This paper presents a numerical study on a possible piezoelectric effect in thermal drilling of Quartz bearing rocks. For this end, the governing piezoelectro-thermo-mechanical problem is solved with the finite element method. The granitic rock material, consisting of Quartz, Feldspar and Biotite minerals, is taken as linear elastic but heterogeneous and anisotropic. Temperature dependence of material properties is neglected. The simulation demonstrates that the secondary stresses arising from converse piezoelectric effect are three orders of magnitude smaller than the primary thermal stresses, which means that the piezoelectric effect is negligible.
Electrification effects, such as piezoelectricity and seismoelectricity, in rocks have important applications in the field of geophysical exploration. Moreover, piezoelectric properties and the thermal drillability of rocks containing piezoelectric minerals are interrelated to some extent [1]. Therefore, the drillability of, e.g Quartz bearing rocks, could be predicted based on their piezoelectric properties. Parkhomenko [1] hypothesised that there is an inverse secondary piezoelectric effect present in thermal drilling, accentuating the primary thermal stresses by secondary stresses arising from the electric charges due to thermal expansion of the quartz grains.
The principle of thermal drilling based on spallation phenomenon is illustrated schematically in Figure 1. Accordingly, when a rock surface is exposed to an intensive heating the resulting thermal gradient induces a compressive stress state, which leads to crack growth in the rock surface layer. When the cracks reach the critical length, spallation, i.e. ejection of rock chips, occurs. The minimal required temperature for spallation to occur in granitic rocks is about 500-600 °C [2]. Now, the Quartz grains in granite rock generate electric charges by the direct piezoelectric effect. This in turn, as hypothesised by Parkhomenko, accentuates the thermal stress states due to secondary piezoelectric stresses.
The present study addresses this topic by a numerical study. More specifically, the piezoelectric effect of Quartz is tested in rapid surface heating of a granite-like rock. For this end, a numerical method, based on finite elements, for solving the governing piezoelectro-thermo-mechanical problem is developed. The axisymmetric model, with the strong (local) form of the partial differential equations, is discretized with polygonal finite elements. Only the heat equation, having the external heat influx as the load term, depends on time and it is solved with the implicit Euler time integrator, while the quasi-static piezoelectric and mechanical balance equations are time independent. The generic granite like rock is modelled as heterogeneous and anisotropic linear elastic material, and it consist of Quartz, Feldspar and Biotite minerals.