Numerical modelling of thermal weakening of granite under dynamic loading

Abstract

A numerical method to predict thermal weakening of granite rock under low- and moderate rate dynamic loading conditions is developed. Thermal weakening of granite under uniform heating, leading to degradation of the material stiffness and strength, is modelled with the continuum approach, using a damage-viscoplasticity model. The viscoplastic part is based on a special power law criterion for granite under compression and the rounded tensile cut-off surface, while the damage part is equipped with separate damage variables in tension and compression. The strain rate sensitivity of rock is accounted for by viscoplasticity. The global thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method with mass scaling applied to increase the critical time step. Rock heterogeneity is described as random clusters of linear tetrahedral finite elements assigned with the constituent mineral, here quartz, feldspar, and biotite, material properties. The temperature dependence of the thermal and elasticity properties of the minerals is included in the model up to 850 ◦C, i.e. well beyond the α-β transition of quartz. However, as the model aims to predict the thermal weakening, the temperature dependence of the rock strength is not used as an input. In the numerical examples, low-rate uniaxial tension and compression tests are first simulated on heated and intact rock samples to demonstrate the performance of the model. Finally, crushing of heat-treated and intact granite balls by diametral dynamic compression is numerically replicated with a fair accuracy.