On determining the elastic modulus of a cylindrical sample subjected to flexural excitation in a resonant column apparatus

Abstract

For resonant column tests conducted in the flexure mode of excitation, a new methodology has been proposed to find the elastic modulus and associated axial strain of a cylindrical sample. The proposed method is an improvement over the existing one, and it does not require the assumption of either the mode shape or zero bending moment condition at the top of the sample. A stepwise procedure is given to perform the necessary calculations. From a number of resonant column experiments on aluminum bars and dry sand samples, it has been observed that the present method as compared with the one available in literature provides approximately (i) 5.9%-7.3% higher values of the elastic modulus and (ii) 6.5%-7.3% higher values of the associated axial strains.Résumé : Une nouvelle méthodologie est proposée pour déterminer le module élastique et les déformations axiales associées pour un échantillon cylindrique, à l'aide d'essais en colonne de résonance effectués dans le mode d'excitation en flexion. La méthode proposée améliore la méthode existante puisqu'elle ne nécessite pas la supposition de la forme du mode ni de la condition zéro du moment de torsion dans le haut de l'échantillon. Une procédure étape-par-étape est présentée afin d'effectuer les calculs nécessaires. Dans le cas de plusieurs essais en colonne de résonance sur des barres d'aluminium et des échantillons de sable sec, la méthode proposée comparativement à la méthode de la littérature offre approximativement (i) des valeurs du module élastique supérieures de 5,9% à 7,3%, et (ii) des valeurs des déformations axiales associées supérieures de 6,5% à 7,3%.

Damping of Sands for Varying Saturation

“…The resonant column test is generally used to measure the dynamic properties for soils corresponding to a strain level in a range of 10 24 -10 21 % (Chung et al 1984;Saxena and Reddy 1989;Cascante et al 1998;Kumar and Clayton 2007;Kumar and Madhusudhan 2010c). In the past, due to the difficulties involved in eliminating background noise and equipment-generated damping from the back electromotive force (EMF) effect, the determination of the damping ratio using resonant column tests corresponding to a very small strain range (10…”

Effect of Saturation on Dynamic Soil Properties in Low Strain Range Using Resonant Column Apparatus

“…The methodology of Kumar and Madhusudhan [6] (2010); is used to find the elastic modulus of the sample from resonant frequency. The basic principle of the resonant column test is to vibrate a cylindrical soil specimen in a fundamental mode of vibration, in torsion or flexure.…”

Properties of soils using laboratory seismic methods and numerical modelling

“…Cascante et al (1998) described how the Young's modulus of the specimen can be determined from the resonant frequency for the flexural mode of excitation. This is the method often used for resonant column tests in flexural mode of vibration (Karl et al 2003, Kumar andMadhusudhan 2010) due to its simplicity. Kumar and Madhusudhan (2010) derived another method to account for the insufficiency of the method presented by Cascante et al (1998) but the method requires iteration of the Young's modulus of the specimen.…”

“…This is the method often used for resonant column tests in flexural mode of vibration (Karl et al 2003, Kumar andMadhusudhan 2010) due to its simplicity. Kumar and Madhusudhan (2010) derived another method to account for the insufficiency of the method presented by Cascante et al (1998) but the method requires iteration of the Young's modulus of the specimen. Neither method was included in ASTM D4015-07 (2013).…”

“…where a 0 , a 1 , a 2 and a 3 are coefficients for the equation. Kumar and Madhusudhan (2010) proposed a different mode shape function from Cascante et al (1998) for the flexural resonant column test as shown in Equation 4.5.…”