Ralf Jänicke

Requirements on Periodic Micromorphic Media

In order to investigate the properties of microstructured materials, the underlying heterogeneous material is commonly replaced by a homogeneous material involving additional degrees of freedom. Making use of an appropriate homogenization methodology, the present contribution compares deformation states predicted by the homogenization technique to the deformation state within a reference solution. The results indicate on what terms the predicted deformation modes can be clearly interpreted from the physical point of view.

Computational Homogenization of Seismic Attenuation in Fractured Rock

© ASCE. Fluid-saturated fractured rock is well-known to exhibit a pronounced attenuation of elastic waves at low seismic frequencies due to the equilibration of wave-induced pressure gradients by pressure diffusion. At low seismic frequencies, the Poiseuille flow model results in a Darcy-type behavior for the pressure diffusion along the fractures. Moreover, it is reasonable to assume that pressure diffusion occurs on a length scale much smaller than the seismic wave length, and we, therefore, consider it as a local process. On the geological scale the material can then be interpreted as a viscoelastic medium. In the present contribution we aim to develop a computational homogenization scheme substituting the heterogeneous fractured medium by a homogeneous viscoelastic substitute model. We make use of the systems linearity and derive a reduced order formulation for the upscaling problem. Hence, we detect a reduced basis for the fluid pressure field and superimpose the stress response due to transient external loadings. Altogether, the viscoelastic substitute model can be identified at reasonable numerical costs and can be validated by numerical simulations at full mesoscopic resolution.

Numerical Investigation of the Effective Skempton Coefficient in Porous Rock Containing Fluid-Filled Fracture Networks

Modern interpretation of seismic surveys aims at going beyond structural characterization of reservoirs on the basis of the spatial distribution of velocity. In particular, hydraulic properties of fluid-filled reservoirs are of prime interest for hydrocarbon exploration or water-reservoir management. Such analyses require a physics-based understanding of the processes involved with the propagation of seismic waves in fractured rocks. The main objective of this work is the investigation of the hydro-mechanics of fluid-filled fracture networks and the related diffusion of fluid pressure in the conduits. We apply methods of computational homogenization to discuss an effective Skempton coefficient and analyze it for different setups in time as well as in frequency domain. In the first setup we investigate a modified version of Cryers problem embedding a spherical sample in a mantle of constant thickness. The kernel and the mantle constitute porous media but with different material properties. The second setup aims to investigate the hydro-mechanical properties of stochastically generated fracture networks. In both setups we apply Biots theory of linear consolidation. Evaluating the effective Skempton coefficient predicted by computational homogenization for those cases we can show limitations of previously performed laboratory measurements of the Skempton coefficient.