Uncertainty of volume fraction in bimrock using the scan-line method and its application in the estimation of deformability parameters

Abstract

The volume fraction within a bimrock or bimsoil is an essential parameter that is useful for estimating the engineering properties of heterogeneous geomaterials. This paper presents analytical and numerical solutions to quantify the uncertainty of volume fraction measurements in bimrock/bimsoil using a scan-line method. The analytical solutions for the mean and variance of volume fraction estimates are based on a representative volume element model. The numerical solution is obtained through simulations of scan-line measurements. This work also employs physical tests using CT scan images from artificial bimrock/bimsoil to validate these solutions. The results demonstrate that the uncertainties of the volume fraction depend on the magnitude of the volume fraction of the blocks, the diameter of the blocks, and the length of the scan line. The proposed analytical and numerical solutions are compared with existing physical experimental tests and analytical solutions. An illustrative example to demonstrate the estimation of the uncertainty of volume fraction using the scan-line measurement is present. Finally, an example application of the volume fraction characterization in the geological engineering, in terms of Young’s modulus estimation and characterization, is provided.