Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Dark energy in five-dimensional Brans-Dicke cosmology with dimensional reduction

We explore a 5D Brans-Dicke scalar cosmology by conjecturing that the four-dimensional Hubble parameter varies as H = εφs,ε∈ R and s is some unknown power index and that the extra-dimensions compactify as the visible dimensions expand as b(t) ≈ ax(t) ,x ∈ R-. We mainly discuss the case x =-1. For critical values of ε close to unity,it was observed that the acceleration of the universe occurs at redshift close to z = 0.8 which indicates that in our model,accelerated expansion of the universe began only recen...     

Modeling three‐dimensional hydraulic fracture propagation using virtual multidimensional internal bonds

Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.     

Petrogenesis and tectonic setting of bimodal volcanism in the Sakoli Mobile Belt, Central Indian shield

The Sakoli Mobile Belt comprises bimodal volcanic rocks that include metabasalt, rhyolite, tuffs, and epiclastic rocks with metapelites, quartzite, arkose, conglomerate, and banded iron formation (BIF). Mafic volcanic rocks are tholeiitic to quartz‐tholeiitic with normative quartz and hypersthene. SiO₂ shows a large compositional gap between the basic and acidic volcanics, depicting their bimodal nature. Both the volcanics have distinct geochemical trends but display some similarity in terms of enriched light rare earth element–large ion lithophile element characteristics with positive anomalies for U, Pb, and Th and distinct negative anomalies for Nb, P, and Ti. These characteristics are typical of continental rift volcanism. Both the volcanic rocks show strong negative Sr and Eu anomalies indicating fractionation of plagioclases and K‐feldspars, respectively. The high Fe/Mg ratios for the basic rocks indicate their evolved nature. Whole rock Sm–Nd isochrons for the acidic volcanic rocks indicate an age of crystallization for these volcanic rocks at about 1675 ± 180 Ma (initial ¹⁴³Nd/¹⁴⁴Nd = 0.51017 ± 0.00017, mean square weighted deviate [MSWD] = 1.6). The εNd_t (t = 2000 Ma) varies between ?0.19 and +2.22 for the basic volcanic rock and between ?2.85 and ?4.29 for the acidic volcanic rocks. Depleted mantle model ages vary from 2000 to 2275 Ma for the basic and from 2426 to 2777 Ma for the acidic volcanic rocks, respectively. These model ages indicate that protoliths for the acidic volcanic rocks probably had a much longer crustal residence time. Predominantly basaltic magma erupted during the deposition of the Dhabetekri Formation and part of it pooled at crustal or shallower subcrustal levels that probably triggered partial melting to generate the acidic magma. The influence of basic magma on the genesis of acidic magma is indicated by the higher Ni and Cr abundance at the observed silica levels of the acidic magma. A subsequent pulse of basic magma, which became crustally contaminated, erupted as minor component along with the dominantly acidic volcanics during the deposition of the Bhiwapur Formation.     

Stiffness identification of a tall building during construction period using ambient tests

Ambient response measurements were made on an eighteen-storey building at three different stages of construction to detect any changes in the frequencies, mode shapes and stiffness with construction. The first nine frequencies and corresponding mode shapes for each stage of construction are found. A comparison is made among these mode shapes and frequencies and with the mode shapes and frequencies of an analytical model incorporating beams, columns, shear walls, panels and diagonal elements. The added effects, on frequencies and mode shapes, of non-structural elements such as stairs, elevators, claddings and partition walls are studied. Using Improved Statistical Structural Identification, an attempt is made to study the stiffening effect of non-structural elements by updating the stiffness matrix of the building.     

Photogrammetric Capabilities of the Kodak DC40, DCS420 and DCS460 Digital Cameras

The aim of this study is to assess the impact of sensor size and resolution of different digital camera sensors upon the accuracy and precision of three dimensional data derived by photogrammetry. Kodak DC40, DCS420 and DCS460 digital cameras were used to produce digital images of retroreflective targets in a 4 m three dimensional test field. The image locations of the targeted points were automatically measured using an off the shelf image processing software package. Two different sub-pixel measurement approaches were examined: centre of gravity and weighted mean. From the automated sub-pixel measurement of the targeted points, results indicate that the high resolution DCS460 camera produces optimum results using either the weighted mean or centre of gravity approaches. Although this was perhaps expected, the far lower resolution DC40 camera performed better than was originally anticipated, suggesting potential for the cheaper DC40 for many applications.