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Basics of groundwater flow
Published in Mark Bakker, Vincent Post, Analytical Groundwater Modeling, 2022
The variables for the macroscopic description of groundwater flow are associated with a spatial scale that is representative of the system considered. The volume for which a macroscopic property is valid is called the representative elementary volume (REV). The REV must not be too small, because it will not form a representative average. In the extreme, an REV smaller than the size of a pore or soil particle either represents an opening between soil particles or a soil particle itself, but not the average of many of these combined. The size of an REV must therefore exceed a multiple of the representative pore size. Conversely, an REV must not be too large either as it may no longer be suited to resolve the spatial variability of the subsurface at the macroscopic level. If the properties of the subsurface vary over a few meters, the REV must be significantly smaller than a few meters to capture this variability in a model. The REV relevant to practical groundwater problems varies. For unconsolidated sands, with a pore and grain size on the order of tenths of a millimeter, an REV of a few centimeters already captures the average behavior.
Some critical factors in modeling of rock mass stability around underground excavations
Published in Yan Xing, Pinnaduwa H.S.W. Kulatilake, Louis Sandbak, Rock Mass Stability Around Underground Excavations in a Mine, 2019
Yan Xing, Pinnaduwa H.S.W. Kulatilake, Louis Sandbak
The numerical method, which takes advantage of the high efficiency of computer technology, is another indirect way to estimate the rock mass properties. Kulatilake (1985) introduced a procedure to determine the elastic constants and strength of different-sized blocks using the finite element analysis. The representative elementary volume (REV) is a certain minimum volume over which the rock mass properties may not change significantly with respect to the effect of fractures. By generating realistic fracture systems, Wang et al. (2002) and Wu and Kulatilake (2012a) obtained the sizes and property values of the REV for their models. In the subsequent study of Wu and Kulatilake (2012b), the REV properties were used to represent the combined rock mass properties of intact rock and four sets of minor discontinuities; the continuum/discontinuum stress analysis was performed by incorporating the major discontinuities explicitly. In addition, the back-analysis based on the field measurements also provides a way to estimate the in-situ properties of rock masses (Sakurai and Takeuchi, 1983; Cai et al., 2007b; Shreedharan and Kulatilake, 2016).
Literature review of modelling approaches for ASR in concrete: a new perspective
Published in European Journal of Environmental and Civil Engineering, 2019
R. Esposito, M. A. N. Hendriks
Three typologies of approaches can be recognised: (1) mathematical models that describe damage mechanisms at aggregate level, (2) micro-poro-mechanical methods that analytically correlate the local and global quantities at aggregate and concrete level and (3) numerical methods that compute, through FEM techniques, the damage at aggregate level within the different phases of concrete. All the approaches adopted the concept of representative elementary volume (REV) that has been defined as an infinitesimal portion of the three-dimensional material system under consideration.