Resilience assessment and prediction of metro shield tunnels under explosive conditions

doi:10.16265/j.cnki.issn1003-3033.2026.04.0085

Abstract

Abstract:

To ensure the operational and structural safety of the subway system, an assessment of the resilience of metro shield tunnels under explosive loading was conducted. A resilience assessment framework and grading criteria for shield tunnels under blast loading were established, and a resilience prediction model was developed based on a backpropagation (BP) neural network with a three-input, five-hidden-layer, single-output architecture. This model and evaluation approach were applied in a case study on the Xi'an Metro Line 1 to assess and predict the tunnel's resilience. The results indicate that a shorter standoff distance, a higher explosive yield, and a higher number of explosions each accelerate the decline in the tunnel's resilience. The resilience exhibited the most pronounced drop after the first explosion; the subsequent rate of decline was relatively gradual until the fifth explosion, after which it increased significantly. After the fifth explosion, the tunnel entered a low-resilience state requiring prompt repairs to meet operational requirements, and by the seventh explosion, the resilience had fallen to an extremely low level that could no longer ensure operational safety. The resilience assessment framework and prediction model developed in this study can be used to assess the safety status of metro shield tunnels under repeated external explosions.

Key words: explosions effect, metro shield tunnels, resilience assessment, back propagation(BP) neural network, resilience prediction

CLC Number:

Wang Rui, Zhang Xun, Deng Xianghui, Wang Ping'an, Wang Xu, Zhang Wei. Resilience assessment and prediction of metro shield tunnels under explosive conditions[J]. China Safety Science Journal, 2026, 36(4): 123-131.

Figures/Tables 13

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指标名称	表达式	注释
直径变形	${q}_{1}\left(t\right)=\frac{{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}-\lambda \left(t\right)}{{\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}}$	λ_max为隧道结构允许的最大直径变形率,取为9‰;λ(t)为随时间隧道结构直径变形率
竖向位移	${q}_{2}\left(t\right)=\frac{{V}_{\mathrm{m}\mathrm{a}\mathrm{x}}-V\left(t\right)}{{V}_{\mathrm{m}\mathrm{a}\mathrm{x}}}$	V_max为隧道结构允许的最大竖向位移,取为20 mm;V(t)为随时间隧道结构竖向位移量
水平位移	${q}_{3}\left(t\right)=\frac{{H}_{\mathrm{m}\mathrm{a}\mathrm{x}}-H\left(t\right)}{{H}_{\mathrm{m}\mathrm{a}\mathrm{x}}}$	H_max为隧道结构允许的最大水平位移,取为20 mm;H(t)为随时间隧道结构水平位移
接缝张开量	${q}_{4}\left(t\right)=\frac{\mathrm{\Delta }{L}_{1\mathrm{m}\mathrm{a}\mathrm{x}}-\Delta {L}_{1}\left(t\right)}{2\mathrm{\Delta }{L}_{1\mathrm{m}\mathrm{a}\mathrm{x}}}+\frac{\mathrm{\Delta }{L}_{2\mathrm{m}\mathrm{a}\mathrm{x}}-\Delta {L}_{2}\left(t\right)}{2\mathrm{\Delta }{L}_{2\mathrm{m}\mathrm{a}\mathrm{x}}}$	ΔL_1max为隧道结构允许的最大纵缝张开量;ΔL_2max为隧道结构允许的最大环缝张开量,均取3 mm;ΔL₁(t)为随时间隧道结构纵缝张开量;ΔL₂(t)为随时间隧道结构环缝张开量
错台量	${q}_{5}\left(t\right)=\frac{\mathrm{\Delta }{S}_{1\mathrm{m}\mathrm{a}\mathrm{x}}-\Delta {S}_{1}\left(t\right)}{2\mathrm{\Delta }{S}_{1\mathrm{m}\mathrm{a}\mathrm{x}}}+\frac{\mathrm{\Delta }{S}_{2\mathrm{m}\mathrm{a}\mathrm{x}}-\Delta {S}_{2}\left(t\right)}{2\mathrm{\Delta }{S}_{2\mathrm{m}\mathrm{a}\mathrm{x}}}$	ΔS_1max为隧道结构允许的最大纵缝错台量;ΔS_2max为隧道结构允许的最大环缝错台量,均取10 mm;ΔS₁(t)为随时间隧道结构纵缝错台量;ΔS₂(t)为随时间隧道结构环缝错台量

管片	Z	经验公式预测值/MPa	数值模拟值/MPa	误差/ %
H1	0.2	23.508	21.206	-9.79
	0.4	3.494	3.169	-9.30
	0.6	1.146	1.041	-9.16
	0.8	0.519	0.468	-9.83
H2	0.2	23.508	21.351	-9.18
	0.4	3.494	3.189	-8.73
	0.6	1.146	1.037	-9.51
	0.8	0.519	0.472	-9.06
H3	0.2	23.508	21.428	-8.85
	0.4	3.494	3.291	-5.81
	0.6	1.146	1.248	8.90
	0.8	0.519	0.482	-7.13
H4	0.2	23.508	21.917	-6.77
	0.4	3.494	3.765	7.76
	0.6	1.146	1.206	5.24
	0.8	0.519	0.479	-7.71
H5	0.2	23.508	25.641	9.07
	0.4	3.494	3.798	8.70
	0.6	1.146	1.247	8.81
	0.8	0.519	0.533	2.70
H6	0.2	23.508	25.846	9.95
	0.4	3.494	3.822	9.39
	0.6	1.146	1.254	9.42
	0.8	0.519	0.566	9.06

爆炸次数	炸药当量/kg	管片编号
爆炸次数	炸药当量/kg	H1	H2	H3	H4	H5	H6
1	500	0.951(I)	0.952(I)	0.947(I)	0.947(I)	0.928(I)	0.937(I)
	1 000	0.942(I)	0.942(I)	0.931(I)	0.931(I)	0.907(I)	0.913(I)
	1 500	0.939(I)	0.939(I)	0.923(I)	0.908(I)	0.897(I)	0.902(I)
	2 000	0.941(I)	0.939(I)	0.921(I)	0.913(I)	0.903(I)	0.901(I)
	2 500	0.934(I)	0.928(I)	0.911(I)	0.902(I)	0.874(I)	0.881(I)
2	500	0.922(I)	0.921(I)	0.913(I)	0.914(I)	0.884(I)	0.895(I)
	1 000	0.910(I)	0.907(I)	0.889(I)	0.890(I)	0.852(I)	0.861(I)
	1 500	0.906(I)	0.904(I)	0.880(I)	0.856(I)	0.840(I)	0.847(I)
	2 000	0.909(I)	0.905(I)	0.878(I)	0.864(I)	0.852(I)	0.846(I)
	2 500	0.900(I)	0.887(I)	0.860(I)	0.845(I)	0.804(I)	0.813(I)
3	500	0.890(I)	0.887(I)	0.875(I)	0.876(I)	0.839(I)	0.848(I)
	1 000	0.875(I)	0.867(I)	0.844(I)	0.844(I)	0.797(Ⅱ)	0.804(I)
	1 500	0.870(I)	0.863(I)	0.834(I)	0.803(I)	0.782(Ⅱ)	0.787(Ⅱ)
	2 000	0.874(I)	0.863(I)	0.831(I)	0.811(I)	0.794(Ⅱ)	0.784(Ⅱ)
	2 500	0.863(I)	0.840(I)	0.805(I)	0.779(Ⅱ)	0.730(Ⅱ)	0.742(Ⅱ)
4	500	0.863(I)	0.857(I)	0.839(I)	0.839(I)	0.797(Ⅱ)	0.803(I)
	1 000	0.844(I)	0.830(I)	0.803(I)	0.799(Ⅱ)	0.745(Ⅱ)	0.751(Ⅱ)
	1 500	0.834(I)	0.822(I)	0.790(Ⅱ)	0.751(Ⅱ)	0.725(Ⅱ)	0.728(Ⅱ)
	2 000	0.833(I)	0.819(I)	0.785(Ⅱ)	0.757(Ⅱ)	0.733(Ⅱ)	0.720(Ⅱ)
	2 500	0.821(I)	0.790(Ⅱ)	0.748(Ⅱ)	0.714(Ⅱ)	0.660(Ⅱ)	0.670(Ⅱ)
5	500	0.837(I)	0.829(I)	0.806(I)	0.804(I)	0.757(Ⅱ)	0.760(Ⅱ)
	1 000	0.816(I)	0.797(Ⅱ)	0.764(Ⅱ)	0.756(Ⅱ)	0.695(Ⅱ)	0.701(Ⅱ)
	1 500	0.797(Ⅱ)	0.782(Ⅱ)	0.746(Ⅱ)	0.702(Ⅱ)	0.671(Ⅱ)	0.671(Ⅱ)
	2 000	0.789(Ⅱ)	0.774(Ⅱ)	0.738(Ⅱ)	0.704(Ⅱ)	0.670(Ⅱ)	0.655(Ⅱ)
	2 500	0.777(Ⅱ)	0.740(Ⅱ)	0.691(Ⅱ)	0.650(Ⅱ)	0.592(Ⅲ)	0.599(Ⅲ)

数据集	R²	MAE	MBE	RMSE
训练集	0.975 5	0.009 113 2	0.000 678 49	0.011 486
测试集	0.977 5	0.011 143	0.002 151 6	0.013 799

管片标号	爆炸次数	预测韧性	爆炸次数	预测韧性	爆炸次数	预测韧性
1	6	0.713	7	0.608	8	0.494
2	6	0.661	7	0.557	8	0.444
3	6	0.619	7	0.491	8	0.382
4	6	0.555	7	0.426	8	0.309
5	6	0.490	7	0.352	8	0.248
6	6	0.504	7	0.361	8	0.255