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Bender elements are more and more often used in geotechnical engineering to assess the elastic pr... more Bender elements are more and more often used in geotechnical engineering to assess the elastic properties of soils [1, 2, 3 & 4]. Although the principle, based on the propagation of compression and shear waves, is simple, the interpretation of the tests requires an educated judgment, in particular in granular soils [5, 6 & 7]. The international parallel test organized by TC29 of the ISSMFE in 2002 thus showed a surprising discrepancy between the values of the shear modulus of Toyoura sand in the same conditions of density, the same state of stresses, the same method of sample preparation, using the same method of interpretation. That interpretation method consists in determining the time of flight of the waves by comparison of the input signal and the output signals. Further interpretation methods were developed in the recent past to confirm the results of the previous time analysis: cross-correlation and frequency analysis [2, 8 & 9]. Contrary to the time analysis, frequency analysis provides additional relevant information because the whole output signal is considered. The frequency analysis was therefore carried out to analyze the propagation of both compression and shear waves in various granular packings : glass beads, Fontainebleau sand, Toyoura sand … In this paper, we first present the methodology adopted to analyze the signals, mainly the decomposition of the signal into a coherent part and a random part. The coherent part corresponds to the propagation into an effective continuous medium whereas the random part can be related to the complex interactions at the microscopic scale between the waves and the grains. Then, we show some experimental results of pulse tests in granular packings at different stress levels. The analysis of the output signals reveals (i) an increase of the wave velocities as a power law of the mean effective stress and (ii) an increase of the peak frequency (peak of maximum magnitude in frequency). We observe that the evolution of the peak frequency follows a power law similar to the one obtained for wave velocities. Finally, different assumptions are made to explain such an evolution of the peak frequency: the first one is based on the Hertz's theory [10] of contact (microscopic point of view), the second one is based on the natural vibrations of the couple {bender -extender element; surrounding soil}. Additional original tests were carried out to validate or invalidate each of these two approaches. The conclusions are presented and discussed.

The effect of the mean effective stress on the elastic properties of unbound granular materials i... more The effect of the mean effective stress on the elastic properties of unbound granular materials is a well-known experimental result. Power laws between the mean effective stress and the shear modulus G vhmax of three natural sands are established for isotropic stress paths using bender elements. Triaxial test results reveal that such power laws are also suitable for contracting deviatoric stress paths whereas it is no longer the case for dilating deviatoric stress paths. Fabric changes during shearing are therefore highlighted. These observations seem to be a typical feature of the behavior of granular materials.

New piezo-ceramics transducers called bender-extender elements are used to characterize the mecha... more New piezo-ceramics transducers called bender-extender elements are used to characterize the mechanical behavior of the alluvial Loire River sand in the small strain domain. An unique couple of bender-extender elements is necessary to transmit and/or receive both compression waves and shear waves. Therefore, the simultaneous identification of the Young's modulus E max and the shear modulus G max in the small strain domain is possible along isotropic and deviatoric stress paths.

The effect of particles roughness on wave velocities is investigated in granular materials using ... more The effect of particles roughness on wave velocities is investigated in granular materials using bender-extender elements.

Experiments of wave propagation through assemblies of glass beads, using bender-extender elements... more Experiments of wave propagation through assemblies of glass beads, using bender-extender elements, are presented in this paper. Wave velocities are determined using many procedures of interpretation to be meticulously accurate about the results. The experimental results are then compared to theoretical predictions and experimental results in granular materials found in the literature. The effect of the beads diameter on the shear wave velocity is also investigated.

Bender elements are more and more often used in geotechnical engineering to assess the elastic pr... more Bender elements are more and more often used in geotechnical engineering to assess the elastic properties of soils [1, 2, 3 & 4]. Although the principle, based on the propagation of compression and shear waves, is simple, the interpretation of the tests requires an educated judgment, in particular in granular soils [5, 6 & 7]. The international parallel test organized by TC29 of the ISSMFE in 2002 thus showed a surprising discrepancy between the values of the shear modulus of Toyoura sand in the same conditions of density, the same state of stresses, the same method of sample preparation, using the same method of interpretation. That interpretation method consists in determining the time of flight of the waves by comparison of the input signal and the output signals. Further interpretation methods were developed in the recent past to confirm the results of the previous time analysis: cross-correlation and frequency analysis [2, 8 & 9]. Contrary to the time analysis, frequency analysis provides additional relevant information because the whole output signal is considered. The frequency analysis was therefore carried out to analyze the propagation of both compression and shear waves in various granular packings : glass beads, Fontainebleau sand, Toyoura sand … In this paper, we first present the methodology adopted to analyze the signals, mainly the decomposition of the signal into a coherent part and a random part. The coherent part corresponds to the propagation into an effective continuous medium whereas the random part can be related to the complex interactions at the microscopic scale between the waves and the grains. Then, we show some experimental results of pulse tests in granular packings at different stress levels. The analysis of the output signals reveals (i) an increase of the wave velocities as a power law of the mean effective stress and (ii) an increase of the peak frequency (peak of maximum magnitude in frequency). We observe that the evolution of the peak frequency follows a power law similar to the one obtained for wave velocities. Finally, different assumptions are made to explain such an evolution of the peak frequency: the first one is based on the Hertz's theory [10] of contact (microscopic point of view), the second one is based on the natural vibrations of the couple {bender -extender element; surrounding soil}. Additional original tests were carried out to validate or invalidate each of these two approaches. The conclusions are presented and discussed.

The effect of the mean effective stress on the elastic properties of unbound granular materials i... more The effect of the mean effective stress on the elastic properties of unbound granular materials is a well-known experimental result. Power laws between the mean effective stress and the shear modulus G vhmax of three natural sands are established for isotropic stress paths using bender elements. Triaxial test results reveal that such power laws are also suitable for contracting deviatoric stress paths whereas it is no longer the case for dilating deviatoric stress paths. Fabric changes during shearing are therefore highlighted. These observations seem to be a typical feature of the behavior of granular materials.

New piezo-ceramics transducers called bender-extender elements are used to characterize the mecha... more New piezo-ceramics transducers called bender-extender elements are used to characterize the mechanical behavior of the alluvial Loire River sand in the small strain domain. An unique couple of bender-extender elements is necessary to transmit and/or receive both compression waves and shear waves. Therefore, the simultaneous identification of the Young's modulus E max and the shear modulus G max in the small strain domain is possible along isotropic and deviatoric stress paths.

The effect of particles roughness on wave velocities is investigated in granular materials using ... more The effect of particles roughness on wave velocities is investigated in granular materials using bender-extender elements.

Experiments of wave propagation through assemblies of glass beads, using bender-extender elements... more Experiments of wave propagation through assemblies of glass beads, using bender-extender elements, are presented in this paper. Wave velocities are determined using many procedures of interpretation to be meticulously accurate about the results. The experimental results are then compared to theoretical predictions and experimental results in granular materials found in the literature. The effect of the beads diameter on the shear wave velocity is also investigated.