Backstress-dominated regimes of fluid-driven fractures in poroelastic media: a simplified asymptotic framework

This paper examines how poroelastic backstress induced by fluid leak-off modifies the asymptotic propagation regimes of fluid-driven fractures. We consider a simplified theoretical framework in which the diffusion zone remains small relative to the fracture size, so that Carter-type leak-off can be coupled consistently with one-dimensional fracture models. Within this setting, leak-off-induced pore-pressure diffusion generates a backstress that acts against fracture-opening and alters the classical regime structure. Three typical geometries are studied: plane strain; radial; constant-height fractures. For each geometry, we derive the corresponding backstress-dominated self-similar limit, referred to as the

-vertex, and incorporate it into the classical parametric space of hydraulic fracture propagation. The analysis shows that, when poroelastic effects are sufficiently strong, the classical leak-off-dominated asymptotic regimes may cease to exist and the fracture evolves instead towards the backstress-dominated state. Transition solutions connecting the classical limiting regimes to the

upper B B $B$

-vertex are also obtained. The results extend the standard asymptotic classification of hydraulic fractures by identifying a distinct regime controlled by poroelastic backstress. They also provide a simple framework for assessing when backstress is expected to play a leading role in fluid-driven fracture propagation across different geometries and scales.