Arja Saarenheimo, Heikki Keinänen and Heli Talja VTT Manufacturing Technology
Espoo, Finland
1. Introduction
Capabilities for effective structural integrity assessment have been created and extended in several important cases. In the following presented applications deal with pressurised thermal shock loading, PTS, and severe dynamic loading cases of containment, reinforced concrete structures and piping components.
Hydrogen combustion within the containment is considered in some severe accident scenarios. Can a steel containment withstand the postulated hydrogen detonation loads and still maintain its integrity? This is the topic of Chapter 2. The following Chapter 3 deals with a reinforced concrete floor subjected to jet impingement caused by a postulated rupture of a near-by high-energy pipe and Chapter 4 deals with dynamic loading resistance of the pipe lines under postulated pressure transients due to water hammer.
The reliability of the structural integrity analysing methods and capabilities, which have been developed for application in NPP component assessment, shall be evaluated and verified. The resources available within the RATU2 programme alone cannot allow performing of the large scale experiments needed for that purpose. Thus, the verification of the PTS analysis capabilities has been conducted by participation in international co-operative programmes (Keinänen et al. 1998a). Participation to the European Network for Evaluating Steel Components (NESC) is the topic of a parallel paper in this symposium. The results obtained in two other international programmes are summarised in
2. Steel containment analyses
Containment performance is of general interest for nuclear reactor safety assessment. Hydrogen detonation loads are considered within the scope of so- called severe accident analyses. Hydrogen combustion within containment rooms can lead to high pressures and temperatures, which may loose containment integrity. Transport and mixing of hydrogen inside the containment are critical factors determining the hydrogen burning mode. If the reacting gases, hydrogen and oxygen, are initially premixed, deflagration and detonation are possible combustion modes.
Gaseous detonations are shock waves driven by a chemical reaction. Unlike a deflagration, the chemical reaction is caused by shock wave compression in unburnt gas, and takes place slightly behind the shock wave. Typical speeds for detonation waves are 1000 - 2200 m/s, and they result in rapidly varying, dynamic pressure loads on containment structures.
The steel containment considered under hydrogen detonation conditions has the dimensions of the containment of Loviisa nuclear power plant. The initial hypothetical detonation loading data used in three-dimensional analyses was defined by the Radiation and Nuclear Safety Authority (STUK).
Dynamic structural analyses (Saarenheimo 1994) were performed with the commercial general purpose finite element code, ABAQUS 5.2 and 5.4. Several axisymmetric materially and geometrically non-linear analyses were carried out using different kinds of detonation impulses acting in the middle of the dome. Success criteria for dynamic loading were presented for elastic and inelastic analyses.
Extensive three-dimensional analyses comprised elastic, elastic-plastic and elastic-visco-plastic calculations under one detonation impulse at the belt line, at the same axial position where the fifth stiffener is located. According to materially non-linear three-dimensional calculations the containment succeeded this hypothetical detonation. The effect of the detonation is rather local and the effect of the strain rate to the yield strength is remarkable. Especially, when the strain rate dependence is considered, the period needed to achieve the maximum
peak value of the impulse is essential and affects considerably the results. The effect of the geometrical non-linearity is essential.
The amount of the plastic deformation is roughly taken dependent of the area of the triangle shaped impulse. According to the elastic-plastic and elastic-visco- plastic three-dimensional analyses the containment succeeded the criteria for free field strains considered in this study. Lack of considering geometrical non- linearity makes these results conservative.
Figure 1. The displacements due to a hydrogen detonation impulse at the belt line of a steel containment.
detonation load evaluation. Two detonation pulses corresponding the amount of 5 kg and 10 kg hydrogen were analysed. The detonation centre located in the lower part of the dome 4 m from the wall, Fig. 1. Also the parameters simulating the strain rate dependence of the yield strength were varied in order to find out the effect of this phenomenon. With the assumptions used in this study the containment withstands the smaller load which corresponds to a maximum impulse of 12 kPa. The containment does not withstand the higher load corresponding to a maximum impulse of 26 kPa. Deformation rates were about 10 - 25 s-1 and the effect of the strain rate on the yield strength is remarkable. The effect of the geometrical non-linearity is crucial. It is important to note that details like penetrations where stress peaks easily occur were not considered in this study. The main aim of this study was to determine detonation transients, predict the structural response and evaluate the capability of the tools available.
3. Reinforced concrete structures under
impact loads
Safety-related reinforced concrete structures in nuclear power plants shall be designed to withstand specified operation and accident conditions. A particular concern is dynamic loading arising from ruptures of near-by high-energy piping. Such loading typically includes effects of pipe whip, missile and jet impingement.
In this study the capabilities of commercial general purpose finite element analysis programs ADINA and ABAQUS for analysing reinforced concrete structures under impact loads were evaluated and tested. The main differences between the programs lie in the constitutive modelling of concrete, in the available element types and in time integration procedures. Also the ways to model reinforcement varies a lot. Explicit time integration proved to be necessary for practical applications. Thus, the ABAQUS/Explicit program was chosen for further use.
ABAQUS/Explicit allows the combination of two- and three-dimensional solid elements with rebar layers. Brittle concrete Mode I cracking with crack closure and reopening can be modelled. Concrete is assumed to behave linearly elastic under compression. The tension softening model is user defined and based on
fracture energy, displacement or strain. The plastic deformations of the reinforcement are proportional to the plastic energy absorbed in the structure. Bond slip and dowel action at rebar/concrete interface can not be simulated. Numerical examples were calculated to assess the capability of ABAQUS/ Explicit to simulate numerically the behaviour of impact loaded reinforced concrete structures (Saarenheimo 1997a). Calculational results were evaluated for impact loaded beams against test results found in the literature. The effects of modelling the load and choosing the parameters defining the concrete behaviour after cracking were studied. Fig. 2 compares calculated and measured strain values in the reinforcement of the lower surface of the beam. According to the results, ABAQUS/Explicit can be successfully applied in cases, where the compression crushing of concrete is not decisive.