We present numerical simulations of elastic wave propagation, scattering and attenuation in two-dimensional fractured media. Natural fracture systems following a power law length scaling are modeled by the discrete fracture network approach for the geometrical representation of fracture distributions and the displacement discontinuity method for the mechanical computation of fracture-wave interactions. The model is validated against analytical solutions for wave reflection, transmission and scattering by single fractures, after which we apply it to solve the spatiotemporal wavefield evolution in various synthetic fracture networks. We find that the dimensionless angular frequency ῶ plays a crucial role in governing wave transport. When ῶ is smaller than the critical frequency ῶc (≈ 5), waves are in the extended mode, either propagating (for small ῶ) or diffusing by multiple scattering (for intermediate ῶ); as ῶ exceeds ῶc, the wave energy becomes trapped, entering either the Anderson localization regime (kl* ≈ 1) in well-connected fracture systems or the weak localization regime (kl* > 1) in poorly-connected fracture systems, where k is the incident wavenumber and l* is the mean free path length. Consequently, the inverse quality factor Q-1 scales with ῶ obeying a two-branch power law dependence, showing significant frequency dependence when ῶ < ῶc and almost frequency independence when ῶ > ῶc. In addition, when ῶ < ῶc, the wavefield exhibits a weak dependence on fracture network geometry, whereas when ῶ > ῶc, the fracture network connectivity has an important impact on the wave behavior such that strong attenuation occurs in well-connected fracture systems.

We study the physical mechanisms that drive alpine slope deformation during water infiltration and depletion into fractured bedrocks. We develop a fully coupled hydromechanical model at the valley scale with multiscale fracture systems ranging from meter to kilometer scales represented. The model parameterized with realistic rock mass properties captures the effects of fractures via an upscaling framework with equivalent hydraulic and mechanical properties assigned to local rock mass blocks. The important heterogeneous and anisotropic characteristics of bedrocks due to depth-dependent variations of fracture density and stress state are taken into account and found to play a critical role in groundwater recharge and valley-scale deformation. Our simulation results show that pore pressure actively diffuses downward from the groundwater table during a recharge event, rendering a critical hydraulic response zone controlling surface deformation patterns. During the recession, the hydraulic front migrates downwards and the deformation recorded at the surface (up to ~4 cm) rotates accordingly. The most essential parameters in our model are the fracture network geometry, initial fracture aperture (controlling the rock mass permeability), and regional stress conditions. The magnitude and orientation of our model’s transient annual slope surface deformation are consistent with field observations at our study site in the Aletsch valley. Our research findings have important implications for understanding groundwater flow and slope deformations in alpine mountain environments.