ABSTRACT

The article presents a comparison of static and dynamic elasticity constants of sandstones and Shales based on an uniaxial compression test. The results of the test indicated that the static elasticity constants are generally more sensitive to changes in stress than their dynamic equivalents. It was also demonstrated that Within the full range of applied stresses the dynamic Young's modulus is about twice as high as its static equivalent and reaches the maximum value for stresses for which a specimen volume is minimal. In the case of Poisson's ratio it turned out its dynamic and static values are closely approximate for stresses which do not exceed 40% of the Specimen strength limit. After crossing that limit the static ratio values increase rapidly whereas the dynamic ratio values change only to a slight degree.

INTRODUCTION

Both Young's modulus and Poisson's ratio are the two basic constants permitting the determination of the dependence between stresses and strains for a linearly elastic material. The values of those constants depend, among other things, on the static or dynamic character of the process. The static Young's modulus (E) or Poissons's ratio (v) are determined by the analysis of the curves of dependence between the stress (σ1) and longitudinal (ε1) and lateral (ε 3) strains, obtained during the uniaxial compression test. On the other hand, their dynamic equivalents (E* and v*) are based on the measurements of the velocity values of sound waves passing through the specimen. This is described by the following formulae (Lama & Vutukuri 1978):

(Equation and Figure in full paper)

On the other hand, the dynamic elasticity constants do not refer to numbers but rather to certain relations between the material constant w value and the stress applied to the specimen. In order to make it possible to compare the static constants with the dynamic ones, the present study required an introduction of differential static elasticity constants Est and vst, determined in the way illustrated in Fig. 1. Assuming that the values iEst and i presented in Fig.1., are assigned to the stress corresponding to the middle of the interval ∆iσ1, the curves obtained in this way illustrate the relation between the longitudinal stress in the specimen and the differential static elasticity constants Est and vst.

THE SUBJECT OF RESEARCH, THE METHODS AND WAY OF PRESENTING THE RESULTS

The results of uniaxial compression tests were obtained for specimens cut out of blocks of six different sandstones and five shale rocks taken from the "siodlowe" layers of the hard coal mine "Jasmos".

Cylindrical specimens of the diameter equal to d = 22 mm and the height h = 44 mm were uniaxially compressed with the constant stress rate 2.5 MPa × min−1. During the experiment the loading force was registered as well as longitudinal and circumferential strains of the specimen and the time of its being crossed by both the longitudinal and transverse sound waves (respectively, tp and ts) with the frequency of 1 MHz.vst(, calculated according to the formulae

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