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

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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 (%)
			K-feldspar (%)	Plagioclase (%)
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]	τs=c‘+(σn-uw) tan(ϕ‘)	1
Fredlund and Rahardjo [60]	τu=c‘+(σn-ua) tan(ϕ‘)+(ua-uw) tan(ϕb)	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]	τu=c‘+(σn-ua) tan(ϕ‘)+(χ)(ua-uw) tan(ϕ‘)	4
	χ=ua−uwAEV−0.55 \chi = {\left[ {{{\left( {{{\rm{u}}_{\rm{a}}} - {{\rm{u}}_{\rm{w}}}} \right)} \over {{\rm{AEV}}}}} \right]^{ - 0.55}}
Vanapalli and Fredlund [18]	τu=c‘+(σn-ua) tan(ϕ‘)+χ(ua-uw) tan(ϕ‘)	5
	χ=(Sr)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]	τu =c‘+(σn-ua) tan(ϕ‘)+ θk (ua-uw) tan(ϕ‘)	7
	k=0.00161 PI2+0.0975 PI+1
Guan et al. [29]	τu =c‘+(σn-ua) tan(ϕ‘)+(ua-uw) tan(ϕb) where ϕ‘=ϕb if (ua-uw)< AEV τu =c‘+[(σn-ua)+AEV] tan(ϕ‘)+[(ua-uw)-AEV] bθk tan(ϕ‘) if (ua-uw)≥ AEV k=[log(ua - uw)-log(AEV)]y For drying: yd=0.502 ln(PI+2.7)-0.387 bd=-0.254{ln[nd(PI+4.4)]-0.387}2+2.114 {ln[nd(PI+4.4)] }-3.522 For wetting: yw=3.55yd-3.00 bw=0.542bd (nd/nw)+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‘ =5.059e0.108gd (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‘ = 26.81e0.0574 Plagioclase (%)	0.53	22

Unsaturated shear strength parameters_

Soil	Water content (%)	c‘ (kPa)	tan (ϕ‘) (Degree)	(σn-ua) (kPa)	τs (kPa)	(ua-uw) (kPa)	tan (ϕb) Degree	τu (kPa)	τu/τs
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
ϕb = 106.51e−0.05Fine content (%)	0.92	23
ϕb = 27.04e−0.054Clay (%)	0.92	24
ϕb = 84.48e−0.048LL (%)	0.93	25
ϕb = 25.95e−0.046PI (%)	0.92	26
ϕb = 5.E + 08e−6.883Gs	0.88	27
ϕb = 0.0022e0.438gd (kNm3)	0.81	28
ϕb = 166.47e−0.161W (%)	0.88	29
ϕb = 20.29e−0.119AEV (kPa)	0.92	30
ϕb = 18 e−0.018FSI (%)	0.93	31
ϕb = 37.03e−0.038Smectite (%)	0.79	32
ϕb = 1.884e0.229Plagiocalse (%)	0.67	33
ϕb = 1.167e0.0833K-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‘ = 13.201e0.0776gd (kN/m3)	0.54	42
c‘ = 73.71e−0.007Smectite (%)	0.52	43
c‘ = 65.22e−0.003FSI (%)	0.62	44
c‘ = 39.19e0.0162K-feldspar (%)	0.53	45
c‘ = 43.63e0.0407Plagioclase (%)	0.50	46

Compaction characteristics_

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