Estimating rock mass elastic modulus from seismic resonance measurements

Measuring the elastic modulus of in-situ rock masses over scales of tens of meters remains an important challenge in experimental rock mechanics. We present a new approach using ambient resonance measurements of freestanding rock masses to identify vibrational modes, which are then matched with 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 four natural rock arches in southern Utah where we have acquired resonance data and been able to match experimental resonant modes using 3D numerical analysis. Two material properties can be varied to match experimental data, density and modulus; we hold the former constant applying measured or common values and solve for 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 features that exhibit clear vibrational modes. Errors arise with uncertain mechanical boundary conditions. We propose the resolved global value of modulus adds relevant information describing the variation of elastic properties over scales from lab samples to in-situ rock masses. resonance measurements of freestanding geological features with dimensions of tens of meters. We present data from four natural arches in Utah formed in Navajo Sandstone, where we have measured resonant modes from ambient seismic data and used these results to calibrate 3D numerical models. The elastic modulus resolved from this procedure represents the small-strain dynamic behavior of the entire feature, thus integrating rock mass heterogeneity over large scales to provide a representative value not readily determined from alternative in-situ testing procedures. 2. STUDY SITES AND MATERIALS