Study of relationship between static and dynamic young modulus

ISSN 0543-5846 A. MOCKOVČIAKOVÁ, B.at all.: STUDY OF THE RELATION BETWEEN THE STATIC AND DYNAMIC ... MOCKOVČIAKOVÁ PANDULA METABK 42 (1) 37 (2003) UDC - UDK 552.1:539.3:534.88=20

STUDY OF THE RELATION BETWEEN THE STATIC AND DYNAMIC MODULI OF ROCKS
Received - Primljeno: 2002-04-30 Accepted - Prihvaćeno: 2002-09-09 Preliminary Note - Prethodno priopćenje

Non-destructive techniques based onthe propagation of ultrasonic wave through the elastic medium were used for determination of dynamic modulus of selected samples of rocks in laboratory. The calculated values of dynamic modulus were compared with values of static modulus determined in laboratory on samples tested by applied loading. A method of estimation of the static modulus in situ conditions, where the measurements cannot becarried out, is discussed. Key words: ultrasonic waves, static and dynamic modulus, rocks Proučavanje odnosa između statičnog i dinamičnog modula stijena. Za laboratorijsko određivanje elastičnog i dinamičnog modula odabranih uzoraka stijena uporabljene su nerazarajuće tehnike temeljene na širenju ultrazvučnih valova kroz elastični medij. Izračunate vrijednosti dinamičkog modula su uspoređene svrijednostima statičnog modula određenog u laboratoriju na uzorcima testiranim primjenom opterćivanja. Raspravljena je i metoda utvrđivanja statičnog modula u uvjetima “in situ” gdje mjerenja ne mogu biti provedena. Ključne riječi: ultrazvučni valovi, statički i dinamički modul, stijene

INTRODUCTION Determination of the physical and mechanical properties of rocks as well as the behaviour of therock massive after the deformation are the most interesting problems, which are still not sufficiently and definitely solved. Solving some stability problems referring not only the mining, but also to other branches of industry, it seems to be very important to make an assessment of the elastic properties of the media. They are mostly determined under laboratory conditions on the collected samplesand used directly or modified to the solution of problem. In mining conditions it is often meeting a problem, when the rock is investigated as the rock-massive with a very complicated structure. For the simplicity the elastic properties are determined on the base of measurements in laboratory. The common method used in laboratory is the static testing, where the mechanic properties of rocks aredetermined on the samples of rocks. Bearing in mind the assumption of homogeneity of the investigated media, the elastic properties are characterized by constant - static
A. Mockovčiaková, Institute of Geotechnics of Slovak Academy of Sciences, B. Pandula, BERG Faculty, Technical University of Košice, Košice, Slovakia

modulus ES which specifies the relation between the applied stress and strain.The other group of techniques involve the application of non-destructive seismic or acoustic waves [1, 2]. The main advantage of these methods is that there does not come to the destruction of the specimen. The basis of this method is the theory of elasticity. From the values of velocities of propagation of waves, which reflect the properties of the elastic, isotropic media, it is possible todeterminate the dynamic modulus ED. The method enabling the determination of the dynamic modulus is relatively simple, inexpensive and suitable for application also in situ. It is known from various sources [3, 4], that the correlation between two moduli does exist; the aim of this paper is, basing on the values of dynamic elastic modulus, to find an analytical expression that allows the determinationof modulus ES. Basing on measurements of dynamic modulus measured in situ conditions, it will be possible to estimate the correspondent static modulus, the measurement of which cannot be carried out in operational conditions. It seems to be very important, as the evaluation of the elastic properties of rock should correspond to requirements, which refer to long [5, 6], (stability problems at...