A non-linear elastic approach to study the effect of ambient humidity on sandstone

Abstract

We demonstrate that strong elastic pump wave pulses soften sandstone more in humidified conditions than they do in dry conditions and that this effect is repeatable and reversible. We assess these changes via the non-linear interactions of a strong pump wave with a weaker probe wave. We find that there is an exponential time constant (τ≈13days) associated with this process that is independent of the amplitudes of the pump and the probe, the phase delay between the two waves (the time between transmission of the pump and probe waves), the sampling rate, and whether the sample is being dried or humidified. We demonstrate that the humidity-dependent differences in the amount of softening are induced by only a very small amount of absorbed water vapor and argue that this water is intercalated within clay particles. We also show that our pump–probe experiments detect these humidity-dependent differences in the amount of softening easily and repeatably using an experimental design that does not rely on resonance conditions. This means that, in principle, our experiments could be more easily generalized to other experimental geometries to investigate non-linear elastic properties in complex or irregular sample geometries. Our method and findings have potential relevance in oil and gas exploration, civil engineering, and understanding of the mechanism of earthquakes.

Effect of Grain Shape and Relative Humidity on the Nonlinear Elastic Properties of Granular Media

“…Additionally, we do not see any significant changes in (linear) wave velocity with RH in sand (Figure S7 in the Supporting Information ), and this is unlike the decrease in linear wave velocity with RH observed in glass beads (Gao et al., 2022). All in all, the previous observations made in consolidated sandstones (Abeele et al., 2002; Johnson et al., 2004; Pimienta et al., 2014; Tadavani et al., 2020; Yurikov et al., 2018) differ drastically from our results in "bare" sand particles. This seems to suggest that the linear and nonlinear elastic properties of consolidated sandstones are not dictated by grain shape, but rather by the soft bonds that sinter the grains.…”

“…Nonlinear elastic effects arise in solids due to the presence of imperfections at the micro/mesoscopic scale, such as cracks or dislocations (Guyer & Johnson, 2009; Ostrovsky & Johnson, 2001). Understanding the origins of these nonlinear elastic effects is critical to numerous fields, from geophysics (Abeele et al., 2002; Delorey et al., 2021; Feng et al., 2018, 2022; Guyer & Johnson, 2009; Hillers et al., 2015; Johnson & Sutin, 2005; Johnson et al., 2004; Manogharan et al., 2021; McCall & Guyer, 1994; Pimienta et al., 2014; Renaud et al., 2012; Shokouhi et al., 2020; Tadavani et al., 2020; TenCate et al., 1996, 2016) and civil engineering (Abeele & De Visscher, 2000; Astorga et al., 2018; Bittner & Popovics, 2022; Kim et al., 2017; Lacouture et al., 2003; Payan et al., 2014; Shokouhi et al., 2017) to the non‐destructive evaluation of materials (Breazeale & Ford, 1965; Buck et al., 1978; Jin et al., 2020; Kim et al., 2006; Matlack et al., 2015; Williams et al., 2022). Elastic nonlinearity is particularly large in poorly consolidated or unconsolidated materials, where it arises from weak junctions between grains (Brunet et al., 2008; Guyer & Johnson, 1999, 2009; Jia et al., 2011; Johnson & Jia, 2005; Langlois & Jia, 2014; Renaud et al., 2012; Rivière et al., 2015; Yoritomo & Weaver, 2020a, 2020b, 2020c).…”

Spatial Dependence of Dynamic Nonlinear Rock Weakening at the Alpine Fault, New Zealand

“…High pore fluid pressures in the core of fault zones (Sutherland et al, 2017) reduces effective pressure, increasing the depth to which elastic nonlinearity persists (Johnson & Jia, 2005;Shokouhi et al, 2020). Also, the presence of pore fluids and higher temperatures are likely to significantly increase the nonlinear response in rocks (Johnson, 2006;Johnson et al, 2004;Tadavani et al, 2020;Van Den Abeele et al, 2002). These factors are particularly important at the Alpine Fault, which has an anomalously large temperature gradient and an above-hydrostatic pore fluid pressure gradient in the hanging wall (Sutherland et al, 2017).…”

Experimental monitoring of nonlinear wave interactions in crab orchard sandstone under uniaxial load

“…Figure 1 shows our experimental setup and Table 2 summarizes the experimental parameters. We use an established experimental setup (Gallot et al, 2015; Khajehpour Tadavani et al, 2020; TenCate et al, 2016) and place it inside a hydraulic press. Using this setup, we report two types of data.

Figure 1. (a) The experimental setup, including the coordinate system to be used later.

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