Numerical Study of Crack Propagation in Boulders Subjected to Diurnal Solar Irradiation

Abstract

Considerable evidence from field observations and measurements suggests that thermal stresses induced by daily exposure to the sun contribute significantly to mechanical weathering, the breakdown of rocks at the ground surface (Mcfadden et al. 2005; Aldred et al. 2016; Eppes et al. 2016). A solid theoretical foundation for quantifying and understanding these stresses is, however, currently lacking. We develop it using a 3d finite element (FE) model, coupling radiation and conduction with elastic response, to compute the time-varying stress state in mechanically isotropic, homogenous boulders exposed to the sun on Earth. As crack growth in brittle materials are generally dominated by tensile stresses, we focus on the temporal relationship between temperature and solar induced tensile stresses at a macroscopic level in distinct regions of boulders of different sizes. We found significant temporal variation in the magnitude, location, and spatial extent of elevated tensile stresses. Since fracture in brittle materials generally initiates from pre-existing defects, which are widely distributed through most materials (Danzer et al. 2007), the strength of a specimen is strongly affected by its size. To assess how the interaction of time varying tensile stresses with pre-existing defects in surface boulders affects their resistance to thermal breakdown, we carried out a probabilistic study. Using the Weibull theory, we calculated the probability of crack growth caused solely by diurnal solar exposure in boulders of different size. Our numerical results do illuminate the complex size-dependent thermo-mechanical behavior. Interestingly, they suggest that solar induced stresses for 0.3 m-diameter boulder are most likely to initiate crack growth between 4:00 pm to 6:00 pm, which is consistent with the field measurements of acoustic emissions that are only available for this boulder size (Eppes et al. 2016).