DETERMINATION OF THE YOUNG'S MODULUS OF TOGO ROCKS BY THE MORI-TANAKA HOMOGENIZATION

The article presents the study of the application of the porous media model (case of the Mori-Tanaka homogenization model) in order to determine the Young's modulus of the granites, quartzites and gneisses taken from the quarries and outcrops of Togo. 91 rock samples including 49 granite and quartzite samples and 42 gneiss samples were studied. The complexity of the mechanical behavior of rocks, related to rock diversity from the petrographic, textural, structural and physical point of view, is demonstrated by weak correlations between these features. In this context, we propose the use of the classical and modified Mori-Tanaka models applied to the three groups of rocks (the set of samples, the granites and the quartzites, the gneisses). In the classical MoriTanaka method (E (YMT)), according to which the rock is considered to be a biphase solid medium (matrix + inclusion), the role of the matrix is attributed to feldspar, the majority mineral of the rocks, and the collection of other minerals represents inclusions. The second method proposes to consider the rock as a tetraphase medium (feldspar, quartz, biotite and amphibole) and the Young's modulus of the rock (E (YT)) is determined as the sum of the elemental values of the module of each mineral according to the classical method of homogenization of Mori-Tanaka. For rocks with a Young's modulus of less than 70 Gpa – low resistance rocks – the application of the modified Mori-Tanaka method is of interest in the determination of the Young's modulus of gneiss, whereas of the classical Mori-Tanaka method gives satisfactory results for granites and quartzites. Neither method can be used to estimate the Young's modulus of granites, quartzites and gneisses, which Young's modulus is high (> 70 GPa)