Background and Aims The competition of silicate and phosphate for sorption sites results in Si additions releasing P into the soil solution, increasing P availability for crops. Another potential effect of Si in promoting P uptake is the stimulation of root growth. Although there has been evidence of these effects since the early twentieth century, they are currently not utilized in agricultural production. In this review, we...

A multiphase-field approach for elasto-plastic and anisotropic brittle crack propagation in geological systems consisting of different regions of brittle and ductile materials is presented and employed to computationally study crack propagation. Plastic deformation in elasto-plastic materials such as frictional, granular or porous materials is modelled with the pressure-sensitive Drucker-Prager plasticity model. This plasticit...

We developed a generalized multiphase-field modeling framework for addressing the problem of brittle fracture propagation in quartz sandstones at microscopic length scale. Within this numerical approach, the grain boundaries and crack surfaces are modeled as diffuse interfaces. The two novel aspects of the model are the formulations of (I) anisotropic crack resistance in order to account for preferential cleavage planes within...