Localization phenomena in geological settings

This thesis explores localization in geological applications in the context of multi-physics, nonequilibrium systems. The term multi-physics refers to systems that contain a mix of physical processes that are allowed to operate simulateneously. The thesis begins with an investigation of purely mechanical systems and reviews localized structures stemming from material nonlinearities. In later chapters further processes are considered and nonlinear effects due to feedback mechanisms are studied and we describe how these feedback mechanisms can lead to fascinating spatio/temporal structures.

The simplest model considered here is that of a strut on aWinkler type foundation and it is well known that depending on the foundation characteristics various localized buckling patterns can emerge if the strut is under compression. Owing to the steady movement of tectonic plates the strut is deformed at a constant rate. We investigate how the buckling pattern evolves over time and offer qualitative interpretations of the observed behaviour.

Other localization patterns encountered in geological applications are the formation of shear zones. The chapter on energy based localization criteria introduces a generalization to the slip line field theory for application in such problems. The new formulation proposes a thermodynamic continuum-mechanic framework that fulfils the energy balance under consideration of the second law. The energy balance admits multiple steady states and, thus, this approach allows us to identify a critical mechanical dissipation parameter, here called the Gruntfest number, which separates loading conditions that lead either to homogeneous or localized plastic deformation. The geometry of the localized failure follows the generalized slip line pattern and this is used to simplify the semi-analytical solution of localization problem using the method of characteristics. The result is verified in numerical studies that are performed with the newly developed code REDBACK that is capable to handle thermo-mechanical coupling simultaneously. The structure of REDBACK is detailed here as well.