TECHNICAL NOTE On the Ratios between Elastic Modulus and Uniaxial Compressive Strength of Heterogeneous Carbonate Rocks V. Palchik Received: 18 March 2010 / Accepted: 29 July 2010 / Published online: 12 August 2010 Ó Springer-Verlag 2010 Abstract The ratios M R = E/r c for 11 heterogeneous carbonate (dolomites, limestones and chalks) rock forma- tions collected from different regions of Israel were examined. Sixty-eight uniaxial compressive tests were conducted on weak-to-strong (5 MPa \r c \100 MPa) and very strong (r c [ 100 MPa) rock samples exhibiting wide ranges of elastic modulus (E = 6100–82300 MPa), uniaxial compressive strength (r c = 14–273.9 MPa), Poisson’s ratio (m = 0.13–0.49), and dry bulk density (q = 1.7–2.7 g/cm 3 ). The observed range of M R = 60.9–1011.4 and mean value of M R = 380.5 are compared with the results obtained by Deere (Rock mechanics in engineering practice, Wiley, London, pp 1–20, 1968) for limestones and dolomites, and the statistical analysis of M R distribution is performed. Mutual relations between E, r c , q, M R for all studied rocks, and separately for concrete rock formations are revealed. Linear multiple correlations between E on the one hand and r c and q on the other for Nekorot and Bina limestone and Aminadav dolomite are obtained. It is established that the elastic modulus and M R in very strong carbonate samples are more correlated with q-r c combination and e a max , respectively, than in weak to strong samples. The relation between M R and maximum axial strain (e a max ) for all studied rock samples (weak-to-strong and very strong) is discussed. Keywords Uniaxial compressive test  Elastic modulus  Maximum axial strain  Rock density 1 Introduction For a successful solution of different problems in rock engineering, two important mechanical parameters, namely, uniaxial compressive strength (r c ) and elastic modulus of rock (E) should be estimated correctly. It is well known that the elastic modulus increases with increasing uniaxial compressive strength; and there are different empirical relations between r c and E obtained for greywackes, limestones, agglomerates, dolomites, chalks, sandstones, and basalts (Deere 1968; ACI 1989; Palchik 1999; Al-Shayea 2004; Gokceoglu and Zorlu 2004; Sonmez et al. 2004; Vasarhelyi 2005; Palchik 2007; Ocak 2008). The values of empirical coefficients involved in r c -E depen- dencies, mathematical forms of these dependencies, and values of squared regression coefficient (0.57 \ R 2 \ 0.98) vary with rock formation. Some of these empirical relations are presented elsewhere (Palchik 2007). Deere (1968) has established ranges of ratios M R = E/r c for ten different types of intact rocks (diabase, granite, basalts, limestones and dolomites, sandstones, shales, quartzite, gneiss, marble and schist) and mean values of M R in each of these ten rock types. In particular, the value of M R for carbonate rocks (limestone and dolomites) ranges from 250 to 700 with the mean of 420. However, the mean value of M R cannot be used to define reliable relations between r c and E in each of rock samples, in particular, in heterogeneous carbonate rocks, where rock samples exhibit different mechanical properties even within the same rock formation. Therefore, a study of the influence of mechan- ical properties on the value of M R is required. The objective of this study was to examine the values of M R = E/r c for different heterogeneous carbonate rocks (dolomites, limestones and chalks) exhibiting a wide range of uniaxial compressive strength (14 \ r c \ 273.9 MPa) V. Palchik (&) Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel e-mail: vplachek@bgu.ac.il 123 Rock Mech Rock Eng (2011) 44:121–128 DOI 10.1007/s00603-010-0112-7