Pressure−impulse diagram method – a fundamental review

Abstract

Accidental and deliberate explosions stemming from catastrophic events in the petroleum industry, incidents during complex manufacturing processes, mishandling or failure of domestic gas appliances or installations, terrorist attacks and military engagements, are becoming increasingly relevant in structural design. Pressureimpulse (P-I) diagrams are widely used for the preliminarily assessment and design of structures subjected to such extreme loading conditions. A typical P-I diagram provides information concerning the level of damage sustained by a specific structural member when subjected to a blast load. This paper presents a state-of-the-art review describing the development of the P-I diagram method over the last 70 years, the main assumptions upon which its development is based and the framework through which such the method is applied in practice. The structural analysis methods used for the derivation of P-I curves are discussed and the existing approaches are categorised according to algorithms used. A review of the P-I curve formulae proposed to date is performed, where the formulae are classified according to the formulation methods.

Extended P-I diagram method

“…These three parts represent the (I) impulsive, (II) dynamic and (III) static or quasi-static loading regimes. The vertical asymptote is called impulsive while the horizontal asymptote can be static or quasi-static depending on the blast load rise time [7,12]. In this paper, a zero-rise time is considered; therefore, the horizontal asymptote becomes quasi-static.…”

“…The derivation of P-I curves using the NLFEM analysis requires generation of multiple points on the P-I plane by multiple simulations of the column subjected to a blast load with different combinations of peak pressure 0 and impulse . To make the process of curve derivation more efficient, various search algorithms can be applied [7]. These search algorithms can be divided into a pressure-controlled, impulsecontrolled or mixed unidirectional search.…”

“…Additionally, it is often important to be able to quickly but realistically assess the residual load-carrying capacity of a structure in the aftermath of an explosion in order to determine its survivability or enable the evacuation of injured occupants and allow access to critical services/controls. Pressure-impulse (P-I) diagrams can be used for developing an effective and practical method for the preliminary assessment of structures damaged by explosions, e.g., [1][2][3][4][5][6][7]. They provide explicit visual information concerning the loading regime and the post-blast (residual) condition of a structure.…”

“…This method can also be adopted for assessing the residual load-carrying capacity and the survivability of a structure after an explosion event. P-I diagrams are usually developed for a single structural element, e.g., beam, column, wall, slab [7], although the application of P-I diagrams to frames [8] and even whole buildings [9] is possible. Each P-I curve is built for a unique combination of loads acting on a specific structure and for a specific level of damage [7].…”

“…P-I diagrams are usually developed for a single structural element, e.g., beam, column, wall, slab [7], although the application of P-I diagrams to frames [8] and even whole buildings [9] is possible. Each P-I curve is built for a unique combination of loads acting on a specific structure and for a specific level of damage [7]. The P-I diagrams are sensitive to variations in the design parameters of the structure considered and load time-history applied.…”