Effect of the air blast on glazing systems safety: structural analysis of window panel responses to air blast for mitigating the injuries from flying glass

Glass fragments are a prime source of injury to occupants of buildings subjected to an air blast event. Health and safety considerations and the principles of a reasonable degree of protection impose strict requirements on design engineers as well as on the building owners and managers. Since windows serve an important role in modern buildings design, balancing the safety requirements with physical appearance and cost-effectiveness is essential for the successful design and implementation of special security window systems. If the building might be exposed to air blast loadings, it is essential to enhance the safety and security; reduce the injuries and protect the occupants against the impacts caused by the generated glass shards or fragments. Therefore, it is necessary to have a better understanding of the mechanics of glass panel responses to different parameters of the glazing systems and the air blast characteristics. ❧ In this dissertation, the response of glazing systems subjected to air blast loadings is studied by application of an explicit finite element analysis in conjunction with fracture micromechanics principles. The window panel failure patterns and the glass crack propagation paths have been investigated and analyzed through the use of advanced finite element modeling techniques. The results of this research indicate that the response of window panels to blast loading cases is dependent upon the glazing material properties, window panel sizes, window framing and boundary conditions and the blast load intensities. ❧ These findings will eventually be helpful in developing more comprehensive flying glass injury models based on glass fragments (or shards) sizes, flying velocities and flying distances that enable the decision makers to use the appropriate structural, architectural and building perimeter choices to better address the threats facing the safety of the building occupants during an air blast event. ❧ In the first Chapter of this research, the resistance of glass panels to air blast loadings is studied and the finite element analysis results have been compared with those obtained using SDOF techniques. This comparison is mainly focused on the results for stresses, maximum reaction forces along the window panel edges and the mid-surface displacements. The scope of this comparison is also extended to modal analysis and the natural frequencies of oscillation for the first modes as well as determining the higher mode frequencies and the participation factors of each mode in different directions of the window glass motion. In the initial Chapter, glass panels are assumed to have elastic-perfectly plastic behavior. Therefore, the results of the analysis enable a better understanding of the nature of the window panel responses with respect to the studied parameters of the glazing system as well as the blast load characteristics. ❧ The second Chapter of this thesis is focused on developing a glass fracture model based on Griffith's brittle material failure model which is more compatible and more integrated with constructed finite element models. The proposed failure criterion is based on the concepts of the released strain energy and the stored surface energy at the time of crack formation or propagation. This leads to the definition of the ""Damage Index"" concept that addresses the failure time histories in the window panels. This model sets the foundations in Chapter 7 for finding the number of generated glass fragments and their flying velocities as well as the traveled distances of the shards in the air. This is crucial for developing a more comprehensive blast injury model. ❧ The existing retrofit techniques for blast resistant glazing that are discussed in Chapter 3, will help broaden the structural engineer's perspective with regards to the choice of the most efficient and cost-effective retrofit techniques, given the glazing system characteristics and the blast load intensities, in order to enhance the safety of the building occupants during an air blast. ❧ Introduction of the brittle failure principles and the yield line analysis method in Chapter 4 set the stage for predicting the crack propagation paths across the glass panels and the general failure paths of the glazing systems which include the glass panel material (annealed glass, fully tempered or laminated panels), window panel framing conditions (simply-supported or fixed-in-place) and the blast load intensities. ❧ In Chapter 5, the application of more advanced finite element techniques and the element removal method in modeling the brittle failure of the glazing systems make it possible to study and investigate the effect of glass panel sizes and aspect ratios on crack propagation paths and glazing system failure patterns for small, medium and large windows. Annealed, fully tempered and laminated glass panels for both conventional and fixed-in-place framing conditions subjected to small, medium and high-intensity air blasts are considered. Brittle failure fracture mechanics criteria are defined into the material properties. ❧ As the window panel response to blast loading cases is also dependent upon the glass imperfections, the type and location of glass defects across the window panel play a major role in determining the failure pattern of the glazing system. For this purpose, in Chapter 6, the failure of defective annealed and fully tempered conventional glass panels are modeled and investigated using explicit finite element analysis in conjunction with fracture micromechanics' principles. ❧ Finally, in the last Chapter, conventional simplified and empirical methods for evaluating glass fragmentation hazards are discussed and the findings are compared with those of the analytical calculations and the numerical simulation for the glass fragmentation problem: particularly the glass fragments (or shards) ejection velocities, flying distances and fragment sizes. Furthermore, the existing blast hazard mitigation standards and regulations are introduced and discussed in order to assess the hazard level of the proposed glazing systems used in this dissertation when submitted to different air blast loadings. The outcome of this Chapter will be used towards the development of a more comprehensive blast-resistant glazing injury model and design guidelines for security enhancement of glazing systems and safety improvement of building occupants during an air blast.

玻璃碎片是遭遇空气冲击波（air blast）事件的建筑内人员受伤的主要诱因。健康与安全考量及合理防护等级的原则，对设计工程师、建筑业主及管理者均提出了严苛要求。鉴于窗户在现代建筑设计中占据重要地位，平衡安全要求与外观美观性、成本效益，对于特种安全窗户系统的成功设计与落地至关重要。若建筑可能承受空气冲击波荷载，提升安全防护能力、降低人员受伤风险，保护建筑内人员免受玻璃碎片冲击危害，便显得尤为必要。因此，深入掌握玻璃面板对玻璃系统各类参数及空气冲击波特性的响应机理，实属必要。

❧ 本论文采用显式有限元分析（explicit finite element analysis）结合断裂细观力学（fracture micromechanics）原理，研究了空气冲击波荷载作用下玻璃系统的响应特性。通过先进有限元建模技术，对窗面板的失效模式与玻璃裂纹扩展路径开展了研究与分析。本研究结果表明，窗面板在冲击波荷载下的响应，取决于玻璃材料属性、窗面板尺寸、窗户框架及边界条件，以及冲击波荷载强度。

❧ 上述研究成果最终可助力开发基于玻璃碎片尺寸、飞行速度及飞行距离的更完善的玻璃飞溅损伤模型，辅助决策者选取合适的结构、建筑及建筑周边方案，以更好地应对空气冲击波事件中建筑内人员面临的安全威胁。

❧ 本研究的第一章围绕玻璃面板对空气冲击波荷载的抗荷载性能展开研究，并将有限元分析结果与单自由度（SDOF）技术的计算结果进行对比。该对比主要聚焦于应力、窗面板边缘最大反力及中面位移的计算结果。对比范围还拓展至模态分析，涵盖一阶振荡固有频率、高阶模态频率，以及各模态在窗玻璃运动不同方向上的参与因子。在本章开篇，假设玻璃面板呈现弹性-理想塑性行为，因此分析结果可帮助研究者更深入理解玻璃系统研究参数及冲击波荷载特性下的窗面板响应本质。

❧ 本论文第二章聚焦于开发基于格里菲斯（Griffith）脆性材料失效模型的玻璃断裂模型，该模型与已构建的有限元模型兼容性更强、集成度更高。所提出的失效准则基于裂纹形成或扩展时释放的应变能与储存的表面能的概念，由此定义了“损伤指数（Damage Index）”，用于描述窗面板的失效时程。该模型为第七章中计算玻璃碎片生成数量、飞行速度及碎片在空气中的飞行距离奠定了基础，这对于开发更完善的冲击波损伤模型至关重要。

❧ 第三章中讨论的抗冲击波玻璃现有加固技术，将帮助结构工程师拓宽视野，在已知玻璃系统特性与冲击波荷载强度的前提下，选择最高效且具成本效益的加固技术，以提升空气冲击波事件中建筑内人员的安全性。

❧ 第四章介绍脆性失效原理与屈服线分析法，为预测玻璃面板的裂纹扩展路径及玻璃系统的整体失效模式奠定基础，其中需考量的因素包括玻璃面板材料（退火玻璃（annealed glass）、全钢化玻璃（fully tempered glass）或夹层玻璃（laminated glass））、窗面板框架条件（简支（simply-supported）或固支（fixed-in-place））以及冲击波荷载强度。

❧ 第五章中，将更先进的有限元技术与单元删除法（element removal method）应用于玻璃系统脆性失效的建模，使得研究者能够探究玻璃面板尺寸与长宽比对小、中、大尺寸窗户的裂纹扩展路径及玻璃系统失效模式的影响。本章考虑了常规框架与固支框架条件下的退火玻璃、全钢化玻璃及夹层玻璃面板，分别承受低、中、高强度空气冲击波的场景，并将脆性断裂力学准则嵌入材料属性参数中。

❧ 由于窗面板对冲击波荷载的响应还受玻璃缺陷的影响，玻璃面板上缺陷的类型与位置，对确定玻璃系统的失效模式起着关键作用。为此，第六章采用显式有限元分析结合断裂细观力学原理，对存在缺陷的退火玻璃与全钢化常规玻璃面板的失效过程进行建模与研究。

❧ 最后，在最后一章中，本文讨论了用于评估玻璃碎片危害的现有简化方法与经验方法，并将研究结果与玻璃碎片问题的解析计算及数值模拟结果进行对比，尤其针对玻璃碎片的喷射速度、飞行距离及碎片尺寸。此外，本文还介绍并讨论了现有的冲击波危害缓解标准与法规，以评估本论文中所采用的玻璃系统在遭遇不同空气冲击波荷载时的危害等级。本章的研究成果将用于开发更完善的抗冲击波玻璃损伤模型及设计指南，以提升玻璃系统的防护能力，改善空气冲击波事件中建筑内人员的安全状况。