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.

Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the possibility of including matrix properties, choosing the right cell size to discretize the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process we term intersection flow localization (IFL). We propose a new method to generate ECMs that includes this effect with a directional pipe flow parameterization: the fracture-and-pipe model. Our approach is compared against an ECM method that does not take IFL into account by performing ECM-based upscaling with a massively parallelized Darcy flow solver capable of representing permeability anisotropy for individual grid cells. While IFL results in an increase in permeability at the local scale of the ECM cell (fracture scale), its effects on network-scale flow are minor. We investigated the effects of IFL for test cases with orthogonal fracture formations for various scales, fracture lengths, hydraulic apertures, and fracture densities. Only for global fracture porosities above 30 % does IFL start to increase the systems permeability. For lower fracture densities, the effects of IFL are smeared out in the upscaling process. However, we noticed a strong dependency of ECM-based upscaling on its grid resolution. Resolution tests suggests that, as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECMs are applicable to upscale flow in fracture networks.

Equivalent Shell Model of Elastic Gridshells Including the Effect of the Geometric Curvature

In this work, an equivalent continuum of a barrel gridshell is introduced. Constitutive identification procedures based on periodic homogenization are provided in the literature for this purpose, based on a flat Representative Element Volume (REV), notwithstanding that the geometry of the structures concerned is curved. Therefore, the novelty of the present study is the selection of a curved REV to obtain the equivalent elastic constants. The numerical validation of the identification procedure is made comparing gridshell response to that of the equivalent shell under homogeneous load conditions. Finally, in order to highlight the effect of the curved geometry on the constitutive law of the continuum, the response of the proposed model is also compared to that of a continuum obtained from a flat REV.

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.

Equivalent Continuum Coupling-Based Slope Stability Analysis of Zhouning Pumped Storage Power Station

A 3D equivalent continuum coupling analysis of the slope of the Zhouning pumped storage power station was proposed in this study. Firstly, the hydraulic properties of rock mass, groundwater, and deformation mechanism under high-frequency fluctuations of the water level are analyzed. Secondly, the three-dimensional Digital Terrain Model (DTM) with surface image information was established by digital photogrammetry technology for cataloging field fracture information. Third, stress-seepage coupling simulation using a hybrid grid approach and the FLAC3D equivalent continuum model was implemented. The results show that the permeability of rock mass is stress-dependent and anisotropic, and the direction of maximum principal permeability of both bank slopes is approximately parallel to the river. Slope deformations induced by impoundment during the operation period are the superposition results of two mechanisms, referred to as “mattress effect” and “swelling effect.” Attention should be paid to the tensile strength of the rock mass during operation.

Numerical Study on Application Conditions of Equivalent Continuum Method for Modeling Heat Transfer in Fractured Geothermal Reservoirs

The equivalent continuum method an effective approach for modeling heat transfer in fractured geothermal reservoirs. However, presently there is a lack of systematical and profound study on application conditions of the equivalent porous media (EPM) method. In this study, we numerically investigated the application conditions of the EPM method based on geological data of Yangbajing geothermal field. The results indicate that when fracture spacing is within 3–25 m, the results of the EPM method are basically in the same levels as those of the MINC method. However, when the fracture spacing is within 25–300 m, differences of the EPM method from the MINC method increase with the fracture spacing, so when the fracture spacing is within 25–300 m, it is unreasonable to adopt the EPM method to simulate the fractured reservoirs. With the fracture spacing increasing within 25–300 m, the system production temperature and electric power will gradually decrease; the injection pressure, reservoir impedance and pump power will gradually increase; and the energy efficiency will gradually decrease.