Study on the upscaling transformation of hydraulic conductivity in fractured media

Abstract

Objective It is very important to study the upscaling transformation of hydraulic conductivity in fracture media for accurately characterizing the seepage field characteristics. Methods Based on the fracture medium statistics of crystalline rock in an underground water-sealed cavern, a 2-dimensional discrete fracture network (DFN) model is generated using the Monte-Carlo stochastic simulation technique. The hydraulic conductivity parameters of the variable size simulation domain and the equivalent hydraulic conductivity of each grid element after meshing in different sizes are calculated. The hydraulic conductivity representative elementary volume (REV) of the study area was analysed by the variation in hydraulic conductivity parameters with the size of the simulation area, and the equivalent hydraulic conductivity of grid cells smaller than REV was calculated by upscaling. Results The results show that the simulation domain can be regarded as an equivalent continuum when the size of the REV reaches 22 m×22 m. After meshing treatment, the equivalent hydraulic conductivity of the mesh cells which is smaller than REV calculated by the upscaling operation is significantly smaller than that of the corresponding composite mesh cells calculated by the crack network model. Conclusion Therefore, when the size of the seepage calculation unit reaches the REV size, its hydraulic conductivity parameters can effectively represent the hydraulic conductivity characteristics of a larger area in the study area. However, when the size of the seepage calculation unit is smaller than the REV size, its hydraulic conductivity parameters cannot effectively represent the hydraulic conductivity characteristics of the larger area in the study area. As a consequence, parameter upscaling calculation on the hydraulic conductivity parameters often has underestimated errors and is not of practical significance. For fractured media study areas with insufficient data, it is often difficult to determine the hydraulic conductivity REV of the study area. In this case, it can be considered that there is usually an underestimation error when the hydraulic conductivity of the small-scale area obtained from the hydrogeological test is upscaled. This conclusion provides a theoretical basis for the numerical simulation of the seepage field in fracture media in various related engineering projects.

Keywords

• discrete fracture network model
• upscaling
• rev
• hydraulic conductivity tensor
• fractured media