Non-classical, non-linear elasticity in rocks: experiments in a triaxial cell with pore pressure control

<p><span lang="en-US">In rocks </span><span lang="en-US">and </span><span lang="en-US">concrete, dynamic excitation leads to a <strong>fast softening</strong> of the material, followed by a <strong>slower recovery</strong> process where the material recovers part of its initial stiffness as a <strong>logarithmic function of time</strong>. This requires us to exit the convenient framework of time independent elastic properties, </span><span lang="en-US">linear or not,</span> <span lang="en-US">and investigate <strong>non-classical, non-linear elastic behavior</strong></span><span lang="en-US">. </span></p> <p><span lang="en-US">These phenomena can be observed during seismic events in affected infrastructure as well as in the </span><span lang="en-US">subsurface. </span><span lang="en-US">Since </span><span lang="en-US">the transient material changes are not restricted to elastic parameters but also affect hydraulic and electric parameter</span><span lang="en-US">s</span><span lang="en-US"> as well as material strength, as documented for instance by long lasting changes in landslide rates, it </span><span lang="en-US">is of major interest </span><span lang="en-US">to characterize the softening and recovery phases. I</span><span lang="en-US">t may help us gain more insight in hazard prediction from both a geological and engineering perspective. </span></p> <p><span lang="en-US">T</span><span lang="en-US">he underlying physics </span><span lang="en-US">behind those non-classical, non-linear effects, sometimes referred to as </span><span lang="en-US">&#8220;</span><strong><span lang="en-US">N</span><span lang="en-US">onlinear </span><span lang="en-US">M</span><span lang="en-US">esoscopic </span><span lang="en-US">E</span></strong><span lang="en-US"><strong>lasticity</strong>&#8221;, are not agreed upo</span><span lang="en-US">n. T</span><span lang="en-US">here is a lack of experiments that would allow us to discriminate between the existing models.: </span><span lang="en-US">we </span><span lang="en-US">aim to </span><span lang="en-US">contribute to</span> <span lang="en-US">filling </span><span lang="en-US">that </span><span lang="en-US">knowledge gap</span><span lang="en-US">.</span></p> <p><span lang="en-US">Our experiments are made on a sample of Bentheim sandstone, initially dry and then fully saturated, in a triaxial cell. We </span><span lang="en-US">subject the sample </span><span lang="en-US">to loading and holding cycles in the microstrain range, while also varying confining </span><span lang="en-US">pressure </span><span lang="en-US">and pore pressure. </span><span lang="en-US"><strong>Active acoustic measurements</strong> </span><span lang="en-US">during those loading cycles with an array of 1</span><span lang="en-US">4</span> <span lang="en-US">piezoelectric </span><span lang="en-US">sensors </span><span lang="en-US">allow us </span><span lang="en-US">to </span><span lang="en-US">monitor </span><span lang="en-US">relative </span><span lang="en-US">velocity </span><span lang="en-US">changes </span><span lang="en-US">during </span><span lang="en-US">the experiment </span><span lang="en-US">by using <strong>Coda Wave Interferometry</strong></span> <span lang="en-US">(CWI).</span></p> <p><span lang="en-US">We</span> <span lang="en-US">observe the <strong>dynamic softening </strong>as well as the <strong>recovery process</strong></span><strong><span lang="en-US">es</span></strong><span lang="en-US"> in the sample </span><span lang="en-US">during repea</span><span lang="en-US">t</span><span lang="en-US">ed loading phases of different duration</span><span lang="en-US">s</span><span lang="en-US">. We find that </span><span lang="en-US"> characteristics </span><span lang="en-US">of the observed velocity changes vary </span><span lang="en-US">depending on the observed </span><span lang="en-US">sensor combination, indicating <strong>spatial variability</strong> of the response</span><span lang="en-US">, as well as </span><strong><span lang="en-US">depending on </span><span lang="en-US">the </span><span lang="en-US">lapse time and frequency </span><span lang="en-US">content</span></strong> <span lang="en-US">of the acoustic measurements that we perform the CWI on.</span></p> <p><span lang="en-US">These experiments </span><span lang="en-US">serve to estimate </span><span lang="en-US">the </span><span lang="en-US">exact </span><span lang="en-US">capabilities of </span><span lang="en-US">our experimental setup</span><span lang="en-US"> in terms of signal quality, </span><span lang="en-US">signal </span><span lang="en-US">stability and lapse time dependent decorrelation of coda waves. </span><span lang="en-US">We expect our results to inform a future series of similar but more refined experiments </span><span lang="en-US">addressing the <strong>pore pressure dependence</strong> of the non-classical response of rocks</span><span lang="en-US">.</span></p>