爆炸载荷作用下不同强度超高性能混凝土梁毁伤效应

doi:10.12382/bgxb.2024.0390

摘要/Abstract

摘要：

以典型建筑目标构件爆炸防护为背景,研究了不同强度超高性能纤维混凝土(UHPFRC)梁爆炸载荷作用下的毁伤效应。开展UHPFRC梁爆炸毁伤实验,获得纤维含量和纵筋类型对UHPFRC梁破坏模式和动态响应的影响规律,实验结果表明,增加纤维含量和使用高强钢筋可提高UHPFRC梁的抗弯能力;为进一步拓展毁伤效应研究,构建了爆炸载荷作用下UHPFRC梁有限元模型,采用单元方法从三个强度面、状态方程、剪胀、损伤演化和应变率效应等方面改进了K&C本构模型参数,通过准静态实验表明,改进的本构模型参数可以更准确描述UHPFRC的力学性质,并基于爆炸实验数据验证了有限元模型的正确性;最后,通过参数分析研究了混凝土强度、钢筋类型和炸药药量对UHPFRC梁爆炸毁伤效应的影响规律。

关键词: 爆炸载荷, UHPFRC梁, 抗爆性能, K&C模型, 参数分析

Abstract:

The damage effects of ultra-high performance fiber reinforced concrete (UHPFRC) beams with different strengths subjected to blast loading are studied,with a focus on protecting typical architectural components from explosion.The influences of fiber content and longitudinal reinforcement type on the failure mode and dynamic response of UHPFRC beams are studied througth experiment.The results show that the increase in the fiber content and the use of high-strength steel (HSS) longitudinal reinforcement can improve the bending resistance of UHPFRC beams.A finite element model for UHPFRC beams under blast loading is developed to expand the research on damage effect.The parameters of the K&C constitutive model are calibrated using the single element test method,considering the factors like strength planes,equations of state,shear dilation,damage evolution,and strain rate effects.The quasi-static experiments demonstrate that the modified constitutive model parameters provide a more precise description of the mechanical characteristics of UHPFRC.Furthermore,the accuracy of the finite element model is also validated based on explosive experimental data.Finally,the influences of concrete strength,steel reinforcement type,and charge masses on the damage effects of UHPFRC beams at close range are further analyzed through parameter analysis.

Key words: blast loading, UHPFRC beam, blast resistance, K&C model, parameter analysis

张琪悦, 刘彦, 闫俊伯, 许迎亮, 王百川, 黄风雷. 爆炸载荷作用下不同强度超高性能混凝土梁毁伤效应[J]. 兵工学报, 2025, 46(2): 240390-.

ZHANG Qiyue, LIU Yan, YAN Junbo, XU Yingliang, WANG Baichuan, HUANG Fenglei. Dynamic Response of UHPFRC Beams with Different Strengths under Blast Loading[J]. Acta Armamentarii, 2025, 46(2): 240390-.

图/表 32

图1 试件构造

Fig.1 Test specimen construction

表1 实验工况

Table 1 Experimental conditions

试件	装药质量/kg	爆距/ m		比例距离/ (m·kg^-1/3)			纤维体积含量		钢筋类型
UHPFRC-ϕ16 NSS-1.0%	2.0	0.25		0.20			1.0%		NSS
UHPFRC-ϕ16 NSS-2.5%	2.0	0.25		0.20			2.5%		NSS
UHPFRC-ϕ16 HSS-2.1%	2.0		0.25		0.20	2.1%		HSS
UHPFRC-ϕ16 HSS-2.5%	2.5		0.25		0.18	2.5%
UHPFRC-ϕ16 HSS-2.5%						2.5%

图2 钢筋特性和钢纤维实物图

Fig.2 Characteristics of steel reinforcement and steel fiber

表2 钢筋力学参数

Table 2 Mechanical parameters of steel reinforcement

钢筋	屈服应变	屈服应力/MPa	极限应变	极限应力/MPa	断裂应变
ϕ16 NSS	0.0021	413	0.16	518	0.22
ϕ16 HSS	0.0031	617	0.15	793	0.167

表3 钢纤维的特性

Table 3 Characteristics of steel fibers

直径/mm	长度/mm	纵横比	密度/(g·cm^-3)	抗拉强度/MPa
0.2	13	65	7.8	2000

图3 爆炸实验测试装置

Fig.3 Explosion experimental test system

表4 实验总体结果

Table 4 Overall experimental results

试件	M/kg	h_m/m	Z/(m·kg^-1/3)	δ_max/mm	δ_res/mm	C_L/mm	C_H/mm	S_L/mm	S_H/mm
UHPFRC-ϕ16 NSS-1.0%	2.0	0.25	0.198	79.13	55.44	310	155	-	-
UHPFRC-ϕ16 NSS-2.5%	2.0	0.25	0.198	63.70	39.65	300	148	-	-
UHPFRC-ϕ16 HSS-2.1%	2.0	0.25	0.198	64.50	48.80	125	176	526	51
UHPFRC-ϕ16 HSS-2.5%	2.0	0.25	0.198	43.53	8.74	300	120	-	-
UHPFRC-ϕ16 HSS-2.5%	2.5	0.20	0.147	54.19	1.90	320	125	-	-

图4 不同纤维含量的UHPFRC梁跨中位移-时间曲线

Fig.4 Displacement-time curves of UHPFRC-beams with different fiber contents

图5 不同纤维含量的UHPFRC-ϕ16 NSS的损伤模式

Fig.5 Damage modes of UHPFRC-ϕ16NSS beams with different fiber contents

图6 不同纤维含量的UHPFRC-ϕ16 HSS的损伤模式

Fig.6 Damage modes of UHPFRC-ϕ16 HSS beams with different fiber contents

图7 NSS和HSS加固UHPFRC梁跨中位移-时间曲线

Fig.7 Displacement-time curves of UHPFRC beams strengthened with NSS and HSS

图8 NSS和HSS加固UHPFRC梁的损伤模式比较

Fig.8 Comparison of damage modes of UHPFRC beams strengthened with NSS and HSS

图9 单元模型

Fig.9 Single element model

表5 UHPFRC的EOS输入参数

Table 5 EOS input parameters of UHPFRC m-s-kg Pa

i	1	2	3	4	5	6	7	8	9	10
μ_i	0	-0.0053	-0.0101	-0.0305	-0.0513	-0.0726	-0.0943	-0.120	-0.174	-0.208
K_i/GPa	30	30	30.13	35.97	40.89	45.94	51.07	57.16	69	69
P_i/GPa	0	0.159	0.300	0.901	1.514	2.141	2.780	3.537	5.164	6.973

图10 损伤演化函数η(λ)的比较[4,38]

Fig.10 Comparison of damage evolution functions η(λ)[4,38]

表6 UHPFRC的K&C模型输入参数

Table 6 K&C model input parameters of 135MPa UHPFRC m-s kg Pa

参数	值	参数	值	参数	值	参数	值
RO/kg·m³	2470	UCF	1.45×10^-4	λ10	6.20×10^-4	η07	0.80
PR	0.23	LCRATE	1	λ11	9.00×10^-4	η08	0.60
FT/Pa	见表7	LOCWID/m	0.045	λ12	5.00×10^-3	η09	0.50
A0/Pa	0.19256f_c	NPTS	13	λ13	10	η10	0.40
A1	0.36	λ01	0	B3	1.15	η11	0.30
A2/Pa^-1	$0.157 f c$	λ02	4.40×10^-5	A0Y/Pa	0.1053f_c	η12	0.07
B1	0.55	λ03	7.00×10^-5	A1Y	0.23	η13	0
OMEGA	0.75	λ04	7.48×10^-5	η01	0	A2F/Pa^-1	$0.1024 f c$
A1F	0.42	λ05	9.50×10^-5	η02	0.85	A2Y/Pa^-1	$0.536 f c$
Sλ	100	λ06	1.20×10^-4	η03	0.98
NOUT	2	λ07	2.10×10^-4	η04	0.99
EDROP	1	λ08	3.40×10^-4	η05	1.00
RSIZE	39.37	λ09	4.56×10^-4	η06	0.98

表6 UHPFRC的K&C模型输入参数

Table 6 K&C model input parameters of 135MPa UHPFRC m-s kg Pa

参数	值	参数	值	参数	值	参数	值
RO/kg·m³	2470	UCF	1.45×10^-4	λ10	6.20×10^-4	η07	0.80
PR	0.23	LCRATE	1	λ11	9.00×10^-4	η08	0.60
FT/Pa	见表7	LOCWID/m	0.045	λ12	5.00×10^-3	η09	0.50
A0/Pa	0.19256f_c	NPTS	13	λ13	10	η10	0.40
A1	0.36	λ01	0	B3	1.15	η11	0.30
A2/Pa^-1	$0.157 f c$	λ02	4.40×10^-5	A0Y/Pa	0.1053f_c	η12	0.07
B1	0.55	λ03	7.00×10^-5	A1Y	0.23	η13	0
OMEGA	0.75	λ04	7.48×10^-5	η01	0	A2F/Pa^-1	$0.1024 f c$
A1F	0.42	λ05	9.50×10^-5	η02	0.85	A2Y/Pa^-1	$0.536 f c$
Sλ	100	λ06	1.20×10^-4	η03	0.98
NOUT	2	λ07	2.10×10^-4	η04	0.99
EDROP	1	λ08	3.40×10^-4	η05	1.00
RSIZE	39.37	λ09	4.56×10^-4	η06	0.98

图11 通过单元模型确定软化性参数b1和b2[4]

Fig.11 Determining the softening parameters b1 and b2 through single element model

图12 使用改进后的关键模型参数的K&C模型的UHPFRC应力-应变曲线[4]

Fig.12 UHPFRC stress-strain curves of K&C model using improved key model parameters

表7 不同强度UHPFRC的K&C模型输入的强度面参数和单轴抗拉强度

Table 7 K&C model input parameters and uniaxial tensile strengths.of UHPFRC beams with different strengths m-s-kg Pa

抗压强度/MPa	a₀	a₁	a₂	a_1f	a_2f	a_0y	a_1y	a_2y	FT
105	20.22	0.36	1.495×10^-3	0.42	9.752×10^-4	11.06	0.23	5.105×10^-3	7.00e6
121	23.30	0.36	1.298×10^-3	0.42	8.463×10^-4	12.74	0.23	4.430×10^-3	8.07e6
135	25.30	0.36	1.163×10^-3	0.42	7.585×10^-4	14.22	0.23	3.970×10^-3	9.00e6
150	28.88	0.36	1.047×10^-3	0.42	6.827×10^-4	15.80	0.23	3.573×10^-3	1.00e7
165	31.77	0.36	9.515×10^-4	0.42	6.206×10^-4	17.38	0.23	3.249×10^-3	1.10e7
180	34.66	0.36	8.722×10^-4	0.42	5.689×10^-4	18.95	0.23	2.978×10^-3	1.20e7
200	38.51	0.36	7.850×10^-4	0.42	5.12×10^-4	21.06	0.23	2.680×10^-3	1.33e7
220	42.36	0.36	7.136×10^-4	0.42	4.655×10^-4	23.17	0.23	2.436×10^-3	1.47e7

图13 钢筋混凝土梁近距离爆炸仿真模型

Fig.13 Simulation model for close range explosion of reinforced concrete beams

表8 TNT炸药的材料参数

Table 8 Material parameters of TNT explosives

ρ_e/(g·cm^-3)	D/(cm·μs^-1)	P_CJ/MPa	A/MPa	B/MPa	R₁	R₂	ω	e₀/MPa
1.63	6.93	0.21	3.712	0.03231	4.15	0.95	0.30	0.07

表9 空气的材料参数

Table 9 Material parameters of air

ρ_e/(g·cm^-3)	C₀	C₁	C₂	C₃	C₄	C₅	C₆	E₀/MPa
1.23	0	0	0	0	0	0.4	0.4	2.58×10^-6

图14 仿真与实验结果局部损伤对比

Fig.14 Local damage comparison of simulated and test results

图15 仿真与实验结果跨中位移对比

Fig.15 Comparison of simulated and experimental results of mid span displacement

表10 数值模拟与实验结果的最大位移偏差

Table 10 Maximum displacement deviation between numerical simulated and experimental results

梁	数值模拟最大位移/mm	实验最大位移/mm	偏差/ %
UHPFRC-ϕ16 NSS-2.5%	63.00	63.70	1.1
UHPFRC-ϕ16 NSS-1.0%	84.16	79.13	6.4
UHPFRC-ϕ16 HSS-2.5%	42.36	43.53	2.7
UHPFRC-ϕ16 HSS-2.1%	65.30	64.50	1.2

图16 不同药量下不同强度UHPFRC梁的最大位移

Fig.16 Maximum displacements of UHPFRC beams with different strengths under different dosages of explosives

图17 相同药量下不同强度UHPFRC梁的损伤模式

Fig.17 Damage modes of UHPFRC beams with different strengths under the same dosage of explosives

表11 50ms时间3kg TNT爆炸下,不同强度UHPFRC梁的损伤模式比较

Table 11 Comparison of damage modes of UHPFRC beams with different strengths under a 3kgTNT explosion at 50ms

梁	损伤区域直径/mm	损伤区域深度/mm
UHPFRC-ϕ16 NSS-105MPa	-	-
UHPFRC-ϕ16 NSS-121MPa	580	195
UHPFRC-ϕ16 NSS-135MPa	320	150
UHPFRC-ϕ16 NSS-150MPa	270	143
UHPFRC-ϕ16 NSS-180MPa	240	138

图18 不同类型钢筋应力-应变曲线[44]

Fig.18 Stress-strain curves of different types of steel bars[44]

图19 不同药量下不同钢筋类型UHPFRC梁的最大位移

Fig.19 Maximum displacements of UHPFRC beams with different steel reinforcement types under different dosages of explosives

表12 不同钢筋类型135MPa UHPFRC梁的损伤模式比较(50ms时间1.5kg TNT爆炸下)

Table 12 Comparison of damage modes of 135MPa UHPFRC beams with different steel reinforcement types under 1.5kg TNT explosion at 50ms

梁	损伤区域直径/mm	损伤区域深度/mm
UHPFRC-ϕ16 NSS-135MPa	190	83
UHPFRC-ϕ16 HSS-135MPa	180	48
UHPFRC-ϕ16 MMFX -135MPa	180	9

图20 相同药量下不同钢筋UHPFRC梁的损伤模式

Fig.20 Damage modes of UHPFRC beams with different steel bars under the same dosage of explosives

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