Analysis of long-term behaviour of nuclear reactor containment

For assessment of safety and durability of a nuclear power plant, knowledge of the containment behaviour under various service and extreme conditions is of crucial importance. The reliable analysis of a such large scale structure requires sufficiently realistic but still feasible numerical model to use, in which all relevant physical phenomena are reflected. The constitutive model for long-term behavior of concrete should include effects of moisture and heat transfer, cement hydration, creep, and shrinkage. This page illustrates the results of a such analysis.

The containment is a massive concrete structure with inner steel lining, heavilly reinforced and prestressed in cylindrical and dome parts.

Geometry of test

The problem consists in coupled heat&mass and mechanical analyses. Numerical model of heat&mass transport is based on coupled description of heat and miosture transport, hydration, creep, and shrinkage of concrete by Hellmich et all [1]. The structural analysis uses a constitutive model based on the microprestress-solidification theory by Bazant et al.[2]. The model neglects the influence of strains on transport properties caused by changes in porosity. Thus the analysis has been splitted into two subsequent parts in each solution step: transport and mechanical analysis. The model takes also into account four construction phases.

The boundary conditions were taken from NPP monitoring system. At the beginning, constitutive properties were estimated from laboratory experiments or table values. Then the parameters were calibrated using data taken from NPP monitoring system. Systematic recalibration is planned, to enable reliable service life planing. The results, that are presented, consist in strain history compared to measured values from two type of sensors (PLDS placed in concrete and PSAS placed on reinforcement) systematically located in seven height levels and four vertical positions around the containment, measuring strains in vertical, circumferential, and radial directions. in ten years period. For comparison, the computed strain values are shifted according to measured strains at the end of prestressing, because the initial deformation of the fresh concrete cannot be simulated by he present model. The strain scale in all graphs is 10e-5, time is in years.

Coparison with experimental dataCoparison with experimental data
Coparison with experimental dataCoparison with experimental data
Coparison with experimental data

After putting the contaiment into a service, deterioration of measurement quality of certain sensors can be observed. Also the boubdary conditions have changed during the time, which has not been fully reflected in the model. Detailed report can be found in [3].

  1. HELLMICH, C., MANG, H.A., ULM, F.-J. - Shotcrete as Part of the New Austrian Tunnelling Method: From Thermochemomechanical Material Modelling to Structural Analysis and Safety Assessment of Tunnels. PhD thesis, Vienna University of Technology, Vienna, Austria, 1999.
  2. BAZANT, Z.P., HAUGGAARD, A.B., BAWEJA, S., ULM, F.-J. - Microprestress-Solidification Theory for Concrete Creep I: Aging and Drying Effects. Journal of Engineering Mechanics, ASCE, 123(11): 1188-1194, 1997.
  3. Z. HORA and B. PATZAK. Analysis of long-term behaviour of nuclear reactor containment. Nuclear Engineering and Design, 273(3):253--259, February 2007.

This page is part of the OOFEM project documentation (
(c) 2006 Borek Patzak, e-mail:
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