Embedded Discrete Fracture Networks to Analyze Groundwater Inflows during Tunnel Drilling

Tunnels commonly go through fracture zones that used to be analyzed as an equivalent porous medium with homogeneous permeability. However, it is a rough simplification that overlooks the connection triggered by underground works in fractured massifs. This study introduces the use of synthetic discrete fracture networks (DFN) to analyze groundwater inflows through tunnel excavation in a fractured zone considering the daily advance of the drilling front. First, a hypothetical case with six different settings varying the fracture density, the fracture length, and the aperture distribution is analyzed. Each setting has about 100 iterations. DFN hydraulic properties were estimated and compared with previous DFN studies, displaying the same behavior even though the magnitude of the estimated parameters differs. As an application example, structural measurements of the Alaska fault zone in the La Linea massif (Colombia) are used to obtain the statistical parameters of the fracture length and aperture distributions to generate the DFN. Five settings varying the fracture density are built, obtaining measured and simulated groundwater inflows of the same order of magnitude. These results highlight the potential of the synthetic DFN to analyze tunnels’ effects on groundwater flow.

An Improved Pattern Synthesis Iterative Method in Planar Arrays for Obtaining Efficient Footprints with Arbitrary Boundaries

In the present paper, an iterative technique devoted to reproducing efficient footprints with arbitrary boundaries for planar arrays is addressed. The methodology here depicted is based on exploiting the nature of the continuous aperture distribution by expressing it as a Fourier series of moderately high orders. In this manner, the resulting illumination boundary is defined by a target three-dimensional flat-topped pattern composed of stretching and shrinking modified circular Taylor patterns and the maximum order of the series to obtain a good reconstruction is determined by means of the iterative process. Examples and comparisons with the previous literature were conducted by analyzing square and rectangular contoured beams as test cases. Additionally, interesting potentials regarding space applications from a geostationary satellite are outlined by means of the EuTELSAT (European Telecommunications Satellite Organization) European coverage case study. In such a way, its numerical approach was analyzed by including subarray architectures and discussing improvements about dynamic range ratio of the excitations without critical power losses within the illumination region.

A Fractal Model for Predicting the Relative Permeability of Rough-Walled Fractures

The relative permeability and saturation relationships through fractures are fundamental for modeling multiphase flow in underground geological fractured formations. In contrast to the traditional straight capillary model from porous media, the realistic flow paths in rough-walled fractures are tortuous. In this study, a fractal relationship between relative permeability and saturation of rough-walled fractures is proposed associated with the fractal characteristics of tortuous parallel capillary plates, which can be generalized to several existing models. Based on the consideration that the aperture distribution of rough-walled fracture can be represented by Gaussian and lognormal distributions, aperture-based expressions between relative permeability and saturation are explicitly derived. The developed relationships are validated by the experimental observations on Gaussian distributed fractures and numerical results on lognormal distributed fractures, respectively.

Influence of Aperture Distribution on Flow in Fractal-Fracture Networks

<p>While fractal models are often employed for describing the geometry of fracture networks, a constant aperture is mostly assigned to all the fractures when such models are flow simulated. While network geometry controls connectivity, it is fracture aperture that controls the conductivity of individual fractures as described by the well-known cubic-law. It would therefore be of practical interest to investigate flow patterns in a fractal-fracture network where the apertures also scale as a power-law in accordance to their position in the hierarchy of the fractal. A set of synthetic fractal-fracture networks and two well-connected natural fracture maps that belong to the same fractal system are used for this purpose. The former, with connectivity above the percolation threshold, are generated by spatially locating the fractured and un-fractured blocks in a deterministic and random manner. A set of sub-networks are generated from a given fractal-fracture map by systematically removing the smaller fracture segments. A streamline simulator based on Darcy's law is used for flow simulating the fracture networks, which are conceptualized as two-dimensional fracture continuum models. Porosity and permeability are assigned to a fracture within the continuum model based on its aperture value and there is nearly no matrix porosity or permeability. The recovery profiles and time-of-flight values for each network and its dominant sub-networks at different time steps are compared.</p><p>The results from both the synthetic networks and the natural maps show that there is no significant decrease in recovery in the dominant sub-networks of a given fractal-fracture network. It may therefore be concluded that in the case of such hierarchical fractal-fracture systems with scaled aperture, the smaller fractures do not significantly contribute to the fluid flow.</p><p><strong>Key-words: </strong>Fractal-fracture; Connectivity; Aperture; Dominant Sub-networks; Streamline Simulator; Recovery</p>

Technique for spatial interference reduction and its application in monopulse radar with active phased array antenna

The paper describes monopulse radar with sidelobe-blanking system. The antenna of the sidelobe-blanking system is one subarray of the radar’s active phased array antenna. The elements of the subarray is also used for sum and difference pattern generation. It is shown that if aperture distribution required to produce low-sidelobe sum pattern is used, the pattern of one subarray will satisfy the requrements for antenna of the sidelobe-blanking system. An example of designing the monopulse radar with sidelobe-blanking system is presented. Sum pattern of the radar anettena is produced with different low-sidelobe pattern synthesis procedures. The analysis of monopulse radar parameters and sidelobe-blanking system performance is done.

A novel fractal model for the prediction and analysis of the equivalent thermal conductivity in wood

This study proposes a new fractal model to improve the accuracy of equivalent thermal conductivity (ETC) prediction for wood and determine how the wood’s pore structure influences ETC. Using fractal theory and mercury injection porosimetry data, a fractal model for the geometry of the wood’s pore structure was built. The geometric model was then transformed into an equivalent thermal resistance model to calculate ETC. The calculations produced an explicit expression for ETC derived from the wood’s structural parameters including the minimum and maximum pore apertures, aperture distribution, porosity, and fractal dimension. The model also includes a probability factor. The simulated ETC produced by the model was validated by experiments and it was found to be in good agreement with these. These simulation results will be used to study the influence of several factors on ETC. The proposed model has the potential to be able to predict and analyzing other wood properties such as its electrical conductivity, diffusivity, and permeability and the model can likely also be used to analyze other porous materials.

Effect of Shearing on Non-Darcian Fluid Flow Characteristics through Rough-Walled Fracture

The heterogeneous fracture geometry induced by the presence of roughness and shearing complicates the fracture flow. This paper presents a numerical investigation of the non-Darcian flow characteristics of rough-walled fractures during shear processes. A series of fracture flow simulations were performed on four types of fractures with different joint roughness coefficients (JRCs), and the different shear displacements were imitated by degrees of mismatch on two fracture surfaces. The results show that the disorder of fracture geometries and the increase in flow rate are the main causes for the emergence of an eddy flow region, which can significantly reduce the fracture conductivity and change the fracture flow from linear to nonlinear. The Forchheimer equation provides a good model for the nonlinear relationship between the hydraulic gradient and the flow rate in the fracture flow. When the shear displacement or JRC increased, the linear permeability coefficient kv decreased, while the nonlinear coefficient β increased. A three-parameter equation of β was used to examine the inertial effect induced by the fracture roughness JRC and the variation coefficient of aperture distribution σs/em. The critical Reynolds number was a combined effect of aperture, viscous permeability, and inertial resistance, assuming the flow becomes non-Darcian when the inertial part is greater than 10%.