Mining - Some Correlations Between Rock Parameters, Derived from Wuerker's "Annotated Tables of Strength and Elastic Properties," 1956

The aim of this paper is to disclose some of the correlations between rock parameters, hidden in Wuerker's "Annotated Tables of Strength and Elastic Properties of Rocks," 1956. The empirical relations concern dry rocks of varying porosity. Curves and equations interrelating the specific gravity, compressive strength, bar velocity, and Poisson's ratio are presented. In 1956 Wuerker published his "Annotated Tables of Strength and Elastic Properties of Rock", in which various physical properties of rocks determined by different authorities, are tabulated systematically. The tables are primarily intended for use by mining-, quarrying- and ore-dressing engineers. Since the list of measured parameters for each type of rock includes properties such as — grain size, specific gravity, porosity, compressive strength, static elastic cons:ants (moduli of elasticity, rigidity, specific damping capacity and longitudinal bar velocity) the tables are also of considerable interest to the practical geophysicist. Correlations between rock parameters may enable geophysicists, geologists and civil engineers to transiate measurements from one parameter to another. Even if these translations are of limited accuracy, or valid only within certain specified ranges, they often serve a useful parpose. The aim of this paper is to disclose some of the correlations between rock parameters concealed in wuerker's Tables. Throughout this paper the following symbols and units are used unless otherwise stated: Sg is Specific gravity, the ratio of the density of a specimen to the density of water at 4°C. P is Porosity, in %, the ratio of the volume of voids in a specimen to its total volume. CS is Compressive strength in 1000 p.s.i., the stress under which a specimen will fracture when undergoing a standard compression test. V is Bar Velocity in kilo-feet/sec, the velocity of longitudinal seismic waves measured in a slender bar type specimen. Vc is Bulk or Constraint Velocity in kilo-feet/ sec, the velocity of longitudinal seismic waves measured in a very large specimen.+is Reciprocai bar velocity in millisecs/ft (1 millisec = 10-3 sec). cis Poisson's ratio, the ratio of the lateral to longitudinal strain of a body under longitudinal stress. CORRELATIONS Specific Gravity (Sg) vs. Porosity (P) Figure 1 is a diagram illustrating the relatiooship between specific gravity and porosity for approuirr~ately 70 samples of dry rocks. A curve fitted by estimation to this data yields the empirical formula: Sg =-0.0268P + 2.67 * 0.2 (1) Considering unit volume of a porogs specimen then