Behavior of Vertically Confined Square Footing on Reinforced Sand under Centric Inclined Loading

Figures & Tables

Material (sand)	Value
Classification of sand As per ISSCS (Indian Standard Soil Classification	SP
Specific gravity	2.64
Coefficient of curvature(C_c)	1.13
Uniformity coefficient(C_u)	2.62
Maximum void ratio(e_max)	0.87
Minimum void ratio(e_min)	0.55
Natural void ratio(e_natural)	0.68
Maximum dry unit weight (kN/m³)	16.46
Minimum dry unit weight (kN/m³)	13.62
Natural dry unit weight (kN/m³)	15.24
Angle of shearing resistance (¢) (Direct Shear Test)	32.6°
Relative Density	50%

Footing configuration	Confiner dimension	Horizontal reinforcement Spacing (Y)	Load intensity (kN/m²) (i=5°)	Load intensity (kN/m²) (i=10°)	Load intensity (kN/m²) (i=20°)
Surface footing			35.45	34.19	31.80
	D/B = 1.0; d/B = 1.0		50.06	47.98	33.77
	D/B = 1.0; d/B = 1.5		59.55	53.04	34.94
Footing with confiner	D/B = 1.0; d/B = 2.0		67.02	57.42	35.18
	D/B = 1.5; d/B = 1.0		48.91	46.52	32.81
	D/B = 1.5; d/B = 1.5		53.45	48.59	33.71
	D/B = 1.5; d/B = 2.0		57.1	50.81	34.49
	D/B = 2.0; d/B = 1.0		46.43	44.25	30.56
	D/B = 2.0 ; d/B = 1.5		48.61	46.49	30.87
	D/B = 2.0; d/B = 2.0		50.42	47.28	31.15
Footing with confiner and horizontal reinforcement	D/B = 1.0; d/B = 1.0	0.25B	79.93	69.64	59.47
		0.5B	73.13	62.94	54.29
		0.75B	62.56	50.83	45.59
		1B	55.55	48.49	42.49
	D/B = 1.0; d/B = 1.5	0.25B	101.74	83.16	76.10
		0.5B	90.5	80.28	71.39
		0.75B	84.37	66.57	57.39
		1B	70.9	60.45	50.09
	D/B = 1.0; d/B = 2.0	0.25B	105.96	91.54	84.89
		0.5B	90.5	85.12	78.49
		0.75B	85.78	77.34	69.69
		1B	78.43	64.82	51.29
	D/B = 1.5; d/B = 1.0	0.25B	120.20	102.30	83.42
		0.5B	96.21	89.0	73.4
		0.75B	82.13	76.39	59.55
		1B	61.10	59.40	53.64
	D/B = 1.5; d/B = 1.5	0.25B	171.10	146.44	102.47
		0.5B	110.0	94.42	77.89
		0.75B	82.51	80	69.47
		1B	62.80	61.76	54.31
	D/B = 1.5; d/B = 2.0	0.25B	213.91	195.31	127.29
		0.5B	138.75	118.91	98.01
		0.75B	85.52	82.6	73.67
		1B	62.80	65	60.91
	D/B = 2.0; d/B = 1.0	0.25B	136.0	110.53	102.44
		0.5B	102.91	91.71	86.11
		0.75B	87.22	84.23	74.23
		1B	75.54	73.4	57.89
	D/B = 2.0; d/B = 1.5	0.25B	177.62	146.0	114.9
		0.5B	123.8	100.5	92.9
		0.75B	91.1	85.12	76.38
		1B	80.0	75.23	66.41
	D/B = 2.0; d/B = 2.0	0.25B	228.22	188.57	134.39
		0.5B	151.10	143.72	102.2
		0.75B	111.21	102.66	86.14
		1B	90.0	81.4	69.47

Footing configuration	Confiner dimension	Horizontal reinforcement Spacing (Y)	SRF (i=5°)	SRF (i=10°)	SRF (i=20°)
Surface footing
Footing with confiner	D/B = 1.0; d/B = 1.0		0.47	0.43	0.10
	D/B = 1.0; d/B = 1.5		0.54	0.48	0.14
	D/B = 1.0; d/B = 2.0		0.57	0.52	0.18
	D/B = 1.5; d/B = 1.0		0.41	0.36	0.06
	D/B = 1.5; d/B = 1.5		0.43	0.40	0.08
	D/B = 1.5; d/B = 2.0		0.46	0.50	0.10
	D/B = 2.0; d/B = 1.0		0.36	0.35	0.003
	D/B = 2.0 ; d/B = 1.5		0.41	0.39	0.01
	D/B = 2.0; d/B = 2.0		0.43	0.44	0.02
Footing with confiner and horizontal reinforcement	D/B = 1.0; d/B = 1.0	0.25B	0.67	0.63	0.60
		0.5B	0.54	0.53	0.52
		0.75B	0.44	0.43	0.37
		1B	0.39	0.36	0.31
	D/B = 1.0; d/B = 1.5	0.25B	0.74	0.64	0.65
		0.5B	0.70	0.60	0.63
		0.75B	0.62	0.50	0.49
		1B	0.53	0.42	0.41
	D/B = 1.0; d/B = 2.0	0.25B	0.86	0.84	0.78
		0.5B	0.71	0.65	0.64
		0.75B	0.63	0.58	0.58
		1B	0.54	0.46	0.43
	D/B = 1.5; d/B = 1.0	0.25B	0.80	0.73	0.68
		0.5B	0.66	0.64	0.59
		0.75B	0.56	0.54	0.52
		1B	0.45	0.35	0.41
	D/B = 1.5; d/B = 1.5	0.25B	0.89	0.85	0.73
		0.5B	0.78	0.70	0.66
		0.75B	0.64	0.58	0.55
		1B	0.51	0.46	0.43
	D/B = 1.5; d/B = 2.0	0.25B	0.90	0.86	0.79
		0.5B	0.77	0.73	0.69
		0.75B	0.64	0.59	0.55
		1B	0.59	0.43	0.42
	D/B = 2.0; d/B = 1.0	0.25B	0.80	0.79	0.79
		0.5B	0.71	0.71	0.69
		0.75B	0.66	0.64	0.57
		1B	0.61	0.55	0.49
	D/B = 2.0; d/B = 1.5	0.25B	0.89	0.83	0.78
		0.5B	0.77	0.77	0.72
		0.75B	0.69	0.68	0.64
		1B	0.62	0.59	0.51
	D/B = 2.0; d/B = 2.0	0.25B	0.90	0.88	0.80
		0.5B	0.85	0.80	0.76
		0.75B	0.72	0.71	0.65
		1B	0.60	0.59	0.52

Test series	Foundation configuration	Test parameters		Number of tests

		Variable	Constant
A	Only footing (surface footing)	i=0,5°,10°,20°		4
B	Footing with confiner	d/B=1,1.5,2i= 5°,10°,20°	D/B=1.0	9
		d/B=1,1.5,2	D/B=1.5	9
		i= 5°,10°,20°d/B=1,1.5,2i= 5°,10°,20°	D/B=2.0	9
C	Footing with confiner and reinforcement	d/B=1,1.5,2; N=1–8Y/B=0.25,0.5,0.75,1i=5°10°20°	D/B=1.0,L/B=1, y/B=0.1B	36
		d/B=1,1.5,2; N=1–8Y/B=0.25,0.5,0.75,1i=5°,10°,20° d/B=1,1.5,2;	D/B=1.5,L/B=1.5, y/B=0.1B	36
		N=1–8Y/B=0.25,0.5,0.75,1i=5°,10°,20°	D/B=2.0,L/B=2.0, y/B=0.1B	36

Footing zonfiguration	Confiner dimension	Horizontal reinforcement Spacing (Y)	BCR (i=5°)	BCR (i=10°)	BCR (i=20°)
Surface footing
Footing with confiner	D/B = 1.0; d/B = 1.0		1.41	1.4	1.10
	D/B = 1.0; d/B = 1.5		1.67	1.55	1.14
	D/B = 1.0; d/B = 2.0		1.89	1.67	1.15
	D/B = 1.5; d/B = 1.0		1.37	1.36	1.07
	D/B = 1.5; d/B = 1.5		1.5	1.42	1.1
	D/B = 1.5; d/B = 2.0		1.61	1.48	1.13
	D/B = 2.0; d/B = 1.0		1.3	1.29	1.0
	D/B = 2.0 ; d/B = 1.5		1.37	1.35	1.01
	D/B = 2.0; d/B = 2.0		1.42	1.38	1.02
Footing with confiner and horizontal reinforcement	D/B = 1.0; d/B = 1.0	0.25B	2.25	2.04	1.95
		0.5B	2.06	1.84	1.73
		0.75B	1.76	1.48	1.49
		1B	1.56	1.41	1.39
	D/B = 1.0; d/B = 1.5	0.25B	2.87	2.43	2.5
		0.5B	2.55	2.35	2.34
		0.75B	2.38	1.95	1.88
		1B	2.00	1.77	1.64
	D/B = 1.0; d/B = 2.0	0.25B	3.00	2.68	2.78
		0.5B	2.55	2.49	2.57
		0.75B	2.42	2.26	2.28
		1B	2.21	1.90	1.68
	D/B = 1.5; d/B = 1.0	0.25B	3.39	3.0	2.74
		0.5B	2.71	2.61	2.41
		0.75B	2.31	2.23	1.95
		1B	1.72	1.73	1.76
	D/B = 1.5; d/B = 1.5	0.25B	4.82	4.29	3.36
		0.5B	3.1	2.76	2.55
		0.75B	2.32	2.33	2.28
		1B	1.77	1.8	1.78
	D/B = 1.5; d/B = 2.0	0.25B	6.03	5.71	4.18
		0.5B	3.91	3.47	3.21
		0.75B	2.41	2.41	2.42
		1B	1.91	1.9	2.0
	D/B = 2.0; d/B = 1.0	0.25B	3.83	3.23	3.36
		0.5B	2.9	2.68	2.82
		0.75B	2.45	2.46	2.43
		1B	2.12	2.14	1.9
	D/B = 2.0; d/B = 1.5	0.25B	5.0	4.27	3.77
		0.5B	3.49	2.93	3.05
		0.75B	2.56	2.48	2.5
		1B	2.25	2.19	2.18
	D/B = 2.0; d/B = 2.0	0.25B	6.43	5.51	4.41
		0.5B	4.25	4.2	3.35
		0.75B	3.13	3.0	2.82
		1B	2.54	2.38	2.28