We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle {\alpha} with respect to the critical angle \alpha_c. We find that the shear modulus of the system decreases with {\alpha}, but reaches a finite value as \alpha tends to \alpha_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.
@article{arxiv.1203.5996,
title = {Mechanical response of an inclined frictional granular layer approaching unjamming},
author = {A. P. F. Atman and P. Claudin and G. Combe and R. Mari},
journal= {arXiv preprint arXiv:1203.5996},
year = {2015}
}