D relationship of (ϕb) dependence on plagioclase (%) and K-feldspar (%)

3D relationship of (c‘) dependence on water content (%) and specific gravity.

3D relationship of (c‘) dependence on liquid limit (%) and plasticity index (%).

3D relationship of (c‘) dependence on fine content (%) and clay content (%).

3D relationship of (c‘) dependence on dry unit weight and void ratio.

3D relationship of (c‘) dependence on smectite (%) and free swell index (%).

3D relationship of (c‘) dependence on K-feldspar (%) and plagioclase (%).

Correlation diagram of ϕ‘ and the soil properties.

Correlation diagram of ϕb and the soil properties.

Correlation diagram of c‘ and the soil properties.

Grain size distribution curves of four soil samples

Soil–water characteristic curve for BFS as compacted

Soil–water characteristic curve for WIS as compacted

Soil–water characteristic curve for WES as compacted

Soil–water characteristic curve for BES as compacted

Graph of correlations between friction angle (ϕ‘) and water content.

Graph of relationships between friction angle (ϕ‘) and specific gravity (Gs).

Graph of correlations between friction angle (ϕ‘) and liquid limit (LL).

Graph of relationships between effective cohesion (c‘) and water content.

Graph of correlations between effective cohesion (c‘) and specific gravity (Gs).

Graph of relationships between effective cohesion (ϕ‘) and liquid limit (LL).

Swelling potential test results_

Soil	Swelling potential Classification IS 2720 - 40 (1977) [38]		Swelling potential classification, Sridharan & Prakash (2000) [39]

	(FSI¹), %	Soil expansivity	(FSR²)	Soil expansivity
BFS	64.31	Moderate	1.64	Moderate
WIS	81.37	Moderate	1.73	Moderate
WES	116.60	High	2.20	High
BES	35.81	Moderate	1.17	Low

Suction test results_

Soils	Soil water content (%)	Dry unit weight, (kN/m³)	Total suction (kPa)	Matric suction (kPa)	Osmotic suction (kPa)	Air entry value (kPa)
BFS	12.06	15.60	5883.92	4741.62	1142.3	10
	14.02	16.21	4064.22	3327.18	737.04
	17.03	17.01	1923.09	1388.22	534.87
	20.07	17.58	1036.11	671.89	364.22
	24.8	17.20	340.034	200	140.034
WIS	14.98	15.60	7439.15	5984.56	1454.59	14.82
	17.50	16.05	5410.66	4332.678	1077.982
	21	16.58	3580.89	2748.30	832.59
	24.03	16.85	1699.05	1199.35	499.70
	28.06	16.70	816.77	450.227	366.543
WES	15.93	14.94	9926.183	7693.666	2232.517	16.13
	19.25	15.48	6922.321	5227.777	1694.544
	23.37	16.09	4011.482	2986.456	1025.026
	26.14	16.29	2475.62	1778.651	696.969
	29.10	15.85	1397.745	890.47	507.275
BES	9.18	16.35	4163.35	3312.26	851.09	6.00
	12.42	18.01	2510.04	1982.31	527.73
	14.54	18.95	830.926	538.11	292.816
	17.23	19.60	323.818	225.609	98.209
	20.30	19.10	109.66	79.70	29.96

X-ray diffraction results_

Soils	Smectite (%)	Silica (%)	Group of feldspar minerals		Illite (%)	Calcite (%)
Soils	Smectite (%)	Silica (%)	K-feldspar (%)	Plagioclase (%)	Illite (%)	Calcite (%)
BFS	56.83	12.47	23.51	3.29	1.89	2.01
WIS	58.22	25.08	10.42	2.45	2.02	trace
WES	67.05	19.98	10.66	2.31	trace	trace
BES	31.67	31.39	21.22	8.15	3.36	4.21

Shear strength equations of saturated and unsaturated soils_

Authors	Equation	Number
Terzaghi [80]	τ_s=c‘+(σ_n-u_w) tan(ϕ‘)	1
Fredlund and Rahardjo [60]	τ_u=c‘+(σ_n-u_a) tan(ϕ‘)+(u_a-u_w) tan(ϕ^b)	2
Vanapalli et al. [27]	τu=c‘+σn−uatanϕ‘+θ−θrθs−θrua−uwtanϕ‘ {\tau _{\rm{u}}} = c' + \left( {{\sigma _{\rm{n}}} - {{\rm{u}}_{\rm{a}}}} \right)\tan \left( {\phi '} \right) + \left( {{{\theta - {\theta _{\rm{r}}}} \over {{\theta _{\rm{s}}} - {\theta _{\rm{r}}}}}} \right)\left( {{{\rm{u}}_{\rm{a}}} - {{\rm{u}}_{\rm{w}}}} \right)\tan \left( {\phi '} \right)	3
Khalili and Khabbaz [25]	τ_u=c‘+(σ_n-u_a) tan(ϕ‘)+(χ)(u_a-u_w) tan(ϕ‘)	4
Khalili and Khabbaz [25]	χ=ua−uwAEV−0.55 \chi = {\left[ {{{\left( {{{\rm{u}}_{\rm{a}}} - {{\rm{u}}_{\rm{w}}}} \right)} \over {{\rm{AEV}}}}} \right]^{ - 0.55}}	4
Vanapalli and Fredlund [18]	τ_u=c‘+(σ_n-u_a) tan(ϕ‘)+χ(u_a-u_w) tan(ϕ‘)	5
	χ=(S_r)^k
	k=0.98+0.0874 (PI)-0.001 (PI)²
Tekinsoy et al. [28]	τu=c‘+σn−uatanϕ‘+tanϕ‘AEV+Patlnua−uw+PatPat {\tau _{\rm{u}}} = {\rm{c}}' + \left( {{\sigma _{\rm{n}}} - {{\rm{u}}_{\rm{a}}}} \right)\tan \left( {\phi '} \right) + \tan \left( {\phi '} \right)\left( {{\rm{AEV}} + {\rm{Pat}}} \right)\ln \left[ {{{\left( {{{\rm{u}}_{\rm{a}}} - {{\rm{u}}_{\rm{w}}} } \right)}+{{\rm{P}}_{{\rm{at}}}} \over {{{\rm{P}}_{{\rm{at}}}}}}} \right]	6
Garven and Vanapalli [19]	τ_u =c‘+(σ_n-u_a) tan(ϕ‘)+ θ^k (u_a-u_w) tan(ϕ‘)	7
Garven and Vanapalli [19]	k=0.00161 PI²+0.0975 PI+1	7
Guan et al. [29]	τ_u =c‘+(σ_n-u_a) tan(ϕ‘)+(u_a-u_w) tan(ϕ^b) where ϕ‘=ϕ^b if (u_a-u_w)< AEV τ_u =c‘+[(σ_n-u_a)+AEV] tan(ϕ‘)+[(u_a-u_w)-AEV] bθ^k tan(ϕ‘) if (u_a-u_w)≥ AEV k=[log(u_a - u_w)-log(AEV)]^y For drying: y_d=0.502 ln(PI+2.7)-0.387 b_d=-0.254{ln[n_d(PI+4.4)]-0.387}²+2.114 {ln[n_d(PI+4.4)] }-3.522 For wetting: y_w=3.55y_d-3.00 b_w=0.542b_d (n_d/n_w)+0.389	8

ϕ‘ relationship with soil properties’ equations_

Correlation equations	R²	Equation number
ϕ‘ = 3739.6e^{−1.753Gs (%)}	0.72	11
ϕ‘ = 82.81e^{−0.04W (%)}	0.71	12
ϕ‘ = 68.87e^{−0.012LL (%)}	0.68	13
ϕ‘ = 51.04e^{−0.011PI (%)}	0.64	14
ϕ‘ = 73.63e^{−0.012Fine-grained (%)}	0.72	15
ϕ‘ = 52.34e^{−0.014Clay (%)}	0.74	16
ϕ‘ =5.059e^{0.108gd (kN/m3)}	0.62	17
ϕ‘ = 57.16e^{−0.932Void ratio}	0.69	18
ϕ‘ = 63.49e^−0.368FSR	0.74	19
ϕ‘ = 46.72e^{−0.004FSI (%)}	0.70	20
ϕ‘ = 56.134e^{−0.01Smectite (%)}	0.61	21
ϕ‘ = 26.81e^{0.0574 Plagioclase (%)}	0.53	22

Unsaturated shear strength parameters_

Soil	Water content (%)	c‘ (kPa)	tan (ϕ‘) (Degree)	(σ_n-u_a) (kPa)	τ_s (kPa)	(u_a-u_w) (kPa)	tan (ϕ^b) Degree	τ_u (kPa)	τ_u/τ_s
BFS	12.06	75.05	52.09	605.5	853	4741.62	6.77	1414.44	1.66
	14.02	72.05	48.55	547.78	692	3327.18	6.77	1086.56	1.57
	17.03	67.11	44.65	485.53	547	1388.22	6.77	711.25	1.30
	20.07	58.10	39.66	406.30	395	671.89	6.77	474.56	1.20
	24.80	51.54	32.71	333.87	266	200	6.77	289.67	1.09
WIS	14.98	69.42	50.75	537.59	727	5984.56	5.02	1253.44	1.72
	17.50	63.89	47.18	492.32	595	4332.68	5.02	976.02	1.64
	21	57.95	42.75	423.28	449	2748.30	5.02	690.80	1.54
	24.03	55.60	37.21	365.56	333	1199.35	5.02	438.60	1.32
	28.06	49.30	32.51	282.94	230	450.23	5.02	269.20	1.17
WES	15.93	62.39	42.07	452.71	471	7693.67	2.67	830.31	1.76
	19.25	57.32	37.95	413.10	379	5227.78	2.67	623.62	1.65
	23.37	50.11	34.31	328.78	274	2986.46	2.67	413.94	1.51
	26.14	48.85	28.8	284.07	205	1778.65	2.67	288.08	1.41
	29.1	45.31	24.92	234.84	154	890.47	2.67	196.01	1.27
BES	9.18	78.34	53.21	645.11	941	3312.26	10	1512.02	1.61
	12.42	69.05	50.08	554.57	732	1982.31	10	1073.58	1.47
	14.54	64.56	46.03	503.07	586	538.11	10	678.82	1.16
	17.23	61.09	42.42	431.77	456	225.61	10	494.52	1.08
	20.3	54.93	33.05	350.85	283	79.70	10	296.95	1.05

Degrees of correlation between dependent variables (Kalayci, 2010) [63]_

Coefficient of correlation (R²)	Degrees of correlation
0.00 – 0.25	Very weak correlation
0.26 – 0.49	Weak correlation
0.50 – 0.69	Moderate correlation
0.70 – 0.89	Strong correlation
0.90 – 1.00	Very strong correlation

Material properties_

Soils	Liquid limit (%)	Plasticity index (%)	Clay (%)	Ac*	Silt (%)	Fine content (%)	Sand (%)	Gravel (%)	Specific Gravity (Gs)	USCS
BFS	58.98	36.82	30.40	1.21	29.11	59.51	29.39	10.09	2.64	CH
WIS	63.78	42.48	34.03	1.25	33.49	67.52	26.80	4.85	2.73	CH
WES	69.45	49.87	40.00	1.25	33.00	73.00	23.50	2.56	2.73	CH
BES	40.29	19.23	17.11	1.12	28.03	45.14	43.76	11.10	2.55	CL

Swelling potential classification [39]_

FSR	Clay type	Soil expansivity	Dominant clay mineral type
=1	Non-swelling	Negligible	Kaolinite
1.0 – 1.5	Mixture of swelling and non-swelling	Low	Mixture of Kaolinitic and Montmorillonitic
1.5 – 2.0	Swelling	Moderate	Montmorillonitic
2.0 – 4.0	Swelling	High	Montmorillonitic
> 4.0	Swelling	Very high	Montmorillonitic

Sampling location coordinates_

Samples	Global positioning system
BFS	29° 05′30,50″S / 26° 07′46,60″E
WES	27° 57′51,80″S / 26° 45′36,90″E
WIS	28° 30′43,50″S / 27° 00′12,80″E
BES	28° 13′23,40″S / 28° 19′23,00″E

ϕb relationship with soil properties’ equations_

Correlation equations	R²	Equation number
ϕ^b = 106.51e^{−0.05Fine content (%)}	0.92	23
ϕ^b = 27.04e^{−0.054Clay (%)}	0.92	24
ϕ^b = 84.48e^{−0.048LL (%)}	0.93	25
ϕ^b = 25.95e^{−0.046PI (%)}	0.92	26
ϕ^b = 5.E + 08e^−6.883Gs	0.88	27
ϕ^b = 0.0022e^{0.438gd (kNm3)}	0.81	28
ϕ^b = 166.47e^{−0.161W (%)}	0.88	29
ϕ^b = 20.29e^{−0.119AEV (kPa)}	0.92	30
ϕ^b = 18 e^{−0.018FSI (%)}	0.93	31
ϕ^b = 37.03e^{−0.038Smectite (%)}	0.79	32
ϕ^b = 1.884e^{0.229Plagiocalse (%)}	0.67	33
ϕ^b = 1.167e^{0.0833K-feldspar (%)}	0.66	34

c‘ relationship with soil properties’ equations_

Correlation equations	R²	Equation number
c‘ = 98.71e^{−0.03W (%)}	0.73	35
c‘ = 1887e^−1.341Gs	0.71	36
c‘ = 86.53e^{−0.009LL (%)}	0.61	37
c‘ = 69.26e^{−0.008PI (%)}	0.56	38
c‘ = 91.84e^{−0.009Fine content (%)}	0.68	39
c‘ = 71.59e^{−0.01Clay (%)}	0.71	40
c‘ = 75.759e^{−0.629Void ratio}	0.63	41
c‘ = 13.201e^{0.0776gd (kN/m3)}	0.54	42
c‘ = 73.71e^{−0.007Smectite (%)}	0.52	43
c‘ = 65.22e^{−0.003FSI (%)}	0.62	44
c‘ = 39.19e^{0.0162K-feldspar (%)}	0.53	45
c‘ = 43.63e^{0.0407Plagioclase (%)}	0.50	46

Compaction characteristics_

Soil	OWC (%)	γ_dmax (kN/m³)
BFS	20.10	17.60
WIS	24.00	16.90
WES	26.10	16.30
BES	17.20	19.60

DOI: https://doi.org/10.2478/sgem-2025-0006 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365

Journal RSS Feed

Language: English

Page range: 65 - 88

Submitted on: Jun 19, 2024

Accepted on: Nov 23, 2024

Published on: Mar 24, 2025

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Expansive soils,

shear strength,

matric suction,

soil index properties,

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2025 Armand Augustin Fondjo, Sai K. Vanapalli, Richard P. Ray, Elizabeth Theron, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

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Relationships between Shear Strength Parameters with Mineralogy and Index Properties of Compacted, Unsaturated Soils

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Swelling potential test results_

Suction test results_

X-ray diffraction results_

Shear strength equations of saturated and unsaturated soils_

ϕ‘ relationship with soil properties’ equations_

Unsaturated shear strength parameters_

Degrees of correlation between dependent variables (Kalayci, 2010) [63]_

Material properties_

Swelling potential classification [39]_

Sampling location coordinates_

ϕb relationship with soil properties’ equations_

c‘ relationship with soil properties’ equations_

Compaction characteristics_