Evaluate best-mixing model for estimating thermal conductivity for granitoids from mineralogy: A case study for the granitoids of the Bundelkhand craton, central India

Abstract

Granitoid is an important part of the upper continental crust, and therefore its thermal conductivity (TC) plays an important role in understanding the lithospheric thermal structure in a region and for geotechnical or geoengineering purposes. In above context, due to the lack of TC data or absence of proper sample for its measurements, TC values are assumed which can lead to erroneous results. In such scenario, when direct measurements are not possible, TC can be estimated by indirect methods with proper precautions. An attempt is made here to arrive at the best mixing model for granitic rocks by using TC of the individual minerals and compare the deviation between the measured and calculated values. The considered mean models are: arithmetic, geometric, harmonic, effective, Voigt-Reuss-Hill and Hashin-Shtrikman along with its lower and upper bound. Studied rocks are potassic granitoid (PG), biotite granitoid (BG), sodic granitoid (GG) and gneisses (BnG) from the Bundelkhand craton, central India. Measurements of TC are done in the laboratory on 21 samples using steady-state method. Data show wide variations in TC values for granitoids (PG: 2.7 − 3.2, BG: 2.6 − 2.9, GG: 2.9 − 3.0 Wm−1 K−1) and gneisses (2.9 − 3.7 Wm−1 K−1). Modal mineralogy of the rocks are determined using petrological and geochemical data through modal analysis and normative (CIPW-NORM) methods. The calculated TC arrived by both the methods provide a satisfactory agreement for the harmonic mean model, showing deviation from −10.9 to 17.6% for modal analysis and −16.1 to 11.5% for NORM method. Deviations from the above methods decrease further (−23.3 to 2.8% and −27.7 to −3.1%, respectively) using minimum mineral TC. Therefore, we suggest that, in the case of non-availability of the proper sample for direct measurement, the TC of very low porous granitoids could be satisfactorily determined by assessing their modal mineralogy and considering the harmonic mean model.