基于量纲分析法的钢筋混凝土柱体缩比模型的构建

doi:10.12382/bgxb.2023.0716

摘要/Abstract

摘要：

以典型钢筋混凝土柱体为主要研究对象,基于相似理论和量纲分析法推导爆炸加载下钢筋混凝土柱体的相似律关系,并使用有限元仿真软件LS-DYNA对不同比例缩比模型进行数值模拟,以验证相似律关系;通过量纲分析法得到相似律关系式,对柱体挠度进行等比例计算转化。相似律计算结果和数值模拟结果对比表明,柱中最大位移误差小于10%,表明新建立的相似律关系式精度满足工程应用,可以为后来学者研究爆炸加载下钢筋混凝土柱体的毁伤提供一定帮助。

关键词: 钢筋混凝土柱, 量纲分析法, 缩比模型, 爆炸载荷

Abstract:

Taking the typical reinforced concrete columns as the main research object, the similarity law relationship of reinforced concrete columns under explosive loading is derived based on similarity theory and dimensional analysis method. The different scaled models are established using the finite element simulation software LS-DYNA for numerical simulation to verify the similarity law relationship. The dimensional analysis method is used to obtain a relationship formula of similarity law, which can be used to calculate and convert the deflection of a column in an equal proportion; By comparing the calculated results of similarity law and the numerically simulated results, it is found that the error of maximum displacement in the column is less than 10%. This indicates that the accuracy of the established similarity law relationship satisfies engineering applications, which can provide some help for later scholars to study the damage of concrete columns under explosive loading of steel bars.

Key words: reinforced concrete column, dimensional analysis method, scaled model, explosive loading

中图分类号:

TJ413.2

王佳, 尹建平, 李旭东, 伊建亚, 王志军. 基于量纲分析法的钢筋混凝土柱体缩比模型的构建[J]. 兵工学报, 2023, 44(S1): 189-195.

WANG Jia, YIN Jianping, LI Xudong, YI Jianya, WANG Zhijun. Construction of Scaled Model of Reinforced Concrete Column Based on Dimensional Analysis[J]. Acta Armamentarii, 2023, 44(S1): 189-195.

图/表 18

图1 钢筋混凝土柱体毁伤示意图

Fig.1 Schematic diagram of damage to reinforced concrete columns

表1 毁伤模型中物理参量释义

Table 1 Explanation of physical parameters in the damage model

符号	单位	解释说明
W	J	炸药能量
r	cm	球形炸药的半径
L	m	炸药起爆点至钢筋混凝土柱体表面的最小距离
ρ	g/cm³	柱体密度
H	mm	柱体高度
a	mm	柱体的截面(正方形)边长
σ	MPa	柱体的屈服强度
E	MPa	柱体的杨氏模量
I	mm⁴	柱体的截面惯性矩
M₀	N·m	柱体的最大弯矩
b	mm²	柱体截面上,纵筋的总截面积
ξ	cm	柱中挠度

表2 物理量的量纲幂次指数

Table 2 Dimensional power exponents of physical quantities

量纲	ξ	L	W	r	ρ	H	a	σ	EI	M₀	b
M	0	0	1	0	1	0	0	1	1	1	0
L	1	1	2	1	-3	1	1	-1	3	2	2
T	0	0	-2	0	0	0	0	-2	-2	-2	0

表3 物理量的量纲幂次指数(排序后)

Table 3 Dimensional power exponents of physical quantities (sorted)

量纲	ρ	L	W	r	H	a	b	σ	EI	M₀	ξ
M	1	0	1	0	0	0	0	1	1	1	0
L	-3	1	2	1	1	1	2	-1	3	2	1
T	0	0	-2	0	0	0	0	-2	-2	-2	0

表4 物理量的量纲幂次指数(变换后)

Table 4 Dimensional power exponents of physical quantities (transformed)

参考物理量	ρ	L	W	r	H	a	b	σ	EI	M₀	ξ
ρ	1	0	0	0	0	0	0	0	0	0	0
L	0	1	0	1	1	1	2	-3	1	0	1
W	0	0	1	0	0	0	0	1	1	1	0

图2 仿真实验中柱中位移曲线

Fig.2 Displacement curves in the column in simulation experiment

图3 原模型配筋图

Fig.3 Reinforcement diagram of the original model

图4 原型的钢筋混凝土柱体网格模型

Fig.4 Grid model of prototype reinforced concrete column

表5 TNT的JWL状态方程参数

Table 5 Parameters of JWL equation of state for TNT

密度/(g·cm^-3)	爆速/(m·s^-1)	爆压/GPa	A/GPa
1.63	6930	21	373.8
B/GPa	R₁	R₂	ω
3.75	4.15	0.9	0.35

表6 空气模型参数

Table 6 Air model parameters

密度/(g·cm^-3)	内能/(J·m^-3)	截断压力/GPa	μ
1.63	6930	21	0
C₀、C₁、C₂、C₃、C₆		C₄、C₅
0		0.4

图5 1/2缩比模型配筋图

Fig.5 Reinforcement diagram of 1/2 scaled model

图6 1/2缩比模型的柱体网格模型

Fig.6 Cylinder grid model of 1/2 scaled,model

图7 1/4缩比模型配筋图

Fig.7 Reinforcement diagram of 1/4 scaled model

图8 1/4缩比模型的柱体网格模型

Fig.8 Cylinder grid model of 1/4 scaled model

图9 原模型柱中位移曲线

Fig.9 Displacement curves in the original model column

图10 1/2缩比模型柱中位移曲线图

Fig.10 Displacement curves in 1/2 scale model column

图11 1/4缩比模型柱中位移曲线图

Fig.11 Displacement curves of 1/4 scaled model column

表7 数据记录

Table 7 Data record

理论值、模拟值及相对误差	柱中最大位移/cm
理论值、模拟值及相对误差	原型	1/2缩比模型	1/4缩比模型
模拟值		0.665	0.275
理论值	1.2	0.6	0.3
相对误差/%		9.8	9.1

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