@article{LI2026, 
author = {Haoyang LI and Li CHEN and Yonghai LIU},
title = {Boundary condition effects on failure of tempered glass subject to wind-borne debris impact and a quantification model for fragment distribution},
year = {2026},
journal = {Explosion and Shock Waves},
volume = {46},
number = {7},
keywords = {dimensional analysis, wind-borne debris, projectile impact, tempered glass, parametric influence, semi-empirical modeling},
url = {https://www.sciopen.com/article/10.11883/bzycj-2025-0220},
doi = {10.11883/bzycj-2025-0220},
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.}
}