REFEREED PUBLICATIONS IN JOURNALS
Nejati, M., M.L.T. Dambly, and M.O. Saar, A methodology to determine the elastic properties of anisotropic rocks from a single uniaxial compression test, Journal of Rock Mechanics and Geotechnical Engineering, 11/6, pp. 1166-1183, 2019. [Download PDF] [View Abstract]This paper introduces a new methodology to measure the elastic constants of transversely isotropic rocks from a single uniaxial compression test. We first give the mathematical proof that a uniaxial compression test provides only four independent strain equations. As a result, the exact determination of all five independent elastic constants from only one test is not possible. An approximate determination of the Young's moduli and the Poisson's ratios is however practical and efficient when adding the Saint–Venant relation as the fifth equation. Explicit formulae are then developed to calculate both secant and tangent definitions of the five elastic constants from a minimum of four strain measurements. The results of this new methodology applied on three granitic samples demonstrate a significant stress-induced nonlinear behavior, where the tangent moduli increase by a factor of three to four when the rock is loaded up to 20 MPa. The static elastic constants obtained from the uniaxial compression test are also found to be significantly smaller than the dynamic ones obtained from the ultrasonic measurements.
Dambly, M.L.T., M. Nejati, D. Vogler, and M.O. Saar, On the direct measurement of shear moduli in transversely isotropic rocks using the uniaxial compression test, International Journal of Rock Mechanics and Mining Sciences (IJRMMS), 113, pp. 220-240, 2019. [Download PDF] [View Abstract]This paper introduces a methodology for the direct determination of the shear moduli in transversely isotropic rocks, using a single test, where a cylindrical specimen is subjected to uniaxial compression. A method is also developed to determine the orientation of the isotropy plane as well as the dynamic elastic constants using ultrasonic measurements on a single cylindrical specimen. Explicit formulae are developed to calculate the shear moduli from strain gauge measurements at different polar angles. The calculation of shear moduli from these formulae requires no knowledge about Young's moduli or Poisson's ratios and depends only on the orientation of the isotropy plane. Several strain gauge setups are designed to obtain the shear moduli from different numbers and arrangements of strain gauges. We demonstrate, that the shear moduli can be determined accurately and efficiently with only three strain gauge measurements. The orientation of the isotropy plane is measured with different methods, including ultrasonic measurements. The results show, that the isotropy plane of the tested granitic samples slightly deviates from the foliation plane. However, the foliation plane can still determine the orientation of the isotropy plane with a good approximation.
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Dambly, L., On the direct measurement of the shear modulus in transversely isotropic rocks using the uniaxial compression test, MSc Thesis, 31 pp., 2017. [View Abstract]This paper presents a novel method to directly measure the out-of-plane shear modulus of transversely isotropic rocks by using a single cylindrical specimen subjected to uniaxial compression. This simple methodology relies on the measurement of strain at single or multiple points around the sample, and using those in an explicit formula to directly determine the shear modulus. In addition to the shear modulus, the plane of symmetry, the Young's moduli and the Poisson's ratio transverse to the plane of isotropy can be determined from this single test. Several experimental setups are proposed depending on whether the plane of symmetry is known or needs to be determined. Experimental results on three granitic samples show that the measured plane of symmetry is significantly deviated from the one apparent from the visual inspection of the foliation plane. In addition, the Saint-Venant formula is found to give an error of more than 10% for samples exhibiting a higher anisotropy ratio than 1.85.