Sensitivity analysis of fracture parameters in discrete fracture network (DFN) models for effective hydraulic conductivity under StandAG

Ensuring the safe disposal of high-level radioactive waste in a suitable host rock requires compliance with several legally defined criteria. In Germany, these criteria are established by Repository Site Selection Act (Standortauswahlgesetz – StandAG). One of the key hydrogeological criteria constrains the hydraulic conductivity of the host rock to values below 10^-10 m/s. In crystalline rocks, hydraulic conductivity is governed by contributions from both the rock matrix and the fracture network, with transport typically dominated by fractures.

Fractures are characterized by multiple parameters, including orientation (strike and dip angles), fracture size (strike and dip lengths), volumetric fracture density (number of fractures per unit volume), and hydraulic aperture. The main objectives of this study are to (i) evaluate the sensitivity of effective hydraulic conductivity to individual fracture parameters and their correlations, (ii) test a DFN-based workflow for hydraulic upscaling at the representative elementary volume (REV) scale, and (iii) identify parameter combinations that satisfy the hydraulic safety criterion defined by StandAG for nuclear waste repositories.

Parameter correlations represent dependent relationships between fracture properties. Semi-correlated DFN models account for relationships between fracture aperture, strike length, and fracture density while incorporating a stochastic term to capture natural variability, whereas uncorrelated DFN models assume full parameter independence.

Both semi-correlated and uncorrelated DFN models were considered to investigate the influence of correlations between fracture length, aperture, and volumetric fracture density on hydraulic behavior. The proposed workflow integrates DFN generation using the software Frackit, the upscale of fracture-scale properties to an equivalent porous medium (EPM) based on Oda’s method assuming cubic-law fracture-scale flow, and flow simulations performed with FEFLOW 10 to derive effective hydraulic conductivity.

The DFNs were generated within a cubic volume of 50×50×50 m³. Fracture lengths range from a few to several tens of meters, volumetric fracture densities vary between approximately 10^-4 and 10^-2 m^-3, strike and dip angles span 0–180° and 0–90°, respectively, and fracture apertures extend from 10^-7 to 10^-2 m.

The results show that (1) fracture aperture was consistently found to be the strongest parameter controlling hydraulic conductivity in both semi-correlated and uncorrelated models. In semi-correlated models, volumetric fracture density and fracture dimensions such as strike and dip lengths also significantly affect the effective hydraulic conductivity. Strike and dip angles exhibited low sensitivity. In uncorrelated models, the aperture alone dominates flow, while other parameters show negligible influence. (2) Effective hydraulic conductivity compatible with the StandAG limit is typically found when fracture apertures are small, i.e., smaller than 10^-4 m, strike lengths are short, i.e., shorter than 10 m, and fracture density is moderate to high, i.e., higher than 1 × 10^-3 m^-3, in semi-correlated models. In uncorrelated models, hydraulic conductivity below the standard limit is primarily controlled by small apertures, i.e., smaller than 10^-4 m, independent of fracture density.