Numerical simulations of energy absorbing boundaries for elastic wave propagation in thick concrete structures subjected to impact loading

Abstract: As many of the world’s nuclear power plants are near the end of their supposed life span a need arise to assess the components crucial to the safety of these plants. One of these crucial components is the concrete reactor confinement; to assess its condition, non-destructive testing (NDT) is an attractive method. Traditional testing of concrete structures has comprised of drilling out a sample and performing stress tests on it, but because of the radioactive environment inside the containment this method is far from ideal. NDT is of course possible to use at any structure but at reactor containments the benefits from not creating holes in the structure are prominent; NDT is also an attractive option from an esthetical point of view because it leaves the structure intact. The NDT method pertaining to this study is the impact echo method which comprise of applying a force on the structure, usually a hammer blow, and measuring the response with a receiver. The impact will excite waves propagating in the structure which gives rise to Lamb modes. Lamb modes are structural oscillations of the wall and it is the frequency of these modes that are used to determine the thickness of the wall. The elastic properties of the structure can in turn be obtained by measuring the velocities of the waves propagation. It is also possible to use the impact echo method to detect irregularities in the structure such as cracks or delamination. To simulate the dynamics of a system using NDT numerical methods such as finite element modeling (FEM) is often used. The purpose of this study is to assess the possibility to utilize absorbing layers using increasing damping (ALID) in models to reduce the computational time of FEM analyses. ALIDs are used at the edges to simulate an infinite system and are thus supposed to cancel out incoming waves to prevent unwanted reflection from the edges. The models in this study have all pertained to two dimensional plates utilizing infinitesimal strain theory; the decrease in computational time is significant when using ALIDs and for three dimensional models it would be even more so. The ALIDs are specified by length and maximum mass proportional Rayleigh damping (CMmax), in this study three different lengths are tested, 0.5, 1.5 and 4.5 m for CMmax ranging from 103 to 2'105 Ns/m. The damping is increased with increasing distance into the ALID with specified maximum value at the back edge. However, it should be noted that the increase in damping causes difference in impedance between elements and if this difference is too large it will cause reflections of waves at the boundary between the elements. The ALID must thus be defined so that it sufficiently cancels out the wave without causing unwanted reflections due to impedance differences. The conclusion is that the 0.5 m long ALID does not provide good results for any choice of maximum mass proportional Rayleigh damping. Both the 1.5 and 4.5 m long ALIDs are, however, concluded to be applicable; the 1.5 m ALID having 2'104 < CMmax <5'104 Ns/m and the 4.5 m ALID having 5'103 < CMmax < 104 Ns/m are choices that have shown promise in the performed simulations. The hope is that the results obtained in this study will aid in the development of numerical analysis techniques for NDT methods that can be used in the construction of new reactor confinements and/or maintenance of existing reactor confinements and other thick concrete structures.