Projection-based model order reduction for prestressed concrete with an application to the standard section of a nuclear containment building

TL;DR

The paper addresses the long-term ageing of large prestressed concrete structures, focusing on nuclear containment buildings, by developing a projection-based ROM with offline-online POD-Greedy training and empirical quadrature hyper-reduction to accelerate nonlinear 3D-1D THM simulations. The methodology handles a coupled THM problem (concrete 3D rheology and 1D thermo-elastic cables) via a weakly coupled, multi-model formulation and reconstructs full-field responses with Gappy-POD on a reduced mesh. Numerical results on a standard containment-section RSV demonstrate strong speedups (up to an order of magnitude or more) while maintaining high-fidelity displacement fields and accurate quantities of interest such as prestress loss and cable forces, both for non-parametric reproduction and parametric variations. The work provides a practical, industrially relevant ROM framework suitable for rapid scenario analysis and data assimilation in NCB ageing studies, with clear avenues for extending error indicators, larger parameter spaces, and finer meshes.

Abstract

We propose a projection-based model order reduction procedure for the ageing of large prestressed concrete structures. Our work is motivated by applications in the nuclear industry, particularly in the simulation of containment buildings. Such numerical simulations involve a multi-modeling approach: a three-dimensional nonlinear thermo-hydro-visco-elastic rheological model is used for concrete; and prestressing cables are described by a one-dimensional linear thermo-elastic behavior. A kinematic linkage is performed in order to connect the concrete nodes and the steel nodes: coincident points in each material are assumed to have the same displacement. We develop an adaptive algorithm based on a Proper Orthogonal Decomposition (POD) in time and greedy in parameter to build a reduced order model (ROM). The nonlinearity of the operator entails that the computational cost of the ROM assembly scales with the size of the high-fidelity model. We develop an hyper-reduction strategy based on empirical quadrature to bypass this computational bottleneck: our approach relies on the construction of a reduced mesh to speed up online assembly costs of the ROM. We provide numerical results for a standard section of a double-walled containment building using a qualified and broadly-used industrial grade finite element solver for structural mechanics (code$\_$aster).

Figures (28)

• Figure 1: Highlighting the relevance of the ROM methodology for an industrial application: application to an HF finite element (FE) model for the simulation of a containment building modeled by a THM approach for prestressed concrete
• Figure 2: Key ideas of the greedy methodology and the ROM approach adopted for the mechanical simulation of prestressed concrete. The different components needed to define are provided in colors: blue corresponds to components similar to the previous work, whereas red corresponds to the specific components within the multi-modeling framework for prestressed concrete
• Figure 3: Weakly-coupled chained THM approach for large prestressed concrete structures. Each step provides different fields of interest: at the end of the thermal calculation, we get the temperature field ($T$) and the degree of hydration of the concrete ($\xi$; which will be always analytically given in our simulations); at the end of the hydric calculation, we get the water content of concrete ($C_w$); at the end of the mechanical calculation, we get the displacement fields in the steel cables and in the concrete, the associated deformations ($\varepsilon = [\varepsilon^{\rm c}, \varepsilon^{\rm s}]$), the stresses in the concrete ($\sigma$) and the normal forces in the cables ($\text{N}$).
• Figure 4: Definition of the sorption-desorption function $f_d$ (defined in Eq \ref{['sec:THMmodel:subsec:consEq:subsubsec:THEq:eq:sorptionfunc']}). The table shows the point values given to define the function. The function is computed by linear interpolation between those points. The reference configuration corresponds to $h=100$, which is the initial RH value in the wall.
• Figure 5: Parameters for the three-dimensional mechanical model (concrete)