Dynamic response of a reinforced concrete slab subjected to air blast load

doi:10.1016/j.tafmec.2011.11.002

Theoretical and Applied Fracture Mechanics

Volume 56, Issue 3, December 2011, Pages 140-147

https://doi.org/10.1016/j.tafmec.2011.11.002 Get rights and content

Abstract

Reinforced concrete is the principal material for military engineering and nuclear power plant containment. However, impacts and explosions could completely destroy such structures, causing tremendous casualties and property loss. Hence, this study conducts an analysis on the propagation law of a blast pressure wave and the dynamic response of reinforced concrete structures under explosive pressure wave effects. This study uses proper state material parameters and equations and then applies the nonlinear finite element analysis software LS-DYNA to conduct a numerical simulation of a free-field explosion model. After comparison with the computed results from empirical equations and validating the reliability of the numerical analysis model, the destruction and influencing factors on reinforced concrete slabs, under the effects of a blast pressure wave, are investigated. The results can serve as a reference for future analysis and design.

Introduction

Reinforced concrete is the principal material used for the military engineering and containment of nuclear power plants. Its mechanical responses under the effects of dynamic loads are complicated. If the load acts slowly on a large plane, it can be analyzed using the structural mechanics theory. If the load acts rapidly on the concrete structure, due to the inertia and a short duration effects, the response forms a local region of high pressure and high temperature. The response is centered on the load point and an outgoing shock wave is formed inside the concrete. The compressive wave reflection from the rear faces of the target produce a tensile wave which interacts with compressive waves resulting in spalling. Concrete behavior is also different from that under the effect of a quasi-static load. This problem is complicated as the behavior of the material is difficult to control and the mechanical behaviors vary under different load conditions. The methods for studying this problem include (1) analytical methods: under appropriate assumed conditions, solving the problem using a theoretical model after idealizing the shock wave propagation or impact load, however this method is only applicable to simple problems; (2) experiments: conducting small-scale or prototype testing experiments by selecting the proper effect parameters for the blast pressure wave and analyzing the results using the statistical regression method to obtain the empirical formula or figures for the structural dynamic response; (3) numerical analysis: using a computer and the fundamental laws of mechanics (the laws of mass, energy, and momentum), to properly introduce a dynamic response in the material and the failure criterion using numerical methods, such as the finite element method or finite difference method [1], [2], [3], [4], [5], [6].

A number of papers [7], [8], [9], [10] conducted in-depth studies on the propagation law of blast pressure waves in different mediums and proposed some computing formulas. The work in [11] proposed the equivalent conversion law for different kinds of explosives. The TM5-855-1 [12] and TM5-1300 [13] explained the principles of explosion and calculation methods. To explore the anti-explosion performance of structural components, [14] carried out experiments and numerical simulations on the visco-plastic behavior of thin metallic plates subjected to an explosion. The work in [15] conducted experimental and numerical studies on the response of stiffened slabs subjected to gas explosions. The work in [16] analyzed the transient response of isotropic and laminated plates to close proximity blast loads. Li et al. [17] investigated the explosion resistance of a metallic plate with a square hole. The work in [18] studied the modeling considerations of impulsive loads on reinforced concrete slabs. Hao et al. [19] conducted numerical analysis on the elastic–plastic dynamic response of steel columns subjected to the pressure wave from an underground explosion. In [20] performed an analysis on explosive damage to reinforced concrete columns. In respect to the explosion resistance of walls, Nash et al. [21] examined the spall damage to concrete walls from close-up cased and uncased explosions in the air. Varma et al. [22] discussed the damage to brick masonry panel walls under high explosive detonations. Makovicka [23] studied the dynamic response of thin masonry walls under explosion effects. Mays et al. [24] considered the dynamic response to the blast load of concrete wall panels with openings.

Although the above studies provided plentiful results, considering the dynamic response of reinforced concrete structures subjected to blast loads is complicated, this study conducts an analysis of the dynamic response and damage pattern of an RC plate subjected to different blast loads using the nonlinear finite element analysis program LS-DYNA [25]. The results can serve as reference for future analysis and design.

Section snippets

Law of propagation of explosions in the air

The sudden release of energy from an explosion in the air produces an instantaneous high-temperature, high-pressure detonation wave in the atmosphere. This pressure wave causes the rapid expansion and propagation of ambient gases. The high-pressure air at the front end of these gases contains most of the explosive energy and is known as the blast pressure wave. The energy carried by the blast pressure wave will decrease as the propagation distance and time increases. The pressure behind the

Analysis of reinforced concrete plate subjected to a blast pressure wave

In the analysis model built upon Lagrangian elements for explosives and ambient mediums, the finite element mesh instantly distorts when studying the blast pressure wave effects on the structure and the medium moving with the explosives. Hence, the Jacobian of the integration point may become a negative value and the stable time step size needed for the calculation approaches zero. As a result, either the overall computing time extends infinitely or the computing process diverges. If the model

Concrete

The dynamic behavior of concrete determines the concrete’s strength characteristics. The constitutive law employs the plastic flow rule on its principal stress space to differentiate between the hydrostatic and deviatoric stress portions. Different load functions are used to describe the behavior of the two parts. The material model based on a low compressive pressure zone is described in terms of the deviatoric stress. In the impacting process where the shock pressure induced on the material

Results and discussion

In order to validate the accuracy of the analysis results, we conducted a free-field explosion simulation and compared the blast pressure wave parameters. Fig. 5 shows a time history comparison of the finite element mesh to blast pressure. When the time history comparison was conducted at a distance of 200 cm from the center point of the explosion, it was found that the blast pressure wave time is very short. The blast pressure wave attenuates quickly after arriving at the peak. As shown in the

Conclusions

This study employed the nonlinear finite element analysis software LS-DYNA to discuss the dynamic responses of an RC slab under blast load. The results are summarized as follows:

(1)
The free-field blast pressure wave simulation indicates that the mesh size is very sensitive to shock wave propagation, thus, to guarantee that the results are close to the actual situation the finite element mesh division should be as fine as possible.
(2)
For the RC slab dynamic response the computed results show that

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Dynamic response of a reinforced concrete slab subjected to air blast load

Abstract

Introduction

Section snippets

Law of propagation of explosions in the air

Analysis of reinforced concrete plate subjected to a blast pressure wave

Concrete

Results and discussion

Conclusions

Comput. Struct.

Int. J. Impact Eng.

Int. J. Impact Eng.

Int. J. Impact Eng.

Journal of Constructional Steel Research

Int. J. Impact Eng.

Int. J. Impact Eng.

Eng. Fract. Mech.

Modelling of concrete structures subjected to shock and blast loading: an overview and some recent studies

Struct. Eng. Mech.

Validation study on numerical simulation of RC response to close-in blast with a fully coupled model

Struct. Eng. Mech.

Dynamics of Framed Structures

Explosions in Air

Explosive Shocks in Air

Blast Effects on Building