Assessing the representative elementary volume of rock types by X-ray computed tomography (CT) – a simple approach to demonstrate the heterogeneity of the Boda Claystone Formation in Hungary

X-ray computed tomography (CT) can reveal internal, three-dimensional details of objects in a non-destructive way and provide high-resolution, quantitative data in the form of CT numbers. The sensitivity of the CT number to changes in material density means that it may be used to identify lithology changes within cores of sedimentary rocks. The present pilot study confirms the use of Representative Elementary Volume (REV) to quantify inhomogeneity of CT densities of rock constituents of the Boda Claystone Formation. Thirty-two layers, 2 m core length, of this formation were studied. Based on the dominant rock-forming constituent, two rock types could be defined, i.e., clayey siltstone (20 layers) and fine siltstone (12 layers). Eleven of these layers (clayey siltstone and fine siltstone) showed sedimentary features such as, convolute laminations, desiccation cracks, cross-laminations and cracks. The application of the Autoregressive Integrated Moving Averages, Statistical Process Control (ARIMA SPC) method to define Representative Elementary Volume (REV) of CT densities (Hounsfield unit values) affirmed the following results: i) the highest REV values corresponded to the presence of sedimentary structures or high ratios of siltstone constituents (> 60%). ii) the REV average of the clayey siltstone was (5.86 cm3) and (6.54 cm3) of the fine siltstone. iii) normalised REV percentages of the clayey siltstone and fine siltstone, on the scale of the core volume studied were 19.88% and 22.84%; respectively. iv) whenever the corresponding layer did not reveal any sedimentary structure, the normalised REV values would be below 10%. The internal void space in layers with sedimentary features might explain the marked textural heterogeneity and elevated REV values. The drying process of the core sample might also have played a significant role in increasing erroneous pore proportions by volume reducation of clay minerals, particularly within sedimentary structures, where authigenic clay and carbonate cement were presumed to be dominant.

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.

The investigation of the porosity scale effect and elastic anisotropy in Bashkirian limestones

The article presents the methodology of the representative elementary volume definition for 1 m long whole core segments. Scientific articles focused on factors controlling elastic properties are analysed. Terms of additivity and nonadditivity for physical properties of rocks are discussed. The algorithm of core sampling including drilling out of three perpendicular core samples for estimation of elastic anisotropy was used. Porosity values of 1 m long whole core fragment evaluated in two ways using original core samples in the first approach and core samples having volume 133 cm3 in the second way have been compared. Peculiarities of scale effect of porosity in core samples of limestones are analysed.

Million node fracture: size matters?

Transmissivity of self-affine fractures was computed numerically as a function of the grid size. One-million-node fractures (1024 × 1024 nodes) with fractal dimensions of 2.2–2.6 were cut into successively smaller fractures (“generations”), and transmissivities computed. The number of fractures in each generation was increased by a factor of 4. Considerable scatter in transmissivity was observed for smaller grid sizes. Average transmissivity of the fractures in the generation decreased with the grid size, without approaching any asymptotic value, which indicates no representative elementary volume (REV). This happened despite the average mean aperture being the same in each generation. The results indicate that it is not possible to estimate the transmissivity of a large fracture by cutting it into smaller fractures, running flow simulations on those and averaging the results. The decrease in transmissivity with the grid size was found to be due to an increase in the flow tortuosity.

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.

The investigation of the scale effect on porosity in Bashkirian limestones

The article presents the methodology of the representative elementary volume definition for two 1 m long whole core segments. Scientific articles focused on practical methods of representative volume calculations using various physical parameter fluctuations have been studied. Porosity values of every whole core fragment evaluated in two ways using the 7.3 cm diameter core samples in the first approach and the 3 cm diameter core samples in the second one have been compared. Particularities of the scale effect occurring in core samples and depending on core size and porosity type have been analyzed. The cause of porosity increase in big core samples has been determined. The reason due to which porosity changes are explained by fracture porosity occurring in core samples having big volumes has been found. The comparison between neutron log porosity and core porosity has been made. Reasons of similarities or differences of core and log data have been established.

On the Tortuosity-Connectivity of Cement-Based Porous Materials

In this work, the transport equations of ionic species in concrete are studied. First, the equations at the porescale are considered, which are then averaged over a representative elementary volume. The so obtained transport equations at the macroscopic scale are thoroughly examined and each term is interpreted. Furthermore, it is shown that the tortuosity-connectivity does not slow the average speed of the ionic species down. The transport equations in the representative elementary volume are then compared with the equations obtained in an equivalent pore. Lastly, comparing Darcy’s law and the Hagen–Poiseuille equation in a cylindrical equivalent pore, the tortuosity-connectivity parameter is obtained for four different concretes. The proposed model provides very good results when compared with the experimentally obtained chloride profiles for two additional concretes.