Numerical analysis of local strain measurements in fluid-saturated rock samples submitted to forced oscillations

Abstract

The forced oscillation method is used to experimentally study the viscoelastic behavior of fluid-saturated rocks at seismic frequencies by measuring their dynamic stress-strain response. The strain on a sample can be measured locally with strain gauges or on the entire sample, here referred to as bulk strain, with a displacement transducer. The local response can vary greatly from the bulk because of heterogeneities in the rock, which can be structural in nature, for example, fractures, or they can arise from partial fluid saturation. Comparing the results from experimental setups that measure strains by different methods can therefore become problematic, and setups that exclusively measure local strains can be inadequate for performing certain experiments. To better understand these limitations, we numerically simulate forced oscillation tests on models representative of laboratory samples, using Biot’s quasistatic equations for poroelastic media. The main objective is to analyze the discrepancies that can arise between local and bulk measurements, with a specific focus on the frequency-dependent attenuation and the Young’s modulus dispersion. We find that, for a fully water-saturated sample having a single fracture and for a partially saturated sample, the local responses deviate significantly from the bulk responses. In addition, the average of three local measurements along a sample allows for approximating the bulk response for the case of a partially water-saturated sample having a homogeneous solid frame. Such an average is not sufficient for the fractured sample. In summary, the averaging of local strain measurements can provide a partial solution to accurately characterize the dynamic stress-strain response of the sample in certain cases, but in other cases, it can lead to results that strongly deviate from the bulk measurements. We advocate for experimental setups to be built to measure the bulk strain on rock samples or modified to include this measurement in addition to local ones.