Undrained seismic bearing capacity of strip footing adjacent to a heterogeneous excavation

doi:10.1007/s11709-023-0905-x

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (4) : 566-583 https://doi.org/10.1007/s11709-023-0905-x

RESEARCH ARTICLE

Undrained seismic bearing capacity of strip footing adjacent to a heterogeneous excavation

Ramin VALI¹(

), Saeed KHOSRAVI², Majid BEYGI³

¹. Department of Civil Engineering, Technical and Vocational University, Tehran 1435761137, Iran
². Department of Mining Engineering, Shahid Bahonar University of Kerman, Kerman 7616913439, Iran
³. Department of Civil Engineering, Yazd University, Yazd 8915818411, Iran

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Abstract

The analysis of the bearing capacity of strip footings sited near an excavation is critical in geotechnics. In this study, the effects of the geometrical features of the excavation and the soil strength properties on the seismic bearing capacity of a strip footing resting on an excavation were evaluated using the lower and upper bounds of the finite element limit analysis method. The effects of the setback distance ratio (L/B), excavation height ratio (H/B), soil strength heterogeneity (kB/c_u), and horizontal earthquake coefficient (k_h) were analyzed. Design charts and tables were produced to clarify the relationship between the undrained seismic bearing capacity and the selected parameters.

Keywords excavation finite element limit analysis heterogeneous soil strip footing undrained bearing capacity

Corresponding Author(s): Ramin VALI

About author:

^* These authors contributed equally to this work.

Just Accepted Date: 02 February 2023 Online First Date: 12 May 2023 Issue Date: 25 June 2023

Cite this article:

Ramin VALI,Saeed KHOSRAVI,Majid BEYGI. Undrained seismic bearing capacity of strip footing adjacent to a heterogeneous excavation[J]. Front. Struct. Civ. Eng., 2023, 17(4): 566-583.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-023-0905-x
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I4/566

Fig.1 Model geometry and typical FELA mesh. (Note: Dimensions are not on the main scale.)

Tab.1 Validation of q_u/(γB) (upper bound values) for homogenous soil excavation (β = 90°)

Tab.2 Validation of bearing capacity factor, N_c, for strip footing on level ground

Tab.3 Validation of q_u/(γB) under undrained conditions for the range of c_u/(γB) of perfectly smooth footing (L/B = 1) on level ground

soil-foundation interface	$φ$ (° )	Ukritchon et al. [47]		Hjiaj et al. [48]		Kumar and Kouzer [49]	Kumar [50]	Kumar and Chakraborty [51]	Veiskarami et al. [13]	Pakdel et al. [52]	Izadi et al. [42]	present study
soil-foundation interface	$φ$ (° )	LB^a)	UB^a)	LB^b)	UB^b)	UB	SC	LB	LB	LE	LB	LB	UB
perfectly smooth (δ = 0)	10	0.27	0.30	0.28	0.30	0.31	0.28	0.29	0.29	0.33	0.29	0.27	0.29
	20	1.52	1.73	1.58	1.67	1.74	1.57	1.59	1.59	1.62	1.59	1.54	1.71
	30	7.18	8.54	7.62	8.08	8.47	7.65	7.58	7.85	7.9	7.85	7.56	8.28
	40	38.5	54.2	42.77	45.42	50.38	43.08	41.95	43.9	44.25	41.59	40.17	49.53
perfectly rough (δ = $φ$ )	10	0.41	0.47	0.43	0.46	0.49	0.43	0.43	0.44	0.47	0.44	0.42	0.48
	20	2.67	3.27	2.82	2.96	3.16	2.82	2.82	2.88	3.12	2.89	2.75	3.18
	30	13.2	17.4	14.57	15.24	16.64	14.68	14.53	15.03	15.25	15.06	13.72	16.92
	40	69.9	111.1	83.33	88.39	98.53	85.01	81.8	70.62	77.75	79.19	75.96	97.83

Tab.4 Validation of bearing capacity factor, N_γ, for perfectly smooth and rough footings [35]

Fig.2 Graphs for q_uk_h/c_u versus k_h for various conditions of L/B and H/B. (a) L/B = 0; (b) L/B = 0.25; (c) L/B = 0.5; (d) L/B = 1; (e) L/B = 2; (f) L/B ≥ 3.

Fig.3 Mean values of q_u/(γB) for smooth strip footing adjoining excavation (k_h = 0.0). (a) c_u/(γB) = 0.5; (b) c_u/(γB) = 1.0; (c) c_u/(γB) = 1.5; (d) c_u/(γB) = 2.0; (e) c_u/(γB) = 2.5; (f) c_u/(γB) = 5.0.

Fig.4 Mean values of q_u/(γB) for rough strip footing adjoining excavation (k_h = 0.0). (a) c_u/(γB) = 0.5; (b) c_u/(γB) = 1.0; (c) c_u/(γB) = 1.5; (d) c_u/(γB) = 2.0; (e) c_u/(γB) = 2.5; (f) c_u/(γB) = 5.0.

Fig.5 Effect of L/B on ultimate bearing capacity (H/B = 2, c_u/(γB) = 1, kB/c_u = 0.5, k_h = 0.25, rough footing). (a) L/B = 0.5; (b) L/B = 1; (c) L/B = 2; (d) L/B = 4.

Fig.6 Effect of H/B on ultimate bearing capacity (c_u/(γB) = 3, kB/c_u = 0.5, k_h = 0.05, rough footing). (a) L/B = 0.25; (b) L/B = 0.5; (c) L/B = 1; (d) L/B = 2.

Fig.7 Mean values of q_u/(γB) for rough strip footing adjoining excavation (k_h = 0.1). (a) c_u/(γB) = 0.5; (b) c_u/(γB) = 1.0; (c) c_u/(γB) = 1.5; (d) c_u/(γB) = 2.0; (e) c_u/(γB) = 2.5; (f) c_u/(γB) = 5.0.

Fig.8 Mean values of q_u/(γB) for rough strip footing adjoining excavation (k_h = 0.2). (a) c_u/(γB) = 0.5; (b) c_u/(γB) = 1.0; (c) c_u/(γB) = 1.5; (d) c_u/(γB) = 2.0; (e) c_u/(γB) = 2.5; (f) c_u/(γB) = 5.0.

Fig.9 Mean values of q_u/(γB) for rough strip footing adjoining excavation (k_h = 0.3). (a) c_u/(γB) = 0.5; (b) c_u/(γB) = 1.0; (c) c_u/(γB) = 1.5; (d) c_u/(γB) = 2.0; (e) c_u/(γB) = 2.5; (f) c_u/(γB) = 5.0.

Fig.10 Mean values of q_u/(γB) for rough strip footing adjoining excavation (k_h = 0.4). (a) c_u/(γB) = 0.5; (b) c_u/(γB) = 1.0; (c) c_u/(γB) = 1.5; (d) c_u/(γB) = 2.0; (e) c_u/(γB) = 2.5; (f) c_u/(γB) = 5.0.

c_u/(γB)	H/B	kB/c_u = 0					kB/c_u = 1
c_u/(γB)	H/B	k_h = 0.0	k_h = 0.1	k_h = 0.2	k_h = 0.3	k_h = 0.4	k_h = 0.0	k_h = 0.1	k_h = 0.2	k_h = 0.3	k_h = 0.4
0.5	0.5	(18.68) 17.39	16.59	–	–	–	(25.92) 27.97	23.15	19.21	16.03	13.53
	1	(10.11) 8.11	–	–	–	–	(23.41) 23.65	19.69	17.29	14.69	12.53
	3	–	–	–	–	–	(23.40) 23.65	20.28	17.30	14.70	12.54
	5	–	–	–	–	–	(23.45) 23.65	20.27	17.24	14.67	NaN
	10	–	–	–	–	–	(23.41) 23.51	20.26	NaN	NaN	NaN
1	0.5	(43.67) 47.31	39.88	33.94	–	–	(58.20) 62.41	52.68	44.30	37.52	32.26
	1	(36.05) 36.19	32.35	28.67	–	–	(55.24) 57.11	49.79	42.64	36.64	32.64
	3	(30.94) 31.06	25.82	–	–	–	(55.42) 57.35	50.71	42.78	36.81	31.83
	5	–	–	–	–	–	(55.16) 57.10	49.67	42.78	36.80	31.89
	10	–	–	–	–	–	(55.17) 57.15	49.77	42.82	36.82	31.90
1.5	0.5	(69.13) 73.95	63.12	54.15	46.82	40.81	(90.32) 96.76	82.11	69.07	58.93	50.65
	1	(59.71) 59.95	53.88	48.06	42.76	–	(86.58) 90.18	78.66	67.61	58.15	50.54
	3	(59.01) 59.00	53.63	46.95	–	–	(86.22) 90.39	78.37	67.69	58.37	51.23
	5	(50.02) 50.40	6.43	–	–	–	(86.72) 89.78	78.68	67.74	58.36	50.57
	10	–	–	–	–	–	(86.94) 90.09	78.85	67.53	58.34	50.56
2	0.5	(94.35) 100.92	86.44	74.34	64.42	56.35	(121.54) 131.24	111.30	94.24	80.17	69.32
	1	(83.27) 83.59	75.24	67.42	60.08	53.33	(117.67) 123.47	107.32	92.54	79.53	69.07
	3	(82.89) 82.93	75.25	67.48	60.03	48.93	(118.07) 123.38	107.51	92.34	79.72	69.17
	5	(82.85) 82.99	75.34	67.46	–	–	(117.73) 123.12	107.38	92.59	79.78	69.11
	10	–	–	–	–	–	(118.21) 122.09	107.37	92.57	79.67	68.54
2.5	0.5	(119.52) 127.84	109.52	94.45	82.07	71.86	(157.01) 165.49	140.75	119.21	101.61	87.80
	1	(106.91) 107.04	96.88	86.76	77.22	68.71	(148.59) 155.77	135.70	117.40	101.02	87.42
	3	(104.13) 106.07	96.68	86.61	77.21	68.83	(149.61) 156.23	136.74	117.36	100.59	87.56
	5	(106.50) 106.36	96.85	86.68	77.22	68.87	(148.99) 156.19	136.13	117.16	101.10	87.43
	10	–	–	–	–	–	(148.82) 155.73	135.95	117.21	101.02	87.56
5	0.5	(245.45) 261.89	225.88	195.08	169.82	149.08	(314.90) 337.17	287.96	243.58	207.87	180.09
	1	(223.63) 225.69	204.20	181.79	163.53	144.84	(306.26) 320.98	279.90	241.12	207.32	179.26
	3	(224.59) 224.71	203.69	182.32	162.51	144.93	(305.77) 320.86	279.10	241.05	207.57	179.07
	5	(224.42) 224.15	204.01	182.55	162.59	144.96	(304.71) 321.03	280.15	241.27	207.61	179.91
	10	(223.82) 224.87	203.40	182.77	162.55	144.99	(305.66) 320.61	280.00	240.76	207.71	179.66

Tab.5 Values of q_u (kPa) at L/B = 0 for footing adjoining excavation (kB/c_u = 0 and 1)

soil-foundation interface	k_h	c_u/(γB)	kB/c_u
			2		5		10		20
			mean	SD	mean	SD	mean	SD	mean	SD
perfectly smooth (δ = 0)	0	0.5	30.815	0.786	48.053	0.106	67.964	0.696	102.523	0.262
		1	69.612	0.770	100.595	0.284	139.357	0.832	207.688	0.493
		1.5	107.844	0.818	152.684	0.900	211.327	0.789	312.741	1.199
		2	145.546	1.262	205.260	0.480	281.812	0.766	417.853	3.601
		2.5	183.780	1.018	256.138	3.828	351.594	4.670	520.176	5.783
		5	373.843	2.012	519.978	1.179	711.589	2.853	1049.911	3.931
perfectly rough (δ = $φ$ )	0	0.5	33.670	0.963	53.424	0.221	78.258	0.195	118.253	0.182
		1	74.420	1.245	112.295	0.127	160.953	0.413	239.816	0.822
		1.5	115.307	1.595	170.893	0.563	243.082	0.336	361.418	1.629
		2	155.714	2.151	229.932	0.270	325.793	0.714	481.924	1.824
		2.5	195.892	0.279	288.513	0.523	407.711	0.441	603.755	1.865
		5	400.044	4.257	583.593	1.238	819.858	1.008	1209.966	3.708
	0.1	0.5	28.150	0.523	44.114	0.296	62.366	0.357	87.737	0.282
		1	64.305	2.403	92.831	0.055	126.802	3.630	176.942	0.636
		1.5	97.916	0.580	141.305	0.166	194.301	0.563	265.494	0.043
		2	133.031	0.608	190.020	0.327	261.087	1.682	355.263	1.215
		2.5	168.077	1.533	239.038	0.061	325.944	0.855	443.232	0.504
		5	340.585	1.416	481.650	1.252	654.638	2.429	887.860	0.159
	0.2	0.5	23.475	0.235	35.222	0.168	45.208	0.082	50.202	0.643
		1	52.963	0.172	73.754	0.371	91.647	0.243	100.013	0.053
		1.5	82.280	0.055	112.580	0.245	137.792	0.175	150.032	0.122
		2	110.817	1.310	151.083	0.259	184.189	0.013	200.382	0.352
		2.5	140.504	0.360	189.712	0.248	231.015	1.019	250.026	0.039
		5	286.315	0.198	381.161	3.303	462.136	0.042	500.155	0.253
	0.3	0.5	19.676	0.112	28.020	0.029	32.434	0.013	33.351	0.013
		1	44.787	0.534	58.439	0.178	64.022	1.273	66.668	0.022
		1.5	69.095	0.077	88.851	0.046	96.815	1.719	100.637	0.725
		2	93.576	0.072	119.163	0.085	131.212	1.654	133.657	0.320
		2.5	118.018	0.747	149.359	0.152	164.591	0.013	166.754	0.098
		5	240.140	0.319	300.617	0.115	329.714	0.244	332.034	3.257
	0.4	0.5	16.638	0.062	22.754	0.017	24.676	0.692	25.022	0.017
		1	37.971	0.225	46.925	0.005	50.021	0.021	49.654	1.270
		1.5	58.701	0.015	71.157	0.390	74.992	0.400	75.179	0.371
		2	79.523	0.237	93.692	2.628	100.029	0.051	100.158	0.116
		2.5	100.142	0.006	118.822	0.031	125.184	0.308	125.028	0.027
		5	203.310	0.436	238.356	0.544	249.886	0.299	248.301	3.859

Tab.6 Mean and standard deviation values of q_u (kPa) at L/B = 0 for strip footing adjoining excavation in full ranges of H/B (kB/c_u = 2, 5, 10, and 20)

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