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

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.

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

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.

A Novel Equivalent Continuum Approach for Modelling Hydraulic Fractures

Hydraulic fracturing has transitioned into widespread use over the last few decades. There are a variety of numerical methods available to simulate hydraulic fracturing. However, most current methods require a large number of input parameters, of which the values of some parameters are poorly constrained. This paper proposes a new method of modelling the hydraulically fractured region using void-ratio dependent relation to define the permeability of the fractured region. This approach is computationally efficient and reduces the number of input parameters. By implementing this method with an equivalent continuum representation, uncertainties are reduced arising from heterogeneity and anisotropy of earth materials. The computational efficiency improves modelling performance in stress sensitive zones such as in the vicinity of the injection well or near faults.

Comparison of discrete fracture network and equivalent continuum simulations of fluid flow through two-dimensional fracture networks for the DECOVALEX–2011 project

Fluid flow through a two-dimensional fracture network has been simulated using a discrete fracture model. The computed field-scale permeabilities were then compared to those obtained using an equivalent continuum approach in which the permeability of each grid block is first obtained by performing fine-scale simulations of flow through the fracture network within that region. In the equivalent continuum simulations, different grid-sizes were used, corresponding to N by N grids with N = 10, 40, 100 and 400. The field-scale permeabilities found from the equivalent continuum simulations were generally within 10% of the values found from the discrete fracture simulations. The discrepancies between the two approaches seemed to be randomly related to the grid size, as no convergence was observed as N increased. An interesting finding was that the equivalent continuum approach gave accurate results in cases where the grid block size was clearly smaller than the 'representative elementary volume'.