钢筋混凝土构件在爆炸载荷作用下的毁伤效应及评估方法研究
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摘要
建筑物的爆炸破坏效应分析和破坏程度评估在爆炸事故分析、结构抗爆设计、反恐怖袭击和军事领域均是一个重要的课题。无论是进行建筑物结构的抗爆设计，还是爆炸事故中的威力评估或进行爆炸破坏效果评估，首先要做的工作都是建立破坏效果和爆炸威力之间的对应关系。目前常用的办法是对现场勘查的数据进行分析，并结合数值模拟验证的办法来寻找这种对应关系。由于涉及到爆炸力学、结构动力学和计算力学等相关内容，爆炸破坏评估是一项复杂而耗时的工作。这使得相关工作的开展必须依赖极少数的专业人员，这种模式严重影响了评估工作的效率，特别不能满足战场快速评估的实际需要。因此迫切需要一种快速、准确的评估方法完成这项工作，相关评估方法在武器毁伤效能预测方面也有明显的军事应用价值。
本文从爆炸冲击波与钢筋混凝土结构的相互作用及作用于结构上的爆炸载荷的预测，建筑物结构构件在爆炸载荷作用下的动态响应和损伤破坏模式，钢筋混凝土结构在爆炸载荷作用下毁伤破坏的等效单自由度快速分析方法及P-I曲线评估方法等几个方面对爆炸载荷作用下钢筋混凝土结构的动态响应行为和损伤破坏评估方法进行研究，并建立了钢筋混凝土构件爆炸载荷作用下快速评估分析方法。主要研究工作和创新成果包括以下几个方面：
（1）利用数值模拟方法研究了爆炸冲击波与结构相互作用，提出了结构表面上的不同点处爆炸载荷的预测方法，并建立了结构表面不同特征点处爆炸载荷参数的简化预测公式。通过显式有限元动力分析软件AUTODYN数值模拟了爆炸波传播及其与结构的相互作用过程。通过参数分析，研究了结构各参数对爆炸波与结构的相互作用以及作用于结构上不同点的爆炸载荷的影响。研究表明，结构的宽度对爆炸波的冲量具有正向作用，但对爆炸载荷的峰值压力影响较小。据此建立了求解结构表面上任意点爆炸载荷的各参数的一般方法。
（2）通过试验研究了钢筋混凝土构件在近爆炸载荷作用下的破坏损伤特征，得到了近距离爆炸作用下钢筋混凝土板和梁的破坏等级及破坏模式，利用曲线拟合的方法建立了考虑缩比度和比例距离修正的爆炸变形相似律。研究表明，单向方形钢筋混凝土板在近爆作用下易于发生弯曲和底部层裂破坏，层裂破坏区域随着比例距离的减小而不断增加。钢筋混凝土梁在近爆作用下易于发生正面混凝土压缩碎裂破坏，梁背面和侧面混凝土的剥落和层裂弯曲破坏。进一步研究了钢筋混凝土板和梁在爆炸载荷作用下的爆炸相似律，研究表明，不同尺寸构件呈现相似的破坏模式和破坏效果，但随着构件尺寸的增加，破坏程度略有增加。
（3）利用数值模拟方法研究了爆炸载荷作用下钢筋混凝土板动力响应，分析了不同装药量作用下钢筋混凝土板的损伤破坏特征，提出了钢筋混凝土板的一种经验损伤准则。研究表明，在近爆载荷作用下，钢筋混凝土板中压缩应力波传播至板的背面形成强拉伸波造成板背爆面混凝土的剥落和层裂破坏。随着装药量的加大，方形钢筋混凝土板的破坏逐渐由整体弯曲破坏转变为板中央局部的冲剪破坏。进一步研究了均布爆炸载荷作用下钢筋混凝土构件可能的破坏模式，研究表明，在冲量载荷作用下，钢筋混凝土板倾向于发生剪切破坏；在准静态载荷作用下，钢筋混凝土板倾向于发生弯曲破坏；而在动力载荷作用下，钢筋混凝土板更容易发生弯剪破坏。
（4）研究了利用等效单自由度方法对钢筋混凝土板等构件在近爆载荷作用下的损伤进行分析的方法。基于虚功相等的原理，提出了一种建筑物构件表面等效均布载荷的计算方法，将该等效均布载荷作为外载荷应用到等效单自由度损伤分析中。同时对相互耦合的弯曲和剪切响应的等效单自由度系统进行初步探讨，推导得到了不同载荷分布系数对应的非均布载荷作用下动态剪切力的求解方法，并分别利用数值模拟计算结果对弯剪耦合的等效单自由度系统进行了验证。
（5）研究了利用相互耦合的弯曲和剪切响应等效单自由度系统对爆炸载荷作用下钢筋混凝土构件损伤程度进行评估的P-I曲线方法，建立了考虑不同破坏模式和不同载荷形状的P-I曲线经验公式。分析了爆炸载荷形状及钢筋混凝土构件的各参数对相应的各临界损伤程度P-I曲线的超压渐近线及冲量渐近线的影响。研究表明，矩形爆炸载荷的P-I曲线最低，e指数型爆炸载荷的P-I曲线最高，但爆炸载荷形状对P-I曲线的渐近线影响不大；弯曲失效模式的P-I曲线压力和冲量渐近线的值均随着板跨度增加而逐渐降低，剪切失效模式的P-I曲线压力和冲量渐近线的值均随着板跨度增加而逐渐增加；当混凝土强度和配筋率增大时，钢筋混凝土板P-I曲线的超压渐近线和冲量渐近线的值均随之增大。据此提出了通过等效单自由度方法确定钢筋混凝土构件P-I曲线的一种简化方法。
Damage effects analysis and assessment of buildings under blast loading is animportant problem concerned by the area of explosion accident analysis, blast-resistantdesign, anti-terrorist and military weapon design. When designing of blast-resistantbuildings or assessing and analyzing of damage effects of buildings under blast loading,the relationship of blast damage effects and explosive source should be found first. Themost often used method is analysing the data obtained in the blast scene and validatednumerical simulation to find the relationship of blast damage effects and explosivesource. But due to the work related to blast mechanics, dynamics of structures andcompute mechanics and so on related contents, damage effects analysis and assessmentis a complex and time-consuming work. This made the related assessment workdepended on few special men to do. So there is much need to find a fast and exactassessment method to accomplish this work, and the related assessment method is ofdirect military value in weapon damage efficiency and forecast.
Several main problems in research of dynamic response and damage mechanism ofbuilding structures under blast loading are studied in this dissertation．They are:simulmion of interaction between blast wave and structural element and derivation ofthe formulae to estimate blast loads acting on the elements; dynamic response anddamage modes of reinforced concrete (RC) structural members under blast loading;single degree of freedom (SDOF) method of structure elements under blast loading andthe corresponding pressure-impulse (P-I) damage evaluation method. The primary workand achievements are as follows：
(1) Simulation of blast wave propogation and its interaction with structuralmembers are studied. A method to simulate the interaction between blast wave and aalone structural members is established using Hydrocode AUTODYN．Parametricstudies are carried out to study the influence of structure parameters on the blastwave-element interaction and the blast loads acting on different points of the structuralmembers．It is found that the width of the structural element has a positive effect on theimpulse of the blast loads acting on the structural element．However, it has nosignificant effect on the peak pressure of the blast loads on the structural element. Basedon the numerical results of the parametric studies, some formulae are proposed toestimate the blast overpressure and impulse of the characteristic points on the frontsurfaces of any standalone structural elements. A common method is established toestimat the blast loads’ parameters of any points on the structural element.
(2) The damage mechanism of RC structure member under close-in blast loading isinvestigated by experiments. The damage modes and damage levels of RC slabs and beams are studied under different blast loads. The results show that one-way RC slabsare prone to be damaged by flexure and spallation on the back surface of the slabs, andthe spallation area increases with the increase of the scaled distance. The concretebeams are prone to be damged in flexure with concrete crushed on the front face,concrete spllsation on the back surface and concrete flake off on the side surface. Thescaling of the dynamic response of one-way square reinforced concrete slabs and beamssubjected to close-in blast loadings are also studied. The test results show that themacrostructure damage and fracture in the experiments are almost with similarity. Butthe local damage of concrete slabs with smaller specimen has been reduced a little ascompared with that of concrete slabs with larger specimen. Based on the results,empirical equations are proposed to correct the scaling model of center deflection toheight ratio when scaling the results from the model up to the prototype.
(3) A method for simulating the dynamic response and damage of RC slabs underblast loading is established. The damage mechanism and damage features are alsostudied by numerical simulation, and an emperial damage criterion is established fordifferent damage levels of concrete slabs. The results show that the initial compressiveshock wave generated by the blast passes through the concrete slab and is reflected offthe free surface, the shock wave is converted into a tensile wave, resulting in high levelsof cracking and spallation damage. The damge modes are changed from intial wholeflexural damge to local punch shear failure in the center of the slabs. The damge modesof the slabs under uniform blast loading are also studied. The results indicated that whenthe slab is subjected to impulsive blast load, the slab is inclined to be damaged by shear;however, the slab is likely damaged by flexural mode in the quasi-static region; and inthe region of dynamic loading, the failure of the slab might be a combination of shearand flexural damage.
(4) The single degree of freedom (SDOF) method of concrete structute membersunder close-in blast loading is studied. A new effective model for calculation of theequivalent uniform blast load for non-uniform blast load such as close-in explosion ofRC strucutre members is proposed. The model is then validated using SDOF systemwith the experiments and blast tests for square slabs, rectangle slabs and beams. Twocoupled SDOF systems used to model the flexural and direct shear responses of RCmembers subjected to explosive loading are investigated. The equations of shear SDOFdynamic shear force of RC slabs under nonuniform blast loading are derived. The twocoupled SDOF systems are validated with numerical tests. The numerical results showthat the SDOF systems are accurate in predicting the failure mode of the RC membersunder blast loads.
(5) Pressure-impulse (P-I) diagram methods with the two coupled SDOF systemsfor evaluate the damage degree of RC members under blast loading are studied．The influence of blast load shapes and the RC structure parameters on the different damagelevel P-I curve quasi-static asymptote and impulse asymptote is investigated. The resultsshown that the blast load shape influences the pressure-impulse shape in the dynamicdamage region for all damage levels; the curves of rectangular load are the lowest in thediagrams and the curves of exponential load are the highest. The impulsive asymptoteand the quasi-static asymptote are almost the same for the three blast load shapes. Thevalues of flexural damage P-I curve’s impulsive asymptote and the quasi-staticasymptote decrease with the increasing of members’ length, however the values of sheardamage P-I curve’s impulsive asymptote and the quasi-static asymptote increase withthe increasing of members’ length. The values of both flexural and shear damage P-Icurve’s impulsive asymptote and the quasi-static asymptote increase with the increasingof the concrete strength and reinforced ratio. Based on the results, an empirical equationof the P-I curves of different damage modes and blast load shapes is established and asimplified numerical method to generate P-I diagram for RC members is proposed．
本文从爆炸冲击波与钢筋混凝土结构的相互作用及作用于结构上的爆炸载荷的预测，建筑物结构构件在爆炸载荷作用下的动态响应和损伤破坏模式，钢筋混凝土结构在爆炸载荷作用下毁伤破坏的等效单自由度快速分析方法及P-I曲线评估方法等几个方面对爆炸载荷作用下钢筋混凝土结构的动态响应行为和损伤破坏评估方法进行研究，并建立了钢筋混凝土构件爆炸载荷作用下快速评估分析方法。主要研究工作和创新成果包括以下几个方面：
（1）利用数值模拟方法研究了爆炸冲击波与结构相互作用，提出了结构表面上的不同点处爆炸载荷的预测方法，并建立了结构表面不同特征点处爆炸载荷参数的简化预测公式。通过显式有限元动力分析软件AUTODYN数值模拟了爆炸波传播及其与结构的相互作用过程。通过参数分析，研究了结构各参数对爆炸波与结构的相互作用以及作用于结构上不同点的爆炸载荷的影响。研究表明，结构的宽度对爆炸波的冲量具有正向作用，但对爆炸载荷的峰值压力影响较小。据此建立了求解结构表面上任意点爆炸载荷的各参数的一般方法。
（2）通过试验研究了钢筋混凝土构件在近爆炸载荷作用下的破坏损伤特征，得到了近距离爆炸作用下钢筋混凝土板和梁的破坏等级及破坏模式，利用曲线拟合的方法建立了考虑缩比度和比例距离修正的爆炸变形相似律。研究表明，单向方形钢筋混凝土板在近爆作用下易于发生弯曲和底部层裂破坏，层裂破坏区域随着比例距离的减小而不断增加。钢筋混凝土梁在近爆作用下易于发生正面混凝土压缩碎裂破坏，梁背面和侧面混凝土的剥落和层裂弯曲破坏。进一步研究了钢筋混凝土板和梁在爆炸载荷作用下的爆炸相似律，研究表明，不同尺寸构件呈现相似的破坏模式和破坏效果，但随着构件尺寸的增加，破坏程度略有增加。
（3）利用数值模拟方法研究了爆炸载荷作用下钢筋混凝土板动力响应，分析了不同装药量作用下钢筋混凝土板的损伤破坏特征，提出了钢筋混凝土板的一种经验损伤准则。研究表明，在近爆载荷作用下，钢筋混凝土板中压缩应力波传播至板的背面形成强拉伸波造成板背爆面混凝土的剥落和层裂破坏。随着装药量的加大，方形钢筋混凝土板的破坏逐渐由整体弯曲破坏转变为板中央局部的冲剪破坏。进一步研究了均布爆炸载荷作用下钢筋混凝土构件可能的破坏模式，研究表明，在冲量载荷作用下，钢筋混凝土板倾向于发生剪切破坏；在准静态载荷作用下，钢筋混凝土板倾向于发生弯曲破坏；而在动力载荷作用下，钢筋混凝土板更容易发生弯剪破坏。
（4）研究了利用等效单自由度方法对钢筋混凝土板等构件在近爆载荷作用下的损伤进行分析的方法。基于虚功相等的原理，提出了一种建筑物构件表面等效均布载荷的计算方法，将该等效均布载荷作为外载荷应用到等效单自由度损伤分析中。同时对相互耦合的弯曲和剪切响应的等效单自由度系统进行初步探讨，推导得到了不同载荷分布系数对应的非均布载荷作用下动态剪切力的求解方法，并分别利用数值模拟计算结果对弯剪耦合的等效单自由度系统进行了验证。
（5）研究了利用相互耦合的弯曲和剪切响应等效单自由度系统对爆炸载荷作用下钢筋混凝土构件损伤程度进行评估的P-I曲线方法，建立了考虑不同破坏模式和不同载荷形状的P-I曲线经验公式。分析了爆炸载荷形状及钢筋混凝土构件的各参数对相应的各临界损伤程度P-I曲线的超压渐近线及冲量渐近线的影响。研究表明，矩形爆炸载荷的P-I曲线最低，e指数型爆炸载荷的P-I曲线最高，但爆炸载荷形状对P-I曲线的渐近线影响不大；弯曲失效模式的P-I曲线压力和冲量渐近线的值均随着板跨度增加而逐渐降低，剪切失效模式的P-I曲线压力和冲量渐近线的值均随着板跨度增加而逐渐增加；当混凝土强度和配筋率增大时，钢筋混凝土板P-I曲线的超压渐近线和冲量渐近线的值均随之增大。据此提出了通过等效单自由度方法确定钢筋混凝土构件P-I曲线的一种简化方法。
Damage effects analysis and assessment of buildings under blast loading is animportant problem concerned by the area of explosion accident analysis, blast-resistantdesign, anti-terrorist and military weapon design. When designing of blast-resistantbuildings or assessing and analyzing of damage effects of buildings under blast loading,the relationship of blast damage effects and explosive source should be found first. Themost often used method is analysing the data obtained in the blast scene and validatednumerical simulation to find the relationship of blast damage effects and explosivesource. But due to the work related to blast mechanics, dynamics of structures andcompute mechanics and so on related contents, damage effects analysis and assessmentis a complex and time-consuming work. This made the related assessment workdepended on few special men to do. So there is much need to find a fast and exactassessment method to accomplish this work, and the related assessment method is ofdirect military value in weapon damage efficiency and forecast.
Several main problems in research of dynamic response and damage mechanism ofbuilding structures under blast loading are studied in this dissertation．They are:simulmion of interaction between blast wave and structural element and derivation ofthe formulae to estimate blast loads acting on the elements; dynamic response anddamage modes of reinforced concrete (RC) structural members under blast loading;single degree of freedom (SDOF) method of structure elements under blast loading andthe corresponding pressure-impulse (P-I) damage evaluation method. The primary workand achievements are as follows：
(1) Simulation of blast wave propogation and its interaction with structuralmembers are studied. A method to simulate the interaction between blast wave and aalone structural members is established using Hydrocode AUTODYN．Parametricstudies are carried out to study the influence of structure parameters on the blastwave-element interaction and the blast loads acting on different points of the structuralmembers．It is found that the width of the structural element has a positive effect on theimpulse of the blast loads acting on the structural element．However, it has nosignificant effect on the peak pressure of the blast loads on the structural element. Basedon the numerical results of the parametric studies, some formulae are proposed toestimate the blast overpressure and impulse of the characteristic points on the frontsurfaces of any standalone structural elements. A common method is established toestimat the blast loads’ parameters of any points on the structural element.
(2) The damage mechanism of RC structure member under close-in blast loading isinvestigated by experiments. The damage modes and damage levels of RC slabs and beams are studied under different blast loads. The results show that one-way RC slabsare prone to be damaged by flexure and spallation on the back surface of the slabs, andthe spallation area increases with the increase of the scaled distance. The concretebeams are prone to be damged in flexure with concrete crushed on the front face,concrete spllsation on the back surface and concrete flake off on the side surface. Thescaling of the dynamic response of one-way square reinforced concrete slabs and beamssubjected to close-in blast loadings are also studied. The test results show that themacrostructure damage and fracture in the experiments are almost with similarity. Butthe local damage of concrete slabs with smaller specimen has been reduced a little ascompared with that of concrete slabs with larger specimen. Based on the results,empirical equations are proposed to correct the scaling model of center deflection toheight ratio when scaling the results from the model up to the prototype.
(3) A method for simulating the dynamic response and damage of RC slabs underblast loading is established. The damage mechanism and damage features are alsostudied by numerical simulation, and an emperial damage criterion is established fordifferent damage levels of concrete slabs. The results show that the initial compressiveshock wave generated by the blast passes through the concrete slab and is reflected offthe free surface, the shock wave is converted into a tensile wave, resulting in high levelsof cracking and spallation damage. The damge modes are changed from intial wholeflexural damge to local punch shear failure in the center of the slabs. The damge modesof the slabs under uniform blast loading are also studied. The results indicated that whenthe slab is subjected to impulsive blast load, the slab is inclined to be damaged by shear;however, the slab is likely damaged by flexural mode in the quasi-static region; and inthe region of dynamic loading, the failure of the slab might be a combination of shearand flexural damage.
(4) The single degree of freedom (SDOF) method of concrete structute membersunder close-in blast loading is studied. A new effective model for calculation of theequivalent uniform blast load for non-uniform blast load such as close-in explosion ofRC strucutre members is proposed. The model is then validated using SDOF systemwith the experiments and blast tests for square slabs, rectangle slabs and beams. Twocoupled SDOF systems used to model the flexural and direct shear responses of RCmembers subjected to explosive loading are investigated. The equations of shear SDOFdynamic shear force of RC slabs under nonuniform blast loading are derived. The twocoupled SDOF systems are validated with numerical tests. The numerical results showthat the SDOF systems are accurate in predicting the failure mode of the RC membersunder blast loads.
(5) Pressure-impulse (P-I) diagram methods with the two coupled SDOF systemsfor evaluate the damage degree of RC members under blast loading are studied．The influence of blast load shapes and the RC structure parameters on the different damagelevel P-I curve quasi-static asymptote and impulse asymptote is investigated. The resultsshown that the blast load shape influences the pressure-impulse shape in the dynamicdamage region for all damage levels; the curves of rectangular load are the lowest in thediagrams and the curves of exponential load are the highest. The impulsive asymptoteand the quasi-static asymptote are almost the same for the three blast load shapes. Thevalues of flexural damage P-I curve’s impulsive asymptote and the quasi-staticasymptote decrease with the increasing of members’ length, however the values of sheardamage P-I curve’s impulsive asymptote and the quasi-static asymptote increase withthe increasing of members’ length. The values of both flexural and shear damage P-Icurve’s impulsive asymptote and the quasi-static asymptote increase with the increasingof the concrete strength and reinforced ratio. Based on the results, an empirical equationof the P-I curves of different damage modes and blast load shapes is established and asimplified numerical method to generate P-I diagram for RC members is proposed．
引文
[1]李忠献,方秦.工程结构抗爆防爆的研究与发展[M].国家自然科学基金委员会材料与工程学部学科发展战略研究报告系列之《土木工程卷》,2006.
[2]胡联台.当代世界恐怖主义与对策[M].北京:东方出版社,2002.
[3] Li Z X, Du H, Bao C X. Review of current researches on blast load effects ofbuilding structures in China [J]. Transactions of Tianjin University,2006,12(Suppl):35-41.
[4] Smith P D, Rose T A. Blast wave propagation in city streets-an overview [J].Progress in Structural Engineering and Materials.2006,8(1):16-28.
[5] Henrych J. The dynamics of explosion and its use [M]. New York: ElsevierScientific Pub co,1979.
[6] Smith P D, Mays G C, Rose TA. Small scale models of complex geometry for blastoverpressure assessment [J]. International Journal of Impact Engineering,1992,12(3):345-360.
[7] Smith P D, Vismeg P, Teo L C. Blast wave transmission along rough-walled tunnels[J]. Intemational Journal of Impact Engineering,1998,21(6):419-432.
[8] Rose T A, Smith P D. Influence of the principal geometrical parameters of straightcity streets on positive and negative phase blast wave impulses [J]. InternationalJournal of Impact Engineering,2002,27(4):359-376.
[9] Remennikov A M. Modelling blast loads on buildings in complex city geometries [J].Computers and Structures,2005,83(27):2197-2205.
[10] Army TM5-1300, Structures to resist the effects of accidental explosions [R], USDepartment of the Army.1990.
[11] UFC3-340-02(TM5-1300), Structures to resist the effects of accidental explosions[R], December2008.
[12]杨鑫,石少卿,程鹏飞.空气中TNT爆炸冲击波超压峰值的预测及数值模拟[J].爆破,2008,25(1):15-19.
[13]顾垒,向文飞.爆炸空气冲击波超压影响因素分析及控制[J].爆破,2002,19(2):15-17.
[14]林大超,白春华,张奇.空气中爆炸时爆炸波的超压函数[J].爆炸与冲击,2001,2l(1):41-46.
[15] Shi Y C, Hao H, Li Z X. Numerical simulation of blast wave interaction withstructure columns [J]. Shock Waves,2007,17:113-133.
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[36] Dakhakhni W W, Mekky W F, Changiz S H. Vulnerability screening and capacityassessment of reinforced concrete columns subjected to blast [J]. Journal ofPerformance of Constructed Facilities,2009,23(5):353-365.
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[2]胡联台.当代世界恐怖主义与对策[M].北京:东方出版社,2002.
[3] Li Z X, Du H, Bao C X. Review of current researches on blast load effects ofbuilding structures in China [J]. Transactions of Tianjin University,2006,12(Suppl):35-41.
[4] Smith P D, Rose T A. Blast wave propagation in city streets-an overview [J].Progress in Structural Engineering and Materials.2006,8(1):16-28.
[5] Henrych J. The dynamics of explosion and its use [M]. New York: ElsevierScientific Pub co,1979.
[6] Smith P D, Mays G C, Rose TA. Small scale models of complex geometry for blastoverpressure assessment [J]. International Journal of Impact Engineering,1992,12(3):345-360.
[7] Smith P D, Vismeg P, Teo L C. Blast wave transmission along rough-walled tunnels[J]. Intemational Journal of Impact Engineering,1998,21(6):419-432.
[8] Rose T A, Smith P D. Influence of the principal geometrical parameters of straightcity streets on positive and negative phase blast wave impulses [J]. InternationalJournal of Impact Engineering,2002,27(4):359-376.
[9] Remennikov A M. Modelling blast loads on buildings in complex city geometries [J].Computers and Structures,2005,83(27):2197-2205.
[10] Army TM5-1300, Structures to resist the effects of accidental explosions [R], USDepartment of the Army.1990.
[11] UFC3-340-02(TM5-1300), Structures to resist the effects of accidental explosions[R], December2008.
[12]杨鑫,石少卿,程鹏飞.空气中TNT爆炸冲击波超压峰值的预测及数值模拟[J].爆破,2008,25(1):15-19.
[13]顾垒,向文飞.爆炸空气冲击波超压影响因素分析及控制[J].爆破,2002,19(2):15-17.
[14]林大超,白春华,张奇.空气中爆炸时爆炸波的超压函数[J].爆炸与冲击,2001,2l(1):41-46.
[15] Shi Y C, Hao H, Li Z X. Numerical simulation of blast wave interaction withstructure columns [J]. Shock Waves,2007,17:113-133.
[16] Lan S R, Lok T S, Heng L. Composite structural panels subjected to explosiveloading [J]. Construction and Building Materials,2005,19:387-395.
[17] Low H Y, Hao H. Reliability analysis of reinforced concrete slabs under explosiveloading [J]. Structural Safety,2001,23(2):157-178.
[18] Low H Y, Hao H. Reliability analysis of direct shear and flexural failure modes ofRC slabs under explosive loading [J]. Engineering Structures,2002,24:189-198.
[19] Jones J, Wu C, Oehlers D J, et al. Finite difference analysis of simply supported RCslabs for blast loadings [J]. Engineering Structures,2009,31(12):2825-2832.
[20] Ohkubo K, Beppu M, Ohno T, Satoh K. Experimental study on the effectiveness offiber sheet reinforcement on the explosive-resistant performance of concreteplates[J]. International Journal of Impact Engineering,2008,35:1702-1708.
[21] Wu C, Oehlers D J, Rebentrost M, Burman N, Whittaker AS. Blast testing ofultrahigh performance fiber concrete slabs and FRP retrofitted RC slabs [J].Engineering Structures,2009,31:2060-2069.
[22] Nash P T, Vallabhan C V G, Knight T C. Spall damage to concrete walls fromclosein cased and uncased explosions in air [J]. ACI Structural Journal,1995,92(6):680-688.
[23] Rabczuk T, Eibl J, Stempniewski L. Numerical analysis of high speed concretefragmentation using a meshfree Lagrangian method [J]. Engineering FractureMechanics,2004,71(4-6):547-556.
[24] Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation usingSPH/MLSPH [J]. International Journal for Numerical Methods in Engineering,2003,56(10):1421-1444.
[25] Xu K, Lu Y. Numerical simulation study of spallation in reinforced concrete platessubjected to blast loading [J]. Computers and Structures,2006,84:431-438.
[26] Zhou X Q, Hao H, Deeks A J. Modeling dynamic damage of concrete slab underblast loading [C]. In: Hao H, Lok T S, Lu G X, editors. Proceeding of the6thAsia-Pacific Conference on Shock and Impact Loads on StructuStructures,December, Perth, WA, Australia;2005. p.703-10. ISBN:981-05-3550-3.
[27] Zhou X Q, Hao H. Mesoscale modelling and analysis of damage and fragmentationof concrete slab under contact detonation [J]. International Journal of ImpactEngineering,2009,36:1315-1326.
[28]阎石,张亮,王丹.钢筋混凝土板在爆炸载荷作用下的破坏模式分析[J].沈阳建筑大学学报(自然科学版),2005,21(3):177-180.
[29] Mayrhofer C. Reinforced masonry walls under blast loading[J]. InternationalJournal of Mechanical Sciences,2002,44:1067-1080.
[30] Davidson J S, Jeff W, et al. Failure mechanisms of polymer-reinforced concretemasonry walls subjected to blast[J]. Journal of Structural Engineering.2005,131(8):1194-1205.
[31] Fatt M S H, Ouyang X, Dinan R J. Blast response of walls retrofitted withelastomer coatings [J]. Structures and Materials,2004,15:129-138.
[32] Lan S R, John E C, Kenneth B M. Design of reinforced concrete columns to resistthe effects of suitcase bombs [C]. The6th Asia-Pacific conference shock&impactloads on structures. Perth W Australia,2005:325-331.
[33] Hao H, Cheong H K, Cui S J. Numerical study of dynamic buckling of steelcolumns subjected to underground explosion [J]. Key Engineering Materials,2002,233-236:211-216.
[34] Cui S J, Cheong H K, Hao H. Elastic-plastic dynamic response and buckling ofsteel columns under ground strong vertical ground motion [J]. Key EngineeringMaterials,2002,233-236:217-222.
[35] Bao X, Li B. Residual strength of blast damaged reinforced concrete columns [J].International Journal of Impact Engineering,2010,37(3):295-308.
[36] Dakhakhni W W, Mekky W F, Changiz S H. Vulnerability screening and capacityassessment of reinforced concrete columns subjected to blast [J]. Journal ofPerformance of Constructed Facilities,2009,23(5):353-365.
[37] Shi Y C, Hao H, Li Z X. Numerical derivation of pressure-impulse diagrams forprediction of RC column damage to blast loads [J]. International Journal of ImpactEngineering,2008,35:1213-1227.
[38]师燕超,李忠献.爆炸载荷作用下钢筋混凝土柱的动力响应与破坏模式[J].建筑结构学报,2008,29(4):112-117.
[39] Krauthammer T. Shallow buried RC box-type structures [J]. Journal of StructuralEngineering,1984,110(3):637-651.
[40] Krauthammer T, Bazeos N, Holmquist T J. Modified SDOF analysis of RCbox-type structures [J]. Journal of Structural Engineering,1986,1l2(4):726-744.
[41] Ghabossi J, Millavec W A, Isenberg J. RC structures under impulsive loading [J].Journal of Structural Engineering,1984,1l0(3):505-522.
[42] Ross T J. Direct shear failure in reinforced concrete beams under impulsive loading[R]. FWL-TR-83-84, Kirtland Air Force Base, NM:Air Force Weapons Laboratory,1983.
[43]方秦,吴平安.爆炸载荷作用下RC梁破坏形态的主要因素分析[J].计算力学学报,2003,20(1):39-42.
[44]方秦,柳锦春.爆炸载荷作用下钢板与钢筋混凝土组合梁动力响应分析[J].工程力学,1997,(A03):321-325.
[45]方秦,柳锦春,钱七虎.爆炸载荷作用下钢筋混凝土梁破坏形态有限元分析[J].工程力学,2001,18(2):1-8.
[46]柳锦春,方秦,龚自明等.爆炸载荷作用下钢筋混凝土梁的动力响应及破坏形态分析[J].爆炸与冲击,2003,23(1):25-30.
[47] Pan Y G, Watson A J. Effect of panel stiffness on resistance of cladding panels toblast loading[J]. ASCE: Journal of Engineering Mechanics,1998,124(4):414-421.
[48] Mays G C, Hetherington J G. Response to blast loading of concrete wall panelswith openings [J]. ASCE: Journal of Structural Engineering.1999,125(12):1448-1450.
[49]王正明,卢芳云.导弹试验的设计与评估[M].科学出版社.2010.
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