Quasi-brittle fractures appear across multiple scales in geomaterials – from a few microns to kilometric faults. For all engineering applications in the upper crust, the quantification of how fractures initiate, grow, and interact across scales is paramount to i) assess the ultimate failure of man-made structures (such as tunnels & dams, among others), and ii) control hydraulic pathways in the underground.

The mechanics of damage and fracture in fluid-infiltrated geomaterials provide the necessary tools to address a wide range of important problems, from the sealing properties of radioactive waste repositories to the hydraulic stimulation of pre-existing fractures in deep geothermal reservoirs, and the risks of fault reactivation in CO2 geological storage. Geomaterials are inherently heterogeneous and always include preexisting (micro- and macro-) discontinuities. Moreover, their mechanical behavior is frictional: it strongly depends on the mean stress. The mechanics of fracture and damage in geomaterials is, therefore, inherently more complex than in other materials, not to mention the strong coupling between fractures and fluid flow.

This one-week school aims to provide a complete review of the theoretical foundations and modern experimental and numerical techniques to address the quasi-brittle failure of geomaterials at multiple scales. The course will discuss experimental and field-scale observations to introduce essential mechanisms necessary to understand damage and fracture in fluid-saturated porous media. The lectures will then present in detail the thermodynamics of non-local damage, plasticity and fracture of fluid-infiltrated porous solids, analytical micro-mechanical approaches. Semi-analytical solutions for fluid-driven rupture growth and their use to analyze experiments and large-scale observations will be presented.
Complex geometries and non-linearities require numerical modeling. The course will thus present traditional and novel numerical methods for damage and fracture and their couplings with fluid flow. Notably, finite element methods and their extension to non-local damage and phase-field models will be thoroughly presented. How to account for the effect of randomness and heterogeneity in these materials will be the focus of lectures introducing novel techniques on these issues. Special attention will be made to the importance of advanced experimental techniques at different scales to guide the development of quantitative models. Examples of novel imaging techniques on different experimental setups will be presented in several lectures.
Applications of the theory to relevant problems encountered in radioactive waste storage, hydraulic stimulation of deep reservoirs, natural hazards, gas storage but also in the fracture of soft matter (e.g. hydrogels).

Two brainstorming sessions will be held on day 3 and day 4, aiming at fostering discussion on emerging research topics in the field in relation to:
1) The links between advanced imaging techniques and constitutive modeling;
2) Model complexity vs predictability in practice.
The course is addressed to doctoral students, young & senior researchers, and practicing engineers.