Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars

A closed-form description is proposed to explain nonlinear and slow dynamics effects exhibited by sandstone bars in longitudinal resonance experiments. Along with the fast subsystem of longitudinal nonlinear displacements we examine the strain-dependent slow subsystem of broken intergrain and interlamina cohesive bonds. We show that even the simplest but phenomenologically correct modeling of their mutual feedback elucidates the main experimental findings typical for forced longitudinal oscillations of sandstone bars, namely, (i) hysteretic behavior of a resonance curve on both its upward and downward slopes, (ii) linear softening of resonant frequency with an increase of driving level, and (iii) gradual recovery (increase) of resonant frequency at low dynamical strain after the sample was conditioned by high strain. In order to reproduce the highly nonlinear elastic features of sandstone grained structure a realistic nonperturbative form of stress-strain relation was adopted. In our theory slow dynamics associated with the experimentally observed memory of peak strain history are attributed to strain-induced kinetic changes in concentration of ruptured intergrain and interlamina cohesive bonds, causing a net hysteretic effect on the elastic Young's modulus. Finally, we explain how enhancement of hysteretic phenomena originates from an increase in equilibrium concentration of ruptured cohesive bonds that are due to water saturation.