How we designed the Paris 2024 Olympic track

Design of synthetic sports surfaces is a challenging task, since the final product must balance different performance needs and athletes’ safety; shock absorption is a key parameter that must be controlled to achieve this goal. The current state of the art is represented by multi-layered prefabricated tracks: their complex geometrical patterns, in combination with specific material formulation, allow for unprecedented performance tuning. This has been carried out in the past with the development of 3D visco-hyperelastic finite element (FE) models, able to predict the shock absorption characteristics of a given sports surface with very high accuracy. Numerical simulations can be an extremely useful tool to optimize the track design; however, the sheer number of involved parameters coupled with the high computational cost (usually due to non-linearities arising from material behaviour and high deformations, to complex contact phenomena and to dynamic effects) pose serious limits to the practical exploitation of this tool. To overcome these limitations, we built a high-level surrogate model, calibrated on the results of a sufficiently large but limited number of FE simulations, to evaluate the shock absorption characteristics of a much broader set of geometrical variants. Among the different variables of the existing hexagonal pattern used for the previous Mondotrack surface used for the Tokyo Olympics, we selected four to compose the design space: the height, the main width, the cavities depth and the thickness of the upper layer (since the overall thickness is fixed, this also determines the thickness of the bottom layer). Said design space was sampled using a 3rd order Clenshaw-Curtis hierarchical sparse grid. The sample points obtained were fed to a parametrized version of the Abaqus/Explicit FE model previously developed. Kriging interpolation of the obtained data was performed with the Matlab package DACE Toolbox using 2nd order polynomials as basis functions and gaussian correlation as kernel. The obtained surrogate model was validated on 16 additional design points selected using Latin Hyper-cube Sampling: we compared its predictions with the values computed using the standard FE model, with an accuracy within a few tenths of percent. The proposed surrogate model can easily highlight the role of the key variables determining shock absorption and performance, and could be potentially implemented in an optimization algorithm to perform an online computation. Moreover, the good predictive capability of the model in a reduced design space opens to a future expansion of this strategy, including a combined optimization of geometry and material formulation.