Use of Seismic Resonance Measurements to Determine the Elastic Modulus of Freestanding Rock Masses

Measuring the elastic modulus of in situ rock masses over scales of tens of meters remains an important challenge in experimental rock mechanics. Here we present a new approach using ambient resonance measurements of freestanding rock landforms to identify vibrational modes, which are then matched with 3D numerical models implementing bulk, globally representative material properties. The result is an experimentally determined, albeit numerically calibrated, estimate of rock mass elastic modulus. We demonstrate the approach at five natural rock arches in southern Utah, each formed in Navajo Sandstone, where we have acquired resonance data and matched experimental resonant modes using 3D numerical modal analysis. Two material properties can be varied to match experimental data: density and modulus. We hold density constant, applying measured or reference values, and solve for elastic modulus using a forward approach. The resolved modulus is representative of the global small-strain dynamic behavior, integrating rock mass heterogeneity over the scale of the feature. The technique works well for freestanding geological landforms that exhibit clear vibrational modes. Errors arise with uncertain mechanical boundary conditions or strong material anisotropy. The resolved modulus values add relevant information describing the variation of elastic properties over scales from lab samples to in situ rock masses.