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

Abstract

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.

The time dependence of rock healing as a universal relaxation process, a tutorial

“…Relaxation of the seismic velocity after perturbing rocks has been observed in laboratory studies (Ten Cate & Shankland 1996;Zaitsev et al 2003;Vakhnenko et al 2004;Ten Cate 2011) and field observations (Poupinet et al 1984;Schaff & Beroza 2004;Wegler & Sens-Schönfelder 2007;Brenguier et al 2008;Wu et al 2009;Nakata & Snieder 2011Wu & Peng 2012;Brenguier et al 2014;Obermann et al 2014;Richter et al 2014), and is thus an observable property under the right conditions. These observations usually show a recovery similar to the relaxation shown in Fig.…”

“…Laboratory studies (Ten Cate & Shankland 1996;Zaitsev et al 2003;Vakhnenko et al 2004;Ten Cate 2011) and seismological field observations (Poupinet et al 1984;Schaff & Beroza 2004;Wegler & SensSchönfelder 2007;Brenguier et al 2008;Wu et al 2009;Nakata & Snieder 2011;Hobiger et al 2012;Nakata & Snieder 2012;Wu & Peng 2012;Brenguier et al 2014;Obermann et al 2014;Richter et al 2014;Gassenmeier et al 2016) show that the seismic velocity of rocks is often reduced during shaking, and recovers afterwards. Gassenmeier et al (2016) demonstrated that, at least in some cases, these changes are caused by the shaking of the subsurface that damages the material.…”

Slow dynamics and anomalous nonlinear fast dynamics in diverse solids

“…Conditioning is considered by many to be the manifestation of slow dynamics during wave excitation, although this has not been quantitatively demonstrated. Existing theories that address conditioning include those described by Scalerandi and Delsanto 4 and Vakhnenko et al 16 The recent model of Vaknenko et al is based on the physics of bond rupture as the underlying mechanism of ANFD/SD. The ramifications of conditioning in ANFD are only beginning to be unraveled experimentally however, and will not be addressed further here, except to say our group is working on separating ANFD and SD at present.…”

Analysis of elastic nonlinearity using the scaling subtraction method

“…1,3,10,[20][21][22][23][24] In fact, both the resonance frequency shift and the phase dependence on amplitude are linked to a velocity variation in the waves in the medium. Also, the changes in the Q factor of the sample with amplitude can be extracted from resonance measurements with an often complex mathematical approach.…”