Thermo-Acousto-Elasticity (TAE) of natural rock cliffs: toward better understanding and monitoring damage and erosion process

Rainfalls and freeze-thaw cycles are well known to largely contribute to rock slopes erosion, including chemical processes (dissolution, alteration) together with mechanical action (stress change in fractures due to water freezing). The role of heat waves and thermal cycles is less studied in dry conditions. Here we present a thermo-acousto-elastic (TAE) model for rock volumes exposed to cyclic (daily to seasonal) thermal forcings, as an application of environmental seismology (1).

In our model, we assume that the rock temperature is constant at depth (a few meters in general), and that the free surface is exposed to heat fluxes (radiative and convective ones). In practice, these heat fluxes can be respectively derived from solar radiation normal to the rock surface and from the air temperature, both parameters are easily measured in the field. We then develop a numerical model based on a) thermal diffusion (heat propagation in the rock in 2D or 3D models, including complex geometries as cracks, rock columns…), b) thermal expansion relating temperature to strain, and c) acousto-elasticity relating the elastic parameters to the state of stress, (2). Such a model is run, for example, with COMSOL Multiphysics with a finite element scheme. We end up with a 2D or 3D numerical model of stress and deformation of the rock volume evolving over time ranging from sub-daily to yearly time scales.

As an application we test this model on various rock columns and observe that the developed model properly reproduces field observations, including daily and seasonal cycles: the natural resonance frequency of the rock column, a proxy for its rigidity, increases with increasing heat flux (3) and the rear crack closes up. As a result of fitting our numerical model to natural rock columns, we can evaluate the acousto-elastic constant that relates the rigidity to the state of stress, a parameter that is known to mainly depend on the state of damage of the material, opening the route for rockfall risk assessment, monitoring and early warning systems. Our model also allows to shed new light into fatigue and cyclic damage process of rock slopes and cliffs, a key to rock erosion.

 

References:

• (1) Guillemot, L. Baillet, E. Larose, P. Bottelin : Changes in resonance frequency of rock columns due to thermoelastic effects on a daily scale : observations, modeling and insights to improve monitoring, Geoph. J. Int. 231, 894-906 (2022).
• (2) Larose, E. & Hall, S.: Monitoring stress related velocity variation in concrete with a 2.10−5 relative resolution using diffuse ultrasound, J. acoust. Soc. Am., 125, 1853–1856 (2009).
• (3) Bottelin, P., Levy, C., Baillet, L., Jongmans, D. & Gueguen, P.: Modal and thermal analysis of Les Arches unstable rock column (Vercors massif, French Alps), Geophys. J. Int., 194, 849–858 (2013).