Security risks and probabilistic risk assessment of glazing subject to explosive blast loading

A probabilistic risk assessment (PRA) procedure is developed which can predict risks of explosive blast damage to built infrastructure. The present paper focuses on window glazing since this is a load-capacity system which, when subject to blast loading, has caused significant damage and injury to building occupants. Structural reliability techniques are used to derive fragility and blast reliability curves (BRCs) for annealed and toughened glazing subjected to explosive blast, for a variety of threat scenarios. The probabilistic analyses include the uncertainties associated with blast modelling, glazing response and glazing failure criteria. Damage risks are calculated for an individual window and for windows in the facade of a multi-storey commercial building. If threat probabilities can be estimated then the paper shows illustrative examples of how this information, when combined with risk-based decision-making criteria, can be used to optimise risk mitigation strategies.     

Damage prediction of concrete gravity dams subjected to underwater explosion shock loading

The damage prediction of concrete gravity dams under blast loads has gained importance in recent years due to the great number of accidental events and terrorist bombing attacks that affected engineering safety. It has long been known that an underwater explosion can cause significantly more damage to the targets in water than the same amount of explosive in air. While the physical processes during an underwater explosion and the subsequent response of structures are extremely complex, which involve lots of complex issues such as the explosion, shock wave propagation, shock wave-structure interaction and structural response. Hence a sophisticated numerical model for the loading and material responses would be required to enable more realistic reproduction of the underlying physical processes. In this paper, a fully coupled numerical approach with combined Lagrangian and Eulerian methods, incorporating the explosion processes, is performed. The RHT (Riedel–Hiermaier–Thoma) model including the strain rate effect is employed to model the concrete material behavior subjected to blast loading. Detailed numerical simulation and analysis of a typical concrete gravity dam subjected to underwater explosion are presented in this study. In terms of different TNT charge weights, the structural response and damage characteristics of the dam at different standoff distances are investigated. Based on the numerical results, critical curves related to different damage levels are derived.     

Response of laminated architectural glazing subjected to blast loading

Solutions based on the classical small deflection and large deflection plate theories are presented for a rectangular laminated architectural glazing subjected simulated blast loading. The results of the analytical models are compared with a three-dimensional nonlinear dynamic finite element analysis. Most of the recent studies have emphasized the effect of the positive phase of blast loading while determining the structural response. This study shows that for certain laminated glass panel configurations, the negative phase of a blast loading has a significant effect on the dynamic response. In particular, mid-span panel deflection and maximum tensile stress due to negative pressure are almost double the corresponding quantities due to positive blast loading phase. This means that if the glazing does not fail in the positive loading duration, it may do so in the negative loading phase because of higher dynamic stresses during this later phase.     

Model validation and parametric study on the blast response of unreinforced brick masonry walls

Numerical simulations are carried out to estimate the response and damage of unreinforced brick masonry walls subjected to explosive blast loading based on the transient dynamic finite element program LS-DYNA. A previously developed dynamic plastic damage model was used for brick and mortar. A new model for strain rate effects of bricks and mortar is included in the numerical analysis. The results obtained from the numerical models are compared with field test data and good agreement can be found. Parametric studies are conducted to evaluate the effect of material strength, boundary conditions, and thickness of the wall on the blast response of unreinforced brick masonry walls. It was found that boundary conditions and wall thickness significantly affect the blast response, while the effect of material strength is relatively small.     

Establishing a predictive method for blast induced masonry debris distribution using experimental and numerical methods

When subjected to blast loading, fragments ejected by concrete or masonry structures present a number of potential hazards. Airborne fragments pose a high risk of injury and secondary damage, with the resulting debris field causing major obstructions. The capability to predict the spatial distribution of debris of any structure as a function of parameterised blast loads will offer vital assistance to both emergency response and search and rescue operations and aid improvement of preventative measures. This paper proposes a new method to predict the debris distribution produced by masonry structures which are impacted by blast. It is proposed that describing structural geometry as an array of simple modular panels, the overall debris distribution can be predicted based on the distribution of each individual panel. Two experimental trials using 41 kg TNT equivalent charges, which subjected a total of nine small masonry structures to blast loading, were used to benchmark a computational modelling routine using the Applied Element Method (AEM). The computational spatial distribution presented good agreement with the experimental trials, closely matching breakage patterns, initial fragmentation and ground impact fragmentation. The collapse mechanisms were unpredictable due to the relatively low transmitted impulse; however, the debris distributions produced by AEM models with matching collapse mechanisms showed good agreement with the experimental trials.     

Predicting the effectiveness of blast wall barriers using neural networks

Blast damage assessment of buildings and structural elements requires an accurate prediction of the blast loads in terms of the peak pressures and impulses. Blast loadings on structures have typically been evaluated using empirical relationships. These relationships assume that there are no obstacles between the explosive device and the target. If a blast barrier is used to protect personnel or a structure behind it, the actual blast loading environment will be significantly reduced for some distance behind the barrier. This paper is concerned with an accurate prediction of the area of effectiveness behind the barrier using experimental data and a neural network-based model. To train and validate the neural network, a database is developed through a series of measurements of the blast environment behind the barrier. The principal parameters controlling the blast environment, such as wall height, distance behind the wall, height above ground, and standoff distance are used as the training input data. Peak overpressure and peak scaled impulse are used as the outputs in the neural network configuration. The trained and validated neural network is used to develop contour plots of overpressure and impulse adjustment factors to simplify the process of predicting the effectiveness of blast barriers. The developed model is also deployed in a stand-alone application that is used as a fast-running predictive tool for the blast overpressures and impulses behind the wall.     

Numerical prediction of concrete slab response to blast loading

In this paper, a dynamic plastic damage model for concrete material has been employed to estimate responses of both an ordinary reinforced concrete slab and a high strength steel fibre concrete slab subjected to blast loading. In the concrete material model, the strength envelope is a damage-based modified piece-wise Drucker–Prager model; the strain rate effect on tension and compression are considered separately; the damage variable is based on Mazars’ damage model, which is a combination of tensile and compressive damage. The equation of state (EOS) is also a combination of the porous and solid EOS of concrete with different forms for tension and compression states. The interaction between the blast wave and the concrete slab is considered in the 3D simulation. In the first stage, the initial detonation and blast wave propagation is modelled in a 2D simulation before the blast wave reaches the concrete slab, then the results obtained from the 2D calculation are remapped to a 3D model. The calculated blast load is compared with that obtained from TM5-1300. The numerical results of the concrete slab response are compared with the explosive tests carried out in the Weapons System Division, Defence Science and Technology Organisation, Department of Defence, Australia. Repetitive applications of blast loading on slabs are also simulated and the results compared with test data.     

基于时间序列分析的结构损伤识别

针对如何从结构响应信息中提取结构损伤指标的问题,提出了一种基于时间序列分析的结构损伤识别方法。对结构响应数据进行预处理,利用完好工况下的结构响应数据作为参考数据,建立自回归(Auto regression-AR)预测参考模型。利用已建立的AR预测参考模型计算待识别工况的残差,将待识别工况的残差与AR预测参考模型的残差的方差之比作为损伤指标,对结构损伤进行识别;通过算例表明:该损伤指标不仅可以判断结构是否发生损伤,而且可以识别结构的损伤位置。     

冲击波作用下巷道破坏规律相似模拟研究

利用爆炸加载的方式,采用相似材料模拟试验方法,借助数字散斑观测手段(DSCM),研究不同炮孔位置和装药量条件下巷道变形破坏规律。试验结果表明,微量炸药引爆后,冲击应力波以巷道方向传递为主,巷道顶板附近形成裂纹、破碎或坍塌区;当装药量足够大时,冲击波对上部岩体破坏力明显增大,冲击能是影响巷道破坏程度的主要因素。试验结果还表明,高速冲击载荷作用下巷道围岩体破坏过程可分为拉剪裂缝、重复拉剪破碎和破坏三个阶段。其中,当炮孔距离巷道为450mm,装药量为6.0g时,巷道顶板附近出现裂缝,属于拉剪裂缝阶段;当炮孔距离巷道为300mm,装药量为6.0g时,巷道顶板附近裂缝较为发育,且巷道顶层出现部分塌落,属于重复拉剪破坏阶段;当炮孔距离巷道为200mm,装药量为8.0g时,巷道顶板出现塌落,且四周破坏,属于破坏阶段。研究结果为冲击地压巷道破坏预测和防治提供了有力参考。     

Data-driven probabilistic quantification and assessment of the prediction error model in damage detection applications

Advances in computer hardware and sensor technologies have led to a surge in the use of data-driven modeling and machine learning for structural engineering applications, with Structural Health Monitoring (SHM) being one of them. Despite considerable interest, it remains a research topic due to the difficulty in accurately quantifying aleatoric and epistemic uncertainty in SHM systems. Sources of uncertainty are related to operational and environmental variability, as well as measurement noise and the model prediction error associated with the data used to train damage identification algorithms. In this work, the authors aim to explicitly quantify the statistical structure of model prediction error and assess its influence on the detection performance of strain-based SHM architectures under the existence of aleatoric variability. A structural beam, subjected to probabilistic static loading is used as the reference structure and strain measurements as the damage-sensitive features. Model prediction error is quantified explicitly using robust statistical tools through available laboratory observations and synthetic (Finite Element) data. Monte Carlo simulations enabled the forward propagation of uncertainty to the feature space to generate training data for three binary detectors (Likelihood Ratio Test, Quadratic Discriminant Analysis and Mahalanobis Distance), based on statistical pattern recognition. Detection performance was compared between the explicitly quantified prediction model error and the commonly assumed white Gaussian noise model, showcasing the influence of systematic error (bias) and correlation on the robustness of an SHM system using real-world data.     

基于蜂窝材料结构相似有限元模型的夹层结构抗爆炸冲击特性优化设计分析

根据蜂窝材料压缩力学理论,提出了一种蜂窝材料的结构相似有限元模型构建方法,并在蜂窝材料轴向压缩和夹层结构抗爆炸冲击2种分析工况下对结构相似模型计算分析的等效性进行了验证。结果表明,蜂窝材料的结构相似有限元模型不仅能够描述原蜂窝材料的宏观压缩力学特性,而且可以大幅地提高模型计算效率,为蜂窝材料夹层结构的抗爆炸冲击特性分析与设计优化提供条件。基于该结构相似有限元模型,以最小化蜂窝材料夹层结构的面密度为设计目标,利用自适应响应面方法对夹层结构的主要设计参数进行了优化,在结构的爆炸冲击响应速度峰值不增大的条件下提高了结构的轻量化水平。     

外接触爆炸荷载作用下大口径钢管变形与破坏效应的数值模拟

摘 要：基于动力有限元程序LS-DYNA及Lagrangian-Eulerian耦合方法,对大口径钢管在凝聚态炸药外接触爆炸载荷作用下的非线性动态响应过程进行数值模拟,描述了管道的变形情况、破坏过程以及管道内部应力的发展过程,分析了炸药质量、管道壁厚等因素对钢管破坏效应的影响。并在相同的条件下进行了实验研究,计算结果与实验数据具有较好的一致性。研究表明,小质量炸药爆炸后在装药与钢管接触处产生凹坑、鼓包及层裂等破坏效应;而较大质量炸药爆炸后在其爆破部位发生剪切破坏产生类似弹丸的破片,破片具有较大的动能,能够击穿另一侧管壁。研究结果可应用于管道结构在接触爆炸作用下的毁伤或防护方面的预测,从而为管道的安全防护设计提供理论依据。     

Dynamic response of cylindrical explosive chambers to internal blast loading produced by a concentrated charge

The structural dynamic behaviour of cylindrical explosive chambers to internal blast loading produced by concentrated explosive charges is studied. Special attention is given to the formation and development of dynamic strain growth and the factors which affect it in the dynamic loading of explosive chambers. Theoretical treatment of the strain growth and strain growth factor is given for the first time. It is pointed out that the superposition and interaction of different modes of response with similar frequencies is regarded as the mechanism of strain growth and that the geometry of the chamber is the crucial aspect controlling the degree of strain growth. In the theoretical analysis, the shell equations which consider transverse shear and rotatory inertia are adopted. Two test vessels with length to diameter ratios of 1 and 2, respectively, are used in loading experiments with three different amounts of explosive charge. The experimental data and theoretical computations are compared and show very good agreement, confirming that the method proposed in this paper can be applied to estimate the strength of cylindrical explosive chambers subjected to internal dynamic loading.     

不确定爆炸荷载作用下钢梁的可靠度分析

通过对已有爆炸荷载预测公式、计算图表和试验的海量数据的统计分析,建立了作用于建筑结构上爆炸荷载的统计模型;以典型钢梁为研究对象,考虑材料强度和构件尺寸的不确定性,基于单自由度体系理论和蒙特卡洛方法,建立了不确定爆炸荷载作用下钢梁失效概率的计算方法,并开发了实用计算程序;分析了炸药质量以及爆炸荷载和结构材料属性的不确定性等对钢梁失效概率的影响。研究表明:炸药质量和比例距离是影响爆炸荷载作用下钢梁失效概率的重要因素,在建筑结构抗爆分析中,必须考虑爆炸荷载的不确定性。     

RC beams under blast load: Reliability and sensitivity analysis

The effects of blast loading on structures can be very dangerous: damages and failures are expected with serious threats to structural safety and human life. Materials stresses and strains are often pushed to the limit and the modelling of these phenomena can be very complex. In order to design blast-resistant structures it is very important to determine what are the key parameters of this problem.This paper presents a reliability and parametric analysis of the response of reinforced concrete (RC) beams under blast loads. The main aim is to highlight the key parameters of the problem in order to produce information useful for the design of reliable blast-resistant RC structures.The beam has been idealised as an equivalent SDOF system, in which strain-rate effects are accounted for. This approach is convenient from a computational point of view and it has been validated by a direct comparison with a more sophisticated finite element model and with experimental results found in literature. Then a sensitivity analysis of the parameters involved in beam response under blast load has been developed. Slenderness (which has a direct effect on stiffness) and peak load prove to be the most important parameters, but span length (which has an important influence on the mass) is also a key parameter. Other variables such as concrete strength and reinforcement ratio do not seem to have a strong correlation with the beam response.     

Experimental study and numerical simulation of the damage mode of a square reinforced concrete slab under close-in explosion

Terrorist attacks using improvised explosive devices on reinforced concrete buildings generate a rapid release of energy in the form of shock waves. Therefore, analyzing the damage mode and damage mechanism of structures for different blast loadings is important. The current study investigates the behavior of one-way square reinforced concrete (RC) slabs subjected to a blast load through experiments and numerical simulations. The experiments are conducted using four 1000 mm × 1000 mm × 40 mm slabs under close-in blast loading. The blast loads are generated by the detonations of 0.2–0.55 kg trinitrotoluene explosive located at a 0.4 m standoff above the slabs. Different damage levels and modes are observed. Numerical simulation studies of the concrete damage under various blast loadings are also conducted. A three-dimensional solid model, including explosive, air, and RC slab with separated concrete and reinforcing bars, is created to simulate the experiments. The sophisticated concrete and reinforcing bar material models, considering the strain rate effects and the appropriate coupling at the air–solid interface, are applied to simulate the dynamic response of RC slab. The erosion technique is adopted to simulate the damage process. Comparison of the numerical results with experimental data shows a favorable agreement. Based on the experimental and numerical results, the damage criteria are established for different levels of damage. With the increase of the explosive charge, the failure mode of RC slab is shown to gradually change from overall flexure to localized punching failure.     

爆炸冲击下水底隧道的动态响应及毁伤模式研究

考虑炸药起爆、冲击波传播、冲击波与结构的相互作用以及结构的动态响应等复杂过程,基于Lagrange-Euler耦合算法,建立了水底隧道水下爆炸的全耦合数值仿真模型。通过与爆炸试验结果进行对比,验证了数值模型的可靠性;研究了水下爆炸冲击荷载作用下的水底隧道的毁伤破坏过程、空间分布规律及破坏模式。结果表明:水底隧道的破坏模式不仅与隧道自身的动力特性有关,还取决于起爆距离及炸药当量等;隧道的破坏模式为局部冲切或剥落破坏、弯曲破坏伴随着局部剥落破坏以及整体弯曲破坏。     

爆炸冲击下水底隧道的动态响应及毁伤模式研究

考虑炸药起爆、冲击波传播、冲击波与结构的相互作用以及结构的动态响应等复杂过程,基于Lagrange-Euler耦合算法,建立了水底隧道水下爆炸的全耦合数值仿真模型。通过与爆炸试验结果进行对比,验证了数值模型的可靠性;研究了水下爆炸冲击荷载作用下的水底隧道的毁伤破坏过程、空间分布规律及破坏模式。结果表明:水底隧道的破坏模式不仅与隧道自身的动力特性有关,还取决于起爆距离及炸药当量等;隧道的破坏模式为局部冲切或剥落破坏、弯曲破坏伴随着局部剥落破坏以及整体弯曲破坏。     

Numerical simulations of blast loads and structural deformation from near-field explosions in air

Numerical simulations of air blast loading in the near-field acting on deformable steel plates have been performed and compared to experiments. Two types of air blast setups have been used, cylindrical explosive placed either in free air or in a steel pot. A numerical finite element convergence study of the discretisation sensitivity for the gas dynamics has been performed, with use of mapping results from 2D to 3D in an Eulerian reference frame. The result from the convergence study served as a foundation for development of the simulation models. Considering both air blast setups, the numerical results under predicted the measured plate deformations with 9.4-11.1%. Regarding the impulse transfer, the corresponding under prediction was only 1.0-1.6%. An influence of the friction can be shown, both in experiments and the simulations, although other uncertainties are involved as well. A simplified blast model based on empirical blast loading data representing spherical and hemispherical explosive shapes has been tested as an alternative to the Eulerian model. The result for the simplified blast model deviates largely compared to the experiments and the Eulerian model. The CPU time for the simplified blast model is however considerably shorter, and may still be useful in time consuming concept studies.All together, reasonable numerical results using reasonable model sizes can be achieved from near-field explosions in air.