Résumé
The variability of plant root architecture is generally attributed to genetic, physiological and environmental factors such as the mechanical strength of soil. However, the soil has often been modeled as a continuum, and the complex particle-scale mechanisms at the origin of root development are not easily accessible to direct measurements [1,2]. In particular, a key issue is to determine how the inhomogeneous distribution of force chains are reflected in the forces experienced by the root cap. We introduce a numerical model of a growing flexible root inside a granular assembly composed of solid particles. The particle motions are computed by stepwise integration of the equations of motion for all particles by accounting for their frictional contact interactions and the gravity and boundary forces. We use the same framework to model the root, defined as a flexible tube represented by an array of segments interconnected by linear springs and growing as a result of its continuous elongation. The general numerical model and simulations are in two dimensions as the root growth requires long-time simulations and we needed to perform a large number of independent simulations in order to be able to assess the variability of the results and the effect of system parameters. We present the particle interactions and the root model, and we investigate the mean force experienced by the root cap as a function of root flexibility, gain size, soil cohesion and particle size distribution. We showthat a single dimensionless parameter combining different root and soil parameters controls the mean force. We also show that the distribution of root cap forces reflects that of interparticle forces [3].References[1] A. G. Bengough, M. F. Bransby, J. Hans, S. J. McKenna, T. J. Roberts, and T. A. Valentine, Journal of Experimental Botany 57, 437 (2006).[2] M. Yang, P. Défossez, F. Danjon, S. Dupont, and T. Fourcaud, Plant and Soil 411, 275 (2017).[3] M. Fakih, J.-Y. Delenne, F. Radjai, T. Fourcaud, « Root growth and force chains in a granular soil », arXiv preprint arXiv:1811.09342 (2018).