Prediction of fragment size and ejection distance of masonry wall under blast load using homogenized masonry material properties

The fragment hazard resulting from a nearby explosion is a major concern in the design of structures which may be subjected to blast loads. This paper presents a predictive method based on the theories of continuum damage mechanics and mechanics of micro-crack development, and numerical simulation to determine the probabilistic fragment size distribution and the launch distances. Theoretical derivations are presented to calculate fragment distribution. The fragmentation process is modeled according to the crack initiation and propagation, which depend on the material damage levels and are estimated using continuum damage mechanics theory. The proposed method involves two steps. First a finite element model is developed to estimate the material damage, fragment distribution and the ejection velocity. Then a simple algorithm is used to predict the fragment trajectory and the launch distance based on the fragment size and the ejection velocity. A masonry wall is used as an example in this study. The wall is modeled with both the distinctive consideration of the brick and mortar material properties and the homogenized masonry material properties. The reliability and efficiency of using the homogenized masonry material model in predicting the masonry wall damage and fragmentation are proven. The program AUTODYN is used in this study to conduct the numerical simulations with the proposed models linked to it as user subroutines. The numerical results indicate that the masonry fragments approximately follow the Weibull distribution, which is consistent with some empirical fragment distributions. The proposed method avoids using erosion technique, which inevitably results in a loss of fragment mass, and avoids discretizing the structure into particles or predefining the failure planes, which may lead to unrealistic prediction of damage propagation and evolution and therefore inaccurate fragmentation process and fragment size distributions.     

Fragmentation of targets during ballistic penetration events

An analytical target fragmentation model is developed to predict the number of armor debris fragments produced in a ballistic penetration event. The model employs an energy balance to estimate the energy available to propagate cracks in the target material and thus produce an estimate of the mean number of behind-armor debris fragments. The expected number of behind-armor debris fragments agrees well with the results of conventional ordnance velocity target penetration behind-armor debris tests. This analytical fragmentation model and test results were used as the basis for the development of a means of calibrating the parameters of a Weibull statistical distribution function to predict the probability distribution of the number of debris fragments produced in a ballistic impact. It was concluded that the armor fragmentation model was a good predictor of the number of fragments produced in a ballistic penetration event deserving further investigation.     

A study on burden distribution of blast furnace with a bell‐less top

Abstract

The so‐called coke layer collapse phenomenon was observed on a blast furnace top model which was 1/4‐scale of No. 2 blast furnace of China Steel. A simulation program based on the Bishop simplified method of soil mechanics and the material balance was developed to identify the collapse occurrence and to predict the burden distribution after the collapse. A close agreement between the experimental results and the prediction of simulation program was found.     

核爆冲击波作用下空心砌块墙对主体结构的作用

该文采用显式动力有限元软件LS-DYNA对核爆冲击波作用下高层建筑混凝土小型空心砌块外墙(以下简称砌块墙)的破坏模式进行了数值模拟,计算模型考虑了材料非线性、接触非线性、大应变、大变形等主要特征。在此基础上讨论了砌块墙在破坏飞散过程中传给结构的荷载,得到了不同冲击波超压作用下砌块墙传给结构的荷载时程。计算结果表明:核爆冲击波作用下,砌块墙的破坏模式与冲击波超压的大小有关;其传给结构的荷载时程基本呈三角形分布,荷载峰值随超压的增加而增大,墙体顶部与结构构件之间接触面的允许抗剪强度对荷载峰值时间和持续作用时间起关键作用。     

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.     

A parametric investigation of the seismic capacity for masonry arches and portals of different shapes

Masonry arches are typical components of historic buildings throughout the world, and their damage or collapse is very often caused by earthquakes. The first-order seismic assessment of masonry structures can be represented by the equivalent static analysis method, which does not capture all of the dynamics, but provides a measure of the lateral loading that the structure can withstand before collapse. This study aims to understand the stability of unreinforced masonry arches and portals (i.e. buttressed arches) subjected to constant horizontal ground accelerations, combined with the vertical acceleration due to gravity. An analytical model based on limit analysis is developed to describe the relative stability of pointed and basket-handle arches and portals with respect to circular ones, for varying geometry parameters. The equivalent static analysis determines the value of the constant lateral acceleration needed to cause collapse of the structure, which coincides with the minimum peak ground acceleration needed to transform the vaulted system into a mechanism. Predictions of the analytical model are compared with results of numerical modelling by the Discrete Element Method (DEM). This numerical model considers masonry as an assemblage of rigid blocks with no-tension frictional joints, and is based on a time stepping integration of the equations of motion of the individual blocks. The satisfactory agreement between predictions of the two approaches validates the analytical model and verifies the potentials of the discrete element framework as a method of evaluating the quasi-static behavior of unreinforced masonry structures.     

Numerical studies of the combined effects of blast and fragment loading

The well-known synergetic effect of blast and fragment loading, observed in numerous experiments, is often pointed out in design manuals for protective structures. However, since this synergetic effect is not well understood it is often not taken into account, or is treated in a very simplified manner in the design process itself. A numerical-simulation tool has been used to further study the combined blast and fragment loading effects on a reinforced concrete wall. Simulations of the response of a wall strip subjected to blast loading, fragment loading, and combined blast and fragment loading were conducted and the results were compared. Most damage caused by the impact of fragments occurred within the first 0.2 ms after fragments' arrival, and in the case of fragment loading (both alone and combined with blast) the number of flexural cracks formed was larger than in the case of blast loading alone. The overall damage of the wall strip subjected to combined loading was more severe than if adding the damages caused by blast and fragment loading treated separately, which also indicates the synergetic effect of the combined loading.     

化爆作用下FRP加固RC板的试验研究及动力响应分析

我国20世纪60年代、70年代修建的大量防护工程抗力等级较低,急需进行加固补强。进行了化爆作用下,外贴FRP条带加固钢筋混凝土(RC)双向板抗爆性能的试验研究。按介质-结构相互作用理论确定结构的爆炸冲击荷载,建立了加固板的三折线弯曲抗力模型,利用虚功原理建立了加固RC板的运动微分方程,按数值方法求解了外贴FRP加固双向板在化爆冲击波作用下的动力响应时程,分析结果与试验结果吻合较好。研究结果表明:外贴FRP条带加固可以有效延缓混凝土的开裂、限制裂缝的开展,提高RC双向板的刚度,减小结构位移,减轻结构破坏程度,外贴FRP加固RC双向板的抗爆炸冲击波能力得到了明显提高,外贴FRP条带在极限状态时发生了剥离破坏和断裂破坏。     

Fragmentation from spallation of RC slabs due to airblast loads

Terrorist attacks using improvised explosive devices on reinforced concrete buildings create a rapid release of energy in the form of a shock wave. Most casualties and injuries resulting from such an attack are not caused by the blast itself, but rather by the disintegration and fragmentation of the RC member due to concrete spallation on the opposite side of the member and which is propelled at high velocities depending on the size of the fragments. Therefore, it is important to analyze the size distributions of the concrete fragments from spallation. In this paper, two RC specimens were tested under explosive loading in a blast chamber: the first, a reinforced concrete (RC) specimen; and the second, an identical RC specimen retrofitted with 6 near surface mounted (NSM) carbon fibre reinforced polymer (CFRP) plates on both the top and bottom faces. Both specimens were subjected to the equivalent 2.1 kg of TNT at a standoff distance of 0.6 m, resulting in significant scabbing of the concrete. All fragments resulting from the blast tests were collected and analyzed. A sieve analysis was carried out to investigate the size distributions of the fragments from the two specimens. It was found that the fragment size followed both a Weibull distribution and a Rosin–Rammler–Sperling–Bennet (RRSB) distribution. The distribution of the fragment shape factor was also studied. The fragment shape factors were distributed according to the lognormal distribution. Furthermore, the influence of fragment size distribution on energy density dissipation was evaluated.     

Residual axial compression capacity of localized blast-damaged RC columns

The risks associated with suitcase bombs are of serious concern because they can be easily handled and placed within close proximity of key structural components of building structures. The most common failure mode of the structures subjected to blast loads from satchel and suitcase bombs is progressive collapse. High-fidelity physics based computer program, LS-DYNA is utilized in this study to provide numerical simulations of the dynamic response and residual axial capacity of reinforced concrete (RC) columns subjected to blast loads. Field tests using near-field explosive charge were conducted on two RC column specimens. The test results were compared with the analytical results to validate the finite element model. An extensive parametric study was conducted to investigate the relationship between residual axial capacity and structural and loading parameters such as material strength, column detail and blast conditions. Two empirical equations were derived through a multivariable regression analysis in terms of the various parameters to predict the residual capacity index based on a non-dimensional column dimension parameter (ω_TNT). According to the proposed equations, the residual capacity index can be determined and compared with a service axial load index.     

Simulation of the response of fibre–metal laminates to localised blast loading

The response of Fibre–Metal Laminates (FML) to localised blast loading is studied numerically in order to interpret the deformation mechanism due to highly localised pressure pulses causing permanent deformations and damage observed experimentally in FML panels comprising different numbers of aluminium alloy layers and different thickness blocks of GFPP material [Langdon GS, Lemanski SL, Nurick GN, Simmons MS, Cantwell WJ, Schleyer GK. Behaviour of fibre–metal laminates subjected to localised blast loading: part I – experimental observations and failure analysis. International Journal of Impact Engineering 2007;34:1202–22; Lemanski SL, Nurick GN, Langdon GS, Simmons MS, Cantwell WJ, Schleyer GK. Behaviour of fibre–metal laminates subjected to localised blast loading: part II – quantitative analysis. International Journal of Impact Engineering 2007;34:1223–45; Langdon GS, Nuric GN, Lemanski SL, Simmons MS, Cantwell WJ, Schleyer GK. Failure characterisation of blast-loaded fibre–metal laminate panels based on aluminium and glass-fibre reinforced polypropylene. Composite Science and Technology 2007;67:1385–405]. The influence of the loading and material parameters on the final deformation characteristics is examined. Particular attention is paid to the transient deformation process by using finite element and analytical models to analyse the panel behaviour. It is shown that the response of the FML panels is extremely sensitive to the spatial and temporal distribution variation of the pressure caused by the blast loading. The study reveals that the properties of GFPP in the through-thickness direction play an essential role in the velocity transfer, which influences considerably the failure and final deformed shape of the FML panel. Good agreement between the experimental and numerical results is observed. Comparisons between the responses of relatively thin FML panels, monolithic aluminium alloy plates of equivalent mass and a foam-core panel to localised blast are also presented and discussed.     

冲击载荷下(纤维/聚合物)-金属层合板的大挠度动力响应

对冲击载荷下固支（纤维/聚合物）-金属层合方板和圆板的大挠度动力响应进行了理论研究。基于理想刚塑性假定和塑性极限屈服条件,建立了质量块体和爆炸冲击载荷下（纤维/聚合物）-金属层合板大挠度动力响应的理论模型,给出了固支（纤维/聚合物）-金属层合方板和圆板考虑弯曲和拉伸相互作用的大挠度响应解析解,进一步忽略弯曲的影响,得到了其动力响应的膜力解。研究结果表明,理论预测与已有实验结果吻合较好,该理论模型可以有效地预测质量块体和爆炸冲击载荷下（纤维/聚合物）-金属层合板的最大挠度。      

Impact fragmentation of high-velocity compact projectiles on thin plates: a physical and statistical characterization of fragment debris

The high-velocity impact of a projectile onto a structure results in the creation and energetic expulsion of fragments of the interacting materials. The nature of this fragment debris is of concern in certain applications. Although more broadly applicable, the present study is motivated by a need to characterize the size and velocity distribution of fragments generated by orbital debris impacting external components of spacecraft structure, such as shielding and radiators. In this effort, statistical relations are developed to predict size, momentum and trajectory distributions of the debris. The underlying physics applied are those used in the fields of impact mechanics, thermodynamics of shocks, and statistical fragmentation. Equations from impact mechanics lead to predictions for mass, global momentum, and excess energy of the fragment debris. Relations from shock thermodynamics are developed to partition the initial kinetic energy into thermal and mechanical energies, and therefore to predict mass fractions of solid, liquid and vapor components and the subsequent dispersing motion of this fragment debris. Statistical methods of the energy-based Maxwell-Boltzmann type are pursued to characterize the inherently stochastic fragmentation event, emphasizing the extremes of fragment size and velocity. Computational simulations of impact events and data from impact fragmentation experiments are exploited in validating the underlying theoretical assumptions and the resulting impact fragmentation model.     

CFRP加固砌体结构的力学性能分析

在分析碳纤维加固的砖砌体在水平周期反复荷载作用下试验结果的基础上,研究了碳纤维加固砖砌体的约束及抗倒塌机理;建立了墙体侧向位移与碳纤维应变、碳纤维应变与墙体抗震剪切强度的关系;讨论了不同加固方式、碳纤维面积百分率等在墙体不同受力阶段对墙体抗剪承载能力和变形性能的作用与影响;提出了计算碳纤维加固墙体承载能力和变形的计算方法。计算方法考虑了不同粘贴碳纤维角度、碳纤维面积百分率等对墙体承载能力和变形性能的影响;推导了最优粘贴加固角;提出了改进的粘贴加固方法以提高加固效果。     

Load carrying capacity of 2D FRP/strengthened masonry structures

An adaptive discontinuous finite element model is formulated for limit analysis of masonry structures strengthened by fiber composites. The model is able to predict the effects of fracture damage and delamination on the load carrying capacity of the reinforced structures. A numerical investigation on the collapse mechanisms of masonry structures under plain strain/stress is presented, accounting for different mechanical properties of FRP–masonry interface and different placements of the reinforcement in the masonry structures.     

Damage Monitoring of an Historical Masonry Building by the Acoustic Emission Technique

Acoustic Emission (AE) of the materials that are subject to stress and strain states is a methodology for non-destructive investigation, originally applied to industrial steel structures. Here it is proposed by the authors for identifying the damage in masonry buildings. This experimental method was used to monitor the masonry structure of an historical building, “Casa Capello”, located in the centre of the Rivoli Municipality (near Turin, Italy). This house, built on pre-existing 14th century foundations, was thoroughly restructured at the end of the 18th century and has recently undergone restoration and enlargement works. Non-destructive AE tests were carried out on a few masonry portions of the building in order to evaluate and define the development of the cracking phenomena which had been observed in a number of structural parts after the collapse of a breast wall on the down hill side of the building. With the measurement system adopted, entailing no loading or invasive procedures, it proved possible to predict the arrest of crack growth and the concomitant onset of a new stability condition.     

Prediction of debris launch velocity of vented concrete structures under internal blast

The debris hazard resulting from an internal explosion is a major concern in the design of explosives storage magazines and protective structures. This paper presents a simple predictive method for the debris launch velocity from a concrete storage magazine subjected to internal blast load, with particular focus on the effect of initial vent openings. The method is developed using a combined theoretical–empirical approach, in which the debris launch velocity is formulated based on energy considerations, whereas the reduction coefficient of pressure caused by the flow of explosive gas from the vent openings is established from experimental data. The analytical model is verified against available experimental data and other numerical predictions. Example cases are given to demonstrate the application of the general formulation to particular structures and illustrate the effect of venting and its location on the debris velocity for structures of different sizes.     

Quantitative analysis of debris clouds from SiC-fiber-reinforced silicon nitride bumpers

In order to investigate the dynamic response of lightweight ceramic matrix bumpers against hypervelocity projectile impact, silicon carbide continuous-fiber-reinforced silicon nitride matrix composite plates were prepared and subjected to the impact experiments using duralumin projectiles in the velocity range of 2.2 to 3.6 km/s. The debris clouds of the composites were taken by flash, soft X-ray radiography, and the fragmentation of the bumpers and the spatial distribution of the main parts of the debris clouds were quantified in mass, velocity and kinetic energy and compared with those of monolithic duralumin bumpers and monolithic silicon nitride ceramic bumpers. Almost all the average mass and kinetic energy of the in-flight fragments of the composite were smaller than those of the duralumin and monolithic ceramics. The composite provided thinner distributions of the mass and kinetic energy densities of its debris in an area extending farther from the ballistic line for higher impact velocity, while the monolithic ceramics gave massive and energetic debris distributions in a narrow area around the ballistic line. Total mass and kinetic energy of the composite debris were smaller than those of the duralumin, and for impacts over 3 km/s the volumetric energy density of the composite debris was comparable to that of the duralumin. Embedding the fibers to a ceramic matrix was thought to give the composite the heterogeneous microstructure to result in a non-uniform dynamic response of the composite, followed by the bumper fragmentation and the debris dispersion.     

Investigation of fragments size resulting from dynamic fragmentation in melted state of laser shock-loaded tin

The understanding of dynamic fragmentation in shock-loaded metals and the evaluation of geometrical and kinematical properties of the resulting fragments are issues of considerable importance for both basic and applied science, for instance to predict the evolution of engineering structures submitted to high-velocity impact or explosive detonation. Among dynamic failure processes, spall fracture in solid materials has been extensively studied for many years, while scarce data can be found yet about how such phenomenon could evolve after partial or full melting on compression or on release. In this case, the dynamic fragmentation process, which may be referred to as ‘micro-spalling’, takes place in a liquid medium. It results in the formation of a cloud of fine molten droplets, ejected at high-velocity. The present work is devoted to experimental characterization, theoretical modelling and simulation of the ‘micro-spalling’ process in tin, with a specific emphasis on the size of the resulting fragments, namely the melted droplets. Laser-driven shock-loading experiments on tin have been performed. Post-test observations of the recovered fragments provide an insight into the actual fragmentation process and allow to infer the distribution of the fragments size which are found to be mostly sub-micrometric. Fragmentation modelling is based on a widely employed, energetic approach adapted to the case of liquids. This approach is implemented as a failure criterion in an one-dimensional hydrocode including a multiphase equation of state for tin. A fairly good agreement is obtained between experimental and computed sizes range. Some discrepancies are explained by both experimental uncertainties and model limitations which are carefully pointed out and discussed.