Abstract. Many evidences of oscillations accompanying the acceleration of critical systems have been reported. These oscillations are usually related to discrete scale invariance properties of the systems and exhibit a logarithmic periodicity. In this paper we propose another explanation for these oscillations in the case of shearing fracture. Using a continuum damage model, we show that oscillations emerge from the anisotropic properties of the cracks in the shearing fracture zone. These oscillations no longer exhibit a logarithmic but rather a power-law periodicity. The power-periodic oscillation is a more general formulation. Its reduces to a log-periodic oscillation when the exponent of the power-law equals one. We apply this model to fit the measured displacements of unstable ice masses of hanging glaciers for which data are available. Results show that power-periodic oscillations adequately fit the observations.