Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method
Introduction
In recent years, interest has increased in the fracture behavior of reinforced concrete structures under impact loading, especially that for an aircraft crash into a nuclear power facility, and there is an urgent need to establish structural design methods for impact load. In general, structural damage to reinforced concrete structures under impact load includes global damage and local damage. Global damage is characterized as a dynamic elasto-plastic response over a large region of the structure for a relatively long period. Quite a good appraisal of global damage is possible with a conventional nonlinear finite element method using a time-response dynamic analysis. Local damage to reinforced concrete structures may include spalling of concrete from the front face, scabbing of concrete from the rear face and perforation of the missile through the structure. Since an extremely brief stress wave occurring immediately after impact causes this behavior, it has been very difficult to derive an analytical method which can estimate local damage. Therefore, until now, local damage to reinforced concrete structures has been evaluated mainly with empirical formulas derived from various types of impact tests. However, in recent years, research in the field of numerical analysis on fracture mechanics has advanced and various fracture analysis methods have been proposed and tried. Among them, the discrete element method (DEM) originally developed by Cundall (1971)can easily treat fracture mechanics of concrete such as cracking, splitting and crushing. This paper proposes a new analytical approach for assessing local damage to reinforced concrete structures subjected to impact load, by applying the DEM. It first outlines the basic concept and analytical formulation of the DEM. Next, it discusses the results of simulation analyses of concrete material tests, uni-axial compression tests and tensile splitting tests conducted to determine appropriate analytical parameters such as material constants, failure criteria and strength increase factors depending on strain rate. Finally, the adaptability of the DEM to local damage to reinforced concrete structures is verified through simulation analyses of various types of impact tests (Sugano et al., 1993a, Sugano et al., 1993b).
Section snippets
Analytical model and failure criterion
The DEM idealizes a structure as an assemblage of rigid circular elements connected to each other by non-linear springs and dashpots, as shown in Fig. 1. The following two states are defined for interaction forces between adjacent particles:
State 1: In the initial state, the interaction forces between particles are defined as compression, tension and shear. When these forces exceed the tensile failure criterion, the interactive condition changes to State 2.
State 2: In the secondary state,
Simulation analysis of concrete material tests
Simulation analyses of concrete material tests, uni-axial compressive tests and tensile splitting tests, were performed to investigate the validity of the analytical parameters employed in the DEM.
Outline of impact tests and analytical model
In the tests, target square concrete panels of 150 cm side length, and varying from 6 to 35 cm in thickness, were impacted by rigid and deformable missiles of diameter 101 mm and mass 3.6 kgf projected at 215 m s−1 perpendicular to the panel (Sugano et al., 1993a, Sugano et al., 1993b). Simulation analyses were performed for four panels: T180R and T180D of thickness 18 cm showing different damage modes according to the types of missiles, panel T300R of 30 cm thickness unperforated by a rigid
Outline of the tests
Full-scale impact tests were carried out using an actual aircraft engine (GE-J79 Engine) impacting reinforced concrete panels with and without a steel liner (Koshika et al., 1993; Sugano et al., 1993a, Sugano et al., 1993b). In the tests, a reinforced concrete panel specimen 7 m square and 115 cm thick, with 2.4 mm-thick corrugated deck plate (termed liner hereafter) attached using shear studs, was impacted by an actual engine (mass approximately 1.5 ton) at a velocity of 215 m s−1 (Test No.
Conclusions
This paper has discussed a new analytical approach for evaluating local damage to reinforced concrete structures subjected to impact loading by applying a DEM. The main conclusions are as follows:
The suitability of the analytical parameters employed in the DEM such as material constants, failure criteria and strength increase factors depending on strain rate, was confirmed through simulation analyses of concrete material tests on simple uni-axial compression tests as well as tensile splitting
References (10)
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