NON LINEAR BEHAVIOUR OF NUCLEAR CONTAINMENT SHELLS UNDER IMPACT AND BLAST LOADING

Abstract

The impact of an aircraft, missiles and explosions has been drawing attention of the engineers all over the world after the first World War. Nuclear containment shells in many countries are pre-stressed concrete shells with an outer reinforced concrete shell. Studies are reported in literature on the impact of an aircraft on the outer reinforced concrete shell. Studies are rarely available on the effect of explosions on the containment shells. Material constitutive relationships under intense dynamic loads is relatively less known, though few models are available to model the non-linear behavior under these loads. These models need refinement with the availability of more experimental tests on concrete. In the present study an effort has been made to study the effect of aircraft impact and external and internal explosions on nuclear containment shells with major attention to explosions. Explosives detonated in air produce shock waves, which travel with the velocity of sound. The shock wave is composed of high intensity shock front, which impinges on structures lying in its path. Present state of knowledge has many limitations in assessing the effects of shock waves especially the shock wave interaction with the structure. In this study a rational way of computer simulation of blast loading on different parts of a cylindrical shell has been proposed. Blast load is specified by the amount of blast charge and the detonation distance. Total blast load on a structure is composed of three parts viz. incident over-pressure, reflected overpressure and drag pressure of the accompanying blast wind. The net effect is obtained by interaction of the three parts. Over-pressure depends primarily upon the detonation distance and the magnitude of the blast charge. The reflected overpressure depends upon the angle of incidence, which varies on different parts of the cylindrical structure along circumference and there is time lag in different parts along the circumference. Both these effects have been considered in the computer simulation. The dynamic pressure depends upon the shape of the structure and incident overpressure. There is difference in the blast load on the front and back face of the cylindrical structure. vm The reinforced cement concrete and pre-stressed concrete nuclear containment shells have been modeled using the 20-noded iso-parametric brick elements. The nuclear containment shells are heavily reinforced and therefore the modeling of reinforcement in reinforced concrete nuclear containment shells and pre-stressing cables in pre-stressed concrete nuclear containment shells are important in the determination of response. An embedded formulation has been used to model the reinforcement and a discrete formulation lying inside the brick element has been used to model pre-stressing cables. The formulation accurately accounts for the line load exerted by the cable by the pre-stressing cable on the concrete. Integration points are the sampling points used in the determination of material state in the non-linear analysis and therefore sufficient number of gauss points are required to accurately model the material state and at the same time the formulation should be computationally efficient. Reduced integration with 15 gauss points has been used in the present formulation. The predictor corrector form of Newmark Constant Average Acceleration Method has been used to integrate the non-linear dynamic equilibrium equations. The non-linear deformation in concrete is caused by two sources; firstly the cracking of concrete takes place at low level of tensile stress and secondly the initiation of plastic and viscoplastic deformation starts at low level of stress (0.3 to 0.4 fc) in compression. The cracking of concrete in the present formulation has been modeled using smeared cracking approach, which is computationally attractive and viable for massive concrete structures like nuclear containment shells under transient dynamic loading. Maximum principal strain criterion has been used for initiation of cracking in concrete. Different models available for modeling tension softening and tension stiffening have been reviewed and a suitable model for tension stiffening has been implemented into the finite element code. The adopted tension stiffening rule in the present formulation depends upon the modulus of elasticity ratio of steel and concrete, area ratio of steel and concrete and yield strain of steel. The shear transfer through aggregate interlock has been accounted for using a simple model. To model the non-linearity in concrete under three-dimensional stress condition and to include the strain rate effect, plasticity and viscoplasticity have been discussed. The Perzyna's theory of visco-plasticity has been used to model the material non-linearity and strain rate IX effect. Material modeling in plasticity and visco-plasticity requires a yield and failure criterion. A recently developed three-dimensional failure criterion has been implemented into finite element code. The meridians of the failure criterion are parabolic and the deviatoric section changes from triangular to circular form with increasing confinement pressure. The failure criterion is described by three parameters of which the two parameters ie; uni-axial tensile and compressive strengths are well defined for concrete. The third parameter is an eccentricity parameter, which is a function ofthe bi-axial compressive strength and the ratio of compressive and tensile strengths of concrete. The strain rate effect has been included at two levels. The fludity parameter has been made strain rate dependent from experimental stress strain curves available under uni-axial dynamic loading conditions at different strain rates. The failure surface has been made to expand or shrink at a gauss point depending upon the. strain rate again as a function of the dynamic to static strength ratios available as determined from uni-axial loading conditions. Two validation problems have been solved using the developed methodology and finite element software for reinforced concrete structures. An outer reinforced concrete nuclear containment shell has been analyzed for impact of Boeing 707-320, which earlier has been studies by many researchers and results have been compared to validate the algorithm and software. Four different problems have been analyzed to validate the developed methodology and finite element software for pre-stressed concrete structures. One validation problem is a pre stressed concrete nuclear containment shell subjected to a pressure loading for which the experimental deflections are available. The same pre-stressed concrete nuclear containment shell has been analyzed for an internal blast loading of 175 kg TNT. The results indicate that the shell is capable of withstanding the above internal blast loading without any cracking or non linear deflections in the structure. From the validation problems and other problems of the reinforced concrete and pre-stressed concrete structures analyzed, it can be concluded that the developed algorithm and the software is capable of predicting the non-linear response with a reasonable degree of accuracy for impact and blast loading. The behaviour of the outer reinforced concrete nuclear containment shell has been studied for impact of Boeing-707-320 and Phantom aircraft. From the study it has been found that Phantom aircraft is having more damage potential compared to Boeing 707-320. Parametric studies have been made for different amounts of blast charge at a detonation distance of 100m. Some of important parameters like percentage cracked volume, stresses in the concrete and reinforcement, number of gauss points crossing the yield and failure surfaces have been determined for different amount of blast charges and results have been compared. It has been found from the study that for small detonation distance of 20 m, the blast pressures are impulsive in nature and the structure is capable of withstanding much more blast pressure compared to dynamic pressure from greater detonation distances. The effect of variation of percentage reinforcement has been studied for a surface blast of 20t TNT at a detonation distance of 100 m. Critical distances have been evaluated different amount of blast charges varying from 0.5t to 20t TNT.