Mechanical response of an inclined frictional granular layer approaching   unjamming
  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. 
A. P. F. Atman, P. Claudin, G. Combe, R. Mari
cond-mat.soft cond-mat.dis-nn cond-mat.stat-mech