Investigation of a tensor renormalization method to determine the effective conductivity of heterogeneous subsoils

摘要

For consultancy in civil and environmental engineering there is a need for a fast yet sufficiently accurate estimate of the hydraulic conductivity field of always heterogeneous subsoils. Therefore, a simple semi-analytical upscale procedure using the renormalization method is investigated to determine the hydraulic conductivity of heterogeneous soil with a schematized sedimentary structure. The investigated procedure is faster than traditional numerical upscaling methods in that the small-scale conductivity fields is scaled up analytically to the scale of a unit cell for application in for example finite element modelling. The upscaling of various unit cells (with statistical characteristics of the small-scale structure) to the desired scale is performed with two tensor renormalization methods. Both methods have been tested for several analytical configurations.