Computational and experimental analysis of the scattering byrotating fans

The electromagnetic scattering of rotating blades is investigated both theoretically and experimentally. We have developed an analytical method based on physical optics (PO) and the method of equivalent currents (MEC), in conjunction with the quasi-stationary method. We have predicted the bistatic field scattered by a multiple skew-plated rotating fan. Comparisons with a numerical calculation based on the method of moments and with measurements have given very satisfactory results. A comparison with previously published results has also been carried out. Physical interpretations are given both in time and frequency domains. Our analytical model correctly predicts the spreading and magnitude of the frequency response as a function of the scatterer's skew angles, its rotation frequency, and the directions of incidence and scattering     

Modeling of complex modulus of bituminous mixtures measured in tension/compression to estimate secant modulus in indirect tensile test

For mechanistic based pavement design, it is necessary to know the stiffness of materials used for road construction. In the European standard EN 12697-26, several experimental tests are proposed to measure the modulus of bituminous mixtures. However, bituminous materials exhibit strong viscoelastic behavior. Hence, the stiffness of this specific material depends not only on the sample geometry but also on the loading law (strain or stress curve versus time). As a consequence, comparison between these different tests, performed in time or frequency domain, is not straight forward. The present paper focuses on measurement of secant modulus using the Indirect tensile (IT) test and comparison with complex modulus. In the IT test, the loading law is not systematically controlled. So, it is important to investigate the influence of the loading waveform on the test result. For this study, the case of a High Modulus Bituminous Mixture for base course (French EME) has been considered. Its viscoelastic behavior has been firstly determined using complex modulus measurements and using Prony series model. An intermediate step, based on an original master curve construction method is used. Doing so, the viscoelastic model is validated on the time domain by simulating direct tensile tests. The case of IT test is then considered. The Prony series model is conformed against IT test results for which the force waveform is known. For this last test, the dependance of the Poisson ratio with temperature and loading time is highlighted. Assuming a purely elastic behavior in isotropic compression, a formula, able to derive the viscoelastic Poisson ratio from the complex modulus is presented. Finally, a theoretical parametric study considering the IT loading waveform is undertaken. It appears that the correction factor given in the standard EN 12697-26 cannot be applied at all temperatures. Actually, this correction factor should be material dependent. This study has been carried out in the framework of collaboration between LCPC and USIRF (Union des Syndicats de l’Industrie Routière française).     

Evaluation of the structure-induced rolling resistance (SRR) for pavements including viscoelastic material layers

This article addresses the question of whether the viscoelastic behavior of asphalt pavements, as part of the factors that impact the rolling resistance, might lead to substantially higher energy consumption of road traffic, as compared to non-dissipative pavements. In the context of sustainable development (fuel consumption, gas emission), this is a current issue for the pavement design community. This problem is tackled by a theoretical approach which consists in computing the structure-induced rolling resistance (SRR) for a vehicle by using the mechanical response of a layered viscoelastic medium excited by moving loads (i.e. tires of the vehicle). The structure-induced power dissipation is shown to be proportional to the integral over contours of the applied loads of the pavement deflection, times the outward normal to these contours. Following the developed approach, the determination of the SRR force engendered by the structure-induced dissipation is obtained from the computation of the deflection of the viscoelastic pavement to an assumed pressure distribution. Such an approach applied to a thick asphalt pavement allows the SRR for a typical road structure to be evaluated as a function of temperature and speed. A non-dimensional analysis is also presented to extend the results to some other contexts. Under the assumptions made for the derivation of the SRR, the main conclusion of the case study is that the extra fuel consumption for a vehicle resulting from the viscoelastic behavior of asphalt pavements is small.     

Note on the ineffective length of a fiber

A general definition is given of the concept of ineffective length of a fiber, which is of use in the statistical theories of composite strength. The ineffective length, as formulated, may also serve as a measure of the total supporting capability of a fiber. The paper then sets forth models of an in situ fiber, deterministic or stochastic, and shows that the ineffective length may be by orders larger than predicted by the previous formulation. In extreme cases it may become comparable to the fiber length. Particular examples illustrating the above models are also given.     

Crack-induced anisotropy and scattering in stressed rocks: Effective elastic moduli and attenuation

A modelling of the effective anisotropic elasticity tensor is presented for elastic rocks permeated by a rather dilute concentration of stress-induced dry and saturated flat cracks. An exact analytical expression of the three wave velocities and attenuations in any oblique direction is obtained for the various crack distributions considered. A comparison is made with spherical cavities. This study is linked to the mechanical behaviour of cracked rocks under varying stress and has also relevance in a seismological context to the detection of cracked zones and may be useful in the investigation of earthquake dilatancy.     

Asphalt material fatigue test under cyclic loading: the lengthening of samples as a way to characterize the material damage experiments and modelling

Fatigue tests of bituminous materials performed on trapezoidal specimens induce a loss of stiffness, combined with a significant extension of the specimens at the beginning of the test when applying high strain levels. This paper presents the development of a viscoelastic constitutive law with unilateral damage for asphalt materials, based on the observation of tensile failure tests on asphalt binder lenses between two metal spheres. The unilateral damage is defined as the opening of the micro-cracks in the bitumen during extension and their closing during contraction. When put into a semi-analytical structural model of the trapezoidal specimen, this constitutive law leads to results close to those highlighted at the beginning of fatigue experiments for various experimental conditions (temperature, load frequency and strain amplitude level). According to the used modelling, the damage evolution law describes the fast initial homogeneous creation of the micro-cracks and then their slow development. The modelling is also able to explain a given percentage of the loss of stiffness. These results show mainly that the bituminous material extension is due to the dissymetric behaviour induced by the unilateral damage coupled with viscoelasticity. Therefore the asphalt mix extension is a way to quantify the level of the material damage.     

Ambiguous Shape from Shading with Critical Points

The eikonal equation can have an infinite number of solutions when the image has critical points. We exhibit a family, indexed by a continuous parameter, of non isomorphic surfaces with one critical point, which give the same simple image. Hence, shape from shading can be an ill-posed problem when no additional condition on the shape is imposed, even when the image has critical points. Also, deformations without distortion are possible, i.e., there can exist a continuous deformation of the surface which does not modify its image.     

Heterodyne detection of tunable FIR sidebands

Continuously tunable far infrared (FIR) laser sidebands have been generated in a Schottky diode by nonlinear mixing the radiation from an optically pumped FIR laser operating between 0.6 and 3 THz with that from a microwave source in the 2-4 GHz range. A very sensitive heterodyne detection is adapted to detect the sidebands generated not only at the sum or difference frequency of the two radiations, but also, for the first time in the FIR region, those related to the mixing of the FIR radiation with the second and third harmonics of the microwaves. The high selectivity of the superheterodyne detection allows easy separation of the various sidebands. The global tunability of this system is 2 × 10 GHz for the more powerful FIR emission lines. To demonstrate the tunability of the device absorption signals of several molecules are presented in the whole range of operation of the system (0.6-3 THz) using either direct or lock-in detection techniques.     

Effectiveness and longevity of a green/food waste derived compost packed column to reduce Cr(VI) contamination in groundwater

PAS100 accredited compost derived from green and food waste sources was used to remediate groundwater containing Cr(VI) at a historically contaminated site in Falkirk, Scotland, UK. The compost was mixed with gravel at a ratio of 1:1 (v/v) to provide a reactive bedding material in an upflow column. The Cr(VI) concentration in the groundwater (inlet) ranged from 0.5 to 7.8 mg L(-1) during the 168 d trial period. After an acclimation period of 54 d, the flow rate was increased in the column from 5.8 to 8 mL min(-1). Cr(VI) in the outlet was less than 100 μg L(-1) up to 134 d, after which the concentration steadily increased till 168 d. Compost analysis following completion of the trial confirmed that Cr(VI) was captured within the column. Anaerobic microbial reduction of Cr(VI) to Cr(III) was thought to be a key mechanism responsible for the longevity of the system to remove Cr(VI) from the groundwater. Requiring no additional organic carbon or nitrogen during the trial period, this setup represents a cost-effective treatment approach for low flow-through systems.