地震水平动态放大效应下三维加筋边坡稳定性研究

doi:10.16265/j.cnki.issn1003-3033.2026.06.0393

摘要/Abstract

摘要：

为提高三维富水加筋边坡的稳定性,构建三维边坡计算模型,在牛角破坏体中插入宽度为b的块体表征边坡在纵向方向上的三维效应,同时考虑地震水平动态放大效应、孔隙水效应以及加筋效应,采用上限定理求解极限破坏状态时的外力功率和内能耗散率,并引入稳定系数评估三维边坡的稳定性。结果表明:简化计算模型后,文中结果与已有成果高度吻合,验证了文中结果的有效性。三维边坡抗震稳定性问题可简化为二维平面应变问题的前提条件为宽高比B/H≥10。地震、孔隙水效应会显著降低三维边坡的稳定性以及扩大其破坏范围,地震烈度级别和孔隙水压力的大小主要影响三维边坡潜在滑裂面的位置,地震水平动态放大效应主要影响坡顶后缘的宽度和深度。顶疏底密的布筋效果优于均匀加筋,可采用顶疏底密布筋方式以及增大布筋密度提高三维边坡的抗震能力。

关键词: 地震水平动态放大效应, 3D加筋边坡, 边坡稳定性, 孔隙水, 布筋方式

Abstract:

To improve the stability of three-dimensional water-rich reinforced slopes, a three-dimensional slope computational model was constructed. A block of width b was inserted into the bullhorn failure body to characterize the three-dimensional effects along the slope's longitudinal direction. Seismic horizontal dynamic amplification effects, pore water effects, and reinforcement effects were considered simultaneously. The upper bound theorem was employed to solve for the external force power and internal energy dissipation rate at the ultimate failure state. A stability coefficient was introduced to evaluate the stability of the three-dimensional slope. Results indicate that after simplifying the computational model, the findings in this paper are highly aligned with existing research, validating the effectiveness of the presented results. The prerequisite for simplifying the seismic stability problem of a three-dimensional slope into a two-dimensional plane strain problem is a width-to-height ratio B/H ≥ 10. The stability of three-dimensional slopes is significantly reduced and their failure zones are expanded by earthquakes and pore water effects. The location of potential slip planes within the slope is primarily influenced by the intensity level of seismic activity and the magnitude of pore water pressure. The width and depth of the rear edge at the crest are mainly affected by the horizontal dynamic amplification effect of earthquakes. Uniformly distributed reinforcement is outperforms by a reinforcement pattern with sparse reinforcement at the top and dense reinforcement at the bottom. The seismic resistance of three-dimensional slopes can be enhanced by adopting this sparse-top/dense-bottom reinforcement configuration and increasing reinforcement density.

Key words: seismic horizontal dynamic amplification effect, 3D reinforced slope, slope stability, pore water, reinforcement pattern

中图分类号:

X936

张佳华, 韦云俊, 源小梦, 何金. 地震水平动态放大效应下三维加筋边坡稳定性研究[J]. 中国安全科学学报, 2026, 36(6): 91-101.

Zhang Jiahua, Wei Yunjun, Yuan Xiaomeng, He Jin. Stability of 3D reinforced slopes subjected to seismic horizontal dynamic amplification effect[J]. China Safety Science Journal, 2026, 36(6): 91-101.

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B/ H	β/ (°)	N_s			Δ₁/ %	Δ₂/ %
B/ H	β/ (°)	文献[24]	文献[14]	文中模型	Δ₁/ %	Δ₂/ %
1	45	54.07	54.19	54.41	0.63	0.41
2	45	42.60	42.63	43.11	1.20	1.13
3	45	39.85	39.89	40.58	1.83	1.73
5	45	37.97	37.97	38.62	1.71	1.71
10	45	36.70	36.70	37.32	1.69	1.69
1	60	23.40	23.41	23.59	0.81	0.77
2	60	18.94	18.94	18.94	0	0
3	60	17.82	17.83	17.85	0.17	0.11
5	60	17.05	17.05	17.09	0.23	0.23
10	60	16.52	16.52	16.58	0.36	0.36
1	75	14.63	14.46	14.72	0.62	1.80
2	75	11.84	11.84	11.86	0.17	0.17
3	75	11.12	11.12	11.12	0	0
5	75	10.61	10.61	10.61	0	0
10	75	10.26	10.26	10.26	0	0

地震烈度	B/H	忽略q_ε		考虑q_ε
地震烈度	B/H	N_s	Δ₃/%	N_s	Δ₄/%
7度	100	11.22	—	8.86	—
	50	11.26	0.36	8.89	0.34
	10	11.6	3.39	9.17	3.50
	9	11.65	3.83	9.21	3.95
	8	11.72	4.46	9.26	4.51
	7	11.79	5.08	9.33	5.30
	6	11.9	6.06	9.42	6.32
	5	12.06	7.49	9.56	7.90
	4	12.32	9.80	9.77	10.27
	3	12.77	13.81	10.15	14.56
	2	13.81	23.09	11.04	24.60
	1	17.76	58.29	14.43	62.87
	0.8	20.71	84.58	16.95	91.31
8度	100	8.42	—	6.18	—
	50	8.46	0.48	6.2	0.32
	10	8.73	3.68	6.43	4.05
	9	8.77	4.16	6.47	4.69
	8	8.82	4.75	6.51	5.34
	7	8.89	5.58	6.57	6.31
	6	8.98	6.65	6.64	7.44
	5	9.11	8.19	6.76	9.39
	4	9.32	10.69	6.92	11.97
	3	9.66	14.73	7.21	16.67
	2	10.44	23.99	7.9	27.83
	1	13.69	62.59	10.63	72.01
	0.8	16.12	91.45	12.66	104.8
9度	100	5.44	—	3.93	—
	50	5.47	0.55	3.95	0.51
	10	5.68	4.41	4.12	4.83
	9	5.71	4.96	4.14	5.34
	8	5.74	5.51	4.17	6.12
	7	5.79	6.43	4.21	7.12
	6	5.85	7.54	4.27	8.65
	5	5.94	9.19	4.34	10.43
	4	6.1	12.13	4.47	13.74
	3	6.36	16.91	4.7	19.59
	2	6.91	27.02	5.19	32.06
	1	9.29	70.77	7.24	84.22
	0.8	11.02	102.57%	8.82	124.4

β/ (°)	q_max	k_v=k_h		布筋方式		N_s
β/ (°)	q_max	k_v=k_h		布筋方式		B/H=1		Δ₅/%		B/H=100		Δ₆/%
90	3	0.1		J		8.28		—		4.26		—
	3	0.1		D		9.72		17.39		4.54		6.57
	2.5	0.2		J		7.18		—		3.41		—
	2.5	0.2		D		8.40		17.00		3.66		7.33
	2	0.4		J		5.76		—		2.49		—
	2	0.4		D		6.75		17.19		2.70		8.43
75	3	0.1		J		8.75		—		5.29		—
	3	0.1		D		10.10		15.43		5.66		6.99
	2.5	0.2		J		7.42		—		4.09		—
	2.5	0.2		D		8.57		15.50		4.41		7.82
	2	0.4		J		5.83		—		2.90		—
	2	0.4		D		6.73		15.44		3.13		7.93
60	3	0.1		J		10.39		—		6.72		—
	3	0.1		D		11.92		14.73		7.16		6.55
	2.5	0.2		J		8.63		—		4.96		—
	2.5	0.2		D		9.90		14.72		5.32		7.26
	2	0.4		J		6.63		—		3.37		—
	2	0.4		D		7.61		14.78		3.63		7.72
45	3	0.1		J		12.05		—		8.80		—
	3	0.1		D		13.38		11.04		9.49		7.84
	2.5	0.2		J		9.74		—		6.13		—
	2.5	0.2		D		10.81		10.99		6.61		7.83
	2	0.4		J		7.27		—		3.96		—
	2	0.4		D		8.07		11.00		4.37		10.35
30	3		0.1		J		16.57		—		11.54		—
	3		0.1		D		19.04		14.91		13.32		15.42
	2.5		0.2		J		12.67		—		7.56		—
	2.5		0.2		D		14.55		14.84		8.50		12.43
	2		0.4		J		9.01		—		4.75		—
	2		0.4		D		10.35		14.87		5.35		12.63

工况	k₀/c	N_s
工况	k₀/c	B/H=1	Δ₇/%	B/H=100	Δ₈/%
自然工况 (r_u=0;k_h= k_v=0)	0	18.72	—	12.12	—
	1	21.32	13.89	17.81	46.95
	2	23.48	25.43	20.27	67.24
	3	25.64	36.97	22.01	81.60
	4	27.80	48.50	23.61	94.80
地震烈度 7度(r_u=0; k_h=k_v=0.1)	0	11.74	—	7.14	—
	1	13.66	16.35	9.26	29.69
	2	15.04	28.11	10.07	41.04
	3	16.42	39.86	10.70	49.86
	4	17.81	51.70	11.23	57.28
地震烈度 7度+孔隙水(r_u=0.2; k_h=k_v=0.1)	0	8.29	—	5.68	—
	1	9.38	13.15	7.45	31.16
	2	10.33	24.61	8.08	42.25
	3	11.28	36.07	8.52	50.00
	4	12.23	47.53	8.94	57.39

工况	k₀/c	B/H=10
工况	k₀/c	忽略q_ε	考虑q_ε	忽略q_ε	考虑q_ε
自然工况	0	31.56	—	49.94	—
	1	47.93	—	69.04	—
	2	57.67	—	84.99	—
	3	66.81	—	99.93	—
	4	73.47	—	112.7	—
烈度 7度+ 孔隙水 (r_u=0.1)	0	9.87	8.04	13.99	12.03
	1	14.52	10.91	16.38	14.32
	2	16.75	12.11	18.58	16.25
	3	18.03	12.94	20.79	18.17
	4	19.06	13.68	22.99	20.10