Chemical element transport processes are among the crucial physical processes needed for precise stellar modelling. Atomic diffusion by gravitational settling nowadays is usually taken into account, and is essential for helioseismic studies. On the other hand, radiative accelerations are rarely accounted for, act differently on the various chemical elements, and can strongly counteract gravity in some stellar mass domains. In this study we aim at determining whether radiative accelerations impact the structure of solar-like oscillating main-sequence stars observed by asteroseismic space missions. We implemented the calculation of radiative accelerations in the CESTAM code using the Single-Valued Parameter method. We built and compared several grids of stellar models including gravitational settling, but some with and others without radiative accelerations. We found that radiative accelerations may not be neglected for stellar masses larger than 1.1~M$_{odot}$ at solar metallicity. The difference in age due to their inclusion in models can reach 9% for the more massive stars of our grids. We estimated that the percentage of the PLATO core program stars whose modelling would require radiative accelerations ranges between 33 and 58% depending on the precision of the seismic data. We conclude that, in the context of Kepler, TESS, and PLATO missions, which provide (or will provide) high quality seismic data, radiative accelerations can have a significant effect when inferring the properties of solar-like oscillators properly. This is particularly important for age inferences. However, the net effect for each individual star results from the competition between atomic diffusion including radiative accelerations and other internal transport processes. This will be investigated in a forthcoming companion paper.
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