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建筑抗爆研究中国足球协会超级联赛压的分布特征及确定方法

2020-05-19 15:06:35 《土木建筑与环境工程》 2020年2期

杨涛春 罗尧治

摘 要: 爆炸超压是描述爆炸荷载的重要指标,不同方法的超压计算结果具有较高的离散性。通过分析试验数据图表拟合确定入射超压与反射超压关系的反射系数计算式,搜集转化得到大量爆炸超压理论计算公式与爆炸试验数据,从而对爆炸超压在不同比例距离下的分布特征进行分析。研究结果表明:当比例距离小于0.5? m/kg1/3时,爆炸超压概率密度服从指数分布;当比例距离大于0.5? m/kg1/3时,爆炸超压概率密度服从正态分布。当比例距离小于0.5? m/kg1/3时,爆炸超压变异系数达最大值1,比例距离在1.5~6.0? m/kg1/3之间时,变异系数较小,在0.13~0.2? m/kg1/3之间;反射超压变异系数较入射超压略大。依据不同比例距离下爆炸超压分布希望数据,拟合得到爆炸超压的计算公式与具有95%保证率条件下的爆炸超压分布范围计算公式。

关键词: 爆炸超压;比例距离;变异系数;分布特征

中图分类号:TU312? ? 文献标志码:A? ?文章编号:2096-6717(2020)02-0115-10

Distribution characteristic and determination of overpressure for blast resistant study of buildings

Yang Taochun1,2, Luo Yaozhi1

(1.College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310027,P.R.China; 2.School of Civil Engineering and Architecture, University of Jinan, Jinan 250022, P.R.China)

Abstract: Explosion overpressure is an important indicator to describe blast load.And the results obtained by different methods have high discreteness.Based on this, the reflection coefficient formula of the relationship between incident overpressure and reflection overpressure is determined firstly by analyzing the experimental data chart fitting.Then a large number of theoretical calculation formulas and explosion test data were collected and transformed to analyze the distribution characteristics of explosion overpressure at different proportional distances.The results show that the probability density of explosion overpressure obeys exponential distribution when the scaled distance less than 0.5? m/kg1/3.And obeys normal distribution when the scaled distance greater than 0.5 m/kg1/3.The variation coefficient reaches the maximum value 1 when the scaled distance less than 0.5 m/kg1/3.While variation coefficient is in the range of 0.13 to 0.2 when the scaled distance within the range of 1.5 m/kg1/3 to 6 m/kg1/3.The variation coefficient of reflect overpressure is a little bigger than that of incident overpressure.According to the expected data of explosion overpressure distribution at different proportional distances, the calculation formula of explosion overpressure and the calculation formula of explosion overpressure distribution range with 95% guarantee rate are obtained by fitting.

Keywords: explosion overpressure; scale distance; variation coefficient; distribution characteristic

隨着恐怖袭击事件和偶然爆炸事故的不断发生,建筑结构防爆、抗爆研究已成为土木工程领域的热点问题,特别是从“9·11”事件以来,世界多国学者已开展很多相关建筑结构的抗爆研究工作,如爆炸荷载、结构动力响应、破坏模式及简化计算、抗爆分析方法及抗爆加固措施等,得出很多非常有意义的结论,对引导工程结构防爆、抗爆安全有重要参考价值。

在搜集的试验数据中,既有垂直入射数据,也有非垂直入射数据,为分析数据的统一和严谨性,仅保留垂直入射的数据,即上述数据共计125组。而在这125组试验数据中,有的仅有入射超压,有的仅有反射超压,入射超压与反射超压同时存在的只有11组,对于同批试验,有22组数据存在较大差异,在分析中未考虑,因此,实际使用的试验统计数据有103组。

分析爆炸超压计算公式发现,入射超压的计算公式主要有两种形式,如式(4)、式(5)所示,在每个公式中,均存在3个待定系数。其中,式(4)通过爆炸力学理论求得,并通过试验确定相关系数,此方法在已有入射超压的计算公式中得到更多应用,式(5)主要通过试验数据拟合而得,在入射超压的计算公式中也有一定应用。对于统计的仅有入射超压或反射超压的试验数据,通过反射系数式(2)和入射超压计算公式可得到该组试验条件下的相关入射超压公式和反射超压相关数据,为分析得到爆炸超压的概率分布特征提供统计样本。

P0= a Z + b Z2 + c Z3? (4)

P0=d·Ze+f (5)

式中:Z为比例距离。

2 超压分布特征

基于统计的爆炸超压数据,对不同比例距离下的离散超压值进行分析,画出对应不同比例距离的超压分布直方图,结合超压直方图分布特征,并通过K-S检验和Lilliefors检验分别开展不同比例距离下的超压概率分布拟合优度检验。结果表明,当比例距离小于0.5 m/kg1/3时,入射超压和反射超压分布均服从指数分布,当比例距离大于0.5 m/kg1/3时,超压分布均服从正态分布。在确定概率分布模型基础上,计算得到不同比例距离条件下的超压均值和标准差的极大似然估计值,同时,得到超压均值在95%保证率条件下的置信区间,如表2、表3所示,从而得到不同比例距离下的超压分布概率密度曲线,如图4、图5所示(指数分布和正态分布各两组)。从表2、表3中可以看出,比例距离较小时,标准差最大,超压分布越分散。

为对比不同比例距離条件下入射超压与反射超压的分散程度,通过表2、表3中国足球协会超级联赛压希望和标准差的极大似然估计值得到超压分布的变异系数,如图6所示。从图6可以看出,比例距离小于0.5 m/kg1/3时,超压变异系数达到最大,为指数分布的常值1;当比例距离约在1.5~6 m/kg1/3之间时,得益于较多的试验数据,变异系数较小,在0.13~0.2之间,且反射超压的变异系数较入射超压略大。

3 爆炸超压公式确定

根据表2、表3中国足球协会超级联赛压希望的极大似然估计值,可得到入射超压和反射超压95%置信区间上、下限随比例距离的变化关系,分别如图7、图8所示,因不同比例距离的超压值相差较大,故将比例距离分3段分别绘制,从图中也可看出超压分散程度随比例距离的变化趋势,比例距离越小,超压分布越分散。取比例距离和超压值的自然对数,再通过最小二乘法对自然对数超压进行多项式拟合,如图9、图10所示,入射超压和反射超压拟合曲线的回归系数均大于0.99,最终得到入射超压的计算公式为

ln P0=0.158 3ln2Z-2.342ln Z-0.097 7 (6)

入射超压95%置信区间上、下限的计算公式为

ln P0=0.214 9ln2Z-2.486 7ln Z+0.071 1(上限) (7)

ln P0=0.111 1ln2Z-2.242 8ln Z-0.250 6(下限) (8)

同理,可得到反射超压的计算公式为

ln Pr=0.208 7ln2Z-2.926 3ln Z+1.564 7 (9)

反射超压95%置信区间上、下限的计算公式为

ln Pr=0.264 3ln2Z-3.065 2ln Z+1.751 2(上限) (10)

ln Pr=0.162ln2Z-2.833 9ln Z+1.389 8(下限) (11)

其中,比例距离Z在0.1~15 m/kg1/3范围内。

4 结论

通过搜集文献获取大量爆炸超压的试验与理论数据,并从不确定性角度出发,研究了爆炸超压的概率分布特征,主要得到以下结论:

1)爆炸超压试验数据受炸药类型、当量、形状及试验环境等因素影响明显,超压分布具有较高的离散性,且试验数据多以小当量炸药为主,比例距离多集中于0.4~2.0 m/kg1/3之间。

2)基于试验数据,针对垂直入射情况拟合给出反射系数公式,并得到根据入射超压获取反射超压的计算公式。

3)比例距离小于0.5 m/kg1/3时,爆炸超压概率密度服从指数分布;比例距离大于0.5 m/kg1/3时,爆炸超压概率密度服从正态分布。

4)比例距离小于0.5 m/kg1/3时,爆炸超压变异系数达最大值1;比例距离约在1.5~6 m/kg1/3间时,变异系数较小,在0.13~0.2之间;反射超压变异系数较入射超压略大。

5)根据不同比例距离下爆炸超压分布希望数据,拟合得到爆炸超压的计算公式与具有95%保证率条件下的超压分布范围计算公式。

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(编辑 胡玥)

收稿日期:2019-05-15

基金项目:? 国家自然科学基金(51608229);山东省高校科研发展计划(J18KA206)

编辑概况:? 杨涛春(1983- ),男,副教授,博士,主要从事爆炸灾害分析评估研究,E-mail:[email protected]

Received: 2019-05-15

Foundation items:? National Natural Science Foundation of China (No.51608229); Project of Shandong Province Higher Educational Science and Technology Program (No. J18KA206).

Author brief:? Yang Taochun (1983- ), associate professor, PhD, main research interest: anlysis and assessment of explosion disaster, E-mail: [email protected]

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