Determination of representative elementary volume (REV) for jointed rock masses exhibiting scale-dependent behavior: A numerical investigation

Abstract

Representative elementary volume (REV) is defined as the usual size of a rock mass structure beyond which its mechanical properties are homogenous and isotropic, and its behavior can be modeled using the equivalent continuum approach. Determination of REV is a complex problem in rock engineering due to its definition ambiguity and application area. This study is one of the first attempts to define a REV for jointed rock masses using the equivalent continuum approach. It is aimed to numerically search a ratio between the characteristic size of an engineering structure and pre-existing joint spacing, which are the two most important contributing elements in assessing REV. For this purpose, four hypothetical engineering cases were investigated using the RS2 (Phase2 v. 9.0) finite element (FE) analysis program. An underground circular opening with a constant diameter, an open-pit mine with varying bench heights, a single bench with a constant height, and an underground powerhouse cavern with a known dimension were executed for possible changes in the safety factor and total displacement measurements under several joint spacing values. Different cut-off REVs were calculated for FE models depending on the type of excavation and measurement method. An average REV size of 19.0, ranging between a minimum of 2 for tunnels and a maximum of 48 for slopes, was found in numerical analysis. The calculated sizes of REV were significantly larger than the range of values (5 to 10) commonly reported in the relevant geotechnical literature.

Size effect on hydraulic properties of rough-walled fractures upscaled from meter-scale granite fractures

“…However, the capacity to accurately estimate the hydraulic properties of fractures is hindered by complex influencing factors such as stress conditions (Gale and Raven 1980;Raven and Gale 1985;Yeo et al 1998;Olsson and Barton 2001;Baghbanan and Jing 2008;Rutqvist 2014;, geometric properties (e.g., roughness, aperture dimensions), and fracture stiffness (Zimmerman and Bodvarsson 1996;Konzuk and Kueper 2004;Li et al 2020;He et al 2021). In addition, a number of scholars have reported that the hydraulic properties of fractured rock masses are size-dependent (Bear 1972(Bear , 1979Azizmohammadi and Sedaghat 2020;Han et al 2021;Sari 2021;Ghanbarian 2022;Yu et al 2022), which further compounds the difficulty in estimating representative hydraulic properties. Thus, another important requirement is to establish the relationships between fracture sizes and hydraulic properties (Witherspoon et al 1979;Min et al 2004;Baghbanan and Jing 2007;Sari 2021;Sawayama 2021).…”

“…In addition, a number of scholars have reported that the hydraulic properties of fractured rock masses are size-dependent (Bear 1972(Bear , 1979Azizmohammadi and Sedaghat 2020;Han et al 2021;Sari 2021;Ghanbarian 2022;Yu et al 2022), which further compounds the difficulty in estimating representative hydraulic properties. Thus, another important requirement is to establish the relationships between fracture sizes and hydraulic properties (Witherspoon et al 1979;Min et al 2004;Baghbanan and Jing 2007;Sari 2021;Sawayama 2021).…”