Explosive damage to industrial buildings: Assessment by resampling limited experimental data on blast loading

Abstract

Assessment of damage to industrial buildings due to accidental explosions in air is considered. It is suggested to formulate the result of the damage assessment in the form of risk. The expression of risk embraces probabilities of foreseeable damage events (damage probabilities) and outcomes (consequences) of suffering these events. The situation is examined when blast loading imposed by an accidental explosion is predicted by a series of experiments. They yield a small‐size sample of blast loading characteristics. It is suggested to idealise the formation of explosive damage to industrial buildings by means of event trees diagrams. A quantitative analysis of these diagrams can be carried out by developing fragility functions for their branching points. Each branching point is used to represent a structural failure contributing to the final explosive damage. The fragility functions are applied to expressing the conditional probabilities of explosive damage. With these probabilities, a technique of frequentist (Fisherian) inference is applied to assessing the explosive damage. This technique is called statistical resampling (Efron's bootstrap) and applied as a practical, albeit not equivalent alternative to the Bayesian approaches. It is shown that statistical resampling is capable to yield confidence intervals of damage probabilities and can be applied almost automatically. It operates without using cumbersome methods of statistical inference developed in the classical statistics. The bootstrap confidence intervals do not contain any subjective information except the degree of confidence for which these intervals are computed. The degree of confidence must be chosen by the engineer. The bootstrap confidence intervals are applied to estimating damage probabilities on the basis of the small‐size sample of blast loading characteristics. An estimate of the risk of explosive damage is expressed as a set of bootstrap confidence intervals computed for damage probabilities and related outcomes of this damage.

Santrauka

Pramoniniu pastatu pažaidu, kurios gali būti sukeltos avariniu (atsitiktiniu) sprogimu, vertinima siūloma formuluoti rizikos skaičiavimo uždavinio pavidalu. Ši rizika aprepia nuspejamu atsitiktiniu pažaidu ivykiu tikimybes (pažaidu tikimybes) ir padarinius, kurie gali būti patirti, pasireiškus šiems ivykiams. Nagrinejamas atvejis, kai pažaidas reikia prognozuoti atliekant nedideli skaičiu kartotiniu eksperimentu ir gaunant santykinai maža statistine sprogimo apkrovu imti. Pažaidas siūloma vertinti idealizuojant ju kilimo procesa naudojant ivykiu medžio diagramas. Teigiama, kad skaičiuoti galima kiekvienam diagramos išsišakojimui sudarant pažeidžiamumo funkcijas. Kiekvienas išsišakojimas turi vaizduoti konkrečia pažaida. Pažeidžiamumo funkcijos taikomos salyginems pažaidu tikimybems išreikšti. Ivertinus šias tikimybes, besalygines pažaidu tikimybes siūloma vertinti kartotinio statistinio emimo metodu. Jis laikomas vertinimo, pagristo Bejeso statistines teorijos metodais, alternatyva. Kartotinis statistinis emimas leidžia skaičiuoti besalyginiu pažaidu tikimybiu pasikliautinuosius intervalus. Taikant ši metoda, galima išvengti sudetingu klasikines matematines statistikos procedūru taikymo. Skaičiuojant pasikliautinuosius intervalus kartotinio statistinio emimo būdu išvengiama subjektyvios informacijos. Inžinieriui tereikia priimti subjektyvu sprendima, koki pasikliautinumo lygmeni naudoti skaičiuojant pasikliautinuosius intervalus. Parodyta, kad šiuos intervalus galima skaičiuoti net kai statistine sprogimo apkrovu imtis yra maža. Sprogimu sukeliama rizika siūloma išreikšti pasikliautinaisiais pažaidu tikimybiu intervalais.

Keywords:

• panel
• cladding
• explosion
• damage
• impulsive loading
• resampling
• bootstrap
• simulation
• fragility function
• vulnerability

Raktažodžiai::

• plokšte
• apdaras
• sprogimas
• pažaida
• impulsine apkrova
• kartotinis statistinis emimas
• stochastinis modeliavimas
• pažeidžiamumo funkcija