Dynamic Response of UHPFRC Beams with Different Strengths under Blast Loading

doi:10.12382/bgxb.2024.0390

Abstract

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

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-.

Figures/Tables 32

Fig.1 Test specimen construction

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%

Fig.2 Characteristics of steel reinforcement and steel fiber

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

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

Fig.3 Explosion experimental test system

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	-	-

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

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

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

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

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

Fig.9 Single element model

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

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

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

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

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

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

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

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

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

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

Fig.14 Local damage comparison of simulated and test results

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

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

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

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

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

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

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

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

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

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