On the interpretation of rocks elasticity modulus

We consider the experimental data of the testing of rocks, performed by K. Mogi in his monograph “Experimental rock mechanics” which was published in 2007. Cylindrical samples of rocks were tested according to T. Karman’s scheme: on the first step, hydrostatic pressure was created up to different stress levels, on the second step the axial load was increased at a constant level of reached lateral pressure. During such a complex loading on the second step only the increment of axial strain was measured, which depends of the increment of the axial stress. In origin this dependence is presented in the form of graphs in real scale, which made it possible to convert these graphs into digital format in the form of tabular values. Two rocks are considered: Orikabe Diorite and Nabe-ishi Peridotite. According to the tables obtained, the stress-deformed state of these rocks in the second stage of complex loading for six test programs carried out in the experiment was analyzed. On each implemented loading path, a point is selected that corresponds to the axial stress with the same form of stress state. The latter, as is customary in geomechanics, is characterized by the ratio of the average principal stress to the maximum main stress. Thus, a (calculated) trajectory of proportional loading is distinguished for all stress levels within the elastic range. It is demonstrated that for such calculated loading paths, the experimental value of the increment of axial strain (within the elastic range) is a linear function of the increment of the axial stress. This proves the applicability of the generalized Hooke’s law. As a result, the Young’s modulus and the Poisson’s ratio are determined and shown that they (with respect to rocks) are indeed elastic constants, and not variable quantities, as it is sometimes interpreted.

elastic deformation of rocks, elastic constants, applicability of Hooke’s law under complex loading