High-fidelity physics-based earthquake simulations : seismic vulnerability assessment of the Cadarache nuclear site.

Episteme is a philosophical term derived from the Ancient Greek word έπιστ ήμη, which can refer to knowledge, science or understanding and which comes from the verb έπίστ ασθαι, meaning to know, to understand, or to be acquainted with. In this sense, earthquakes are one of the most complex natural phenomena for scientists to understand and predict. This high uncertainty, coupled with their disaster potential, increases the overall associated seismic risk. The latter can be assessed by either following a deterministic approach (i.e. by directly modelling the physics behind the ground shaking phenomenon) or by either considering a fully probabilistic approach (baring on the statistics drawn from previous strong ground motion observations). However, in areas of moderate seismicity, such as metropolitan France, a general lack of direct observations limits the extensive application of non-linear data regression, due to scarcity of available recording databases. This drawback clashes with the demand of updated seismic safety margins for critical structures and infrastructures (nuclear power plants and dams especially). Given the fact that the majority of them has been constructed a few decades ago, French authorities face the urgency of a general reassessment of the seismic safety margins foreseen at the design stage, exploiting the gathered  nowledge in seismology, earthquake engineering, the new geophysical and geological data, as well as the new  echnological tools available. Nuclear facilities, dams and other important infrastructures must undergo extensive stress testing, to assess and update their status and functionality, in case an unexpected (at the design stage) earthquake occurs. This commitment fosters the definition of site-specific studies (the Cadarache nuclear site for instance) which can now be virtually tested via high-fidelity digital twins.

For a long time, geophysicists and seismologists have exploited rather simplified and generic seismological models, based on closed form solutions of the viscoelastic wave propagation problem, in simplified geological media (e.g. considering the Earth’s crust as sub-horizontally layered visco-elastic half-space). Many crucial issues have been neglected, due to the intrinsic complexity of the analytical models and the general lack of data to quantify them : 

— the heterogeneities in the Earth’s crust (at regional and site scale)

— the non-linearity of shallow soil deposits

— the surface topography

— solid-fluid interaction (coastlines, bathymetry etc)

Although the mentioned numerical models were capable of reproducing reasonably well the P, S or Rayleigh waves arrival times and the main reflections within the Earth’s crust, they were generally limited to the very low-frequency part of the radiated spectrum ( 0-1 Hz). On the other hand, the seismic design of critical structures (such as nuclear power plants) requires reliable input motion in a broader frequency band, ranging within 0 and 30 Hz : reactor and turbine buildings are very stiff and rigid structures, with non-negligible resonance modes at frequencies higher than 10 Hz. Moreover, a broad-band input motion is required whenever the nuclear facility equipment (piping system for instance) is taken into consideration.

This incompatibility trenched seismologists and structural engineers apart for a long time : the transient dynamics of aboveground structures (eventually with soil-structure interaction at the site scale) has been traditionally studied separately, by employing selected spectrum-compatible recordings as input motion.

In recent years, the ever increasing availability of computer power and related numerical methods paved the way to deterministic exploration of the scenarios space, compatibly with the degree of knowledge of focal issues, such as :

1. the 3-D geological structure of the Earth’s crust

2. the geomechanical properties of soil deposits and deep bedrock

3. the surface morphology (topography, bathymetry, coastlines)

4. the characteristics of the active faults (tectonic context, slip patches, focal mechanisms)

This physics-based numerical approach thrives nowadays : many historical strong ground motions have been successfully reproduced by HPC-based numerical codes, providing subtle insights on the anatomy of the earthquakes [5, 10, 14, 18, 19, 22, 24, 31, 33]. An impressive result was obtained by a Chinese research group, who run an non-linear earthquake simulation over a continental 320 km by 312 km by 40 km region, up to 18 Hz [26]. The use of octrees has made possible a high degree of scalability in mesh generation using up to 220.000 cores [12]. Moreover, high-fidelity modeling widened the research horizons concerning the study of complex features such as the attenuation and coherency of coda wave in the seismic signals [2], the directivity and the incoherence of the wave motion near-source [32], the non-linear site effects [27] among others. So far, very rare are the examples of complete fault-to-structure interaction studies, with strong Soil-Structure Interaction coupling (see for instance [16, 29, 42]). The most reliable and efficient method was proposed by Bielak et al. [8], called the Domain Reduction Method. It consists into a two-step analysis, declined as follows : (i) regional scale wave-propagation in simplified geological medium (typically the deep visco-elastic stratified Earth’s crust), not including the non-linear site-effects ; (ii) a second run of the analysis on a smaller domain (eventually adding the structure) delimited by an artificial boundary at which equivalent inertial forces and free-field velocities, obtained in the precedent step, are applied. Quinay et al. [17] applied this method to study the structural response of the Kashiwazaki-Kariwa Nuclear Power Plant (KKNPP) in a fault-to-structure framework, up to 1 Hz. Albeit the outstanding results obtained by HPC physics based modeling, due to its ontological determinism and to the large computational costs at stake, the methodology is still hardly adaptable to tackle large parameter sweeps, 

provided with the high level of uncertainty related to geology, source and site, convolved with the numerical dispersion. Moreover, uncertainty propagates through the model, which must be quantified when performing seismic risk assessment of critical structures by exploiting synthetics time-histories.

In this project, submitted to the 2019 Jean Zay Grand Challenge, hosted by GENCI, we aim at constructing an earthquake scenario space for the Cadarache nuclear site (France)

at the occurrence of extreme ground shaking events. This represents one of the major goals of the PIA 2 project SINAPS@ , benefited from French state funding managed by the National Research Agency under program RNSR Future Investments bearing reference No. ANR-11-RSNR-0022-04 4. For this purpose, a strict collaboration with Commissariat à l’énergie atomique et aux énergies alternatives (CEA) and Institut des Sciences de la Terre (IsTerre) is established, in the framework of the SINAPS@ ANR project. The paradigm we pursue seeks the progressive integration of high-fidelity numerical simulations and recorded data, towards robust hybrid earthquake prediction. Figure 1a shows this paradigm schematically. We intend to tackle this challenge by employing an efficient HPC multi-tool platform developed jointly by MSSMat UMR CNRS 8579 Laboratory (CentraleSupélec), CEA and Insitut de Physique du Globe de Paris (see Figure 1b), capable of simulating broad-band non-linear seismic wave propagation in highly heterogeneous media, from the fault to the aboveground structures (i.e. at a regional scale).