Extended P-I diagram method

Leon Chernin (Lead / Corresponding author), Margi Vilnay, Demetrios M. Cotsovos

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
135 Downloads (Pure)


The pressure-impulse (P-I) diagram method is used in practice (for civilian and military applications) for predicting the level of damage sustained by structures when subjected to blast loads and for assessing the imposed loading regime. Each P-I curve is associated with a certain structural configuration as well as a specific form of blast load and level of damage sustained. When assessing the effect of different parameters (associated with the form of the imposed load and the design of the structure considered) on structural performance, a series of new P-I curves need to be derived. This paper presents an extended P-I diagram method, which is based on derivation of complementary diagrams that can define the effect of two parameters (e.g., the level of axial loading imposed onto a column and the level of damage sustained) on the quasi-static and impulsive asymptotes, thus governing the positions of P-I curves in the diagram plane. The extended P-I diagram method is presented in dimensional and normalised forms. The dimensional form simplifies the derivation of new P-I curves, while the normalised form simplifies the procedure adopted for assessing the behaviour of a certain structure when subjected to a new set of loads. The application of the proposed method is demonstrated in both forms using a typical reinforced concrete (RC) column subjected to a blast load. The column is modelled using finite element analysis capable of accounting for the nonlinear behaviour of concrete and steel. A novel method is proposed for material modelling of concrete. The new material model is validated at both material and structural levels against relevant experimental data. P-I diagrams are initially derived for the axially unloaded column, while complementary diagrams are derived for the column loaded by different axial forces. The framework of the extended P-I diagram method employed for the derivation of new P-I curves and the assessment of the level of damage sustained by the column when subjected to different loading conditions is provided herein.

Original languageEnglish
Article number111217
Number of pages18
JournalEngineering Structures
Early online date25 Aug 2020
Publication statusPublished - 1 Dec 2020


  • Blast
  • Column
  • Damage
  • Finite element modelling
  • P-I diagram method
  • Reinforced concrete

ASJC Scopus subject areas

  • Civil and Structural Engineering


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