风致飞射物冲击下钢化玻璃破坏的边界条件效应及碎片分布量化模型

李昊洋; 陈力; 刘用海

doi:10.11883/bzycj-2025-0220

风致飞射物冲击下钢化玻璃破坏的边界条件效应及碎片分布量化模型

doi: 10.11883/bzycj-2025-0220

李昊洋^1,,
陈力^2, ,,
刘用海¹

1.
宁波建工建乐工程有限公司，浙江宁波 315020
2.
东南大学土木工程学院，江苏南京 214135

详细信息

作者简介:
李昊洋（1994－　），男，博士，工程师，lhy19940313@126.com

通讯作者:
陈　力（1982－　），男，博士，教授，博士生导师，li.chen@seu.edu.cn

中图分类号: O383
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- 被引次数: 0
出版历程
- 收稿日期: 2025-07-16
- 修回日期: 2025-12-18
- 网络出版日期: 2025-12-23
- 刊出日期: 2026-07-13

Boundary condition effects on failure of tempered glass subject to wind-borne debris impact and a quantification model for fragment distribution

LI Haoyang^1
,,
CHEN Li^{2
, ,},
LIU Yonghai¹

1.
Ningbo Jiangong Jianle Engineering Co., Ltd., Ningbo 315020, Zhejiang, China
2.
School of Civil Engineering, Southeast University, Nanjing 214135, Jiangsu, China

摘要

摘要: 针对老旧建筑单层钢化玻璃幕墙抗风致飞射物冲击的安全隐患，填补既有研究多聚焦夹层玻璃或爆炸荷载的空白，旨在量化风致飞射物冲击下单层钢化玻璃的破坏特征、碎片分布规律及参数耦合影响机制。通过系统设计混合正交冲击实验，综合考查冲击类型、冲击物质量、速度、角度、边界条件及玻璃厚度和正方形表面边长等7个关键因素对玻璃的破坏模式和碎片质量分布的影响。基于实验矩阵的极差分析与方差解析，量化揭示了各参数对玻璃破坏特征、冲击物速度衰减率及碎片质量分布特征的敏感性权重。依据量纲齐次原理与Π定理，构建了表征碎片质量分布规律的无量纲函数关系式框架。基于实验数据，通过正交距离回归迭代算法拟合确立半经验预测公式的参数取值，验证公式具有明确的物理意义与预测可靠性。结果表明：边界条件对玻璃破坏程度和碎片飞散起决定性作用（解释53.1%的大块碎片总质量变化、97.9%的破坏面积变化），明框支撑工况碎片质量最低（最优防飞散方案），隐框支撑冲击物动能衰减率最大但碎片量次之（最优抗冲击方案），点支撑工况下玻璃均完全破碎（高危工况）；冲击物的冲击角度、速度和玻璃表面边长对钢化玻璃的破坏响应也有显著影响。研究采用效应量分析(η²)方法量化各参数对破坏行为的敏感性权重，建立了钢化玻璃冲击破坏的参数影响层次体系。最终建立的预测公式能精准表征钢化玻璃破碎特征，为建筑围护系统抗风设计提供关键理论依据。
- 风致飞射物 /
- 冲击作用 /
- 钢化玻璃 /
- 影响程度 /
- 量纲分析 /
- 预测公式
Abstract: This study addressed critical safety concerns in wind-resistant design of building envelope systems, aiming to quantify secondary fragmentation effects and potential risks from tempered glass breakage under wind-borne debris impact. A systematic orthogonal experimental design was developed and implemented to comprehensively investigate the influence of seven key parameters on failure modes and fragment mass distribution. These parameters include impact type (point-to-surface and surface-to-surface), impactor mass (30 and 50 g), impact velocity (50, 100, and 150 m/s), impact angle (60°, 75°, and 90°), boundary conditions (exposed frame support, concealed frame support, and point fixing), glass thickness (6 and 8 mm), and glass square surface side length (110, 200, 290 mm). A single-stage light-gas gun was employed to reproduce wind-borne debris impact scenarios with a velocity measurement accuracy of ±5 m/s. Two high-speed cameras were used to record the dynamic response and crack propagation process of glass during impact, while an oscilloscope was utilized to collect strain data at the impact point and impact velocity. After each impact experiment, glass fragments were fully recovered from a predefined area encompassing the entire experiment chamber. This area was divided into nine zones, extending 20 mm from the impact surface and 70 mm from the non-impact surface of the glass specimen. Fragment mass distribution was then statistically analyzed with a collection efficiency exceeding 98%. Range analysis and analysis of variance (ANOVA) were performed on the experimental matrix to quantitatively reveal the relative influence of each parameter on glass fracture characteristics, impactor energy dissipation, and fragment mass distribution. To avoid overreliance on statistical significance derived solely on P-values, effect size analysis using partial Eta squared (η²) was innovatively incorporated to quantify the practical engineering significance of each parameter, complementing traditional variance analysis that relies solely on P-values. A normalized formulation characterizing fragment mass distribution was established based on the principle of dimensional homogeneity and Buckinghamʼs Π theorem. Parameter values for the semi-empirical prediction model were determined through an orthogonal distance regression iterative algorithm, which effectively accounts for errors in both independent and dependent variables. The hybrid normal distribution model was adopted to fit the fragment mass distribution data, with shape parameters fixed in accordance with boundary conditions and key parameters optimized to ensure engineering applicability. Results demonstrate that boundary conditions dominantly control glass fracture extent and fragment dispersion. Specially, exposed framing support yields the minimal fragment mass, corresponding to an optimal anti-scattering solution. The structural glazing support exhibiting the maximum kinetic energy attenuation alongside a moderate fragment quantities, and point fixing induces complete fragmentation, representing a high-risk scenario. Impact angle, glass dimensions, and velocity also exert significant influences on fragmentation behavior. The established parameter influence hierarchy for the impact failure of tempered glass, along with the semi-empirical predictive formula, accurately characterizes the fracture patterns of tempered glass. Parameters for exposed frame and concealed frame supports are both approximately unity, enabling their integration into a unifiedframed support system model. This research provided crucial theoretical foundations for wind-resistant design and reinforcementof building envelope systems, particularly for aging structures equipped with single-layer tempered glass curtain walls.
- wind-borne debris /
- projectile impact /
- tempered glass /
- parametric influence /
- dimensional analysis /
- semi-empirical modeling

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图 1 玻璃和冲击物的示意图

Figure 1. Schematic diagrams of glass and impactors

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图 2 碎片区域划分和实验装置

Figure 2. Fragment collection area division and experimental apparatus

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图 3 不同边界条件下钢化玻璃冲击破坏过程

Figure 3. Impact damage processes of tempered glass under different boundary conditions

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图 4 碎片质量分布

Figure 4. Fragment mass distribution

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图 5 实验结果与拟合结果比较

Figure 5. Comparison of experimental results and fitted results

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表 1 实验方案

Table 1. Experimental schemes

实验编号	冲击类型	冲击物质量/g	冲击速度/(m·s⁻¹)	玻璃尺寸/mm		冲击角度/(°)	边界条件	空白列
实验编号	冲击类型	冲击物质量/g	冲击速度/(m·s⁻¹)	厚度	表面边长	冲击角度/(°)	边界条件	空白列
1	点vs面	30	50	6	110	90	明框	1
2	点vs面	30	100	8	290	60	隐框	2
3	点vs面	50	50	8	290	75	点支撑	3
4	点vs面	50	150	6	200	60	明框	1
5	点vs面	50	100	6	110	90	隐框	2
6	点vs面	50	150	8	200	75	点支撑	3
7	点vs面	30	50	6	200	60	点支撑	1
8	点vs面	30	150	6	290	75	隐框	2
9	面vs面	50	100	8	200	75	明框	3
10	点vs面	50	150	8	110	90	隐框	1
11	面vs面	50	50	8	110	90	明框	2
12	面vs面	50	100	6	290	60	点支撑	3
13	面vs面	30	100	6	200	75	明框	1
14	面vs面	30	150	8	110	90	点支撑	2
15	面vs面	30	50	8	290	60	隐框	3
16	面vs面	30	100	6	110	90	点支撑	1
17	面vs面	30	50	8	200	75	隐框	2
18	面vs面	50	150	6	290	60	明框	3

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表 2 实验结果

Table 2. Experimental results

实验编号	大块碎片总质量/g	冲击物速度衰减率/%	破坏面积百分比/%	最远区域碎片总质量/g	冲击点最大主应变/10⁻⁶
1	15.25	8.50	16.22	3.44	−2.52
2	0.99	20.45	0.31	1.12	−2.66
3	1515.19	11.27	100	25.80	−3.24
4	35.11	14.86	7.55	3.29	−3.20
5	47.56	27.37	25.52	2.28	−3.85
6	714.99	12.72	100	13.05	−7.14
7	545.32	13.35	100	37.02	−1.81
8	0.80	16.43	0.21	0.48	−9.99
9	24.37	10.44	5.40	5.06	−5.90
10	3.99	13.81	1.54	1.94	−2.98
11	35.35	15.47	19.63	5.09	−3.96
12	875.97	8.78	100	55.94	−4.30
13	5.63	16.65	2.31	3.57	−8.38
14	135.18	20.20	100	4.02	−4.85
15	44.87	9.84	3.43	20.37	−3.35
16	107.51	13.84	100	7.51	−10.70
17	57.79	33.57	8.80	20.50	−3.21
18	25.85	12.10	3.03	5.61	−7.87

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表 3 折算后极差$R' $

Table 3. Reduced range $R' $

项目	冲击类型	冲击物质量	冲击速度	玻璃尺寸		冲击角度	边界条件
项目	冲击类型	冲击物质量	冲击速度	厚度	表面边长	冲击角度	边界条件
最大主应变	3.58	1.19	3.81	3.63	0.54	3.11	1.27
大块碎片总质量	370.78	559.73	275.52	206.78	449.8	419.04	796.64
最远区域碎片总质量	9.29	4.74	17.8	5.25	18.05	21.03	24.9
破坏面积百分比	2.07	7.43	7.59	3.72	11.87	10.32	118.92
冲击物速度衰减率	0.5	6.16	1.57	3.76	4.82	4.61	9.22

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表 4 各影响因素各水平下4个响应指标的统计结果（均值±标准差）

Table 4. Statistical results (mean ± standard deviation) of the four response variables across different levels of each factor

项目	水平	样本量	大块碎片总质量/g	破坏面积百分比/%	最远区域碎片总质量/g	冲击物速度衰减率/%
冲击类型	点vs面	9	319.91±522.86	39.60±44.74	9.82±12.44	15.42±5.58
冲击类型	面vs面	9	145.84±276.96	38.08±46.31	14.19±16.72	15.65±7.64
冲击物质量/g	30	9	101.48±173.26	36.92±46.47	11.23±13.28	16.98±7.92
冲击物质量/g	50	9	364.26±546.14	40.76±44.68	12.78±16.07	14.09±4.41
冲击速度/(m·s⁻¹)	50	6	368.96±597.20	28.18±36.54	16.20±13.47	15.33±8.41
	100	6	177.01±344.62	32.51±41.36	11.83±19.47	16.26±6.57
	150	6	152.65±279.84	52.12±50.05	6.77±4.44	15.02±2.71
玻璃厚度/mm	6	9	184.33±311.23	46.43±46.82	13.52±16.64	14.65±5.13
玻璃厚度/mm	8	9	281.41±514.76	31.25±43.26	10.49±10.60	16.42±7.16
玻璃表面边长/mm	110	6	57.47±52.48	39.77±44.12	4.30±2.35	16.53±6.31
	200	6	230.54±314.62	37.29±44.08	13.75±13.46	16.93±7.69
	290	6	410.61±641.00	40.79±48.74	17.18±18.85	13.15±4.64
冲击角度/(°)	90	6	57.47±52.48	39.77±44.12	4.30±2.35	16.53±6.31
	75	6	386.46±618.84	27.12±38.98	13.47±11.86	16.85±7.78
	60	6	254.69±368.66	52.03±46.34	19.80±19.87	13.23±4.37
边界条件	明框	6	23.59±11.57	9.02±8.55	4.34±1.12	13.00±2.86
	隐框	6	26.00±26.75	6.64±10.21	7.78±9.20	20.25±8.44
	点支撑	6	649.03±524.30	100.00±0.00	23.85±19.45	13.36±3.86

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表 5 最优水平对应的工况

Table 5. Optimal levels corresponding to operating conditions

最优水平	冲击类型	冲击物质量/g	冲击速度/(m·s⁻¹)	玻璃尺寸/mm		冲击角度/(°)	边界条件
最优水平	冲击类型	冲击物质量/g	冲击速度/(m·s⁻¹)	厚度	表面边长	冲击角度/(°)	边界条件
大块碎片总质量最少	面vs面	30	150	6	110	90	明框
玻璃破坏面积百分比最小	面vs面	30	50	8	200	75	隐框
最远区域碎片总质量最少	点vs面	30	150	8	110	90	明框
冲击物速度衰减率最大	面vs面	30	100	8	200	75	隐框

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表 6 各影响因素的显著性

Table 6. Significances of influencing factors

项目	P
项目	冲击类型	冲击物质量	冲击速度	玻璃厚度	玻璃表面边长	冲击角度	边界条件
大块碎片总质量	0.391	0.188	0.642	0.635	0.360	0.410	0.003
冲击物速度衰减率	0.941	0.360	0.949	0.580	0.568	0.593	0.086
破坏面积百分比	0.965	0.876	0.977	0.938	0.942	0.947	1.0×10⁻⁴
最远区域碎片总质量	0.551	0.762	0.281	0.737	0.255	0.159	0.041
最大主应变	0.194	0.674	0.08	0.188	0.966	0.302	0.788

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表 7 不同影响因素的效应量

Table 7. Effect sizes of different influencing factors

项目	偏η²/%
项目	冲击类型	冲击物质量	冲击速度	玻璃厚度	玻璃表面边长	冲击角度	边界条件
大块碎片总质量	4.6（小）	10.6（中）	5.7（小）	1.4（小）	12.7（中）	11.2（中）	53.1（大）
冲击物速度衰减率	0（无）	5.3（小）	0.7（无）	2.0（小）	7.3（中）	6.7（中）	27.9（大）
破坏面积百分比	0（无）	0.2（无）	0.3（无）	0（无）	0.8（无）	0.7（无）	97.9（大）
最远区域碎片总质量	2.3（小）	0.6（无）	15.6（大）	0.7（无）	16.7（大）	21.7（大）	34.6（大）
最大主应变	10.3（中）	1.1（小）	28.6（大）	10.6（中）	0.5（无）	14.8（大）	3.1（小）

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表 8 影响因素对碎片质量分布的效应量

Table 8. Effect size of influencing factors on debris mass distribution

碎片区域	偏η²/%
碎片区域	冲击类型	冲击物质量	冲击速度	玻璃厚度	玻璃表面边长	冲击角度	边界条件
①	1.0	11.3	1.5	0.1	10.9	6.6	62.5
②	1.3	11.3	1.9	0.1	11.3	6.7	61.5
③	4.3	12.5	4.6	3.6	13.5	12.3	40.6
④	6.0	8.3	10.4	2.4	13.7	10.9	34.6
⑤	3.5	12.2	6.5	2.6	16.5	10.8	31.9
⑥	2.7	16.1	0.7	2.0	11.7	13.4	48.9
⑦	6.2	5.3	7.1	0.3	14.8	14.0	58.4
⑧	0.7	0.4	17.3	0.8	16.4	22.1	37.6
⑨	2.3	0.6	15.6	0.7	16.7	21.7	34.6

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表 9 碎片质量分布中相关物理量及其单位和量纲

Table 9. Parameters, unit and dimensions related to fragments mass distribution

对象	物理量	符号	单位	量纲
碎片	质量	m	kg	M
碎片	碎片飞散距离	L	m	L
冲击物	冲击类型	T_i	1	DQ
	冲击物质量	m_i	kg	M
	冲击速度	v	m/s	LT⁻¹
	冲击角度	θ	°	DQ
空气	初始压力	p_a	kg/(m·s²)	ML⁻¹T⁻²
	空气密度	ρ_a	kg/m³	ML⁻³
	运动黏度	ν_a	m²/s	L²T⁻¹
	绝热指数	γ_a	1	DQ
玻璃	密度	ρ_g	kg/m³	ML⁻³
	厚度	d_g	m	L
	长度	l	m	L
	宽度	w	m	L
	杨氏模量	E	kg/(m·s²)	ML⁻¹T⁻²
	泊松比	ν	1	DQ
	屈服强度	γ	kg/(m·s²)	ML⁻¹T⁻²
	抗拉强度	S	kg/(m·s²)	ML⁻¹T⁻²
	边界条件	B_c	m²	L²

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表 10 实验参数

Table 10. Experimental parameters

实验编号	m_i/g	θ/(°)	B_c/mm²	v/(m·s⁻¹)	l/mm	L_p1/mm	L_p2/mm
1	30	90	8000	50	110	5	35
2	30	60	11200	100	290	−5	55
3	50	75	138	50	290	−5	35
4	50	60	15200	150	200	−5	35
5	50	90	4000	100	110	−5	35
6	50	75	138	150	200	−5	35
7	30	60	138	50	200	−5	35
8	30	75	11200	150	290	−5	35
9	50	75	15200	100	200	−5	35
10	50	90	4000	150	110	−5	45
11	50	90	8000	50	110	−5	35
12	50	60	138	100	290	−5	25
13	30	75	15200	100	200	−5	55
14	30	90	138	150	110	−5	25
15	30	60	11200	50	290	−5	55
16	30	90	138	100	110	−5	45
17	30	75	7600	50	200	−5	55
18	50	60	2240	150	290	−5	35

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表 11 部分参数取值

Table 11. Partial parameter values

边界条件	a	c	e	f	g
明框	−0.15	2.3	0.07	−0.05	2.5
隐框	0.68	2.9	0.2	0.06	2.5
点支撑	0.76	2.5	0.3	0.09	2.5

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表 12 $b $和$d $的取值、决定系数$R^2 $和权重因子${\pi} $

Table 12. Parameter values (b, d), determination coefficient (R²) and weight factor π

支撑条件	实验编号	b	d	R²	π
明框	1	0.42013	0.26194	0.99521	0.31
	4	0.40986	0.26303	0.99493	0.278
	9	0.39813	0.26186	0.99145	0.36
	11	0.38804	0.24603	0.98352	0.42
	13	0.46035	0.29631	0.99447	0.28
	18	0.39785	0.26591	0.99259	0.4
隐框	2	2.234	0.7248	0.99995	0.08
	5	0.23	0.35	0.99064	0.87
	8	2.0125	0.7361	0.98542	0.11
	10	1.9542	0.7248	0.9991	0.13
	15	2.0682	0.7329	0.94719	0.04
	17	2.1609	0.6835	0.93524	0.05
点支撑	3	−0.05301	0.0935	0.94322	0.837
	6	−0.05109	0.10964	0.95684	0.64
	7	−0.0669	0.1541	0.84013	0.67
	12	−0.06393	0.1138	0.81784	0.76
	14	−0.05679	0.1353	0.98469	0.87
	16	−0.0509	0.10541	0.96742	0.84

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