Improved correlation between the static and dynamic elastic modulus of different types of rocks

摘要

The relationship between the static and dynamic elastic modulus in rock materials has been frequently addressed in scientific literature. Overall, when it comes to the study of materials with a wide range of elastic moduli, the functions that best represent this relationship are non-linear and do not depend on a single parameter. In this study, the relationships between the static and dynamic elastic modulus of eight different igneous, sedimentary and metamorphic rock types, all of which are widely used as construction material, were studied. To this end, the elastic modulus values of 33 samples were obtained which, together with the values obtained for 24 other samples in a previous study, allowed a new relationship between these parameters to be proposed. Firstly, linear and nonlinear classical models were used to correlate static and dynamic moduli, giving R2 of 0.97 and 0.99, respectively. A classical power correlation between static modulus and P-wave velocity has also been proposed, giving an R2 of 0.99 and a sum of the squared differences (SSE) of 553.93. Finally, new equations relating static and dynamic modulus values have been proposed using new nonlinear expressions. These consider: (a) bulk density (R2 = 0.993 and SSE = 362.66); (b) bulk density and total porosity of rock (R2 = 0.994 and SSE = 332.16); and (c) bulk density, total porosity of rock and uniaxial compressive strength (R2 = 0.996 and SSE = 190.27). The expressions obtained can be used to calculate the static elastic modulus using non-destructive techniques, in a broad range of rock materials.