A new mixed-mode fracture criterion for large-scale lattice models

Abstract

Abstract. Reasonable fracture criteria are crucial for the modeling of dynamic failure in computational lattice models. Successful criteria exist for experiments on the micro-and on the mesoscale, which are based on the stress that a bond experiences. In this paper, we test the applicability of these failure criteria to large-scale models, where gravity plays an important role in addition to the externally applied deformation. Brittle structures, resulting from these criteria, do not resemble the outcome predicted by fracture mechanics and by geological observations. For this reason we derive an elliptical fracture criterion, which is based on the strain energy stored in a bond. Simulations using the new criterion result in realistic structures. It is another great advantage of this fracture model that it can be combined with classic geological material parameters: the tensile strength σ 0 and the shear cohesion τ 0 . The proposed fracture criterion is much more robust with regard to numerical strain increments than fracture criteria based on stress (e.g., Drucker-Prager). While we tested the fracture model only for large-scale structures, there is strong reason to believe that the model is equally applicable to lattice simulations on the micro-and on the mesoscale.

Relative rates of fluid advection, elemental diffusion and replacement govern reaction front patterns

“…We use a coupled hydro-dynamic model within the microstructural modelling ELLE Koehn et al, 2003;2005;2019;Bons et al, 2008;Sachau and Koehn, 2010;Sachau and Koehn, 2013;Ghani et al, 2013Ghani et al, , 2015 and expand the model by adding advective and diffusive matter transport as well as a simplified isovolumetric replacement reaction. We set-up the model to simulate the infiltration of a grain aggregate with more permeable grain boundaries and the progression of the reaction front where reactions are triggered by the presence of certain element concentrations that are changing due to advection, diffusion and reaction (fig.…”

Fracturing and Porosity Channeling in Fluid Overpressure Zones in the Shallow Earth’s Crust

“…Failure in the elastic network will happen once a critical strain energy for shear and tensile failure is reached. In order to model combinations between the two failure modes, an elliptical energy model for mixed failure is used [39]. The strain energy (U tot ) in the elastic network is…”

“…We expect grid effects to become largest under shear fracturing especially when the grid weakness is oriented close to the actual fracture orientation. However, the model does still produce listric and curving faults [39,41]. Fractures are not wrapping in the model, which leads to boundary effects on the leftand right-hand side and the upper and lower boundary.…”

Simulating Hydraulic Fracturing: Failure in Soft Versus Hard Rocks

“…Once the change in relative particle positions 8 occurs, the resulting force can be decomposed into tensile and shear components. Further 9 details on this methodology can be found in work bySachau & Koehn (2014).…”